From 5a06ba55fc5e5b6897787042cde2b30dddb3c70e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Wed, 2 Apr 2025 15:18:08 +0200 Subject: [PATCH 01/23] Support Python 3.13 (#475) Closes #476: * Do not restrict the maximum Python version to 3.12 in `pyproject.toml` * Require `Cython >= 3` to avoid `h5py` installation crash w/ Python 3.13 * Require `sympde == 0.19.2` which supports Python 3.13 * Run unit tests with Python 3.13 too --- .github/workflows/continuous-integration.yml | 16 +++++++--------- pyproject.toml | 4 ++-- requirements.txt | 2 +- 3 files changed, 10 insertions(+), 12 deletions(-) diff --git a/.github/workflows/continuous-integration.yml b/.github/workflows/continuous-integration.yml index 7a6e6fe6a..ae4c2e09d 100644 --- a/.github/workflows/continuous-integration.yml +++ b/.github/workflows/continuous-integration.yml @@ -15,18 +15,16 @@ jobs: strategy: fail-fast: false matrix: - os: [ ubuntu-24.04 ] - python-version: [ 3.9, '3.10', '3.11', '3.12' ] + os: [ ubuntu-24.04, macos-14 ] + python-version: [ '3.9', '3.10', '3.11', '3.12', '3.13' ] isMerge: - ${{ github.event_name == 'push' && github.ref == 'refs/heads/devel' }} exclude: - - { isMerge: false, python-version: '3.10' } - - { isMerge: false, python-version: '3.11' } - include: - - os: macos-14 - python-version: '3.10' - - os: macos-14 - python-version: '3.11' + - { isMerge: false, python-version: '3.9' , os: macos-14 } + - { isMerge: false, python-version: '3.10', os: ubuntu-24.04 } + - { isMerge: false, python-version: '3.11', os: macos-14 } + - { isMerge: false, python-version: '3.12', os: ubuntu-24.04 } + - { isMerge: false, python-version: '3.13', os: macos-14 } name: ${{ matrix.os }} / Python ${{ matrix.python-version }} diff --git a/pyproject.toml b/pyproject.toml index 45e6ee4cd..43d4c527a 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -7,7 +7,7 @@ name = "psydac" version = "0.1" description = "Python package for isogeometric analysis (IGA)" readme = "README.md" -requires-python = ">= 3.9, < 3.13" +requires-python = ">= 3.9" license = {file = "LICENSE"} authors = [ {name = "Psydac development team", email = "psydac@googlegroups.com"} @@ -30,7 +30,7 @@ dependencies = [ 'pyevtk', # Our packages from PyPi - 'sympde == 0.19.1', + 'sympde == 0.19.2', 'pyccel >= 1.11.2', 'gelato == 0.12', diff --git a/requirements.txt b/requirements.txt index 8890db2f9..8cd73ee05 100644 --- a/requirements.txt +++ b/requirements.txt @@ -2,7 +2,7 @@ wheel setuptools >= 61, != 67.2.0 numpy >= 1.16 scipy >= 1.12 -Cython >= 0.25, < 3.0 +Cython >= 3 mpi4py >= 4 # Required to build h5py from source From 42033436b81379aac2f966957ab2315f3ae7e5f6 Mon Sep 17 00:00:00 2001 From: Max Date: Mon, 7 Apr 2025 17:17:58 +0200 Subject: [PATCH 02/23] Fix PSYDAC_BACKEND_GPYCCEL flags on latest Apple silicon (#480) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Currently, Psydac can not be used on Apple M4 computers since the `PSYDAC_BACKEND_GPYCCEL['flags']` is not set correctly. This change sets the flag for `Apple MX (etc.)` to `apple-mX`, which should work so long as the naming scheme stays unchanged. In addition, the regular expression used to find the GFortran version is now defined in a raw string instead of a standard Python UTF8 string. This avoids a `SyntaxWarning: invalid escape sequence`. --------- Co-authored-by: Yaman Güçlü --- psydac/api/settings.py | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/psydac/api/settings.py b/psydac/api/settings.py index 3a3830107..94762b5a9 100644 --- a/psydac/api/settings.py +++ b/psydac/api/settings.py @@ -45,7 +45,7 @@ # Get gfortran version gfortran_version_output = subprocess.check_output(['gfortran', '--version']).decode('utf-8') # nosec B603, B607 -gfortran_version_string = re.search("(\d+\.\d+\.\d+)", gfortran_version_output).group() +gfortran_version_string = re.search(r"(\d+\.\d+\.\d+)", gfortran_version_output).group() gfortran_version = Version(gfortran_version_string) # Platform-dependent flags @@ -53,10 +53,11 @@ # Apple silicon requires architecture-specific flags (see https://github.com/pyccel/psydac/pull/411) # which are only available on GCC version >= 14 - cpu_brand = subprocess.check_output(['sysctl','-n','machdep.cpu.brand_string']).decode('utf-8') # nosec B603, B607 - if "Apple M1" in cpu_brand: PSYDAC_BACKEND_GPYCCEL['flags'] += ' -mcpu=apple-m1' - elif "Apple M2" in cpu_brand: PSYDAC_BACKEND_GPYCCEL['flags'] += ' -mcpu=apple-m2' - elif "Apple M3" in cpu_brand: PSYDAC_BACKEND_GPYCCEL['flags'] += ' -mcpu=apple-m3' + cpu_brand = subprocess.check_output(['sysctl','-n','machdep.cpu.brand_string']).decode('utf-8').strip() # nosec B603, B607 + if cpu_brand.startswith("Apple M"): + # Example: "Apple M3 Pro (virtual)" --> " -mcpu=apple-m3" + cpu_flag = '-'.join(cpu_brand.lower().split()[:2]) + PSYDAC_BACKEND_GPYCCEL['flags'] += f' -mcpu={cpu_flag}' else: # TODO: Support later Apple CPU models. Perhaps the CPU naming scheme could be easily guessed # based on the output of 'sysctl -n machdep.cpu.brand_string', but I wouldn't rely on this From 1b34019ca6275e7807bf4dd2d12b32d2dea90ac1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Tue, 8 Apr 2025 17:07:58 +0200 Subject: [PATCH 03/23] Resolve warnings in sequential unit tests (#481) * Use raw strings for docstrings with LaTeX to avoid UTF8 syntax warnings on escape sequences; * Use CSC matrices to avoid SciPy sparse solver warning. We do not address the NumPy warnings which arise in our MPI unit tests (see #353). --- psydac/feec/global_projectors.py | 2 +- psydac/feec/multipatch/examples/timedomain_maxwell.py | 5 +++-- psydac/linalg/basic.py | 8 ++++---- 3 files changed, 8 insertions(+), 7 deletions(-) diff --git a/psydac/feec/global_projectors.py b/psydac/feec/global_projectors.py index 3e40bf361..e5a61a0bb 100644 --- a/psydac/feec/global_projectors.py +++ b/psydac/feec/global_projectors.py @@ -356,7 +356,7 @@ def _function(self, dim): pass def __call__(self, fun): - """ + r""" Project vector function onto the given finite element space by the instance of this class. This happens in the logical domain $\hat{\Omega}$. diff --git a/psydac/feec/multipatch/examples/timedomain_maxwell.py b/psydac/feec/multipatch/examples/timedomain_maxwell.py index 6a6300772..9e772f3e5 100644 --- a/psydac/feec/multipatch/examples/timedomain_maxwell.py +++ b/psydac/feec/multipatch/examples/timedomain_maxwell.py @@ -420,9 +420,10 @@ def solve_td_maxwell_pbm(*, # Absorbing dC_m CH2 = C_m.transpose() @ H2_m H1A = H1_m + dt * A_eps - dC_m = sp.sparse.linalg.spsolve(H1A, CH2) - dCH1_m = sp.sparse.linalg.spsolve(H1A, H1_m) + H1A_csc = H1A.tocsc() + dC_m = sp.sparse.linalg.spsolve(H1A_csc, CH2.tocsc()) + dCH1_m = sp.sparse.linalg.spsolve(H1A_csc, H1_m.tocsc()) print(' .. matrix of the dual div (still in primal bases)...') div_m = dH0_m @ cP0_m.transpose() @ bD0_m.transpose() @ H1_m diff --git a/psydac/linalg/basic.py b/psydac/linalg/basic.py index db28bfd7a..80bcac3d0 100644 --- a/psydac/linalg/basic.py +++ b/psydac/linalg/basic.py @@ -614,7 +614,7 @@ def dot(self, v, out=None): #=============================================================================== class SumLinearOperator(LinearOperator): - """ + r""" Sum $\sum_{i=1}^n A_i$ of linear operators $A_1,\dots,A_n$ acting between the same vector spaces V (domain) and W (codomain). """ @@ -728,7 +728,7 @@ def dot(self, v, out=None): #=============================================================================== class ComposedLinearOperator(LinearOperator): - """ + r""" Composition $A_n\circ\dots\circ A_1$ of two or more linear operators $A_1,\dots,A_n$. """ @@ -788,7 +788,7 @@ def codomain(self): @property def multiplicants(self): - """ + r""" A tuple $(A_1,\dots,A_n)$ containing the multiplicants of the linear operator $self = A_n\circ\dots\circ A_1$. @@ -851,7 +851,7 @@ def set_backend(self, backend): #=============================================================================== class PowerLinearOperator(LinearOperator): - """ + r""" Power $A^n$ of a linear operator $A$ for some integer $n\geq 0$. """ From adb453a98d1bef53992fb34f798d38a6bd7e03b6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Elena=20Moral=20S=C3=A1nchez?= <88042165+e-moral-sanchez@users.noreply.github.com> Date: Sat, 12 Apr 2025 00:33:31 +0200 Subject: [PATCH 04/23] Pass `out` parameter to `petsc_to_psydac` (#483) --- psydac/linalg/utilities.py | 24 +++++++++++++++++++++--- 1 file changed, 21 insertions(+), 3 deletions(-) diff --git a/psydac/linalg/utilities.py b/psydac/linalg/utilities.py index eb150f138..57a9a6b86 100644 --- a/psydac/linalg/utilities.py +++ b/psydac/linalg/utilities.py @@ -74,7 +74,7 @@ def _array_to_psydac_recursive(x, u): raise NotImplementedError(f'Can only handle StencilVector or BlockVector spaces, got {type(V)} instead') #============================================================================== -def petsc_to_psydac(x, Xh): +def petsc_to_psydac(x, Xh, out=None): """ Convert a PETSc.Vec object to a StencilVector or BlockVector. It assumes that PETSc was installed with the configuration for complex numbers. Uses the index conversion functions in psydac.linalg.topetsc.py. @@ -84,6 +84,12 @@ def petsc_to_psydac(x, Xh): x : PETSc.Vec PETSc vector + Xh : psydac.linalg.stencil.StencilVectorSpace | psydac.linalg.block.BlockVectorSpace + Space of the coefficients of the Psydac vector. + + out : psydac.linalg.stencil.StencilVector | psydac.linalg.block.BlockVector, optional + The Psydac vector where to store the result. + Returns ------- u : psydac.linalg.stencil.StencilVector | psydac.linalg.block.BlockVector @@ -94,7 +100,13 @@ def petsc_to_psydac(x, Xh): if any([isinstance(Xh.spaces[b], BlockVectorSpace) for b in range(len(Xh.spaces))]): raise NotImplementedError('Block of blocks not implemented.') - u = BlockVector(Xh) + if out is not None: + assert isinstance(out, BlockVector) + assert out.space is Xh + u = out + else: + u = BlockVector(Xh) + comm = x.comm dtype = Xh._dtype localsize, globalsize = x.getSizes() @@ -117,7 +129,13 @@ def petsc_to_psydac(x, Xh): elif isinstance(Xh, StencilVectorSpace): - u = StencilVector(Xh) + if out is not None: + assert isinstance(out, StencilVector) + assert out.space is Xh + u = out + else: + u = StencilVector(Xh) + comm = x.comm dtype = Xh.dtype localsize, globalsize = x.getSizes() From 24646ef35acc46d06b37af7d615d2ce06c7a8d7b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Mon, 5 May 2025 17:37:18 +0200 Subject: [PATCH 05/23] Rename `dot` as `inner` in `Vector`, `VectorSpace`, and subclasses (#484) Main changes -------------- * Rename the method `dot` of the base class `VectorSpace` as `inner`, and make it an abstract method (which must be implemented by the subclasses). * Rename the method `dot` of the base class `Vector` as `inner`. This is a concrete method which calls `self.space.inner` and does not need to be overridden by the subclasses. * Add `inner` methods to the classes `StencilVector`, `BlockVectorSpace`, and `DenseVectorSpace`. These methods override the abstract method of the base class as required, and are derived from the former functions `Stencil.dot`, `BlockVector.dot`, and `DenseVector.dot`, which have been removed (see next point). * Remove the property `dtype` and the method `dot` (now `inner`) from the classes `StencilVector`, `BlockVector`, and `DenseVector`, because the default methods of the base class already provide a sufficient implementation. This fixes #330. Necessary additional changes ------------------------------ * Update all linear solvers in `linalg.solvers` with the new method calls; * Update all unit tests with the new method calls, in files: - `api/tests/test_assembly.py` - `feec/tests/test_commuting_projections.py` - `feec/tests/test_global_projectors.py` - `linalg/tests/test_block.py` - `linalg/tests/test_linalg.py` - `linalg/tests/test_stencil_interface_matrix.py` - `linalg/tests/test_stencil_vector.py` Unrelated additional changes ----------------------------- * Rename the class `VectorDot` as `VectorInner` in module `api.ast.linalg`, although never used in Psydac. * Speed up 3D unit tests in: - `feec/tests/test_commuting_projectors.py` - `feec/tests/test_global_projectors.py` --- psydac/api/ast/linalg.py | 2 +- psydac/api/tests/test_assembly.py | 16 +- .../feec/tests/test_commuting_projections.py | 63 ++++---- psydac/feec/tests/test_global_projectors.py | 16 +- psydac/linalg/basic.py | 70 +++++--- psydac/linalg/block.py | 102 +++++++----- psydac/linalg/solvers.py | 90 +++++------ psydac/linalg/stencil.py | 150 +++++++++--------- psydac/linalg/tests/test_block.py | 8 +- psydac/linalg/tests/test_linalg.py | 20 +-- .../tests/test_stencil_interface_matrix.py | 2 +- psydac/linalg/tests/test_stencil_vector.py | 12 +- psydac/polar/dense.py | 97 +++++++---- 13 files changed, 377 insertions(+), 271 deletions(-) diff --git a/psydac/api/ast/linalg.py b/psydac/api/ast/linalg.py index f3a13b740..b44f3d753 100644 --- a/psydac/api/ast/linalg.py +++ b/psydac/api/ast/linalg.py @@ -428,7 +428,7 @@ def _compile_pyccel(self, mod, backend, verbose=False): return fmod #============================================================================== -class VectorDot(SplBasic): +class VectorInner(SplBasic): def __new__(cls, ndim, backend=None): tag = random_string(8) diff --git a/psydac/api/tests/test_assembly.py b/psydac/api/tests/test_assembly.py index a3bdb57e5..d00c58840 100644 --- a/psydac/api/tests/test_assembly.py +++ b/psydac/api/tests/test_assembly.py @@ -78,7 +78,7 @@ def test_field_and_constant(backend, dtype): # Test matrix A x = fh.coeffs #TODO change res into np.conj(res) when the conjugate is applied in the dot product in sympde - assert abs(x.dot(A.dot(x)) - res) < 1e-12 + assert abs(x.inner(A.dot(x)) - res) < 1e-12 # Test vector b assert abs(b.toarray().sum() - res) < 1e-12 @@ -138,10 +138,10 @@ def test_bilinearForm_complex(backend): x = fh.coeffs #TODO change res into np.conj(res) when the conjugate is applied in the dot product in sympde - assert abs(x.dot(A1.dot(x)) - res) < 1e-12 - assert abs(x.dot(A2.dot(x)) - res) < 1e-12 - assert abs(x.dot(A3.dot(x)) - res) < 1e-12 - assert abs(x.dot(A4.dot(x)) - res) < 1e-12 + assert abs(x.inner(A1.dot(x)) - res) < 1e-12 + assert abs(x.inner(A2.dot(x)) - res) < 1e-12 + assert abs(x.inner(A3.dot(x)) - res) < 1e-12 + assert abs(x.inner(A4.dot(x)) - res) < 1e-12 print("PASSED") @@ -375,7 +375,7 @@ def test_multiple_fields(backend, dtype): # Test matrix A #TODO change res into np.conj(res) when the conjugate is applied in the dot product in sympde - assert abs(x.dot(A.dot(x)) - res) < 1e-12 + assert abs(x.inner(A.dot(x)) - res) < 1e-12 # Test vector b assert abs(b.toarray().sum() - res) < 1e-12 @@ -518,10 +518,10 @@ def test_assembly_no_synchr_args(backend): rhoh3 = div.dot(uh) rhof3 = FemField(V1h, rhoh3) weight_mass_matrix = weight_int_prod_h.assemble(rho=rhof1) - inte_bilin = const_1.dot(weight_mass_matrix.dot(const_1)) + inte_bilin = const_1.inner(weight_mass_matrix.dot(const_1)) int_prod_rho = int_prod_h.assemble(rho=rhof2) - inte_lin = int_prod_rho.dot(const_1) + inte_lin = int_prod_rho.inner(const_1) inte_norm = func_h.assemble(rho=rhof3) diff --git a/psydac/feec/tests/test_commuting_projections.py b/psydac/feec/tests/test_commuting_projections.py index ba44ccd08..38881220f 100644 --- a/psydac/feec/tests/test_commuting_projections.py +++ b/psydac/feec/tests/test_commuting_projections.py @@ -1,4 +1,7 @@ # -*- coding: UTF-8 -*- +from mpi4py import MPI +import numpy as np +import pytest from psydac.feec.global_projectors import Projector_H1, Projector_L2, Projector_Hcurl, Projector_Hdiv from psydac.fem.tensor import TensorFemSpace, SplineSpace @@ -11,18 +14,14 @@ from psydac.linalg.solvers import inverse from psydac.linalg.basic import IdentityOperator -from mpi4py import MPI -import numpy as np -import pytest - #============================================================================== # 3D tests #============================================================================== -@pytest.mark.parametrize('Nel', [8, 12]) -@pytest.mark.parametrize('Nq', [5]) -@pytest.mark.parametrize('p', [2,3]) +@pytest.mark.parametrize('m', [1, 2]) @pytest.mark.parametrize('bc', [True, False]) -@pytest.mark.parametrize('m', [1,2]) +@pytest.mark.parametrize('p', [2, 3]) +@pytest.mark.parametrize('Nq', [5]) +@pytest.mark.parametrize('Nel', [5, 6]) def test_3d_commuting_pro_1(Nel, Nq, p, bc, m): fun1 = lambda xi1, xi2, xi3 : np.sin(xi1)*np.sin(xi2)*np.sin(xi3) @@ -83,20 +82,20 @@ def test_3d_commuting_pro_1(Nel, Nq, p, bc, m): Id_0 = IdentityOperator(H1.coeff_space) Err_0 = P0.solver @ P0.imat_kronecker - Id_0 e0 = Err_0 @ u0.coeffs # random vector could be used as well - norm2_e0 = np.sqrt(e0.dot(e0)) + norm2_e0 = np.sqrt(e0.inner(e0)) assert norm2_e0 < 1e-12 Id_1 = IdentityOperator(Hcurl.coeff_space) Err_1 = P1.solver @ P1.imat_kronecker - Id_1 e1 = Err_1 @ u1.coeffs # random vector could be used as well - norm2_e1 = np.sqrt(e1.dot(e1)) + norm2_e1 = np.sqrt(e1.inner(e1)) assert norm2_e1 < 1e-12 -@pytest.mark.parametrize('Nel', [8, 12]) -@pytest.mark.parametrize('Nq', [8]) -@pytest.mark.parametrize('p', [2,3]) +@pytest.mark.parametrize('m', [1, 2]) @pytest.mark.parametrize('bc', [True, False]) -@pytest.mark.parametrize('m', [1,2]) +@pytest.mark.parametrize('p', [2, 3]) +@pytest.mark.parametrize('Nq', [7]) +@pytest.mark.parametrize('Nel', [5, 6]) def test_3d_commuting_pro_2(Nel, Nq, p, bc, m): fun1 = lambda xi1, xi2, xi3 : np.sin(xi1)*np.sin(xi2)*np.sin(xi3) @@ -175,20 +174,20 @@ def test_3d_commuting_pro_2(Nel, Nq, p, bc, m): Id_1 = IdentityOperator(Hcurl.coeff_space) Err_1 = P1.solver @ P1.imat_kronecker - Id_1 e1 = Err_1 @ u1.coeffs # random vector could be used as well - norm2_e1 = np.sqrt(e1.dot(e1)) + norm2_e1 = np.sqrt(e1.inner(e1)) assert norm2_e1 < 1e-12 Id_2 = IdentityOperator(Hdiv.coeff_space) Err_2 = P2.solver @ P2.imat_kronecker - Id_2 e2 = Err_2 @ u2.coeffs # random vector could be used as well - norm2_e2 = np.sqrt(e2.dot(e2)) + norm2_e2 = np.sqrt(e2.inner(e2)) assert norm2_e2 < 1e-12 -@pytest.mark.parametrize('Nel', [8, 12]) -@pytest.mark.parametrize('Nq', [8]) -@pytest.mark.parametrize('p', [2,3]) +@pytest.mark.parametrize('m', [1, 2]) @pytest.mark.parametrize('bc', [True, False]) -@pytest.mark.parametrize('m', [1,2]) +@pytest.mark.parametrize('p', [2, 3]) +@pytest.mark.parametrize('Nq', [7]) +@pytest.mark.parametrize('Nel', [5, 6]) def test_3d_commuting_pro_3(Nel, Nq, p, bc, m): fun1 = lambda xi1, xi2, xi3 : np.sin(xi1)*np.sin(xi2)*np.sin(xi3) @@ -258,13 +257,13 @@ def test_3d_commuting_pro_3(Nel, Nq, p, bc, m): Id_2 = IdentityOperator(Hdiv.coeff_space) Err_2 = P2.solver @ P2.imat_kronecker - Id_2 e2 = Err_2 @ u2.coeffs # random vector could be used as well - norm2_e2 = np.sqrt(e2.dot(e2)) + norm2_e2 = np.sqrt(e2.inner(e2)) assert norm2_e2 < 1e-12 Id_3 = IdentityOperator(L2.coeff_space) Err_3 = P3.solver @ P3.imat_kronecker - Id_3 e3 = Err_3 @ u3.coeffs # random vector could be used as well - norm2_e3 = np.sqrt(e3.dot(e3)) + norm2_e3 = np.sqrt(e3.inner(e3)) assert norm2_e3 < 1e-12 #============================================================================== @@ -334,13 +333,13 @@ def test_2d_commuting_pro_1(Nel, Nq, p, bc, m): Id_0 = IdentityOperator(H1.coeff_space) Err_0 = P0.solver @ P0.imat_kronecker - Id_0 e0 = Err_0 @ u0.coeffs # random vector could be used as well - norm2_e0 = np.sqrt(e0.dot(e0)) + norm2_e0 = np.sqrt(e0.inner(e0)) assert norm2_e0 < 1e-12 Id_1 = IdentityOperator(Hcurl.coeff_space) Err_1 = P1.solver @ P1.imat_kronecker - Id_1 e1 = Err_1 @ u1.coeffs # random vector could be used as well - norm2_e1 = np.sqrt(e1.dot(e1)) + norm2_e1 = np.sqrt(e1.inner(e1)) assert norm2_e1 < 1e-12 @pytest.mark.parallel @@ -407,13 +406,13 @@ def test_2d_commuting_pro_2(Nel, Nq, p, bc, m): Id_0 = IdentityOperator(H1.coeff_space) Err_0 = P0.solver @ P0.imat_kronecker - Id_0 e0 = Err_0 @ u0.coeffs # random vector could be used as well - norm2_e0 = np.sqrt(e0.dot(e0)) + norm2_e0 = np.sqrt(e0.inner(e0)) assert norm2_e0 < 1e-12 Id_1 = IdentityOperator(Hdiv.coeff_space) Err_1 = P1.solver @ P1.imat_kronecker - Id_1 e1 = Err_1 @ u1.coeffs # random vector could be used as well - norm2_e1 = np.sqrt(e1.dot(e1)) + norm2_e1 = np.sqrt(e1.inner(e1)) assert norm2_e0 < 1e-12 @pytest.mark.parallel @@ -487,13 +486,13 @@ def test_2d_commuting_pro_3(Nel, Nq, p, bc, m): Id_2 = IdentityOperator(Hdiv.coeff_space) Err_2 = P2.solver @ P2.imat_kronecker - Id_2 e2 = Err_2 @ u2.coeffs - norm2_e2 = np.sqrt(e2.dot(e2)) + norm2_e2 = np.sqrt(e2.inner(e2)) assert norm2_e2 < 1e-12 Id_3 = IdentityOperator(L2.coeff_space) Err_3 = P3.solver @ P3.imat_kronecker - Id_3 e3 = Err_3 @ u3.coeffs - norm2_e3 = np.sqrt(e3.dot(e3)) + norm2_e3 = np.sqrt(e3.inner(e3)) assert norm2_e3 < 1e-12 @pytest.mark.parallel @@ -567,13 +566,13 @@ def test_2d_commuting_pro_4(Nel, Nq, p, bc, m): Id_1 = IdentityOperator(Hcurl.coeff_space) Err_1 = P1.solver @ P1.imat_kronecker - Id_1 e1 = Err_1 @ u1.coeffs - norm2_e1 = np.sqrt(e1.dot(e1)) + norm2_e1 = np.sqrt(e1.inner(e1)) assert norm2_e1 < 1e-12 Id_2 = IdentityOperator(L2.coeff_space) Err_2 = P2.solver @ P2.imat_kronecker - Id_2 e2 = Err_2 @ u2.coeffs - norm2_e2 = np.sqrt(e2.dot(e2)) + norm2_e2 = np.sqrt(e2.inner(e2)) assert norm2_e2 < 1e-12 #============================================================================== @@ -637,13 +636,13 @@ def test_1d_commuting_pro_1(Nel, Nq, p, bc, m): Id_0 = IdentityOperator(H1.coeff_space) Err_0 = P0.solver @ P0.imat_kronecker - Id_0 e0 = Err_0 @ u0.coeffs - norm2_e0 = np.sqrt(e0.dot(e0)) + norm2_e0 = np.sqrt(e0.inner(e0)) assert norm2_e0 < 1e-12 Id_1 = IdentityOperator(L2.coeff_space) Err_1 = P1.solver @ P1.imat_kronecker - Id_1 e1 = Err_1 @ u1.coeffs - norm2_e1 = np.sqrt(e1.dot(e1)) + norm2_e1 = np.sqrt(e1.inner(e1)) assert norm2_e1 < 1e-12 #============================================================================== diff --git a/psydac/feec/tests/test_global_projectors.py b/psydac/feec/tests/test_global_projectors.py index 303044f37..1d1f64282 100644 --- a/psydac/feec/tests/test_global_projectors.py +++ b/psydac/feec/tests/test_global_projectors.py @@ -248,7 +248,7 @@ def test_derham_projector_2d_hcurl(ncells, degree, periodic, multiplicity): assert maxnorm_error <= 1e-3 #============================================================================== -@pytest.mark.parametrize('ncells', [[30,30,30]]) +@pytest.mark.parametrize('ncells', [[20,20,20]]) @pytest.mark.parametrize('degree', [[2,2,2], [2,3,2], [3,3,3]]) @pytest.mark.parametrize('periodic', [[False, False, False], [True, True, True]]) @pytest.mark.parametrize('multiplicity', [[1,1,1], [1,2,2], [2,2,2]]) @@ -289,19 +289,23 @@ def test_derham_projector_3d(ncells, degree, periodic, multiplicity): # Test if max-norm of error is <= TOL maxnorm_error = abs(vals_u0 - vals_f).max() print(ncells, maxnorm_error) - assert maxnorm_error <= 3e-2 + assert maxnorm_error <= 0.01 + maxnorm_error = abs(vals_u1_1 - vals_f).max() print(ncells, maxnorm_error) - assert maxnorm_error <= 3e-2 + assert maxnorm_error <= 0.01 + maxnorm_error = abs(vals_u2_1 - vals_f).max() print(ncells, maxnorm_error) - assert maxnorm_error <= 3e-2 + assert maxnorm_error <= 0.05 + maxnorm_error = abs(vals_u3 - vals_f).max() print(ncells, maxnorm_error) - assert maxnorm_error <= 3e-2 + assert maxnorm_error <= 0.05 + maxnorm_error = abs(vals_ux_1 - vals_f).max() print(ncells, maxnorm_error) - assert maxnorm_error <= 3e-2 + assert maxnorm_error <= 0.02 #============================================================================== if __name__ == '__main__': diff --git a/psydac/linalg/basic.py b/psydac/linalg/basic.py index 80bcac3d0..bf88dbd07 100644 --- a/psydac/linalg/basic.py +++ b/psydac/linalg/basic.py @@ -34,7 +34,7 @@ #=============================================================================== class VectorSpace(ABC): """ - Finite-dimensional vector space V with a scalar (dot) product. + Finite-dimensional vector space V with a scalar (inner) product. """ @property @@ -66,10 +66,35 @@ def zeros(self): """ -# @abstractmethod - def dot(self, a, b): + @abstractmethod + def inner(self, x, y): """ - Evaluate the scalar product between two vectors of the same space. + Evaluate the inner vector product between two vectors of this space V. + + If the field of V is real, compute the classical scalar product. + If the field of V is complex, compute the classical sesquilinear + product with linearity on the second vector. + + TODO [YG 01.05.2025]: Currently, the first vector is conjugated. We + want to reverse this behavior in order to align with the convention + of FEniCS. + + Parameters + ---------- + x : Vector + The first vector in the scalar product. In the case of a complex + field, the inner product is antilinear w.r.t. this vector (hence + this vector is conjugated). + + y : Vector + The second vector in the scalar product. The inner product is + linear w.r.t. this vector. + + Returns + ------- + float | complex + The scalar product of the two vectors. Note that inner(x, x) is + a non-negative real number which is zero if and only if x = 0. """ @@ -108,7 +133,7 @@ def dtype(self): """ The data type of the vector field V this vector belongs to. """ return self.space.dtype - def dot(self, v): + def inner(self, v): """ Evaluate the scalar product with the vector v of the same space. @@ -120,7 +145,7 @@ def dot(self, v): """ assert isinstance(v, Vector) assert self.space is v.space - return self.space.dot(self, v) + return self.space.inner(self, v) def mul_iadd(self, a, v): """ @@ -150,8 +175,26 @@ def toarray(self, **kwargs): @abstractmethod def copy(self, out=None): - """Ensure x.copy(out=x) returns x and not a new object.""" - pass + """ + Return an identical copy of this vector. + + Subclasses must ensure that x.copy(out=x) returns x and not a new + object. + """ + + @abstractmethod + def conjugate(self, out=None): + """ + Compute the complex conjugate vector. + + Please note that x.conjugate(out=x) modifies x in place and returns x. + + If the field is real (i.e. `self.dtype in (np.float32, np.float64)`) this method is equivalent to `copy`. + If the field is complex (i.e. `self.dtype in (np.complex64, np.complex128)`) this method returns + the complex conjugate of `self`, element-wise. + + The behavior of this function is similar to `numpy.conjugate(self, out=None)`. + """ @abstractmethod def __neg__(self): @@ -181,17 +224,6 @@ def __iadd__(self, v): def __isub__(self, v): pass - @abstractmethod - def conjugate(self, out=None): - """Compute the complex conjugate vector. - - If the field is real (i.e. `self.dtype in (np.float32, np.float64)`) this method is equivalent to `copy`. - If the field is complex (i.e. `self.dtype in (np.complex64, np.complex128)`) this method returns - the complex conjugate of `self`, element-wise. - - The behavior of this function is similar to `numpy.conjugate(self, out=None)`. - """ - #------------------------------------- # Methods with default implementation #------------------------------------- diff --git a/psydac/linalg/block.py b/psydac/linalg/block.py index 49e29b60d..f2a755015 100644 --- a/psydac/linalg/block.py +++ b/psydac/linalg/block.py @@ -73,6 +73,7 @@ def dimension(self): def dtype(self): return self._dtype + # ... def zeros(self): """ Get a copy of the null element of the product space V = [V1, V2, ...] @@ -85,6 +86,44 @@ def zeros(self): """ return BlockVector(self, [Vi.zeros() for Vi in self._spaces]) + # ... + def inner(self, x, y): + """ + Evaluate the inner vector product between two vectors of this space V. + + If the field of V is real, compute the classical scalar product. + If the field of V is complex, compute the classical sesquilinear + product with linearity on the second vector. + + TODO [YG 01.05.2025]: Currently, the first vector is conjugated. We + want to reverse this behavior in order to align with the convention + of FEniCS. + + Parameters + ---------- + x : Vector + The first vector in the scalar product. In the case of a complex + field, the inner product is antilinear w.r.t. this vector (hence + this vector is conjugated). + + y : Vector + The second vector in the scalar product. The inner product is + linear w.r.t. this vector. + + Returns + ------- + float | complex + The scalar product of the two vectors. Note that inner(x, x) is + a non-negative real number which is zero if and only if x = 0. + + """ + + assert isinstance(x, BlockVector) + assert isinstance(y, BlockVector) + assert x.space is self + assert y.space is self + return sum(Vi.inner(xi, yi) for Vi, xi, yi in zip(self.spaces, x.blocks, y.blocks)) + #... def axpy(self, a, x, y): """ @@ -233,18 +272,13 @@ def __init__(self, V, blocks=None): #-------------------------------------- @property def space(self): + """ Vector space to which this vector belongs. """ return self._space - #... - @property - def dtype(self): - return self.space.dtype - - #... - def dot(self, v): - assert isinstance(v, BlockVector) - assert v._space is self._space - return sum(b1.dot(b2) for b1, b2 in zip(self._blocks, v._blocks)) + # ... + def toarray(self, order='C'): + """ Convert to Numpy 1D array. """ + return np.concatenate([bi.toarray(order=order) for bi in self._blocks]) #... def copy(self, out=None): @@ -256,6 +290,19 @@ def copy(self, out=None): w._sync = self._sync return w + #... + def conjugate(self, out=None): + if out is not None: + assert isinstance(out, BlockVector) + assert out.space is self.space + else: + out = BlockVector(self.space) + + for (Lij, Lij_out) in zip(self.blocks, out.blocks): + Lij.conjugate(out=Lij_out) + out._sync = self._sync + return out + #... def __neg__(self): w = BlockVector(self._space, [-b for b in self._blocks]) @@ -311,7 +358,16 @@ def __isub__(self, v): #-------------------------------------- # Other properties/methods #-------------------------------------- + @property + def blocks(self): + return tuple(self._blocks) + + #... + @property + def n_blocks(self): + return len(self._blocks) + # ... def __getitem__(self, key): return self._blocks[key] @@ -321,18 +377,6 @@ def __setitem__(self, key, value): assert isinstance(value, Vector) self._blocks[key] = value - def conjugate(self, out=None): - if out is not None: - assert isinstance(out, BlockVector) - assert out.space is self.space - else: - out = BlockVector(self.space) - - for (Lij, Lij_out) in zip(self.blocks, out.blocks): - Lij.conjugate(out=Lij_out) - out._sync = self._sync - return out - # ... @property def ghost_regions_in_sync(self): @@ -428,20 +472,6 @@ def exchange_assembly_data(self): for vi in self.blocks: vi.exchange_assembly_data() - # ... - @property - def n_blocks(self): - return len(self._blocks) - - # ... - @property - def blocks(self): - return tuple(self._blocks) - - # ... - def toarray(self, order='C'): - return np.concatenate([bi.toarray(order=order) for bi in self._blocks]) - # ... def toarray_local(self, order='C'): """ Convert to petsc Nest vector. diff --git a/psydac/linalg/solvers.py b/psydac/linalg/solvers.py index 3f81f64fa..8c6505ca7 100644 --- a/psydac/linalg/solvers.py +++ b/psydac/linalg/solvers.py @@ -143,7 +143,7 @@ def solve(self, b, out=None): b : psydac.linalg.basic.Vector Right-hand-side vector of linear system Ax = b. Individual entries b[i] need not be accessed, but b has 'shape' attribute and provides 'copy()' and - 'dot(p)' functions (dot(p) is the vector inner product b*p ); moreover, + 'inner(p)' functions (b.inner(p) is the vector inner product b*p); moreover, scalar multiplication and sum operations are available. out : psydac.linalg.basic.Vector | NoneType @@ -190,7 +190,7 @@ def solve(self, b, out=None): A.dot(x, out=v) b.copy(out=r) r -= v - am = r.dot(r).real + am = r.inner(r).real r.copy(out=p) tol_sqr = tol**2 @@ -209,12 +209,12 @@ def solve(self, b, out=None): m -= 1 break A.dot(p, out=v) - l = am / v.dot(p) + l = am / v.inner(p) x.mul_iadd(l, p) # this is x += l*p r.mul_iadd(-l, v) # this is r -= l*v - am1 = r.dot(r).real + am1 = r.inner(r).real p *= (am1/am) p += r am = am1 @@ -351,9 +351,9 @@ def solve(self, b, out=None): A.dot(x, out=v) b.copy(out=r) r -= v - nrmr_sqr = r.dot(r).real + nrmr_sqr = r.inner(r).real pc.dot(r, out=s) - am = s.dot(r) + am = s.inner(r) s.copy(out=p) tol_sqr = tol**2 @@ -374,15 +374,15 @@ def solve(self, b, out=None): break v = A.dot(p, out=v) - l = am / v.dot(p) + l = am / v.inner(p) x.mul_iadd(l, p) # this is x += l*p r.mul_iadd(-l, v) # this is r -= l*v - nrmr_sqr = r.dot(r).real + nrmr_sqr = r.inner(r).real pc.dot(r, out=s) - am1 = s.dot(r) + am1 = s.inner(r) # we are computing p = (am1 / am) * p + s by using axpy on s and exchanging the arrays s.mul_iadd((am1/am), p) @@ -466,7 +466,7 @@ def solve(self, b, out=None): b : psydac.linalg.basic.Vector Right-hand-side vector of linear system. Individual entries b[i] need not be accessed, but b has 'shape' attribute and provides 'copy()' and - 'dot(p)' functions (dot(p) is the vector inner product b*p ); moreover, + 'inner(p)' functions (b.inner(p) is the vector inner product b*p); moreover, scalar multiplication and sum operations are available. out : psydac.linalg.basic.Vector | NoneType @@ -523,7 +523,7 @@ def solve(self, b, out=None): p.copy(out=ps) v.copy(out=vs) - res_sqr = r.dot(r).real + res_sqr = r.inner(r).real tol_sqr = tol**2 if verbose: @@ -548,10 +548,10 @@ def solve(self, b, out=None): #----------------------- # c := (rs, r) - c = rs.dot(r) + c = rs.inner(r) # a := (rs, r) / (ps, v) - a = c / ps.dot(v) + a = c / ps.inner(v) #----------------------- # SOLUTION UPDATE @@ -567,10 +567,10 @@ def solve(self, b, out=None): rs.mul_iadd(-a.conjugate(), vs) # ||r||_2 := (r, r) - res_sqr = r.dot(r).real + res_sqr = r.inner(r).real # b := (rs, r)_{m+1} / (rs, r)_m - b = rs.dot(r) / c + b = rs.inner(r) / c # p := r + b*p p *= b @@ -654,7 +654,7 @@ def solve(self, b, out=None): b : psydac.linalg.basic.Vector Right-hand-side vector of linear system. Individual entries b[i] need not be accessed, but b has 'shape' attribute and provides 'copy()' and - 'dot(p)' functions (dot(p) is the vector inner product b*p ); moreover, + 'inner(p)' functions (b.inner(p) is the vector inner product b*p); moreover, scalar multiplication and sum operations are available. out : psydac.linalg.basic.Vector | NoneType The output vector, or None (optional). @@ -715,7 +715,7 @@ def solve(self, b, out=None): r.copy(out=r0) - res_sqr = r.dot(r).real + res_sqr = r.inner(r).real tol_sqr = tol ** 2 if verbose: @@ -739,10 +739,10 @@ def solve(self, b, out=None): # ----------------------- # c := (r0, r) - c = r0.dot(r) + c = r0.inner(r) # a := (r0, r) / (r0, v) - a = c / (r0.dot(v)) + a = c / (r0.inner(v)) # r := r - a*v r.mul_iadd(-a, v) @@ -751,7 +751,7 @@ def solve(self, b, out=None): vr = A.dot(r, out=vr) # w := (r, A*r) / (A*r, A*r) - w = r.dot(vr) / vr.dot(vr) + w = r.inner(vr) / vr.inner(vr) # ----------------------- # SOLUTION UPDATE @@ -765,13 +765,13 @@ def solve(self, b, out=None): r.mul_iadd(-w, vr) # ||r||_2 := (r, r) - res_sqr = r.dot(r).real + res_sqr = r.inner(r).real if res_sqr < tol_sqr: break # b := a / w * (r0, r)_{m+1} / (r0, r)_m - b = r0.dot(r) * a / (c * w) + b = r0.inner(r) * a / (c * w) # p := r + b*p- b*w*v p *= b @@ -853,7 +853,7 @@ def solve(self, b, out=None): b : psydac.linalg.basic.Vector Right-hand-side vector of linear system. Individual entries b[i] need not be accessed, but b has 'shape' attribute and provides 'copy()' and - 'dot(p)' functions (dot(p) is the vector inner product b*p ); moreover, + 'inner(p)' functions (b.inner(p) is the vector inner product b*p); moreover, scalar multiplication and sum operations are available. out : psydac.linalg.basic.Vector | NoneType The output vector, or None (optional). @@ -939,14 +939,14 @@ def solve(self, b, out=None): pc.dot(r, out=rp) rp.copy(out=pp) - rhop = rp.dot(rp) + rhop = rp.inner(rp) # save initial residual vector rp0 rp0 = self._tmps['rp0'] rp.copy(out=rp0) # squared residual norm and squared tolerance - res_sqr = r.dot(r).real + res_sqr = r.inner(r).real tol_sqr = tol**2 if verbose: @@ -964,7 +964,7 @@ def solve(self, b, out=None): # v = A @ pp, vp = PC @ v, alphap = rhop/(vp.rp0) A.dot(pp, out=v) pc.dot(v, out=vp) - alphap = rhop / vp.dot(rp0) + alphap = rhop / vp.inner(rp0) # s = r - alphap*v, sp = PC @ s r.copy(out=s) @@ -976,7 +976,7 @@ def solve(self, b, out=None): # t = A @ sp, tp = PC @ t, omegap = (tp.sp)/(tp.tp) A.dot(sp, out=t) pc.dot(t, out=tp) - omegap = tp.dot(sp) / tp.dot(tp) + omegap = tp.inner(sp) / tp.inner(tp) # x = x + alphap*pp + omegap*sp pp.copy(out=app) @@ -996,7 +996,7 @@ def solve(self, b, out=None): rp -= tp # rhop_new = rp.rp0, betap = (alphap*rhop_new)/(omegap*rhop) - rhop_new = rp.dot(rp0) + rhop_new = rp.inner(rp0) betap = (alphap*rhop_new) / (omegap*rhop) rhop = 1*rhop_new @@ -1007,7 +1007,7 @@ def solve(self, b, out=None): pp += rp # new residual norm - res_sqr = r.dot(r).real + res_sqr = r.inner(r).real niter += 1 @@ -1097,7 +1097,7 @@ def solve(self, b, out=None): b : psydac.linalg.basic.Vector Right-hand-side vector of linear system. Individual entries b[i] need not be accessed, but b has 'shape' attribute and provides 'copy()' and - 'dot(p)' functions (dot(p) is the vector inner product b*p ); moreover, + 'inner(p)' functions (b.inner(p) is the vector inner product b*p); moreover, scalar multiplication and sum operations are available. out : psydac.linalg.basic.Vector | NoneType @@ -1167,7 +1167,7 @@ def solve(self, b, out=None): y *= -1.0 y.copy(out=res_old) # res = b - A*x - beta = sqrt(res_old.dot(res_old)) + beta = sqrt(res_old.inner(res_old)) # Initialize other quantities oldb = 0 @@ -1211,7 +1211,7 @@ def solve(self, b, out=None): if itn >= 2: y.mul_iadd(-(beta/oldb), res_old) - alfa = v.dot(y) + alfa = v.inner(y) y.mul_iadd(-(alfa/beta), res_new) # We put res_new in res_old and y in res_new @@ -1219,7 +1219,7 @@ def solve(self, b, out=None): y.copy(out=res_new) oldb = beta - beta = sqrt(res_new.dot(res_new)) + beta = sqrt(res_new.inner(res_new)) tnorm2 += alfa**2 + oldb**2 + beta**2 # Apply previous rotation Qk-1 to get @@ -1266,7 +1266,7 @@ def solve(self, b, out=None): # Estimate various norms and test for convergence. Anorm = sqrt(tnorm2) - ynorm = sqrt(x.dot(x)) + ynorm = sqrt(x.inner(x)) rnorm = phibar if ynorm == 0 or Anorm == 0:test1 = inf @@ -1416,7 +1416,7 @@ def solve(self, b, out=None): b : psydac.linalg.basic.Vector Right-hand-side vector of linear system. Individual entries b[i] need not be accessed, but b has 'shape' attribute and provides 'copy()' and - 'dot(p)' functions (dot(p) is the vector inner product b*p ); moreover, + 'inner(p)' functions (b.inner(p) is the vector inner product b*p); moreover, scalar multiplication and sum operations are available. out : psydac.linalg.basic.Vector | NoneType @@ -1482,16 +1482,16 @@ def solve(self, b, out=None): btol = tol b.copy(out=u) - normb = sqrt(b.dot(b).real) + normb = sqrt(b.inner(b).real) A.dot(x, out=u_work) u -= u_work - beta = sqrt(u.dot(u).real) + beta = sqrt(u.inner(u).real) if beta > 0: u *= (1 / beta) At.dot(u, out=v) - alpha = sqrt(v.dot(v).real) + alpha = sqrt(v.inner(v).real) else: x.copy(out=v) alpha = 0 @@ -1554,14 +1554,14 @@ def solve(self, b, out=None): u *= -alpha A.dot(v, out=u_work) u += u_work - beta = sqrt(u.dot(u).real) + beta = sqrt(u.inner(u).real) if beta > 0: u *= (1 / beta) v *= -beta At.dot(u, out=v_work) v += v_work - alpha = sqrt(v.dot(v).real) + alpha = sqrt(v.inner(v).real) if alpha > 0:v *= (1 / alpha) # At this point, beta = beta_{k+1}, alpha = alpha_{k+1}. @@ -1638,7 +1638,7 @@ def solve(self, b, out=None): # Compute norms for convergence testing. normar = abs(zetabar) - normx = sqrt(x.dot(x).real) + normx = sqrt(x.inner(x).real) # Now use these norms to estimate certain other quantities, # some of which will be small near a solution. @@ -1751,7 +1751,7 @@ def solve(self, b, out=None): b : psydac.linalg.basic.Vector Right-hand-side vector of linear system Ax = b. Individual entries b[i] need not be accessed, but b has 'shape' attribute and provides 'copy()' and - 'dot(p)' functions (dot(p) is the vector inner product b*p ); moreover, + 'inner(p)' functions (b.inner(p) is the vector inner product b*p); moreover, scalar multiplication and sum operations are available. out : psydac.linalg.basic.Vector | NoneType @@ -1803,7 +1803,7 @@ def solve(self, b, out=None): A.dot( x , out=r) r -= b - am = sqrt(r.dot(r).real) + am = sqrt(r.inner(r).real) if am < tol: self._info = {'niter': 1, 'success': am < tol, 'res_norm': am } return x @@ -1877,10 +1877,10 @@ def arnoldi(self, k, p): self._A.dot( self._Q[k] , out=p) # Krylov vector for i in range(k + 1): # Modified Gram-Schmidt, keeping Hessenberg matrix - h[i] = p.dot(self._Q[i]) + h[i] = p.inner(self._Q[i]) p.mul_iadd(-h[i], self._Q[i]) - h[k+1] = sqrt(p.dot(p).real) + h[k+1] = sqrt(p.inner(p).real) p /= h[k+1] # Normalize vector if len(self._Q) > k + 1: diff --git a/psydac/linalg/stencil.py b/psydac/linalg/stencil.py index 882d2c854..0db30d639 100644 --- a/psydac/linalg/stencil.py +++ b/psydac/linalg/stencil.py @@ -214,6 +214,56 @@ def zeros(self): """ return StencilVector(self) + #... + def inner(self, x, y): + """ + Evaluate the inner vector product between two vectors of this space V. + + If the field of V is real, compute the classical scalar product. + If the field of V is complex, compute the classical sesquilinear + product with linearity on the second vector. + + TODO [YG 01.05.2025]: Currently, the first vector is conjugated. We + want to reverse this behavior in order to align with the convention + of FEniCS. + + Parameters + ---------- + x : Vector + The first vector in the scalar product. In the case of a complex + field, the inner product is antilinear w.r.t. this vector (hence + this vector is conjugated). + + y : Vector + The second vector in the scalar product. The inner product is + linear w.r.t. this vector. + + Returns + ------- + float | complex + The scalar product of the two vectors. Note that inner(x, x) is + a non-negative real number which is zero if and only if x = 0. + + """ + + assert isinstance(x, StencilVector) + assert isinstance(y, StencilVector) + assert x.space is self + assert y.space is self + + inner_func = self._inner_func + inner_args = (x._data, y._data, *self._inner_consts) + + if self.parallel: + # Sometimes in the parallel case, we can get an empty vector that breaks our kernel + x._dot_send_data[0] = 0 if x._data.shape[0] == 0 else inner_func(*inner_args) + self.cart.global_comm.Allreduce((x._dot_send_data, self.mpi_type), + (x._dot_recv_data, self.mpi_type), + op=MPI.SUM ) + return x._dot_recv_data[0] + else: + return inner_func(*inner_args) + # ... def axpy(self, a, x, y): """ @@ -424,46 +474,47 @@ def __del__(self): def space(self): return self._space - #... - @property - def dtype(self): - return self._space.dtype - - #... - def dot(self, v): + # ... + def toarray(self, *, order='C', with_pads=False): """ - Return the inner vector product between self and v. - - If the values are real, it returns the classical scalar product. - If the values are complex, it returns the classical sesquilinear product with linearity on the vector v. + Return a numpy 1D array corresponding to the given StencilVector, + with or without pads. Parameters ---------- - v : StencilVector - Vector of the same space than self needed for the scalar product. + with_pads : bool + If True, include pads in output array (ignored in serial case). + + order: {'C','F'} + Memory representation of the data ‘C’ for row-major ordering (C-style), ‘F’ column-major ordering (Fortran-style). Returns ------- - null: self._space.dtype - Scalar containing scalar product of v and self. + array : numpy.ndarray + A copy of the data array collapsed into one dimension. """ - assert isinstance(v, StencilVector) - assert v._space is self._space + # In parallel case, call different functions based on 'with_pads' flag + if self.space.parallel: + if with_pads: + return self._toarray_parallel_with_pads(order=order) + else: + return self._toarray_parallel_no_pads(order=order) - inner_func = self._space._inner_func - inner_args = (self._data, v._data, *self._space._inner_consts) + # In serial case, ignore 'with_pads' flag + return self.toarray_local(order=order) - if self._space.parallel: - # Sometimes in the parallel case, we can get an empty vector that breaks our kernel - self._dot_send_data[0] = 0 if self._data.shape[0] == 0 else inner_func(*inner_args) - self._space.cart.global_comm.Allreduce((self._dot_send_data, self._space.mpi_type), - (self._dot_recv_data, self._space.mpi_type), - op=MPI.SUM ) - return self._dot_recv_data[0] - else: - return inner_func(*inner_args) + #... + def copy(self, out=None): + if self is out: + return self + w = out or StencilVector( self._space ) + np.copyto(w._data, self._data, casting='no') + for axis, ext in self._space.interfaces: + np.copyto(w._interface_data[axis, ext], self._interface_data[axis, ext], casting='no') + w._sync = self._sync + return w #... def conjugate(self, out=None): @@ -478,17 +529,6 @@ def conjugate(self, out=None): out._sync = self._sync return out - #... - def copy(self, out=None): - if self is out: - return self - w = out or StencilVector( self._space ) - np.copyto(w._data, self._data, casting='no') - for axis, ext in self._space.interfaces: - np.copyto(w._interface_data[axis, ext], self._interface_data[axis, ext], casting='no') - w._sync = self._sync - return w - #... def __neg__(self): w = StencilVector( self._space ) @@ -583,38 +623,6 @@ def __str__(self): txt += '> sync :: {sync}\n' .format( sync = self._sync ) return txt - # ... - def toarray(self, *, order='C', with_pads=False): - """ - Return a numpy 1D array corresponding to the given StencilVector, - with or without pads. - - Parameters - ---------- - with_pads : bool - If True, include pads in output array. - - order: {'C','F'} - Memory representation of the data ‘C’ for row-major ordering (C-style), ‘F’ column-major ordering (Fortran-style). - - Returns - ------- - array : numpy.ndarray - A copy of the data array collapsed into one dimension. - - """ - - - # In parallel case, call different functions based on 'with_pads' flag - if self.space.parallel: - if with_pads: - return self._toarray_parallel_with_pads(order=order) - else: - return self._toarray_parallel_no_pads(order=order) - - # In serial case, ignore 'with_pads' flag - return self.toarray_local(order=order) - # ... def toarray_local(self , *, order='C'): """ return the local array without the padding""" diff --git a/psydac/linalg/tests/test_block.py b/psydac/linalg/tests/test_block.py index e2e4c9640..ff3bf1e6c 100644 --- a/psydac/linalg/tests/test_block.py +++ b/psydac/linalg/tests/test_block.py @@ -328,10 +328,10 @@ def test_block_serial_dimension( ndim, p, P1, P2, P3, dtype ): Y[1] = y2 # Test dot product - exact_dot = x1.dot(y1)+x2.dot(y2) + exact_inner = V.inner(x1, y1) + V.inner(x2, y2) assert X.dtype == dtype - assert np.allclose(X.dot(Y), exact_dot, rtol=1e-14, atol=1e-14 ) + assert np.allclose(W.inner(X, Y), exact_inner, rtol=1e-14, atol=1e-14 ) # Test axpy product axpy_exact = X + np.pi * cst * Y @@ -372,8 +372,8 @@ def test_block_serial_dimension( ndim, p, P1, P2, P3, dtype ): M = BlockLinearOperator(W, W, blocks=[[M1, M2], [M3, None]]) - Y[0]=M1.dot(x1)+M2.dot(x2) - Y[1]=M3.dot(x1) + Y[0] = M1.dot(x1) + M2.dot(x2) + Y[1] = M3.dot(x1) assert M.dtype == dtype assert np.allclose((M.dot(X)).toarray(), Y.toarray(), rtol=1e-14, atol=1e-14 ) diff --git a/psydac/linalg/tests/test_linalg.py b/psydac/linalg/tests/test_linalg.py index 3e03e8185..56c826df1 100644 --- a/psydac/linalg/tests/test_linalg.py +++ b/psydac/linalg/tests/test_linalg.py @@ -643,26 +643,26 @@ def test_inverse_transpose_interaction(n1, n2, p1, p2, P1=False, P2=False): assert isinstance(C_T, ConjugateGradient) assert isinstance(inverse(B_T, 'cg', tol=tol), ConjugateGradient) diff = C_T @ u - inverse(B_T, 'cg', tol=tol) @ u - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # -1,T,T -> equal -1 diff = C_T.T @ u - C @ u - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # -1,T,-1 -> equal T assert isinstance(inverse(C_T, 'bicg'), BlockLinearOperator) diff = inverse(C_T, 'bicg') @ u - B_T @ u - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # T,-1,-1 -> equal T assert isinstance(inverse(inverse(B_T, 'cg', tol=tol), 'pcg', pc=P), BlockLinearOperator) diff = inverse(inverse(B_T, 'cg', tol=tol), 'pcg', pc=P) @ u - B_T @ u - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # T,-1,T -> equal -1 assert isinstance(inverse(B_T, 'cg', tol=tol).T, ConjugateGradient) diff = inverse(B_T, 'cg', tol=tol) @ u - C @ u - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 ### ### StencilMatrix Transpose - Inverse Tests @@ -680,26 +680,26 @@ def test_inverse_transpose_interaction(n1, n2, p1, p2, P1=False, P2=False): assert isinstance(C_T, ConjugateGradient) assert isinstance(inverse(S_T, 'cg', tol=tol), ConjugateGradient) diff = C_T @ v - inverse(S_T, 'cg', tol=tol) @ v - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # -1,T,T -> equal -1 diff = C_T.T @ v - C @ v - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # -1,T,-1 -> equal T assert isinstance(inverse(C_T, 'bicg'), StencilMatrix) diff = inverse(C_T, 'bicg') @ v - S_T @ v - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # T,-1,-1 -> equal T assert isinstance(inverse(inverse(S_T, 'cg', tol=tol), 'pcg', pc=P), StencilMatrix) diff = inverse(inverse(S_T, 'cg', tol=tol), 'pcg', pc=P) @ v - S_T @ v - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 # T,-1,T -> equal -1 assert isinstance(inverse(S_T, 'cg', tol=tol).T, ConjugateGradient) diff = inverse(S_T, 'cg', tol=tol) @ v - C @ v - assert diff.dot(diff) == 0 + assert diff.inner(diff) == 0 #=============================================================================== @pytest.mark.parametrize('n1', [3, 5]) diff --git a/psydac/linalg/tests/test_stencil_interface_matrix.py b/psydac/linalg/tests/test_stencil_interface_matrix.py index 63001a766..60693952c 100644 --- a/psydac/linalg/tests/test_stencil_interface_matrix.py +++ b/psydac/linalg/tests/test_stencil_interface_matrix.py @@ -369,7 +369,7 @@ def test_stencil_interface_matrix_2d_parallel_dot(n1, n2, p1, p2, expected): y = A.dot(x) # Check the results - assert y.dot(y) == expected + assert y.inner(y) == expected #=============================================================================== # SCRIPT FUNCTIONALITY diff --git a/psydac/linalg/tests/test_stencil_vector.py b/psydac/linalg/tests/test_stencil_vector.py index 95200ba37..0983edf80 100644 --- a/psydac/linalg/tests/test_stencil_vector.py +++ b/psydac/linalg/tests/test_stencil_vector.py @@ -288,8 +288,8 @@ def test_stencil_vector_2d_serial_dot(dtype, n1, n2, p1, p2, s1, s2, P1=True, P2 y[i1, i2] = f2(i1,i2) # Create inner vector product (x,y) and (y,x) - z1 = x.dot(y) - z2 = y.dot(x) + z1 = x.inner(y) + z2 = y.inner(x) # Exact value by Numpy dot and vdot if dtype==complex: @@ -939,8 +939,8 @@ def test_stencil_vector_2d_parallel_dot(dtype, n1, n2, p1, p2, s1, s2, P1=True, y[i1, i2] = f2(i1,i2) # Create scalar product (x,y) and (y,x) - res1 = x.dot(y) - res2 = y.dot(x) + res1 = x.inner(y) + res2 = y.inner(x) # Compute exact value with Numpy dot if dtype==complex: @@ -1008,8 +1008,8 @@ def test_stencil_vector_3d_parallel_dot(dtype, n1, n2, n3, p1, p2, p3, s1, s2, s x[i1, i2, i3] = f2(i1,i2,i3) # Create scalar product (x,y) and (y,x) - res1 = x.dot(y) - res2 = y.dot(x) + res1 = x.inner(y) + res2 = y.inner(x) # Compute exact value with Numpy dot if dtype == complex: diff --git a/psydac/polar/dense.py b/psydac/polar/dense.py index 2e209f95e..963333665 100644 --- a/psydac/polar/dense.py +++ b/psydac/polar/dense.py @@ -137,14 +137,66 @@ def zeros(self): data = np.zeros(self.ncoeff, dtype=self.dtype) return DenseVector(self, data) + # ... + def inner(self, x, y): + """ + Evaluate the inner vector product between two vectors of this space V. + + If the field of V is real, compute the classical scalar product. + If the field of V is complex, compute the classical sesquilinear + product with linearity on the second vector. + + TODO [YG 01.05.2025]: Currently, the first vector is conjugated. We + want to reverse this behavior in order to align with the convention + of FEniCS. + + Parameters + ---------- + x : Vector + The first vector in the scalar product. In the case of a complex + field, the inner product is antilinear w.r.t. this vector (hence + this vector is conjugated). + + y : Vector + The second vector in the scalar product. The inner product is + linear w.r.t. this vector. + + Returns + ------- + float | complex + The scalar product of the two vectors. Note that inner(x, x) is + a non-negative real number which is zero if and only if x = 0. + + """ + assert isinstance(x, DenseVector) + assert isinstance(y, DenseVector) + assert x.space is self + assert y.space is self + + res = np.dot(x._data, y._data) + + V = self + if V.parallel: + if V.radial_comm.rank == V.radial_root: + res = V.tensor_comm.allreduce(res) + res = V.radial_comm.bcast(res, root=V.radial_root) + + return res + # ... def axpy(self, a, x, y): + + assert isinstance(a, (int, float, complex)) + assert isinstance(x, DenseVector) + assert isinstance(y, DenseVector) + assert x.space is self + assert y.space is self + y += a * x #------------------------------------- # Other properties/methods #------------------------------------- - @property def parallel(self): return (self._cart is not None) @@ -202,33 +254,8 @@ def space(self): return self._space # ... - @property - def dtype(self): - return self.space.dtype - - # ... - def dot(self, v): - assert isinstance(v, DenseVector) - assert v._space is self._space - - res = np.dot(self._data, v._data) - - V = self._space - if V.parallel: - if V.radial_comm.rank == V.radial_root: - res = V.tensor_comm.allreduce(res) - res = V.radial_comm.bcast(res, root=V.radial_root) - - return res - - def conjugate(self, out=None): - if out is not None: - assert isinstance(out, DenseVector) - assert out.space is self.space - else: - out = DenseVector(self.space) - np.conjugate(self._data, out=out._data, casting='no') - return out + def toarray(self, **kwargs): + return self._data.copy() # ... def copy(self, out=None): @@ -242,6 +269,16 @@ def copy(self, out=None): else: return DenseVector(self._space, self._data.copy()) + # ... + def conjugate(self, out=None): + if out is not None: + assert isinstance(out, DenseVector) + assert out.space is self.space + else: + out = DenseVector(self.space) + np.conjugate(self._data, out=out._data, casting='no') + return out + # ... def __neg__(self): return DenseVector(self._space, -self._data) @@ -284,10 +321,6 @@ def __isub__(self, v): #------------------------------------- # Other properties/methods #------------------------------------- - def toarray(self, **kwargs): - return self._data.copy() - - # ... def update_ghost_regions(self, *, direction=None): pass From f96e8883ef580b49fcfddc18a64ff031fe308c2a Mon Sep 17 00:00:00 2001 From: Martin Campos Pinto Date: Fri, 9 May 2025 17:19:09 +0200 Subject: [PATCH 06/23] Update docstring for inner product in polar/dense.py (#488) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --------- Co-authored-by: Yaman Güçlü --- psydac/polar/dense.py | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/psydac/polar/dense.py b/psydac/polar/dense.py index 963333665..302e0a529 100644 --- a/psydac/polar/dense.py +++ b/psydac/polar/dense.py @@ -150,12 +150,16 @@ def inner(self, x, y): want to reverse this behavior in order to align with the convention of FEniCS. + TODO [MCP 07.05.2025]: Actually, there is currently no conjugation, + since `numpy.dot` is being called. + Parameters ---------- x : Vector The first vector in the scalar product. In the case of a complex field, the inner product is antilinear w.r.t. this vector (hence this vector is conjugated). + NOTE [MCP 07.05.2025]: currently without conjugate, see np.dot y : Vector The second vector in the scalar product. The inner product is From 54ea3cea9c34af651b0f8864ca8b47b56534da47 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Mon, 26 May 2025 09:38:19 +0200 Subject: [PATCH 07/23] Add a `dot_inner` concrete method to the base class `LinearOperator` (#493) Implement `M.dot(u).inner(v)`, or `(M @ u).inner(v)`, without creating a temporary vector. The result of the dot product is written to a local work vector stored in the `LinearOperator` object. This work vector is then used to compute the inner product with the vector `v`. The subclasses do not need to override this method, unless a more efficient implementation which avoids writing to the work vector altogether (reducing memory pressure) is needed. A unit test is added: function `test_dot_inner` in file psydac/linalg/tests/test_linalg.py. Additionally, the helper function `get_StencilVectorSpace` defined in psydac/linalg/tests/test_linalg.py (only used in the same file and in test_matrix_free.py) has a new signature and now works in any number of dimensions. Fixes #491. --- psydac/linalg/basic.py | 98 ++++++++++++++++++++++--- psydac/linalg/tests/test_linalg.py | 84 +++++++++++++++++---- psydac/linalg/tests/test_matrix_free.py | 6 +- 3 files changed, 159 insertions(+), 29 deletions(-) diff --git a/psydac/linalg/basic.py b/psydac/linalg/basic.py index bf88dbd07..f9f63406d 100644 --- a/psydac/linalg/basic.py +++ b/psydac/linalg/basic.py @@ -267,32 +267,51 @@ def shape(self): @abstractmethod def domain(self): """ The domain of the linear operator - an element of Vectorspace """ - pass @property @abstractmethod def codomain(self): """ The codomain of the linear operator - an element of Vectorspace """ - pass @property @abstractmethod def dtype(self): - pass + """ The data type of the coefficients of the linear operator, + upon convertion to matrix. + """ @abstractmethod def tosparse(self): - pass + """ Convert to a sparse matrix in any of the formats supported by scipy.sparse.""" @abstractmethod def toarray(self): """ Convert to Numpy 2D array. """ - pass @abstractmethod def dot(self, v, out=None): - """ Apply linear operator to Vector v. Result is written to Vector out, if provided.""" - pass + """ Apply the LinearOperator self to the Vector v. + + The result is written to the Vector out, if provided. + + Parameters + ---------- + v : Vector + The vector to which the linear operator (self) is applied. It must + belong to the domain of self. + + out : Vector + The vector in which the result of the operation is stored. It must + belong to the codomain of self. If out is None, a new vector is + created and returned. + + Returns + ------- + Vector + The result of the operation. If out is None, a new vector is + returned. Otherwise, the result is stored in out and out is + returned. + """ @abstractmethod def transpose(self, conjugate=False): @@ -301,7 +320,6 @@ def transpose(self, conjugate=False): If conjugate is True, return the Hermitian transpose. """ - pass # TODO: check if we should add a copy method!!! @@ -335,7 +353,32 @@ def __rmul__(self, c): return self * c def __matmul__(self, B): - """ Creates an object of the class ComposedLinearOperator. """ + """ + Matrix multiplication using the @ operator. + + If B is a LinearOperator, create a ComposedLinearOperator object. + This is simplified to self if B is an IdentityOperator, and to a + ZeroOperator if B is a ZeroOperator. + + If B is a Vector, the @ operator is treated as a matrix-vector + multiplication and returns the result of self.dot(B). + + Parameters + ---------- + B : LinearOperator | Vector + The object to be multiplied with self. If B is a LinearOperator, + its codomain must be equal to the domain of self. If B is a Vector, + it must belong to the domain of self. + + Returns + ------- + LinearOperator | Vector + If B is a LinearOperator, return a ComposedLinearOperator object, + or a simplification to self or a ZeroOperator. In all cases the + resulting LinearOperator has the same domain as self and the same + codomain as B. If B is a Vector, return the result of self.dot(B), + which is a Vector belonging to the codomain of self. + """ assert isinstance(B, (LinearOperator, Vector)) if isinstance(B, LinearOperator): assert self.domain == B.codomain @@ -380,7 +423,6 @@ def __itruediv__(self, c): #------------------------------------- # Methods with default implementation #------------------------------------- - @property def T(self): """ Calls transpose method to return the transpose of self. """ @@ -403,6 +445,42 @@ def idot(self, v, out): assert out.space == self.codomain out += self.dot(v) + def dot_inner(self, v, w): + """ + Compute the inner product of (self @ v) with w, without a temporary. + + This is equivalent to self.dot(v).inner(w), but avoids the creation of + a temporary vector because the result of self.dot(v) is stored in a + local work array. If self is a positive-definite operator, this + operation is a (weighted) inner product. + + Parameters + ---------- + v : Vector + The vector to which the linear operator (self) is applied. It must + belong to the domain of self. + + w : Vector + The second vector in the inner product. It must belong to the + codomain of self. + + Returns + ------- + float | complex + The result of the inner product between (self @ v) and w. If the + field of self is real, this is a real number. If the field of self + is complex, this is a complex number. + """ + assert isinstance(v, Vector) + assert isinstance(w, Vector) + assert v.space is self.domain + assert w.space is self.codomain + + if not hasattr(self, '_work'): + self._work = self.codomain.zeros() + + return self.dot(v, out=self._work).inner(w) + #=============================================================================== class ZeroOperator(LinearOperator): """ diff --git a/psydac/linalg/tests/test_linalg.py b/psydac/linalg/tests/test_linalg.py index 56c826df1..8ce093094 100644 --- a/psydac/linalg/tests/test_linalg.py +++ b/psydac/linalg/tests/test_linalg.py @@ -40,13 +40,12 @@ def compute_global_starts_ends(domain_decomposition, npts): return global_starts, global_ends -def get_StencilVectorSpace(n1, n2, p1, p2, P1, P2): - npts = [n1, n2] - pads = [p1, p2] - periods = [P1, P2] +def get_StencilVectorSpace(npts, pads, periods): + assert len(npts) == len(pads) == len(periods) + shifts = [1] * len(npts) D = DomainDecomposition(npts, periods=periods) global_starts, global_ends = compute_global_starts_ends(D, npts) - C = CartDecomposition(D, npts, global_starts, global_ends, pads=pads, shifts=[1,1]) + C = CartDecomposition(D, npts, global_starts, global_ends, pads=pads, shifts=shifts) V = StencilVectorSpace(C) return V @@ -94,7 +93,7 @@ def test_square_stencil_basic(n1, n2, p1, p2, P1=False, P2=False): ### # Initiate StencilVectorSpace - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) # Initiate Linear Operators Z = ZeroOperator(V, V) @@ -280,7 +279,7 @@ def test_square_block_basic(n1, n2, p1, p2, P1=False, P2=False): # 3. Test special cases # Initiate StencilVectorSpace - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) # Initiate Linear Operators Z = ZeroOperator(V, V) @@ -449,8 +448,8 @@ def test_in_place_operations(n1, n2, p1, p2, P1=False, P2=False): # testing __imul__ although not explicitly implemented (in the LinearOperator class) # Initiate StencilVectorSpace - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) - Vc = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) + Vc = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) Vc._dtype = complex v = StencilVector(V) vc = StencilVector(Vc) @@ -544,9 +543,9 @@ def test_inverse_transpose_interaction(n1, n2, p1, p2, P1=False, P2=False): # 2. For both B and S, check whether all possible combinations of the transpose and the inverse behave as expected # Initiate StencilVectorSpace - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) - V2 = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) - W = get_StencilVectorSpace(n1+2, n2, p1, p2+1, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) + V2 = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) + W = get_StencilVectorSpace([n1+2, n2], [p1, p2+1], [P1, P2]) # Initiate positive definite StencilMatrices for which the cg inverse works (necessary for certain tests) S = StencilMatrix(V, V) @@ -710,7 +709,7 @@ def test_inverse_transpose_interaction(n1, n2, p1, p2, P1=False, P2=False): def test_positive_definite_matrix(n1, n2, p1, p2): P1 = False P2 = False - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) S = get_positive_definite_StencilMatrix(V) assert_pos_def(S) @@ -753,7 +752,7 @@ def test_operator_evaluation(n1, n2, p1, p2): P2 = False # Initiate StencilVectorSpace V - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) # Initiate positive definite StencilMatrices for which the cg inverse works (necessary for certain tests) S = get_positive_definite_StencilMatrix(V) @@ -919,7 +918,7 @@ def test_internal_storage(): p2=1 P1=False P2=False - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) U1 = BlockVectorSpace(V, V) U2 = BlockVectorSpace(V, V, V) @@ -970,7 +969,7 @@ def test_x0update(solver): p2 = 2 P1 = False P2 = False - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) A = get_positive_definite_StencilMatrix(V) assert_pos_def(A) b = StencilVector(V) @@ -1005,6 +1004,59 @@ def test_x0update(solver): x = A_inv.dot(b, out=b) assert A_inv.get_options('x0') is x +#=============================================================================== +def test_dot_inner(): + + n1, n2 = 4, 7 + p1, p2 = 2, 3 + P1, P2 = False, False + + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) + M = get_positive_definite_StencilMatrix(V) + N = get_positive_definite_StencilMatrix(V) + + U1 = BlockVectorSpace(V, V) + U2 = BlockVectorSpace(V, V, V) + A = BlockLinearOperator(U1, U2, ((M, None), + (M, N), + (None, N))) + + b = A.domain.zeros() + c = A.codomain.zeros() + + # Set the values of b and c randomly from a uniform distribution over the + # interval [0, 1) + rng = np.random.default_rng(seed=42) + for bj in b: + Vj = bj.space + rng.random(size=Vj.shape, dtype=Vj.dtype, out=bj._data) + for ci in c: + Vi = ci.space + rng.random(size=Vi.shape, dtype=Vi.dtype, out=ci._data) + + # Create a work vector for the dot product, needed to compare results + work_vec = A.codomain.zeros() + + # Result of dot product is a temporary vector, which is allocated and then + # discarded. This is the default behavior of the dot method. + r0 = A.dot(b).inner(c) + + # Result of dot product is stored in work_vec and used in the next line + A.dot(b, out=work_vec) + r1 = work_vec.inner(c) + + # Result of dot product is stored in work_vec and used in the same line + r2 = A.dot(b, out=work_vec).inner(c) + + # Calling the dot_inner method, which uses an internal work vector to store + # the result of the dot product, and then uses it for the inner product. + r3 = A.dot_inner(b, c) + + # Check if the results are equal + assert r0 == r1 + assert r0 == r2 + assert r0 == r3 + #=============================================================================== # SCRIPT FUNCTIONALITY #=============================================================================== diff --git a/psydac/linalg/tests/test_matrix_free.py b/psydac/linalg/tests/test_matrix_free.py index e475fb15f..43531cbaf 100644 --- a/psydac/linalg/tests/test_matrix_free.py +++ b/psydac/linalg/tests/test_matrix_free.py @@ -63,8 +63,8 @@ def test_fake_matrix_free(n1, n2, p1, p2): m2 = n1+1 q1 = p1 # using same degrees because both spaces must have same padding for now q2 = p2 - V1 = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) - V2 = get_StencilVectorSpace(m1, m2, q1, q2, P1, P2) + V1 = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) + V2 = get_StencilVectorSpace([m1, m2], [q1, q2], [P1, P2]) S = get_random_StencilMatrix(codomain=V2, domain=V1) O = MatrixFreeLinearOperator(codomain=V2, domain=V1, dot=lambda v: S @ v) @@ -91,7 +91,7 @@ def test_solvers_matrix_free(solver): p2 = 2 P1 = False P2 = False - V = get_StencilVectorSpace(n1, n2, p1, p2, P1, P2) + V = get_StencilVectorSpace([n1, n2], [p1, p2], [P1, P2]) A_SM = get_positive_definite_StencilMatrix(V) assert_pos_def(A_SM) AT_SM = A_SM.transpose() From 5e3d7699734a0f074441fb2c157a6ba247c2d44e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Fri, 30 May 2025 08:51:42 +0200 Subject: [PATCH 08/23] Install PETSc-3.23.2 (latest version) (#499) --- .github/workflows/{continuous-integration.yml => testing.yml} | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) rename .github/workflows/{continuous-integration.yml => testing.yml} (97%) diff --git a/.github/workflows/continuous-integration.yml b/.github/workflows/testing.yml similarity index 97% rename from .github/workflows/continuous-integration.yml rename to .github/workflows/testing.yml index ae4c2e09d..115ae117f 100644 --- a/.github/workflows/continuous-integration.yml +++ b/.github/workflows/testing.yml @@ -66,6 +66,7 @@ jobs: - name: Install non-Python dependencies on macOS if: matrix.os == 'macos-14' run: | + brew install make brew install open-mpi brew install hdf5-mpi brew install libomp @@ -79,6 +80,7 @@ jobs: ln -s ${gfort_path} ${folder}/gfortran fi echo "MPI_OPTS=--oversubscribe" >> $GITHUB_ENV + echo "/opt/homebrew/opt/make/libexec/gnubin" >> $GITHUB_PATH - name: Print information on MPI and HDF5 libraries run: | @@ -111,7 +113,7 @@ jobs: - if: steps.cache-petsc.outputs.cache-hit != 'true' name: Download a specific release of PETSc run: | - git clone --depth 1 --branch v3.22.2 https://gitlab.com/petsc/petsc.git + git clone --depth 1 --branch v3.23.2 https://gitlab.com/petsc/petsc.git - if: steps.cache-petsc.outputs.cache-hit != 'true' name: Install PETSc with complex support From 2f242b1bd66f674fabc4134a4a430eb667813792 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Fri, 30 May 2025 16:25:59 +0200 Subject: [PATCH 09/23] Update authors (#500) --- AUTHORS | 20 +++++++++++++------- pyproject.toml | 4 ++-- 2 files changed, 15 insertions(+), 9 deletions(-) diff --git a/AUTHORS b/AUTHORS index c09d4ae7f..609b8c3e5 100644 --- a/AUTHORS +++ b/AUTHORS @@ -1,16 +1,22 @@ Maintainers ----------- -* Yaman Güçlü (administrator, owner) -* Ahmed Ratnani (owner) -* Said Hadjout +* Yaman Güçlü (original author, project lead) +* Martin Campos Pinto +* Ahmed Ratnani (original author) Contributors ------------ -* Jalal Lakhlili -* Martin Campos Pinto -* Antoine Lavandier -* David Schneller +* Said Hadjout (original author) * Julian Owezarek +* Antoine Lavandier * Tom Caruso * Elena Moral Sánchez +* Paul Rigor +* Frederik Schnack +* David Schneller * Valentin Carlier +* Stefan Possanner +* Jalal Lakhlili (original author) +* William Barham +* Max Lindqvist +* Emily Bourne diff --git a/pyproject.toml b/pyproject.toml index 43d4c527a..2d42320d2 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -13,9 +13,9 @@ authors = [ {name = "Psydac development team", email = "psydac@googlegroups.com"} ] maintainers = [ - {name = "Yaman Güçlü" , email = "yaman.guclu@gmail.com"}, + {name = "Yaman Güçlü", email = "yaman.guclu@gmail.com"}, + {name = "Martin Campos Pinto", email = "martin.campos-pinto@ipp.mpg.de"}, {name = "Ahmed Ratnani", email = "ratnaniahmed@gmail.com"}, - {name = "Said Hadjout"}, ] keywords = ["FEM", "IGA", "B-spline", "NURBS"] classifiers = ["Programming Language :: Python :: 3"] From b5230b42ba92864748d12c5efe7b05214505205e Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Fri, 13 Jun 2025 14:27:01 +0200 Subject: [PATCH 10/23] Fix the code generation of unnecessary derivatives (#490) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This PR changes the code generation involved in the `discretize` function to avoid calculating unnecessary derivatives. This allows for using constant spline (degree 0) discretizations, for which we have to make a special case in the calculation of ghost regions in `psydac/linalg/stencil.py`. Additionally, we add basic unit tests checking discretizations using zero-degree splines. This fixes #489 and fixes #307. On this occasion, we also do small changes in the `.github/workflows/testing.yml` script as some tests had complications without them. --------- Co-authored-by: Yaman Güçlü --- .github/workflows/testing.yml | 4 +-- psydac/api/ast/expr.py | 12 ++++--- psydac/api/ast/fem.py | 18 ++++++---- psydac/api/ast/glt.py | 14 +++++--- psydac/api/ast/nodes.py | 1 - psydac/api/ast/utilities.py | 54 ++++++++++++++++++++++++++++ psydac/api/tests/test_api_feec_1d.py | 53 +++++++++++++++++++++++++++ psydac/api/tests/test_assembly.py | 54 ++++++++++++++++++++++++++++ psydac/linalg/stencil.py | 37 +++++++++++++++---- 9 files changed, 222 insertions(+), 25 deletions(-) diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml index 115ae117f..802657cd0 100644 --- a/.github/workflows/testing.yml +++ b/.github/workflows/testing.yml @@ -87,9 +87,9 @@ jobs: ompi_info h5pcc -showconfig -echo || true - - name: Upgrade pip + - name: Upgrade pip, setuptools, and wheel run: | - python -m pip install --upgrade pip + python -m pip install --upgrade pip setuptools wheel - name: Determine directory of parallel HDF5 library run: | diff --git a/psydac/api/ast/expr.py b/psydac/api/ast/expr.py index 0e72504fd..4805b85d7 100644 --- a/psydac/api/ast/expr.py +++ b/psydac/api/ast/expr.py @@ -22,7 +22,6 @@ from sympde.topology.space import IndexedVectorFunction from sympde.topology.derivatives import _partial_derivatives from sympde.topology.derivatives import _logical_partial_derivatives -from sympde.topology.derivatives import get_max_partial_derivatives from sympde.topology.derivatives import get_atom_derivatives from sympde.topology.derivatives import get_index_derivatives from sympde.topology import LogicalExpr @@ -34,6 +33,7 @@ from .utilities import build_pythran_types_header, variables from .utilities import build_pyccel_type_annotations from .utilities import math_atoms_as_str +from .utilities import get_max_partial_derivatives from psydac.fem.vector import MultipatchFemSpace from .nodes import Zeros @@ -306,15 +306,19 @@ def _initialize(self): cls = IndexedVariable ) # ... TODO add it as a method to basic class - nderiv = 1 + nderiv = 0 + if isinstance(expr, Matrix): n_rows, n_cols = expr.shape for i_row in range(0, n_rows): for i_col in range(0, n_cols): - d = get_max_partial_derivatives(expr[i_row,i_col]) + d_atoms = _atomic(expr[i_row,i_col], cls=atoms_types) + Fs = [get_atom_derivatives(a) for a in d_atoms] + d = get_max_partial_derivatives(expr[i_row,i_col], logical=False, F=Fs) nderiv = max(nderiv, max(d.values())) else: - d = get_max_partial_derivatives(expr) + Fs = [get_atom_derivatives(a) for a in atoms] + d = get_max_partial_derivatives(expr, logical=False, F=Fs) nderiv = max(nderiv, max(d.values())) self._max_nderiv = nderiv diff --git a/psydac/api/ast/fem.py b/psydac/api/ast/fem.py index 1743518cd..b56ee3d28 100644 --- a/psydac/api/ast/fem.py +++ b/psydac/api/ast/fem.py @@ -11,7 +11,7 @@ from sympde.topology.basic import Boundary, Interface from sympde.topology import H1SpaceType, HcurlSpaceType, HdivSpaceType, L2SpaceType, UndefinedSpaceType, IdentityMapping from sympde.topology.space import ScalarFunction, VectorFunction, IndexedVectorFunction -from sympde.topology.derivatives import _logical_partial_derivatives, get_max_logical_partial_derivatives +from sympde.topology.derivatives import _logical_partial_derivatives, get_atom_logical_derivatives from sympde.topology.mapping import InterfaceMapping from sympde.calculus.core import is_zero, PlusInterfaceOperator @@ -44,7 +44,7 @@ from .nodes import GlobalThreadStarts, GlobalThreadEnds, GlobalThreadSizes from .nodes import Allocate, Array from .nodes import Block, ParallelBlock - +from .utilities import get_max_partial_derivatives from psydac.api.ast.utilities import variables from psydac.api.utilities import flatten @@ -339,7 +339,7 @@ def __init__(self, expr, terminal_expr, spaces, *, nquads, mapping_space=None, t fields = expand_hdiv_hcurl(fields) kwargs['nquads'] = nquads atoms_types = (ScalarFunction, VectorFunction, IndexedVectorFunction) - nderiv = 1 + nderiv = 0 terminal_expr = terminal_expr.expr if isinstance(terminal_expr, (ImmutableDenseMatrix, Matrix)): @@ -347,8 +347,6 @@ def __init__(self, expr, terminal_expr, spaces, *, nquads, mapping_space=None, t atomic_expr_field = {f:[] for f in fields} for i_row in range(0, n_rows): for i_col in range(0, n_cols): - d = get_max_logical_partial_derivatives(terminal_expr[i_row,i_col]) - nderiv = max(nderiv, max(d.values())) atoms = _atomic(terminal_expr[i_row, i_col], cls=atoms_types+_logical_partial_derivatives) #-------------------------------------------------------------------- # TODO [YG, 05.02.2021]: create 'get_test_function' and use it below: @@ -359,10 +357,12 @@ def __init__(self, expr, terminal_expr, spaces, *, nquads, mapping_space=None, t a = _atomic(f, cls=atoms_types) assert len(a) == 1 atomic_expr_field[a[0]].append(f) + + Fs = [get_atom_logical_derivatives(a) for a in atoms] + d = get_max_partial_derivatives(terminal_expr[i_row,i_col], logical=True, F=Fs) + nderiv = max(nderiv, max(d.values())) else: - d = get_max_logical_partial_derivatives(terminal_expr) - nderiv = max(nderiv, max(d.values())) atoms = _atomic(terminal_expr, cls=atoms_types+_logical_partial_derivatives) #-------------------------------------------------------------------- # TODO [YG, 05.02.2021]: create 'get_test_function' and use it below: @@ -375,6 +375,10 @@ def __init__(self, expr, terminal_expr, spaces, *, nquads, mapping_space=None, t assert len(a) == 1 atomic_expr_field[a[0]].append(f) + Fs = [get_atom_logical_derivatives(a) for a in atoms] + d = get_max_partial_derivatives(terminal_expr, logical=True, F=Fs) + nderiv = max(nderiv, max(d.values())) + terminal_expr = Matrix([[terminal_expr]]) d_tests = {v: {'global': GlobalTensorQuadratureTestBasis(v), diff --git a/psydac/api/ast/glt.py b/psydac/api/ast/glt.py index f0fc64ee8..00c80a1c4 100644 --- a/psydac/api/ast/glt.py +++ b/psydac/api/ast/glt.py @@ -26,8 +26,7 @@ from sympde.topology.space import VectorFunction from sympde.topology.space import IndexedVectorFunction from sympde.topology.derivatives import _partial_derivatives -from sympde.topology.derivatives import _logical_partial_derivatives -from sympde.topology.derivatives import get_max_partial_derivatives +from sympde.topology.derivatives import _logical_partial_derivatives, get_atom_derivatives from sympde.topology import LogicalExpr from sympde.topology import SymbolicExpr from sympde.calculus.matrices import SymbolicDeterminant @@ -43,6 +42,7 @@ from .utilities import build_pyccel_type_annotations from .utilities import is_mapping from .utilities import math_atoms_as_str +from .utilities import get_max_partial_derivatives from .evaluation import EvalArrayMapping, EvalArrayField from psydac.fem.vector import MultipatchFemSpace @@ -329,15 +329,19 @@ def _initialize(self, **kwargs): # ... # ... TODO add it as a method to basic class - nderiv = 1 + nderiv = 0 + if isinstance(expr, Matrix): n_rows, n_cols = expr.shape for i_row in range(0, n_rows): for i_col in range(0, n_cols): - d = get_max_partial_derivatives(expr[i_row,i_col]) + d_atoms = _atomic(expr[i_row,i_col], cls=atoms_types) + Fs = [get_atom_derivatives(a) for a in d_atoms] + d = get_max_partial_derivatives(expr[i_row,i_col], logical=False, F=Fs) nderiv = max(nderiv, max(d.values())) else: - d = get_max_partial_derivatives(expr) + Fs = [get_atom_derivatives(a) for a in atoms] + d = get_max_partial_derivatives(expr, logical=False, F=Fs) nderiv = max(nderiv, max(d.values())) self._max_nderiv = nderiv diff --git a/psydac/api/ast/nodes.py b/psydac/api/ast/nodes.py index 8a1cd5e63..caa76b554 100644 --- a/psydac/api/ast/nodes.py +++ b/psydac/api/ast/nodes.py @@ -2372,7 +2372,6 @@ def __new__(cls, M, nderiv, dtype='real'): if not M.is_analytical: dim = M.ldim - nderiv = 1 if nderiv == 0 else nderiv ops = [dx1, dx2, dx3][:dim] r = range(nderiv+1) ranges = [r]*dim diff --git a/psydac/api/ast/utilities.py b/psydac/api/ast/utilities.py index b4601b27d..61056c6b1 100644 --- a/psydac/api/ast/utilities.py +++ b/psydac/api/ast/utilities.py @@ -1,6 +1,7 @@ import re import string import random +from itertools import chain from sympy import Symbol, IndexedBase, Indexed, Idx from sympy import Mul, Pow, Function, Tuple @@ -19,6 +20,7 @@ from sympde.topology.derivatives import get_index_derivatives from sympde.topology.derivatives import get_atom_logical_derivatives from sympde.topology.derivatives import get_index_logical_derivatives +from sympde.topology.derivatives import get_index_derivatives_atom, get_index_logical_derivatives_atom from sympde.topology import LogicalExpr from sympde.topology import SymbolicExpr from sympde.core import Constant @@ -55,6 +57,58 @@ 'variables', ) +#============================================================================== +def get_max_partial_derivatives(expr, logical=False, F=None): + """ + Compute the maximum order of partial derivatives for each coordinate in an expression. + + TODO + ---- + Move to SymPDE and combine the `get_index(_logical)_derivatives_atom` functions there. + + Parameters + ---------- + expr : sympy.Expr + The SymPDE expression to analyze for partial derivatives. + + logical : bool, optional + If True, it considers logical coordinates (x1, x2, x3); otherwise, it considers physical coordinates (x, y, z). + + F : sympy.Atom | list[sympy.Atom], optional + If provided, it restricts the analysis to the specified atom(s). Otherwise, + it uses all atoms of default types that are contained in `expr`. The default + types represent elements of function spaces in SymPDE: `ScalarFunction`, + `VectorFunction`, and `IndexedVectorFunction`. + + Returns + ------- + d : dict[str, int] + A dictionary with keys ('x1', 'x2', 'x3') for logical or ('x', 'y', 'z') for physical coordinates and their corresponding maximum order of partial derivatives. + """ + + if logical: + d = {'x1': 0, 'x2': 0, 'x3': 0} + get_index = get_index_logical_derivatives_atom + else: + d = {'x': 0, 'y': 0, 'z': 0} + get_index = get_index_derivatives_atom + + if F is None: + F = (list(expr.atoms(ScalarFunction)) + + list(expr.atoms(VectorFunction)) + + list(expr.atoms(IndexedVectorFunction))) + elif not hasattr(F, '__iter__'): + F = [F] + + indices = chain.from_iterable(get_index(expr, Fi) for Fi in F) + + for dd in indices: + for k, v in dd.items(): + if v > d[k]: + d[k] = v + + return d + #============================================================================== def random_string( n ): chars = string.ascii_lowercase + string.digits diff --git a/psydac/api/tests/test_api_feec_1d.py b/psydac/api/tests/test_api_feec_1d.py index d9337f4a9..ad60a2c02 100644 --- a/psydac/api/tests/test_api_feec_1d.py +++ b/psydac/api/tests/test_api_feec_1d.py @@ -499,6 +499,32 @@ def test_maxwell_1d_periodic(): assert abs(namespace['error_E'] - ref['error_E']) / ref['error_E'] <= TOL assert abs(namespace['error_B'] - ref['error_B']) / ref['error_B'] <= TOL + +def test_maxwell_1d_periodic_deg_1(): + + namespace = run_maxwell_1d( + L = 1.0, + eps = 0.5, + ncells = 30, + degree = 1, + periodic = True, + Cp = 0.5, + nsteps = 1, + tend = None, + splitting_order = 2, + plot_interval = 0, + diagnostics_interval = 0, + tol = 1e-6, + bc_mode = None, + verbose = False + ) + + TOL = 1e-6 + ref = dict(error_E = 0.0072675885645832605, + error_B = 0.06600368653495972) + + assert abs(namespace['error_E'] - ref['error_E']) / ref['error_E'] <= TOL + assert abs(namespace['error_B'] - ref['error_B']) / ref['error_B'] <= TOL def test_maxwell_1d_periodic_mult(): @@ -608,6 +634,33 @@ def test_maxwell_1d_periodic_par(): assert abs(namespace['error_l2_E'] - ref['error_l2_E']) / ref['error_l2_E'] <= TOL assert abs(namespace['error_l2_B'] - ref['error_l2_B']) / ref['error_l2_B'] <= TOL +@pytest.mark.parallel +def test_maxwell_1d_periodic_par_deg_1(): + + namespace = run_maxwell_1d( + L = 1.0, + eps = 0.5, + ncells = 30, + degree = 1, + periodic = True, + Cp = 0.5, + nsteps = 1, + tend = None, + splitting_order = 2, + plot_interval = 0, + diagnostics_interval = 0, + tol = 1e-6, + bc_mode = None, + verbose = False + ) + + TOL = 1e-6 + ref = dict(error_l2_E = 0.0024771477815803107, + error_l2_B = 0.016857601931265228) + + assert abs(namespace['error_l2_E'] - ref['error_l2_E']) / ref['error_l2_E'] <= TOL + assert abs(namespace['error_l2_B'] - ref['error_l2_B']) / ref['error_l2_B'] <= TOL + @pytest.mark.parallel def test_maxwell_1d_dirichlet_strong_par(): diff --git a/psydac/api/tests/test_assembly.py b/psydac/api/tests/test_assembly.py index d00c58840..a84a41a2b 100644 --- a/psydac/api/tests/test_assembly.py +++ b/psydac/api/tests/test_assembly.py @@ -84,6 +84,60 @@ def test_field_and_constant(backend, dtype): assert abs(b.toarray().sum() - res) < 1e-12 print("PASSED") +#============================================================================== +def test_field_and_constant_deg_0(backend, dtype): + + # If 'backend' is specified, accelerate Python code by passing **kwargs + # to discretization of bilinear forms, linear forms and functionals. + kwargs = {'backend': PSYDAC_BACKENDS[backend]} if backend else {} + + domain = Square() + V = ScalarFunctionSpace('V', domain) + + # TODO: remove codomain_type when It is implemented in sympde + u = element_of(V, name='u') + v = element_of(V, name='v') + f = element_of(V, name='f') + + if dtype == 'complex': + c = Constant(name='c', complex=True) + V.codomain_type = dtype + g = I * c * f**2 + res = 1.j + cst=complex(1.0) + else: + c = Constant(name='c', real=True) + g = c * f**2 + res = 1 + cst=1.0 + + a = BilinearForm((u, v), integral(domain, g * u * v)) + l = LinearForm(v, integral(domain, g * v)) + + ncells = (5, 5) + degree = (0, 0) + domain_h = discretize(domain, ncells=ncells) + Vh = discretize(V, domain_h, degree=degree) + ah = discretize(a, domain_h, [Vh, Vh], **kwargs) + lh = discretize(l, domain_h, Vh , **kwargs) + + fh = FemField(Vh) + fh.coeffs[:] = 1 + + # Assembly call should not crash if correct arguments are used + A = ah.assemble(c=cst, f=fh) + b = lh.assemble(f=fh, c=cst) + + # Test matrix A + x = fh.coeffs + + #TODO change res into np.conj(res) when the conjugate is applied in the dot product in sympde + assert abs(x.inner(A.dot(x)) - res) < 1e-12 + + # Test vector b + assert abs(b.toarray().sum() - res) < 1e-12 + print("PASSED") + #============================================================================== def test_bilinearForm_complex(backend): diff --git a/psydac/linalg/stencil.py b/psydac/linalg/stencil.py index 0db30d639..73599655a 100644 --- a/psydac/linalg/stencil.py +++ b/psydac/linalg/stencil.py @@ -626,14 +626,13 @@ def __str__(self): # ... def toarray_local(self , *, order='C'): """ return the local array without the padding""" - - idx = tuple( slice(m*p,-m*p) for p,m in zip(self.pads, self.space.shifts) ) + idx = tuple( slice(m*p,-m*p) if p != 0 else slice(0, None) for p,m in zip(self.pads, self.space.shifts) ) return self._data[idx].flatten( order=order) # ... def _toarray_parallel_no_pads(self, order='C'): a = np.zeros( self.space.npts, self.dtype ) - idx_from = tuple( slice(m*p,-m*p) for p,m in zip(self.pads, self.space.shifts) ) + idx_from = tuple( slice(m*p,-m*p) if p != 0 else slice(0, None) for p,m in zip(self.pads, self.space.shifts) ) idx_to = tuple( slice(s,e+1) for s,e in zip(self.starts,self.ends) ) a[idx_to] = self._data[idx_from] return a.flatten( order=order) @@ -664,6 +663,9 @@ def _toarray_parallel_with_pads(self, order='C'): p = pads[direction] + if p == 0: + continue + # Left-most process: copy data from left to right if coord == 0: idx_from = tuple( @@ -689,7 +691,7 @@ def _toarray_parallel_with_pads(self, order='C'): a[idx_to] = a[idx_from] # Step 3: remove ghost regions from global array - idx = tuple( slice(p,-p) for p in pads ) + idx = tuple( slice(p,-p) if p != 0 else slice(0, None) for p in pads ) out = a[idx] # Step 4: return flattened array @@ -776,6 +778,9 @@ def _update_ghost_regions_serial(self): periodic = self._space.periods[direction] p = self._space.pads [direction] * self._space.shifts[direction] + if p == 0: + continue + idx_front = [slice(None)] * direction idx_back = [slice(None)] * (ndim-direction-1) @@ -820,6 +825,10 @@ def exchange_assembly_data(self): p = self._space.pads [direction] m = self._space.shifts[direction] + + if p == 0: + continue + idx_from = tuple(idx_front + [slice(-m*p,None) if (-m*p+p)!=0 else slice(-m*p,None)] + idx_back) self._data[idx_from] = 0. idx_from = tuple(idx_front + [slice(0,m*p)] + idx_back) @@ -835,6 +844,9 @@ def _exchange_assembly_data_serial(self): p = self._space.pads [direction] m = self._space.shifts [direction] + if p == 0: + continue + if periodic: idx_front = [slice(None)] * direction idx_back = [slice(None)] * (ndim-direction-1) @@ -1355,6 +1367,10 @@ def exchange_assembly_data(self): p = self._codomain.pads [direction] m = self._codomain.shifts[direction] + + if p == 0: + continue + idx_from = tuple( idx_front + [ slice(-m*p,None) if (-m*p+p)!=0 else slice(-m*p,None)] + idx_back ) self._data[idx_from] = 0. idx_from = tuple( idx_front + [ slice(0,m*p)] + idx_back ) @@ -1370,6 +1386,9 @@ def _exchange_assembly_data_serial(self): p = self._codomain.pads [direction] m = self._codomain.shifts[direction] + if p == 0: + continue + if periodic: idx_front = [slice(None)]*direction idx_back = [slice(None)]*(ndim-direction-1) @@ -1548,7 +1567,7 @@ def _tocoo_no_pads(self , order='C'): pp = [np.int64(compute_diag_len(p,mj,mi)-(p+1)) for p,mi,mj in zip(self._pads, cm, dm)] # Range of data owned by local process (no ghost regions) - local = tuple( [slice(mi*p,-mi*p) for p,mi in zip(cpads, cm)] + [slice(None)] * nd ) + local = tuple( [slice(mi*p,-mi*p) if p != 0 else slice(p, None) for p,mi in zip(cpads, cm)] + [slice(None)] * nd ) size = self._data[local].size # COO storage @@ -1681,6 +1700,9 @@ def _update_ghost_regions_serial(self): periodic = self._codomain.periods[direction] p = self._codomain.pads [direction] + if p == 0: + continue + idx_front = [slice(None)]*direction idx_back = [slice(None)]*(ndim-direction-1 + ndim) @@ -2598,7 +2620,7 @@ def _tocoo_no_pads(self): cols = [] data = [] # Range of data owned by local process (no ghost regions) - local = tuple( [slice(m*p,-m*p) for m,p in zip(cm, pp)] + [slice(None)] * nd ) + local = tuple( [slice(m*p,-m*p) if p != 0 else slice(0, None) for m,p in zip(cm, pp)] + [slice(None)] * nd ) pp = [compute_diag_len(p,mj,mi)-(p+1) for p,mi,mj in zip(self._pads, cm, dm)] for (index,value) in np.ndenumerate( self._data[local] ): @@ -2658,6 +2680,9 @@ def _update_ghost_regions_serial(self, direction: int): periodic = self._codomain.periods[direction] p = self._codomain.pads [direction] + if p == 0: + return + idx_front = [slice(None)] * direction idx_back = [slice(None)] * (ndim-direction-1) From f38741084f6f0ad5c108b5b74edb1c60a4aa1c6b Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 18 Jun 2025 17:53:14 +0200 Subject: [PATCH 11/23] Fix bug in `allocate_matrices` in `DiscreteBilinearForm` (#507) Always use the maximum padding between test and trial spaces in `allocate_matrices` in `DiscreteBilinearForm`. (Earlier this was not done in the case of scalar spaces.) Fixes #504. --- psydac/api/fem.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/psydac/api/fem.py b/psydac/api/fem.py index 7b4ff7e11..21b3b4f6a 100644 --- a/psydac/api/fem.py +++ b/psydac/api/fem.py @@ -728,7 +728,7 @@ def allocate_matrices(self, backend=None): trd = trial_degree[j] pads[i,j][:] = np.array([td, trd]).max(axis=0) else: - pads = test_degree + pads = np.maximum(test_degree, trial_degree) if self._matrix is None and (is_broken or isinstance(expr, (ImmutableDenseMatrix, Matrix))): self._matrix = BlockLinearOperator(trial_space, test_space) From bccddfc04a1a08b78c689ecef6978fc3625e9d53 Mon Sep 17 00:00:00 2001 From: Max Date: Sat, 28 Jun 2025 09:21:03 +0200 Subject: [PATCH 12/23] Enable Pyccel 2.0 (#503) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Pyccel 2.0 was just released, which means some of the kernels in Psydac need to be updated: - Remove the `template` decorator (see https://github.com/pyccel/pyccel/pull/2331) * Add `T` as `TypeVar` * Specify `T`, `T[:]`, `T[:,:]`, ... in function arguments. - Replace `@types` decorators (see https://github.com/pyccel/pyccel/pull/2329) - Replace `const` with `Final` (see https://github.com/pyccel/pyccel/pull/2340) Further changes: - Update import path for `epyccel` (fixes #426) - Update arguments to `epyccel` (see https://github.com/pyccel/pyccel/pull/2348): * Rename `fflags` to `flags` * Replace `accelerators` list with `openmp` bool - Require Pyccel >= 2.0.1 (fixes #471) --------- Co-authored-by: Yaman Güçlü Co-authored-by: Elena Moral Sánchez Co-authored-by: Emily Bourne --- psydac/api/ast/linalg.py | 24 ++-- psydac/api/basic.py | 25 ++-- psydac/api/glt.py | 18 +-- psydac/api/settings.py | 8 +- psydac/api/tests/test_epyccel_flags.py | 16 ++- psydac/core/field_evaluation_kernels.py | 129 +++++++------------ psydac/linalg/kernels/axpy_kernels.py | 8 +- psydac/linalg/kernels/inner_kernels.py | 8 +- psydac/linalg/kernels/matvec_kernels.py | 6 +- psydac/linalg/kernels/stencil2IJV_kernels.py | 7 +- psydac/linalg/kernels/stencil2coo_kernels.py | 10 +- psydac/linalg/kernels/transpose_kernels.py | 10 +- pyproject.toml | 2 +- 13 files changed, 112 insertions(+), 159 deletions(-) diff --git a/psydac/api/ast/linalg.py b/psydac/api/ast/linalg.py index b44f3d753..0bdde2aba 100644 --- a/psydac/api/ast/linalg.py +++ b/psydac/api/ast/linalg.py @@ -410,21 +410,21 @@ def _compile(self, backend=None): def _compile_pyccel(self, mod, backend, verbose=False): # ... convert python to fortran using pyccel - compiler = backend['compiler'] - fflags = backend['flags'] - _PYCCEL_FOLDER = backend['folder'] - accelerators = ["openmp"] if backend["openmp"] else [] + compiler_family = backend['compiler_family'] + flags = backend['flags'] + _PYCCEL_FOLDER = backend['folder'] + openmp = backend["openmp"] - from pyccel.epyccel import epyccel + from pyccel import epyccel fmod = epyccel(mod, - accelerators = accelerators, - compiler = compiler, - fflags = fflags, - comm = self.comm, - bcast = True, - folder = _PYCCEL_FOLDER, - verbose = verbose) + openmp = openmp, + compiler_family = compiler_family, + flags = flags, + comm = self.comm, + bcast = True, + folder = _PYCCEL_FOLDER, + verbose = verbose) return fmod #============================================================================== diff --git a/psydac/api/basic.py b/psydac/api/basic.py index c63bb370f..2eb77abeb 100644 --- a/psydac/api/basic.py +++ b/psydac/api/basic.py @@ -254,20 +254,21 @@ def _compile_pythran(self, mod): def _compile_pyccel(self, mod, verbose=False): # ... convert python to fortran using pyccel - compiler = self.backend['compiler'] - fflags = self.backend['flags'] - accelerators = ["openmp"] if self.backend["openmp"] else [] - _PYCCEL_FOLDER = self.backend['folder'] + compiler_family = self.backend['compiler_family'] + flags = self.backend['flags'] + openmp = self.backend["openmp"] + _PYCCEL_FOLDER = self.backend['folder'] - from pyccel.epyccel import epyccel + # from pyccel.epyccel import epyccel + from pyccel import epyccel fmod = epyccel(mod, - accelerators = accelerators, - compiler = compiler, - fflags = fflags, - comm = self.comm, - bcast = True, - folder = _PYCCEL_FOLDER, - verbose = verbose) + openmp = openmp, + compiler_family = compiler_family, + flags = flags, + comm = self.comm, + bcast = True, + folder = _PYCCEL_FOLDER, + verbose = verbose) return fmod diff --git a/psydac/api/glt.py b/psydac/api/glt.py index fb58a3585..027b1ff23 100644 --- a/psydac/api/glt.py +++ b/psydac/api/glt.py @@ -334,12 +334,12 @@ def _compile_pyccel(self, namespace, verbose=False): module_name = self.dependencies_modname # ... - from pyccel.epyccel import epyccel + from pyccel import epyccel # ... convert python to fortran using pyccel - compiler = self.backend['compiler'] - fflags = self.backend['flags'] - _PYCCEL_FOLDER = self.backend['folder'] + compiler_family = self.backend['compiler_family'] + flags = self.backend['flags'] + _PYCCEL_FOLDER = self.backend['folder'] # ... # ... @@ -351,11 +351,11 @@ def _compile_pyccel(self, namespace, verbose=False): sys.path.append(self.folder) package = importlib.import_module( module_name ) f2py_module = epyccel( package, - compiler = compiler, - fflags = fflags, - comm = self.comm, - bcast = False, - folder = _PYCCEL_FOLDER ) + compiler_family = compiler_family, + flags = flags, + comm = self.comm, + bcast = False, + folder = _PYCCEL_FOLDER ) sys.path.remove(self.folder) # ... diff --git a/psydac/api/settings.py b/psydac/api/settings.py index 94762b5a9..d96c420c7 100644 --- a/psydac/api/settings.py +++ b/psydac/api/settings.py @@ -15,28 +15,28 @@ PSYDAC_BACKEND_PYTHON = {'name': 'python', 'tag':'python', 'openmp':False} PSYDAC_BACKEND_GPYCCEL = {'name': 'pyccel', - 'compiler': 'GNU', + 'compiler_family': 'GNU', 'flags' : '-O3 -ffast-math', 'folder' : '__gpyccel__', 'tag' : 'gpyccel', 'openmp' : False} PSYDAC_BACKEND_IPYCCEL = {'name': 'pyccel', - 'compiler': 'intel', + 'compiler_family': 'intel', 'flags' : '-O3', 'folder' : '__ipyccel__', 'tag' :'ipyccel', 'openmp' : False} PSYDAC_BACKEND_PGPYCCEL = {'name': 'pyccel', - 'compiler': 'PGI', + 'compiler_family': 'PGI', 'flags' : '-O3 -Munroll', 'folder' : '__pgpyccel__', 'tag' : 'pgpyccel', 'openmp' : False} PSYDAC_BACKEND_NVPYCCEL = {'name': 'pyccel', - 'compiler': 'nvidia', + 'compiler_family': 'nvidia', 'flags' : '-O3 -Munroll', 'folder' : '__nvpyccel__', 'tag' : 'nvpyccel', diff --git a/psydac/api/tests/test_epyccel_flags.py b/psydac/api/tests/test_epyccel_flags.py index cdbcb0906..3a85ddcf0 100644 --- a/psydac/api/tests/test_epyccel_flags.py +++ b/psydac/api/tests/test_epyccel_flags.py @@ -4,13 +4,17 @@ @pytest.mark.pyccel def test_epyccel_flags(): - from pyccel.epyccel import epyccel - from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL as backend + from pyccel import epyccel + from psydac.api.settings import PSYDAC_BACKENDS + # Select the Pyccel backend which uses the GCC compilers + backend = PSYDAC_BACKENDS['pyccel-gcc'] + + # Arguments for `epyccel` kwargs = {'language' : 'fortran', - 'compiler' : backend['compiler'], - 'fflags' : backend['flags'], - 'accelerators' : ['openmp'] if backend['openmp'] else [], + 'compiler_family' : backend['compiler_family'], + 'flags' : backend['flags'], + 'openmp' : backend['openmp'], 'verbose' : True, } @@ -20,7 +24,7 @@ def f(x : float): # Pyccel magic # ------------ - # Fortran code is generated and then compiled with the selected compiler. + # Fortran code is generated and then compiled with the selected compiler family. # The compiled function is callable from Python through the C Python API. # The necessary C wrapper functions are also generated by Pyccel. fast_f = epyccel(f, **kwargs) diff --git a/psydac/core/field_evaluation_kernels.py b/psydac/core/field_evaluation_kernels.py index 689646bc5..e75854d98 100644 --- a/psydac/core/field_evaluation_kernels.py +++ b/psydac/core/field_evaluation_kernels.py @@ -1,18 +1,18 @@ import numpy as np -from pyccel.decorators import template +from typing import TypeVar +T = TypeVar('T', float, complex) # ============================================================================= # Field evaluation functions # ============================================================================= # ----------------------------------------------------------------------------- # 1: Regular tensor grid without weight # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:,:]', 'complex[:,:,:,:]']) def eval_fields_3d_no_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_spans_3: 'int[:]', - glob_arr_coeff: 'T', out_fields: 'T'): + glob_arr_coeff: 'T[:,:,:,:]', out_fields: 'T[:,:,:,:]'): """ Parameters ---------- @@ -95,11 +95,10 @@ def eval_fields_3d_no_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int :] += spline * coeff_fields -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_fields_2d_no_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', - global_spans_1: 'int[:]', global_spans_2: 'int[:]', glob_arr_coeff: 'T', - out_fields: 'T'): + global_spans_1: 'int[:]', global_spans_2: 'int[:]', glob_arr_coeff: 'T[:,:,:]', + out_fields: 'T[:,:,:]'): """ Parameters ---------- @@ -161,12 +160,11 @@ def eval_fields_2d_no_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, :] += spline * coeff_fields -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_fields_1d_no_weights(nc1: int, f_p1: int, k1: int, global_basis_1: 'float[:,:,:,:]', global_spans_1: 'int[:]', - glob_arr_coeff: 'T', - out_fields: 'T'): + glob_arr_coeff: 'T[:,:]', + out_fields: 'T[:,:]'): """ Parameters ---------- @@ -207,12 +205,11 @@ def eval_fields_1d_no_weights(nc1: int, f_p1: int, k1: int, # ----------------------------------------------------------------------------- # 2: Irregular tensor grid without weights # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:,:]', 'complex[:,:,:,:]']) def eval_fields_3d_irregular_no_weights(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_basis_3: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_spans_3: 'int[:]', - glob_arr_coeff: 'T', out_fields: 'T'): + glob_arr_coeff: 'T[:,:,:,:]', out_fields: 'T[:,:,:,:]'): """ Parameters ---------- @@ -292,12 +289,11 @@ def eval_fields_3d_irregular_no_weights(np1: int, np2: int, np3: int, f_p1: int, out_fields[i_p_1, i_p_2, i_p_3, :] += spline * coeff_fields -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_fields_2d_irregular_no_weights(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', - global_spans_1: 'int[:]', global_spans_2: 'int[:]', glob_arr_coeff: 'T', - out_fields: 'T'): + global_spans_1: 'int[:]', global_spans_2: 'int[:]', glob_arr_coeff: 'T[:,:,:]', + out_fields: 'T[:,:,:]'): """ Parameters ---------- @@ -359,13 +355,12 @@ def eval_fields_2d_irregular_no_weights(np1: int, np2: int, f_p1: int, f_p2: int out_fields[i_p_1, i_p_2, :] += spline * coeff_fields -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_fields_1d_irregular_no_weights(np1: int, f_p1: int, cell_index_1: 'int[:]', global_basis_1: 'float[:,:,:]', global_spans_1: 'int[:]', - glob_arr_coeff: 'T', - out_fields: 'T'): + glob_arr_coeff: 'T[:,:]', + out_fields: 'T[:,:]'): """ Parameters ---------- @@ -409,13 +404,12 @@ def eval_fields_1d_irregular_no_weights(np1: int, f_p1: int, # ----------------------------------------------------------------------------- # 3: Regular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:,:]', 'complex[:,:,:,:]']) def eval_fields_3d_weighted(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_spans_3: 'int[:]', - glob_arr_coeff: 'T', global_arr_weights: 'float[:,:,:]', - out_fields: 'T'): + glob_arr_coeff: 'T[:,:,:,:]', global_arr_weights: 'float[:,:,:]', + out_fields: 'T[:,:,:,:]'): """ Parameters ---------- @@ -521,11 +515,10 @@ def eval_fields_3d_weighted(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, :] += fields / weight -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_fields_2d_weighted(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', - global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff: 'T', - global_arr_weights: 'float[:,:]', out_fields: 'T'): + global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff: 'T[:,:,:]', + global_arr_weights: 'float[:,:]', out_fields: 'T[:,:,:]'): """ Parameters ---------- @@ -610,11 +603,10 @@ def eval_fields_2d_weighted(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k :] += fields / weight -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_fields_1d_weighted(nc1: int, f_p1: int, k1: int, global_basis_1: 'float[:,:,:,:]', - global_spans_1: 'int[:]', global_arr_coeff: 'T', - global_arr_weights: 'float[:]', out_fields: 'T'): + global_spans_1: 'int[:]', global_arr_coeff: 'T[:,:]', + global_arr_weights: 'float[:]', out_fields: 'T[:,:]'): """ Parameters ---------- @@ -680,13 +672,12 @@ def eval_fields_1d_weighted(nc1: int, f_p1: int, k1: int, # ----------------------------------------------------------------------------- # 4: Iregular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:,:]', 'complex[:,:,:,:]']) def eval_fields_3d_irregular_weighted(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_basis_3: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_spans_3: 'int[:]', - glob_arr_coeff: 'T', global_arr_weights: 'float[:,:,:]', - out_fields: 'T'): + glob_arr_coeff: 'T[:,:,:,:]', global_arr_weights: 'float[:,:,:]', + out_fields: 'T[:,:,:,:]'): """ Parameters ---------- @@ -785,12 +776,11 @@ def eval_fields_3d_irregular_weighted(np1: int, np2: int, np3: int, f_p1: int, f out_fields[i_p_1, i_p_2, i_p_3, :] += temp_fields / temp_weight -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_fields_2d_irregular_weighted(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', - global_arr_coeff: 'T', global_arr_weights: 'float[:,:]', - out_fields: 'T'): + global_arr_coeff: 'T[:,:,:]', global_arr_weights: 'float[:,:]', + out_fields: 'T[:,:,:]'): """ Parameters ---------- @@ -871,12 +861,11 @@ def eval_fields_2d_irregular_weighted(np1: int, np2: int, f_p1: int, f_p2: int, out_fields[i_p_1, i_p_2, :] += temp_fields / temp_weight -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_fields_1d_irregular_weighted(np1: int, f_p1: int, cell_index_1: 'int[:]', global_basis_1: 'float[:,:,:]', global_spans_1: 'int[:]', - global_arr_coeff: 'T', global_arr_weights: 'float[:]', - out_fields: 'T'): + global_arr_coeff: 'T[:,:]', global_arr_weights: 'float[:]', + out_fields: 'T[:,:]'): """ Parameters ---------- @@ -935,12 +924,11 @@ def eval_fields_1d_irregular_weighted(np1: int, f_p1: int, # ----------------------------------------------------------------------------- # 1: Regular tensor grid without weights # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_jac_det_3d(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', - global_spans_3: 'int[:]', global_arr_coeff_x: 'T', global_arr_coeff_y: 'T', - global_arr_coeff_z: 'T', jac_det: 'T'): + global_spans_3: 'int[:]', global_arr_coeff_x: 'T[:,:,:]', global_arr_coeff_y: 'T[:,:,:]', + global_arr_coeff_z: 'T[:,:,:]', jac_det: 'T[:,:,:]'): """ Parameters @@ -1096,11 +1084,10 @@ def eval_jac_det_3d(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: in - x_x3 * y_x2 * z_x1) -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_jac_det_2d(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', - global_arr_coeff_x: 'T', global_arr_coeff_y: 'T', - jac_det: 'T'): + global_arr_coeff_x: 'T[:,:]', global_arr_coeff_y: 'T[:,:]', + jac_det: 'T[:,:]'): """ Parameters ---------- @@ -1200,14 +1187,13 @@ def eval_jac_det_2d(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, # ----------------------------------------------------------------------------- # 2: Irregular tensor grid without weights # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_jac_det_irregular_3d(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_basis_3: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', - global_spans_3: 'int[:]', global_arr_coeff_x: 'T', - global_arr_coeff_y: 'T', global_arr_coeff_z: 'T', - jac_det: 'T'): + global_spans_3: 'int[:]', global_arr_coeff_x: 'T[:,:,:]', + global_arr_coeff_y: 'T[:,:,:]', global_arr_coeff_z: 'T[:,:,:]', + jac_det: 'T[:,:,:]'): """ Parameters ---------- @@ -1350,11 +1336,10 @@ def eval_jac_det_irregular_3d(np1: int, np2: int, np3: int, f_p1: int, f_p2: int - temp_x_x3 * temp_y_x2 * temp_z_x1) -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_jac_det_irregular_2d(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', - global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T', - global_arr_coeff_y: 'T', jac_det: 'T'): + global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', + global_arr_coeff_y: 'T[:,:]', jac_det: 'T[:,:]'): """ Parameters ---------- @@ -1445,14 +1430,13 @@ def eval_jac_det_irregular_2d(np1: int, np2: int, f_p1: int, f_p2: int, cell_ind # 3: Regular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_jac_det_3d_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_spans_3: 'int[:]', - global_arr_coeff_x: 'T', global_arr_coeff_y: 'T', - global_arr_coeff_z: 'T', global_arr_coeff_weights: 'float[:,:,:]', - jac_det: 'T'): + global_arr_coeff_x: 'T[:,:,:]', global_arr_coeff_y: 'T[:,:,:]', + global_arr_coeff_z: 'T[:,:,:]', global_arr_coeff_weights: 'float[:,:,:]', + jac_det: 'T[:,:,:]'): """ Parameters @@ -1674,12 +1658,11 @@ def eval_jac_det_3d_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, - x_x3 * y_x2 * z_x1) -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_jac_det_2d_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', - global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T', - global_arr_coeff_y: 'T', global_arr_coeff_weights: 'float[:,:]', - jac_det: 'T'): + global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', + global_arr_coeff_y: 'T[:,:]', global_arr_coeff_weights: 'float[:,:]', + jac_det: 'T[:,:]'): """ Parameters ---------- @@ -1830,14 +1813,13 @@ def eval_jac_det_2d_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k # ----------------------------------------------------------------------------- # 4: Irregular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=['float[:,:,:]', 'complex[:,:,:]']) def eval_jac_det_irregular_3d_weights(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_basis_3: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', - global_spans_3: 'int[:]', global_arr_coeff_x: 'T', - global_arr_coeff_y: 'T', global_arr_coeff_z: 'T', - global_arr_coeff_weights: 'float[:,:, :]', jac_det: 'T'): + global_spans_3: 'int[:]', global_arr_coeff_x: 'T[:,:,:]', + global_arr_coeff_y: 'T[:,:,:]', global_arr_coeff_z: 'T[:,:,:]', + global_arr_coeff_weights: 'float[:,:, :]', jac_det: 'T[:,:,:]'): """ Parameters ---------- @@ -2030,14 +2012,13 @@ def eval_jac_det_irregular_3d_weights(np1: int, np2: int, np3: int, f_p1: int, f - x_x3 * y_x2 * z_x1) -@template(name='T', types=['float[:,:]', 'complex[:,:]']) def eval_jac_det_irregular_2d_weights(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', - global_arr_coeff_x: 'T', global_arr_coeff_y: 'T', + global_arr_coeff_x: 'T[:,:]', global_arr_coeff_y: 'T[:,:]', global_arr_coeff_weights: 'float[:,:]', - jac_det: 'T'): + jac_det: 'T[:,:]'): """ Parameters ---------- @@ -2170,7 +2151,6 @@ def eval_jac_det_irregular_2d_weights(np1: int, np2: int, f_p1: int, f_p2: int, # ----------------------------------------------------------------------------- # 1: Regular tensor grid without weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_3d(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', @@ -2328,7 +2308,6 @@ def eval_jacobians_3d(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: [z_x1, z_x2, z_x3]]) -@template(name='T', types=[float, complex]) def eval_jacobians_2d(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', global_arr_coeff_y: 'T[:,:]', @@ -2434,7 +2413,6 @@ def eval_jacobians_2d(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int # ----------------------------------------------------------------------------- # 2: Irregular tensor grid without weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_irregular_3d(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', @@ -2580,7 +2558,6 @@ def eval_jacobians_irregular_3d(np1: int, np2: int, np3: int, f_p1: int, f_p2: i [temp_z_x1, temp_z_x2, temp_z_x3]]) -@template(name='T', types=[float, complex]) def eval_jacobians_irregular_2d(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', @@ -2677,7 +2654,6 @@ def eval_jacobians_irregular_2d(np1: int, np2: int, f_p1: int, f_p2: int, cell_i # ----------------------------------------------------------------------------- # 3: Regular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_3d_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', @@ -2904,7 +2880,6 @@ def eval_jacobians_3d_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: in [z_x1, z_x2, z_x3]]) -@template(name='T', types=[float, complex]) def eval_jacobians_2d_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', @@ -3061,7 +3036,6 @@ def eval_jacobians_2d_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int # ----------------------------------------------------------------------------- # 4: Irregular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_irregular_3d_weights(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', @@ -3258,7 +3232,6 @@ def eval_jacobians_irregular_3d_weights(np1: int, np2: int, np3: int, f_p1: int, [z_x1, z_x2, z_x3]]) -@template(name='T', types=[float, complex]) def eval_jacobians_irregular_2d_weights(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', @@ -3400,7 +3373,6 @@ def eval_jacobians_irregular_2d_weights(np1: int, np2: int, f_p1: int, f_p2: int # ----------------------------------------------------------------------------- # 1: Regular tensor grid without weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_inv_3d(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', global_spans_1: 'int[:]', @@ -3575,7 +3547,6 @@ def eval_jacobians_inv_3d(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, [a_13, a_23, a_33]]) / det -@template(name='T', types=[float, complex]) def eval_jacobians_inv_2d(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', global_arr_coeff_y: 'T[:,:]', @@ -3683,7 +3654,6 @@ def eval_jacobians_inv_2d(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2 # ----------------------------------------------------------------------------- # 2: Irregular tensor grid without weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_inv_irregular_3d(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', @@ -3851,7 +3821,6 @@ def eval_jacobians_inv_irregular_3d(np1: int, np2: int, np3: int, f_p1: int, f_p [a_13, a_23, a_33]]) / det -@template(name='T', types=[float, complex]) def eval_jacobians_inv_irregular_2d(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', @@ -3951,7 +3920,6 @@ def eval_jacobians_inv_irregular_2d(np1: int, np2: int, f_p1: int, f_p2: int, ce # ----------------------------------------------------------------------------- # 3: Regular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_inv_3d_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2: int, f_p3: int, k1: int, k2: int, k3: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_basis_3: 'float[:,:,:,:]', @@ -4193,7 +4161,6 @@ def eval_jacobians_inv_3d_weights(nc1: int, nc2: int, nc3: int, f_p1: int, f_p2 [a_13, a_23, a_33]]) / det -@template(name='T', types=[float, complex]) def eval_jacobians_inv_2d_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: int, k2: int, global_basis_1: 'float[:,:,:,:]', global_basis_2: 'float[:,:,:,:]', global_spans_1: 'int[:]', global_spans_2: 'int[:]', global_arr_coeff_x: 'T[:,:]', @@ -4352,7 +4319,6 @@ def eval_jacobians_inv_2d_weights(nc1: int, nc2: int, f_p1: int, f_p2: int, k1: # ----------------------------------------------------------------------------- # 4: Irregular tensor grid with weights # ----------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def eval_jacobians_inv_irregular_3d_weights(np1: int, np2: int, np3: int, f_p1: int, f_p2: int, f_p3: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', cell_index_3 : 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', @@ -4567,7 +4533,6 @@ def eval_jacobians_inv_irregular_3d_weights(np1: int, np2: int, np3: int, f_p1: [a_13, a_23, a_33]]) / det -@template(name='T', types=[float, complex]) def eval_jacobians_inv_irregular_2d_weights(np1: int, np2: int, f_p1: int, f_p2: int, cell_index_1: 'int[:]', cell_index_2: 'int[:]', global_basis_1: 'float[:,:,:]', global_basis_2: 'float[:,:,:]', @@ -4710,7 +4675,6 @@ def eval_jacobians_inv_irregular_2d_weights(np1: int, np2: int, f_p1: int, f_p2: # -------------------------------------------------------------------------- # 1: L2 Push-forward # -------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def pushforward_2d_l2(fields_to_push: 'T[:,:,:]', sqrt_met_dets: 'float[:,:]', pushed_fields: 'T[:,:,:]'): """ @@ -4733,7 +4697,6 @@ def pushforward_2d_l2(fields_to_push: 'T[:,:,:]', sqrt_met_dets: 'float[:,:]', pushed_fields[:, :, i_f] = fields_to_push[:, :, i_f] / sqrt_met_dets[:, :] -@template(name='T', types=[float, complex]) def pushforward_3d_l2(fields_to_push: 'T[:,:,:,:]', sqrt_met_dets: 'float[:,:,:]', pushed_fields: 'T[:,:,:,:]'): """ Parameters @@ -4759,7 +4722,6 @@ def pushforward_3d_l2(fields_to_push: 'T[:,:,:,:]', sqrt_met_dets: 'float[:,:,:] # -------------------------------------------------------------------------- # 2: Hcurl Push-forward # -------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def pushforward_2d_hcurl(fields_to_push: 'T[:,:,:,:]', inv_jac_mats: 'float[:,:,:,:]', pushed_fields: 'T[:,:,:,:]'): """ @@ -4787,7 +4749,6 @@ def pushforward_2d_hcurl(fields_to_push: 'T[:,:,:,:]', inv_jac_mats: 'float[:,:, + inv_jac_mats[:, :, 1, 1] * fields_to_push[1, :, :, i_f]) -@template(name='T', types=[float, complex]) def pushforward_3d_hcurl(fields_to_push: 'T[:,:,:,:,:]', inv_jac_mats: 'float[:,:,:,:,:]', pushed_fields: 'T[:,:,:,:,:]'): """ @@ -4829,7 +4790,6 @@ def pushforward_3d_hcurl(fields_to_push: 'T[:,:,:,:,:]', inv_jac_mats: 'float[:, # -------------------------------------------------------------------------- # 1: Hdiv Push-forward # -------------------------------------------------------------------------- -@template(name='T', types=[float, complex]) def pushforward_2d_hdiv(fields_to_push: 'T[:,:,:,:]', jac_mats: 'float[:,:,:,:]', sqrt_met_dets: 'float[:,:]', pushed_fields: 'T[:,:,:,:]'): """ @@ -4861,7 +4821,6 @@ def pushforward_2d_hdiv(fields_to_push: 'T[:,:,:,:]', jac_mats: 'float[:,:,:,:]' + jac_mats[:, :, 1, 1] * fields_to_push[1, :, :, i_f]) / sqrt_met_dets[:, :] -@template(name='T', types=[float, complex]) def pushforward_3d_hdiv(fields_to_push: 'T[:,:,:,:,:]', jac_mats: 'float[:,:,:,:,:]', sqrt_met_dets: 'float[:,:,:]', pushed_fields: 'T[:,:,:,:,:]'): """ diff --git a/psydac/linalg/kernels/axpy_kernels.py b/psydac/linalg/kernels/axpy_kernels.py index 7cf7c81d4..5c3ca65ad 100644 --- a/psydac/linalg/kernels/axpy_kernels.py +++ b/psydac/linalg/kernels/axpy_kernels.py @@ -1,7 +1,9 @@ -from pyccel.decorators import template +from typing import TypeVar + +T = TypeVar('T', float, complex) + #======================================================================================================== -@template(name='T', types=[float, complex]) def axpy_1d(alpha: 'T', x: 'T[:]', y: 'T[:]'): """ Kernel for computing y = alpha * x + y. @@ -19,7 +21,6 @@ def axpy_1d(alpha: 'T', x: 'T[:]', y: 'T[:]'): y[i1] += alpha * x[i1] #======================================================================================================== -@template(name='T', types=[float, complex]) def axpy_2d(alpha: 'T', x: 'T[:,:]', y: 'T[:,:]'): """ Kernel for computing y = alpha * x + y. @@ -38,7 +39,6 @@ def axpy_2d(alpha: 'T', x: 'T[:,:]', y: 'T[:,:]'): y[i1, i2] += alpha * x[i1, i2] #======================================================================================================== -@template(name='T', types=[float, complex]) def axpy_3d(alpha: 'T', x: 'T[:,:,:]', y: 'T[:,:,:]'): """ Kernel for computing y = alpha * x + y. diff --git a/psydac/linalg/kernels/inner_kernels.py b/psydac/linalg/kernels/inner_kernels.py index 6da0dc238..a90316027 100644 --- a/psydac/linalg/kernels/inner_kernels.py +++ b/psydac/linalg/kernels/inner_kernels.py @@ -1,4 +1,3 @@ -from pyccel.decorators import template #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!# #!!!!!!!!!!!!!!!!!!! WARNING !!!!!!!!!!!!!!!!!!!# @@ -6,8 +5,11 @@ #!!!!!!!!!! This will need an update !!!!!!!!!!!# #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!# +from typing import TypeVar + +T = TypeVar('T', float, complex) + #============================================================================== -@template(name='T', types=[float, complex]) def inner_1d(v1: 'T[:]', v2: 'T[:]', nghost0: 'int64'): """ Kernel for computing the inner product (case of two 1D vectors). @@ -34,7 +36,6 @@ def inner_1d(v1: 'T[:]', v2: 'T[:]', nghost0: 'int64'): return res #============================================================================== -@template(name='T', types=[float, complex]) def inner_2d(v1: 'T[:,:]', v2: 'T[:,:]', nghost0: 'int64', nghost1: 'int64'): """ Kernel for computing the inner product (case of two 2D vectors). @@ -65,7 +66,6 @@ def inner_2d(v1: 'T[:,:]', v2: 'T[:,:]', nghost0: 'int64', nghost1: 'int64'): return res #============================================================================== -@template(name='T', types=[float, complex]) def inner_3d(v1: 'T[:,:,:]', v2: 'T[:,:,:]', nghost0: 'int64', nghost1: 'int64', nghost2: 'int64'): """ Kernel for computing the inner product (case of two 3D vectors). diff --git a/psydac/linalg/kernels/matvec_kernels.py b/psydac/linalg/kernels/matvec_kernels.py index 40b474275..d85c0dcc2 100644 --- a/psydac/linalg/kernels/matvec_kernels.py +++ b/psydac/linalg/kernels/matvec_kernels.py @@ -1,7 +1,7 @@ -from pyccel.decorators import template +from typing import TypeVar +T = TypeVar('T', float, complex) -@template(name='T', types=[float, complex]) def matvec_1d(mat00:'T[:,:]', x0:'T[:]', out0:'T[:]', starts: 'int64[:]', nrows: 'int64[:]', nrows_extra: 'int64[:]', dm:'int64[:]', cm:'int64[:]', pad_imp:'int64[:]', ndiags:'int64[:]', gpads: 'int64[:]'): @@ -38,7 +38,6 @@ def matvec_1d(mat00:'T[:,:]', x0:'T[:]', out0:'T[:]', starts: 'int64[:]', nrows: -@template(name='T', types=[float, complex]) def matvec_2d(mat00:'T[:,:,:,:]', x0:'T[:,:]', out0:'T[:,:]', starts:'int64[:]', nrows:'int64[:]', nrows_extra:'int64[:]', dm:'int64[:]', cm:'int64[:]', pad_imp:'int64[:]', ndiags:'int64[:]', gpads: 'int64[:]'): @@ -104,7 +103,6 @@ def matvec_2d(mat00:'T[:,:,:,:]', x0:'T[:,:]', out0:'T[:,:]', starts:'int64[:]', out0[pxm1 + i1, pxm2 + i2] = v00 -@template(name='T', types=[float, complex]) def matvec_3d(mat00:'T[:,:,:,:,:,:]', x0:'T[:,:,:]', out0:'T[:,:,:]', starts:'int64[:]', nrows:'int64[:]', nrows_extra:'int64[:]', dm:'int64[:]', cm:'int64[:]', pad_imp:'int64[:]', ndiags:'int64[:]', gpads: 'int64[:]'): diff --git a/psydac/linalg/kernels/stencil2IJV_kernels.py b/psydac/linalg/kernels/stencil2IJV_kernels.py index 21eae3cb4..133ab45f7 100644 --- a/psydac/linalg/kernels/stencil2IJV_kernels.py +++ b/psydac/linalg/kernels/stencil2IJV_kernels.py @@ -1,9 +1,10 @@ # coding: utf-8 -from pyccel.decorators import template +from typing import TypeVar + +T = TypeVar('T', float, complex) #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2IJV_1d_C(A:'T[:,:]', Ib:'int64[:]', Jb:'int64[:]', Vb:'T[:]', rowmapb:'int64[:]', cnl1:'int64', dng1:'int64', cs1:'int64', cp1:'int64', cm1:'int64', dsh:'int64[:]', csh:'int64[:]', dgs1:'int64[:]', dge1:'int64[:]', @@ -57,7 +58,6 @@ def stencil2IJV_1d_C(A:'T[:,:]', Ib:'int64[:]', Jb:'int64[:]', Vb:'T[:]', rowmap return nnz_rows, nnz #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2IJV_2d_C(A:'T[:,:,:,:]', Ib:'int64[:]', Jb:'int64[:]', Vb:'T[:]', rowmapb:'int64[:]', cnl1:'int64', cnl2:'int64', dng1:'int64', dng2:'int64', cs1:'int64', cs2:'int64', cp1:'int64', cp2:'int64', cm1:'int64', cm2:'int64', @@ -132,7 +132,6 @@ def stencil2IJV_2d_C(A:'T[:,:,:,:]', Ib:'int64[:]', Jb:'int64[:]', Vb:'T[:]', ro return nnz_rows, nnz #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2IJV_3d_C(A:'T[:,:,:,:,:,:]', Ib:'int64[:]', Jb:'int64[:]', Vb:'T[:]', rowmapb:'int64[:]', cnl1:'int64', cnl2:'int64', cnl3:'int64', dng1:'int64', dng2:'int64', dng3:'int64', cs1:'int64', cs2:'int64', cs3:'int64', cp1:'int64', cp2:'int64', cp3:'int64', diff --git a/psydac/linalg/kernels/stencil2coo_kernels.py b/psydac/linalg/kernels/stencil2coo_kernels.py index 81c278df6..2985b5ad7 100644 --- a/psydac/linalg/kernels/stencil2coo_kernels.py +++ b/psydac/linalg/kernels/stencil2coo_kernels.py @@ -1,15 +1,16 @@ # coding: utf-8 -from pyccel.decorators import template #!!!!!!!!!!!!! #TODO avoid using The expensive modulo operator % in the non periodic case to make the methods faster #!!!!!!!!!!!!! +from typing import TypeVar + +T = TypeVar('T', float, complex) #__all__ = ['stencil2coo_1d_C','stencil2coo_1d_F','stencil2coo_2d_C','stencil2coo_2d_F', 'stencil2coo_3d_C', 'stencil2coo_3d_F'] #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2coo_1d_C(A:'T[:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', nrl1:'int64', ncl1:'int64', s1:'int64', nr1:'int64', nc1:'int64', dm1:'int64', cm1:'int64', p1:'int64', dp1:'int64'): nnz = 0 @@ -28,7 +29,6 @@ def stencil2coo_1d_C(A:'T[:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', return nnz #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2coo_1d_F(A:'T[:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', nrl1:'int64', ncl1:'int64', s1:'int64', nr1:'int64', nc1:'int64', dm1:'int64', cm1:'int64', p1:'int64', dp1:'int64'): nnz = 0 @@ -47,7 +47,6 @@ def stencil2coo_1d_F(A:'T[:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', return nnz #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2coo_2d_C(A:'T[:,:,:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', nrl1:'int64', nrl2:'int64', ncl1:'int64', ncl2:'int64', s1:'int64', s2:'int64', nr1:'int64', nr2:'int64', @@ -78,7 +77,6 @@ def stencil2coo_2d_C(A:'T[:,:,:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[: return nnz #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2coo_2d_F(A:'T[:,:,:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', nrl1:'int64', nrl2:'int64', ncl1:'int64', ncl2:'int64', s1:'int64', s2:'int64', nr1:'int64', nr2:'int64', @@ -109,7 +107,6 @@ def stencil2coo_2d_F(A:'T[:,:,:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[: return nnz #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2coo_3d_C(A:'T[:,:,:,:,:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', nrl1:'int64', nrl2:'int64', nrl3:'int64', ncl1:'int64', ncl2:'int64', ncl3:'int64', s1:'int64', s2:'int64', s3:'int64', nr1:'int64', nr2:'int64', nr3:'int64', @@ -147,7 +144,6 @@ def stencil2coo_3d_C(A:'T[:,:,:,:,:,:]', data:'T[:]', rows:'int64[:]', cols:'int #======================================================================================================== -@template(name='T', types=[float, complex]) def stencil2coo_3d_F(A:'T[:,:,:,:,:,:]', data:'T[:]', rows:'int64[:]', cols:'int64[:]', nrl1:'int64', nrl2:'int64', nrl3:'int64', ncl1:'int64', ncl2:'int64', ncl3:'int64', s1:'int64', s2:'int64', s3:'int64', nr1:'int64', nr2:'int64', nr3:'int64', diff --git a/psydac/linalg/kernels/transpose_kernels.py b/psydac/linalg/kernels/transpose_kernels.py index ef61fed0f..19513f296 100644 --- a/psydac/linalg/kernels/transpose_kernels.py +++ b/psydac/linalg/kernels/transpose_kernels.py @@ -1,7 +1,8 @@ -from pyccel.decorators import template +from typing import TypeVar + +T = TypeVar('T', float, complex) #======================================================================================================== -@template(name='T', types=[float, complex]) def transpose_1d(M : "T[:,:]", Mt : "T[:,:]", n : "int64[:]", @@ -35,7 +36,6 @@ def transpose_1d(M : "T[:,:]", return #======================================================================================================== -@template(name='T', types=[float, complex]) def transpose_2d(M : "T[:,:,:,:]", Mt : "T[:,:,:,:]", n : "int64[:]", @@ -79,7 +79,6 @@ def transpose_2d(M : "T[:,:,:,:]", return #======================================================================================================== -@template(name='T', types=[float, complex]) def transpose_3d(M : "T[:,:,:,:,:,:]", Mt : "T[:,:,:,:,:,:]", n : "int64[:]", @@ -131,7 +130,6 @@ def transpose_3d(M : "T[:,:,:,:,:,:]", return #======================================================================================================== -@template(name='T', types=[float, complex]) def interface_transpose_1d(M : "T[:,:]", Mt : "T[:,:]", n : "int64[:]", @@ -168,7 +166,6 @@ def interface_transpose_1d(M : "T[:,:]", return #======================================================================================================== -@template(name='T', types=[float, complex]) def interface_transpose_2d(M : "T[:,:,:,:]", Mt : "T[:,:,:,:]", n : "int64[:]", @@ -214,7 +211,6 @@ def interface_transpose_2d(M : "T[:,:,:,:]", return #======================================================================================================== -@template(name='T', types=[float, complex]) def interface_transpose_3d(M : "T[:,:,:,:,:,:]", Mt : "T[:,:,:,:,:,:]", n : "int64[:]", diff --git a/pyproject.toml b/pyproject.toml index 2d42320d2..21bd7fb70 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -31,7 +31,7 @@ dependencies = [ # Our packages from PyPi 'sympde == 0.19.2', - 'pyccel >= 1.11.2', + 'pyccel >= 2.0.1', 'gelato == 0.12', # In addition, we depend on mpi4py and h5py (MPI version). From 42b214e2bd39f33d9fe5ba21ce5483806f402d7b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Mon, 14 Jul 2025 15:43:07 +0200 Subject: [PATCH 13/23] New installation procedure and README (#510) Recently the installation of `h5py` in parallel mode (i.e. with MPI support through `mpi4py`) seems to have been simplified. This may be due to the recent move of `mpi4py` to wheels, or other factors. Therefore we can now simplify our installation procedure as follows: ```sh pip install h5py --no-cache-dir --no-binary h5py pip install .[test] ``` We update here the CI workflows and completely rewrite our README file. **Commit summary** - Completely rewrite `README.md`: * Expand initial description * Add Citing and Contributing sections * Shorten Installation section * Reorganize documentation sections * Move detailed installation instructions to separate file `docs/installation.md` * Move mesh generation to separate file `docs/psydac-mesh.md` - Add BibTeX file `CITING.bib` with citation of 2022 ECCOMAS proceedings - Remove obsolete files `requirements.txt` and `requirements_extra.txt` - Rename (and move) `docs_requirements.txt` as `docs/requirements.txt` - Update installation procedure in `testing` CI workflow - Change name in `testing` workflow from "Run tests" to "Unit tests" - Modify `testing` and `documentation` workflows so that they only run when needed - Allow running workflows manually - Fix broken CI badge in `README.md` --- .github/workflows/documentation.yml | 15 +- .github/workflows/testing.yml | 27 ++- .gitignore | 3 + CITATION.bib | 10 + README.md | 223 +++++------------- docs/installation.md | 202 ++++++++++++++++ output.md => docs/output.md | 0 docs/psydac-mesh.md | 9 + .../requirements.txt | 0 pyproject.toml | 17 +- requirements.txt | 9 - requirements_extra.txt | 9 - 12 files changed, 334 insertions(+), 190 deletions(-) create mode 100644 CITATION.bib create mode 100644 docs/installation.md rename output.md => docs/output.md (100%) create mode 100644 docs/psydac-mesh.md rename docs_requirements.txt => docs/requirements.txt (100%) delete mode 100644 requirements.txt delete mode 100644 requirements_extra.txt diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml index be24f89c9..41896bbb9 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/documentation.yml @@ -1,10 +1,19 @@ -name: documentation +name: Documentation on: push: branches: [ devel ] + paths: + - 'docs/**' + - 'psydac/**.py' + pull_request: branches: [ devel ] + paths: + - 'docs/**' + - 'psydac/**.py' + + workflow_dispatch: permissions: contents: read @@ -29,7 +38,7 @@ jobs: sudo apt install graphviz - name: Install Python dependencies run: | - python -m pip install -r docs_requirements.txt + python -m pip install -r docs/requirements.txt - name: Make the sphinx doc run: | rm -rf docs/source/modules/STUBDIR @@ -44,7 +53,7 @@ jobs: path: 'docs/build/html' deploy_docs: - if: github.event_name != 'pull_request' + if: github.event_name == 'push' && github.ref == 'refs/heads/devel' needs: build_docs runs-on: ubuntu-latest environment: diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml index 802657cd0..d8ff30b1c 100644 --- a/.github/workflows/testing.yml +++ b/.github/workflows/testing.yml @@ -1,13 +1,33 @@ # This workflow will install Python dependencies and run tests with a variety of Python versions # For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions -name: Run tests +name: Unit tests on: push: branches: [ devel ] + paths: + - 'psydac/**' + - 'pyproject.toml' + - 'setup.py' + - 'pytest.ini' + - 'mpi_tester.py' + pull_request: branches: [ devel ] + types: + - opened + - synchronize + - reopened + - ready_for_review + paths: + - 'psydac/**' + - 'pyproject.toml' + - 'setup.py' + - 'pytest.ini' + - 'mpi_tester.py' + + workflow_dispatch: jobs: test: @@ -142,12 +162,11 @@ jobs: python -m pip install wheel Cython numpy python -m pip install src/binding/petsc4py - - name: Install Python dependencies + - name: Install h5py in parallel mode run: | export CC="mpicc" export HDF5_MPI="ON" - python -m pip install -r requirements.txt - python -m pip install -r requirements_extra.txt --no-build-isolation --no-cache-dir + python -m pip install h5py --no-cache-dir --no-binary h5py python -m pip list - name: Check parallel h5py installation diff --git a/.gitignore b/.gitignore index 71dfeaf04..b3cf64508 100644 --- a/.gitignore +++ b/.gitignore @@ -30,3 +30,6 @@ __test__/ # pycharm directory .idea + +# Visual Studio Code workspace files +*.code-workspace \ No newline at end of file diff --git a/CITATION.bib b/CITATION.bib new file mode 100644 index 000000000..24b0ca77b --- /dev/null +++ b/CITATION.bib @@ -0,0 +1,10 @@ +@inproceedings{Guclu2022, + title = {{{PSYDAC}}: A High-Performance {{IGA}} Library in {{Python}}}, + booktitle = {8th {{European Congress}} on {{Computational Methods}} in {{Applied Sciences}} and {{Engineering}}}, + author = {Güçlü, Y. and Hadjout, S. and Ratnani, A.}, + year = {2022}, + publisher = {CIMNE}, + doi = {10.23967/eccomas.2022.227}, + url = {https://www.scipedia.com/public/Guclu_et_al_2022a}, + eventtitle = {8th {{European Congress}} on {{Computational Methods}} in {{Applied Sciences}} and {{Engineering}}}, +} diff --git a/README.md b/README.md index 65c51f99f..d218c17cb 100644 --- a/README.md +++ b/README.md @@ -1,24 +1,28 @@ # Welcome to PSYDAC -[![devel_tests](https://github.com/pyccel/psydac/actions/workflows/continuous-integration.yml/badge.svg)](https://github.com/pyccel/psydac/actions/workflows/continuous-integration.yml) [![docs](https://github.com/pyccel/psydac/actions/workflows/documentation.yml/badge.svg)](https://github.com/pyccel/psydac/actions/workflows/documentation.yml) +[![devel_tests](https://github.com/pyccel/psydac/actions/workflows/testing.yml/badge.svg)](https://github.com/pyccel/psydac/actions/workflows/testing.yml) [![docs](https://github.com/pyccel/psydac/actions/workflows/documentation.yml/badge.svg)](https://github.com/pyccel/psydac/actions/workflows/documentation.yml) -**PSYDAC** is a Python 3 Library for isogeometric analysis. +PSYDAC is a Python 3 library for isogeometric analysis. +It is an academic, open-source project created by numerical mathematicians at the [Max Planck Institute for Plasma Physics](https://www.ipp.mpg.de/en) ([NMPP](https://www.ipp.mpg.de/ippcms/eng/for/bereiche/numerik) division, [FEM](https://www.ipp.mpg.de/5150531/fem) group). -## Table of contents +PSYDAC can solve general systems of partial differential equations in weak form, which users define using the domain-specific language provided by [SymPDE](https://github.com/pyccel/sympde). +It supports finite element exterior calculus ([FEEC](https://en.wikipedia.org/wiki/Finite_element_exterior_calculus)) with tensor-product spline spaces and handles multi-patch geometries in various ways. -- [Requirements](#requirements) -- [Python setup and project download](#python-setup-and-project-download) -- [Installing the library](#installing-the-library) -- [Optional PETSc installation](#optional-petsc-installation) -- [Uninstall](#uninstall) -- [Running tests](#running-tests) -- [Speeding up Psydac's core](#speeding-up-psydacs-core) -- [User Documentation](#user-documentation) -- [Code Documentation](#code-documentation) +PSYDAC automatically generates Python code for the assembly of user-defined functionals and linear and bilinear forms from the weak formulation of the problem. +This Python code is then accelerated to C/Fortran speed using [Pyccel](https://github.com/pyccel/pyccel). +The library also enables large parallel computations on distributed-memory supercomputers using [MPI](https://en.wikipedia.org/wiki/Message_Passing_Interface) and [OpenMP](https://en.wikipedia.org/wiki/OpenMP). -## Requirements +## Citing -Psydac requires a certain number of components to be installed on the machine: +If PSYDAC has been significant in your research, and you would like to acknowledge the project in your academic publication, we would ask that you cite the following paper: + +Güçlü, Y., S. Hadjout, and A. Ratnani. “PSYDAC: A High-Performance IGA Library in Python.” In 8th European Congress on Computational Methods in Applied Sciences and Engineering. CIMNE, 2022. https://doi.org/10.23967/eccomas.2022.227. + +The associated BibTeX file can be found [here](./CITATION.bib). + +## Installation + +PSYDAC requires a certain number of components to be installed on the machine: - Fortran and C compilers with OpenMP support - OpenMP library @@ -26,189 +30,90 @@ Psydac requires a certain number of components to be installed on the machine: - MPI library - HDF5 library with MPI support -The installations instructions depend on the operating system and on the packaging manager used. - -### Linux Debian-Ubuntu-Mint - -To install all requirements on a Linux Ubuntu operating system, just use APT, the Advanced Packaging Tool: -```sh -sudo apt update -sudo apt install python3 python3-dev python3-pip -sudo apt install gcc gfortran -sudo apt install libblas-dev liblapack-dev -sudo apt install libopenmpi-dev openmpi-bin -sudo apt install libomp-dev libomp5 -sudo apt install libhdf5-openmpi-dev -``` - -### macOS - -To install all the requirements on a macOS operating system we recommend using [Homebrew](https://brew.sh/): - -```eh -brew update -brew install gcc -brew install openblas -brew install lapack -brew install open-mpi -brew install libomp -brew install hdf5-mpi -``` - -### Other operating systems - -Please see the [instructions for the pyccel library](https://github.com/pyccel/pyccel#Requirements) for further details. +The installation instructions depend on the operating system and on the packaging manager used. +It is particularly important to determine the **HDF5 root folder**, as this will be needed to install the [`h5py`](https://docs.h5py.org/en/latest/build.html#source-installation) package in parallel mode. +Detailed instructions can be found in the [documentation](./docs/installation.md). -## Python setup and project download - -We recommend creating a clean Python virtual environment using [venv](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/#creating-a-virtual-environment): -```sh +Once those components are installed, we recommend using [`venv`](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/#creating-a-virtual-environment) to set up a fresh Python virtual environment at a location ``: +```bash python3 -m venv -``` -where `` is the location to create the virtual environment. -(A new directory will be created at the required location.) - -In order to activate the environment from a new terminal session just run the command -```sh source /bin/activate ``` -One can clone the Psydac repository at any location `` in the filesystem which does not require administrator privileges, using either -```sh +PSYDAC and its Python dependencies can now be installed in the virtual environment using [`pip`](https://pip.pypa.io/en/stable/), the Python package manager: +```bash git clone https://github.com/pyccel/psydac.git -``` -or -```sh -git clone git@github.com:pyccel/psydac.git -``` -The latter command requires a GitHub account. -## Installing the library - -Psydac depends on several Python packages, which should be installed in the newly created virtual environment. -These dependencies can be installed from the cloned directory `/psydac` with the following steps. - -First, set an environment variable with the path to the parallel HDF5 library. -This path can be obtained with a command which depends on your system. - -- **Ubuntu/Debian**: - ```sh - export HDF5_DIR=$(dpkg -L libhdf5-openmpi-dev | grep "libhdf5.so" | xargs dirname) - ``` - -- **macOS**: - ```sh - export HDF5_DIR=$(brew list hdf5-mpi | grep "libhdf5.dylib" | xargs dirname | xargs dirname) - ``` - -Next, install the Python dependencies using `pip`: -```sh export CC="mpicc" export HDF5_MPI="ON" +export HDF5_DIR= -python3 -m pip install --upgrade pip -python3 -m pip install -r requirements.txt -python3 -m pip install -r requirements_extra.txt --no-build-isolation --no-cache-dir +pip install --upgrade pip +pip install h5py --no-cache-dir --no-binary h5py +pip install ./psydac ``` +Here `` is the path to the HDF5 root folder, such that `/lib/` contains the HDF5 dynamic libraries with MPI support. +For an editable install, the `-e/--editable` flag should be provided to the last command above. -At this point the Psydac library may be installed in **standard mode**, which copies the relevant files to the correct locations of the virtual environment, or in **development mode**, which only installs symbolic links to the Psydac directory. The latter mode allows one to effect the behavior of Psydac by modifying the source files. - -- **Standard mode**: - ```bash - python3 -m pip install . - ``` - -- **Development mode**: - ```bash - python3 -m pip install --editable . - ``` +Again, for more details we refer to our [documentation](./docs/installation.md). -## Optional PETSc installation +> [!TIP] +> PSYDAC provides the functionality to convert its MPI-parallel matrices and vectors to their [PETSc](https://petsc.org) equivalent, and back. +> This gives the user access to a wide variety of linear solvers and other algorithms. +> Instructions for installing [PETSc](https://petsc.org) and `petsc4py` can be found in our [documentation](.docs/installation.md#optional-petsc-installation). -Although Psydac provides several iterative linear solvers which work with our native matrices and vectors, it is often useful to access a dedicated library like [PETSc](https://petsc.org). To this end, our matrices and vectors have the method `topetsc()`, which converts them to the corresponding `petsc4py` objects. -(`petsc4py` is a Python package which provides Python bindings to PETSc.) After solving the linear system with a PETSc solver, the function `petsc_to_psydac` allows converting the solution vector back to the Psydac format. +## Running Tests -In order to use these additional feature, PETSc and petsc4py must be installed as follows. -First, we download the latest release of PETSc from its [official Git repository](https://gitlab.com/petsc/petsc): -```sh -git clone --depth 1 --branch v3.21.4 https://gitlab.com/petsc/petsc.git -``` -Next, we specify a configuration for complex numbers, and install PETSc in a local directory: -```sh -cd petsc - -export PETSC_DIR=$(pwd) -export PETSC_ARCH=petsc-cmplx - -./configure --with-scalar-type=complex --with-fortran-bindings=0 --have-numpy=1 - -make all check - -cd - -``` -Finally, we install the Python package `petsc4py` which is included in the `PETSc` source distribution: -```sh -python3 -m pip install wheel Cython numpy -python3 -m pip install petsc/src/binding/petsc4py +The test suite of PSYDAC is based on [`pytest`](https://docs.pytest.org/en/stable/), which should be installed in the same virtual environment: +```bash +source /bin/activate +pip install pytest ``` -## Uninstall - -- **Whichever the install mode**: - ```bash - python3 -m pip uninstall psydac - ``` -- **If PETSc was installed**: - ```bash - python3 -m pip uninstall petsc4py - ``` - -The non-Python dependencies can be uninstalled manually using the package manager. -In the case of PETSc, it is sufficient to remove the cloned source directory given that the installation has been performed locally. - -## Running tests - -Let `` be the installation directory of Psydac. +Let `` be the installation directory of PSYDAC. In order to run all serial and parallel tests which do not use PETSc, just type: ```bash export PSYDAC_MESH_DIR=/mesh/ -python3 -m pytest --pyargs psydac -m "not parallel and not petsc" -python3 /mpi_tester.py --pyargs psydac -m "parallel and not petsc" +pytest --pyargs psydac -m "not parallel and not petsc" +python /mpi_tester.py --pyargs psydac -m "parallel and not petsc" ``` If PETSc and petsc4py were installed, some additional tests can be run: ```bash -python3 -m pytest --pyargs psydac -m "not parallel and petsc" -python3 /mpi_tester.py --pyargs psydac -m "parallel and petsc" +pytest --pyargs psydac -m "not parallel and petsc" +python /mpi_tester.py --pyargs psydac -m "parallel and petsc" ``` -## Speeding up **Psydac**'s core +## Speeding up PSYDAC's core -Many of Psydac's low-level Python functions can be translated to a compiled language using the [Pyccel](https://github.com/pyccel/pyccel) transpiler. Currently, all of those functions are collected in modules which follow the name pattern `[module]_kernels.py`. +Many of PSYDAC's low-level Python functions can be translated to a compiled language using the [Pyccel](https://github.com/pyccel/pyccel) transpiler. Currently, all of those functions are collected in modules which follow the name pattern `[module]_kernels.py`. The classical installation translates all kernel files to Fortran without user intervention. This does not happen in the case of an editable install, but the command `psydac-accelerate` is made available to the user instead. This command applies Pyccel to all the kernel files in the source directory. The default language is currently Fortran, C should also be supported in a near future. - **Only in development mode**: ```bash - python3 /path/to/psydac/psydac_accelerate.py [--language LANGUAGE] [--openmp] + python /path/to/psydac/psydac_accelerate.py [--language LANGUAGE] [--openmp] ``` -## User documentation +## Examples and Tutorials -- [Output formats](./output.md) -- [Notebook examples](./examples/notebooks/) -- [Other examples](./examples/) +A [tutorial](https://pyccel.github.io/IGA-Python/intro.html) on isogeometric analysis, with many example notebooks where various PDEs are solved with PSYDAC, is under construction in the [IGA-Python](https://github.com/pyccel/IGA-Python) repository. +Some other examples can be found [here](./examples/). -## Code documentation +## Library Documentation -Find our latest code documentation [here](https://pyccel.github.io/psydac/). +- [Output formats](./docs/output.md) +- [Mesh generation](./docs/psydac-mesh.md) +- [Library reference](https://pyccel.github.io/psydac/) -## Mesh Generation +## Contributing -After installation, a command `psydac-mesh` will be available. +There are several ways to contribute to this project! -### Example of usage +If you find a problem, please check if this is already discussed in one of [our issues](https://github.com/pyccel/psydac/issues) and feel free to add your opinion; if not, please create a [new issue](https://docs.github.com/en/issues/tracking-your-work-with-issues/using-issues/creating-an-issue). +If you want to fix an issue, improve our notebooks, or add a new example, please [fork](https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/working-with-forks/fork-a-repo) our Git repository, make and commit your changes, and create a [pull request](https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/proposing-changes-to-your-work-with-pull-requests/creating-a-pull-request) (PRs). +All PRs are reviewed by the project maintainers. +During the PR review, GitHub workflows are triggered on various platforms. -```bash -psydac-mesh -n='16,16' -d='3,3' square mesh.h5 -``` +We keep an up-to-date list of maintainers and contributors in our [AUTHORS](./AUTHORS) file. +Thank you! diff --git a/docs/installation.md b/docs/installation.md new file mode 100644 index 000000000..e71e4ddef --- /dev/null +++ b/docs/installation.md @@ -0,0 +1,202 @@ +# Installation + +- [Requirements](#requirements) +- [Python setup and project download](#python-setup-and-project-download) +- [Installing the library](#installing-the-library) +- [Optional PETSc installation](#optional-petsc-installation) +- [Uninstall](#uninstall) + +## Requirements + +Psydac requires a certain number of components to be installed on the machine: + +- Fortran and C compilers with OpenMP support +- OpenMP library +- BLAS and LAPACK libraries +- MPI library +- HDF5 library with MPI support + +The installation instructions depend on the operating system and on the packaging manager used. + +### Linux Debian-Ubuntu-Mint + +To install all requirements on a Linux Ubuntu operating system, just use APT, the Advanced Packaging Tool: +```sh +sudo apt update +sudo apt install python3 python3-dev python3-pip +sudo apt install gcc gfortran +sudo apt install libblas-dev liblapack-dev +sudo apt install libopenmpi-dev openmpi-bin +sudo apt install libomp-dev libomp5 +sudo apt install libhdf5-openmpi-dev +``` + +### macOS + +To install all the requirements on a macOS operating system we recommend using [Homebrew](https://brew.sh/): + +```eh +brew update +brew install gcc +brew install openblas +brew install lapack +brew install open-mpi +brew install libomp +brew install hdf5-mpi +``` + +### Other operating systems + +Please see the [instructions for the pyccel library](https://github.com/pyccel/pyccel#Requirements) for further details. + +### High-performance computers using Environment Modules + +Many high-performance computers use [Environment Modules](https://modules.sourceforge.net/). +On those systems one typically needs to load the correct versions (i.e. compatible with each other) of the modules `gcc`, `openmpi`, and `hdf5-mpi`, e.g. + +```sh +module load gcc/15 +module load openmpi/5.0 +module load hdf5-mpi/1.14.1 +``` +OpenMP instructions should work out of the box. +For access to BLAS and LAPACK routines there are usually different options, we refer therefore to any documentation provided by the supercomputer's maintainers. + +## Python setup and project download + +We recommend creating a clean Python virtual environment using [venv](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/#creating-a-virtual-environment): +```sh +python3 -m venv +``` +where `` is the location to create the virtual environment. +(A new directory will be created at the required location.) +In order to activate the environment just run the command +```sh +source /bin/activate +``` +At this point the commands `python` and [`pip`](https://pip.pypa.io/en/stable/) will refer to the Python 3 interpreter and package manager of the virtual environment, respectively. +Additionally, the command `deactivate` closes the environment. +It is good practice to keep `pip` up to date with +```sh +pip install --upgrade pip +``` + +One can clone the Psydac repository at any location `` in the filesystem which does not require administrator privileges, using either +```sh +git clone https://github.com/pyccel/psydac.git +``` +or +```sh +git clone git@github.com:pyccel/psydac.git +``` +The latter command requires a GitHub account. + +## Installing the library + +Psydac depends on several Python packages, which should be installed in the newly created virtual environment. +Almost all of these dependencies will be automatically installed by `pip` at the time of installing the `psydac` package later on. + +The single exception is the `h5py` package, which needs to be installed in parallel mode. +This means that a wheel will be built from sources and linked to the local parallel HDF5 library. + +To this end, we first set the environment variable `HDF5_DIR` s.t. the path `$HDF5_DIR/lib/` will correspond to the folder containing the dynamic library `libhdf5.so` (on Ubuntu/Debian) or `libhdf5.dylib` (on macOS). +This path can be obtained with a command which depends on your system. + +- **Ubuntu/Debian**: + ```sh + export HDF5_DIR=$(dpkg -L libhdf5-openmpi-dev | grep "libhdf5.so" | xargs dirname) + ``` + +- **macOS**: + ```sh + export HDF5_DIR=$(brew list hdf5-mpi | grep "libhdf5.dylib" | xargs dirname | xargs dirname) + ``` + +- **High-performance computers using [Environment Modules](https://modules.sourceforge.net/)**: + + The correct location of the HDF5 library can be found using the `module show` command, which reveals any environment variables after the `setenv` keyword. + For example, on this system both `HDF5_HOME` and `HDF5_ROOT` contain the information we need: + + ```sh + > module show hdf5-mpi/1.14.1 + + ------------------------------------------------------------------- + /mpcdf/soft/SLE_15/sub/gcc_15/sub/openmpi_5_0/modules/libs/hdf5-mpi/1.14.1: + + module-whatis {HDF5 library 1.14.1 with MPI support, built for openmpi_5_0_7_gcc_15_1} + conflict hdf5-serial + conflict hdf5-mpi + setenv HDF5_HOME /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1 + setenv HDF5_ROOT /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1 + prepend-path PATH /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1/bin + ------------------------------------------------------------------- + ``` + + Therefore it is sufficient to set + + ```sh + export HDF5_DIR=$HDF5_HOME + ``` + +Next, install `h5py` in parallel mode using `pip`: +```sh +export CC="mpicc" +export HDF5_MPI="ON" + +pip install h5py --no-cache-dir --no-binary h5py +``` + +At this point the Psydac library may be installed from the cloned directory `/psydac` in **standard mode**, which copies the relevant files to the correct locations of the virtual environment, or in **development mode**, which only installs symbolic links to the Psydac directory. The latter mode allows one to affect the behavior of Psydac by modifying the source files. + +- **Standard mode**: + ```bash + pip install . + ``` + +- **Development mode**: + ```bash + pip install --editable . + ``` + +## Optional PETSc installation + +Although Psydac provides several iterative linear solvers which work with our native matrices and vectors, it is often useful to access a dedicated library like [PETSc](https://petsc.org). To this end, our matrices and vectors have the method `topetsc()`, which converts them to the corresponding `petsc4py` objects. +(`petsc4py` is a Python package which provides Python bindings to PETSc.) After solving the linear system with a PETSc solver, the function `petsc_to_psydac` allows converting the solution vector back to the Psydac format. + +In order to use these additional feature, PETSc and petsc4py must be installed as follows. +First, we download the latest release of PETSc from its [official Git repository](https://gitlab.com/petsc/petsc): +```sh +git clone --depth 1 --branch v3.21.4 https://gitlab.com/petsc/petsc.git +``` +Next, we specify a configuration for complex numbers, and install PETSc in a local directory: +```sh +cd petsc + +export PETSC_DIR=$(pwd) +export PETSC_ARCH=petsc-cmplx + +./configure --with-scalar-type=complex --with-fortran-bindings=0 --have-numpy=1 + +make all check + +cd - +``` +Finally, we install the Python package `petsc4py` which is included in the `PETSc` source distribution: +```sh +pip install wheel Cython numpy +pip install petsc/src/binding/petsc4py +``` + +## Uninstall + +- **Whichever the install mode**: + ```bash + pip uninstall psydac + ``` +- **If PETSc was installed**: + ```bash + pip uninstall petsc4py + ``` + +The non-Python dependencies can be uninstalled manually using the package manager. +In the case of PETSc, it is sufficient to remove the cloned source directory given that the installation has been performed locally. diff --git a/output.md b/docs/output.md similarity index 100% rename from output.md rename to docs/output.md diff --git a/docs/psydac-mesh.md b/docs/psydac-mesh.md new file mode 100644 index 000000000..20a543c34 --- /dev/null +++ b/docs/psydac-mesh.md @@ -0,0 +1,9 @@ +# Mesh Generation + +After installation, the command `psydac-mesh` will be available. + +## Example of usage + +```bash +psydac-mesh -n='16,16' -d='3,3' square mesh.h5 +``` diff --git a/docs_requirements.txt b/docs/requirements.txt similarity index 100% rename from docs_requirements.txt rename to docs/requirements.txt diff --git a/pyproject.toml b/pyproject.toml index 21bd7fb70..c20cf49d3 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -1,5 +1,5 @@ [build-system] -requires = ["setuptools >= 64.0", "wheel", "numpy", "pyccel >= 1.9.2"] +requires = ["setuptools >= 64.0, != 67.2.0", "wheel", "numpy", "pyccel >= 2.0.1"] build-backend = "setuptools.build_meta" [project] @@ -34,12 +34,17 @@ dependencies = [ 'pyccel >= 2.0.1', 'gelato == 0.12', - # In addition, we depend on mpi4py and h5py (MPI version). - # Since h5py must be built from source, we run the commands + # MPI for Python provides Python bindings for the + # Message Passing Interface (MPI) standard + 'mpi4py >= 4', + + # In addition, we depend on h5py (MPI version). Since h5py must + # be built from source, we install it with the commands # - # python3 -m pip install requirements.txt - # python3 -m pip install . - 'mpi4py', + # export CC="mpicc" + # export HDF5_MPI="ON" + # export HDF5_DIR= + # pip install --no-cache-dir --no-binary h5py 'h5py', # When pyccel is run in parallel with MPI, it uses tblib to pickle diff --git a/requirements.txt b/requirements.txt deleted file mode 100644 index 8cd73ee05..000000000 --- a/requirements.txt +++ /dev/null @@ -1,9 +0,0 @@ -wheel -setuptools >= 61, != 67.2.0 -numpy >= 1.16 -scipy >= 1.12 -Cython >= 3 -mpi4py >= 4 - -# Required to build h5py from source -pkgconfig diff --git a/requirements_extra.txt b/requirements_extra.txt deleted file mode 100644 index 5f4a812d3..000000000 --- a/requirements_extra.txt +++ /dev/null @@ -1,9 +0,0 @@ -# h5py must be built from source using the MPI compiler -# and linked to the parallel HDF5 library. To do so set -# -# CC="mpicc" -# HDF5_MPI="ON" -# HDF5_DIR=/usr/lib/x86_64-linux-gnu/hdf5/openmpi -# -h5py ---no-binary h5py From 776ac29310d1d1e1d375f7035ad5f9956ee39729 Mon Sep 17 00:00:00 2001 From: Julian Owezarek Date: Wed, 10 Sep 2025 16:40:56 +0200 Subject: [PATCH 14/23] Fast Matrix Assembly (#448) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This PR implements the sum factorization algorithm as shown in **Sum factorization techniques in Isogeometric Analysis** by Andrea Bressan & Stefan Takacs for **bilinear forms on 3D volumes**. The old element-by-element assembly can still be employed by passing a corresponding flag ```python # a some BilinearForm a_h = discretize(a, domain_h, (Vh, Vh), backend=backend, sum_factorization=False) ``` Currently, the new generated code does not make use of OpenMP. Main changes -------------- - Write new module `psydac.api.fem_common` which: * Contains the old functions previously in module `psydac.api.fem`. * Has functions `construct_test_space_arguments` and `construct_trial_space_arguments` returning also the multiplicity. * Has new functions `compute_max_nderiv`, `compute_imports`, `compute_free_arguments`. - Move `DiscreteSumForm` to a new module `psydac.api.fem_sum_form`. - Create a new module `psydac.api.fem_bilinear_form` which only contains one new class `DiscreteBilinearForm`. The new module shows all imports clearly. The new class: * Generates the code to assemble the given discrete bilinear form into a matrix (a `BlockLinearOperator` object of `StencilMatrix` objects, or just a single `StencilMatrix` object), using sum factorization. * Does not inherit from `BasicDiscrete` (and hence `BasicCodeGen`). Accordingly, no PSYDAC abstract syntax tree (an object representing a function, of class `DefNode`) is created by the constructor of `AST`, which stores it in its `expr` attribute. (Both classes `DefNode` and `AST` are defined in module `psydac.api.ast.fem`.) * Does not create a `Parser` object from `psydac.api.ast.parser`, which used to convert a PSYDAC `DefNode` to an old-Pyccel `FunctionDef` from `psydac.pyccel.ast.core`. * Does not generate the old assembly Python code (in the form of a string) using the function `pycode` from `psydac.pyccel.codegen.printing.pycode`. - Add a new unit test file `api/tests/test_sum_factorization_assembly_3d`. - Modify function `discretize` in module `psydac.api.discretization` so that, given a bilinear form in 3D and not asking for OpenMP support, it creates an object of type `DiscreteBilinearForm` from module `psydac.api.fem_bilinear_form`. In all other cases, or if `sum_factorization=False`, it creates an object of namesake type from the old module `psydac.api.fem`. Other changes -------------- - Expand docstring of class `AST` in module `psydac.api.ast.fem`. - Expand docstrings of function `parse` and class `Parser` in module `psydac.api.ast.parser`. Clean up `Parser.__init__`. - Minor cleanup in class `BasicCodeGen` in module `psydac.api.basic`. - Generate random filenames using `random.choice()` instead of `random.SystemRandom().choice()`. Unrelated to matrix assembly: - Add method `set_scalar` to `ScaledLinearOperator`. - Reimplement method `idot` of `LinearOperator` using local storage. This avoids creating unnecessary temporary vectors (especially beneficial for the method `dot` of `SumLinearOperator`). --------- Co-authored-by: Yaman Güçlü Co-authored-by: elmosa --- .../compare_3d_matrix_assembly_speed.py | 643 +++++ performance/matrix_assembly_speed_log.md | 86 + psydac/api/ast/fem.py | 8 +- psydac/api/ast/parser.py | 113 +- psydac/api/basic.py | 8 +- psydac/api/discretization.py | 30 +- psydac/api/equation.py | 4 +- psydac/api/fem.py | 246 +- psydac/api/fem_bilinear_form.py | 2226 +++++++++++++++++ psydac/api/fem_common.py | 286 +++ psydac/api/fem_sum_form.py | 123 + psydac/api/tests/test_api_feec_3d.py | 49 +- .../test_sum_factorization_assembly_3d.py | 592 +++++ psydac/api/utilities.py | 43 +- psydac/linalg/basic.py | 98 +- 15 files changed, 4221 insertions(+), 334 deletions(-) create mode 100644 performance/compare_3d_matrix_assembly_speed.py create mode 100644 performance/matrix_assembly_speed_log.md create mode 100644 psydac/api/fem_bilinear_form.py create mode 100644 psydac/api/fem_common.py create mode 100644 psydac/api/fem_sum_form.py create mode 100644 psydac/api/tests/test_sum_factorization_assembly_3d.py diff --git a/performance/compare_3d_matrix_assembly_speed.py b/performance/compare_3d_matrix_assembly_speed.py new file mode 100644 index 000000000..0bc8678a5 --- /dev/null +++ b/performance/compare_3d_matrix_assembly_speed.py @@ -0,0 +1,643 @@ +import os +import shutil +import time +from pathlib import Path +from datetime import datetime + +from mpi4py import MPI +import numpy as np +#import matplotlib.pyplot as plt +from sympy import sin + +from sympde.calculus import dot, cross, grad, curl +from sympde.expr import BilinearForm, integral +from sympde.topology import element_of, elements_of, Cube, Mapping, ScalarFunctionSpace, Domain, Derham + +from psydac.api.discretization import discretize +from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL +from psydac.cad.geometry import Geometry +from psydac.fem.basic import FemField +from psydac.mapping.discrete import SplineMapping + +datetime_md = datetime.today().strftime('%Y-%m-%d %H:%M:%S') +datetime_file = datetime.today().strftime('%Y-%m-%d_%H:%M:%S') + +""" +Executing this file will add new tables to the matrix_assembly_speed_log.md file in which we keep track of assembly and discretization speed. +Estimated runtime: ~4 min. + +""" + +comm = MPI.COMM_WORLD +backend = PSYDAC_BACKEND_GPYCCEL +mpi_rank = comm.rank + +if mpi_rank == 0: + print('Expected runtime: 4 min.') + print() + +class SquareTorus(Mapping): + + _expressions = {'x': 'x1 * cos(x2)', + 'y': 'x1 * sin(x2)', + 'z': 'x3'} + + _ldim = 3 + _pdim = 3 + +def make_square_torus_geometry_3d(ncells, degree, comm=None): + + if comm is not None: + mpi_rank = comm.Get_rank() + else: + mpi_rank = 0 + + if (ncells[0] == ncells[1]) and (ncells[0] == ncells[2]): + nc = f'{ncells[0]}' + else: + nc = f'{ncells[0]}_{ncells[1]}_{ncells[2]}' + + if (degree[0] == degree[1]) and (degree[0] == degree[2]): + de = f'{degree[0]}' + else: + de = f'{degree[0]}_{degree[1]}_{degree[2]}' + + name = f'st_3d_nc_{nc}_d_{de}' + + r = 0.5 + R = 1. + logical_domain = Cube('C', bounds1=(r, R), bounds2=(0, 2*np.pi), bounds3=(0, 1)) + domain_h = discretize(logical_domain, ncells=ncells, comm=comm) + + V = ScalarFunctionSpace('V', logical_domain) + V_h = discretize(V, domain_h, degree=degree) + + mapping = SquareTorus('S') + map_discrete = SplineMapping.from_mapping(V_h, mapping.get_callable_mapping()) + + geometry = Geometry.from_discrete_mapping(map_discrete, comm=comm) + + if mpi_rank == 0: + if not os.path.isdir('geometry'): + os.makedirs('geometry') + os.makedirs('geometry/files') + else: + if not os.path.isdir('geometry/files'): + os.makedirs('geometry/files') + + geometry.export(f'geometry/files/{name}.h5') + + return f'geometry/files/{name}.h5' + +# ---------- 1 ---------- +#t0_1_glob = time.time() +# +#ncells = [32, 32, 32] +#degree_list = [[2, 2, 2], [3, 3, 3], [4, 4, 4], [5, 5, 5]] +#degree_list2 = [[2, 2, 2], [3, 3, 3], [4, 4, 4]] +#periodic = [False, False, False] +# +##mapping = HalfHollowTorusMapping3D('M', R=2, r=1) +#mapping = SquareTorus('S') +##logical_domain = Cube('C', bounds1=(0,1), bounds2=(0,1), bounds3=(0,1)) +#r = 0.5 +#R = 1. +#logical_domain = Cube('C', bounds1=(r, R), bounds2=(0, 2*np.pi), bounds3=(0, 1)) +# +#domain = mapping(logical_domain) +#derham = Derham(domain) +#plot_domain(domain, draw=True, isolines=True) +# +#ass_time_H1_old = [[] for _ in degree_list] +#ass_time_H1_new = [[] for _ in degree_list] +# +#ass_time_Hcurl_old = [[] for _ in degree_list2] +#ass_time_Hcurl_new = [[] for _ in degree_list2] +# +#for i, degree in enumerate(degree_list): +# +# domain_h = discretize(domain, ncells=ncells, periodic=periodic, comm=comm) +# derham_h = discretize(derham, domain_h, degree=degree) +# +# V0 = derham.V0 +# V0h = derham_h.V0 +# +# u, v = elements_of(V0, names='u, v') +# +# a = BilinearForm((u, v), integral(domain, u*v)) +# +# a_h = discretize(a, domain_h, (V0h, V0h), backend=backend, sum_factorization=False) +# +# t0_ao = time.time() +# M_o = a_h.assemble() +# t1_ao = time.time() +# +# a_h = discretize(a, domain_h, (V0h, V0h), backend=backend) +# +# t0_an = time.time() +# M_n = a_h.assemble() +# t1_an = time.time() +# +# ass_time_H1_old[i].append(t1_ao - t0_ao) +# ass_time_H1_new[i].append(t1_an - t0_an) +# +# if degree != [5, 5, 5]: +# +# V1 = derham.V1 +# V1h = derham_h.V1 +# +# u, v = elements_of(V1, names='u, v') +# +# a = BilinearForm((u, v), integral(domain, dot(u, v))) +# +# a_h = discretize(a, domain_h, (V1h, V1h), backend=backend, sum_factorization=False) +# +# t0_ao = time.time() +# M_o = a_h.assemble() +# t1_ao = time.time() +# +# a_h = discretize(a, domain_h, (V1h, V1h), backend=backend) +# +# t0_an = time.time() +# M_n = a_h.assemble() +# t1_an = time.time() +# +# ass_time_Hcurl_old[i].append(t1_ao - t0_ao) +# ass_time_Hcurl_new[i].append(t1_an - t0_an) +# +#d = [degree[0] for degree in degree_list] +#d2 = [degree[0] for degree in degree_list2] +# +#ass_time_H1_old_d = [ass_time_H1_old[i][0] for i, _ in enumerate(degree_list)] +#ass_time_H1_new_d = [ass_time_H1_new[i][0] for i, _ in enumerate(degree_list)] +# +#ass_time_Hcurl_old_d = [ass_time_Hcurl_old[i][0] for i, _ in enumerate(degree_list2)] +#ass_time_Hcurl_new_d = [ass_time_Hcurl_new[i][0] for i, _ in enumerate(degree_list2)] +# +#if mpi_rank == 0: +# plt.plot(d, ass_time_H1_old_d, '--.', label=f'old Algorithm') +# plt.plot(d, ass_time_H1_new_d, '--.', label=f'new Algorithm') +# plt.title(r'Assembly times for the $H^1(\Omega)$ mass matrix') +# plt.legend() +# plt.yscale('log') +# plt.ylabel('Wallclock Time [s]') +# plt.xlabel('d - [d, d, d] Bspline degrees') +# plt.xticks(d) +# #plt.savefig(f'figures/H1_{datetime_file}.png') +# plt.show() +# plt.clf() +# +# plt.plot(d2, ass_time_Hcurl_old_d, '--.', label=f'old Algorithm') +# plt.plot(d2, ass_time_Hcurl_new_d, '--.', label=f'new Algorithm') +# plt.title(r'Assembly times for the $H(curl;\Omega)$ mass matrix') +# plt.legend() +# plt.yscale('log') +# plt.ylabel('Wallclock Time [s]') +# plt.xlabel('d - [d, d, d] Bspline degrees') +# plt.xticks(d2) +# #plt.savefig(f'figures/Hcurl_{datetime_file}.png') +# plt.show() +# +#t1_1_glob = time.time() +#if mpi_rank == 0: +# print(f'Part 1 out of 3 done after {(t1_1_glob-t0_1_glob)/60:.2g}min') +# ----------------------- + +# ---------- 2 ---------- +t0_2_glob = time.time() + +ncells = [32, 32, 32] +degree = [3, 3, 3] +periodic = [False, False, False] + +r = 0.5 +R = 1. +logical_domain = Cube('C', bounds1=(r, R), bounds2=(0, 2*np.pi), bounds3=(0, 1)) +logical_derham = Derham(logical_domain) + +logical_domain_h = discretize(logical_domain, ncells=ncells, periodic=periodic, comm=comm) +logical_derham_h = discretize(logical_derham, logical_domain_h, degree=degree) + +filename = make_square_torus_geometry_3d(ncells, degree, comm=comm) + +bspline_domain = Domain.from_file(filename) +bspline_derham = Derham(bspline_domain) + +bspline_domain_h = discretize(bspline_domain, filename=filename, comm=comm) +bspline_derham_h = discretize(bspline_derham, bspline_domain_h, degree=bspline_domain.mapping.get_callable_mapping().space.degree) + +mapping = SquareTorus('S') + +analytical_domain = mapping(logical_domain) +analytical_derham = Derham(analytical_domain) + +analytical_domain_h = discretize(analytical_domain, ncells=ncells, periodic=periodic, comm=comm) +analytical_derham_h = discretize(analytical_derham, analytical_domain_h, degree=degree) + +ax, ay, az = analytical_domain.coordinates +agamma = ax*ay*az + sin(ax*ay+az)**2 + +# 2.1 +dom = logical_domain +domh = logical_domain_h +V = logical_derham.V1 +Vh = logical_derham_h.V1 + +F = element_of(V, name='F') +f = Vh.coeff_space.zeros() +f[0]._data = np.ones(f[0]._data.shape) +f[1]._data = np.ones(f[1]._data.shape) +f[2]._data = np.ones(f[2]._data.shape) +f_field = FemField(Vh, f) + +u, v = elements_of(V, names='u, v') +a = BilinearForm((u, v), integral(dom, dot(cross(F, u), cross(F, v)))) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_21 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble(F=f_field) +t1 = time.time() +old_ass_21 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_21 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble(F=f_field) +t1 = time.time() +new_ass_21 = round(t1-t0, 3) + +# 2.2 +dom = analytical_domain +domh = analytical_domain_h +V = analytical_derham.V2 +Vh = analytical_derham_h.V2 + +u, v = elements_of(V, names='u, v') +a = BilinearForm((u, v), integral(dom, dot(u, v)*agamma)) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_22 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_22 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_22 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_22 = round(t1-t0, 3) + +# 2.3 +dom = bspline_domain +domh = bspline_domain_h +V = bspline_derham.V1 +Vh = bspline_derham_h.V1 + +u, v = elements_of(V, names='u, v') +a = BilinearForm((u, v), integral(dom, dot(curl(u), curl(v)))) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_23 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_23 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_23 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_23 = round(t1-t0, 3) + +t1_2_glob = time.time() +if mpi_rank == 0: + print(f'Part 2 out of 3 done after {(t1_2_glob-t0_2_glob)/60:.2g}min') +# ----------------------- + +# ---------- 3 ---------- +t0_3_glob = time.time() + +ncells = [16, 8, 32] +degree = [2, 4, 3] +periodic = [False, True, False] + +r = 0.5 +R = 1. +logical_domain = Cube('C', bounds1=(r, R), bounds2=(0, 2*np.pi), bounds3=(0, 1)) +logical_derham = Derham(logical_domain) + +logical_domain_h = discretize(logical_domain, ncells=ncells, periodic=periodic, comm=comm) +logical_derham_h = discretize(logical_derham, logical_domain_h, degree=degree) + +filename = make_square_torus_geometry_3d(ncells, degree, comm=comm) + +bspline_domain = Domain.from_file(filename) +bspline_derham = Derham(bspline_domain) + +bspline_domain_h = discretize(bspline_domain, filename=filename, comm=comm) +bspline_derham_h = discretize(bspline_derham, bspline_domain_h, degree=bspline_domain.mapping.get_callable_mapping().space.degree) + +mapping = SquareTorus('S') + +analytical_domain = mapping(logical_domain) +analytical_derham = Derham(analytical_domain) + +analytical_domain_h = discretize(analytical_domain, ncells=ncells, periodic=periodic, comm=comm) +analytical_derham_h = discretize(analytical_derham, analytical_domain_h, degree=degree) + +ax, ay, az = analytical_domain.coordinates +agamma = ax*ay*az + sin(ax*ay+az)**2 + +# 3.1.1 +dom = logical_domain +domh = logical_domain_h +V = logical_derham.V0 +Vh = logical_derham_h.V0 + +u, v = elements_of(V, names='u, v') +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)))) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_311 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_311 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_311 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_311 = round(t1-t0, 3) + +# 3.1.2 +dom = analytical_domain +domh = analytical_domain_h +V = analytical_derham.V0 +Vh = analytical_derham_h.V0 + +u, v = elements_of(V, names='u, v') +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)))) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_312 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_312 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_312 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_312 = round(t1-t0, 3) + +# 3.1.3 +dom = bspline_domain +domh = bspline_domain_h +V = bspline_derham.V0 +Vh = bspline_derham_h.V0 + +u, v = elements_of(V, names='u, v') +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)))) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_313 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_313 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_313 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_313 = round(t1-t0, 3) + +# 3.2 +dom = analytical_domain +domh = analytical_domain_h +V = ScalarFunctionSpace('V', analytical_domain) +Vh = discretize(V, analytical_domain_h, degree=degree) + +u, v = elements_of(V, names='u, v') +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)))) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_32 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_32 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_32 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_32 = round(t1-t0, 3) + +# 3.3 +dom = analytical_domain +domh = analytical_domain_h +V = ScalarFunctionSpace('V', analytical_domain) +Vh = discretize(V, analytical_domain_h, degree=degree) +W = analytical_derham.V0 +Wh = analytical_derham_h.V0 + +u = element_of(V, name='u') +v = element_of(W, name='v') +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)))) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_33 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_33 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_33 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_33 = round(t1-t0, 3) + +# ------------------ +dom = analytical_domain +domh = analytical_domain_h +V = analytical_derham.V0 +Vh = analytical_derham_h.V0 + +u, v = elements_of(V, names='u, v') +# ------------------ + +# 3.4 +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)) * agamma)) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_34 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +old_ass_34 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_34 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble() +t1 = time.time() +new_ass_34 = round(t1-t0, 3) + +# 3.5 +F = element_of(V, name='F') +f = Vh.coeff_space.zeros() +f._data = np.ones(f._data.shape) +f_field = FemField(Vh, f) + +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)) * F)) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_35 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble(F=f_field) +t1 = time.time() +old_ass_35 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_35 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble(F=f_field) +t1 = time.time() +new_ass_35 = round(t1-t0, 3) + +# 3.6 +mult = [1, 3, 2] +analytical_derham_h = discretize(analytical_derham, analytical_domain_h, degree=degree, multiplicity=mult) +Vh = analytical_derham_h.V0 + +a = BilinearForm((u, v), integral(dom, dot(grad(u), grad(v)) * F)) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend, sum_factorization=False) +t1 = time.time() +old_disc_36 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble(F=f_field) +t1 = time.time() +old_ass_36 = round(t1-t0, 3) + +t0 = time.time() +ah = discretize(a, domh, (Vh, Vh), backend=backend) +t1 = time.time() +new_disc_36 = round(t1-t0, 3) +t0 = time.time() +M = ah.assemble(F=f_field) +t1 = time.time() +new_ass_36 = round(t1-t0, 3) + +t1_3_glob = time.time() +if mpi_rank == 0: + print(f'Part 3 out of 3 done after {(t1_3_glob-t0_3_glob)/60:.2g}min') +# ----------------------- + +template = '''| Test case | old assembly | new assembly | old discretization | new discretization | +| --- | --- | --- | --- | --- | +| 2.1 | {old_ass_21} | {new_ass_21} | {old_disc_21} | {new_disc_21} | +| 2.2 | {old_ass_22} | {new_ass_22} | {old_disc_22} | {new_disc_22} | +| 2.3 | {old_ass_23} | {new_ass_23} | {old_disc_23} | {new_disc_23} | +| 3.1.1 | {old_ass_311} | {new_ass_311} | {old_disc_311} | {new_disc_311} | +| 3.1.2 | {old_ass_312} | {new_ass_312} | {old_disc_312} | {new_disc_312} | +| 3.1.3 | {old_ass_313} | {new_ass_313} | {old_disc_313} | {new_disc_313} | +| 3.2 | {old_ass_32} | {new_ass_32} | {old_disc_32} | {new_disc_32} | +| 3.3 | {old_ass_33} | {new_ass_33} | {old_disc_33} | {new_disc_33} | +| 3.4 | {old_ass_34} | {new_ass_34} | {old_disc_34} | {new_disc_34} | +| 3.5 | {old_ass_35} | {new_ass_35} | {old_disc_35} | {new_disc_35} | +| 3.6 | {old_ass_36} | {new_ass_36} | {old_disc_36} | {new_disc_36} |''' + +txt = '' +txt += f'{datetime_md}\n' +txt += f'----------\n\n' +#txt += f'![](tests/figures/H1_{datetime_file}.png)\n' +#txt += f'![](tests/figures/Hcurl_{datetime_file}.png)\n\n' +txt += template.format(old_ass_21=old_ass_21, new_ass_21=new_ass_21, old_disc_21=old_disc_21, new_disc_21=new_disc_21, + old_ass_22=old_ass_22, new_ass_22=new_ass_22, old_disc_22=old_disc_22, new_disc_22=new_disc_22, + old_ass_23=old_ass_23, new_ass_23=new_ass_23, old_disc_23=old_disc_23, new_disc_23=new_disc_23, + old_ass_311=old_ass_311, new_ass_311=new_ass_311, old_disc_311=old_disc_311, new_disc_311=new_disc_311, + old_ass_312=old_ass_312, new_ass_312=new_ass_312, old_disc_312=old_disc_312, new_disc_312=new_disc_312, + old_ass_313=old_ass_313, new_ass_313=new_ass_313, old_disc_313=old_disc_313, new_disc_313=new_disc_313, + old_ass_32=old_ass_32, new_ass_32=new_ass_32, old_disc_32=old_disc_32, new_disc_32=new_disc_32, + old_ass_33=old_ass_33, new_ass_33=new_ass_33, old_disc_33=old_disc_33, new_disc_33=new_disc_33, + old_ass_34=old_ass_34, new_ass_34=new_ass_34, old_disc_34=old_disc_34, new_disc_34=new_disc_34, + old_ass_35=old_ass_35, new_ass_35=new_ass_35, old_disc_35=old_disc_35, new_disc_35=new_disc_35, + old_ass_36=old_ass_36, new_ass_36=new_ass_36, old_disc_36=old_disc_36, new_disc_36=new_disc_36) +txt += '\n\n' + +if mpi_rank == 0: + # Write performance table to MarkDown file + with open('matrix_assembly_speed_log.md', 'a') as f: + f.write(txt) + + # Remove temporary folders + base_dir = Path(__file__).parent + dirs_to_remove = [ + "geometry", + "__psydac__", + "__pycache__", + "__epyccel__", + "__gpyccel__" + ] + for d in dirs_to_remove: + path = base_dir / d + if path.exists(): + try: + shutil.rmtree(path) + except Exception as e: + print(f"Failed to remove {path}: {e}") diff --git a/performance/matrix_assembly_speed_log.md b/performance/matrix_assembly_speed_log.md new file mode 100644 index 000000000..996975d26 --- /dev/null +++ b/performance/matrix_assembly_speed_log.md @@ -0,0 +1,86 @@ +New Matrix Assembly for Psydac +------------------------------ + +Here we keep track on the performance of the new assembly algorithm (sum factorization). +We measure both the discretization time of `BilinearForms` as well as the matrix assembly time of a `DiscreteBilinearForm` +and compare it to the old algorithm. Executing `compare_3d_matrix_assembly_speed.py` will add new data to this file. +This allows us to detect whether any future changes have a positive or negative impact. + +(Of course, runtime depends on the machine used to execute this file. Hence, an even decrease in runtime +is no reason to celebrate, and an even increase in runtime no reason to worry.) + +Test cases +---------- + +1. Scaling Analysis \ (**REMOVED**) + We assemble the H1 and Hcurl mass matrices ($\Omega$ is a half hollow torus (analytical mapping), ncells = [32, 32, 32], periodic=[False, False, False]) for varying degrees + and report the assembly times in Figures. + +2. Three specific test cases \ + We report assembly and discretization time for the following test cases \ + 2.1 "Q" + - $(u, v; F)\mapsto\int_{\Omega}(F\times u)\circ(F\times v)$ + - $u, v, F\in H(curl;\Omega)$, $F$ a "free field" + - no mapping ($\Omega=(0,1)^3$) + - ncells = [32, 32, 32], degree = [3, 3, 3], periodic = [False, False, False] + + 2.2 "weighted $Hdiv$ mass matrix" + - $(u, v; \gamma)\mapsto\int_{\Omega}u\circ v\ \gamma$ + - $u, v\in H(div;\Omega)$, $\gamma$ an analytic scalar weight function + - analytical mapping ($\Omega$ a half hollow torus) + - ncells = [32, 32, 32], degree = [3, 3, 3], periodic = [False, False, False] + + 2.3 "curl curl" + - $(u, v)\mapsto\int_{\Omega}(\nabla\times u)\circ(\nabla\times v)$ + - $u, v\in H(curl;\Omega)$ + - Bspline mapping ($\Omega$ a half hollow torus) + - ncells = [32, 32, 32], degree = [3, 3, 3], periodic = [False, False, False] + +3. More variations! + - $(u, v)\mapsto\int_{\Omega}\nabla u\circ\nabla v$ + - ncells = [16, 8, 32], degree = [2, 4, 3], periodic = [False, True, False] + - 3.1.1 + - `u, v = elements_of(derham.V0, names='u, v')` + - no mapping + - 3.1.2 + - `u, v = elements_of(derham.V0, names='u, v')` + - analytical mapping + - 3.1.3 + - `u, v = elements_of(derham.V0, names='u, v')` + - Bspline mapping + - 3.2 + - `u, v = elements_of(ScalarFunctionSpace('Vs', domain), names='u, v')` + - analytical mapping + - 3.3 + - `u = element_of(derham.V0, name='u')` + - `v = element_of(ScalarFunctionSpace('Vs', domain), name='v')` + - analytical mapping + - `u, v = elements_of(derham.V0, names='u, v')` + - analytical mapping + - 3.4 + - additional analytical weight function $\gamma$ + - 3.5 + - additional scalar free field $F\in H^1(\Omega)$ + - 3.6 + - multiplicity vector [1, 3, 2] + +Data +---- + +2025-09-09 17:28:19 (added by Julian O. - ThinkPad T14 on performance mode) +---------- + +| Test case | old assembly | new assembly | old discretization | new discretization | +| --- | --- | --- | --- | --- | +| 2.1 | 21.358 | 1.676 | 16.568 | 16.589 | +| 2.2 | 2.348 | 0.322 | 4.533 | 3.38 | +| 2.3 | 36.858 | 3.171 | 16.749 | 19.413 | +| 3.1.1 | 0.236 | 0.044 | 1.462 | 1.482 | +| 3.1.2 | 0.54 | 0.051 | 1.722 | 1.52 | +| 3.1.3 | 0.802 | 0.169 | 3.579 | 2.414 | +| 3.2 | 0.517 | 0.045 | 1.027 | 1.425 | +| 3.3 | 0.525 | 0.06 | 1.023 | 1.527 | +| 3.4 | 0.524 | 0.044 | 1.085 | 1.547 | +| 3.5 | 0.577 | 0.057 | 1.51 | 1.784 | +| 3.6 | 0.598 | 0.209 | 2.411 | 1.848 | + diff --git a/psydac/api/ast/fem.py b/psydac/api/ast/fem.py index b56ee3d28..adf7ff05f 100644 --- a/psydac/api/ast/fem.py +++ b/psydac/api/ast/fem.py @@ -238,8 +238,12 @@ def get_degrees(funcs, space): #============================================================================== class AST(object): """ - The Ast class transforms a terminal expression returned from sympde - into a DefNode + The AST class transforms a terminal expression returned from SymPDE + into a DefNode object, which it stores into the attribute `expr`. + + A DefNode represents a function definition, and it contains the full + PSYDAC abstract syntax tree for the assembly function of a BilinearForm, + LinearForm, or Functional. """ def __init__(self, expr, terminal_expr, spaces, *, nquads, mapping_space=None, tag=None, mapping=None, is_rational_mapping=None, diff --git a/psydac/api/ast/parser.py b/psydac/api/ast/parser.py index eb8ac0a79..f85d82600 100644 --- a/psydac/api/ast/parser.py +++ b/psydac/api/ast/parser.py @@ -4,28 +4,29 @@ from sympy import S from sympy import IndexedBase, Indexed -from sympy import Mul, Matrix, Expr +from sympy import Mul, Matrix from sympy import Add, And, StrictLessThan, Eq -from sympy import Abs, Not, floor -from sympy import Symbol, Idx -from sympy import Basic, Function +from sympy import Not +from sympy import Symbol +from sympy import Basic from sympy import MutableDenseNDimArray as MArray from sympy.simplify import cse_main from sympy.core.containers import Tuple from sympde.topology import (dx1, dx2, dx3) from sympde.topology import SymbolicExpr -from sympde.topology import LogicalExpr, Jacobian +from sympde.topology import LogicalExpr from sympde.expr.evaluation import _split_test_function -from sympde.calculus.matrices import SymbolicDeterminant -from sympde.topology import SymbolicWeightedVolume, InterfaceMapping +from sympde.topology import SymbolicWeightedVolume from sympde.topology import Boundary, NormalVector, Interface +from sympde.topology.basic import BasicDomain +from sympde.topology.mapping import Mapping from sympde.topology.derivatives import get_index_logical_derivatives -from psydac.pyccel.ast.core import Assign, Product, AugAssign, For +from psydac.pyccel.ast.core import Assign, AugAssign, For from psydac.pyccel.ast.core import Variable, IndexedVariable, IndexedElement -from psydac.pyccel.ast.core import Slice, String, ValuedArgument +from psydac.pyccel.ast.core import Slice from psydac.pyccel.ast.core import EmptyNode, Import, While, Return, If from psydac.pyccel.ast.core import CodeBlock, FunctionDef, Comment from psydac.pyccel.ast.builtins import Range @@ -37,7 +38,6 @@ from .nodes import AtomicNode from .nodes import BasisAtom -from .nodes import PhysicalBasisValue from .nodes import LogicalBasisValue from .nodes import TensorQuadrature from .nodes import LocalTensorQuadratureBasis @@ -46,7 +46,6 @@ from .nodes import GlobalTensorQuadratureTestBasis from .nodes import GlobalTensorQuadratureTrialBasis from .nodes import GlobalTensorQuadratureBasis -from .nodes import TensorQuadratureBasis from .nodes import SplitArray from .nodes import Reduction from .nodes import LogicalValueNode @@ -72,12 +71,11 @@ from .nodes import WeightedVolumeQuadrature from .nodes import LengthDofTest -from .nodes import index_outer_dof_test from .nodes import index_dof_test, index_dof_trial from .nodes import index_deriv, Max, Min from .nodes import Zeros, ZerosLike, Array -from .fem import expand, expand_hdiv_hcurl +from .fem import expand #============================================================================== # TODO move it @@ -106,23 +104,24 @@ def is_scalar_array(var): #============================================================================== def parse(expr, settings, backend=None): """ - This function takes a Psydac Ast and returns a Pyccel Ast + A function which takes a Psydac AST and transforms it to a Pyccel AST. + + This function takes a Psydac abstract syntax tree (AST) and returns a + Pyccel AST. In turn, this can be translated to Python code through a call + to the function `pycode` from `psydac.pyccel.codegen.printing.pycode`. Parameters ---------- + expr : Any + Psydac AST, of any type supported by the Parser class. - expr: - psydac ast node - - settings : - dictionary that continas number of dimension, mappings and target if provided + settings : dict + Dictionary that contains number of dimension, mappings and target if provided Returns ------- - - ast : Pyccel Ast - pyccel abstract syntax tree that can be translated into a Python code - + ast : psydac.pyccel.ast.basic.PyccelAstNode | psydac.pyccel.ast.core.FunctionDef + Pyccel abstract syntax tree that can be translated into a Python code. """ psy_parser = Parser(settings, backend) ast = psy_parser.doit(expr) @@ -131,37 +130,82 @@ def parse(expr, settings, backend=None): #============================================================================== class Parser(object): """ - This class takes a Psyadac Ast and transforms it to a Pyccel Ast - by calling the Parser.doit method + A Parser which takes a Psydac AST and transforms it to a Pyccel AST. + + This class takes a Psydac AST and transforms it to the AST of an old and + reduced version of Pyccel, which is shipped as `psydac.pyccel`. This + "mini-Pyccel" is then used for printing the Python code. + + The parsing is performed by passing any object of a "supported type" to the + method `Parser.doit`. This in turn calls `Parser._visit` which starts a + recursive tree traversal through specialized `Parser._visit_` + methods. If successful, `Parser.doit` generally returns a `PyccelAstNode` + object (from `psydac.pyccel.ast.basic`). If the input object is a `DefNode` + (representing a function definition) it returns a `FunctionDef` object + (from `psydac.pyccel.ast.core`). The resulting Pyccel AST can be printed to + Python code using the function `pycode` from + `psydac.pyccel.codegen.printing.pycode`. + + By "supported types" we mean any `` type for which a method + `Parser._visit_` is provided. The matching is done by name, and + it also checks any superclasses listed in `.__mro__` in the given + order. + Parameters + ---------- + settings : dict[str, Any] + A dictionary with required integer arguments `dim` (number of dimensions) + and `nderiv` (maximum number of derivatives), required argument `target` + (symbolic domain of expression, of type `BasicDomain` from + `sympde.topology.basic`), and optional argument `mapping` (domain + `Mapping` from `sympde.topology.mapping`). + + backend : dict[str, Any] + The backend dictionary as defined in `psydac.api.settings`. """ def __init__(self, settings, backend=None): + # Copy settings, hence input dictionary is not modified settings = settings.copy() + # ... Pop values from settings and perform sanity checks dim = settings.pop('dim', None) if dim is None: raise ValueError('dim not provided') + else: + assert isinstance(dim, int) - self._dim = dim - # ... - + assert dim > 0 nderiv = settings.pop('nderiv', None) if nderiv is None: raise ValueError('nderiv not provided') - - self._nderiv = nderiv + else: + assert isinstance(nderiv, int) + assert nderiv >= 0 target = settings.pop('target', None) if target is None: raise ValueError('target not provided') + else: + assert isinstance(target, BasicDomain) - self._target = target - - self._mapping = settings.pop('mapping', None) + mapping = settings.pop('mapping', None) + if mapping is not None: + assert isinstance(mapping, Mapping) + # ... + # Store extracted values and other settings + self._dim = dim + self._nderiv = nderiv + self._target = target + self._mapping = mapping self._settings = settings - self.backend = backend + + # Store backend dictionary + if backend is not None: + assert isinstance(backend, dict) + assert 'name' in backend.keys() + self.backend = backend # TODO improve self.indices = {} @@ -171,7 +215,6 @@ def __init__(self, settings, backend=None): self.arguments = {} self.allocated = {} self._math_functions = () - @property def settings(self): diff --git a/psydac/api/basic.py b/psydac/api/basic.py index 2eb77abeb..608a13246 100644 --- a/psydac/api/basic.py +++ b/psydac/api/basic.py @@ -143,9 +143,12 @@ def __init__(self, expr, *, folder=None, comm=None, root=None, discrete_space=No # raise ValueError('can not find {} implementation'.format(f)) if ast: - self._save_code(self._generate_code(), backend=self.backend['name']) + python_code = self._generate_code() + self._save_code(python_code, backend=self.backend['name']) + + if comm is not None and comm.size > 1: + comm.Barrier() - if comm is not None and comm.size>1: comm.Barrier() # compile code self._compile() @@ -259,7 +262,6 @@ def _compile_pyccel(self, mod, verbose=False): openmp = self.backend["openmp"] _PYCCEL_FOLDER = self.backend['folder'] - # from pyccel.epyccel import epyccel from pyccel import epyccel fmod = epyccel(mod, openmp = openmp, diff --git a/psydac/api/discretization.py b/psydac/api/discretization.py index 69dc89679..1cea9397e 100644 --- a/psydac/api/discretization.py +++ b/psydac/api/discretization.py @@ -25,10 +25,11 @@ from gelato.expr import GltExpr as sym_GltExpr +from psydac.api.fem_bilinear_form import DiscreteBilinearForm as DiscreteBilinearForm_SF +from psydac.api.fem_sum_form import DiscreteSumForm from psydac.api.fem import DiscreteBilinearForm from psydac.api.fem import DiscreteLinearForm from psydac.api.fem import DiscreteFunctional -from psydac.api.fem import DiscreteSumForm from psydac.api.feec import DiscreteDerham from psydac.api.glt import DiscreteGltExpr from psydac.api.expr import DiscreteExpr @@ -40,7 +41,6 @@ from psydac.fem.partitioning import create_cart, construct_connectivity, construct_interface_spaces, construct_reduced_interface_spaces from psydac.fem.vector import MultipatchFemSpace, VectorFemSpace from psydac.cad.geometry import Geometry -from psydac.mapping.discrete import NurbsMapping from psydac.linalg.stencil import StencilVectorSpace from psydac.linalg.block import BlockVectorSpace @@ -547,6 +547,27 @@ def discretize(a, *args, **kwargs): domain_h = args[0] assert isinstance(domain_h, Geometry) domain = domain_h.domain + dim = domain.dim + + # The current implementation of the sum factorization algorithm does not support openMP parallelization + # It is not properly tested, whether this way of excluding openMP parallelized code from using the sum factorization algorithm works. + backend = kwargs.get('backend')# or None + assembly_backend = kwargs.get('assembly_backend')# or None + assembly_backend = backend or assembly_backend + openmp = False if assembly_backend is None else assembly_backend.get('openmp') + + # Since all keyword arguments are hidden in kwargs, we cannot set the + # defaults in the function signature. Here we set the defaults for + # sum_factorization using dict.setdefault: we default to True for + # bilinear forms in 3D, and to False otherwise. If the user has chosen + # differently, we let the code run and see what happens! + # + # We also default to False if the code is to be parallelized w/ OpenMP. + # TODO [YG 21.07.2025]: Drop this restriction + if isinstance(a, sym_BilinearForm): + default = (dim == 3 and not openmp) + kwargs.setdefault('sum_factorization', default) + mapping = domain_h.domain.mapping kwargs['symbolic_mapping'] = mapping @@ -593,7 +614,10 @@ def discretize(a, *args, **kwargs): # return DiscreteSesquilinearForm(a, kernel_expr, *args, **kwargs) if isinstance(a, sym_BilinearForm): - return DiscreteBilinearForm(a, kernel_expr, *args, **kwargs) + if kwargs.pop('sum_factorization'): + return DiscreteBilinearForm_SF(a, kernel_expr, *args, **kwargs) + else: + return DiscreteBilinearForm(a, kernel_expr, *args, **kwargs) elif isinstance(a, sym_LinearForm): return DiscreteLinearForm(a, kernel_expr, *args, **kwargs) diff --git a/psydac/api/equation.py b/psydac/api/equation.py index 69ef5a077..deba2d081 100644 --- a/psydac/api/equation.py +++ b/psydac/api/equation.py @@ -105,7 +105,9 @@ def __init__(self, expr, *args, **kwargs): self._lhs = discretize(expr.lhs, domain, trial_test, **kwargs) # ... - + # sum_factorization (sum factorization algorithm) is currently not supported for LinearForms (the rhs) + if 'sum_factorization' in kwargs: + kwargs.pop('sum_factorization') self._rhs = discretize(expr.rhs, domain, test_space, **kwargs) # ... diff --git a/psydac/api/fem.py b/psydac/api/fem.py index 21b3b4f6a..e8cfcd4d1 100644 --- a/psydac/api/fem.py +++ b/psydac/api/fem.py @@ -12,15 +12,8 @@ from sympde.expr import Norm as sym_Norm from sympde.expr import SemiNorm as sym_SemiNorm from sympde.topology import Boundary, Interface -from sympde.topology import VectorFunctionSpace -from sympde.topology import ProductSpace -from sympde.topology import H1SpaceType, L2SpaceType, UndefinedSpaceType from sympde.calculus.core import PlusInterfaceOperator -from psydac.api.basic import BasicDiscrete -from psydac.api.basic import random_string -from psydac.api.grid import QuadratureGrid, BasisValues -from psydac.api.utilities import flatten from psydac.linalg.stencil import StencilVector, StencilMatrix, StencilInterfaceMatrix from psydac.linalg.basic import ComposedLinearOperator from psydac.linalg.block import BlockVectorSpace, BlockVector, BlockLinearOperator @@ -31,132 +24,25 @@ from psydac.fem.projectors import knot_insertion_projection_operator from psydac.core.bsplines import find_span, basis_funs_all_ders from psydac.ddm.cart import InterfaceCartDecomposition +from psydac.api.basic import BasicDiscrete +from psydac.api.grid import QuadratureGrid, BasisValues +from psydac.api.utilities import flatten, random_string +from psydac.api.fem_common import ( + collect_spaces, + construct_test_space_arguments, + construct_trial_space_arguments, + construct_quad_grids_arguments, + reset_arrays, + do_nothing, + extract_stencil_mats, +) __all__ = ( - 'collect_spaces', - 'compute_diag_len', - 'construct_test_space_arguments', - 'construct_trial_space_arguments', - 'construct_quad_grids_arguments', - 'reset_arrays', - 'do_nothing', - 'extract_stencil_mats', 'DiscreteBilinearForm', 'DiscreteFunctional', 'DiscreteLinearForm', - 'DiscreteSumForm', ) -#============================================================================== -def collect_spaces(space, *args): - """ - This function collect the arguments used in the assembly function - - Parameters - ---------- - space: - the symbolic space - - args : - list of discrete space components like basis values, spans, ... - - Returns - ------- - args : - list of discrete space components elements used in the asembly - - """ - - if isinstance(space, ProductSpace): - spaces = space.spaces - indices = [] - i = 0 - for space in spaces: - if isinstance(space, VectorFunctionSpace): - if isinstance(space.kind, (H1SpaceType, L2SpaceType, UndefinedSpaceType)): - indices.append(i) - else: - indices += [i+j for j in range(space.ldim)] - i = i + space.ldim - else: - indices.append(i) - i = i + 1 - args = [[e[i] for i in indices] for e in args] - - elif isinstance(space, VectorFunctionSpace): - if isinstance(space.kind, (H1SpaceType, L2SpaceType, UndefinedSpaceType)): - args = [[e[0]] for e in args] - - return args - -#============================================================================== -def compute_diag_len(p, md, mc): - n = ((np.ceil((p+1)/mc)-1)*md).astype('int') - n = n-np.minimum(0, n-p)+p+1 - return n.astype('int') - -#============================================================================== -def construct_test_space_arguments(basis_values): - space = basis_values.space - test_basis = basis_values.basis - spans = basis_values.spans - test_degrees = space.degree - pads = space.pads - multiplicity = space.multiplicity - - test_basis, test_degrees, spans = collect_spaces(space.symbolic_space, test_basis, test_degrees, spans) - - test_basis = flatten(test_basis) - test_degrees = flatten(test_degrees) - spans = flatten(spans) - pads = flatten(pads) - multiplicity = flatten(multiplicity) - pads = [p*m for p,m in zip(pads, multiplicity)] - return test_basis, test_degrees, spans, pads - -def construct_trial_space_arguments(basis_values): - space = basis_values.space - trial_basis = basis_values.basis - trial_degrees = space.degree - pads = space.pads - multiplicity = space.multiplicity - trial_basis, trial_degrees = collect_spaces(space.symbolic_space, trial_basis, trial_degrees) - - trial_basis = flatten(trial_basis) - trial_degrees = flatten(trial_degrees) - pads = flatten(pads) - multiplicity = flatten(multiplicity) - pads = [p*m for p,m in zip(pads, multiplicity)] - return trial_basis, trial_degrees, pads - -#============================================================================== -def construct_quad_grids_arguments(grid, use_weights=True): - points = grid.points - if use_weights: - weights = grid.weights - quads = flatten(list(zip(points, weights))) - else: - quads = flatten(list(zip(points))) - - nquads = flatten(grid.nquads) - n_elements = grid.n_elements - return n_elements, quads, nquads - -def reset_arrays(*args): - for a in args: - a[:]= 0.j if a.dtype==complex else 0. - -def do_nothing(*args): return 0 - -def extract_stencil_mats(mats): - new_mats = [] - for M in mats: - if isinstance(M, (StencilInterfaceMatrix, StencilMatrix)): - new_mats.append(M) - elif isinstance(M, ComposedLinearOperator): - new_mats += [i for i in M.multiplicants if isinstance(i, (StencilInterfaceMatrix, StencilMatrix))] - return new_mats - #============================================================================== class DiscreteBilinearForm(BasicDiscrete): """ @@ -430,7 +316,7 @@ def __init__(self, expr, kernel_expr, domain_h, spaces, *, nquads, with_openmp = (assembly_backend['name'] == 'pyccel' and assembly_backend['openmp']) if assembly_backend else False # Construct the arguments to be passed to the assemble() function, which is stored in self._func - self._args, self._threads_args = self.construct_arguments(with_openmp=with_openmp) + self._args, self._threads_args = self.construct_arguments(with_openmp) @property def domain(self): @@ -508,7 +394,7 @@ def assemble(self, *, reset=True, **kwargs): trial = True, grid = self.grid[0] ) - bs, d, s, p = construct_test_space_arguments(basis_v) + bs, d, s, p, mult = construct_test_space_arguments(basis_v) basis += bs spans += s degrees += [np.int64(a) for a in d] @@ -525,8 +411,6 @@ def assemble(self, *, reset=True, **kwargs): else: args = self._args -# args = args + self._element_loop_starts + self._element_loop_ends - if reset: reset_arrays(*self.global_matrices) @@ -582,9 +466,9 @@ def construct_arguments(self, with_openmp=False): Extra arguments used in the assembly method in case with_openmp=True. """ - test_basis, test_degrees, spans, pads = construct_test_space_arguments(self.test_basis) - trial_basis, trial_degrees, pads = construct_trial_space_arguments(self.trial_basis) - n_elements, quads, quad_degrees = construct_quad_grids_arguments(self.grid[0], use_weights=False) + test_basis, test_degrees, spans, pads, mult = construct_test_space_arguments(self.test_basis) + trial_basis, trial_degrees, pads, mult = construct_trial_space_arguments(self.trial_basis) + n_elements, quads, quad_degrees = construct_quad_grids_arguments(self.grid[0], use_weights=False) if len(self.grid)>1: quads = [*quads, *self.grid[1].points] @@ -1200,7 +1084,7 @@ def assemble(self, *, reset=True, **kwargs): trial = True, grid = self.grid ) - bs, d, s, p = construct_test_space_arguments(basis_v) + bs, d, s, p, m = construct_test_space_arguments(basis_v) basis += bs spans += s degrees += [np.int64(a) for a in d] @@ -1267,7 +1151,7 @@ def construct_arguments(self, with_openmp=False): Extra arguments used in the assembly method in case with_openmp=True. """ - tests_basis, tests_degrees, spans, pads = construct_test_space_arguments(self.test_basis) + tests_basis, tests_degrees, spans, pads, mult = construct_test_space_arguments(self.test_basis) n_elements, quads, nquads = construct_quad_grids_arguments(self.grid, use_weights=False) global_pads = self.space.coeff_space.pads @@ -1658,95 +1542,3 @@ def assemble(self, **kwargs): else: raise NotImplementedError('TODO') return v - -#============================================================================== -class DiscreteSumForm(BasicDiscrete): - - def __init__(self, a, kernel_expr, *args, **kwargs): - # TODO Uncomment when the SesquilinearForm exist in SymPDE - #if not isinstance(a, (sym_BilinearForm, sym_SesquilinearForm, sym_LinearForm, sym_Functional)): - # raise TypeError('> Expecting a symbolic BilinearForm, SesquilinearForm, LinearForm, Functional') - if not isinstance(a, (sym_BilinearForm, sym_LinearForm, sym_Functional)): - raise TypeError('> Expecting a symbolic BilinearForm, LinearForm, Functional') - - self._expr = a - backend = kwargs.pop('backend', None) - self._backend = backend - - folder = kwargs.get('folder', None) - self._folder = self._initialize_folder(folder) - - # create a module name if not given - tag = random_string(8) - - # ... - forms = [] - free_args = [] - self._kernel_expr = kernel_expr - operator = None - for e in kernel_expr: - if isinstance(a, sym_LinearForm): - kwargs['update_ghost_regions'] = False - ah = DiscreteLinearForm(a, e, *args, backend=backend, **kwargs) - kwargs['vector'] = ah._vector - operator = ah._vector - - # TODO Uncomment when the SesquilinearForm exist in SymPDE - # elif isinstance(a, sym_SesquilinearForm): - # kwargs['update_ghost_regions'] = False - # ah = DiscreteSesquilinearForm(a, e, *args, assembly_backend=backend, **kwargs) - # kwargs['matrix'] = ah._matrix - # operator = ah._matrix - - elif isinstance(a, sym_BilinearForm): - kwargs['update_ghost_regions'] = False - ah = DiscreteBilinearForm(a, e, *args, assembly_backend=backend, **kwargs) - kwargs['matrix'] = ah._matrix - operator = ah._matrix - - elif isinstance(a, sym_Functional): - ah = DiscreteFunctional(a, e, *args, backend=backend, **kwargs) - - forms.append(ah) - free_args.extend(ah.free_args) - - if isinstance(a, sym_BilinearForm): - is_broken = len(args[0].domain)>1 - if self._backend is not None and is_broken: - for mat in kwargs['matrix']._blocks.values(): - mat.set_backend(backend) - elif self._backend is not None: - kwargs['matrix'].set_backend(backend) - - self._forms = forms - self._operator = operator - self._free_args = tuple(set(free_args)) - self._is_functional = isinstance(a, sym_Functional) - # ... - - @property - def forms(self): - return self._forms - - @property - def free_args(self): - return self._free_args - - @property - def is_functional(self): - return self._is_functional - - def assemble(self, *, reset=True, **kwargs): - if not self.is_functional: - if reset : - reset_arrays(*[i for M in self.forms for i in M.global_matrices]) - - for form in self.forms: - form.assemble(reset=False, **kwargs) - self._operator.exchange_assembly_data() - return self._operator - else: - M = [form.assemble(**kwargs) for form in self.forms] - M = np.sum(M) - return M - diff --git a/psydac/api/fem_bilinear_form.py b/psydac/api/fem_bilinear_form.py new file mode 100644 index 000000000..8af05df83 --- /dev/null +++ b/psydac/api/fem_bilinear_form.py @@ -0,0 +1,2226 @@ +import sys +import os +import importlib + +import numpy as np + +from sympy import ImmutableDenseMatrix, Matrix, Symbol, sympify +from sympy.tensor.indexed import Indexed, IndexedBase +from sympy.simplify import cse_main + +from pyccel import epyccel + +from sympde.topology.basic import Boundary, Interface +from sympde.topology.mapping import Mapping, SymbolicExpr +from sympde.topology.space import ScalarFunction, VectorFunction, IndexedVectorFunction +from sympde.topology.derivatives import get_atom_logical_derivatives +from sympde.topology.derivatives import _logical_partial_derivatives +from sympde.topology.derivatives import get_index_logical_derivatives +from sympde.topology.derivatives import get_max_logical_partial_derivatives # NOTE [YG 31.07.2025]: Maybe use the one in ast.utilities +from sympde.expr.expr import BilinearForm +from sympde.expr.evaluation import KernelExpression, TerminalExpr +from sympde.calculus.core import PlusInterfaceOperator + +from psydac.cad.geometry import Geometry +from psydac.mapping.discrete import SplineMapping, NurbsMapping +from psydac.fem.basic import FemSpace, FemField +from psydac.fem.vector import VectorFemSpace +from psydac.linalg.stencil import StencilMatrix +from psydac.linalg.block import BlockVectorSpace, BlockLinearOperator +from psydac.api.grid import QuadratureGrid, BasisValues +from psydac.api.settings import PSYDAC_BACKENDS +from psydac.api.utilities import flatten, random_string +from psydac.api.fem_common import ( + compute_imports, + compute_max_nderiv, + compute_free_arguments, + construct_test_space_arguments, + construct_trial_space_arguments, + construct_quad_grids_arguments, + reset_arrays, + do_nothing, + extract_stencil_mats, +) + +# TODO [YG 01.08.2025]: Avoid importing anything from psydac.pyccel +from psydac.pyccel.ast.core import _atomic, Assign + +__all__ = ('DiscreteBilinearForm',) + +NoneType = type(None) + +#============================================================================== +class DiscreteBilinearForm: + """ + Discrete bilinear form ready to be assembled into a matrix. + + This class represents the concept of a discrete bilinear form in Psydac. + Instances of this class generate an appropriate matrix assembly kernel, + allocate the matrix if not provided, and prepare a list of arguments for + the kernel. + + An implementation of the sum factorization algorithm is used to assemble + the matrix. + + Parameters + ---------- + + expr : sympde.expr.expr.BilinearForm + The symbolic bilinear form. + + kernel_expr : list or tuple of sympde.expr.evaluation.KernelExpression + The atomic representation of the bilinear form. + + domain_h : psydac.cad.geometry.Geometry + The discretized domain. + + spaces : list of psydac.fem.basic.FemSpace + The discrete trial and test spaces. + + nquads : list or tuple of int + The number of quadrature points used in the assembly kernel along each + direction. + + matrix : psydac.linalg.stencil.StencilMatrix or psydac.linalg.block.BlockLinearOperator, optional + The matrix that we assemble into. If not provided, a new matrix is + created with the appropriate domain and codomain (default: None). + + update_ghost_regions : bool, default=True + Accumulate the contributions of the neighbouring processes. + + backend : dict, optional + The backend used to accelerate the computing kernels. + The backend dictionaries are defined in the file psydac/api/settings.py + + assembly_backend : dict, optional + The backend used to accelerate the assembly kernel. + The backend dictionaries are defined in the file psydac/api/settings.py + + linalg_backend : dict, optional + The backend used to accelerate the computing kernels of the linear operator. + The backend dictionaries are defined in the file psydac/api/settings.py + + symbolic_mapping : sympde.topology.mapping.Mapping, optional + The symbolic mapping which defines the physical domain of the bilinear form. + + See Also + -------- + DiscreteLinearForm + DiscreteFunctional + DiscreteSumForm + + """ + def __init__(self, expr, kernel_expr, domain_h, spaces, *, nquads, + matrix=None, update_ghost_regions=True, backend=None, + linalg_backend=None, assembly_backend=None, + symbolic_mapping=None): + + #... Sanity checks + assert isinstance(expr, BilinearForm) + assert isinstance(domain_h, Geometry) + for space in spaces: + assert isinstance(space, FemSpace) + for nquad in nquads: + assert isinstance(nquad, int) + assert nquad > 0 + assert isinstance(matrix, (NoneType, StencilMatrix, BlockLinearOperator)) + assert isinstance(update_ghost_regions, bool) + assert isinstance( backend, (NoneType, dict)) + assert isinstance( linalg_backend, (NoneType, dict)) + assert isinstance(assembly_backend, (NoneType, dict)) + assert isinstance(symbolic_mapping, (NoneType, Mapping)) + #... + + if isinstance(kernel_expr, (tuple, list)): + if len(kernel_expr) == 1: + kernel_expr = kernel_expr[0] + else: + raise ValueError('> Expecting only one kernel') + assert isinstance(kernel_expr, KernelExpression) + + self._kernel_expr = kernel_expr + self._expr = expr + self._target = kernel_expr.target + self._domain = domain_h.domain + self._spaces = spaces + self._matrix = matrix + + domain = self.domain + target = self.target + + # ... + if len(domain) > 1: + i, j = self.get_space_indices_from_target(domain, target) + test_space = self.spaces[1].spaces[i] + trial_space = self.spaces[0].spaces[j] + if isinstance(target, Interface): + m,_ = self.get_space_indices_from_target(domain, target.minus) + p,_ = self.get_space_indices_from_target(domain, target.plus) + mapping_m = list(domain_h.mappings.values())[m] + mapping_p = list(domain_h.mappings.values())[p] + mapping = (mapping_m, mapping_p) if mapping_m else None + else: + mapping = list(domain_h.mappings.values())[i] + else: + trial_space = self.spaces[0] + test_space = self.spaces[1] + mapping = list(domain_h.mappings.values())[0] + + self._mapping = mapping + + is_rational_mapping = False + mapping_space = None + if (mapping is not None) and not isinstance(target, Interface): + is_rational_mapping = isinstance(mapping, NurbsMapping) + mapping_space = mapping.space + elif (mapping is not None) and isinstance(target, Interface): + is_rational_mapping = (isinstance(mapping[0], NurbsMapping), isinstance(mapping[1], NurbsMapping)) + mapping_space = (mapping[0].space, mapping[1].space) + + self._is_rational_mapping = is_rational_mapping + # ... + + if isinstance(test_space.coeff_space, BlockVectorSpace): + coeff_space = test_space.coeff_space.spaces[0] + else: + coeff_space = test_space.coeff_space + + self._coeff_space = coeff_space + self._num_threads = 1 + if coeff_space.parallel and coeff_space.cart.num_threads > 1: + self._num_threads = coeff_space.cart.num_threads + + self._update_ghost_regions = update_ghost_regions + + # In case of multiple patches, if the communicator is MPI_COMM_NULL, we do not generate the assembly code + # because the patch is not owned by the MPI rank. + if coeff_space.parallel and coeff_space.cart.is_comm_null: + self._free_args = () + self._func = do_nothing + self._args = () + self._threads_args = () + self._global_matrices = () + self._update_ghost_regions = False + return + + # ... + test_ext = None + trial_ext = None + if isinstance(target, Boundary): + axis = target.axis + test_ext = target.ext + trial_ext = target.ext + elif isinstance(target, Interface): + # this part treats the cases of: + # integral(v_minus * u_plus) + # integral(v_plus * u_minus) + # the other cases, integral(v_minus * u_minus) and integral(v_plus * u_plus) + # are converted to boundary integrals by Sympde + axis = target.axis + test = self.kernel_expr.test + trial = self.kernel_expr.trial + test_target = target.plus if isinstance( test, PlusInterfaceOperator) else target.minus + trial_target = target.plus if isinstance(trial, PlusInterfaceOperator) else target.minus + test_ext = test_target.ext + trial_ext = trial_target.ext + ncells = tuple(max(i, j) for i, j in zip(test_space.ncells, trial_space.ncells)) + if isinstance(trial_space, VectorFemSpace): + spaces = [] + for sp in trial_space.spaces: + if (trial_target.axis, trial_target.ext) in sp.interfaces: + spaces.append(sp.get_refined_space(ncells).interfaces[trial_target.axis, trial_target.ext]) + + if len(spaces) == len(trial_space.spaces): + sym_space = trial_space.symbolic_space + trial_space = VectorFemSpace(*spaces) + trial_space.symbolic_space = sym_space + + elif (trial_target.axis, trial_target.ext) in trial_space.interfaces: + sym_space = trial_space.symbolic_space + trial_space = trial_space.get_refined_space(ncells).interfaces[trial_target.axis, trial_target.ext] + trial_space.symbolic_space = sym_space + + test_space = test_space.get_refined_space(ncells) + self._test_ext = test_target.ext + self._trial_ext = trial_target.ext + + #... + + # Assuming that all vector spaces (and their Cartesian decomposition, + # if any) are compatible with each other, extract the first available + # vector space from which (starts, ends, npts) will be read: + starts = coeff_space.starts + ends = coeff_space.ends + npts = coeff_space.npts + + # MPI communicator + comm = coeff_space.cart.comm if coeff_space.parallel else None + + # Store the MPI communicator (or None) + self._comm = comm + + #... + # Get default backend from environment, or use 'python'. + default_backend = PSYDAC_BACKENDS.get(os.environ.get('PSYDAC_BACKEND'))\ + or PSYDAC_BACKENDS['python'] + + # Backends for code generation + assembly_backend = backend or assembly_backend + linalg_backend = backend or linalg_backend + + # Store backend dictionary + self._backend = assembly_backend or default_backend + #... + + # TODO: remove + # BasicDiscrete generates the assembly code and sets the following attributes that are used afterwards: + # self._func, self._free_args, self._max_nderiv and self._backend +# BasicDiscrete.__init__(self, expr, kernel_expr, comm=comm, root=0, discrete_space=discrete_space, +# nquads=nquads, is_rational_mapping=is_rational_mapping, mapping=symbolic_mapping, +# mapping_space=mapping_space, num_threads=self._num_threads, backend=assembly_backend) + + + #... Compute the string with all the imports + texpr = kernel_expr + sym_expr = SymbolicExpr(texpr.expr) + imports = compute_imports(sym_expr, spaces=(trial_space, test_space), openmp=False) + indent = 4 + glue = '\n' + ' '* indent + imports_str = glue.join([f"from {m} import {', '.join(vars)}" + for m, vars in imports.items()]) + + # Broadcast the import information (sqrt, sin, pi, ...) to all processes + if (comm is not None) and (comm.size > 1): + imports_str = comm.bcast(imports_str, root=0) + + # Store the imports string as it will be used by make_file() + self._imports_string = imports_str + #... + + # Compute the highest order of derivation in the kernel expression + self._max_nderiv = compute_max_nderiv(kernel_expr) + + # TODO [YG 31.07.2025]: Implement this + self._free_args = compute_free_arguments(expr, kernel_expr) + + #... Handle the special case where the current MPI process does not need to do anything + if isinstance(target, (Boundary, Interface)): + + # If process does not own the boundary or interface, do not assemble anything + if test_ext == -1: + if starts[axis] != 0: + self._func = do_nothing + + elif test_ext == 1: + if ends[axis] != npts[axis]-1: + self._func = do_nothing + + # In case of target==Interface, we only use the MPI ranks that are on the interface to assemble the BilinearForm + if self._func == do_nothing and isinstance(target, Interface): + self._free_args = () + self._args = () + self._global_matrices = () + self._threads_args = () + return + #... + + #... Build the quadrature grids + if isinstance(target, Boundary): + test_grid = QuadratureGrid( test_space, axis=axis, ext= test_ext, nquads=nquads) + trial_grid = QuadratureGrid(trial_space, axis=axis, ext=trial_ext, nquads=nquads) + self._grid = (test_grid,) + elif isinstance(target, Interface): + # this part treats the cases of: + # integral(v_minus * u_plus) + # integral(v_plus * u_minus) + # the other cases, integral(v_minus * u_minus) and integral(v_plus * u_plus) + # are converted to boundary integrals by Sympde + test_grid = QuadratureGrid( test_space, axis=axis, ext= test_ext, nquads=nquads) + trial_grid = QuadratureGrid(trial_space, axis=axis, ext=trial_ext, nquads=nquads) + self._grid = (test_grid, trial_grid) if test_target == target.minus else (trial_grid, test_grid) + self._test_ext = test_target.ext + self._trial_ext = trial_target.ext + else: + test_grid = QuadratureGrid( test_space, nquads=nquads) + trial_grid = QuadratureGrid(trial_space, nquads=nquads) + self._grid = (test_grid,) + #... + + # Extract the basis function values on the quadrature grids + self._test_basis = BasisValues( + test_space, + nderiv = self.max_nderiv, + nquads = nquads, + trial = False, + grid = test_grid + ) + self._trial_basis = BasisValues( + trial_space, + nderiv = self.max_nderiv, + nquads = nquads, + trial = True , + grid = trial_grid + ) + + # Allocate the output matrix, if needed + self.allocate_matrices(linalg_backend) + + # Determine whether OpenMP instructions were generated + self._with_openmp = (assembly_backend['name'] == 'pyccel' and assembly_backend['openmp']) if assembly_backend else False + + # Construct the arguments to be passed to the assemble() function, which is stored in self._func + # First we generate the assembly file + + # pyccelize process of computing the test_trial arrays + # currently set to False, as a Python 3.9 test fails, and due to the "speed up" not being significant + self._pyccelize_test_trial_computation = False + + # no openmp support yet: with_openmp is not passed + self._args, self._threads_args = self.construct_arguments_generate_assembly_file() + + #-------------------------------------------------------------------------- + @property + def comm(self): + return self._comm + + @property + def expr(self): + return self._expr + + @property + def kernel_expr(self): + return self._kernel_expr + + @property + def domain(self): + return self._domain + + @property + def mapping(self): + return self._mapping + + @property + def is_rational_mapping(self): + return self._is_rational_mapping + + @property + def target(self): + return self._target + + @property + def spaces(self): + return self._spaces + + @property + def test_basis(self): + return self._test_basis + + @property + def trial_basis(self): + return self._trial_basis + + @property + def grid(self): + return self._grid + + @property + def nquads(self): + return self._grid[0].nquads + + @property + def free_args(self): + return self._free_args + + @property + def max_nderiv(self): + # TODO: compute with read_BilinearForm and store + return self._max_nderiv + + @property + def backend(self): + return self._backend + + @property + def args(self): + return self._args + + @property + def global_matrices(self): + return self._global_matrices + + #-------------------------------------------------------------------------- + def allocate_matrices(self, backend=None): + """ + Allocate the global matrices used in the assembly method. + In this method we allocate only the matrices that are computed in the self._target domain, + we also avoid double allocation if we have many DiscreteLinearForm that are defined on the same self._target domain. + + Parameters + ---------- + backend : dict + The backend used to accelerate the computing kernels. + + """ + global_mats = {} + + expr = self.kernel_expr.expr + target = self.kernel_expr.target + test_degree = np.array(self.test_basis.space.degree) + trial_degree = np.array(self.trial_basis.space.degree) + test_space = self.spaces[1].coeff_space + trial_space = self.spaces[0].coeff_space + test_fem_space = self.spaces[1] + trial_fem_space = self.spaces[0] + domain = self.domain + is_broken = len(domain) > 1 + is_conformal = True + + if isinstance(expr, (ImmutableDenseMatrix, Matrix)): + if not isinstance(test_degree[0],(list, tuple, np.ndarray)): + test_degree = [test_degree] + + if not isinstance(trial_degree[0],(list, tuple, np.ndarray)): + trial_degree = [trial_degree] + + pads = np.empty((len(test_degree),len(trial_degree),len(test_degree[0])), dtype=int) + for i in range(len(test_degree)): + for j in range(len(trial_degree)): + td = test_degree[i] + trd = trial_degree[j] + pads[i,j][:] = np.array([td, trd]).max(axis=0) + else: + pads = np.maximum(test_degree, trial_degree) + + if self._matrix is None and (is_broken or isinstance(expr, (ImmutableDenseMatrix, Matrix))): + self._matrix = BlockLinearOperator(trial_space, test_space) + + if is_broken: + i, j = self.get_space_indices_from_target(domain, target) + test_fem_space = self.spaces[1].spaces[i] + trial_fem_space = self.spaces[0].spaces[j] + test_space = test_space.spaces[i] + trial_space = trial_space.spaces[j] + ncells = tuple(max(i,j) for i,j in zip(test_fem_space.ncells, trial_fem_space.ncells)) + is_conformal = tuple(test_fem_space.ncells) == ncells and tuple(trial_fem_space.ncells) == ncells + if is_broken and not is_conformal and not i==j: + use_restriction = all(trn>=tn for trn,tn in zip(trial_fem_space.ncells, test_fem_space.ncells)) + use_prolongation = not use_restriction + + else: + ncells = tuple(max(i,j) for i,j in zip(test_fem_space.ncells, trial_fem_space.ncells)) + i=0 + j=0 + #else so initialisation causing bug on line 682 + + if isinstance(expr, (ImmutableDenseMatrix, Matrix)): # case of system of equations + + if is_broken: #multi patch + if not self._matrix[i,j]: + mat = BlockLinearOperator(trial_fem_space.get_refined_space(ncells).coeff_space, test_fem_space.get_refined_space(ncells).coeff_space) + if not is_conformal and not i==j: + if use_restriction: + Ps = [knot_insertion_projection_operator(ts.get_refined_space(ncells), ts) for ts in test_fem_space.spaces] + P = BlockLinearOperator(test_fem_space.get_refined_space(ncells).coeff_space, test_fem_space.coeff_space) + for ni,Pi in enumerate(Ps): + P[ni,ni] = Pi + + mat = ComposedLinearOperator(trial_space, test_space, P, mat) + + elif use_prolongation: + Ps = [knot_insertion_projection_operator(trs, trs.get_refined_space(ncells)) for trs in trial_fem_space.spaces] + P = BlockLinearOperator(trial_fem_space.coeff_space, trial_fem_space.get_refined_space(ncells).coeff_space) + for ni,Pi in enumerate(Ps): + P[ni,ni] = Pi + + mat = ComposedLinearOperator(trial_space, test_space, mat, P) + + self._matrix[i,j] = mat + + matrix = self._matrix[i,j] + else: # single patch + matrix = self._matrix + + shape = expr.shape + for k1 in range(shape[0]): + for k2 in range(shape[1]): + if expr[k1,k2].is_zero: + continue + + if isinstance(test_fem_space, VectorFemSpace): + ts_space = test_fem_space.get_refined_space(ncells).coeff_space.spaces[k1] + else: + ts_space = test_fem_space.get_refined_space(ncells).coeff_space + + if isinstance(trial_fem_space, VectorFemSpace): + tr_space = trial_fem_space.get_refined_space(ncells).coeff_space.spaces[k2] + else: + tr_space = trial_fem_space.get_refined_space(ncells).coeff_space + + if is_conformal and matrix[k1, k2]: + global_mats[k1, k2] = matrix[k1, k2] + elif not i == j: # assembling in an interface (type(target) == Interface) + axis = target.axis + ext_d = self._trial_ext + ext_c = self._test_ext + test_n = self. test_basis.space.spaces[k1].spaces[axis].nbasis + test_s = self. test_basis.space.spaces[k1].coeff_space.starts[axis] + trial_n = self.trial_basis.space.spaces[k2].spaces[axis].nbasis + cart = self.trial_basis.space.spaces[k2].coeff_space.cart + trial_s = cart.global_starts[axis][cart._coords[axis]] + + s_d = trial_n - trial_s - trial_degree[k2][axis] - 1 if ext_d == 1 else 0 + s_c = test_n - trial_s - test_degree[k1][axis] - 1 if ext_c == 1 else 0 + + # We only handle the case where direction = 1 + direction = target.ornt + if domain.dim == 2: + assert direction == 1 + elif domain.dim == 3: + assert all(d==1 for d in direction) + + direction = 1 + flip = [direction]*domain.dim + flip[axis] = 1 + if self._func != do_nothing: + global_mats[k1, k2] = StencilInterfaceMatrix(tr_space, ts_space, + s_d, s_c, + axis, axis, + ext_d, ext_c, + pads=tuple(pads[k1, k2]), + flip=flip) + else: + global_mats[k1, k2] = StencilMatrix(tr_space, ts_space, pads = tuple(pads[k1, k2])) + + if is_conformal: + matrix[k1, k2] = global_mats[k1, k2] + elif use_restriction: + matrix.multiplicants[-1][k1, k2] = global_mats[k1, k2] + elif use_prolongation: + matrix.multiplicants[0][k1, k2] = global_mats[k1, k2] + + else: # case of scalar equation + if is_broken: # multi-patch + if self._matrix[i, j]: + global_mats[i, j] = self._matrix[i, j] + + elif not i == j: # assembling in an interface (type(target) == Interface) + axis = target.axis + ext_d = self._trial_ext + ext_c = self._test_ext + test_n = self.test_basis.space.spaces[axis].nbasis + test_s = self.test_basis.space.coeff_space.starts[axis] + trial_n = self.trial_basis.space.spaces[axis].nbasis + cart = self.trial_basis.space.coeff_space.cart + trial_s = cart.global_starts[axis][cart._coords[axis]] + + s_d = trial_n - trial_s - trial_degree[axis] - 1 if ext_d == 1 else 0 + s_c = test_n - trial_s - test_degree[axis] - 1 if ext_c == 1 else 0 + + # We only handle the case where direction = 1 + direction = target.ornt + if domain.dim == 2: + assert direction == 1 + elif domain.dim == 3: + assert all(d==1 for d in direction) + + direction = 1 + flip = [direction]*domain.dim + flip[axis] = 1 + + if self._func != do_nothing: + mat = StencilInterfaceMatrix(trial_fem_space.get_refined_space(ncells).coeff_space, + test_fem_space.get_refined_space(ncells).coeff_space, + s_d, s_c, + axis, axis, + ext_d, ext_c, + flip=flip) + if not is_conformal: + if use_restriction: + P = knot_insertion_projection_operator(test_fem_space.get_refined_space(ncells), test_fem_space) + mat = ComposedLinearOperator(trial_space, test_space, P, mat) + elif use_prolongation: + P = knot_insertion_projection_operator(trial_fem_space, trial_fem_space.get_refined_space(ncells)) + mat = ComposedLinearOperator(trial_space, test_space, mat, P) + + global_mats[i, j] = mat + + # define part of the global matrix as a StencilMatrix + else: + global_mats[i, j] = StencilMatrix(trial_space, test_space, pads=tuple(pads)) + + if (i, j) in global_mats: + self._matrix[i, j] = global_mats[i, j] + + + # in single patch case, we define the matrices needed for the patch + else: + if self._matrix: + global_mats[0, 0] = self._matrix + else: + global_mats[0, 0] = StencilMatrix(trial_space, test_space, pads=tuple(pads)) + + self._matrix = global_mats[0, 0] + + # Set the backend of our matrices if given + if backend is not None and is_broken: + for mat in global_mats.values(): + mat.set_backend(backend) + elif backend is not None: + self._matrix.set_backend(backend) + + self._global_matrices = [M._data for M in extract_stencil_mats(global_mats.values())] + + #-------------------------------------------------------------------------- + def assemble(self, *, reset=True, **kwargs): + """ + This method assembles the left hand side Matrix by calling the private method `self._func` with proper arguments. + + In the complex case, this function returns the matrix conjugate. This comes from the fact that the + problem `a(u,v)=b(v)` is discretized as `A @ conj(U) = B` due to the antilinearity of `a` in the first variable. + Thus, to obtain `U`, the assemble function returns `conj(A)`. + + TODO: remove these lines when the dot product is changed for complex. + For now, since the dot product does not compute the conjugate in the complex case. We do not use the conjugate in the assemble function. + It should work if the complex only comes from the `rhs` in the linear form. + """ + + if self._free_args: + basis = [] + spans = [] + degrees = [] + pads = [] + coeffs = [] + consts = [] + + for key in self._free_args: + v = kwargs[key] + + if len(self.domain) > 1 and isinstance(v, FemField) and (v.space.is_multipatch or v.space.is_vector_valued): + assert v.space.is_multipatch ## [MCP 27.03.2025] should hold since len(domain) > 1. If Ok we can simplify above if + i, j = self.get_space_indices_from_target(self.domain, self.target) + assert i == j + v = v[i] + if isinstance(v, FemField): + assert len(self.grid) == 1 + if not v.coeffs.ghost_regions_in_sync: + v.coeffs.update_ghost_regions() + basis_v = BasisValues( + v.space, + nderiv = self.max_nderiv, + nquads = self.nquads, + trial = True, + grid = self.grid[0] + ) + bs, d, s, p, mult = construct_test_space_arguments(basis_v) + basis += bs + spans += s + degrees += [np.int64(a) for a in d] + pads += [np.int64(a) for a in p] + if v.space.is_multipatch or v.space.is_vector_valued: + coeffs += (e._data for e in v.coeffs) + else: + coeffs += (v.coeffs._data, ) + else: + consts += (v, ) + + args = (*self.args, *basis, *spans, *degrees, *pads, *coeffs, *consts) + + else: + args = self._args + + if reset: + reset_arrays(*self.global_matrices) + + self._func(*args, *self._threads_args) + if self._matrix and self._update_ghost_regions: + self._matrix.exchange_assembly_data() + + # TODO : uncomment this line when the conjugate is applied on the dot product in the complex case + #self._matrix.conjugate(out=self._matrix) + + if self._matrix: + self._matrix.ghost_regions_in_sync = False + + return self._matrix + + #-------------------------------------------------------------------------- + @property + def _assembly_template_head(self): + """A template for the 'head' of the assembly function. Only used with the sum factorization algorithm.""" + code = '''def assemble_matrix_{FILE_ID}({MAPPING_PART_1} +{SPAN} {MAPPING_PART_2} + global_x1 : "float64[:,:]", global_x2 : "float64[:,:]", global_x3 : "float64[:,:]", + {MAPPING_PART_3} + n_element_1 : "int64", n_element_2 : "int64", n_element_3 : "int64", + nq1 : "int64", nq2 : "int64", nq3 : "int64", + pad1 : "int64", pad2 : "int64", pad3 : "int64", + {MAPPING_PART_4} +{G_MAT}{NEW_ARGS}{FIELD_ARGS}): + + from numpy import abs as Abs + {imports} +''' + return code + + #-------------------------------------------------------------------------- + @property + def _assembly_template_body_bspline(self): + """A template for the 'body' of the assembly function (when using a spline mapping). Only used with the sum factorization algorithm.""" + code = ''' + arr_coeffs_x = zeros((1 + test_mapping_p1, 1 + test_mapping_p2, 1 + test_mapping_p3), dtype='float64') + arr_coeffs_y = zeros((1 + test_mapping_p1, 1 + test_mapping_p2, 1 + test_mapping_p3), dtype='float64') + arr_coeffs_z = zeros((1 + test_mapping_p1, 1 + test_mapping_p2, 1 + test_mapping_p3), dtype='float64') + +{F_COEFFS_ZEROS} + +{KEYS} + for k_1 in range(n_element_1): + span_mapping_1 = global_span_mapping_1[k_1] +{LOCAL_SPAN}{F_SPAN_1}{A1} + for q_1 in range(nq1): + for k_2 in range(n_element_2): + span_mapping_2 = global_span_mapping_2[k_2] +{F_SPAN_2} + for q_2 in range(nq2): + for k_3 in range(n_element_3): + span_mapping_3 = global_span_mapping_3[k_3] +{F_SPAN_3}{F_COEFFS} + arr_coeffs_x[:,:,:] = global_arr_coeffs_x[test_mapping_p1 + span_mapping_1 - test_mapping_p1:test_mapping_p1 + 1 + span_mapping_1,test_mapping_p2 + span_mapping_2 - test_mapping_p2:test_mapping_p2 + 1 + span_mapping_2,test_mapping_p3 + span_mapping_3 - test_mapping_p3:test_mapping_p3 + 1 + span_mapping_3] + arr_coeffs_y[:,:,:] = global_arr_coeffs_y[test_mapping_p1 + span_mapping_1 - test_mapping_p1:test_mapping_p1 + 1 + span_mapping_1,test_mapping_p2 + span_mapping_2 - test_mapping_p2:test_mapping_p2 + 1 + span_mapping_2,test_mapping_p3 + span_mapping_3 - test_mapping_p3:test_mapping_p3 + 1 + span_mapping_3] + arr_coeffs_z[:,:,:] = global_arr_coeffs_z[test_mapping_p1 + span_mapping_1 - test_mapping_p1:test_mapping_p1 + 1 + span_mapping_1,test_mapping_p2 + span_mapping_2 - test_mapping_p2:test_mapping_p2 + 1 + span_mapping_2,test_mapping_p3 + span_mapping_3 - test_mapping_p3:test_mapping_p3 + 1 + span_mapping_3] + for q_3 in range(nq3): + x = 0.0 + y = 0.0 + z = 0.0 + + x_x1 = 0.0 + x_x2 = 0.0 + x_x3 = 0.0 + y_x1 = 0.0 + y_x2 = 0.0 + y_x3 = 0.0 + z_x1 = 0.0 + z_x2 = 0.0 + z_x3 = 0.0 +{D2_1} + +{F_INIT} + +{F_ASSIGN_LOOP} + + for i_1 in range(test_mapping_p1+1): + mapping_1 = global_basis_mapping_1[k_1, i_1, 0, q_1] + mapping_1_x1 = global_basis_mapping_1[k_1, i_1, 1, q_1] + {D2_2} + for i_2 in range(test_mapping_p2+1): + mapping_2 = global_basis_mapping_2[k_2, i_2, 0, q_2] + mapping_2_x2 = global_basis_mapping_2[k_2, i_2, 1, q_2] + {D2_3} + for i_3 in range(test_mapping_p3+1): + mapping_3 = global_basis_mapping_3[k_3, i_3, 0, q_3] + mapping_3_x3 = global_basis_mapping_3[k_3, i_3, 1, q_3] + {D2_4} + + coeff_x = arr_coeffs_x[i_1,i_2,i_3] + coeff_y = arr_coeffs_y[i_1,i_2,i_3] + coeff_z = arr_coeffs_z[i_1,i_2,i_3] + + mapping = mapping_1*mapping_2*mapping_3 + mapping_x1 = mapping_1_x1*mapping_2*mapping_3 + mapping_x2 = mapping_1*mapping_2_x2*mapping_3 + mapping_x3 = mapping_1*mapping_2*mapping_3_x3 + +{D2_5} + + x += mapping*coeff_x + y += mapping*coeff_y + z += mapping*coeff_z + + x_x1 += mapping_x1*coeff_x + x_x2 += mapping_x2*coeff_x + x_x3 += mapping_x3*coeff_x + y_x1 += mapping_x1*coeff_y + y_x2 += mapping_x2*coeff_y + y_x3 += mapping_x3*coeff_y + z_x1 += mapping_x1*coeff_z + z_x2 += mapping_x2*coeff_z + z_x3 += mapping_x3*coeff_z + +{D2_6} + +{TEMPS} +{COUPLING_TERMS} +''' + return code + + #-------------------------------------------------------------------------- + @property + def _assembly_template_body_analytic(self): + """A template for the 'body' of the assembly function (when using an analytic or no mapping). Only used with the sum factorization algorithm.""" + code = ''' + local_x1 = zeros_like(global_x1[0,:]) + local_x2 = zeros_like(global_x2[0,:]) + local_x3 = zeros_like(global_x3[0,:]) + +{F_COEFFS_ZEROS} + +{KEYS} + for k_1 in range(n_element_1): + local_x1[:] = global_x1[k_1,:] +{LOCAL_SPAN}{F_SPAN_1}{A1} + for q_1 in range(nq1): + x1 = local_x1[q_1] + for k_2 in range(n_element_2): + local_x2[:] = global_x2[k_2,:] +{F_SPAN_2} + for q_2 in range(nq2): + x2 = local_x2[q_2] + for k_3 in range(n_element_3): + local_x3[:] = global_x3[k_3,:] +{F_SPAN_3}{F_COEFFS} + for q_3 in range(nq3): + x3 = local_x3[q_3] + +{F_INIT} + +{F_ASSIGN_LOOP} + +{TEMPS} +{COUPLING_TERMS} +''' + return code + + #-------------------------------------------------------------------------- + @property + def _assembly_template_loop(self): + """A template for the 'loop' of the assembly function. Only used with the sum factorization algorithm.""" + code = ''' + {A2}[:] = 0.0 + for k_2 in range(n_element_2): + {SPAN_2} = {GLOBAL_SPAN_2}[k_2] + for q_2 in range(nq2): + {A3}[:] = 0.0 + for k_3 in range(n_element_3): + {SPAN_3} = {GLOBAL_SPAN_3}[k_3] + for q_3 in range(nq3): + a4 = {COUPLING_TERMS}[k_2, q_2, k_3, q_3, :] + for i_3 in range({TEST_V_P3} + 1): + for j_3 in range({TRIAL_U_P3} + 1): + for e in range({NEXPR}): + {A3}[e, {SPAN_3} - {TEST_V_P3} + i_3, {MAX_P3} - {I_3} + j_3] += {TEST_TRIAL_3}[k_3, q_3, i_3, j_3, {KEYS_3}[2*e], {KEYS_3}[2*e+1]] * a4[e] + for i_2 in range({TEST_V_P2} + 1): + for j_2 in range({TRIAL_U_P2} + 1): + for e in range({NEXPR}): + {A2}[e, {SPAN_2} - {TEST_V_P2} + i_2, :, {MAX_P2} - {I_2} + j_2, :] += {TEST_TRIAL_2}[k_2, q_2, i_2, j_2, {KEYS_2}[2*e], {KEYS_2}[2*e+1]] * {A3}[e,:,:] + for i_1 in range({TEST_V_P1} + 1): + for j_1 in range({TRIAL_U_P1} + 1): + {A1}[i_1, :, :, {MAX_P1} - {I_1} + j_1, :, :] += {A2_TEMP} +''' + return code + + #-------------------------------------------------------------------------- + def make_file(self, temps, ordered_stmts, field_derivatives, max_logical_derivative, test_mult, trial_mult, test_v_p, trial_u_p, keys_1, keys_2, keys_3, mapping_option): + """ + Part of the sum factorization algorithm implementation. + Generates the correct assembly file. + Used at the end of construct_arguments_generate_assembly_file, before eventually pyccelizing that file. + + Parameters + ---------- + temps : tuple + Tuple of Assign statements defining temporary values. + Arithmetic combinations of these make up the coupling terms. + + ordered_stmts : dict + Dictionary defining the coupling terms. Keys are combinations of + test and trial function components, values are Assign statements + in terms of temporaries appearing in temps. + + field_derivatives : dict + Dictionary containing information on the derivatives of free FemFields. + Keys are components of free FemFields. Values are dictionaries again. + Their keys are names, as appearing in the assembly file, of partial derivatives of the + corresponding FemField component, and their values are dictionaries again. + Example: {F1_0_x3 : {'x1': 0, 'x2': 0, 'x3': 1}, F1_0_x2 : ...} + Meaning: There exists a free FemField named F1. Among other, the partial derivative w.r.t. x3 + of its first component F1_0 appears. + + max_logical_derivative : int + The largest appearing derivative order. + + test_mult : list + List of length 3(scalar test function) or 9(vector test function) including multiplicity information. + + trial_mult : list + List of length 3(scalar trial function) or 9(vector trial function) including multiplicity information. + + test_v_p : dict + Dictionary of length 1(scalar test function) or length 3(vector test function). + Each key corresponds to a component of the funciton (space), and each corresponding value + is a list of Bspline degrees of length 3. Example: Discretizing a de de Rham sequence using + a degree vector [2, 3, 4] means that test_v_p for a test function belonging to H(curl) will be + {0: [1, 3, 4], 1: [2, 2, 4], 2: [2, 3, 3]} + + trial_u_p : dict + Dictionary of length 1(scalar trial function) or length 3(vector trial function). + Each key corresponds to a component of the funciton (space), and each corresponding value + is a list of Bspline degrees of length 3. Example: Discretizing a de de Rham sequence using + a degree vector [2, 3, 4] means that trial_u_p for a trial function belonging to H^1 will be + {0: [2, 3, 4]} + + keys_1 : dict + Dictionary relating subexpressions to x1-derivative combinations. + Keys are combinations of test and trial function components. + Values are lists, each entry corresponding to one appearing partial derivative + combination of these components. + Example: keys_1[(u[0], v[1])][3] = [1,0] means that the fourth ([3]) + sub-expression (partial derivative combination) corresponding to the trial-test-function-component-product + u[0] * v[1] involves a first derivative in x1 direction of the trial function + and no derivative in x1 direction of the test function. + Information on appearing partial derivatives in x2 and x3 direction is stored in keys_2 and keys_3. + + keys_2 : dict + See keys_1. + + keys_3 : dict + See keys_1. + + mapping_option : None | 'Bspline' + None in case of no mapping or an analytical mapping, 'Bspline' in case of a Bspline mapping. + + Returns + ------- + + file_id : str + random string of length 8, corresponding to the assembly file name located in __psydac__/ + + """ + + #------------------------- FILE_ID ------------------------- + comm = self.comm + + # Root process generates a random string to be used as file_id + if comm is None or comm.rank == 0: + file_id = random_string(size=8) + else: + file_id = None + + # Parallel case: root process broadcasts file_id to all processes + if comm is not None and comm.size > 1: + file_id = comm.bcast(file_id, root=0) + + # ----- free FemField related strings ----- + + # used as {FIELD_ARGS} in _assembly_template_head + # adding the right arguments for free FemFields to the assembly function header + basis_args_block = [f'global_test_basis_'+'{field}'+f'_{i+1} : "float64[:,:,:,:]"' for i in range(3)] + basis_args_block = ", ".join(basis_args_block) + "," + basis_args_block = [basis_args_block.format(field=field) for field in field_derivatives] + basis_args = " " + "\n ".join(basis_args_block) + "\n" + span_args_block = [f'global_span_'+'{field}'+f'_{i+1} : "int64[:]"' for i in range(3)] + span_args_block = ", ".join(span_args_block) + "," + span_args_block = [span_args_block.format(field=field) for field in field_derivatives] + span_args = " " + "\n ".join(span_args_block) + "\n" + degree_args_block = [f'test_'+'{field}'+f'_p{i+1} : "int64"' for i in range(3)] + degree_args_block = ", ".join(degree_args_block) + "," + degree_args_block = [degree_args_block.format(field=field) for field in field_derivatives] + degree_args = " " + "\n ".join(degree_args_block) + "\n" + pad_args_block = [f'pad_'+'{field}'+f'_{i+1} : "int64"' for i in range(3)] + pad_args_block = ", ".join(pad_args_block) + "," + pad_args_block = [pad_args_block.format(field=field) for field in field_derivatives] + pad_args = " " + "\n ".join(pad_args_block) + "\n" + coeff_args_block = [f'global_arr_coeffs_{field} : "float64[:,:,:]"' for field in field_derivatives] + coeff_args = " " + ", ".join(coeff_args_block) + FIELD_ARGS = basis_args+span_args+degree_args+pad_args+coeff_args + + # {F_COEFFS_ZEROS} in both _assembly_template_body_bspline & _analytic + F_COEFFS_ZEROS = "\n".join([f" arr_coeffs_{field} = zeros((1 + test_{field}_p1, 1 + test_{field}_p2, 1 + test_{field}_p3), dtype='float64')" for field in field_derivatives]) + + # {F_SPAN_1}, {F_SPAN_2}, {F_SPAN_3} in both _assembly_template_body_bspline & _analytic + F_SPAN_1 = "\n".join([f" span_{field}_1 = global_span_{field}_1[k_1]" for field in field_derivatives]) + "\n" + F_SPAN_2 = "\n".join([f" span_{field}_2 = global_span_{field}_2[k_2]" for field in field_derivatives]) + "\n" + F_SPAN_3 = "\n".join([f" span_{field}_3 = global_span_{field}_3[k_3]" for field in field_derivatives]) + "\n" + + # {F_COEFFS} in both _assembly_template_body_bspline & _analytic + coeff_ranges = ", ".join([f"pad_"+"{field}"+f"_{i+1} + span_"+"{field}"+f"_{i+1} - test_"+"{field}"+f"_p{i+1}:1 + pad_"+"{field}"+f"_{i+1} + span_"+"{field}"+f"_{i+1}" for i in range(3)]) + F_COEFFS = "\n".join([f" arr_coeffs_{field}[:,:,:] = global_arr_coeffs_{field}[{coeff_ranges.format(field=field)}]" for i, field in enumerate(field_derivatives)]) + + # {F_INIT} + F_INIT = "\n".join([f" {derivative} = 0.0" for field in field_derivatives for derivative in field_derivatives[field]]) + + # + # field_init assigns 0 to appearing free FemField derivatives (F_x1 = 0.0 \n F_x2 = 0.0 \n ...) + # In the following, we assemble loops that correctly compute those free FemField derivatives at + # a specific quadrature point (q_1, q_2, q_3). Those values will then be used in the computation + # of the temps or directly in the computation of the coupling terms + # + assign_loop_contents = {'1':{}, '2':{}, '3':{}} + multiplication_info = {} + + for field, derivatives in field_derivatives.items(): + multiplication_info[field] = {} + assign_statements = {'1':[], '2':[], '3':[]} + for derivative, dxs in derivatives.items(): + multiplication_info[field][derivative] = [] + dx1 = dxs['x1'] + dx2 = dxs['x2'] + dx3 = dxs['x3'] + for i, dx in enumerate([dx1, dx2, dx3]): + name = f"{field}_{i+1}" if dx == 0 else f"{field}_{i+1}_{dx*f'x{i+1}'}" + multiplication_info[field][derivative].append(name) + if dx == 0: + assign_statement = f"{name} = global_test_basis_{field}_{i+1}[k_{i+1}, i_{i+1}, 0, q_{i+1}]" + else: + assign_statement = f"{name} = global_test_basis_{field}_{i+1}[k_{i+1}, i_{i+1}, {dx}, q_{i+1}]" + if assign_statement not in assign_statements[f"{i+1}"]: + assign_statements[f"{i+1}"].append(assign_statement) + for i in range(3): + content = ("\n"+(8+i)*" ").join(assign_statements[f"{i+1}"]) + assign_loop_contents[f"{i+1}"][field] = content + tab = 7*" " + assign = [] + for field in field_derivatives: + txt = f"{tab}for i_1 in range(1 + test_{field}_p1):\n" + \ + f"{tab} {assign_loop_contents['1'][field]}\n" + \ + f"{tab} for i_2 in range(1 + test_{field}_p2):\n" + \ + f"{tab} {assign_loop_contents['2'][field]}\n" + \ + f"{tab} for i_3 in range(1 + test_{field}_p3):\n" + \ + f"{tab} {assign_loop_contents['3'][field]}\n" + \ + f"{tab} coeff_{field} = arr_coeffs_{field}[i_1, i_2, i_3]\n" + for derivative in multiplication_info[field]: + factors = " * ".join(multiplication_info[field][derivative]) + txt += f"{tab} {derivative} += {factors} * coeff_{field}\n" + txt += "\n" + assign.append(txt) + + # {F_ASSIGN_LOOP} in both _assembly_template_body_bspline & _analytic + F_ASSIGN_LOOP = "\n".join(assign) + + # ----------------------------------------- + + # ----- load the templates ----- + # + # head for the function header and imports + # body for the computation of coupling terms + # loop (part of function body): one loop per block ( e.g. (u[0], v[1]) ), each loop effectively + # assembles one StencilMatrix per sub expression ( e.g. (dx1(u[0]), dx3(v[1])) ) + code_head = self._assembly_template_head + code_loop = self._assembly_template_loop + if mapping_option == 'Bspline': + code_body = self._assembly_template_body_bspline + else: + code_body = self._assembly_template_body_analytic + # ------------------------------ + + # ---- obtain basic information not explicitely passed in the args ----- + blocks = ordered_stmts.keys() + block_list = list(blocks) + trial_components = [block[0] for block in block_list] + test_components = [block[1] for block in block_list] + nu = len(set(trial_components)) + nv = len(set(test_components)) + d = 3 + assert d == 3 + # ---------------------------------------------------------------------- + + # Prepare strings and string templates depending on whether the trial and test function are vector-valued or not (nu, nv > 1 or == 1) + + # ------------------------- STRINGS HEAD ------------------------- + + global_span_v_str = 'global_span_v_{v_j}_' if nv > 1 else 'global_span_v_' + + if mapping_option == 'Bspline': + MAPPING_PART_1 = 'global_basis_mapping_1 : "float64[:,:,:,:]", global_basis_mapping_2 : "float64[:,:,:,:]", global_basis_mapping_3 : "float64[:,:,:,:]", ' + MAPPING_PART_2 = 'global_span_mapping_1 : "int64[:]", global_span_mapping_2 : "int64[:]", global_span_mapping_3 : "int64[:]", ' + MAPPING_PART_3 = 'test_mapping_p1 : "int64", test_mapping_p2 : "int64", test_mapping_p3 : "int64", ' + MAPPING_PART_4 = 'global_arr_coeffs_x : "float64[:,:,:]", global_arr_coeffs_y : "float64[:,:,:]", global_arr_coeffs_z : "float64[:,:,:]", ' + else: + MAPPING_PART_1 = '' + MAPPING_PART_2 = '' + MAPPING_PART_3 = '' + MAPPING_PART_4 = '' + + if nv > 1: + tt1_str = 'test_trial_1_u_{u_i}_v_{v_j}' if nu > 1 else 'test_trial_1_u_v_{v_j}' + tt2_str = 'test_trial_2_u_{u_i}_v_{v_j}' if nu > 1 else 'test_trial_2_u_v_{v_j}' + tt3_str = 'test_trial_3_u_{u_i}_v_{v_j}' if nu > 1 else 'test_trial_3_u_v_{v_j}' + a3_str = 'a3_u_{u_i}_v_{v_j}' if nu > 1 else 'a3_u_v_{v_j}' + a2_str = 'a2_u_{u_i}_v_{v_j}' if nu > 1 else 'a2_u_v_{v_j}' + ct_str = 'coupling_terms_u_{u_i}_v_{v_j}' if nu > 1 else 'coupling_terms_u_v_{v_j}' + g_mat_str = 'g_mat_u_{u_i}_v_{v_j}' if nu > 1 else 'g_mat_u_v_{v_j}' + else: + tt1_str = 'test_trial_1_u_{u_i}_v' if nu > 1 else 'test_trial_1_u_v' + tt2_str = 'test_trial_2_u_{u_i}_v' if nu > 1 else 'test_trial_2_u_v' + tt3_str = 'test_trial_3_u_{u_i}_v' if nu > 1 else 'test_trial_3_u_v' + a3_str = 'a3_u_{u_i}_v' if nu > 1 else 'a3_u_v' + a2_str = 'a2_u_{u_i}_v' if nu > 1 else 'a2_u_v' + ct_str = 'coupling_terms_u_{u_i}_v' if nu > 1 else 'coupling_terms_u_v' + g_mat_str = 'g_mat_u_{u_i}_v' if nu > 1 else 'g_mat_u_v' + + # ---------------------------------------------------------------- + + # ------------------------- STRINGS BODY ------------------------- + + span_v_1_str = 'span_v_{v_j}_1' if nv > 1 else 'span_v_1' + test_v_p1_str = 'test_v_{v_j}_p1' if nv > 1 else 'test_v_p1' + + if nv > 1: + keys_2_str = 'keys_2_u_{u_i}_v_{v_j}' if nu > 1 else 'keys_2_u_v_{v_j}' + keys_3_str = 'keys_3_u_{u_i}_v_{v_j}' if nu > 1 else 'keys_3_u_v_{v_j}' + a1_str = 'a1_u_{u_i}_v_{v_j}' if nu > 1 else 'a1_u_v_{v_j}' + else: + keys_2_str = 'keys_2_u_{u_i}_v' if nu > 1 else 'keys_2_u_v' + keys_3_str = 'keys_3_u_{u_i}_v' if nu > 1 else 'keys_3_u_v' + a1_str = 'a1_u_{u_i}_v' if nu > 1 else 'a1_u_v' + + # ---------------------------------------------------------------- + + # ------------------------- STRINGS LOOP ------------------------- + + span_2_str = 'span_v_{v_j}_2' if nv > 1 else 'span_v_2' + span_3_str = 'span_v_{v_j}_3' if nv > 1 else 'span_v_3' + global_span_2_str = 'global_span_v_{v_j}_2' if nv > 1 else 'global_span_v_2' + global_span_3_str = 'global_span_v_{v_j}_3' if nv > 1 else 'global_span_v_3' + + # ---------------------------------------------------------------- + + #------------------------- MAKE HEAD ------------------------- + SPAN = '' + G_MAT = '' + + TT1 = ' ' + TT2 = ' ' + TT3 = ' ' + A3 = ' ' + A2 = ' ' + CT = ' ' + + for v_j in range(nv): + global_span_v = global_span_v_str.format(v_j=v_j) + SPAN += ' ' + for di in range(d): + SPAN += f'{global_span_v}{di+1} : "int64[:]", ' + SPAN = SPAN[:-1] + '\n' + + for block in blocks: + u_i = block[0].indices[0] if nu > 1 else 0 + v_j = block[1].indices[0] if nv > 1 else 0 + + # reverse order intended + if ((nu > 1) and (nv > 1)): + g_mat = g_mat_str.format(u_i=v_j, v_j=u_i) + else: + g_mat = g_mat_str.format(u_i=u_i, v_j=v_j) + G_MAT += f' {g_mat} : "float64[:,:,:,:,:,:]",\n' + + TT1 += tt1_str.format(u_i=u_i, v_j=v_j) + ' : "float64[:,:,:,:,:,:]", ' + TT2 += tt2_str.format(u_i=u_i, v_j=v_j) + ' : "float64[:,:,:,:,:,:]", ' + TT3 += tt3_str.format(u_i=u_i, v_j=v_j) + ' : "float64[:,:,:,:,:,:]", ' + A3 += a3_str.format(u_i=u_i, v_j=v_j) + ' : "float64[:,:,:]", ' + A2 += a2_str.format(u_i=u_i, v_j=v_j) + ' : "float64[:,:,:,:,:]", ' + CT += ct_str.format(u_i=u_i, v_j=v_j) + ' : "float64[:,:,:,:,:]", ' + + TT1 += '\n' + TT2 += '\n' + TT3 += '\n' + A3 += '\n' + A2 += '\n' + CT += '\n' + NEW_ARGS = TT1 + TT2 + TT3 + A3 + A2 + CT + IMPORTS = self._imports_string + + head = code_head.format(FILE_ID = file_id, + SPAN = SPAN, + G_MAT = G_MAT, + NEW_ARGS = NEW_ARGS, + MAPPING_PART_1 = MAPPING_PART_1, + MAPPING_PART_2 = MAPPING_PART_2, + MAPPING_PART_3 = MAPPING_PART_3, + MAPPING_PART_4 = MAPPING_PART_4, + FIELD_ARGS = FIELD_ARGS, + imports = IMPORTS) + + #------------------------- MAKE BODY ------------------------- + A1 = '' + KEYS_2 = '' + KEYS_3 = '' + LOCAL_SPAN = '' + TEMPS = '' + COUPLING_TERMS = '' + + for block in blocks: + u_i = block[0].indices[0] if nu > 1 else 0 + v_j = block[1].indices[0] if nv > 1 else 0 + + keys2 = keys_2[block].copy() + keys3 = keys_3[block].copy() + keys2 = ','.join(str(i) for i in keys2.flatten()) + keys3 = ','.join(str(i) for i in keys3.flatten()) + KEYS2 = keys_2_str.format(u_i=u_i, v_j=v_j) + KEYS3 = keys_3_str.format(u_i=u_i, v_j=v_j) + KEYS_2 += f' {KEYS2} = array([{keys2}])\n' + KEYS_3 += f' {KEYS3} = array([{keys3}])\n' + + test_v_p1, test_v_p2, test_v_p3 = test_v_p[v_j] + a1 = a1_str.format(u_i=u_i, v_j=v_j) + g_mat = g_mat_str.format(u_i=u_i, v_j=v_j) + TEST_V_P1 = test_v_p1_str.format(v_j=v_j) + SPAN_V_1 = span_v_1_str.format(v_j=v_j) + + A1_1 = f'{test_mult[0]}*pad1 + {SPAN_V_1} - {test_v_p1} : {test_mult[0]}*pad1 + {SPAN_V_1} + 1' if test_mult[0] > 1 else f'pad1 + {SPAN_V_1} - {test_v_p1} : pad1 + {SPAN_V_1} + 1' + A1_2 = f'{test_mult[1]}*pad2 : {test_mult[1]}*pad2 + n_element_2 + {test_v_p2} + ({test_mult[1]}-1)*(n_element_2-1)' if test_mult[1] > 1 else f'pad2 : pad2 + n_element_2 + {test_v_p2}' + A1_3 = f'{test_mult[2]}*pad3 : {test_mult[2]}*pad3 + n_element_3 + {test_v_p3} + ({test_mult[2]}-1)*(n_element_3-1)' if test_mult[2] > 1 else f'pad3 : pad3 + n_element_3 + {test_v_p3}' + A1 += f' {a1} = {g_mat}[{A1_1}, {A1_2}, {A1_3}, :, :, :]\n' + + for v_j in range(nv): + local_span_v_1 = span_v_1_str.format(v_j=v_j) + global_span_v = global_span_v_str.format(v_j=v_j) + LOCAL_SPAN += f' {local_span_v_1} = {global_span_v}1[k_1]\n' + + for temp in temps: + TEMPS += f' {temp.lhs} = {temp.rhs}\n' + for block in blocks: + for stmt in ordered_stmts[block]: + COUPLING_TERMS += f' {stmt.lhs} = {stmt.rhs}\n' + + KEYS = KEYS_2 + KEYS_3 + + # This part is interesting. Right now, below you find hardcoded rules regarding lines of code + # that need to be included when max_logical_derivative == 2 ( and mapping_option == 'Bspline'). + # E.g., the bilinear form corresponding to a bilaplacian problem ( laplace(laplace(u)) = f ) satisfies this assumption. + # This hardcoded set of rules could be generalized to n-th max derivatives - if needed! + # But for now, higher than second order derivatives on either trial or test function are not supported. + # + # Additional note: Given a Bspline mapping, the code computing the first order derivatives of mapping related terms is always required! + # Even in the case of a trivial bilinear form without derivatives. But only when there are second order partial derivatives involved + # do we need to compute second derivatives of the mapping (chain rule). + if (mapping_option == 'Bspline') and (max_logical_derivative == 2): + D2_1 = '\n' + spaces1 = ' ' + spaces2 = spaces1 + ' ' + for symbol in ('x', 'y', 'z'): + for d1 in range(1, 4): + for d2 in range(1, 4): + if d2 >= d1: + D2_1 += spaces1 + f'{symbol}_x{d1}x{d2} = 0.0\n' + D2_1 += '\n' + D2_2 = 'mapping_1_x1x1 = global_basis_mapping_1[k_1, i_1, 2, q_1]' + D2_3 = 'mapping_2_x2x2 = global_basis_mapping_2[k_2, i_2, 2, q_2]' + D2_4 = 'mapping_3_x3x3 = global_basis_mapping_3[k_3, i_3, 2, q_3]' + D2_5 = spaces2+'mapping_x1x1 = mapping_1_x1x1 * mapping_2 * mapping_3\n'+spaces2 + D2_5 += 'mapping_x1x2 = mapping_1_x1 * mapping_2_x2 * mapping_3\n'+spaces2 + D2_5 += 'mapping_x1x3 = mapping_1_x1 * mapping_2 * mapping_3_x3\n'+spaces2 + D2_5 += 'mapping_x2x2 = mapping_1 * mapping_2_x2x2 * mapping_3\n'+spaces2 + D2_5 += 'mapping_x2x3 = mapping_1 * mapping_2_x2 * mapping_3_x3\n'+spaces2 + D2_5 += 'mapping_x3x3 = mapping_1 * mapping_2 * mapping_3_x3x3\n' + D2_6 = '' + for symbol in ('x', 'y', 'z'): + for d1 in range(1, 4): + for d2 in range(1, 4): + if d2 >= d1: + D2_6 += f'{spaces2}{symbol}_x{d1}x{d2} += mapping_x{d1}x{d2} * coeff_{symbol}\n' + D2_6 += '\n' + else: + D2_1 = '' + D2_2 = '' + D2_3 = '' + D2_4 = '' + D2_5 = '' + D2_6 = '' + + body = code_body.format(LOCAL_SPAN = LOCAL_SPAN, + KEYS = KEYS, + A1 = A1, + TEMPS = TEMPS, + COUPLING_TERMS = COUPLING_TERMS, + F_COEFFS_ZEROS = F_COEFFS_ZEROS, + F_SPAN_1 = F_SPAN_1, + F_SPAN_2 = F_SPAN_2, + F_SPAN_3 = F_SPAN_3, + F_COEFFS = F_COEFFS, + F_INIT = F_INIT, + F_ASSIGN_LOOP = F_ASSIGN_LOOP, + D2_1 = D2_1, + D2_2 = D2_2, + D2_3 = D2_3, + D2_4 = D2_4, + D2_5 = D2_5, + D2_6 = D2_6) + + #------------------------- MAKE LOOP ------------------------- + assembly_code = head + body + loop_str = '' + + for block in blocks: + u_i = block[0].indices[0] if nu > 1 else 0 + v_j = block[1].indices[0] if nv > 1 else 0 + + A1 = a1_str.format(u_i=u_i, v_j=v_j) + A2 = a2_str.format(u_i=u_i, v_j=v_j) + A3 = a3_str.format(u_i=u_i, v_j=v_j) + TEST_TRIAL_2 = tt2_str.format(u_i=u_i, v_j=v_j) + TEST_TRIAL_3 = tt3_str.format(u_i=u_i, v_j=v_j) + SPAN_2 = span_2_str.format(u_i=u_i, v_j=v_j) + SPAN_3 = span_3_str.format(u_i=u_i, v_j=v_j) + GLOBAL_SPAN_2 = global_span_2_str.format(u_i=u_i, v_j=v_j) + GLOBAL_SPAN_3 = global_span_3_str.format(u_i=u_i, v_j=v_j) + KEYS_3 = keys_3_str.format(u_i=u_i, v_j=v_j) + KEYS_2 = keys_2_str.format(u_i=u_i, v_j=v_j) + COUPLING_TERMS = ct_str.format(u_i=u_i, v_j=v_j) + + TEST_V_P1, TEST_V_P2, TEST_V_P3 = test_v_p[v_j] + TRIAL_U_P1, TRIAL_U_P2, TRIAL_U_P3 = trial_u_p[u_i] + MAX_P1 = max(TEST_V_P1, TRIAL_U_P1) + MAX_P2 = max(TEST_V_P2, TRIAL_U_P2) + MAX_P3 = max(TEST_V_P3, TRIAL_U_P3) + NEXPR = len(ordered_stmts[block]) + + keys1 = keys_1[block] + TEST_TRIAL_1 = tt1_str.format(u_i=u_i, v_j=v_j) + A2_TEMP = " + ".join([f"{TEST_TRIAL_1}[k_1, q_1, i_1, j_1, {keys1[e][0]}, {keys1[e][1]}] * {A2}[{e},:,:,:,:]" for e in range(NEXPR)]) + + I_1 = f'int(floor(i_1/{test_mult[0]})*{trial_mult[0]})' if max(test_mult[0], trial_mult[0]) > 1 else 'i_1' + I_2 = f'int(floor(i_2/{test_mult[1]})*{trial_mult[1]})' if max(test_mult[1], trial_mult[1]) > 1 else 'i_2' + I_3 = f'int(floor(i_3/{test_mult[2]})*{trial_mult[2]})' if max(test_mult[2], trial_mult[2]) > 1 else 'i_3' + #MAX_P1 = max(int( ( MAX_P1 + np.floor(MAX_P1 / test_mult[0]) * trial_mult[0] ) / 2 ), MAX_P1) if max(test_mult[0], trial_mult[0]) > 1 else MAX_P1 + #MAX_P2 = max(int( ( MAX_P2 + np.floor(MAX_P2 / test_mult[1]) * trial_mult[1] ) / 2 ), MAX_P2) if max(test_mult[1], trial_mult[1]) > 1 else MAX_P2 + #MAX_P3 = max(int( ( MAX_P3 + np.floor(MAX_P3 / test_mult[2]) * trial_mult[2] ) / 2 ), MAX_P3) if max(test_mult[2], trial_mult[2]) > 1 else MAX_P3 + n_cols_x1 = max( int(MAX_P1 + 1 + np.floor(MAX_P1 / test_mult[0]) * trial_mult[0]), 2*MAX_P1+1 ) + n_cols_x2 = max( int(MAX_P2 + 1 + np.floor(MAX_P2 / test_mult[1]) * trial_mult[1]), 2*MAX_P2+1 ) + n_cols_x3 = max( int(MAX_P3 + 1 + np.floor(MAX_P3 / test_mult[2]) * trial_mult[2]), 2*MAX_P3+1 ) + MAX_P1 = n_cols_x1 - MAX_P1 - 1 + MAX_P2 = n_cols_x2 - MAX_P2 - 1 + MAX_P3 = n_cols_x3 - MAX_P3 - 1 + + loop = code_loop.format(A1 = A1, + A2 = A2, + A3 = A3, + TEST_TRIAL_2 = TEST_TRIAL_2, + TEST_TRIAL_3 = TEST_TRIAL_3, + SPAN_2 = SPAN_2, + SPAN_3 = SPAN_3, + GLOBAL_SPAN_2 = GLOBAL_SPAN_2, + GLOBAL_SPAN_3 = GLOBAL_SPAN_3, + KEYS_2 = KEYS_2, + KEYS_3 = KEYS_3, + COUPLING_TERMS = COUPLING_TERMS, + TEST_V_P1 = TEST_V_P1, + TEST_V_P2 = TEST_V_P2, + TEST_V_P3 = TEST_V_P3, + TRIAL_U_P1 = TRIAL_U_P1, + TRIAL_U_P2 = TRIAL_U_P2, + TRIAL_U_P3 = TRIAL_U_P3, + MAX_P1 = MAX_P1, + MAX_P2 = MAX_P2, + MAX_P3 = MAX_P3, + NEXPR = NEXPR, + A2_TEMP = A2_TEMP, + I_1 = I_1, + I_2 = I_2, + I_3 = I_3) + + loop_str += loop + + assembly_code += loop_str + assembly_code += '\n return\n' + + #------------------------- MAKE FILE ------------------------- + import os + if not os.path.isdir('__psydac__'): + os.makedirs('__psydac__') + + # Root process writes the assembly code to a file + if comm is None or comm.rank == 0: + filename = f'__psydac__/assemble_{file_id}.py' + f = open(filename, 'w') + f.writelines(assembly_code) + f.close() + + # Parallel case: wait for the file to be closed before proceeding + if comm is not None and comm.size > 1: + _ = comm.bcast(None, root=0) + + return file_id + + #-------------------------------------------------------------------------- + def read_BilinearForm(self): + """ + Part of the sum factorization algorithm implementation. + Used at the beginning of construct_arguments_generate_assembly_file(). + It's output determines both the design of the assembly function, and the arguments passed to it. + + Returns + ------- + + temps : tuple + tuple of Assign objects. Often times usable building blocks of complicated coupling terms. + + ordered_stmts : dict + assigns each block (trial&test component combination) a list of coupling term assignment + + ordered_sub_exprs_keys : dict + relates each coupling term assignment of ordered_stmts a partial derivative combination + + mapping_option : str | None + 'Bspline' if a spline mapping is involved, None if an analytical or no mapping is involved + + field_derivatives : dict + contains information regarding appearing free FemFields and appearing partial derivatives of those + + g_mat_information_false : list + possibly wrong list of non-zero blocks + + g_mat_information_true : list + correct list of non-zero blocks + + max_logical_derivative : int + maximum appearing partial derivative (in any fixed direction) + + """ + + a = self.expr + domain = a.domain + + # Because an analytical mapping only changes the expression, only the case of a Bspline mapping has to be treated + # entirely different + mapping_option = 'Bspline' if isinstance(self._mapping, SplineMapping) else None + + # The following are tuples consisting of test, trial and free FemField functions appearing, e.g. + # u, v, F1, F2 = elements_of(V, names='u, v, F1, F2) + # a = BilinearForm((u, v), integral(domain, dot(u, F1) * dot(v, F2))) + # tests = (v, ), trials = (u, ) fields = (F1, F2) - Note: The order of F1 & F2 is apparently random and changes from time to time! + # tuple entries are either sympde.topology.space.ScalarFunction or sympde.topology.space.VectorFunction objects + tests = a.test_functions + trials = a.trial_functions + fields = a.fields + + # A sympde.expr.evaluation.DomainExpression object + # TODO [YG 31.07.2025]: Why not using self.terminal_expr[0] instead? + texpr = TerminalExpr(a, domain)[0] + + # We extract all appearing components of test, trial and free FemFields, as well as appearing partial derivatives of these. + # e.g. atoms = [F1[1], F2[1], v[0], u[0], F1[2], F2[2], F1[0], v[1], v[2], F2[0], u[1], u[2]] + # for a bilinear form, without derivatives, involving two vector valued Fem fields F1 & F2 and vector valued test & trial functions v and u + atoms_types = (ScalarFunction, VectorFunction, IndexedVectorFunction) + atoms = _atomic(texpr, cls=atoms_types+_logical_partial_derivatives) + + # Preparing to sort all atoms into test_, trial_ and field_atoms + test_atoms = {} + for v in tests: + if isinstance(v, VectorFunction): + for i in range(domain.dim): + test_atoms[v[i]] = [] + else: + test_atoms[v] = [] + + trial_atoms = {} + for u in trials: + if isinstance(u, VectorFunction): + for i in range(domain.dim): + trial_atoms[u[i]] = [] + else: + trial_atoms[u] = [] + + field_atoms = {} + for f in fields: + if isinstance(f, VectorFunction): + for i in range(domain.dim): + field_atoms[f[i]] = [] + else: + field_atoms[f] = [] + + # atoms can consist of scalar functions (u, v), partial derivatives of scalar functions (dx1(u), dx3(v), ...), + # components of vector valued functions (u[0], v[1], ...), partial derivatives of components of vector valued functions + # (dx1(u[0]), dx3(v[1]), ...), and the same thing but for free FemFields. + # With + # get_atom_logical_derivatives(atom) + # we obtain the component without partial derivatives (u -> u ; dx1(u) -> u ; dx2(v[2]) -> v[2] ; ...) + # This way we can gather subexpressions belonging to the same block + for atom in atoms: + a = get_atom_logical_derivatives(atom) + # IF: NOT Indexed Mapping AND NOT VectorFunction + # I guess: <=> IF ScalarFunction + if not ((isinstance(a, Indexed) and isinstance(a.base, Mapping)) or (isinstance(a, IndexedVectorFunction))): + if a in tests: + # tests is a tuple, e.g. (v, ), hence tests[0] = v + test_atoms[tests[0]].append(atom) + elif a in trials: + trial_atoms[trials[0]].append(atom) + elif a in fields: + # while there can only be one trial and one test function, there can be multiple free FemFields. + for f in field_atoms: + if f == a: + field_atoms[f].append(atom) + else: + raise NotImplementedError(f"atoms of type {str(atom)} are not supported") + # IF VectorFunction + elif isinstance(a, IndexedVectorFunction): + # .base returns ... the base of a VectorFunction! E.g., u[2] -> u, v[0] -> v + if a.base in tests: + for vi in test_atoms: + if vi == a: + test_atoms[vi].append(atom) + break + elif a.base in trials: + for ui in trial_atoms: + if ui == a: + trial_atoms[ui].append(atom) + break + elif a.base in fields: + for fi in field_atoms: + if fi == a: + field_atoms[fi].append(atom) + break + else: + raise NotImplementedError(f"atoms of type {str(atom)} are not supported") + + # ----- Julian O. 11.06.25 ----- + # Regarding the code that follows: + # When dealing with a DiscreteBilinearForm depending on two or more free FemFields, + # the order of the dictionary `field_derivatives` must be the same as the order + # of the free FemFields in `self._free_args`. + # For some reason, the order of all appearing "atoms" in a BilinearForm (trial function, test function, free fields, .?.) + # as obtained in the __init__ of AST + # atoms = terminal_expr.expr.atoms(ScalarFunction, VectorFunction) + # is random and changes from code execution to code execution. + # This order of atoms however determines the order of the free FemFields appearing in `self._free_args`. + # In particular, this order only sometimes matches the order of `field_derivatives`, which results in wrong matrices. + # + # Below is the old version of the code that follows: + #field_derivatives = {} + #for key in field_atoms: + # sym_key = SymbolicExpr(key) + # field_derivatives[sym_key] = {} + # for f in field_atoms[key]: + # field_derivatives[sym_key][SymbolicExpr(f)] = get_index_logical_derivatives(f) + # ------------------------------ + + # For the computation of the coupling terms, among other we need to organize information + # related to free FemFields. For now, we have the dictionary field_atoms, whose keys are + # components of appearing fields, and whose values are appearing partial derivatives of these, e.g., + # field_atoms = {'F1[0]':[dx1(F1[0]), ], 'F1[1]':[dx2(F1[1]), ], 'F1[2]':[dx3(F1[2]), ], 'F2':[F2, ]} + # + # We now create the dictionary field_derivatives. + # It's keys are SymbolicExpr of the previous keys (F1[0] -> F1_0, F1[1] -> F1_1, F1[2] -> F1_2, F2 -> F2) + # and its values are again dictionaries, whose keys are symbolic expressions of the appearing partial derivatives, e.g. + # dx1(F1[0]) -> F1_0_x1, dx2(F1[1]) -> F1_1_x2, dx3(F1[2]) -> F1_2_x3, F2 -> F2, + # and whose values are dictionaries that store the respective derivative information. + # Consider for example the BilinearForm (u, v) \mapsto integral(domain, dot(u, grad(Fs)) * dot(v, grad(Fs2)): + # The corresponding field_derivatives dict will be + # {Fs: {Fs_x3: {'x1': 0, 'x2': 0, 'x3': 1}, Fs_x2: {'x1': 0, 'x2': 1, 'x3': 0}, Fs_x1: {'x1': 1, 'x2': 0, 'x3': 0}}, Fs2: {Fs2_x3: {'x1': 0, 'x2': 0, 'x3': 1}, Fs2_x2: {'x1': 0, 'x2': 1, 'x3': 0}, Fs2_x1: {'x1': 1, 'x2': 0, 'x3': 0}}} + + # Amount of free FemFields (NOT counting each component individually) + n_free_fields = len(self._free_args) + field_derivatives = {} + # The keys in field_derivatives will be in the same order as the fields appearing in self._free_args + for n in range(n_free_fields): + # The key might be F1[0], but we want to check whether F1 == self._free_args[0], and ... + for key in field_atoms: + # ... field_name does exactly that + field_name = str(key.base) if hasattr(key, 'base') else str(key) + if field_name == self._free_args[n]: + # SymbolicExpr transforms something like F1[0] into F1_0 (part of the name of a variable in the assembly code later) + sym_key = SymbolicExpr(key) + field_derivatives[sym_key] = {} + for f in field_atoms[key]: + # And similarly f, which might look like dx1(F1[0]), will be transformed to F1_0_x2 + # while get_index_logical_derivatives(dx1(F1[0])) = {'x1': 1, 'x2': 0, 'x3': 0} + field_derivatives[sym_key][SymbolicExpr(f)] = get_index_logical_derivatives(f) + + # This part was proposed by Said at some point + #syme = False + #if syme: + # from symengine import sympify as syme_sympify + # sym_test_atoms = {k:[syme_sympify(SymbolicExpr(ai)) for ai in a] for k,a in test_atoms.items()} + # sym_trial_atoms = {k:[syme_sympify(SymbolicExpr(ai)) for ai in a] for k,a in trial_atoms.items()} + # sym_expr = syme_sympify(SymbolicExpr(texpr.expr)) + #else: + # sym_test_atoms = {k:[SymbolicExpr(ai) for ai in a] for k,a in test_atoms.items()} + # sym_trial_atoms = {k:[SymbolicExpr(ai) for ai in a] for k,a in trial_atoms.items()} + # sym_expr = SymbolicExpr(texpr.expr) + + # test_atoms is a dict whose values are components of the test function and whose values + # are arrays with appearing partial derivatives of those components. + # sym_test_atoms has the same structure, but replaces the appearing partial derivatives with + # symbolic expressions of those partial derivatives. E.g., + # test_atoms: {v2[0]: [dx3(v2[0]), dx2(v2[0])], v2[1]: [dx1(v2[1]), dx3(v2[1])], v2[2]: [dx2(v2[2]), dx1(v2[2])]} + # sym_test_atoms: {v2[0]: [v2_0_x3, v2_0_x2], v2[1]: [v2_1_x1, v2_1_x3], v2[2]: [v2_2_x2, v2_2_x1]} + # In the following, we will gather all (coupling) terms of a specific combination of a sym_test_atom with a sym_trial_atom in sym_expr + sym_test_atoms = {k:[SymbolicExpr(ai) for ai in a] for k,a in test_atoms.items()} + sym_trial_atoms = {k:[SymbolicExpr(ai) for ai in a] for k,a in trial_atoms.items()} + sym_expr = SymbolicExpr(texpr.expr) + + # ----- temps, rhs ----- + + trials_subs = {ui:0 for u in sym_trial_atoms for ui in sym_trial_atoms[u]} + tests_subs = {vi:0 for v in sym_test_atoms for vi in sym_test_atoms[v]} + sub_exprs = {} + + # This is where the real magic happens: The at times extremely long and complicated SymbolicExpr sym_expr + # 0. is brought into a more readable form (sub_exprs) & + # 1. gets split into many small parts (temps), that often times appear in multiple sub_exprs, + # but now only have to be computed once, e.g. (temp_0, -F2_1*F1_1) & + # 2. those temporaries get assigned to coupling terms (rhs), i.e.: + # The coupling term corresponding to the sub-expr dx1(u[0])*dx3(v[1]) might be -temp_7*(temp_22*temp_27 + temp_33*temp_35 + temp_36*temp_37) + for u in sym_trial_atoms: + for v in sym_test_atoms: + if isinstance(u, IndexedVectorFunction) and isinstance(v, IndexedVectorFunction): + sub_expr = sym_expr[v.indices[0], u.indices[0]] + elif isinstance(u, ScalarFunction) and isinstance(v, ScalarFunction): + sub_expr = sym_expr + elif isinstance(u, ScalarFunction) and isinstance(v, IndexedVectorFunction): + sub_expr = sym_expr[v.indices[0]] + elif isinstance(u, IndexedVectorFunction) and isinstance(v, ScalarFunction): + sub_expr = sym_expr[u.indices[0]] + for ui,sui in zip(trial_atoms[u], sym_trial_atoms[u]): + trcp = trials_subs.copy() + trcp[sui] = 1 + newsub_expr = sub_expr.subs(trcp) + for vi,svi in zip(test_atoms[v],sym_test_atoms[v]): + tcp = tests_subs.copy() + tcp[svi] = 1 + expr = newsub_expr.subs(tcp) + if not expr.is_zero: + sub_exprs[ui,vi] = sympify(expr) + + temps, rhs = cse_main.cse(sub_exprs.values(), symbols=cse_main.numbered_symbols(prefix=f'temp_')) + + # ---------------------- + + # Finally, temps and rhs must be brought into a form that can be included in the assembly code, e.g. + # temp_0 = x_x1*y_x2 + # temp_1 = x_x2*z_x1 + # temp_2 = y_x1*z_x2 + # ... + # coupling_terms_u_v[k_2, q_2, k_3, q_3, 0] = temp_7*(temp_10**2*temp_9 + temp_11**2*temp_9 + temp_8**2*temp_9) + # coupling_terms_u_v[k_2, q_2, k_3, q_3, 1] = temp_18 + # coupling_terms_u_v[k_2, q_2, k_3, q_3, 2] = temp_22 + # ... + + # See above example: In our implementation of the sum factorization algorithm, we precompute arrays + # for each quadrature point in x1 direction, meaning that those arrays contain values depending on + # elements and quadrature points in x2 and x3 direction (k_2, k_3 & q_2 & q_3) + element_indices = [Symbol('k_{}'.format(i)) for i in range(2,4)] + quadrature_indices = [Symbol('q_{}'.format(i)) for i in range(2,4)] + # indices = (k_2, q_2, k_3, q_3) + indices = tuple(j for i in zip(element_indices, quadrature_indices) for j in i) + + # From the sub_exprs dictionary, we read all the appearing trial and test component combinations (blocks) that + # add a non-zero contribution to the matrix + ordered_stmts = {} + ordered_sub_exprs_keys = {} + for key in sub_exprs.keys(): + u_i, v_j = [get_atom_logical_derivatives(atom) for atom in key] + ordered_stmts[u_i, v_j] = [] + ordered_sub_exprs_keys[u_i, v_j] = [] + blocks = ordered_stmts.keys() + + block_list = list(blocks) + trial_components = [block[0] for block in block_list] + test_components = [block[1] for block in block_list] + nu = len(set(trial_components)) + nv = len(set(test_components)) + + expr = self.kernel_expr.expr + + # We store the maximum partial derivative (for a fixed direction), not including pertial derivatives + # appearing in mapping related terms (i.e., a BilinearForm on a mapped domain will have max_logical_derivative = 0 + # even though derivatives of the (spline) mapping appear in the coupling terms). + if isinstance(expr, (ImmutableDenseMatrix, Matrix)): + shape = expr.shape + logical_max_derivatives = [] + for k1 in range(shape[0]): + for k2 in range(shape[1]): + logical_max_derivatives.append(get_max_logical_partial_derivatives(expr[k1,k2])) + max_logical_derivative = max([max([value for value in dic.values()]) for dic in logical_max_derivatives]) + else: + max_logical_derivative = max([value for value in get_max_logical_partial_derivatives(expr).values()]) + + # See comment underneath this code block for more details. + # There was a test case, in which the amount of generated StencilMatrices (one for each appearing block, + # i.e., one for each trial&test component combination for which a non-zero coupling term exists) + # was larger than the amount true amount of needed StencilMatrices. + # That discrepancy appears when expr[block].is_zero wrongly does not detect that a block is zero, + # whereas the corresponding block does rightfully not appear in block_list! + if isinstance(expr, (ImmutableDenseMatrix, Matrix)): # only relevenat if either trial or test function is vector valued + g_mat_information_false = [] + shape = expr.shape + for k1 in range(shape[0]): + for k2 in range(shape[1]): + if not expr[k1,k2].is_zero: # although it might actually be zero! + if (nu == 1) and (nv > 1): + g_mat_information_false.append((k2,k1)) + else: + g_mat_information_false.append((k1,k2)) + if nu == 1: + g_mat_information_true = [(0, get_atom_logical_derivatives(block[1]).indices[0]) for block in block_list] + elif nv == 1: + g_mat_information_true = [(get_atom_logical_derivatives(block[0]).indices[0], 0) for block in block_list] + else: + g_mat_information_true = [(get_atom_logical_derivatives(block[0]).indices[0], get_atom_logical_derivatives(block[1]).indices[0]) for block in block_list] + else: + g_mat_information_false = [] + g_mat_information_true = [] + + # Julian O. 17.06.25: Back when I added this unreadable comment below I forgot to write a test for this problem. + # Eventually it might be interesting to remove everything related to `g_mat_information_false/true` + # and see where errors occur. + # + #1, 1: expr[1,1] = F0*sqrt(x1**2*(x1*cos(2*pi*x3) + 2)**2*(sin(pi*x2)**2 + cos(pi*x2)**2)**2*(sin(2*pi*x3)**2 + cos(2*pi*x3)**2)**2)*(pi*(x1*cos(2*pi*x3) + 2)* + # (-2*pi*x1*sin(pi*x2)*sin(2*pi*x3)*dx1(v1[1]) - sin(pi*x2)*cos(2*pi*x3)*dx3(v1[1]))*cos(pi*x2)*w2[1] - pi*(x1*cos(2*pi*x3) + 2)*(-2*pi*x1*sin(2*pi*x3)*cos(pi*x2)*dx1(v1[1]) - + # cos(pi*x2)*cos(2*pi*x3)*dx3(v1[1]))*sin(pi*x2)*w2[1])/(2*pi**2*x1**2*(x1*cos(2*pi*x3) + 2)**2*(sin(pi*x2)**2 + cos(pi*x2)**2)**2*(sin(2*pi*x3)**2 + cos(2*pi*x3)**2)**2) + # = 0 - but is not yet detected as 0! Hence a matrix is generated, that later is not required! + # + + # Here we create a template for the names of the coupling terms arrays, + # depending on whether or not trial and test function are scalar or vector valued + if nv > 1: + ct_str = 'coupling_terms_u_{u_i}_v_{v_j}' if nu > 1 else 'coupling_terms_u_v_{v_j}' + else: + ct_str = 'coupling_terms_u_{u_i}_v' if nu > 1 else 'coupling_terms_u_v' + + # Now we format this template based on the appearing blocks (combinations of trial and test function components) + # and transform those formatted strings into IndexedBase objects + lhs = {} + for block in blocks: + u_i = get_atom_logical_derivatives(block[0]).indices[0] if nu > 1 else 0 + v_j = get_atom_logical_derivatives(block[1]).indices[0] if nv > 1 else 0 + ct = ct_str.format(u_i=u_i, v_j=v_j) + lhs[block] = IndexedBase(f'{ct}') + + # lhs[block] will look w.g. like this coupling_terms_u_v (u, v scalar). + # Now, we add to that [k_2, q_2, k_3, q_3, count], where count enumerates the sub expressions belonging to the same block + # sub expressions corresponding to the block (u[0], v[1]) might be: (u[0], v[1]), (dx1(u[0]), v[1]), (dx2(u[0]), v[1]), ... + # and then assign the corresponding rhs, e.g. temp_7*(temp_10**2*temp_9 + temp_11**2*temp_9 + temp_8**2*temp_9), to obtain: + # coupling_terms_u_v[k_2, q_2, k_3, q_3, 4] = temp_7*(temp_10**2*temp_9 + temp_11**2*temp_9 + temp_8**2*temp_9) + counts = {block:0 for block in blocks} + for r,key in zip(rhs, sub_exprs.keys()): + u_i, v_j = [get_atom_logical_derivatives(atom) for atom in key] + count = counts[u_i, v_j] + counts[u_i, v_j] += 1 + ordered_stmts[u_i, v_j].append(Assign(lhs[u_i, v_j][(*indices, count)], r)) + ordered_sub_exprs_keys[u_i, v_j].append(key) + # ordered_stmts is a dict whose keys are combinations of trial and test functions components (e.g. u[0], v[1]), + # and whose values are a list of coupling term assignments corresponding to this block, e.g. + # (v1[0], v2[0]): [coupling_terms_u_0_v_0[k_2, q_2, k_3, q_3, 0] := -1, coupling_terms_u_0_v_0[k_2, q_2, k_3, q_3, 1] := 1] + # + # The information regarding which partial derivative combination belongs to which coupling term is stored in ordered_sub_exprs_keys. + # This dict has the same keys, but instead of coupling term assignments as values, list of tuples of partial derivative combinations are stored. + + # temps, which previously consisted of tuples like this one: (temp_0, -F2_1*F1_1), + # will now be a tuple consisting of assignments, e.g. (temp_0 := -F2_1*F1_1, ...) + temps = tuple(Assign(a,b) for a,b in temps) + + return temps, ordered_stmts, ordered_sub_exprs_keys, mapping_option, field_derivatives, g_mat_information_false, g_mat_information_true, max_logical_derivative + + #-------------------------------------------------------------------------- + def construct_arguments_generate_assembly_file(self): + """ + Collect the arguments used in the assembly method, and generate and possibly pyccelize the assembly function. + + Used only when sum factorization is enabled, else the method construct_arguments is called. + + Returns + ------- + args: tuple + The arguments passed to the assembly method. + + threads_args: None + None as openMP parallelization is not supported by this implementation. + + """ + temps, ordered_stmts, ordered_sub_exprs_keys, mapping_option, field_derivatives, g_mat_information_false, g_mat_information_true, max_logical_derivative = self.read_BilinearForm() + + # Each block corresponds to a combination of trial and test function components, and thus indeed to a "block" in the matrix. + # Not all possible combination have to exist, e.g., + # given a function space of vector valued functions V (3d) and a bilinear form a: VxV -> R, a(u, v) = (u, v)_L^2(Omega) + # there will be only 3 blocks on a logical domain (u[0]&v[0], u[1]&v[1], u[2]&v[2]), + # but up to 9 blocks on a mapped domain (e.g. u[0]&v[1], ...) + blocks = ordered_stmts.keys() + block_list = list(blocks) + trial_components = [block[0] for block in block_list] + test_components = [block[1] for block in block_list] + # dim = 1 corresponds to a scalar valued function, dim = 3 to a vector valued function + trial_dim = len(set(trial_components)) + test_dim = len(set(test_components)) + + # A reminder that this implementation only supports bilinear forms on 3d domains. + d = 3 + assert d == 3 + + # Rename - also: establish that throughout "u" corresponds to the trial function, whereas "v" corresponds to the test function + nu = trial_dim # dim of trial function; 1 (scalar) or 3 (vector) + nv = test_dim # dim of test function ; 1 (scalar) or 3 (vector) + + # Obtain the most basic information: function values, degrees, spans, ... + test_basis, test_degrees, spans, pads, test_mult = construct_test_space_arguments(self.test_basis) + trial_basis, trial_degrees, pads, trial_mult = construct_trial_space_arguments(self.trial_basis) + n_elements, quads, quad_degrees = construct_quad_grids_arguments(self.grid[0], use_weights=False) + + #! pads is being overwritten. That is because already somewhere else (__init__ of StencilMatrix via self.allocate_matrices) + # do we assert that domain and codomain (trial and test) pads coincide! + # That is not strictly necessary as Valentin at some point proved in one of his branches, but currently not implemented as + # not required. + + #! the above pads variable is multiplied by the multiplicity vector! For the remaining implementation, we need + # the pads vector un-multiplied, as obtained by : + pads = self.test_basis.space.coeff_space.pads + + # quad_degrees is the amount of quadrature points per element in each direction + # Clearly, this amount must coincide with the amount of basis function values stored per element in test_basis and trial_basis + n_element_1, n_element_2, n_element_3 = n_elements + k1, k2, k3 = quad_degrees + + # We store component wise degree and function values for trial and test function in the dictionaries + # trial_u_p, global_basis_u, test_v_p, global_basis_v + if (nu == 3) and (len(trial_basis) == 3): + # Edge Case: If the trial function space V is a VectorFunctionSpace + # but neither an Hdiv nor an Hcurl space, i.e., + # V = VectorFunctionSpace('V', domain) and not +, kind='hcurl') or +, kind='hdiv') + # then the function values in each of the three directions are identical for each of the three components. + # Hence len(trial_basis) == 3 instead of 9. + # + # global_basis_u is a dict whose values are arrays of function values of one particular trial function component, + # hence for this edge case we simply assign the same array trial_basis to each component + # Same function degree in each direction for each component -> do the same thing with trial_u_p + trial_u_p = {u:trial_degrees for u in range(nu)} + global_basis_u = {u:trial_basis for u in range(nu)} + else: + trial_u_p = {u:trial_degrees[d*u:d*(u+1)] for u in range(nu)} + global_basis_u = {u:trial_basis[d*u:d*(u+1)] for u in range(nu)} + if (nv == 3) and (len(test_basis) == 3): + # See above explanation, which also applies for the spans variable + test_v_p = {v:test_degrees for v in range(nv)} + global_basis_v = {v:test_basis for v in range(nv)} + spans = [*spans, *spans, *spans] + else: + test_v_p = {v:test_degrees[d*v:d*(v+1)] for v in range(nv)} + global_basis_v = {v:test_basis[d*v:d*(v+1)] for v in range(nv)} + + # See other method construct_arguments: + # When self._target is an Interface domain len(self._grid) == 2 + # where grid contains the QuadratureGrid of both sides of the interface + assert len(self.grid) == 1 + if self.mapping: + # We gather mapping related information in the case of a Bspline mapping + # self.mapping == False if either no or an analytical mapping + + map_coeffs = [[e._coeffs._data for e in self.mapping._fields]] + spaces = [self.mapping._fields[0].space] + map_degree = [sp.degree for sp in spaces] + map_span = [[q.spans - s for q,s in zip(sp.get_assembly_grids(*self.nquads), sp.coeff_space.starts)] for sp in spaces] + map_basis = [[q.basis for q in sp.get_assembly_grids(*self.nquads)] for sp in spaces] + points = [g.points for g in self.grid] + weights = [self.mapping.weights_field.coeffs._data] if self.is_rational_mapping else [] + + for i in range(len(self.grid)): + axis = self.grid[i].axis + # See construct_arguments - have not come across an example of when axis was not None! + assert axis is None + + map_degree = flatten(map_degree) + map_span = flatten(map_span) + map_basis = flatten(map_basis) + points = flatten(points) + mapping = [*map_coeffs[0], *weights] + else: + + mapping = [] + map_degree = [] + map_span = [] + map_basis = [] + + #---------- The following part is entirely different from the old construct_arguments method ---------- + + # Each block, say u[0]&v[1], + # consists of possibly many derivative combinations (sub-expressions) of these two components, e.g. + # dx1(u[0])&dx1(v[1]) or dx1(u[0])&dx2(v[1]) (dx1, dx2, dx3 representing respective partial derivatives). + # + # For each block, here still e.g. u[0]&v[1], + # and for each sub-expression, we store corresponding derivative information: + # get_index_logical_derivatives(dx1(u[0])) = {'x1': 1, 'x2': 0, 'x3': 0} + # get_index_logical_derivatives(dx2(v[1])) = {'x1': 0, 'x2': 1, 'x3': 0} + # Each of these 6 dicts has for each block an array of length #sub-expressions (appearing derivative combination) stored + # x2_test_keys[(u[0], v[1])][3] = 2 means, that the fourth sub-expression of block (u[0], v[1]) + # involves a second partial derivative of the test function in x2 direction + x1_trial_keys = {block:[] for block in blocks} + x1_test_keys = {block:[] for block in blocks} + x2_trial_keys = {block:[] for block in blocks} + x2_test_keys = {block:[] for block in blocks} + x3_trial_keys = {block:[] for block in blocks} + x3_test_keys = {block:[] for block in blocks} + + for block in blocks: + # alpha, beta for example being dx1(u[0]), dx2(v[1]) + for alpha, beta in ordered_sub_exprs_keys[block]: + x1_trial_keys[block].append(get_index_logical_derivatives(alpha)['x1']) + x1_test_keys [block].append(get_index_logical_derivatives(beta) ['x1']) + x2_trial_keys[block].append(get_index_logical_derivatives(alpha)['x2']) + x2_test_keys [block].append(get_index_logical_derivatives(beta) ['x2']) + x3_trial_keys[block].append(get_index_logical_derivatives(alpha)['x3']) + x3_test_keys [block].append(get_index_logical_derivatives(beta) ['x3']) + + # See sum factorization paper by Bressan & Takacs: + # coupling_terms, a3 and a2 correspond to A^{>=4}_{x1,x2,x3}, A^{>=3}_{x1,x2} and A^{>=2}_{x1} + # Here, for each block we assign a zero-array of the correct size. + coupling_terms = {} + a3 = {} + a2 = {} + + # For each block, we precompute ~enough~ products of partial derivatives of trial and basis functions in each direction + # These precomputed values will then be read rather than computed in the assembly + test_trial_1s = {} + test_trial_2s = {} + test_trial_3s = {} + + # keys_1/2/3 is a restructuring of the 6 dictionaries created above + keys_1 = {} + keys_2 = {} + keys_3 = {} + + assembly_backend = self.backend + if self._pyccelize_test_trial_computation and assembly_backend['name'] == 'pyccel': + + import os + if not os.path.isdir('__psydac__'): + os.makedirs('__psydac__') + + comm = self.comm + + if comm is not None and comm.size > 1: + if comm.rank == 0: + filename = '__psydac__/test_trial_computation.py' + code = self.test_trial_template + f = open(filename, 'w') + f.writelines(code) + f.close() + else: + filename = '__psydac__/test_trial_computation.py' + code = self.test_trial_template + f = open(filename, 'w') + f.writelines(code) + f.close() + + base_dirpath = os.getcwd() + sys.path.insert(0, base_dirpath) + + package = importlib.import_module(f'__psydac__.test_trial_computation') + kwargs = { + 'language' : 'fortran', + 'compiler_family' : assembly_backend['compiler_family'], + 'flags' : assembly_backend['flags'], + 'openmp' : True if assembly_backend['openmp'] else False, + 'verbose' : False, + 'comm' : self.comm, + } + + test_trial_func = epyccel(package.test_trial_array, **kwargs) + + for block in blocks: + # We translate a block, e.g. (u[0], v[1]) into two integers u_i=0, v_j=1. + # In the case of a scalar function (u, v instead of u[0], u[1], u[2], v[0], v[1], v[2]), store 0. + u_i = block[0].indices[0] if nu > 1 else 0 + v_j = block[1].indices[0] if nv > 1 else 0 + + # keys_2[(u[0], v[1])][3] = (1,2) means that the fourth sub-expression corresponding to the trial-test-function-component-product + # u[0] * v[1] involves a first derivative in x2 direction of the trial function and a second derivative in x2 direction of the test function + keys_1[block] = np.array([(alpha_1, beta_1) for alpha_1, beta_1 in zip(x1_trial_keys[block], x1_test_keys[block])]) + keys_2[block] = np.array([(alpha_2, beta_2) for alpha_2, beta_2 in zip(x2_trial_keys[block], x2_test_keys[block])]) + keys_3[block] = np.array([(alpha_3, beta_3) for alpha_3, beta_3 in zip(x3_trial_keys[block], x3_test_keys[block])]) + + # Those are the function values in each direction of a particular component of the trial/test function + global_basis_u_1, global_basis_u_2, global_basis_u_3 = global_basis_u[u_i] + global_basis_v_1, global_basis_v_2, global_basis_v_3 = global_basis_v[v_j] + + # Those are the Bspline degrees in each direction of a particular component of the trial/test function + trial_u_p1, trial_u_p2, trial_u_p3 = trial_u_p[u_i] + test_v_p1, test_v_p2, test_v_p3 = test_v_p [v_j] + + max_p_2 = max(test_v_p2, trial_u_p2) + max_p_3 = max(test_v_p3, trial_u_p3) + + # That's the amount of subexpressions, i.e., combinations of partial derivatives appearing for a specific combination of + # trial and test function components + n_expr = len(ordered_stmts[block]) + + # To compute enough (possibly too many, but never too few) products of trial and test functions, we read the maximum + # appearing partial derivative (for this specific block, in each direction, for both trial and test function) + max_block_trial_x1_derivative = max(x1_trial_keys[block]) + max_block_trial_x2_derivative = max(x2_trial_keys[block]) + max_block_trial_x3_derivative = max(x3_trial_keys[block]) + max_block_test_x1_derivative = max(x1_test_keys[block]) + max_block_test_x2_derivative = max(x2_test_keys[block]) + max_block_test_x3_derivative = max(x3_test_keys[block]) + + # On each Bspline cell (element / subdomain), there are (test_degree+1)*(trial_degree+1) test & trial function pairs + # of non-zero product. + # Hence, we assign zeros for each element, each quadrature point on the element, each test and trial function combination, + # and each (or even more than required) appearing partial derivative combination of these functions - in each direction + test_trial_1 = np.zeros((n_element_1, k1, test_v_p1 + 1, trial_u_p1 + 1, max_block_trial_x1_derivative+1, max_block_test_x1_derivative+1), dtype='float64') + test_trial_2 = np.zeros((n_element_2, k2, test_v_p2 + 1, trial_u_p2 + 1, max_block_trial_x2_derivative+1, max_block_test_x2_derivative+1), dtype='float64') + test_trial_3 = np.zeros((n_element_3, k3, test_v_p3 + 1, trial_u_p3 + 1, max_block_trial_x3_derivative+1, max_block_test_x3_derivative+1), dtype='float64') + + # And that's how we fill the test_trial arrays + if self._pyccelize_test_trial_computation and assembly_backend['name'] == 'pyccel': + for args in zip(n_elements, + quad_degrees, [test_v_p1, test_v_p2, test_v_p3], [trial_u_p1, trial_u_p2, trial_u_p3], + [global_basis_u_1, global_basis_u_2, global_basis_u_3], [global_basis_v_1, global_basis_v_2, global_basis_v_3], + [max_block_trial_x1_derivative, max_block_trial_x2_derivative, max_block_trial_x3_derivative], [max_block_test_x1_derivative, max_block_test_x2_derivative, max_block_test_x3_derivative], + [test_trial_1, test_trial_2, test_trial_3]): + + args = tuple(np.int64(a) if isinstance(a, int) else a for a in args) + + test_trial_func(*args) + else: + for k_1 in range(n_element_1): + for q_1 in range(k1): + for i_1 in range(test_v_p1 + 1): + for j_1 in range(trial_u_p1 + 1): + trial = global_basis_u_1[k_1, j_1, :, q_1] + test = global_basis_v_1[k_1, i_1, :, q_1] + for alpha_1 in range(max_block_trial_x1_derivative+1): + for beta_1 in range(max_block_test_x1_derivative+1): + test_trial_1[k_1, q_1, i_1, j_1, alpha_1, beta_1] = trial[alpha_1] * test[beta_1] + + for k_2 in range(n_element_2): + for q_2 in range(k2): + for i_2 in range(test_v_p2 + 1): + for j_2 in range(trial_u_p2 + 1): + trial = global_basis_u_2[k_2, j_2, :, q_2] + test = global_basis_v_2[k_2, i_2, :, q_2] + for alpha_2 in range(max_block_trial_x2_derivative+1): + for beta_2 in range(max_block_test_x2_derivative+1): + test_trial_2[k_2, q_2, i_2, j_2, alpha_2, beta_2] = trial[alpha_2] * test[beta_2] + + for k_3 in range(n_element_3): + for q_3 in range(k3): + for i_3 in range(test_v_p3 + 1): + for j_3 in range(trial_u_p3 + 1): + trial = global_basis_u_3[k_3, j_3, :, q_3] + test = global_basis_v_3[k_3, i_3, :, q_3] + for alpha_3 in range(max_block_trial_x3_derivative+1): + for beta_3 in range(max_block_test_x3_derivative+1): + test_trial_3[k_3, q_3, i_3, j_3, alpha_3, beta_3] = trial[alpha_3] * test[beta_3] + + test_trial_1s[block] = test_trial_1 + test_trial_2s[block] = test_trial_2 + test_trial_3s[block] = test_trial_3 + + # Instead of having a different a3, a2 & coupling term array for each sub-expression, we choose to have only one + # such array per block. + # a3 will store line integral values for all combinations of test and trial functions in x3 direction, hence the dimension + # (n_element_3 + test_v_p3 + (mult[2]-1)*(n_element_3-1), 2 * max_p_3 + 1) + # a2 will store surface integral values for all combinations of test and trial functions in x2 and x3 direction, hence the dimension ... + # coupling_terms stores point values of the coupling terms at all quadrature points + # but only in x2 and x3 direction, because we only "precompute" this array for a fixed quadrature point in x1 direction + + # a3[block] size explained: #sub expressions ; #test functions depending on x3 ; #complicated expression for the minimum columns needed + # to store local information correctly. 2*degree+1 in the simplest case. + n_funs_x2 = n_element_2 + test_v_p2 + (test_mult[1]-1)*(n_element_2-1) + n_funs_x3 = n_element_3 + test_v_p3 + (test_mult[2]-1)*(n_element_3-1) + n_cols_x2 = max( int(max_p_2 + 1 + np.floor(max_p_2 / test_mult[1]) * trial_mult[1]), 2*max_p_2+1 ) + n_cols_x3 = max( int(max_p_3 + 1 + np.floor(max_p_3 / test_mult[2]) * trial_mult[2]), 2*max_p_3+1 ) + + a3[block] = np.zeros((n_expr, n_funs_x3, n_cols_x3), dtype='float64') + a2[block] = np.zeros((n_expr, n_funs_x2, n_funs_x3, n_cols_x2, n_cols_x3), dtype='float64') + + coupling_terms[block] = np.zeros((n_element_2, k2, n_element_3, k3, n_expr), dtype='float64') + + # We gather the socalled new args - all other args are being obtained in a similar way using the old assembly implementation + new_args = (*list(test_trial_1s.values()), + *list(test_trial_2s.values()), + *list(test_trial_3s.values()), + *list(a3.values()), + *list(a2.values()), + *list(coupling_terms.values())) + + # This part is a bit shady. + # There has been a case, where my code wasn't running, because one instance of deep-(Psydac/Sympde/Sympy)-code + # correctly understood that a possibly complicated expression (corresponding to a block) in fact evaluates to 0, + # and hence no StencilMatrix for that particular block ever needs to be created - but a different part of + # deep-(Psydac/Sympde/Sympy)-code did not get that simplification right (yet?), and decided that the assembly code + # needs a StencilMatrix as input for this particular block. + # See readBilinearForm for additional information. + # This part of the code filters out unnecessary StencilMatrices, such that only the relevant StencilMatrices + # are being passed to the assembly function + expr = self.kernel_expr.expr + if isinstance(expr, (ImmutableDenseMatrix, Matrix)): + matrices = [] + for i, block in enumerate(g_mat_information_false): + if block in g_mat_information_true: + matrices.append(self._global_matrices[i]) + else: + matrices = self._global_matrices + + # We have gathered all args! + args = (*map_basis, *spans, *map_span, *quads, *map_degree, *n_elements, *quad_degrees, *pads, *mapping, *matrices, + *new_args) + + threads_args = () + + args = tuple(np.int64(a) if isinstance(a, int) else a for a in args) + threads_args = tuple(np.int64(a) if isinstance(a, int) else a for a in threads_args) + + #---------- We now generate the assembly file ---------- + + # file_id is a random string that has been used to name the assembly file + file_id = self.make_file(temps, ordered_stmts, field_derivatives, max_logical_derivative, test_mult, trial_mult, test_v_p, trial_u_p, keys_1, keys_2, keys_3, mapping_option) + + # Store the current directory and add it to the variable `sys.path` + # to imitate Python's import behavior + import os + base_dirpath = os.getcwd() + sys.path.insert(0, base_dirpath) + + # Import the generated assembly function + package = importlib.import_module(f'__psydac__.assemble_{file_id}') + + # The assembly function is the one that has been generated in the make_file method + assembly_function_name = f'assemble_matrix_{file_id}' + assembly_function = getattr(package, assembly_function_name) + + # If the backend is pyccel, we compile the new assembly function + assembly_backend = self.backend + if assembly_backend['name'] == 'pyccel': + kwargs = { + 'language' : 'fortran', # hardcoded for now + 'compiler_family' : assembly_backend['compiler_family'], + 'flags' : assembly_backend['flags'], + 'openmp' : True if assembly_backend['openmp'] else False, + 'verbose' : False, + # 'folder': assembly_backend['folder'], + 'comm' : self.comm, + # 'time_execution': verbose, + # 'verbose': verbose + } + new_func = epyccel(assembly_function, **kwargs) + else: + new_func = assembly_function + + # Use the new assembly function (either compiled or not) + self._func = new_func + + return args, threads_args + + #-------------------------------------------------------------------------- + @property + def test_trial_template(self): + code = '''def test_trial_array(n_element : "int64", + quad_degree : "int64", test_degree : "int64", trial_degree : "int64", + trial_basis : "float64[:,:,:,:]", test_basis : "float64[:,:,:,:]", + max_trial_derivative : "int64", max_test_derivative : "int64", + test_trial : "float64[:,:,:,:,:,:]"): + + for k in range(n_element): + for q in range(quad_degree): + for i in range(test_degree + 1): + for j in range(trial_degree + 1): + trial = trial_basis[k, j, :, q] + test = test_basis [k, i, :, q] + for alpha in range(max_trial_derivative + 1): + for beta in range(max_test_derivative + 1): + test_trial[k, q, i, j, alpha, beta] = trial[alpha] * test[beta] + + return +''' + return code diff --git a/psydac/api/fem_common.py b/psydac/api/fem_common.py new file mode 100644 index 000000000..9c6c0bd6a --- /dev/null +++ b/psydac/api/fem_common.py @@ -0,0 +1,286 @@ +from typing import Iterable + +from sympy import Expr, ImmutableDenseMatrix, Matrix + +import numpy as np + +from sympde.expr.basic import BasicForm +from sympde.expr.evaluation import KernelExpression +from sympde.topology.space import ScalarFunction, VectorFunction, IndexedVectorFunction +from sympde.topology.space import ProductSpace, VectorFunctionSpace +from sympde.topology.datatype import H1SpaceType, L2SpaceType, UndefinedSpaceType +from sympde.topology.derivatives import get_atom_logical_derivatives +from sympde.topology.derivatives import _logical_partial_derivatives + +from psydac.fem.basic import FemSpace +from psydac.linalg.stencil import StencilMatrix, StencilInterfaceMatrix +from psydac.linalg.basic import ComposedLinearOperator +from psydac.api.utilities import flatten +from psydac.api.ast.utilities import math_atoms_as_str, get_max_partial_derivatives + +# TODO [YG 01.08.2025]: Avoid importing anything from psydac.pyccel +from psydac.pyccel.ast.core import _atomic + +__all__ = ( + 'compute_max_nderiv', + 'compute_imports', + 'compute_free_arguments', + 'collect_spaces', + 'compute_diag_len', + 'construct_test_space_arguments', + 'construct_trial_space_arguments', + 'construct_quad_grids_arguments', + 'do_nothing', + 'extract_stencil_mats', + 'reset_arrays', +) + +#============================================================================== +def compute_max_nderiv(kernel_expr: KernelExpression) -> int: + """ + Compute the highest derivative order in the given kernel expression. + + Parameters + ---------- + kernel_expr : KernelExpression (from sympde.expr.evaluation) + + Returns + ------- + nderiv : int + The highest order of derivation in `terminal_expr`. + + """ + assert isinstance(kernel_expr, KernelExpression) + + terminal_expr = kernel_expr.expr + if not isinstance(terminal_expr, (ImmutableDenseMatrix, Matrix)): + terminal_expr = ImmutableDenseMatrix([[terminal_expr]]) + n_rows, n_cols = terminal_expr.shape + + atoms_types = (ScalarFunction, VectorFunction, IndexedVectorFunction) + extended_atoms_types = atoms_types + _logical_partial_derivatives + + nderiv = 0 + for i_row in range(n_rows): + for i_col in range(n_cols): + texpr = terminal_expr[i_row, i_col] + atoms = _atomic(texpr, cls=extended_atoms_types) + Fs = [get_atom_logical_derivatives(a) for a in atoms] + d = get_max_partial_derivatives(texpr, logical=True, F=Fs) + nderiv = max(nderiv, max(d.values())) + + return nderiv + +#============================================================================== +def compute_imports(expr: Expr, + spaces: Iterable[FemSpace], + *, + openmp: bool + ) -> dict[str, list[str]]: + """ + Compute all the imports to be added to the generated Python code. + + Parameters + ---------- + expr : sympy.Expr + The integrand expression of a BilinearForm, LinearForm, or + Functional. This is a pure SymPy expression where SymPDE partial + derivatives have been converted to SymPy symbols. See Notes. + + spaces : iterable of psydac.fem.FemSpace + The discrete spaces which define the finite element representation + of a BilinearForm, LinearForm, or Functional. + + openmp : bool + Whether or not OpenMP pragmas and functions are used in the code. + + Returns + ------- + imports : dict[str, list[str]] + A dictionary whose keys are the names of the Python modules to be + imported, and whose values are the names of the corresponding + objects (variables, functions, classes) to be imported from the + modules. + + Notes + ----- + Assume that we start from an object of type BilinearForm, LinearForm, + or Functional. We take the integrand and expand its vector operations + with TerminalExpr(), then pull back from physical to logical + coordinates with LogicalExpr(), and finally convert the symbolic + partial derivatives with SymbolicExpr(). Where: + - TerminalExpr is defined in sympde.expr.evaluation + - LogicalExpr is defined in sympde.topology.mapping + - SymbolicExpr is defined in sympde.topology.mapping + + The resulting expression `expr` can be passed to this function. + """ + assert isinstance(expr, Expr) + assert all(isinstance(V, FemSpace) for V in spaces) + assert isinstance(openmp, bool) + + # Determine the type of scalar quantities to be managed in the code + dtypes = [getattr(V.symbolic_space, 'codomain_type', 'real') for V in spaces] + assert all(t in ['complex', 'real'] for t in dtypes) + dtype = 'complex' if 'complex' in dtypes else 'real' + + # TODO uncomment this line when we have a SesquilinearForm defined in SymPDE + #assert isinstance(expr, SesquilinearForm) + + #... Compute the imports + math_library = 'cmath' if dtype=='complex' else 'math' # Function names are the same + math_imports = math_atoms_as_str(expr, 'math') + numpy_imports = ['array', 'zeros', 'zeros_like', 'floor'] + + imports = {'numpy': numpy_imports} + if math_imports: + imports[math_library] = math_imports + if openmp: + imports['pyccel.stdlib.internal.openmp'] = ['omp_get_thread_num'] + #... + + return imports + +#============================================================================== +def compute_free_arguments(expr: BasicForm, kernel_expr: KernelExpression) -> tuple[str]: + """ + The string representation (i.e. the names) of the free arguments in + the given BilinearForm, LinearForm, or Functional. + + Parameters + ---------- + expr : BilinearForm | LinearForm | Functional + The expression of which we want to compute the free arguments. + + kernel_expr : sympde.expr.evaluation.KernelExpression + The atomic representation of the form, which is obtained after using + LogicalExpr (if there is a mapping) and TerminalExpr on `expr`. + + Returns + ------- + tuple[str] + The string representation (i.e. the names) of the free arguments in + the given BilinearForm, LinearForm, or Functional. + + """ + assert isinstance(expr, BasicForm) + assert isinstance(kernel_expr, KernelExpression) + + free_args_dict = expr.get_free_variables() + free_args_str = tuple(str(a) for a in free_args_dict) + + return free_args_str + +#============================================================================== +def collect_spaces(space, *args): + """ + This function collect the arguments used in the assembly function + + Parameters + ---------- + space: + the symbolic space + + args : + list of discrete space components like basis values, spans, ... + + Returns + ------- + args : + list of discrete space components elements used in the asembly + + """ + + if isinstance(space, ProductSpace): + spaces = space.spaces + indices = [] + i = 0 + for space in spaces: + if isinstance(space, VectorFunctionSpace): + if isinstance(space.kind, (H1SpaceType, L2SpaceType, UndefinedSpaceType)): + indices.append(i) + else: + indices += [i+j for j in range(space.ldim)] + i = i + space.ldim + else: + indices.append(i) + i = i + 1 + args = [[e[i] for i in indices] for e in args] + + elif isinstance(space, VectorFunctionSpace): + if isinstance(space.kind, (H1SpaceType, L2SpaceType, UndefinedSpaceType)): + args = [[e[0]] for e in args] + + return args + +#============================================================================== +def compute_diag_len(p, md, mc): + n = ((np.ceil((p+1)/mc)-1)*md).astype('int') + n = n-np.minimum(0, n-p)+p+1 + return n.astype('int') + +#============================================================================== +def construct_test_space_arguments(basis_values): + space = basis_values.space + test_basis = basis_values.basis + spans = basis_values.spans + test_degrees = space.degree + pads = space.pads + multiplicity = space.multiplicity + + test_basis, test_degrees, spans = collect_spaces(space.symbolic_space, test_basis, test_degrees, spans) + + test_basis = flatten(test_basis) + test_degrees = flatten(test_degrees) + spans = flatten(spans) + pads = flatten(pads) + multiplicity = flatten(multiplicity) + pads = [p*m for p,m in zip(pads, multiplicity)] + return test_basis, test_degrees, spans, pads, multiplicity + +def construct_trial_space_arguments(basis_values): + space = basis_values.space + trial_basis = basis_values.basis + trial_degrees = space.degree + pads = space.pads + multiplicity = space.multiplicity + trial_basis, trial_degrees = collect_spaces(space.symbolic_space, trial_basis, trial_degrees) + + trial_basis = flatten(trial_basis) + trial_degrees = flatten(trial_degrees) + pads = flatten(pads) + multiplicity = flatten(multiplicity) + pads = [p*m for p,m in zip(pads, multiplicity)] + return trial_basis, trial_degrees, pads, multiplicity + +#============================================================================== +def construct_quad_grids_arguments(grid, use_weights=True): + points = grid.points + if use_weights: + weights = grid.weights + quads = flatten(list(zip(points, weights))) + else: + quads = flatten(list(zip(points))) + + nquads = flatten(grid.nquads) + n_elements = grid.n_elements + return n_elements, quads, nquads + +#============================================================================== +def do_nothing(*args): + return 0 + +#============================================================================== +def extract_stencil_mats(mats): + new_mats = [] + for M in mats: + if isinstance(M, (StencilInterfaceMatrix, StencilMatrix)): + new_mats.append(M) + elif isinstance(M, ComposedLinearOperator): + new_mats += [i for i in M.multiplicants if isinstance(i, (StencilInterfaceMatrix, StencilMatrix))] + return new_mats + +#============================================================================== +def reset_arrays(*args): + for a in args: + a[:]= 0.j if a.dtype==complex else 0. diff --git a/psydac/api/fem_sum_form.py b/psydac/api/fem_sum_form.py new file mode 100644 index 000000000..7d387b733 --- /dev/null +++ b/psydac/api/fem_sum_form.py @@ -0,0 +1,123 @@ +import numpy as np + +from sympde.expr.expr import ( + BilinearForm as sym_BilinearForm, + LinearForm as sym_LinearForm, + Functional as sym_Functional +) + +from .basic import BasicDiscrete +from .fem import DiscreteFunctional +from .fem import DiscreteLinearForm +from .fem import DiscreteBilinearForm +from .fem_bilinear_form import DiscreteBilinearForm as DiscreteBilinearForm_SF +from .fem_common import reset_arrays +from .utilities import random_string + +__all__ = ('DiscreteSumForm',) + +#============================================================================== +class DiscreteSumForm(BasicDiscrete): + + def __init__(self, a, kernel_expr, *args, **kwargs): + + # Sum factorization is only implemented for bilinear forms in 3D, in + # which case we use it by default. A 2D implementation should be the + # next step, hence we allow the user to pass `sum_factorization=True` + # even if not supported yet. In the case of linear forms or functionals + # this option is irrelevant for now, so we ignore it. + # + # In every case we remove the `sum_factorization` key from the dict + # in order to avoid errors, because none of the class constructors + # accept this argument. + sum_factorization = kwargs.pop('sum_factorization', a.ldim == 3) + + # TODO Uncomment when the SesquilinearForm exist in SymPDE + #if not isinstance(a, (sym_BilinearForm, sym_SesquilinearForm, sym_LinearForm, sym_Functional)): + # raise TypeError('> Expecting a symbolic BilinearForm, SesquilinearForm, LinearForm, Functional') + if not isinstance(a, (sym_BilinearForm, sym_LinearForm, sym_Functional)): + raise TypeError('> Expecting a symbolic BilinearForm, LinearForm, Functional') + + self._expr = a + backend = kwargs.pop('backend', None) + self._backend = backend + + folder = kwargs.get('folder', None) + self._folder = self._initialize_folder(folder) + + # create a module name if not given + tag = random_string(8) + + # ... + forms = [] + free_args = [] + self._kernel_expr = kernel_expr + operator = None + for e in kernel_expr: + if isinstance(a, sym_LinearForm): + kwargs['update_ghost_regions'] = False + ah = DiscreteLinearForm(a, e, *args, backend=backend, **kwargs) + kwargs['vector'] = ah._vector + operator = ah._vector + + # TODO Uncomment when the SesquilinearForm exist in SymPDE + # elif isinstance(a, sym_SesquilinearForm): + # kwargs['update_ghost_regions'] = False + # ah = DiscreteSesquilinearForm(a, e, *args, assembly_backend=backend, **kwargs) + # kwargs['matrix'] = ah._matrix + # operator = ah._matrix + + elif isinstance(a, sym_BilinearForm): + kwargs['update_ghost_regions'] = False + if sum_factorization: + ah = DiscreteBilinearForm_SF(a, e, *args, assembly_backend=backend, **kwargs) + else: + ah = DiscreteBilinearForm(a, e, *args, assembly_backend=backend, **kwargs) + kwargs['matrix'] = ah._matrix + operator = ah._matrix + + elif isinstance(a, sym_Functional): + ah = DiscreteFunctional(a, e, *args, backend=backend, **kwargs) + + forms.append(ah) + free_args.extend(ah.free_args) + + if isinstance(a, sym_BilinearForm): + is_broken = len(args[0].domain)>1 + if self._backend is not None and is_broken: + for mat in kwargs['matrix']._blocks.values(): + mat.set_backend(backend) + elif self._backend is not None: + kwargs['matrix'].set_backend(backend) + + self._forms = forms + self._operator = operator + self._free_args = tuple(set(free_args)) + self._is_functional = isinstance(a, sym_Functional) + # ... + + @property + def forms(self): + return self._forms + + @property + def free_args(self): + return self._free_args + + @property + def is_functional(self): + return self._is_functional + + def assemble(self, *, reset=True, **kwargs): + if not self.is_functional: + if reset : + reset_arrays(*[i for M in self.forms for i in M.global_matrices]) + + for form in self.forms: + form.assemble(reset=False, **kwargs) + self._operator.exchange_assembly_data() + return self._operator + else: + M = [form.assemble(**kwargs) for form in self.forms] + M = np.sum(M) + return M diff --git a/psydac/api/tests/test_api_feec_3d.py b/psydac/api/tests/test_api_feec_3d.py index d5220b5bc..9da51f784 100644 --- a/psydac/api/tests/test_api_feec_3d.py +++ b/psydac/api/tests/test_api_feec_3d.py @@ -19,7 +19,7 @@ from psydac.fem.basic import FemField from psydac.api.discretization import discretize from psydac.feec.pull_push import push_3d_hcurl, push_3d_hdiv -from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL +from psydac.api.settings import PSYDAC_BACKENDS from psydac.linalg.utilities import array_to_psydac from psydac.linalg.solvers import inverse @@ -112,22 +112,31 @@ def run_maxwell_3d_scipy(logical_domain, mapping, e_ex, b_ex, ncells, degree, pe # Discrete objects: Psydac #------------------------------------------------------------------------------ + # Select backend for acceleration of the generated assembly code + backend = PSYDAC_BACKENDS['pyccel-gcc'] + + # Select multiplicity of internal knots along each direction + multiplicity = [mult, mult, mult] + + # Create Geometry & DiscreteDerham objects domain_h = discretize(domain, ncells=ncells, periodic=periodic, comm=MPI.COMM_WORLD) - derham_h = discretize(derham, domain_h, degree=degree, multiplicity = [mult,mult,mult]) + derham_h = discretize(derham, domain_h, degree=degree, multiplicity=multiplicity) - a1_h = discretize(a1, domain_h, (derham_h.V1, derham_h.V1), backend=PSYDAC_BACKEND_GPYCCEL) - a2_h = discretize(a2, domain_h, (derham_h.V2, derham_h.V2), backend=PSYDAC_BACKEND_GPYCCEL) + # Create DiscreteBilinearForm objects. Assembly code is generated here + a1_h = discretize(a1, domain_h, (derham_h.V1, derham_h.V1), backend=backend) + a2_h = discretize(a2, domain_h, (derham_h.V2, derham_h.V2), backend=backend) - # StencilMatrix objects + # Assemble matrices as StencilMatrix objects, then convert them to SciPy's CSC/CSR formats M1 = a1_h.assemble().tosparse().tocsc() M2 = a2_h.assemble().tosparse().tocsr() - # Diff operators + # Get differential operators as BlockLinearOperator objects GRAD, CURL, DIV = derham_h.derivatives_as_matrices - # Porjectors - P0, P1, P2, P3 = derham_h.projectors(nquads=[5,5,5]) + # Get projectors as objects of type Projector_H1, Projector_Hcurl, Projector_Hdiv, Projector_L2 + P0, P1, P2, P3 = derham_h.projectors(nquads=[5, 5, 5]) + # Convert the CURL BlockLinearOperator to SciPy's CSR format CURL = CURL.transform(lambda block: block.tokronstencil().tostencil()).tosparse().tocsr() # initial conditions @@ -145,7 +154,6 @@ def run_maxwell_3d_scipy(logical_domain, mapping, e_ex, b_ex, ncells, degree, pe # project initial conditions e0_coeff = P1(e0).coeffs - b0_coeff = P2(b0).coeffs # time integrator @@ -207,21 +215,29 @@ def run_maxwell_3d_stencil(logical_domain, mapping, e_ex, b_ex, ncells, degree, # Discrete objects: Psydac #------------------------------------------------------------------------------ + # Select backend for acceleration of the generated assembly code + backend = PSYDAC_BACKENDS['pyccel-gcc'] + + # Select multiplicity of internal knots along each direction + multiplicity = [mult, mult, mult] + + # Create Geometry & DiscreteDerham objects domain_h = discretize(domain, ncells=ncells, periodic=periodic, comm=MPI.COMM_WORLD) - derham_h = discretize(derham, domain_h, degree=degree, multiplicity = [mult,mult,mult]) + derham_h = discretize(derham, domain_h, degree=degree, multiplicity=multiplicity) - a1_h = discretize(a1, domain_h, (derham_h.V1, derham_h.V1), backend=PSYDAC_BACKEND_GPYCCEL) - a2_h = discretize(a2, domain_h, (derham_h.V2, derham_h.V2), backend=PSYDAC_BACKEND_GPYCCEL) + # Create DiscreteBilinearForm objects. Assembly code is generated here + a1_h = discretize(a1, domain_h, (derham_h.V1, derham_h.V1), backend=backend) + a2_h = discretize(a2, domain_h, (derham_h.V2, derham_h.V2), backend=backend) - # StencilMatrix objects + # Assemble matrices as StencilMatrix objects M1 = a1_h.assemble() M2 = a2_h.assemble() - # Diff operators + # Get differential operators as BlockLinearOperator objects GRAD, CURL, DIV = derham_h.derivatives_as_matrices - # Porjectors - P0, P1, P2, P3 = derham_h.projectors(nquads=[5,5,5]) + # Get projectors as objects of type Projector_H1, Projector_Hcurl, Projector_Hdiv, Projector_L2 + P0, P1, P2, P3 = derham_h.projectors(nquads=[5, 5, 5]) # initial conditions e0_1 = lambda x, y, z: e_ex[0](0, x, y, z) @@ -238,7 +254,6 @@ def run_maxwell_3d_stencil(logical_domain, mapping, e_ex, b_ex, ncells, degree, # project initial conditions e0_coeff = P1(e0).coeffs - b0_coeff = P2(b0).coeffs # time integrator diff --git a/psydac/api/tests/test_sum_factorization_assembly_3d.py b/psydac/api/tests/test_sum_factorization_assembly_3d.py new file mode 100644 index 000000000..7aab017a3 --- /dev/null +++ b/psydac/api/tests/test_sum_factorization_assembly_3d.py @@ -0,0 +1,592 @@ +import os +import pytest +import time +import numpy as np + +from sympy import sin, sqrt, pi, Abs, cos, tan + +from sympde.calculus import dot, cross, grad, curl, div, laplace +from sympde.expr import BilinearForm, integral +from sympde.topology import element_of, elements_of, Cube, Mapping, ScalarFunctionSpace, VectorFunctionSpace, Domain, Derham + +from psydac.api.discretization import discretize +from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL +from psydac.linalg.block import BlockVectorSpace +from psydac.fem.basic import FemField + +try: + mesh_dir = os.environ['PSYDAC_MESH_DIR'] + +except: + base_dir = os.path.dirname(os.path.realpath(__file__)) + base_dir = os.path.join(base_dir, '..', '..', '..') + mesh_dir = os.path.join(base_dir, 'mesh') + + +# With PR #448, matrices corresponding to bilinear forms on 3D domains are being assembled using a so called sum factorization algorithm. +# Unless explicitely using the old algorithm, this happens automatically, and hence all old tests passing should indicate that the implementation of the sum factorization algorithm has been successful. +# Nonetheless, there are various difficulties in the implementation, and possibly not all of them are accounted for in the existing tests. + +# This file is designed to test such "difficult" edge cases - for mapped (Bspline & analytical) and parametric domains: + +# Such "difficult" edge cases are: + +# 1. bilinear forms on different spaces +# 2. (FemField / analytical / ...) weight functions +# 3. high derivatives (>=2) +# 4. (multiple) free FemFields +# 5. complicated expressions +# 6. uncommen (numpy) functions that need be imported correctly in the assembly file (here in the weight function) + +# These tests also return old and new discretization and assembly times. + +# Most of the time, being close to the "old matrix" (generated using the old assembly algorithm) will be the requirement to pass a test, +# as the old implementation has not caused problems in a long time and is considered to function properly. + +# Update: Instead of testing all mapping options all of the time, we now rather randomly test one of the three options! +#@pytest.mark.parametrize('mapping', ('None', 'Analytical', 'Bspline')) +def test_assembly(): # mapping): + + rng = np.random.default_rng() # (seed=42) + mapping_options = ['None', 'Analytical', 'Bspline'] + mapping = mapping_options[int(np.floor(rng.random()*3))] + + ncells = [7, 5, 6] + degree = [2, 4, 3] + periodic = [int(np.floor(rng.random()*2))==True for _ in range(3)] + print(f'Random periodicity: {periodic}') + + trial_multiplicity = [1, 3, 2] + test_multiplicity = [2, 2, 3] + + backend = PSYDAC_BACKEND_GPYCCEL + + if mapping == 'None': + + domain = Cube('C', bounds1=(0,1), bounds2=(0,1), bounds3=(0,1)) + derham = Derham(domain) + + domain_h = discretize(domain, ncells=ncells, periodic=periodic) + derham_h = discretize(derham, domain_h, degree=degree, multiplicity=trial_multiplicity) + derham_test_h = discretize(derham, domain_h, degree=degree, multiplicity=test_multiplicity) + + elif mapping == 'Bspline': + + filename = os.path.join(mesh_dir, 'identity_3d.h5') + + domain = Domain.from_file(filename=filename) + derham = Derham(domain) + + domain_h = discretize(domain, filename=filename) + derham_h = discretize(derham, domain_h, degree=domain.mapping.get_callable_mapping().space.degree, multiplicity=trial_multiplicity) + derham_test_h = discretize(derham, domain_h, degree=domain.mapping.get_callable_mapping().space.degree, multiplicity=test_multiplicity) + + elif mapping == 'Analytical': + + class HalfSquareTorusMapping3D(Mapping): + _expressions = {'x': 'x1 * cos(x2)', + 'y': 'x1 * sin(x2)', + 'z': 'x3'} + + _ldim = 3 + _pdim = 3 + + M = HalfSquareTorusMapping3D('M') + logical_domain = Cube('C', bounds1=(0.3,1), bounds2=(0,np.pi), bounds3=(0,1)) + + domain = M(logical_domain) + derham = Derham(domain) + + domain_h = discretize(domain, ncells=ncells, periodic=periodic) + derham_h = discretize(derham, domain_h, degree=degree, multiplicity=trial_multiplicity) + derham_test_h = discretize(derham, domain_h, degree=degree, multiplicity=test_multiplicity) + + x, y, z = domain.coordinates + weight = 1 + sqrt(Abs(x*y**2 + z)) + abs(sin(x-2*y + pi + np.pi)) + + V0 = derham.V0 + V0h = derham_h.V0 + V1 = derham.V1 + V1h = derham_h.V1 + V2 = derham.V2 + V2h = derham_h.V2 + V3 = derham.V3 + V3h = derham_h.V3 + + V0h_test = derham_test_h.V0 + V1h_test = derham_test_h.V1 + V2h_test = derham_test_h.V2 + V3h_test = derham_test_h.V3 + + Vs = ScalarFunctionSpace('Vsh', domain) + Vsh = discretize(Vs, domain_h, degree=degree) + Vvc = VectorFunctionSpace('Vvc', domain, kind='hcurl') + Vvch = discretize(Vvc, domain_h, degree=degree) + Vvd = VectorFunctionSpace('Vvd', domain, kind='hdiv') + Vvdh = discretize(Vvd, domain_h, degree=degree) + + Vsh_test = discretize(Vs, domain_h, degree=degree, multiplicity=test_multiplicity) + Vvch_test = discretize(Vs, domain_h, degree=degree, multiplicity=test_multiplicity) + Vvdh_test = discretize(Vs, domain_h, degree=degree, multiplicity=test_multiplicity) + + u1, u2, F01, F02, F03 = elements_of(V0, names='u1, u2, F01, F02, F03') + v1, v2, F11, F12, F13 = elements_of(V1, names='v1, v2, F11, F12, F13') + w1, w2, F21, F22, F23 = elements_of(V2, names='w1, w2, F21, F22, F23') + f1, f2, F31, F32, F33 = elements_of(V3, names='f1, f2, F31, F32, F33') + + fs1, fs2, Fs1, Fs2, Fs3 = elements_of(Vs, names='fs1, fs2, Fs1, Fs2, Fs3') + fvc1, fvc2, Fvc1, Fvc2, Fvc3 = elements_of(Vvc, names='fvc1, fvc2, Fvc1, Fvc2, Fvc3') + fvd1, fvd2, Fvd1, Fvd2, Fvd3 = elements_of(Vvd, names='fvd1, fvd2, Fvd1, Fvd2, Fvd3') + + trial_spaces = {'V0': {'Vh':V0h, 'funcs':[u1, u2]}, + 'V1': {'Vh':V1h, 'funcs':[v1, v2]}, + 'V2': {'Vh':V2h, 'funcs':[w1, w2]}, + 'V3': {'Vh':V3h, 'funcs':[f1, f2]}, + 'Vs': {'Vh':Vsh, 'funcs':[fs1, fs2]}, + 'Vvc':{'Vh':Vvch, 'funcs':[fvc1, fvc2]}, + 'Vvd':{'Vh':Vvdh, 'funcs':[fvd1, fvd2]}} + + test_spaces = {'V0': {'Vh':V0h_test, 'funcs':[u1, u2]}, + 'V1': {'Vh':V1h_test, 'funcs':[v1, v2]}, + 'V2': {'Vh':V2h_test, 'funcs':[w1, w2]}, + 'V3': {'Vh':V3h_test, 'funcs':[f1, f2]}, + 'Vs': {'Vh':Vsh_test, 'funcs':[fs1, fs2]}, + 'Vvc':{'Vh':Vvch_test, 'funcs':[fvc1, fvc2]}, + 'Vvd':{'Vh':Vvdh_test, 'funcs':[fvd1, fvd2]}} + + F01_coeffs = V0h.coeff_space.zeros() + rng.random(size=F01_coeffs._data.shape, dtype='float64', out=F01_coeffs._data) + F11_coeffs = V1h.coeff_space.zeros() + for block in F11_coeffs.blocks: + rng.random(size=block._data.shape, dtype='float64', out=block._data) + F12_coeffs = V1h.coeff_space.zeros() + for block in F12_coeffs.blocks: + rng.random(size=block._data.shape, dtype='float64', out=block._data) + F21_coeffs = V2h.coeff_space.zeros() + for block in F21_coeffs.blocks: + rng.random(size=block._data.shape, dtype='float64', out=block._data) + Fvc1_coeffs = Vvch.coeff_space.zeros() + for block in Fvc1_coeffs.blocks: + rng.random(size=block._data.shape, dtype='float64', out=block._data) + Fs1_coeffs = Vsh.coeff_space.zeros() + rng.random(size=Fs1_coeffs._data.shape, dtype='float64', out=Fs1_coeffs._data) + Fs2_coeffs = Vsh.coeff_space.zeros() + rng.random(size=Fs2_coeffs._data.shape, dtype='float64', out=Fs2_coeffs._data) + Fvd1_coeffs = Vvdh.coeff_space.zeros() + for block in Fvd1_coeffs.blocks: + rng.random(size=block._data.shape, dtype='float64', out=block._data) + + F01_field = FemField(V0h, F01_coeffs) + F11_field = FemField(V1h, F11_coeffs) + F12_field = FemField(V1h, F12_coeffs) + F21_field = FemField(V2h, F21_coeffs) + Fvc1_field = FemField(Vvch, Fvc1_coeffs) + Fs1_field = FemField(Vsh, Fs1_coeffs) + Fs2_field = FemField(Vsh, Fs2_coeffs) + Fvd1_field = FemField(Vvdh, Fvd1_coeffs) + + bilinear_forms = { # one and two free FemFields without derivatives (with derivatives in seperate test) + # complicated expressions + 'Q' :{'trial' :'V1', 'test':'V1', + 'expr' :dot(cross(F11, v1), cross(F11, v2)), + 'fields':[F11_field, ]}, + 'equilibrium' :{'trial' :'V1', 'test':'V1', + 'expr' :dot(cross(F11, v1), cross(v2, F12)), + 'fields':[F11_field, F12_field]}, + 'Elena' :{'trial' :'V1', 'test':'V1', + 'expr' :dot(F01*v1, v2), + 'fields':[F01_field, ]}, + # weight function, free FemField, different spaces + 'dot(grad(u),v)':{'trial' :'V0', 'test':'V1', + 'expr' :dot(grad(u1), v2)*F01*weight, + 'fields':[F01_field, ]}, + 'dot(curl(v),w)':{'trial' :'V1', 'test':'V2', + 'expr' :dot(curl(v1), F21)*div(w2)*weight, + 'fields':[F21_field, ]}, + # among other difficulties: multiple scalar FemFields + 'ScalarFields' :{'trial' :'V0', 'test':'V1', + 'expr' :dot(grad(u1), curl(Fvc1))*dot(grad(Fs1), curl(v2))*Fs2*div(Fvd1), + 'fields':[Fvc1_field, Fs1_field, Fs2_field, Fvd1_field]}, + # high derivatives, not FEEC + 'bilaplace' :{'trial' :'Vs', 'test':'Vs', + 'expr' :laplace(fs1)*laplace(fs2)} + } + + # test all BFs + # bilinear_form_strings_to_test = list(bilinear_forms.keys()) + + # or only a subset + bilinear_form_strings_to_test = list(bilinear_forms.keys())[:-1] # exclude expensive bilaplace test + + bilinear_forms_to_test = {} + for name in bilinear_form_strings_to_test: + bilinear_forms_to_test[name] = bilinear_forms[name] + + int_0 = lambda expr: integral(domain, expr) + print() + + for bf_name, bf_data in bilinear_forms_to_test.items(): + + trial_space = trial_spaces[bf_data['trial']] + Vh = trial_space['Vh'] + u = trial_space['funcs'][0] + test_space = test_spaces[bf_data['test']] + Wh = test_space ['Vh'] + v = test_space['funcs'][1] + expr = bf_data['expr'] + if 'fields' in bf_data.keys(): + fields = bf_data['fields'] + + a = BilinearForm((u, v), int_0(expr)) + + t0 = time.time() + ah_old = discretize(a, domain_h, (Vh, Wh), backend=backend, sum_factorization=False) + t1 = time.time() + discretization_time_old = t1 - t0 + + t0 = time.time() + ah = discretize(a, domain_h, (Vh, Wh), backend=backend) + t1 = time.time() + discretization_time = t1 - t0 + + if bf_name == 'Q': + t0_old = time.time() + A_old = ah_old.assemble(F11=fields[0]) + t1_old = time.time() + + t0 = time.time() + A = ah.assemble(F11=fields[0]) + t1 = time.time() + elif bf_name == 'equilibrium': + t0_old = time.time() + A_old = ah_old.assemble(F11=fields[0], F12=fields[1]) + t1_old = time.time() + + t0 = time.time() + A = ah.assemble(F11=fields[0], F12=fields[1]) + t1 = time.time() + elif bf_name in ('Elena', 'dot(grad(u),v)'): + t0_old = time.time() + A_old = ah_old.assemble(F01=fields[0]) + t1_old = time.time() + + t0 = time.time() + A = ah.assemble(F01=fields[0]) + t1 = time.time() + elif bf_name == 'dot(curl(v),w)': + t0_old = time.time() + A_old = ah_old.assemble(F21=fields[0]) + t1_old = time.time() + + t0 = time.time() + A = ah.assemble(F21=fields[0]) + t1 = time.time() + elif bf_name == 'ScalarFields': + t0_old = time.time() + A_old = ah_old.assemble(Fvc1=fields[0], Fs1=fields[1], Fs2=fields[2], Fvd1=fields[3]) + t1_old = time.time() + + t0 = time.time() + A = ah.assemble(Fvc1=fields[0], Fs1=fields[1], Fs2=fields[2], Fvd1=fields[3]) + t1 = time.time() + else: + t0_old = time.time() + A_old = ah_old.assemble() + t1_old = time.time() + + t0 = time.time() + A = ah.assemble() + t1 = time.time() + + assembly_time_old = t1_old - t0_old + assembly_time = t1 - t0 + + # Testing whether two linear operators are identical by comparing their arrays is quite expensive. + # Thus we instead test whether three random domain vectors applied to both + # the old and the new matrix produce the same codomain vector. + + domain_vector1 = Vh.coeff_space.zeros() + domain_vector2 = Vh.coeff_space.zeros() + domain_vector3 = Vh.coeff_space.zeros() + domain_vectors = [domain_vector1, domain_vector2, domain_vector3] + + if isinstance(Vh.coeff_space, BlockVectorSpace): + for domain_vector in domain_vectors: + for block in domain_vector.blocks: + rng.random(size=block._data.shape, dtype='float64', out=block._data) + else: + for domain_vector in domain_vectors: + rng.random(size=domain_vector._data.shape, dtype='float64', out=domain_vector._data) + + err = [] + rel_err = [] + + for domain_vector in domain_vectors: + codomain_vector = A @ domain_vector + codomain_vector_old = A_old @ domain_vector + + norm_old = np.sqrt(codomain_vector_old.inner(codomain_vector_old)) + + diff = codomain_vector - codomain_vector_old + + err.append(np.sqrt(diff.inner(diff))) + rel_err.append(err[-1] / norm_old) + + print(f' >>> Mapping: {mapping}') + print(f' >>> BilinearForm: {bf_name}') + print(f' >>> Discretization in: Old {discretization_time_old:.3g} \t\t || New {discretization_time:.3g} \t\t || Old/New {discretization_time_old/discretization_time:.3g}') + print(f' >>> Assembly in: Old {assembly_time_old:.3g} \t \t || New {assembly_time:.3g} \t\t || Old/New {assembly_time_old/assembly_time:.3g}') + print(f' >>> Error: {max(err):.3g}') + print(f' >>> Rel. Error: {max(rel_err):.3g}') + print() + + assert max(rel_err) < 1e-12 # arbitrary rel. error bound (How to test better?) + + +# fixed by PR #507 +#@pytest.mark.xfail +def test_allocate_matrix_bug(): + """ + This test is related to Issue #504. + + The bilinear form + (V0 x V3) ni (u, f) mapsto int_{Omega} u*f + should be the transpose of the bilinear form + (V3 x V0) ni (f, u) mapsto int_{Omega} u*f + but is not. + """ + + ncells = [15, 16, 17] + degree = [4, 3, 2] + periodic = [False, True, False] + + backend = PSYDAC_BACKEND_GPYCCEL + + domain = Cube('C', bounds1=(0,1), bounds2=(0,1), bounds3=(0,1)) + derham = Derham(domain) + + domain_h = discretize(domain, ncells=ncells, periodic=periodic) + derham_h = discretize(derham, domain_h, degree=degree) + + P0, _, _, P3 = derham_h.projectors() + + V0 = derham.V0 + V0h = derham_h.V0 + V3 = derham.V3 + V3h = derham_h.V3 + + u = element_of(V0, name='u') + f = element_of(V3, name='f') + + fun = lambda x, y, z : 1 + u_coeffs = P0(fun).coeffs + f_coeffs = P3(fun).coeffs + + a0 = BilinearForm((u, f), integral(domain, u*f)) + a1 = BilinearForm((f, u), integral(domain, u*f)) + + a0h = discretize(a0, domain_h, (V0h, V3h), backend=backend, sum_factorization=False) + a1h = discretize(a1, domain_h, (V3h, V0h), backend=backend, sum_factorization=False) + + A0 = a0h.assemble() + A1 = a1h.assemble() + A1T = A1.T + + # Clearly, it should hold A1T = A0, and further ||A0|| = ||A1||. + A0arr = A0.toarray() + A1arr = A1.toarray() + A1Tarr = A1T.toarray() + + diff1 = np.linalg.norm(A0arr - A1Tarr) + diff2 = np.linalg.norm(A0arr) - np.linalg.norm(A1arr) + + print(f' || A0 - A1.T || = {diff1:.3g}') + print(f' ||A0|| - ||A1|| = {diff2:.3g}') + + # Further, the following integral should evaluate to 1. + # This however is only the case for the second integral, + # independent on whether one uses the new or old assembly algorithm. + + print(f' 1 =? {A0.dot_inner(u_coeffs, f_coeffs)}') + print(f' 1 =? {A1.dot_inner(f_coeffs, u_coeffs)}') + + assert diff1 <= 1e-12 # arbitrary error bound + assert diff2 <= 1e-12 # arbitrary error bound + +#@pytest.mark.xfail +def test_free_FemField_derivatives(): + """ + These particular bilinear forms, when using a constant 1-vector coefficient vector for the free FemFields, + causes problems in a different test file of mine. + In particular, the assembled matrices used to have really small norms (~e-13). + That is probably due to the constant 1-vector corresponding to a constant function, + which means that all appearing derivatives of free FemFields are 0. + + When using meaningful free FemFields, these dubious observations disappeared. + + """ + + ncells = [5, 2, 4] + degree = [2, 1, 3] + periodic = [False, False, False] + + backend = PSYDAC_BACKEND_GPYCCEL + + domain = Cube('C', bounds1=(0,1), bounds2=(0,1), bounds3=(0,1)) + derham = Derham(domain) + + domain_h = discretize(domain, ncells=ncells, periodic=periodic) + derham_h = discretize(derham, domain_h, degree=degree) + + P0, P1, P2, P3 = derham_h.projectors() + + V0 = derham.V0 + V0h = derham_h.V0 + V1 = derham.V1 + V1h = derham_h.V1 + V2 = derham.V2 + V2h = derham_h.V2 + + u = element_of (V0, name= 'u') + v, F1 = elements_of(V1, names='v, F1') + w1, w2, F2 = elements_of(V2, names='w1, w2, F2') + + u_func = lambda x, y, z: x + y + z + u_coeffs = P0(u_func).coeffs + + v_1 = lambda x, y, z: 1 + v_2 = lambda x, y, z: 1 + v_3 = lambda x, y, z: 1 + v_func = (v_1, v_2, v_3) + v_coeffs = P1(v_func).coeffs + + w_1 = lambda x, y, z: x + w_2 = lambda x, y, z: y + w_3 = lambda x, y, z: z + w_func = (w_1, w_2, w_3) + w_coeffs = P2(w_func).coeffs + + dubious_observations = False + + if dubious_observations: + F1_coeffs = V1h.coeff_space.zeros() + F2_coeffs = V2h.coeff_space.zeros() + for block in F1_coeffs.blocks: + block._data = np.ones(block._data.shape, dtype='float64') + for block in F2_coeffs.blocks: + block._data = np.ones(block._data.shape, dtype='float64') + F1_FF = FemField(V1h, F1_coeffs) + F2_FF = FemField(V2h, F2_coeffs) + else: + F1_1 = lambda x, y, z: z + F1_2 = lambda x, y, z: x + F1_3 = lambda x, y, z: y + F1_func = (F1_1, F1_2, F1_3) + F1_FF = P1(F1_func) + + F2_FF = FemField(V2h, w_coeffs.copy()) + + # with the above choices (dubious_observation = False): + # a0 reduces to 3*int_{Omega}x+y+z with Omega being the unit square. Expected value: 4.5 + a0 = BilinearForm((u, v), integral(domain, dot(grad(u), curl(F1)) * dot(v, F1))) + # a1 reduces to 9* ----------------------------------------- " -------------------- 13.5 + a1 = BilinearForm((u, w2), integral(domain, dot(grad(u), F2)*div(w2)*div(F2))) + # a2 reduces to 3* ----------------------------------------- " --------------------- 4.5 + a2 = BilinearForm((w1, w2), integral(domain, dot(curl(F1), w1)*div(w2))) + + a0h_old = discretize(a0, domain_h, (V0h, V1h), backend=backend, sum_factorization=False) + a1h_old = discretize(a1, domain_h, (V0h, V2h), backend=backend, sum_factorization=False) + a2h_old = discretize(a2, domain_h, (V2h, V2h), backend=backend, sum_factorization=False) + + a0h = discretize(a0, domain_h, (V0h, V1h), backend=backend) + a1h = discretize(a1, domain_h, (V0h, V2h), backend=backend) + a2h = discretize(a2, domain_h, (V2h, V2h), backend=backend) + + bfs = [(a0h_old, a0h), (a1h_old, a1h), (a2h_old, a2h)] + print() + + for i, (ah_old, ah) in enumerate(bfs): + + if i in (0, 2): + A_old = ah_old.assemble(F1=F1_FF) + A = ah.assemble(F1=F1_FF) + else: + A_old = ah_old.assemble(F2=F2_FF) + A = ah.assemble(F2=F2_FF) + + if i == 0: + value_old = A_old.dot_inner(u_coeffs, v_coeffs) + value = A.dot_inner(u_coeffs, v_coeffs) + elif i == 1: + value_old = A_old.dot_inner(u_coeffs, w_coeffs) + value = A.dot_inner(u_coeffs, w_coeffs) + else: + value_old = A_old.dot_inner(w_coeffs, w_coeffs) + value = A.dot_inner(w_coeffs, w_coeffs) + + A_old_arr = A_old.toarray() + A_arr = A.toarray() + A_old_norm = np.linalg.norm(A_old_arr) + A_norm = np.linalg.norm(A_arr) + + err = np.linalg.norm(A_old_arr - A_arr) + rel_err = err / A_old_norm + + print(f' i = {i}') + print(f' >>> Error: {err:.3g}') + print(f' >>> Rel. Error: {rel_err:.3g}') + print(f' >>> Norms: ||A_old|| = {A_old_norm:.3g} \t\t ||A|| = {A_norm:.3g}') + print() + + # arbitrary tolerance + tol = 1e-12 + if not dubious_observations: + assert abs(value-value_old) < tol + assert rel_err < tol + +def test_assembly_free_FemFields(): + + backend = PSYDAC_BACKEND_GPYCCEL + + domain = Cube(bounds1=(2626,3179), bounds2=(-138, 138), bounds3=(-760.3, 69)) + derham = Derham(domain) + V0 = derham.V0 + V1 = derham.V1 + + u = element_of(V1, name='u') + v = element_of(V1, name='v') + p = element_of(V0, name='p') + + p_call = lambda xi,yi,zi: np.cos(2*np.pi*(xi-2626)/553) + np.tan(2*np.pi*(zi+760.3)/(5*829.3)) + x,y,z = domain.coordinates + p_sym = cos(2*np.pi*(x-2626)/553) + tan(2*np.pi*(z+760.3)/(5*829.3)) + + a_sym = BilinearForm((u, v), integral(domain, p_sym*dot(u, v))) + a_fem = BilinearForm((u, v), integral(domain, p*dot(u, v))) + + ncells = (11, 1, 17) + degree = (3, 1, 4) + domain_h = discretize(domain, ncells=ncells, periodic=(False, True, False)) + derham_h = discretize(derham, domain_h, degree=degree) + V1_h = derham_h.V1 + P0 = derham_h.projectors()[0] + + p_fem = P0(p_call) + + a_sym_h = discretize(a_sym, domain_h, (V1_h, V1_h), backend=backend) + a_fem_h = discretize(a_fem, domain_h, (V1_h, V1_h), backend=backend) + + A_sym = a_sym_h.assemble() + A_fem = a_fem_h.assemble(p=p_fem) + + A_sym_sp = A_sym.tosparse() + A_fem_sp = A_fem.tosparse() + diff = A_sym_sp - A_fem_sp + norm_sym = np.linalg.norm(A_sym_sp.data) + norm_fem = np.linalg.norm(A_fem_sp.data) + error = np.linalg.norm(diff.data) + rel_err = error / norm_sym + + #print(norm_sym, norm_fem, error, rel_err) + + assert rel_err < 1e-4 diff --git a/psydac/api/utilities.py b/psydac/api/utilities.py index c8080876b..108398e0f 100644 --- a/psydac/api/utilities.py +++ b/psydac/api/utilities.py @@ -1,16 +1,19 @@ # coding: utf-8 -from sympy.core.containers import Tuple -from sympy import Matrix, ImmutableDenseMatrix, MutableDenseNDimArray - -import inspect -import sys import os -import importlib import string import random -import numpy as np +from sympy.core.containers import Tuple +from sympy import Matrix, ImmutableDenseMatrix, MutableDenseNDimArray + +__all__ = ( + 'flatten', + 'mkdir_p', + 'touch_init_file', + 'random_string', + 'write_code' +) #============================================================================== def flatten(args): @@ -53,11 +56,26 @@ def touch_init_file(path): os.utime(path, None) #============================================================================== -def random_string( n ): - # we remove uppercase letters because of f2py - chars = string.ascii_lowercase + string.digits - selector = random.SystemRandom() - return ''.join( selector.choice( chars ) for _ in range( n ) ) +def random_string(size: int = 8, + chars: int = string.ascii_lowercase + string.digits) -> str: + """ + Create a random string of given length to be used in generated file names. + + Parameters + ---------- + size : int, optional + Length of the string (default: 8). + + chars : str, optional + A string with the avalailable characters for random drawing (default: + ASCII lower case characters + decimal digits) + + Returns + ------- + str + A random string of given length, made of the given characters. + """ + return ''.join(random.choice(chars) for _ in range(size)) #============================================================================== def write_code(filename, code, folder=None): @@ -81,4 +99,3 @@ def write_code(filename, code, folder=None): f.close() return filename - diff --git a/psydac/linalg/basic.py b/psydac/linalg/basic.py index f9f63406d..a6a02f68a 100644 --- a/psydac/linalg/basic.py +++ b/psydac/linalg/basic.py @@ -435,15 +435,35 @@ def H(self): def idot(self, v, out): """ - Implements out += self @ v with a temporary. - Subclasses should provide an implementation without a temporary. + Implements `out += self @ v` without a temporary, using a work array. + + This default implementation uses a local work array to store the result + of `self @ v`, and then sums it to the vector `out`. This doubles the + amount of read/write operations from/to local memory. If possible, + subclasses should provide a more efficient implementation which does + not use work arrays. + + Parameters + ---------- + v : Vector + The vector to which the linear operator `self` is applied. It must + belong to the domain of `self`. + + out : Vector + The vector to be incremented by `self @ v`. It must belong to the + codomain of `self`. """ - assert isinstance(v, Vector) - assert v.space == self.domain + assert isinstance( v, Vector) assert isinstance(out, Vector) - assert out.space == self.codomain - out += self.dot(v) + assert v.space is self.domain + assert out.space is self.codomain + + if not hasattr(self, '_work'): + self._work = self.codomain.zeros() + + self.dot(v, out=self._work) + out += self._work def dot_inner(self, v, w): """ @@ -695,6 +715,10 @@ def operator(self): def dtype(self): return None + def set_scalar(self, c): + """ Modifies the scalar with which this LinearOperator is multiplied. E.g. for updating the stepsize.""" + self._scalar = c + def toarray(self): return self._scalar*self._operator.toarray() @@ -758,7 +782,11 @@ def __init__(self, domain, codomain, *args): self._domain = domain self._codomain = codomain self._addends = addends + self._out = codomain.zeros() + #------------------------------------- + # Abstract interface + #------------------------------------- @property def domain(self): """ The domain of the linear operator, element of class ``VectorSpace``. """ @@ -769,26 +797,39 @@ def codomain(self): """ The codomain of the linear operator, element of class ``VectorSpace``. """ return self._codomain - @property - def addends(self): - """ A tuple containing the addends of the linear operator, elements of class ``LinearOperator``. """ - return self._addends - @property def dtype(self): return None + def tosparse(self): + from scipy.sparse import csr_matrix + out = csr_matrix(self.shape, dtype=self.dtype) + for a in self._addends: + out += a.tosparse() + return out + def toarray(self): out = np.zeros(self.shape, dtype=self.dtype) for a in self._addends: out += a.toarray() return out - def tosparse(self): - from scipy.sparse import csr_matrix - out = csr_matrix(self.shape, dtype=self.dtype) - for a in self._addends: - out += a.tosparse() + def dot(self, v, out=None): + """ Evaluates SumLinearOperator object at a vector v element of domain. """ + + assert isinstance(v, Vector) + assert v.space is self.domain + + if out is not None: + assert isinstance(out, Vector) + assert out.space is self.codomain + out *= 0 + else: + out = self.codomain.zeros() + + for A in self._addends: + A.idot(v, out) + return out def transpose(self, conjugate=False): @@ -797,6 +838,14 @@ def transpose(self, conjugate=False): t_addends = (*t_addends, a.transpose(conjugate=conjugate)) return SumLinearOperator(self.codomain, self.domain, *t_addends) + #-------------------------------------- + # Other properties/methods + #-------------------------------------- + @property + def addends(self): + """ A tuple containing the addends of the linear operator, elements of class ``LinearOperator``. """ + return self._addends + @staticmethod def simplify(addends): """ Simplifies a sum of linear operators by combining addends of the same class. """ @@ -819,23 +868,6 @@ def simplify(addends): out = (*out, A) return out - def dot(self, v, out=None): - """ Evaluates SumLinearOperator object at a vector v element of domain. """ - assert isinstance(v, Vector) - assert v.space == self.domain - if out is not None: - assert isinstance(out, Vector) - assert out.space == self.codomain - out *= 0 - for a in self._addends: - a.idot(v, out) - return out - else: - out = self.codomain.zeros() - for a in self._addends: - a.idot(v, out=out) - return out - #=============================================================================== class ComposedLinearOperator(LinearOperator): r""" From fe56bcd96db042d2048c0d50ca4c5387b94958bd Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Mon, 22 Sep 2025 21:04:18 +0200 Subject: [PATCH 15/23] Improve multipatch FEM API (#509) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit ### Commit summary - Fix #461 : Move contents of `psydac/feec/multipatch/api.py` to `psydac/api/feec.py` and `psydac/api/discretization.py`. - Remove old code from `psydac/feec/multipatch/operators.py` and replace it by the contents in `psydac/feec/multipatch/non_matching_operators.py` to make the structure more clear. - Fix #463 - Fix #272 : keep the `FEMLinearOperator` as a more light-weight class that encapsulates a `LinearOperator` and has a `apply` and `__call__` function to make it act on a `FEMField`. Remove duplicated code with `LinearOperator`. Make operators in `psydac/feec` subclasses of `LinearOperator`. - Fix #462: Add conforming projections and Hodge operators to single-patch `DiscreteDeRham` - Add single-patch test for the conforming projectors - Adapt all the tests/files to the new notations. For the single patch cases mostly renaming `derham_h.derivatives` to `derham_h.derivatives()` and `derham_h.derivatives_as_matrices` to `derham_h.derivatives(kind='linop')` - Merge single-patch and multi-patch operators to the same file if it makes things clearer. Take Hodge and conforming projection operators out of the multipatch subdirectory. - Fix #409 : the global projector interface in DiscreteDeRhamMultipatch - Fix #331. - Add a `SparseMatrixLinearOperator` in `psydac/linalg/sparse.py` to use a sparse matrix as a `LinearOperator`. This is needed for the conforming projections. - Rename `GlobalProjectors` to `GlobalGeometricProjectors` ### Notes With the current changes, we get all FEEC operators directly from the discrete de Rham object. Further, the same code also runs if the domain is a single patch. --------- Co-authored-by: Yaman Güçlü --- docs/source/modules/feec.multipatch.rst | 5 - docs/source/modules/feec.rst | 4 +- docs/source/modules/linalg.rst | 1 + psydac/api/discretization.py | 61 +- psydac/api/feec.py | 484 ++++++- psydac/api/tests/test_api_2d_fields.py | 10 +- psydac/api/tests/test_api_feec_1d.py | 2 +- psydac/api/tests/test_api_feec_2d.py | 2 +- psydac/api/tests/test_api_feec_3d.py | 8 +- psydac/api/tests/test_assembly.py | 2 +- ..._operators.py => conforming_projectors.py} | 573 ++++++-- psydac/feec/derivatives.py | 220 ++- ...tors.py => global_geometric_projectors.py} | 60 +- psydac/feec/hodge.py | 148 ++ psydac/feec/multipatch/api.py | 301 ---- .../examples/h1_source_pbms_conga_2d.py | 162 +-- .../examples/hcurl_eigen_pbms_conga_2d.py | 170 +-- .../examples/hcurl_eigen_pbms_dg_2d.py | 78 +- .../examples/hcurl_eigen_testcases.py | 4 - .../examples/hcurl_source_pbms_conga_2d.py | 207 +-- .../examples/hcurl_source_testcase.py | 4 - .../multipatch/examples/ppc_test_cases.py | 17 +- .../multipatch/examples/timedomain_maxwell.py | 937 +++---------- .../examples/timedomain_maxwell_testcase.py | 159 +-- .../feec/multipatch/fem_linear_operators.py | 218 --- psydac/feec/multipatch/operators.py | 1248 ----------------- .../tests/test_feec_maxwell_multipatch_2d.py | 20 +- .../tests/test_feec_poisson_multipatch_2d.py | 5 +- psydac/feec/multipatch/utils_conga_2d.py | 193 ++- psydac/feec/tests/test_axis_projection.py | 6 +- .../feec/tests/test_commuting_projections.py | 60 +- .../tests/test_commuting_projections_dual.py | 18 +- .../tests/test_differentiation_matrices.py | 58 +- .../test_feec_conf_projectors_cart_2d.py | 193 +-- psydac/feec/tests/test_global_projectors.py | 16 +- .../feec/tests/test_projections_parallel.py | 26 +- psydac/fem/basic.py | 87 +- psydac/fem/projectors.py | 64 +- psydac/linalg/basic.py | 7 +- psydac/linalg/sparse.py | 114 ++ psydac/linalg/tests/test_block.py | 82 ++ psydac/linalg/utilities.py | 4 +- 42 files changed, 2373 insertions(+), 3665 deletions(-) rename psydac/feec/{multipatch/non_matching_operators.py => conforming_projectors.py} (68%) rename psydac/feec/{global_projectors.py => global_geometric_projectors.py} (94%) create mode 100644 psydac/feec/hodge.py delete mode 100644 psydac/feec/multipatch/api.py delete mode 100644 psydac/feec/multipatch/fem_linear_operators.py delete mode 100644 psydac/feec/multipatch/operators.py rename psydac/feec/{multipatch => }/tests/test_feec_conf_projectors_cart_2d.py (54%) create mode 100644 psydac/linalg/sparse.py diff --git a/docs/source/modules/feec.multipatch.rst b/docs/source/modules/feec.multipatch.rst index 64bf49a12..85bf08af1 100644 --- a/docs/source/modules/feec.multipatch.rst +++ b/docs/source/modules/feec.multipatch.rst @@ -7,11 +7,6 @@ feec.multipatch :toctree: STUBDIR :template: autosummary/module.rst - multipatch.api - multipatch.fem_linear_operators multipatch.multipatch_domain_utilities - multipatch.non_matching_operators - multipatch.operators - multipatch.plotting_utilities multipatch.utilities multipatch.utils_conga_2d diff --git a/docs/source/modules/feec.rst b/docs/source/modules/feec.rst index 5d424f396..f75dfb8cc 100644 --- a/docs/source/modules/feec.rst +++ b/docs/source/modules/feec.rst @@ -7,8 +7,10 @@ feec :toctree: STUBDIR :template: autosummary/module.rst + feec.conforming_projectors feec.derivatives - feec.global_projectors + feec.global_geometric_projectors + feec.hodge feec.pull_push feec.pushforward diff --git a/docs/source/modules/linalg.rst b/docs/source/modules/linalg.rst index 7ccbbf491..a625296ef 100644 --- a/docs/source/modules/linalg.rst +++ b/docs/source/modules/linalg.rst @@ -14,6 +14,7 @@ linalg linalg.kernels linalg.kron linalg.solvers + linalg.sparse linalg.stencil linalg.topetsc linalg.utilities diff --git a/psydac/api/discretization.py b/psydac/api/discretization.py index 1cea9397e..bedec470e 100644 --- a/psydac/api/discretization.py +++ b/psydac/api/discretization.py @@ -30,7 +30,7 @@ from psydac.api.fem import DiscreteBilinearForm from psydac.api.fem import DiscreteLinearForm from psydac.api.fem import DiscreteFunctional -from psydac.api.feec import DiscreteDerham +from psydac.api.feec import DiscreteDeRham, DiscreteDeRhamMultipatch from psydac.api.glt import DiscreteGltExpr from psydac.api.expr import DiscreteExpr from psydac.api.equation import DiscreteEquation @@ -47,6 +47,7 @@ __all__ = ( 'discretize', 'discretize_derham', + 'discretize_derham_multipatch', 'reduce_space_degrees', 'discretize_space', 'discretize_domain' @@ -147,10 +148,10 @@ def get_max_degree(*spaces): #============================================================================== def discretize_derham(derham, domain_h, *, get_H1vec_space=False, **kwargs): """ - Create a discrete De Rham sequence from a symbolic one. + Create a discrete de Rham sequence from a symbolic one. This function creates the discrete spaces from the symbolic ones, and then - creates a DiscreteDerham object from them. + creates a DiscreteDeRham object from them. Parameters ---------- @@ -168,18 +169,16 @@ def discretize_derham(derham, domain_h, *, get_H1vec_space=False, **kwargs): Returns ------- - DiscreteDerham - The discrete De Rham sequence containing the discrete spaces, + DiscreteDeRham + The discrete de Rham sequence containing the discrete spaces, differential operators and projectors. See Also -------- discretize_space - """ ldim = derham.shape - mapping = domain_h.domain.mapping # NOTE: assuming single-patch domain! bases = ['B'] + ldim * ['M'] spaces = [discretize_space(V, domain_h, basis=basis, **kwargs) for V, basis in zip(derham.spaces, bases)] @@ -192,7 +191,48 @@ def discretize_derham(derham, domain_h, *, get_H1vec_space=False, **kwargs): #We still need to specify the symbolic space because of "_recursive_element_of" not implemented in sympde spaces.append(Xh) - return DiscreteDerham(mapping, *spaces) + return DiscreteDeRham(domain_h, *spaces) + +#============================================================================== +def discretize_derham_multipatch(derham, domain_h, **kwargs): + """ + Create a discrete multipatch de Rham sequence from a symbolic one. + + This function creates the broken discrete spaces from the symbolic ones, and then + creates a DiscreteDeRhamMultipatch object from them. + + Parameters + ---------- + derham : sympde.topology.space.Derham + The symbolic Derham sequence. + + domain_h : Geometry + Discrete domain where the spaces will be discretized. + + **kwargs : dict + Optional parameters for the space discretization. + + Returns + ------- + DiscreteDeRhamMultipatch + The discrete multipatch de Rham sequence containing the discrete spaces, + differential operators and projectors. + + See Also + -------- + discretize_derham + discretize_space + """ + + ldim = derham.shape + bases = ['B'] + ldim * ['M'] + spaces = [discretize_space(V, domain_h, basis=basis, **kwargs) \ + for V, basis in zip(derham.spaces, bases)] + + return DiscreteDeRhamMultipatch( + domain_h = domain_h, + spaces = spaces + ) #============================================================================== def reduce_space_degrees(V, Vh, *, basis='B', sequence='DR'): @@ -631,9 +671,12 @@ def discretize(a, *args, **kwargs): elif isinstance(a, BasicFunctionSpace): return discretize_space(a, *args, **kwargs) - elif isinstance(a, Derham): + elif isinstance(a, Derham) and not a.V0.is_broken: return discretize_derham(a, *args, **kwargs) + elif isinstance(a, Derham) and a.V0.is_broken: + return discretize_derham_multipatch(a, *args, **kwargs) + elif isinstance(a, Domain): return discretize_domain(a, *args, **kwargs) diff --git a/psydac/api/feec.py b/psydac/api/feec.py index cfec097eb..2bd95ffbd 100644 --- a/psydac/api/feec.py +++ b/psydac/api/feec.py @@ -1,45 +1,54 @@ -from sympde.topology.mapping import Mapping - -from psydac.api.basic import BasicDiscrete -from psydac.feec.derivatives import Derivative_1D, Gradient_2D, Gradient_3D -from psydac.feec.derivatives import ScalarCurl_2D, VectorCurl_2D, Curl_3D -from psydac.feec.derivatives import Divergence_2D, Divergence_3D -from psydac.feec.global_projectors import Projector_H1, Projector_Hcurl, Projector_H1vec -from psydac.feec.global_projectors import Projector_Hdiv, Projector_L2 -from psydac.feec.pull_push import pull_1d_h1, pull_1d_l2 -from psydac.feec.pull_push import pull_2d_h1, pull_2d_hcurl, pull_2d_hdiv, pull_2d_l2, pull_2d_h1vec -from psydac.feec.pull_push import pull_3d_h1, pull_3d_hcurl, pull_3d_hdiv, pull_3d_l2, pull_3d_h1vec -from psydac.fem.basic import FemSpace -from psydac.fem.vector import VectorFemSpace - -__all__ = ('DiscreteDerham',) +from psydac.api.basic import BasicDiscrete + +from psydac.feec.derivatives import Derivative1D, Gradient2D, Gradient3D +from psydac.feec.derivatives import ScalarCurl2D, VectorCurl2D, Curl3D +from psydac.feec.derivatives import Divergence2D, Divergence3D +from psydac.feec.derivatives import BrokenGradient2D +from psydac.feec.derivatives import BrokenScalarCurl2D + +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorH1 +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHcurl +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorH1vec +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHdiv +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorL2 +from psydac.feec.global_geometric_projectors import MultipatchGeometricProjector + +from psydac.feec.conforming_projectors import ConformingProjectionV0 +from psydac.feec.conforming_projectors import ConformingProjectionV1 + +from psydac.feec.hodge import HodgeOperator + +from psydac.feec.pull_push import pull_1d_h1, pull_1d_l2 +from psydac.feec.pull_push import pull_2d_h1, pull_2d_hcurl +from psydac.feec.pull_push import pull_2d_hdiv, pull_2d_l2, pull_2d_h1vec +from psydac.feec.pull_push import pull_3d_h1, pull_3d_hcurl +from psydac.feec.pull_push import pull_3d_hdiv, pull_3d_l2, pull_3d_h1vec + +from psydac.fem.basic import FemSpace, FemLinearOperator +from psydac.fem.vector import VectorFemSpace +from psydac.linalg.basic import IdentityOperator + +__all__ = ('DiscreteDeRham', 'DiscreteDeRhamMultipatch',) #============================================================================== -class DiscreteDerham(BasicDiscrete): +class DiscreteDeRham(BasicDiscrete): """ A discrete de Rham sequence built over a single-patch geometry. Parameters ---------- - mapping : Mapping or None - Symbolic mapping from the logical space to the physical space, if any. + domain_h : Geometry + The discretized domain, which is a single-patch geometry. *spaces : list of FemSpace The discrete spaces of the de Rham sequence. Notes ----- - - The basic type Mapping is defined in module sympde.topology.mapping. - A discrete mapping (spline or NURBS) may be attached to it. - - This constructor should not be called directly, but rather from the `discretize_derham` function in `psydac.api.discretization`. - - - For the multipatch counterpart of this class please see - `MultipatchDiscreteDerham` in `psydac.feec.multipatch.api`. """ - def __init__(self, mapping, *spaces): + def __init__(self, domain_h, *spaces): - assert (mapping is None) or isinstance(mapping, Mapping) assert all(isinstance(space, FemSpace) for space in spaces) self.has_vec = isinstance(spaces[-1], VectorFemSpace) @@ -53,51 +62,75 @@ def __init__(self, mapping, *spaces): dim = len(spaces) - 1 self._spaces = spaces + self._domain_h = domain_h + self._sequence = tuple(space.symbolic_space.kind.name for space in spaces) self._dim = dim - self._mapping = mapping - self._callable_mapping = mapping.get_callable_mapping() if mapping else None + self._mapping = domain_h.domain.mapping + self._callable_mapping = self._mapping.get_callable_mapping() if self._mapping else None if dim == 1: - D0 = Derivative_1D(spaces[0], spaces[1]) + D0 = Derivative1D(spaces[0], spaces[1]) + spaces[0].diff = spaces[0].grad = D0 + self._derivatives = (D0,) + elif dim == 2: kind = spaces[1].symbolic_space.kind.name if kind == 'hcurl': - D0 = Gradient_2D(spaces[0], spaces[1]) - D1 = ScalarCurl_2D(spaces[1], spaces[2]) + D0 = Gradient2D(spaces[0], spaces[1]) + D1 = ScalarCurl2D(spaces[1], spaces[2]) spaces[0].diff = spaces[0].grad = D0 spaces[1].diff = spaces[1].curl = D1 + self._derivatives = (D0, D1) + elif kind == 'hdiv': - D0 = VectorCurl_2D(spaces[0], spaces[1]) - D1 = Divergence_2D(spaces[1], spaces[2]) + D0 = VectorCurl2D(spaces[0], spaces[1]) + D1 = Divergence2D(spaces[1], spaces[2]) spaces[0].diff = spaces[0].rot = D0 spaces[1].diff = spaces[1].div = D1 + self._derivatives = (D0, D1) + + elif dim == 3: - D0 = Gradient_3D(spaces[0], spaces[1]) - D1 = Curl_3D(spaces[1], spaces[2]) - D2 = Divergence_3D(spaces[2], spaces[3]) + D0 = Gradient3D(spaces[0], spaces[1]) + D1 = Curl3D(spaces[1], spaces[2]) + D2 = Divergence3D(spaces[2], spaces[3]) spaces[0].diff = spaces[0].grad = D0 spaces[1].diff = spaces[1].curl = D1 spaces[2].diff = spaces[2].div = D2 + self._derivatives = (D0, D1, D2) + else: raise ValueError('Dimension {} is not available'.format(dim)) + self._hodge_operators = () + self._conf_proj = () #-------------------------------------------------------------------------- @property def dim(self): """Dimension of the physical and logical domains, which are assumed to be the same.""" return self._dim + + @property + def domain_h(self): + """Discretized domain.""" + return self._domain_h + + @property + def spaces(self): + """Spaces of the proper de Rham sequence (excluding Hvec).""" + return self._spaces @property def V0(self): @@ -124,6 +157,10 @@ def V3(self): """Fourth space of the de Rham sequence : L2 space in 3d""" return self._spaces[3] + @property + def sequence(self): + return self._sequence + @property def H1vec(self): """Vector-valued H1 space built as the Cartesian product of N copies of V0, @@ -131,11 +168,6 @@ def H1vec(self): assert self.has_vec return self._H1vec - @property - def spaces(self): - """Spaces of the proper de Rham sequence (excluding Hvec).""" - return self._spaces - @property def mapping(self): """The mapping from the logical space to the physical space.""" @@ -146,32 +178,17 @@ def callable_mapping(self): """The mapping as a callable.""" return self._callable_mapping - @property - def derivatives_as_matrices(self): - """Differential operators of the De Rham sequence as LinearOperator objects.""" - return tuple(V.diff.matrix for V in self.spaces[:-1]) - - @property - def derivatives(self): - """Differential operators of the De Rham sequence as `DiffOperator` objects. - - Those are objects with `domain` and `codomain` properties that are `FemSpace`, - they act on `FemField` (they take a `FemField` of their `domain` as input and return - a `FemField` of their `codomain`. - """ - return tuple(V.diff for V in self.spaces[:-1]) - #-------------------------------------------------------------------------- def projectors(self, *, kind='global', nquads=None): """Projectors mapping callable functions of the physical coordinates to a - corresponding `FemField` object in the De Rham sequence. + corresponding `FemField` object in the de Rham sequence. Parameters ---------- kind : str Type of the projection : at the moment, only global is accepted and returns geometric commuting projectors based on interpolation/histopolation - for the De Rham sequence (GlobalProjector objects). + for the de Rham sequence (GlobalProjector objects). nquads : list(int) | tuple(int) Number of quadrature points along each direction, to be used in Gauss @@ -182,7 +199,7 @@ def projectors(self, *, kind='global', nquads=None): P0, ..., Pn : callables Projectors that can be called on any callable function that maps from the physical space to R (scalar case) or R^d (vector case) and - returns a FemField belonging to the i-th space of the De Rham sequence + returns a FemField belonging to the i-th space of the de Rham sequence """ if not (kind == 'global'): @@ -200,8 +217,8 @@ def projectors(self, *, kind='global', nquads=None): assert all(nq >= 1 for nq in nquads) if self.dim == 1: - P0 = Projector_H1(self.V0) - P1 = Projector_L2(self.V1, nquads) + P0 = GlobalGeometricProjectorH1(self.V0) + P1 = GlobalGeometricProjectorL2(self.V1, nquads) if self.mapping: P0_m = lambda f: P0(pull_1d_h1(f, self.callable_mapping)) P1_m = lambda f: P1(pull_1d_l2(f, self.callable_mapping)) @@ -209,19 +226,19 @@ def projectors(self, *, kind='global', nquads=None): return P0, P1 elif self.dim == 2: - P0 = Projector_H1(self.V0) - P2 = Projector_L2(self.V2, nquads) + P0 = GlobalGeometricProjectorH1(self.V0) + P2 = GlobalGeometricProjectorL2(self.V2, nquads) kind = self.V1.symbolic_space.kind.name if kind == 'hcurl': - P1 = Projector_Hcurl(self.V1, nquads) + P1 = GlobalGeometricProjectorHcurl(self.V1, nquads) elif kind == 'hdiv': - P1 = Projector_Hdiv(self.V1, nquads) + P1 = GlobalGeometricProjectorHdiv(self.V1, nquads) else: raise TypeError('projector of space type {} is not available'.format(kind)) if self.has_vec : - Pvec = Projector_H1vec(self.H1vec, nquads) + Pvec = GlobalGeometricProjectorH1vec(self.H1vec, nquads) if self.mapping: P0_m = lambda f: P0(pull_2d_h1(f, self.callable_mapping)) @@ -242,12 +259,12 @@ def projectors(self, *, kind='global', nquads=None): return P0, P1, P2 elif self.dim == 3: - P0 = Projector_H1 (self.V0) - P1 = Projector_Hcurl(self.V1, nquads) - P2 = Projector_Hdiv (self.V2, nquads) - P3 = Projector_L2 (self.V3, nquads) + P0 = GlobalGeometricProjectorH1 (self.V0) + P1 = GlobalGeometricProjectorHcurl(self.V1, nquads) + P2 = GlobalGeometricProjectorHdiv (self.V2, nquads) + P3 = GlobalGeometricProjectorL2 (self.V3, nquads) if self.has_vec : - Pvec = Projector_H1vec(self.H1vec) + Pvec = GlobalGeometricProjectorH1vec(self.H1vec) if self.mapping: P0_m = lambda f: P0(pull_3d_h1 (f, self.callable_mapping)) P1_m = lambda f: P1(pull_3d_hcurl(f, self.callable_mapping)) @@ -264,3 +281,328 @@ def projectors(self, *, kind='global', nquads=None): else : return P0, P1, P2, P3 + #-------------------------------------------------------------------------- + def derivatives(self, kind='femlinop'): + if kind == 'femlinop': + return self._derivatives + elif kind == 'linop': + return tuple(b_diff.linop for b_diff in self._derivatives) + + #-------------------------------------------------------------------------- + def conforming_projectors(self, kind='femlinop', mom_pres=False, p_moments=-1, hom_bc=False): + """ + return the conforming projectors of the broken multi-patch space + + Parameters + ---------- + + p_moments : + The number of moments preserved by the projector. + + hom_bc: + Apply homogenous boundary conditions if True + + kind : + The kind of the projector, can be 'femlinop' or 'linop'. + - 'femlinop' returns a psydac FemLinearOperator (default) + - 'linop' returns a psydac LinearOperator + + Returns + ------- + cP0, cP1, cP2 : Tuple of or + The conforming projectors of each space and in desired form. + + """ + + if hom_bc is None: + raise ValueError('please provide a value for "hom_bc" argument') + + if self.dim == 1: + raise NotImplementedError("1D projectors are not available") + + elif self.dim == 2: + if self.sequence[1] != 'hcurl': + raise NotImplementedError('2D sequence with H-div not available yet') + + else: + + if not self._conf_proj: + + cP0 = ConformingProjectionV0(self.V0, mom_pres=mom_pres, p_moments=p_moments, hom_bc=hom_bc) + cP1 = ConformingProjectionV1(self.V1, mom_pres=mom_pres, p_moments=p_moments, hom_bc=hom_bc) + + I2 = IdentityOperator(self.V2.coeff_space) + cP2 = FemLinearOperator(fem_domain=self.V2, fem_codomain=self.V2, linop=I2) + + self._conf_proj = (cP0, cP1, cP2) + + if kind == 'femlinop': + return self._conf_proj[0], self._conf_proj[1], self._conf_proj[2] + elif kind == 'linop': + return self._conf_proj[0].linop, self._conf_proj[1].linop, self._conf_proj[2].linop + + elif self.dim == 3: + raise NotImplementedError("3D projectors are not available") + + #-------------------------------------------------------------------------- + def _init_hodge_operators(self, backend_language='python'): + """ + Initialize the Hodge operator for the multipatch de Rham sequence. + + Parameters + ---------- + + backend_language: + The backend used to accelerate the code + + """ + if not self._hodge_operators: + + if self.dim == 1: + H0 = HodgeOperator(self.V0, self.domain_h, backend_language=backend_language) + H1 = HodgeOperator(self.V1, self.domain_h, backend_language=backend_language) + + self._hodge_operators = (H0, H1) + + elif self.dim == 2: + + H0 = HodgeOperator(self.V0, self.domain_h, backend_language=backend_language) + H1 = HodgeOperator(self.V1, self.domain_h, backend_language=backend_language) + H2 = HodgeOperator(self.V2, self.domain_h, backend_language=backend_language) + + self._hodge_operators = (H0, H1, H2) + + elif self.dim == 3: + + H0 = HodgeOperator(self.V0, self.domain_h, backend_language=backend_language) + H1 = HodgeOperator(self.V1, self.domain_h, backend_language=backend_language) + H2 = HodgeOperator(self.V2, self.domain_h, backend_language=backend_language) + H3 = HodgeOperator(self.V3, self.domain_h, backend_language=backend_language) + + self._hodge_operators = (H0, H1, H2, H3) + + #-------------------------------------------------------------------------- + def _get_hodge_operator(self, H, dual=False, kind='femlinop'): + """ + Helper function to return the Hodge operator in the specified form. + + Parameters + ---------- + H : + + dual : + If True, returns the dual Hodge operator + + kind : + The kind of the projector, can be 'femlinop' or 'linop'. + - 'femlinop' returns a psydac FemLinearOperator (default) + - 'linop' returns a psydac LinearOperator + + Returns + ------- + Hodge operator in the specified form. + """ + + if not dual: + if kind == 'femlinop': + return H.hodge + elif kind == 'linop': + return H.linop + else: + if kind == 'femlinop': + return H.dual_hodge + elif kind == 'linop': + return H.dual_linop + + #-------------------------------------------------------------------------- + def hodge_operator(self, space=None, dual=False, kind='femlinop', backend_language='python'): + """ + Returns the Hodge operator for the given space and specified kind. + + Parameters + ---------- + space : str or None + The space for which to return the Hodge operator, can be 'V0', 'V1', 'V2' or None. + If None, returns a tuple with all three Hodge operators. + + dual : bool + If True, returns the dual Hodge operator. + + kind : + The kind of the projector, can be 'femlinop' or 'linop'. + - 'femlinop' returns a psydac FemLinearOperator (default) + - 'linop' returns a psydac LinearOperator + + backend_language : str + The backend used to accelerate the code, default is 'python'. + + Returns + ------- + The Hodge operator of the space of the specified kind. + + H : or + """ + + if not self._hodge_operators: + self._init_hodge_operators(backend_language=backend_language) + + if space == 'V0': + return self._get_hodge_operator(self._hodge_operators[0], dual=dual, kind=kind) + + elif space == 'V1': + return self._get_hodge_operator(self._hodge_operators[1], dual=dual, kind=kind) + + elif space == 'V2': + return self._get_hodge_operator(self._hodge_operators[2], dual=dual, kind=kind) + + elif space == 'V3': + return self._get_hodge_operator(self._hodge_operators[3], dual=dual, kind=kind) + + #-------------------------------------------------------------------------- + def hodge_operators(self, dual=False, kind='femlinop', backend_language='python'): + """ + Returns the Hodge operators for the specified kind. + + Parameters + ---------- + dual : bool + If True, returns the dual Hodge operator. + + kind : + The kind of the projector, can be 'femlinop' or 'linop'. + - 'femlinop' returns a psydac FemLinearOperator (default) + - 'linop' returns a psydac LinearOperator + + backend_language : str + The backend used to accelerate the code, default is 'python'. + + Returns + ------- + The Hodge operators of all spaces and of the specified kind. + """ + + if not self._hodge_operators: + self._init_hodge_operators(backend_language=backend_language) + + return tuple(self._get_hodge_operator(H, dual=dual, kind=kind) for H in self._hodge_operators) + + +#============================================================================== +class DiscreteDeRhamMultipatch(DiscreteDeRham): + """ Represents the discrete de Rham sequence for multipatch domains. + It only works when the number of patches>1. + + Parameters + ---------- + domain_h: + The discrete domain + + spaces: + The discrete spaces that are contained in the de Rham sequence + """ + + def __init__(self, *, domain_h, spaces): + + dim = len(spaces) - 1 + self._spaces = tuple(spaces) + self._dim = dim + self._mapping = domain_h.domain.mapping + self._callable_mapping = [m.get_callable_mapping() for m in self._mapping.mappings.values()] if self._mapping else None + self._domain_h = domain_h + self._sequence = tuple(space.symbolic_space.kind.name for space in spaces) + + + if dim == 1: + raise NotImplementedError('1D FEEC multipatch non available yet') + + elif dim == 2: + + if self._sequence[1] == 'hcurl': + + self._derivatives = ( + BrokenGradient2D(self.V0, self.V1), + BrokenScalarCurl2D(self.V1, self.V2), # None, + ) + + elif self._sequence[1] == 'hdiv': + raise NotImplementedError('2D sequence with H-div not available yet') + + else: + raise ValueError('2D sequence not understood') + + elif dim == 3: + raise NotImplementedError('3D FEEC multipatch non available yet') + + else: + raise ValueError('Dimension {} is not available'.format(dim)) + + self._hodge_operators = () + self._conf_proj = () + + #-------------------------------------------------------------------------- + @property + def H1vec(self): + raise NotImplementedError('Not implemented for Multipatch de Rham sequences.') + + #-------------------------------------------------------------------------- + def projectors(self, *, kind='global', nquads=None): + """ + This method returns the patch-wise commuting projectors on the broken multi-patch space + + Parameters + ---------- + kind: + The projectors kind, can be global or local + + nquads: + The number of quadrature points. + + Returns + ------- + P0: + Patch wise H1 projector + + P1: + Patch wise Hcurl projector + + P2: + Patch wise L2 projector + + Notes + ----- + - when applied to smooth functions they return conforming fields + - default 'global projectors' correspond to geometric interpolation/histopolation operators on Greville grids + - here 'global' is a patch-level notion, as the interpolation-type problems are solved on each patch independently + """ + if not (kind == 'global'): + raise NotImplementedError('only global projectors are available') + + if self.dim == 1: + raise NotImplementedError("1D projectors are not available") + + elif self.dim == 2: + P0 = MultipatchGeometricProjector(self.V0, GlobalGeometricProjectorH1) + + if self.sequence[1] == 'hcurl': + P1 = MultipatchGeometricProjector(self.V1, GlobalGeometricProjectorHcurl, nquads=nquads) + else: + P1 = MultipatchGeometricProjector(self.V1, GlobalGeometricProjectorHdiv, nquads=nquads) + + P2 = MultipatchGeometricProjector(self.V2, GlobalGeometricProjectorL2, nquads=nquads) + + if self.mapping: + P0_m = lambda f : P0([pull_2d_h1(f, m) for m in self.callable_mapping]) + + if self.sequence[1] == 'hcurl': + P1_m = lambda f : P1([pull_2d_hcurl(f, m) for m in self.callable_mapping]) + else: + raise NotImplementedError('2D sequence with H-div not available yet') + + P2_m = lambda f : P2([pull_2d_l2(f, m) for m in self.callable_mapping]) + + return P0_m, P1_m, P2_m + + return P0, P1, P2 + + elif self.dim == 3: + raise NotImplementedError("3D projectors are not available") diff --git a/psydac/api/tests/test_api_2d_fields.py b/psydac/api/tests/test_api_2d_fields.py index abd7a1d75..d829bcfd5 100644 --- a/psydac/api/tests/test_api_2d_fields.py +++ b/psydac/api/tests/test_api_2d_fields.py @@ -32,10 +32,10 @@ from sympde.expr import Norm from sympde.expr import find, EssentialBC -from psydac.fem.basic import FemField -from psydac.api.discretization import discretize -from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL -from psydac.feec.global_projectors import Projector_H1 +from psydac.fem.basic import FemField +from psydac.api.discretization import discretize +from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorH1 # ... get the mesh directory try: @@ -142,7 +142,7 @@ def run_boundary_field_test(domain, boundary, f, ncells): x,y = domain.coordinates f_lambda = lambdify([x,y], f, 'math') - Pi0 = Projector_H1(Vh) + Pi0 = GlobalGeometricProjectorH1(Vh) fh = Pi0(f_lambda) fh.coeffs.update_ghost_regions() diff --git a/psydac/api/tests/test_api_feec_1d.py b/psydac/api/tests/test_api_feec_1d.py index ad60a2c02..fd7e7f7dd 100644 --- a/psydac/api/tests/test_api_feec_1d.py +++ b/psydac/api/tests/test_api_feec_1d.py @@ -145,7 +145,7 @@ class CollelaMapping1D(Mapping): M1 = a1_h.assemble() # Differential operators - D0, = derham_h.derivatives_as_matrices + D0, = derham_h.derivatives(kind='linop') # Transpose of derivative matrix D0_T = D0.T diff --git a/psydac/api/tests/test_api_feec_2d.py b/psydac/api/tests/test_api_feec_2d.py index 40b607615..c221af521 100644 --- a/psydac/api/tests/test_api_feec_2d.py +++ b/psydac/api/tests/test_api_feec_2d.py @@ -325,7 +325,7 @@ class CollelaMapping2D(Mapping): M2 = a2_h.assemble() # Differential operators (StencilMatrix or BlockLinearOperator objects) - D0, D1 = derham_h.derivatives_as_matrices + D0, D1 = derham_h.derivatives(kind='linop') # Discretize and assemble penalization matrix if not periodic: diff --git a/psydac/api/tests/test_api_feec_3d.py b/psydac/api/tests/test_api_feec_3d.py index 9da51f784..3a05bdf0b 100644 --- a/psydac/api/tests/test_api_feec_3d.py +++ b/psydac/api/tests/test_api_feec_3d.py @@ -130,8 +130,8 @@ def run_maxwell_3d_scipy(logical_domain, mapping, e_ex, b_ex, ncells, degree, pe M1 = a1_h.assemble().tosparse().tocsc() M2 = a2_h.assemble().tosparse().tocsr() - # Get differential operators as BlockLinearOperator objects - GRAD, CURL, DIV = derham_h.derivatives_as_matrices + # Diff operators + GRAD, CURL, DIV = derham_h.derivatives(kind='linop') # Get projectors as objects of type Projector_H1, Projector_Hcurl, Projector_Hdiv, Projector_L2 P0, P1, P2, P3 = derham_h.projectors(nquads=[5, 5, 5]) @@ -233,8 +233,8 @@ def run_maxwell_3d_stencil(logical_domain, mapping, e_ex, b_ex, ncells, degree, M1 = a1_h.assemble() M2 = a2_h.assemble() - # Get differential operators as BlockLinearOperator objects - GRAD, CURL, DIV = derham_h.derivatives_as_matrices + # Diff operators + GRAD, CURL, DIV = derham_h.derivatives(kind='linop') # Get projectors as objects of type Projector_H1, Projector_Hcurl, Projector_Hdiv, Projector_L2 P0, P1, P2, P3 = derham_h.projectors(nquads=[5, 5, 5]) diff --git a/psydac/api/tests/test_assembly.py b/psydac/api/tests/test_assembly.py index a84a41a2b..189b6c102 100644 --- a/psydac/api/tests/test_assembly.py +++ b/psydac/api/tests/test_assembly.py @@ -544,7 +544,7 @@ def test_assembly_no_synchr_args(backend): V1h = derham_h.V1 #differential operator - div, = derham_h.derivatives_as_matrices + div, = derham_h.derivatives(kind='linop') rho = element_of(V1h.symbolic_space, name='rho') g = element_of(V1h.symbolic_space, name='g') diff --git a/psydac/feec/multipatch/non_matching_operators.py b/psydac/feec/conforming_projectors.py similarity index 68% rename from psydac/feec/multipatch/non_matching_operators.py rename to psydac/feec/conforming_projectors.py index 4b172e7de..d045a702e 100644 --- a/psydac/feec/multipatch/non_matching_operators.py +++ b/psydac/feec/conforming_projectors.py @@ -1,21 +1,24 @@ -""" -This module provides utilities for constructing the conforming projections -for a H1-Hcurl-L2 broken FEEC de Rham sequence. -""" - +# coding: utf-8 +# Conga operators on piecewise (broken) de Rham sequences import os - import numpy as np -from scipy.sparse import eye as sparse_eye -from scipy.sparse import csr_matrix +from scipy.sparse import eye as sparse_eye +from scipy.sparse import csr_matrix +from scipy.special import comb from sympde.topology import Boundary, Interface -from psydac.fem.splines import SplineSpace -from psydac.utilities.quadratures import gauss_legendre -from psydac.core.bsplines import quadrature_grid, basis_ders_on_quad_grid, find_spans, elements_spans, cell_index, basis_ders_on_irregular_grid +from psydac.core.bsplines import quadrature_grid, basis_ders_on_quad_grid, find_spans, elements_spans, cell_index, basis_ders_on_irregular_grid +from psydac.fem.basic import FemLinearOperator +from psydac.fem.splines import SplineSpace +from psydac.utilities.quadratures import gauss_legendre +from psydac.linalg.sparse import SparseMatrixLinearOperator +__all__ = ( + 'ConformingProjectionV0', + 'ConformingProjectionV1', +) def get_patch_index_from_face(domain, face): """ @@ -118,7 +121,6 @@ def get_corners(domain, boundary_only): patches = domain.interior.args bd = domain.boundary - # corner_data[corner] = (patch_ind => local coordinates) corner_data = dict() if boundary_only: @@ -143,7 +145,6 @@ def get_corners(domain, boundary_only): else: for co in cos: corner_data[co] = dict() - for cb in co.corners: p_ind = patches.index(cb.domain) c_coord = cb.coordinates @@ -192,63 +193,48 @@ def construct_restriction_operator_1D( """ n_c = coarse_space_1d.nbasis n_f = fine_space_1d.nbasis - R = np.zeros((n_c, n_f)) if coarse_space_1d.basis == 'B': + #map V^+ to V^+_0 T = np.zeros((n_f, n_f)) - for i in range(1, n_f - 1): + for i in range(n_f): for j in range(n_f): - T[i, j] = int(i == j) - E[i, 0] * int(0 == j) - \ - E[i, -1] * int(n_f - 1 == j) + T[i, j] = int(i == j) - E[i, 0] * int(0 == j) - E[i, -1] * int(n_f - 1 == j) - cf_mass_mat = calculate_mixed_mass_matrix(coarse_space_1d, fine_space_1d)[ - 1:-1, 1:-1].transpose() - c_mass_mat = calculate_mass_matrix(coarse_space_1d)[1:-1, 1:-1] + cf_mass_mat = calculate_mixed_mass_matrix(coarse_space_1d, fine_space_1d).transpose() + c_mass_mat = calculate_mass_matrix(coarse_space_1d) if p_moments > 0: - - if not p_moments % 2 == 0: - p_moments += 1 - c_poly_mat = calculate_poly_basis_integral( - coarse_space_1d, p_moments=p_moments - 1)[:, 1:-1] - f_poly_mat = calculate_poly_basis_integral( - fine_space_1d, p_moments=p_moments - 1)[:, 1:-1] - - c_mass_mat[0:p_moments // 2, :] = c_poly_mat[0:p_moments // 2, :] - c_mass_mat[-p_moments // 2:, :] = c_poly_mat[-p_moments // 2:, :] - - cf_mass_mat[0:p_moments // 2, :] = f_poly_mat[0:p_moments // 2, :] - cf_mass_mat[-p_moments // 2:, :] = f_poly_mat[-p_moments // 2:, :] - - R0 = np.linalg.solve(c_mass_mat, cf_mass_mat) - R[1:-1, 1:-1] = R0 - R = R @ T - + # L^2 projection from V^+_0 to V^- + R[:, 1:-1] = np.linalg.solve(c_mass_mat, cf_mass_mat[:, 1:-1]) + gamma = get_1d_moment_correction(coarse_space_1d, p_moments=p_moments) + n = len(gamma) + + # maps V^- to V^+_0 in a moment preserving way + T2 = np.eye(n_c) + T2[0, 0] = T2[-1, -1] = 0 + T2[1:n+1, 0] += gamma + T2[-(n+1):-1, -1] += gamma[::-1] + + # maps V^+ to V^- in a moment preserving way + R = T2 @ R @ T + + else: + R[1:-1, 1:-1] = np.linalg.solve(c_mass_mat[1:-1, 1:-1], cf_mass_mat[1:-1, 1:-1]) + R = R @ T + + # add the degrees of freedom of T back R[0, 0] += 1 R[-1, -1] += 1 + else: - cf_mass_mat = calculate_mixed_mass_matrix( - coarse_space_1d, fine_space_1d).transpose() + cf_mass_mat = calculate_mixed_mass_matrix(coarse_space_1d, fine_space_1d).transpose() c_mass_mat = calculate_mass_matrix(coarse_space_1d) - if p_moments > 0: - - if not p_moments % 2 == 0: - p_moments += 1 - c_poly_mat = calculate_poly_basis_integral( - coarse_space_1d, p_moments=p_moments - 1) - f_poly_mat = calculate_poly_basis_integral( - fine_space_1d, p_moments=p_moments - 1) - - c_mass_mat[0:p_moments // 2, :] = c_poly_mat[0:p_moments // 2, :] - c_mass_mat[-p_moments // 2:, :] = c_poly_mat[-p_moments // 2:, :] - - cf_mass_mat[0:p_moments // 2, :] = f_poly_mat[0:p_moments // 2, :] - cf_mass_mat[-p_moments // 2:, :] = f_poly_mat[-p_moments // 2:, :] - + # The pure L^2 projection is already moment preserving R = np.linalg.solve(c_mass_mat, cf_mass_mat) return R @@ -287,8 +273,7 @@ def get_extension_restriction(coarse_space_1d, fine_space_1d, p_moments=-1): spl_type = coarse_space_1d.basis if not matching_interfaces: - grid = np.linspace( - fine_space_1d.breaks[0], fine_space_1d.breaks[-1], coarse_space_1d.ncells + 1) + grid = np.linspace(fine_space_1d.breaks[0], fine_space_1d.breaks[-1], coarse_space_1d.ncells + 1) coarse_space_1d_k_plus = SplineSpace( degree=fine_space_1d.degree, grid=grid, @@ -297,25 +282,17 @@ def get_extension_restriction(coarse_space_1d, fine_space_1d, p_moments=-1): E_1D = construct_extension_operator_1D( domain=coarse_space_1d_k_plus, codomain=fine_space_1d) + R_1D = construct_restriction_operator_1D( coarse_space_1d_k_plus, fine_space_1d, E_1D, p_moments) - ER_1D = E_1D @ R_1D + assert np.allclose(R_1D @ E_1D, np.eye(coarse_space_1d.nbasis), 1e-12, 1e-12) + else: ER_1D = R_1D = E_1D = sparse_eye( fine_space_1d.nbasis, format="lil") - # TODO remove later - assert ( - np.allclose( - np.linalg.norm( - R_1D @ E_1D - - np.eye( - coarse_space_1d.nbasis)), - 0, - 1e-12, - 1e-12)) return E_1D, R_1D, ER_1D @@ -418,8 +395,7 @@ def calculate_mixed_mass_matrix(domain_space, codomain_space): fine_basis = basis_ders_on_quad_grid(fknots, fdeg, quad_x, 0, spl_type) coarse_basis = [ basis_ders_on_irregular_grid( - knots, deg, q, cell_index( - breaks, q), 0, spl_type) for q in quad_x] + knots, deg, q, cell_index(breaks, q), 0, spl_type) for q in quad_x] fine_spans = elements_spans(fknots, deg) coarse_spans = [find_spans(knots, deg, q[0])[0] for q in quad_x] @@ -471,7 +447,6 @@ def calculate_poly_basis_integral(space_1d, p_moments=-1): enddom = breaks[-1] begdom = breaks[0] denom = enddom - begdom - order = max(p_moments + 1, deg + 1) u, w = gauss_legendre(order) @@ -484,8 +459,7 @@ def calculate_poly_basis_integral(space_1d, p_moments=-1): Mass_mat = np.zeros((p_moments + 1, space_1d.nbasis)) for ie1 in range(Nel): # loop on cells - for pol in range( - p_moments + 1): # loops on basis function in each cell + for pol in range(p_moments + 1): # loops on basis function in each cell for il2 in range(deg + 1): # loops on basis function in each cell val = 0. @@ -494,7 +468,7 @@ def calculate_poly_basis_integral(space_1d, p_moments=-1): x = quad_x[ie1, q1] # val += quad_w[ie1, q1] * v0 * ((enddom-x)/denom)**pol val += quad_w[ie1, q1] * v0 * \ - ((enddom - x) / denom)**(p_moments - pol) * (x / denom)**pol + comb(p_moments, pol) * ((enddom - x) / denom)**(p_moments - pol) * ((x - begdom) / denom)**pol locind2 = il2 + spans[ie1] - deg Mass_mat[pol, locind2] += val @@ -520,27 +494,24 @@ def get_1d_moment_correction(space_1d, p_moments=-1): """ if p_moments < 0: - return None + return [] if space_1d.ncells <= p_moments + 1: - print("Careful, the correction term is currently not independent of the mesh.") - + p_moments = space_1d.ncells - 2 + print(f"The prescribed degree of preserved moments was too high, given the number of cells in the patch. It has been reduced to degree {p_moments}.") + if p_moments >= 0: # to preserve moments of degree p we need 1+p conforming basis functions in the patch (the "interior" ones) # and for the given regularity constraint, there are # local_shape[conf_axis]-2*(1+reg) such conforming functions p_max = space_1d.nbasis - 3 if p_max < p_moments: - print( - " ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **") + print(" ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **") print(" ** WARNING -- WARNING -- WARNING ") - print( - f" ** conf. projection imposing C0 smoothness on scalar space along this axis :") - print( - f" ** there are not enough dofs in a patch to preserve moments of degree {p_moments} !") + print(f" ** conf. projection imposing C0 smoothness on scalar space along this axis :") + print(f" ** there are not enough dofs in a patch to preserve moments of degree {p_moments} !") print(f" ** Only able to preserve up to degree --> {p_max} <-- ") - print( - " ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **") + print(" ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** ** **") p_moments = p_max Mass_mat = calculate_poly_basis_integral(space_1d, p_moments) @@ -549,14 +520,16 @@ def get_1d_moment_correction(space_1d, p_moments=-1): return gamma -def construct_h1_conforming_projection( - Vh, reg_orders=0, p_moments=-1, hom_bc=False): +#============================================================================== +# Multipatch conforming projectors +#============================================================================== +def construct_h1_conforming_projection(Vh, reg_orders=0, p_moments=-1, hom_bc=False): """ Construct the conforming projection for a scalar space for a given regularity (0 continuous, -1 discontinuous). Parameters ---------- - Vh : TensorFemSpace + Vh : MultipatchFemSpace Finite Element Space coming from the discrete de Rham sequence. reg_orders : (int) @@ -582,8 +555,8 @@ def construct_h1_conforming_projection( # moment corrections perpendicular to interfaces # assume same moments everywhere - gamma = get_1d_moment_correction( - Vh.patch_spaces[0].spaces[0], p_moments=p_moments) + gamma = get_1d_moment_correction(Vh.spaces[0].spaces[0], p_moments=p_moments) + p_moments = len(gamma)-1 domain = Vh.symbolic_space.domain ndim = 2 @@ -592,22 +565,21 @@ def construct_h1_conforming_projection( l2g = Local2GlobalIndexMap(ndim, len(domain), n_components) for k in range(n_patches): - Vk = Vh.patch_spaces[k] + Vk = Vh.spaces[k] # T is a TensorFemSpace and S is a 1D SplineSpace shapes = [S.nbasis for S in Vk.spaces] l2g.set_patch_shapes(k, shapes) # P vertex # vertex correction matrix - Proj_vertex = sparse_eye(dim_tot, format="lil") + Proj_vertex = sparse_eye(dim_tot, format="lil") corner_indices = set() corners = get_corners(domain, False) def get_vertex_index_from_patch(patch, coords): - # coords = co[patch] - nbasis0 = Vh.patch_spaces[patch].spaces[coords[0]].nbasis - 1 - nbasis1 = Vh.patch_spaces[patch].spaces[coords[1]].nbasis - 1 + nbasis0 = Vh.spaces[patch].spaces[coords[0]].nbasis - 1 + nbasis1 = Vh.spaces[patch].spaces[coords[1]].nbasis - 1 # patch local index multi_index = [None] * ndim @@ -621,12 +593,11 @@ def vertex_moment_indices(axis, coords, patch, p_moments): if coords[axis] == 0: return range(1, p_moments + 2) else: - return range(Vh.patch_spaces[patch].spaces[coords[axis]].nbasis - 1 - 1, - Vh.patch_spaces[patch].spaces[coords[axis]].nbasis - 1 - p_moments - 2, -1) + return range(Vh.spaces[patch].spaces[coords[axis]].nbasis - 1 - 1, + Vh.spaces[patch].spaces[coords[axis]].nbasis - 1 - p_moments - 2, -1) # loop over all vertices for (bd, co) in corners.items(): - # len(co)=#v is the number of adjacent patches at a vertex corr = len(co) @@ -639,9 +610,9 @@ def vertex_moment_indices(axis, coords, patch, p_moments): corner_indices.add(ig) for patch2 in co: - # local vertex coordinates in patch2 coords2 = co[patch2] + # global index jg = get_vertex_index_from_patch(patch2, coords2) @@ -701,7 +672,6 @@ def vertex_moment_indices(axis, coords, patch, p_moments): corners = get_corners(domain, True) if hom_bc: for (bd, co) in corners.items(): - for patch1 in co: # local vertex coordinates in patch2 @@ -714,6 +684,7 @@ def vertex_moment_indices(axis, coords, patch, p_moments): # local vertex coordinates in patch2 coords2 = co[patch2] + # global index jg = get_vertex_index_from_patch(patch2, coords2) @@ -830,8 +801,8 @@ def get_mu_minus(j, coarse_space, fine_space, R): k_minus = get_patch_index_from_face(domain, I.minus) k_plus = get_patch_index_from_face(domain, I.plus) - I_minus_ncells = Vh.patch_spaces[k_minus].ncells - I_plus_ncells = Vh.patch_spaces[k_plus].ncells + I_minus_ncells = Vh.spaces[k_minus].ncells + I_plus_ncells = Vh.spaces[k_plus].ncells # logical directions normal to interface if I_minus_ncells <= I_plus_ncells: @@ -848,8 +819,8 @@ def get_mu_minus(j, coarse_space, fine_space, R): d_fine = 1 - fine_axis d_coarse = 1 - coarse_axis - space_fine = Vh.patch_spaces[k_fine] - space_coarse = Vh.patch_spaces[k_coarse] + space_fine = Vh.spaces[k_fine] + space_coarse = Vh.spaces[k_coarse] coarse_space_1d = space_coarse.spaces[d_coarse] fine_space_1d = space_fine.spaces[d_fine] @@ -962,7 +933,7 @@ def get_mu_minus(j, coarse_space, fine_space, R): if hom_bc: for bn in domain.boundary: k = get_patch_index_from_face(domain, bn) - space_k = Vh.patch_spaces[k] + space_k = Vh.spaces[k] axis = bn.axis d = 1 - axis @@ -979,17 +950,19 @@ def get_mu_minus(j, coarse_space, fine_space, R): pg = edge_moment_index(p, i, axis, ext, space_k, k) Proj_edge[pg, ig] = gamma[p] else: - if corner_indices.issuperset({ig}): - mu_minus = get_mu_minus( - j, space_k_1d, space_k_1d, np.eye( - space_k_1d.nbasis)) + #if corner_indices.issuperset({ig}): + mu_minus = get_mu_minus( + i, space_k_1d, space_k_1d, np.eye( + space_k_1d.nbasis)) - for p in range(p_moments + 1): - for m in range(space_k_1d.nbasis): - pg = edge_moment_index( - p, m, axis, ext, space_k, k) - Proj_edge[pg, ig] = gamma[p] * mu_minus[m] - else: + for p in range(p_moments + 1): + for m in range(space_k_1d.nbasis): + pg = edge_moment_index( + p, m, axis, ext, space_k, k) + Proj_edge[pg, ig] = gamma[p] * mu_minus[m] + + if not corner_indices.issuperset({ig}): + corner_indices.add(ig) multi_index = [None] * ndim for p in range(p_moments + 1): @@ -997,22 +970,20 @@ def get_mu_minus(j, coarse_space, fine_space, R): 1 else space_k.spaces[axis].nbasis - 1 - p - 1 for pd in range(p_moments + 1): multi_index[1 - axis] = pd + \ - 1 if i == 0 else space_k.spaces[1 - - axis].nbasis - 1 - pd - 1 + 1 if i == 0 else space_k.spaces[1 - axis].nbasis - 1 - pd - 1 pg = l2g.get_index(k, 0, multi_index) Proj_edge[pg, ig] = gamma[p] * gamma[pd] return Proj_edge @ Proj_vertex -def construct_hcurl_conforming_projection( - Vh, reg_orders=0, p_moments=-1, hom_bc=False): +def construct_hcurl_conforming_projection(Vh, reg_orders=0, p_moments=-1, hom_bc=False): """ Construct the conforming projection for a vector Hcurl space for a given regularity (0 continuous, -1 discontinuous). Parameters ---------- - Vh : TensorFemSpace + Vh : MultipatchFemSpace Finite Element Space coming from the discrete de Rham sequence. reg_orders : (int) @@ -1037,8 +1008,9 @@ def construct_hcurl_conforming_projection( return sparse_eye(dim_tot, format="lil") # moment corrections perpendicular to interfaces - gamma = [get_1d_moment_correction( - Vh.patch_spaces[0].spaces[1 - d].spaces[d], p_moments=p_moments) for d in range(2)] + # should be in the V^0 spaces + gamma = [get_1d_moment_correction(Vh.spaces[0].spaces[1 - d].spaces[d], p_moments=p_moments) for d in range(2)] + p_moments = min([len(g) for g in gamma])-1 domain = Vh.symbolic_space.domain ndim = 2 @@ -1047,7 +1019,7 @@ def construct_hcurl_conforming_projection( l2g = Local2GlobalIndexMap(ndim, len(domain), n_components) for k in range(n_patches): - Vk = Vh.patch_spaces[k] + Vk = Vh.spaces[k] # T is a TensorFemSpace and S is a 1D SplineSpace shapes = [[S.nbasis for S in T.spaces] for T in Vk.spaces] l2g.set_patch_shapes(k, *shapes) @@ -1073,7 +1045,7 @@ def edge_moment_index(p, i, axis, ext, space, k): multi_index[axis] = p + 1 if ext == - \ 1 else space.spaces[1 - axis].spaces[axis].nbasis - 1 - p - 1 return l2g.get_index(k, 1 - axis, multi_index) - + # loop over all interfaces for I in Interfaces: direction = I.ornt @@ -1086,8 +1058,8 @@ def edge_moment_index(p, i, axis, ext, space, k): minus_axis, plus_axis = I.minus.axis, I.plus.axis # logical directions along the interface d_minus, d_plus = 1 - minus_axis, 1 - plus_axis - I_minus_ncells = Vh.patch_spaces[k_minus].spaces[d_minus].ncells[d_minus] - I_plus_ncells = Vh.patch_spaces[k_plus].spaces[d_plus].ncells[d_plus] + I_minus_ncells = Vh.spaces[k_minus].spaces[d_minus].ncells[d_minus] + I_plus_ncells = Vh.spaces[k_plus].spaces[d_plus].ncells[d_plus] # logical directions normal to interface if I_minus_ncells <= I_plus_ncells: @@ -1104,8 +1076,8 @@ def edge_moment_index(p, i, axis, ext, space, k): d_fine = 1 - fine_axis d_coarse = 1 - coarse_axis - space_fine = Vh.patch_spaces[k_fine] - space_coarse = Vh.patch_spaces[k_coarse] + space_fine = Vh.spaces[k_fine] + space_coarse = Vh.spaces[k_coarse] coarse_space_1d = space_coarse.spaces[d_coarse].spaces[d_coarse] fine_space_1d = space_fine.spaces[d_fine].spaces[d_fine] @@ -1164,7 +1136,7 @@ def edge_moment_index(p, i, axis, ext, space, k): # boundary condition for bn in domain.boundary: k = get_patch_index_from_face(domain, bn) - space_k = Vh.patch_spaces[k] + space_k = Vh.spaces[k] axis = bn.axis if not hom_bc: @@ -1184,3 +1156,346 @@ def edge_moment_index(p, i, axis, ext, space, k): Proj_edge[pg, ig] = gamma[d][p] return Proj_edge + +#============================================================================== +# Singlepatch conforming projectors +#============================================================================== +def construct_h1_singlepatch_conforming_projection(Vh, reg_orders=0, p_moments=-1, hom_bc=False): + """ + Construct the conforming projection for a scalar space for a given regularity (0 continuous, -1 discontinuous). + + Parameters + ---------- + Vh : MultipatchFemSpace + Finite Element Space coming from the discrete de Rham sequence. + + reg_orders : (int) + Regularity in each space direction -1 or 0. + + p_moments : (int) + Number of moments to be preserved. + + hom_bc : (bool) + Homogeneous boundary conditions. + + Returns + ------- + cP : scipy.sparse.csr_array + Conforming projection as a sparse matrix. + """ + + dim_tot = Vh.nbasis + + # fully discontinuous space + if reg_orders < 0 or not hom_bc: + return sparse_eye(dim_tot, format="lil") + + # moment corrections perpendicular to interfaces + # assume same moments everywhere + gamma = get_1d_moment_correction(Vh.spaces[0], p_moments=p_moments) + p_moments = len(gamma)-1 + + domain = Vh.symbolic_space.domain + ndim = 2 + n_components = 1 + n_patches = len(domain) + + l2g = Local2GlobalIndexMap(ndim, len(domain), n_components) + # T is a TensorFemSpace and S is a 1D SplineSpace + shapes = [S.nbasis for S in Vh.spaces] + l2g.set_patch_shapes(0, shapes) + + # P vertex + # vertex correction matrix + Proj_vertex = sparse_eye(dim_tot, format="lil") + + + def get_vertex_index(coords): + nbasis0 = Vh.spaces[coords[0]].nbasis - 1 + nbasis1 = Vh.spaces[coords[1]].nbasis - 1 + + # patch local index + multi_index = [None] * ndim + multi_index[0] = 0 if coords[0] == 0 else nbasis0 + multi_index[1] = 0 if coords[1] == 0 else nbasis1 + + # global index + return l2g.get_index(0, 0, multi_index) + + def vertex_moment_indices(axis, coords, p_moments): + if coords[axis] == 0: + return range(1, p_moments + 2) + else: + return range(Vh.spaces[coords[axis]].nbasis - 1 - 1, + Vh.spaces[coords[axis]].nbasis - 1 - p_moments - 2, -1) + + # boundary conditions + + for co in [(0,0), (1,0), (0,1), (1,1)]: + + # global index + ig = get_vertex_index(co) + + # conformity constraint + Proj_vertex[ig, ig] = 0 + + + if p_moments == -1: + continue + + # moment corrections from patch1 to patch1 + axis = 0 + d = 1 + multi_index_p = [None] * ndim + + d_moment_index = vertex_moment_indices(d, co, p_moments) + axis_moment_index = vertex_moment_indices(axis, co, p_moments) + + for pd in range(0, p_moments + 1): + multi_index_p[d] = d_moment_index[pd] + + for p in range(0, p_moments + 1): + multi_index_p[axis] = axis_moment_index[p] + + pg = l2g.get_index(0, 0, multi_index_p) + Proj_vertex[pg, ig] = gamma[p] * gamma[pd] + + # P edge + # edge correction matrix + Proj_edge = sparse_eye(dim_tot, format="lil") + + def get_edge_index(j, axis, ext): + multi_index = [None] * ndim + multi_index[axis] = 0 if ext == - 1 else Vh.spaces[axis].nbasis - 1 + multi_index[1 - axis] = j + return l2g.get_index(0, 0, multi_index) + + def edge_moment_index(p, i, axis, ext): + multi_index = [None] * ndim + multi_index[1 - axis] = i + multi_index[axis] = p + 1 if ext == -1 else Vh.spaces[axis].nbasis - 1 - p - 1 + return l2g.get_index(0, 0, multi_index) + + + def get_mu_minus(j, coarse_space, fine_space, R): + mu_plus = np.zeros(fine_space.nbasis) + mu_minus = np.zeros(coarse_space.nbasis) + + if j == 0: + mu_minus[0] = 1 + for p in range(p_moments + 1): + mu_plus[p + 1] = gamma[p] + else: + mu_minus[-1] = 1 + for p in range(p_moments + 1): + mu_plus[-1 - (p + 1)] = gamma[p] + + for m in range(coarse_space.nbasis): + for l in range(fine_space.nbasis): + mu_minus[m] += R[m, l] * mu_plus[l] + + if j == 0: + mu_minus[m] -= R[m, 0] + else: + mu_minus[m] -= R[m, -1] + + return mu_minus + + + # boundary condition + for bn in domain.boundary: + space_k = Vh + axis = bn.axis + + d = 1 - axis + ext = bn.ext + space_k_1d = space_k.spaces[d] + + for i in range(0, space_k_1d.nbasis): + ig = get_edge_index(i, axis, ext) + Proj_edge[ig, ig] = 0 + + if (i != 0 and i != space_k_1d.nbasis - 1): + for p in range(p_moments + 1): + + pg = edge_moment_index(p, i, axis, ext) + Proj_edge[pg, ig] = gamma[p] + else: + #if corner_indices.issuperset({ig}): + mu_minus = get_mu_minus( + i, space_k_1d, space_k_1d, np.eye( + space_k_1d.nbasis)) + + for p in range(p_moments + 1): + for m in range(space_k_1d.nbasis): + pg = edge_moment_index( + p, m, axis, ext) + Proj_edge[pg, ig] = gamma[p] * mu_minus[m] + + + return Proj_edge @ Proj_vertex + + +def construct_hcurl_singlepatch_conforming_projection(Vh, reg_orders=0, p_moments=-1, hom_bc=False): + """ + Construct the conforming projection for a single patch vector Hcurl space for a given regularity (0 continuous, -1 discontinuous). + + Parameters + ---------- + Vh : MultipatchFemSpace + Finite Element Space coming from the discrete de Rham sequence. + + reg_orders : (int) + Regularity in each space direction -1 or 0. + + p_moments : (int) + Number of polynomial moments to be preserved. + + hom_bc : (bool) + Tangential homogeneous boundary conditions. + + Returns + ------- + cP : scipy.sparse.csr_array + Conforming projection as a sparse matrix. + """ + + dim_tot = Vh.nbasis + + # fully discontinuous space + if reg_orders < 0 or not hom_bc: + return sparse_eye(dim_tot, format="lil") + + # moment corrections perpendicular to interfaces + # should be in the V^0 spaces + + gamma = [get_1d_moment_correction(Vh.spaces[1 - d].spaces[d], p_moments=p_moments) for d in range(2)] + p_moments = min([len(g) for g in gamma])-1 + + domain = Vh.symbolic_space.domain + ndim = 2 + n_components = 2 + n_patches = len(domain) + + l2g = Local2GlobalIndexMap(ndim, len(domain), n_components) + # T is a TensorFemSpace and S is a 1D SplineSpace + shapes = [[S.nbasis for S in T.spaces] for T in Vh.spaces] + l2g.set_patch_shapes(0, *shapes) + + # P edge + # edge correction matrix + Proj_edge = sparse_eye(dim_tot, format="lil") + + def get_edge_index(j, axis, ext): + multi_index = [None] * ndim + multi_index[axis] = 0 if ext == -1 else Vh.spaces[1 - axis].spaces[axis].nbasis - 1 + multi_index[1 - axis] = j + return l2g.get_index(0, 1 - axis, multi_index) + + def edge_moment_index(p, i, axis, ext): + multi_index = [None] * ndim + multi_index[1 - axis] = i + multi_index[axis] = p + 1 if ext == -1 else Vh.spaces[1 - axis].spaces[axis].nbasis - 1 - p - 1 + return l2g.get_index(0, 1 - axis, multi_index) + + + # boundary condition + for bn in domain.boundary: + + axis = bn.axis + d = 1 - axis + ext = bn.ext + space_1d = Vh.spaces[d].spaces[d] + + for i in range(0, space_1d.nbasis): + ig = get_edge_index(i, axis, ext) + Proj_edge[ig, ig] = 0 + + for p in range(p_moments + 1): + + pg = edge_moment_index(p, i, axis, ext) + Proj_edge[pg, ig] = gamma[d][p] + + return Proj_edge + + +# =============================================================================== + +class ConformingProjectionV0(FemLinearOperator): + """ + Conforming projection from global broken V0 space to conforming global V0 space + Defined by averaging of interface (including vertex) dofs + and adding moment correction terms + + Parameters + ---------- + V0h: + The discrete space + + p_moments: + Number of polynomial moments to be preserved in the projection. + + hom_bc : + Apply homogenous boundary conditions if True + """ + def __init__( + self, + V0h, + mom_pres=False, + p_moments=-1, + hom_bc=False): + + if mom_pres: + if V0h.is_multipatch: + p_moments = max(p_moments, max(V0h.degree[0])) + else: + p_moments = max(p_moments, max(V0h.degree)) + + FemLinearOperator.__init__(self, fem_domain=V0h, fem_codomain=V0h) + + if V0h.is_multipatch: + sparse_matrix = construct_h1_conforming_projection(V0h, reg_orders=0, p_moments=p_moments, hom_bc=hom_bc) + else: + sparse_matrix = construct_h1_singlepatch_conforming_projection(V0h, reg_orders=0, p_moments=p_moments, hom_bc=hom_bc) + + self._linop = SparseMatrixLinearOperator(self.linop_domain, self.linop_codomain, sparse_matrix.tocsr()) + + +class ConformingProjectionV1(FemLinearOperator): + """ + Conforming projection from global broken V1 space to conforming V1 global space + Defined by averaging of (only) interface dofs + and adding moment correction terms + + Parameters + ---------- + V1h: + The discrete space + + p_moments: + Number of polynomial moments to be preserved in the projection. + + hom_bc : + Apply homogenous boundary conditions if True + """ + def __init__( + self, + V1h, + mom_pres=False, + p_moments=-1, + hom_bc=False): + + if mom_pres: + if V1h.is_multipatch: + p_moments = max(p_moments, max(V1h.spaces[0].degree[0])) + else: + p_moments = max(p_moments, max(V1h.degree[0])) + + FemLinearOperator.__init__(self, fem_domain=V1h, fem_codomain=V1h) + + if V1h.is_multipatch: + sparse_matrix = construct_hcurl_conforming_projection(V1h, reg_orders=0, p_moments=p_moments, hom_bc=hom_bc) + else: + sparse_matrix = construct_hcurl_singlepatch_conforming_projection(V1h, reg_orders=0, p_moments=p_moments, hom_bc=hom_bc) + + self._linop = SparseMatrixLinearOperator(self.linop_domain, self.linop_codomain, sparse_matrix.tocsr()) diff --git a/psydac/feec/derivatives.py b/psydac/feec/derivatives.py index f7f28ccbd..1fd3de5d2 100644 --- a/psydac/feec/derivatives.py +++ b/psydac/feec/derivatives.py @@ -9,38 +9,28 @@ from psydac.fem.vector import VectorFemSpace from psydac.fem.tensor import TensorFemSpace from psydac.linalg.basic import IdentityOperator -from psydac.fem.basic import FemField, FemSpace +from psydac.fem.basic import FemField, FemSpace, FemLinearOperator from psydac.linalg.basic import LinearOperator from psydac.ddm.cart import DomainDecomposition, CartDecomposition __all__ = ( 'DirectionalDerivativeOperator', - 'DiffOperator', - 'Derivative_1D', - 'Gradient_2D', - 'Gradient_3D', - 'ScalarCurl_2D', - 'VectorCurl_2D', - 'Curl_3D', - 'Divergence_2D', - 'Divergence_3D', - 'block_tostencil' + 'Derivative1D', + 'Gradient2D', + 'Gradient3D', + 'ScalarCurl2D', + 'VectorCurl2D', + 'Curl3D', + 'Divergence2D', + 'Divergence3D', + 'BrokenGradient2D', + 'BrokenTransposedGradient2D', + 'BrokenScalarCurl2D', + 'BrokenTransposedScalarCurl2D', ) #==================================================================================================== -def block_tostencil(M): - """ - Convert a BlockLinearOperator that contains KroneckerStencilMatrix objects - to a BlockLinearOperator that contains StencilMatrix objects - """ - blocks = [list(b) for b in M.blocks] - for i1,b in enumerate(blocks): - for i2, mat in enumerate(b): - if mat is None: - continue - blocks[i1][i2] = mat.tostencil() - return BlockLinearOperator(M.domain, M.codomain, blocks=blocks) - +# Singlepatch derivative operators #==================================================================================================== class DirectionalDerivativeOperator(LinearOperator): """ @@ -361,40 +351,7 @@ def copy(self): self._diffdir, negative=self._negative, transposed=self._transposed) #==================================================================================================== -class DiffOperator: - def __init__(self, domain, codomain, matrix): - assert isinstance(domain, FemSpace) - assert isinstance(codomain, FemSpace) - assert isinstance(matrix, LinearOperator) - assert domain.coeff_space is matrix.domain - assert codomain.coeff_space is matrix.codomain - - self._domain = domain - self._codomain = codomain - self._matrix = matrix - - @property - def matrix(self): - return self._matrix - - @property - def domain(self): - return self._domain - - @property - def codomain(self): - return self._codomain - - def __call__(self, u): - assert isinstance(u, FemField) - assert u.space == self.domain - - coeffs = self.matrix.dot(u.coeffs) - - return FemField(self.codomain, coeffs=coeffs) - -#==================================================================================================== -class Derivative_1D(DiffOperator): +class Derivative1D(FemLinearOperator): """ 1D derivative. @@ -415,10 +372,10 @@ def __init__(self, H1, L2): assert H1.degree[0] == L2.degree[0] + 1 # Store data in object - super().__init__(H1, L2, DirectionalDerivativeOperator(H1.coeff_space, L2.coeff_space, 0)) + super().__init__(fem_domain = H1, fem_codomain = L2, linop = DirectionalDerivativeOperator(H1.coeff_space, L2.coeff_space, 0)) #==================================================================================================== -class Gradient_2D(DiffOperator): +class Gradient2D(FemLinearOperator): """ Gradient operator in 2D. @@ -434,7 +391,7 @@ class Gradient_2D(DiffOperator): def __init__(self, H1, Hcurl): assert isinstance( H1, TensorFemSpace); assert H1.ldim == 2 - assert isinstance(Hcurl, VectorFemSpace); assert Hcurl.ldim == 2 + assert isinstance(Hcurl, VectorFemSpace); assert Hcurl.ldim == 2 assert Hcurl.spaces[0].periodic == H1.periodic assert Hcurl.spaces[1].periodic == H1.periodic @@ -454,11 +411,10 @@ def __init__(self, H1, Hcurl): matrix = BlockLinearOperator(H1.coeff_space, Hcurl.coeff_space, blocks=blocks) # Store data in object - super().__init__(H1, Hcurl, matrix) - + super().__init__(fem_domain = H1, fem_codomain = Hcurl, linop = matrix) #==================================================================================================== -class Gradient_3D(DiffOperator): +class Gradient3D(FemLinearOperator): """ Gradient operator in 3D. @@ -497,10 +453,10 @@ def __init__(self, H1, Hcurl): matrix = BlockLinearOperator(H1.coeff_space, Hcurl.coeff_space, blocks=blocks) # Store data in object - super().__init__(H1, Hcurl, matrix) + super().__init__(fem_domain = H1, fem_codomain = Hcurl, linop = matrix) #==================================================================================================== -class ScalarCurl_2D(DiffOperator): +class ScalarCurl2D(FemLinearOperator): """ Scalar curl operator in 2D: computes a scalar field from a vector field. @@ -536,10 +492,10 @@ def __init__(self, Hcurl, L2): matrix = BlockLinearOperator(Hcurl.coeff_space, L2.coeff_space, blocks=blocks) # Store data in object - super().__init__(Hcurl, L2, matrix) + super().__init__(fem_domain = Hcurl, fem_codomain = L2, linop = matrix) #==================================================================================================== -class VectorCurl_2D(DiffOperator): +class VectorCurl2D(FemLinearOperator): """ Vector curl operator in 2D: computes a vector field from a scalar field. This is sometimes called the 'rot' operator. @@ -576,10 +532,10 @@ def __init__(self, H1, Hdiv): matrix = BlockLinearOperator(H1.coeff_space, Hdiv.coeff_space, blocks=blocks) # Store data in object - super().__init__(H1, Hdiv, matrix) + super().__init__(fem_domain = H1, fem_codomain = Hdiv, linop = matrix) #==================================================================================================== -class Curl_3D(DiffOperator): +class Curl3D(FemLinearOperator): """ Curl operator in 3D. @@ -626,10 +582,10 @@ def __init__(self, Hcurl, Hdiv): # ... # Store data in object - super().__init__(Hcurl, Hdiv, matrix) + super().__init__(fem_domain = Hcurl, fem_codomain = Hdiv, linop = matrix) #==================================================================================================== -class Divergence_2D(DiffOperator): +class Divergence2D(FemLinearOperator): """ Divergence operator in 2D. @@ -665,10 +621,10 @@ def __init__(self, Hdiv, L2): matrix = BlockLinearOperator(Hdiv.coeff_space, L2.coeff_space, blocks=blocks) # Store data in object - super().__init__(Hdiv, L2, matrix) + super().__init__(fem_domain = Hdiv, fem_codomain = L2, linop = matrix) #==================================================================================================== -class Divergence_3D(DiffOperator): +class Divergence3D(FemLinearOperator): """ Divergence operator in 3D. @@ -707,4 +663,118 @@ def __init__(self, Hdiv, L2): matrix = BlockLinearOperator(Hdiv.coeff_space, L2.coeff_space, blocks=blocks) # Store data in object - super().__init__(Hdiv, L2, matrix) + super().__init__(fem_domain = Hdiv, fem_codomain = L2, linop = matrix) + +#==================================================================================================== +# 2D Multipatch derivative operators +#==================================================================================================== +class BrokenGradient2D(FemLinearOperator): + """ + Gradient operator in a 2D multipatch domain, + acting independently on each patch. + In general, the resulting field is therefore discontinuous, or "broken". + + Parameters + ---------- + V0h : MultipatchFemSpace + Domain of the gradient operator. + + V1h : MultipatchFemSpace + Codomain of the gradient operator. + """ + def __init__(self, V0h, V1h): + + FemLinearOperator.__init__(self, fem_domain=V0h, fem_codomain=V1h) + + D0s = [Gradient2D(V0, V1) for V0, V1 in zip(V0h.spaces, V1h.spaces)] + + self._linop = BlockLinearOperator(self.linop_domain, self.linop_codomain, blocks={ + (i, i): D0i.linop for i, D0i in enumerate(D0s)}) + + def transpose(self, conjugate=False): + # todo (MCP): define as the dual differential operator + return BrokenTransposedGradient2D(self.fem_domain, self.fem_codomain) + +# ============================================================================== +class BrokenTransposedGradient2D(FemLinearOperator): + """ + Transposed gradient operator in a 2D multipatch domain, + acting independently on each patch. + In general, the resulting field is therefore discontinuous, or "broken". + + Parameters + ---------- + V0h : MultipatchFemSpace + Codomain of the transposed gradient operator. + + V1h : MultipatchFemSpace + Domain of the transposed gradient operator. + """ + def __init__(self, V0h, V1h): + + FemLinearOperator.__init__(self, fem_domain=V1h, fem_codomain=V0h) + + D0s = [Gradient2D(V0, V1) for V0, V1 in zip(V0h.spaces, V1h.spaces)] + + self._linop = BlockLinearOperator(self.linop_domain, self.linop_codomain, blocks={ + (i, i): D0i.linop.T for i, D0i in enumerate(D0s)}) + + def transpose(self, conjugate=False): + # todo (MCP): discard + return BrokenGradient2D(self.fem_codomain, self.fem_domain) + +# ============================================================================== +class BrokenScalarCurl2D(FemLinearOperator): + """ + Scalar curl operator in a 2D multipatch domain, + acting independently on each patch. + In general, the resulting field is therefore discontinuous, or "broken". + + Parameters + ---------- + V1h : MultipatchFemSpace + Domain of the scalar curl operator. + + V2h : MultipatchFemSpace + Codomain of the scalar curl operator. + """ + def __init__(self, V1h, V2h): + + FemLinearOperator.__init__(self, fem_domain=V1h, fem_codomain=V2h) + + D1s = [ScalarCurl2D(V1, V2) for V1, V2 in zip(V1h.spaces, V2h.spaces)] + + self._linop = BlockLinearOperator(self.linop_domain, self.linop_codomain, blocks={ + (i, i): D1i.linop for i, D1i in enumerate(D1s)}) + + def transpose(self, conjugate=False): + return BrokenTransposedScalarCurl2D( + V1h=self.fem_domain, V2h=self.fem_codomain) + + +# ============================================================================== +class BrokenTransposedScalarCurl2D(FemLinearOperator): + """ + Transposed scalar curl operator in a 2D multipatch domain, + acting independently on each patch. + In general, the resulting field is therefore discontinuous, or "broken". + + Parameters + ---------- + V1h : MultipatchFemSpace + Codomain of the transposed scalar curl operator. + + V2h : MultipatchFemSpace + Domain of the transposed scalar curl operator. + """ + def __init__(self, V1h, V2h): + + FemLinearOperator.__init__(self, fem_domain=V2h, fem_codomain=V1h) + + D1s = [ScalarCurl2D(V1, V2) for V1, V2 in zip(V1h.spaces, V2h.spaces)] + + self._linop = BlockLinearOperator(self.linop_domain, self.linop_codomain, blocks={ + (i, i): D1i.linop.T for i, D1i in enumerate(D1s)}) + + def transpose(self, conjugate=False): + return BrokenScalarCurl2D(V1h=self.fem_codomain, V2h=self.fem_domain) diff --git a/psydac/feec/global_projectors.py b/psydac/feec/global_geometric_projectors.py similarity index 94% rename from psydac/feec/global_projectors.py rename to psydac/feec/global_geometric_projectors.py index e5a61a0bb..019c2f441 100644 --- a/psydac/feec/global_projectors.py +++ b/psydac/feec/global_geometric_projectors.py @@ -4,26 +4,27 @@ from psydac.linalg.kron import KroneckerLinearSolver, KroneckerStencilMatrix from psydac.linalg.stencil import StencilMatrix, StencilVectorSpace -from psydac.linalg.block import BlockLinearOperator +from psydac.linalg.block import BlockLinearOperator, BlockVector from psydac.core.bsplines import quadrature_grid from psydac.utilities.quadratures import gauss_legendre from psydac.fem.basic import FemField from psydac.fem.tensor import TensorFemSpace -from psydac.fem.vector import VectorFemSpace +from psydac.fem.vector import VectorFemSpace, MultipatchFemSpace from psydac.ddm.cart import DomainDecomposition, CartDecomposition from psydac.utilities.utils import roll_edges from abc import ABCMeta, abstractmethod -__all__ = ('GlobalProjector', 'Projector_H1', 'Projector_Hcurl', 'Projector_Hdiv', 'Projector_L2', +__all__ = ('GlobalGeometricProjector', 'GlobalGeometricProjectorH1', 'GlobalGeometricProjectorHcurl', 'GlobalGeometricProjectorHdiv', 'GlobalGeometricProjectorL2', + 'MultipatchGeometricProjector', 'evaluate_dofs_1d_0form', 'evaluate_dofs_1d_1form', 'evaluate_dofs_2d_0form', 'evaluate_dofs_2d_1form_hcurl', 'evaluate_dofs_2d_1form_hdiv', 'evaluate_dofs_2d_2form', 'evaluate_dofs_3d_0form', 'evaluate_dofs_3d_1form', 'evaluate_dofs_3d_2form', 'evaluate_dofs_3d_3form') #============================================================================== -class GlobalProjector(metaclass=ABCMeta): +class GlobalGeometricProjector(metaclass=ABCMeta): """ Projects callable functions to some scalar or vector FEM space. @@ -43,7 +44,7 @@ class GlobalProjector(metaclass=ABCMeta): space : VectorFemSpace | TensorFemSpace Some finite element space, codomain of the projection operator. The exact structure where to use histopolation and where interpolation - has to be given by a subclass of the GlobalProjector class. + has to be given by a subclass of the GlobalGeometricProjector class. As of now, it is implicitly assumed for a VectorFemSpace, that for each direction that all spaces with interpolation are the same, and all spaces with histopolation are the same (i.e. yield the same quadrature/interpolation points etc.); so use with care on an arbitrary VectorFemSpace. @@ -389,7 +390,9 @@ def __call__(self, fun): return FemField(self._space, coeffs=coeffs) #============================================================================== -class Projector_H1(GlobalProjector): +# SINGLEPATCH PROJECTORS +#============================================================================== +class GlobalGeometricProjectorH1(GlobalGeometricProjector): """ Projector from H1 to an H1-conforming finite element space (i.e. a finite dimensional subspace of H1) constructed with tensor-product B-splines in 1, @@ -439,7 +442,7 @@ def __call__(self, fun): return super().__call__(fun) #============================================================================== -class Projector_Hcurl(GlobalProjector): +class GlobalGeometricProjectorHcurl(GlobalGeometricProjector): """ Projector from H(curl) to an H(curl)-conforming finite element space, i.e. a finite dimensional subspace of H(curl), constructed with tensor-product @@ -512,7 +515,7 @@ def __call__(self, fun): return super().__call__(fun) #============================================================================== -class Projector_Hdiv(GlobalProjector): +class GlobalGeometricProjectorHdiv(GlobalGeometricProjector): """ Projector from H(div) to an H(div)-conforming finite element space, i.e. a finite dimensional subspace of H(div), constructed with tensor-product @@ -589,7 +592,7 @@ def __call__(self, fun): return super().__call__(fun) #============================================================================== -class Projector_L2(GlobalProjector): +class GlobalGeometricProjectorL2(GlobalGeometricProjector): """ Projector from L2 to an L2-conforming finite element space (i.e. a finite dimensional subspace of L2) constructed with tensor-product M-splines in 1, @@ -648,7 +651,8 @@ def __call__(self, fun): """ return super().__call__(fun) -class Projector_H1vec(GlobalProjector): +#============================================================================== +class GlobalGeometricProjectorH1vec(GlobalGeometricProjector): """ Projector from H1^3 = H1 x H1 x H1 to a conforming finite element space, i.e. a finite dimensional subspace of H1^3, constructed with tensor-product @@ -712,6 +716,42 @@ def __call__(self, fun): """ return super().__call__(fun) +#============================================================================== +# MULTIPATCH PROJECTORS (2D) +#============================================================================== +class MultipatchGeometricProjector: + """ + Global Geometric Projector base class for multipatch domains. + + Parameters + ---------- + space : MultipatchFemSpace + Multipatch finite element space, codomain of the projection operator. + Projector : type[GlobalGeometricProjector] + Class of the projector to instantiate for each patch. + nquads : Iterable[int] + Number of quadrature points per cell along each direction. + This is a parameter passed to the constructor of Projector. + """ + + def __init__(self, space, Projector, nquads=None): + assert isinstance(space, MultipatchFemSpace) + assert isinstance(Projector, type) + assert issubclass(Projector, GlobalGeometricProjector) + + self._Vh = Vh = space + self._Ps = [Projector(V, nquads=nquads) for V in Vh.spaces] + + def __call__(self, funs): + """ + project a list of functions given in the logical domain + """ + us = [P(fun) for P, fun, in zip(self._Ps, funs)] + + u_c = BlockVector(self._Vh.coeff_space, blocks=[uj.coeffs for uj in us]) + + return FemField(self._Vh, coeffs=u_c) + #============================================================================== # 1D DEGREES OF FREEDOM #============================================================================== diff --git a/psydac/feec/hodge.py b/psydac/feec/hodge.py new file mode 100644 index 000000000..26cb702b4 --- /dev/null +++ b/psydac/feec/hodge.py @@ -0,0 +1,148 @@ +import os +import numpy as np + +from sympde.topology import elements_of +from sympde.topology.space import ScalarFunction +from sympde.calculus import dot +from sympde.expr.expr import BilinearForm +from sympde.expr.expr import integral + +from psydac.api.settings import PSYDAC_BACKENDS + +# =============================================================================== +class HodgeOperator: + """ + Change of basis operator: dual basis -> primal basis + + self._linop: matrix (LinearOperator) of the primal Hodge = this is the mass matrix ! + self.dual_linop: this is the INVERSE mass matrix (LinearOperator) + + Parameters + ---------- + Vh: + The discrete space + + domain_h: + The discrete domain of the projector + + metric : + the metric of the de Rham complex + + backend_language: + The backend used to accelerate the code + + Notes + ----- + We only support the identity metric, this implies that the dual Hodge is the inverse of the primal one. + # todo: allow for non-identity metrics + """ + + def __init__(self, Vh, domain_h, metric='identity', backend_language='python'): + + self._fem_domain = Vh + self._fem_codomain = Vh + + # FemLinearOperators + self._primal_hodge = None + self._dual_hodge = None + + # LinearOperators + self._linop = None + self._dual_linop = None + + self._domain_h = domain_h + self._backend_language = backend_language + + if not (metric == 'identity'): + raise NotImplementedError('only the identity metric is available') + + self._metric = metric + + def assemble_matrix(self): + """ + the Hodge matrix is the patch-wise multi-patch mass matrix + it is not stored by default but assembled on demand + """ + from psydac.api.discretization import discretize + from psydac.fem.basic import FemLinearOperator + + if self._linop is None: + Vh = self._fem_domain + assert Vh == self._fem_codomain + + V = Vh.symbolic_space + domain = V.domain + u, v = elements_of(V, names='u, v') + + if isinstance(u, ScalarFunction): + expr = u * v + else: + expr = dot(u, v) + + a = BilinearForm((u, v), integral(domain, expr)) + ah = discretize(a, self._domain_h, [Vh, Vh], backend=PSYDAC_BACKENDS[self._backend_language]) + + self._linop = ah.assemble() # Mass matrix in stencil format + + self._primal_hodge = FemLinearOperator(self._fem_domain, self._fem_codomain, linop=self._linop) + + def assemble_dual_matrix(self, solver ='cg', **kwargs): + """ + the dual Hodge matrix is the patch-wise inverse of the multi-patch mass matrix + it is not stored by default but computed on demand, by approximate local (patch-wise) inversion of the mass matrix + """ + from psydac.linalg.solvers import inverse + from psydac.linalg.block import BlockLinearOperator + from psydac.fem.basic import FemLinearOperator + + if self._dual_linop is None: + if not self._linop: + self.assemble_matrix() + + M = self._linop # mass matrix of the (primal) basis + + if self._fem_domain.is_multipatch: + + nrows = M.n_block_rows + ncols = M.n_block_cols + + inv_M_blocks = [list(b) for b in M.blocks] + for i in range(nrows): + Mii = M[i, i] + inv_Mii = inverse(Mii, solver=solver, **kwargs) + inv_M_blocks[i][i] = inv_Mii + + self._dual_linop = BlockLinearOperator(M.codomain, M.domain, blocks=inv_M_blocks) + self._dual_hodge = FemLinearOperator(self._fem_codomain, self._fem_domain, linop=self._dual_linop) + + else: + inv_M = inverse(M, solver=solver, **kwargs) + self._dual_hodge = FemLinearOperator(self._fem_codomain, self._fem_domain, linop=self._dual_linop) + + @property + def linop(self): + if self._linop is None: + self.assemble_matrix() + + return self._linop + + @property + def dual_linop(self): + if self._dual_linop is None: + self.assemble_dual_matrix() + + return self._dual_linop + + @property + def hodge(self): + if self._linop is None: + self.assemble_matrix() + + return self._primal_hodge + + @property + def dual_hodge(self): + if self._dual_linop is None: + self.assemble_dual_matrix() + + return self._dual_hodge diff --git a/psydac/feec/multipatch/api.py b/psydac/feec/multipatch/api.py deleted file mode 100644 index 566815421..000000000 --- a/psydac/feec/multipatch/api.py +++ /dev/null @@ -1,301 +0,0 @@ -# coding: utf-8 -import os - -from sympde.topology import Derham -from sympde.topology import element_of, elements_of -from sympde.topology.space import ScalarFunction -from sympde.calculus import grad, dot, inner, rot, div -from sympde.calculus import laplace, bracket, convect -from sympde.calculus import jump, avg, Dn, minus, plus -from sympde.expr.expr import LinearForm, BilinearForm, integral - -from psydac.api.settings import PSYDAC_BACKENDS - -from psydac.api.discretization import discretize as discretize_single_patch -from psydac.api.discretization import discretize_space -from psydac.api.discretization import DiscreteDerham -from psydac.feec.multipatch.operators import BrokenGradient_2D -from psydac.feec.multipatch.operators import BrokenScalarCurl_2D -from psydac.feec.multipatch.operators import Multipatch_Projector_H1 -from psydac.feec.multipatch.operators import Multipatch_Projector_Hcurl -from psydac.feec.multipatch.operators import Multipatch_Projector_L2 -from psydac.feec.multipatch.operators import ConformingProjection_V0 -from psydac.feec.multipatch.operators import ConformingProjection_V1 -from psydac.feec.multipatch.fem_linear_operators import IdLinearOperator - - -__all__ = ('DiscreteDerhamMultipatch', 'discretize', 'discretize_derham_multipatch') - -#============================================================================== -class DiscreteDerhamMultipatch(DiscreteDerham): - """ Represents the discrete De Rham sequence for multipatch domains. - It only works when the number of patches>1 - - Parameters - ---------- - mapping: - The mapping of the multipatch domain, the multipatch mapping contains the mapping of each patch - - domain_h: - The discrete domain - - spaces: - The discrete spaces that are contained in the De Rham sequence - - sequence: - The space kind of each space in the De Rham sequence - """ - - def __init__(self, *, mapping, domain_h, spaces, sequence=None): - - - dim = len(spaces) - 1 - self._dim = dim - self._mapping = mapping - self._spaces = tuple(spaces) - self._domain_h = domain_h - - if sequence: - if len(sequence) != dim + 1: - raise ValueError('Expected len(sequence) = {}, got {} instead'. - format(dim + 1, len(sequence))) - - if dim == 1: - self._sequence = ('h1', 'l2') - raise NotImplementedError('1D FEEC multipatch non available yet') - - elif dim == 2: - if sequence is None: - raise ValueError('Sequence must be specified in 2D case') - - elif tuple(sequence) == ('h1', 'hcurl', 'l2'): - self._sequence = tuple(sequence) - self._broken_diff_ops = ( - BrokenGradient_2D(self.V0, self.V1), - BrokenScalarCurl_2D(self.V1, self.V2), # None, - ) - - elif tuple(sequence) == ('h1', 'hdiv', 'l2'): - self._sequence = tuple(sequence) - raise NotImplementedError('2D sequence with H-div not available yet') - - else: - raise ValueError('2D sequence not understood') - - elif dim == 3: - self._sequence = ('h1', 'hcurl', 'hdiv', 'l2') - raise NotImplementedError('3D FEEC multipatch non available yet') - - else: - raise ValueError('Dimension {} is not available'.format(dim)) - - #-------------------------------------------------------------------------- - @property - def sequence(self): - return self._sequence - - # ... - @property - def broken_derivatives_as_operators(self): - return self._broken_diff_ops - - # ... - @property - def broken_derivatives_as_matrices(self): - return tuple(b_diff.matrix for b_diff in self._broken_diff_ops) - - #-------------------------------------------------------------------------- - def projectors(self, *, kind='global', nquads=None): - """ - This method returns the patch-wise commuting projectors on the broken multi-patch space - - Parameters - ---------- - kind: - The projectors kind, can be global or local - - nquads: - The number of quadrature points. - - Returns - ------- - P0: - Patch wise H1 projector - - P1: - Patch wise Hcurl projector - - P2: - Patch wise L2 projector - - Notes - ----- - - when applied to smooth functions they return conforming fields - - default 'global projectors' correspond to geometric interpolation/histopolation operators on Greville grids - - here 'global' is a patch-level notion, as the interpolation-type problems are solved on each patch independently - """ - if not (kind == 'global'): - raise NotImplementedError('only global projectors are available') - - if self.dim == 1: - raise NotImplementedError("1D projectors are not available") - - elif self.dim == 2: - P0 = Multipatch_Projector_H1(self.V0) - - if self.sequence[1] == 'hcurl': - P1 = Multipatch_Projector_Hcurl(self.V1, nquads=nquads) - else: - P1 = None # TODO: Multipatch_Projector_Hdiv(self.V1, nquads=nquads) - raise NotImplementedError('2D sequence with H-div not available yet') - - P2 = Multipatch_Projector_L2(self.V2, nquads=nquads) - return P0, P1, P2 - - elif self.dim == 3: - raise NotImplementedError("3D projectors are not available") - - #-------------------------------------------------------------------------- - def conforming_projection(self, space, hom_bc=False, backend_language="python", load_dir=None): - """ - return the conforming projectors of the broken multi-patch space - - Parameters - ---------- - space : - The space of the projector - - hom_bc: - Apply homogenous boundary conditions if True - - backend_language: - The backend used to accelerate the code - - load_dir: - Filename for storage in sparse matrix format - - Returns - ------- - Cp: - The conforming projector - - """ - if hom_bc is None: - raise ValueError('please provide a value for "hom_bc" argument') - - if isinstance(load_dir, str): - if not os.path.exists(load_dir): - os.makedirs(load_dir) - if space == 'V0': - P_name = 'cP0' - elif space == 'V1': - P_name = 'cP1' - elif space == 'V2': - P_name = 'cP2' - else: - raise ValueError(space) - - if hom_bc: - storage_fn = load_dir + '/{}_hom_m.npz'.format(P_name) - else: - storage_fn = load_dir + '/{}_m.npz'.format(P_name) - else: - storage_fn = None - - cP = None - if self.dim == 1: - raise NotImplementedError("1D projectors are not available") - - elif self.dim == 2: - if space == 'V0': - cP = ConformingProjection_V0(self.V0, self._domain_h, hom_bc=hom_bc, backend_language=backend_language, storage_fn=storage_fn) - elif space == 'V1': - if self.sequence[1] == 'hcurl': - cP = ConformingProjection_V1(self.V1, self._domain_h, hom_bc=hom_bc, backend_language=backend_language, storage_fn=storage_fn) - else: - raise NotImplementedError('2D sequence with H-div not available yet') - - elif space == 'V2': - cP = IdLinearOperator(self.V2) # no storage needed! - else: - raise ValueError('Invalid value for "space" argument: {}'.format(space)) - - elif self.dim == 3: - raise NotImplementedError("3D projectors are not available") - - return cP - - def get_dual_dofs(self, space, f, backend_language="python", return_format='stencil_array'): - """ - return the dual dofs tilde_sigma_i(f) = < Lambda_i, f >_{L2} i = 1, .. dim(V^k)) of a given function f, as a stencil array or numpy array - - Parameters - ---------- - space : - The space of the dual dofs - - f : - The function used for evaluation - - backend_language: - The backend used to accelerate the code - - return_format: - The format of the dofs, can be 'stencil_array' or 'numpy_array' - - Returns - ------- - tilde_f: - The dual dofs - """ - if space == 'V0': - Vh = self.V0 - elif space == 'V1': - Vh = self.V1 - elif space == 'V2': - Vh = self.V2 - else: - raise NotImplementedError("The space of kind {} is not available".format(space)) - - V = Vh.symbolic_space - v = element_of(V, name='v') - - if isinstance(v, ScalarFunction): - expr = f*v - else: - expr = dot(f,v) - - l = LinearForm(v, integral( V.domain, expr)) - lh = discretize(l, self._domain_h, Vh, backend=PSYDAC_BACKENDS[backend_language]) - tilde_f = lh.assemble() - - if return_format == 'numpy_array': - return tilde_f.toarray() - else: - return tilde_f - -#============================================================================== -def discretize_derham_multipatch(derham, domain_h, *args, **kwargs): - - ldim = derham.shape - mapping = derham.spaces[0].domain.mapping - - bases = ['B'] + ldim * ['M'] - spaces = [discretize_space(V, domain_h, *args, basis=basis, **kwargs) \ - for V, basis in zip(derham.spaces, bases)] - - return DiscreteDerhamMultipatch( - mapping = mapping, - domain_h = domain_h, - spaces = spaces, - sequence = [V.kind.name for V in derham.spaces] - ) - -#============================================================================== -def discretize(expr, *args, **kwargs): - - if isinstance(expr, Derham) and expr.V0.is_broken: - return discretize_derham_multipatch(expr, *args, **kwargs) - - else: - return discretize_single_patch(expr, *args, **kwargs) diff --git a/psydac/feec/multipatch/examples/h1_source_pbms_conga_2d.py b/psydac/feec/multipatch/examples/h1_source_pbms_conga_2d.py index 7b1e33792..aaebd3140 100644 --- a/psydac/feec/multipatch/examples/h1_source_pbms_conga_2d.py +++ b/psydac/feec/multipatch/examples/h1_source_pbms_conga_2d.py @@ -12,38 +12,21 @@ V0h --grad-> V1h -—curl-> V2h """ - -from mpi4py import MPI - import os import numpy as np -from collections import OrderedDict - -from sympy import lambdify -from scipy.sparse.linalg import spsolve -from sympde.calculus import dot -from sympde.expr.expr import LinearForm -from sympde.expr.expr import integral, Norm from sympde.topology import Derham -from sympde.topology import element_of -from psydac.api.settings import PSYDAC_BACKENDS -from psydac.feec.multipatch.api import discretize -from psydac.feec.pull_push import pull_2d_h1 -from psydac.feec.multipatch.utils_conga_2d import P0_phys +from psydac.api.discretization import discretize +from psydac.linalg.basic import IdentityOperator +from psydac.linalg.solvers import inverse -from psydac.feec.multipatch.fem_linear_operators import IdLinearOperator -from psydac.feec.multipatch.operators import HodgeOperator from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_solution_h1 -from psydac.feec.multipatch.utilities import time_count -from psydac.feec.multipatch.non_matching_operators import construct_h1_conforming_projection, construct_hcurl_conforming_projection -from psydac.api.postprocessing import OutputManager, PostProcessManager +from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_solution_h1 -from psydac.linalg.utilities import array_to_psydac -from psydac.fem.basic import FemField +from psydac.fem.projectors import get_dual_dofs +from psydac.fem.basic import FemField from psydac.api.postprocessing import OutputManager, PostProcessManager @@ -98,9 +81,6 @@ def solve_h1_source_pbm( print('building the multipatch domain...') domain = build_multipatch_domain(domain_name=domain_name) - mappings = OrderedDict([(P.logical_domain, P.mapping) - for P in domain.interior]) - mappings_list = list(mappings.values()) if isinstance(nc, int): ncells = [nc, nc] @@ -114,102 +94,89 @@ def solve_h1_source_pbm( derham = Derham(domain, ["H1", "Hcurl", "L2"]) derham_h = discretize(derham, domain_h, degree=degree) - # multi-patch (broken) spaces - V0h = derham_h.V0 - V1h = derham_h.V1 - V2h = derham_h.V2 + V0h, V1h, V2h = derham_h.spaces print('dim(V0h) = {}'.format(V0h.nbasis)) print('dim(V1h) = {}'.format(V1h.nbasis)) print('dim(V2h) = {}'.format(V2h.nbasis)) print('broken differential operators...') # broken (patch-wise) differential operators - bD0, bD1 = derham_h.broken_derivatives_as_operators - bD0_m = bD0.to_sparse_matrix() - - print('building the discrete operators:') - print('commuting projection operators...') - nquads = [4 * (d + 1) for d in degree] - P0, P1, P2 = derham_h.projectors(nquads=nquads) - - I0 = IdLinearOperator(V0h) - I0_m = I0.to_sparse_matrix() + bD0, bD1 = derham_h.derivatives(kind='linop') print('Hodge operators...') - # multi-patch (broken) linear operators / matrices - H0 = HodgeOperator(V0h, domain_h, backend_language=backend_language) - H1 = HodgeOperator(V1h, domain_h, backend_language=backend_language) - - H0_m = H0.to_sparse_matrix() # = mass matrix of V0 - dH0_m = H0.get_dual_Hodge_sparse_matrix() # = inverse mass matrix of V0 - H1_m = H1.to_sparse_matrix() # = mass matrix of V1 + # multi-patch (broken) linear operators + H0 = derham_h.hodge_operator(space='V0', kind='linop', backend_language=backend_language) + H1 = derham_h.hodge_operator(space='V1', kind='linop', backend_language=backend_language) + dH0 = derham_h.hodge_operator(space='V0', kind='linop', dual=True, backend_language=backend_language) print('conforming projection operators...') # conforming Projections (should take into account the boundary conditions # of the continuous deRham sequence) - cP0_m = construct_h1_conforming_projection(V0h, hom_bc=True) - - def lift_u_bc(u_bc): - if u_bc is not None: - print('lifting the boundary condition in V0h... [warning: Not Tested Yet!]') - d_ubc_c = derham_h.get_dual_dofs(space='V0', f=u_bc, backend_language=backend_language, return_format='numpy_array') - ubc_c = dH0_m.dot(d_ubc_c) + cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', hom_bc = True) - ubc_c = ubc_c - cP0_m.dot(ubc_c) - else: - ubc_c = None - return ubc_c + print('building the discrete operators:') - # Conga (projection-based) stiffness matrices: - # div grad: - pre_DG_m = - bD0_m.transpose() @ H1_m @ bD0_m + I0 = IdentityOperator(V0h.coeff_space) + + # div grad + DG = - bD0.T @ H1 @ bD0 # jump penalization: - jump_penal_m = I0_m - cP0_m - JP0_m = jump_penal_m.transpose() @ H0_m @ jump_penal_m + JP0 = (I0 - cP0).T @ H0 @ (I0 - cP0) # useful for the boundary condition (if present) - pre_A_m = cP0_m.transpose() @ (eta * H0_m - mu * pre_DG_m) - A_m = pre_A_m @ cP0_m + gamma_h * JP0_m + pre_A = cP0.T @ (eta * H0 - mu * DG) + + A = pre_A @ cP0 + gamma_h * JP0 + + + f_scal, u_bc, u_ex = get_source_and_solution_h1(source_type=source_type, eta=eta, mu=mu, domain=domain, domain_name=domain_name,) - print('getting the source and ref solution...') - f_scal, u_bc, u_ex = get_source_and_solution_h1( - source_type=source_type, eta=eta, mu=mu, domain=domain, domain_name=domain_name, - ) + df = get_dual_dofs(Vh=V0h, f=f_scal, domain_h=domain_h, backend_language=backend_language) + f = dH0 @ df + df = cP0.T @ df - # compute approximate source f_h - b_c = derham_h.get_dual_dofs(space='V0', f=f_scal, backend_language=backend_language, return_format='numpy_array') - # source in primal sequence for plotting - f_c = dH0_m.dot(b_c) - b_c = cP0_m.transpose() @ b_c + def lift_u_bc(u_bc): + if u_bc is not None: + du_bc = get_dual_dofs(Vh=V0h, f=u_bc, domain_h = domain_h, backend_language=backend_language) + ubc = dH0.dot(du_bc) + ubc -= cP0.dot(ubc) - ubc_c = lift_u_bc(u_bc) + else: + ubc = None + + return ubc - if ubc_c is not None: + ubc = lift_u_bc(u_bc) + + if ubc is not None: # modified source for the homogeneous pbm print('modifying the source with lifted bc solution...') - b_c = b_c - pre_A_m.dot(ubc_c) + df -= pre_A @ ubc # direct solve with scipy spsolve - print('solving source problem with scipy.spsolve...') - uh_c = spsolve(A_m, b_c) + print('solving source problem with conjugate gradient...') + solver = inverse(A, solver='cg', tol=1e-8) + u = solver.solve(df) # project the homogeneous solution on the conforming problem space print('projecting the homogeneous solution on the conforming problem space...') - uh_c = cP0_m.dot(uh_c) + u = cP0.dot(u) - if ubc_c is not None: + if ubc is not None: # adding the lifted boundary condition print('adding the lifted boundary condition...') - uh_c += ubc_c + u += ubc - print('getting and plotting the FEM solution from numpy coefs array...') if u_ex: - u_ex_c = derham_h.get_dual_dofs(space='V0', f=u_ex, backend_language=backend_language, return_format='numpy_array') - u_ex_c = dH0_m.dot(u_ex_c) + u_ex = get_dual_dofs(Vh=V0h, f=u_ex, domain_h=domain_h, backend_language=backend_language) + u_ex = dH0.dot(u_ex) + if plot_dir is not None: + print('plotting the FEM solution...') + if not os.path.exists(plot_dir): os.makedirs(plot_dir) @@ -217,17 +184,14 @@ def lift_u_bc(u_bc): OM.add_spaces(V0h=V0h) OM.set_static() - stencil_coeffs = array_to_psydac(uh_c, V0h.coeff_space) - vh = FemField(V0h, coeffs=stencil_coeffs) - OM.export_fields(vh=vh) + uh = FemField(V0h, coeffs=u) + OM.export_fields(uh=uh) - stencil_coeffs = array_to_psydac(f_c, V0h.coeff_space) - fh = FemField(V0h, coeffs=stencil_coeffs) + fh = FemField(V0h, coeffs=f) OM.export_fields(fh=fh) if u_ex: - stencil_coeffs = array_to_psydac(u_ex_c, V0h.coeff_space) - uh_ex = FemField(V0h, coeffs=stencil_coeffs) + uh_ex = FemField(V0h, coeffs=u_ex) OM.export_fields(uh_ex=uh_ex) OM.export_space_info() @@ -243,7 +207,7 @@ def lift_u_bc(u_bc): grid=None, npts_per_cell=[6] * 2, snapshots='all', - fields='vh') + fields='uh') PM.export_to_vtk( plot_dir + "/f_h", @@ -263,9 +227,9 @@ def lift_u_bc(u_bc): PM.close() if u_ex: - err = uh_c - u_ex_c - rel_err = np.sqrt(np.dot(err, H0_m.dot(err)))/np.sqrt(np.dot(u_ex_c,H0_m.dot(u_ex_c))) - + err = u - u_ex + rel_err = np.sqrt(H0.dot_inner(err, err) / H0.dot_inner(u_ex, u_ex)) + return rel_err @@ -273,19 +237,21 @@ def lift_u_bc(u_bc): omega = np.sqrt(170) # source eta = -omega**2 + mu=0 + gamma_h = 10 source_type = 'manu_poisson_elliptic' domain_name = 'pretzel_f' - nc = 10 + nc = 4 deg = 2 run_dir = '{}_{}_nc={}_deg={}/'.format(domain_name, source_type, nc, deg) solve_h1_source_pbm( nc=nc, deg=deg, eta=eta, - mu=1, # 1, + mu=mu, # 1, domain_name=domain_name, source_type=source_type, backend_language='pyccel-gcc', diff --git a/psydac/feec/multipatch/examples/hcurl_eigen_pbms_conga_2d.py b/psydac/feec/multipatch/examples/hcurl_eigen_pbms_conga_2d.py index db54565c7..418118469 100644 --- a/psydac/feec/multipatch/examples/hcurl_eigen_pbms_conga_2d.py +++ b/psydac/feec/multipatch/examples/hcurl_eigen_pbms_conga_2d.py @@ -2,41 +2,32 @@ Solve the eigenvalue problem for the curl-curl operator in 2D with a FEEC discretization """ import os -from mpi4py import MPI - import numpy as np -import matplotlib.pyplot as plt -from collections import OrderedDict + from sympde.topology import Derham -from psydac.feec.multipatch.api import discretize +from psydac.api.discretization import discretize from psydac.api.settings import PSYDAC_BACKENDS -from psydac.feec.multipatch.fem_linear_operators import IdLinearOperator -from psydac.feec.multipatch.operators import HodgeOperator from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.utilities import time_count, get_run_dir, get_plot_dir, get_mat_dir, get_sol_dir, diag_fn -from psydac.feec.multipatch.utils_conga_2d import write_diags_to_file +from psydac.feec.multipatch.utilities import time_count -from sympde.topology import Square -from sympde.topology import IdentityMapping, PolarMapping from scipy.sparse.linalg import spilu, lgmres from scipy.sparse.linalg import LinearOperator, eigsh, minres -from scipy.sparse import csr_matrix from scipy.linalg import norm +from psydac.linalg.basic import IdentityOperator from psydac.linalg.utilities import array_to_psydac from psydac.fem.basic import FemField from psydac.feec.multipatch.multipatch_domain_utilities import build_cartesian_multipatch_domain -from psydac.feec.multipatch.non_matching_operators import construct_h1_conforming_projection, construct_hcurl_conforming_projection from psydac.api.postprocessing import OutputManager, PostProcessManager def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), domain=([0, np.pi], [0, np.pi]), domain_name='refined_square', backend_language='pyccel-gcc', mu=1, nu=0, gamma_h=0, generalized_pbm=False, sigma=5, nb_eigs_solve=8, nb_eigs_plot=5, skip_eigs_threshold=1e-7, - plot_dir=None, m_load_dir=None,): + plot_dir=None): """ Solve the eigenvalue problem for the curl-curl operator in 2D with DG discretization @@ -70,8 +61,6 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma Threshold for the eigenvalues to skip plot_dir : str Directory for the plots - m_load_dir : str - Directory to save and load the matrices """ diags = {} @@ -110,10 +99,6 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma elif ncells.ndim == 2: ncells = {patch.name: [ncells[int(patch.name[2])][int(patch.name[4])], ncells[int(patch.name[2])][int(patch.name[4])]] for patch in domain.interior} - - mappings = OrderedDict([(P.logical_domain, P.mapping) - for P in domain.interior]) - mappings_list = list(mappings.values()) t_stamp = time_count(t_stamp) print(' .. discrete domain...') @@ -128,9 +113,7 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma print(' .. discrete derham sequence...') derham_h = discretize(derham, domain_h, degree=degree) - V0h = derham_h.V0 - V1h = derham_h.V1 - V2h = derham_h.V2 + V0h, V1h, V2h = derham_h.spaces print('dim(V0h) = {}'.format(V0h.nbasis)) print('dim(V1h) = {}'.format(V1h.nbasis)) print('dim(V2h) = {}'.format(V2h.nbasis)) @@ -142,64 +125,27 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma print('building the discrete operators:') print('commuting projection operators...') - I1 = IdLinearOperator(V1h) - I1_m = I1.to_sparse_matrix() + I1 = IdentityOperator(V1h.coeff_space) t_stamp = time_count(t_stamp) print('Hodge operators...') # multi-patch (broken) linear operators / matrices - H0 = HodgeOperator( - V0h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=0) - H1 = HodgeOperator( - V1h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=1) - H2 = HodgeOperator( - V2h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=2) - - H0_m = H0.to_sparse_matrix() # = mass matrix of V0 - dH0_m = H0.get_dual_Hodge_sparse_matrix() # = inverse mass matrix of V0 - H1_m = H1.to_sparse_matrix() # = mass matrix of V1 - dH1_m = H1.get_dual_Hodge_sparse_matrix() # = inverse mass matrix of V1 - H2_m = H2.to_sparse_matrix() # = mass matrix of V2 - dH2_m = H2.get_dual_Hodge_sparse_matrix() # = inverse mass matrix of V2 + H0, H1, H2 = derham_h.hodge_operators(kind='linop', backend_language=backend_language) + dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True, backend_language=backend_language) t_stamp = time_count(t_stamp) print('conforming projection operators...') # conforming Projections (should take into account the boundary conditions # of the continuous deRham sequence) - cP0_m = construct_h1_conforming_projection(V0h, hom_bc=True) - cP1_m = construct_hcurl_conforming_projection(V1h, hom_bc=True) + cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', hom_bc = True) - t_stamp = time_count(t_stamp) - print('broken differential operators...') - bD0, bD1 = derham_h.broken_derivatives_as_operators - bD0_m = bD0.to_sparse_matrix() - bD1_m = bD1.to_sparse_matrix() t_stamp = time_count(t_stamp) - print('converting some matrices to csr format...') - - H1_m = H1_m.tocsr() - dH1_m = dH1_m.tocsr() - H2_m = H2_m.tocsr() - bD1_m = bD1_m.tocsr() + print('broken differential operators...') + bD0, bD1 = derham_h.derivatives(kind='linop') - if not os.path.exists(plot_dir): - os.makedirs(plot_dir) print('computing the full operator matrix...') - A_m = np.zeros_like(H1_m) # Conga (projection-based) stiffness matrices if mu != 0: @@ -208,33 +154,29 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma print('mu = {}'.format(mu)) print('curl-curl stiffness matrix...') - pre_CC_m = bD1_m.transpose() @ H2_m @ bD1_m - CC_m = cP1_m.transpose() @ pre_CC_m @ cP1_m # Conga stiffness matrix - A_m += mu * CC_m + CC = cP1.T @ bD1.T @ H2 @ bD1 @ cP1 # Conga stiffness matrix + A = mu * CC if nu != 0: - pre_GD_m = - H1_m @ bD0_m @ cP0_m @ dH0_m @ cP0_m.transpose() @ bD0_m.transpose() @ H1_m - GD_m = cP1_m.transpose() @ pre_GD_m @ cP1_m # Conga stiffness matrix - A_m -= nu * GD_m + GD = - cP1.T @ H1 @ bD0 @ cP0 @ dH0 @ cP0.T @ bD0.T @ H1 @ cP1 + A -= nu * GD # jump stabilization in V1h: if gamma_h != 0 or generalized_pbm: t_stamp = time_count(t_stamp) print('jump stabilization matrix...') - jump_stab_m = I1_m - cP1_m - JS_m = jump_stab_m.transpose() @ H1_m @ jump_stab_m - A_m += gamma_h * JS_m + JS = (I1 - cP1).T @ H1 @ (I1 - cP1) + A += gamma_h * JS if generalized_pbm: print('adding jump stabilization to RHS of generalized eigenproblem...') - B_m = cP1_m.transpose() @ H1_m @ cP1_m + JS_m + B = cP1.T @ H1 @ cP1 + JS else: - B_m = H1_m + B = H1 t_stamp = time_count(t_stamp) print('solving matrix eigenproblem...') - all_eigenvalues, all_eigenvectors_transp = get_eigenvalues( - nb_eigs_solve, sigma, A_m, B_m) + all_eigenvalues, all_eigenvectors_transp = get_eigenvalues(nb_eigs_solve, sigma, A.tosparse(), B.tosparse()) # Eigenvalue processing t_stamp = time_count(t_stamp) print('sorting out eigenvalues...') @@ -262,37 +204,45 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma t_stamp = time_count(t_stamp) print('plotting the eigenmodes...') - OM = OutputManager(plot_dir + '/spaces.yml', plot_dir + '/fields.h5') - OM.add_spaces(V1h=V1h) - OM.export_space_info() - - nb_eigs = len(eigenvalues) - for i in range(min(nb_eigs_plot, nb_eigs)): - - print('looking at emode i = {}... '.format(i)) - lambda_i = eigenvalues[i] - emode_i = np.real(eigenvectors[i]) - norm_emode_i = np.dot(emode_i, H1_m.dot(emode_i)) - eh_c = emode_i / norm_emode_i - - stencil_coeffs = array_to_psydac(cP1_m @ eh_c, V1h.coeff_space) - vh = FemField(V1h, coeffs=stencil_coeffs) - OM.add_snapshot(i, i) - OM.export_fields(vh=vh) - - OM.close() - - PM = PostProcessManager( - domain=domain, - space_file=plot_dir + '/spaces.yml', - fields_file=plot_dir + '/fields.h5') - PM.export_to_vtk( - plot_dir + "/eigenvalues", - grid=None, - npts_per_cell=[6] * 2, - snapshots='all', - fields='vh') - PM.close() + if plot_dir: + + if not os.path.exists(plot_dir): + os.makedirs(plot_dir) + + OM = OutputManager(plot_dir + '/spaces.yml', plot_dir + '/fields.h5') + OM.add_spaces(V1h=V1h) + OM.export_space_info() + + nb_eigs = len(eigenvalues) + H1_m = H1.tosparse() + cP1_m = cP1.tosparse() + + for i in range(min(nb_eigs_plot, nb_eigs)): + + print('looking at emode i = {}... '.format(i)) + lambda_i = eigenvalues[i] + emode_i = np.real(eigenvectors[i]) + norm_emode_i = np.dot(emode_i, H1_m.dot(emode_i)) + eh_c = emode_i / norm_emode_i + + stencil_coeffs = array_to_psydac(cP1_m @ eh_c, V1h.coeff_space) + vh = FemField(V1h, coeffs=stencil_coeffs) + OM.add_snapshot(i, i) + OM.export_fields(vh=vh) + + OM.close() + + PM = PostProcessManager( + domain=domain, + space_file=plot_dir + '/spaces.yml', + fields_file=plot_dir + '/fields.h5') + PM.export_to_vtk( + plot_dir + "/eigenvalues", + grid=None, + npts_per_cell=[6] * 2, + snapshots='all', + fields='vh') + PM.close() t_stamp = time_count(t_stamp) diff --git a/psydac/feec/multipatch/examples/hcurl_eigen_pbms_dg_2d.py b/psydac/feec/multipatch/examples/hcurl_eigen_pbms_dg_2d.py index 58c6a2bb6..0235dd72d 100644 --- a/psydac/feec/multipatch/examples/hcurl_eigen_pbms_dg_2d.py +++ b/psydac/feec/multipatch/examples/hcurl_eigen_pbms_dg_2d.py @@ -3,14 +3,13 @@ A. Buffa and I. Perugia, “Discontinuous Galerkin Approximation of the Maxwell Eigenproblem” SIAM Journal on Numerical Analysis 44 (2006) """ - import os from mpi4py import MPI from collections import OrderedDict import numpy as np import matplotlib.pyplot -from scipy.sparse.linalg import spsolve, inv + from scipy.sparse.linalg import LinearOperator, eigsh, minres from sympde.calculus import grad, dot, curl, cross @@ -26,14 +25,12 @@ from sympde.expr.equation import find, EssentialBC from psydac.linalg.utilities import array_to_psydac -from psydac.api.tests.build_domain import build_pretzel from psydac.fem.basic import FemField -from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL from psydac.feec.pull_push import pull_2d_hcurl from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.utilities import time_count, get_run_dir, get_plot_dir, get_mat_dir, get_sol_dir, diag_fn -from psydac.feec.multipatch.api import discretize +from psydac.feec.multipatch.utilities import time_count +from psydac.api.discretization import discretize from psydac.feec.multipatch.multipatch_domain_utilities import build_cartesian_multipatch_domain from psydac.api.postprocessing import OutputManager, PostProcessManager @@ -194,40 +191,41 @@ def avr(w): return 0.5 * plus(w) + 0.5 * minus(w) t_stamp = time_count(t_stamp) print('plotting the eigenmodes...') - if not os.path.exists(plot_dir): - os.makedirs(plot_dir) - - OM = OutputManager(plot_dir + '/spaces.yml', plot_dir + '/fields.h5') - OM.add_spaces(Vh=Vh) - OM.export_space_info() - - nb_eigs = len(eigenvalues) - for i in range(min(nb_eigs_plot, nb_eigs)): - - print('looking at emode i = {}... '.format(i)) - lambda_i = eigenvalues[i] - emode_i = np.real(eigenvectors[i]) - norm_emode_i = np.dot(emode_i, Bh_m.dot(emode_i)) - eh_c = emode_i / norm_emode_i - - stencil_coeffs = array_to_psydac(eh_c, Vh.coeff_space) - vh = FemField(Vh, coeffs=stencil_coeffs) - OM.add_snapshot(i, i) - OM.export_fields(vh=vh) - - OM.close() - - PM = PostProcessManager( - domain=domain, - space_file=plot_dir + '/spaces.yml', - fields_file=plot_dir + '/fields.h5') - PM.export_to_vtk( - plot_dir + "/eigenvalues", - grid=None, - npts_per_cell=[6] * 2, - snapshots='all', - fields='vh') - PM.close() + if plot_dir: + if not os.path.exists(plot_dir): + os.makedirs(plot_dir) + + OM = OutputManager(plot_dir + '/spaces.yml', plot_dir + '/fields.h5') + OM.add_spaces(Vh=Vh) + OM.export_space_info() + + nb_eigs = len(eigenvalues) + for i in range(min(nb_eigs_plot, nb_eigs)): + + print('looking at emode i = {}... '.format(i)) + lambda_i = eigenvalues[i] + emode_i = np.real(eigenvectors[i]) + norm_emode_i = np.dot(emode_i, Bh_m.dot(emode_i)) + eh_c = emode_i / norm_emode_i + + stencil_coeffs = array_to_psydac(eh_c, Vh.coeff_space) + vh = FemField(Vh, coeffs=stencil_coeffs) + OM.add_snapshot(i, i) + OM.export_fields(vh=vh) + + OM.close() + + PM = PostProcessManager( + domain=domain, + space_file=plot_dir + '/spaces.yml', + fields_file=plot_dir + '/fields.h5') + PM.export_to_vtk( + plot_dir + "/eigenvalues", + grid=None, + npts_per_cell=[6] * 2, + snapshots='all', + fields='vh') + PM.close() t_stamp = time_count(t_stamp) diff --git a/psydac/feec/multipatch/examples/hcurl_eigen_testcases.py b/psydac/feec/multipatch/examples/hcurl_eigen_testcases.py index 4f311a7eb..5e887beda 100644 --- a/psydac/feec/multipatch/examples/hcurl_eigen_testcases.py +++ b/psydac/feec/multipatch/examples/hcurl_eigen_testcases.py @@ -220,9 +220,6 @@ diag_filename = plot_dir + '/' + diag_fn() common_diag_filename = './' + case_dir + '_diags.txt' -# to save and load matrices -# m_load_dir = get_mat_dir(domain_name, nc, deg) -m_load_dir = None print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') print(' Calling hcurl_solve_eigen_pbm() with params = {}'.format(params)) @@ -254,7 +251,6 @@ domain_name=domain_name, domain=domain, backend_language=backend_language, plot_dir=plot_dir, - m_load_dir=m_load_dir, ) elif method == 'dg': diff --git a/psydac/feec/multipatch/examples/hcurl_source_pbms_conga_2d.py b/psydac/feec/multipatch/examples/hcurl_source_pbms_conga_2d.py index b7442e054..e2252a0e2 100644 --- a/psydac/feec/multipatch/examples/hcurl_source_pbms_conga_2d.py +++ b/psydac/feec/multipatch/examples/hcurl_source_pbms_conga_2d.py @@ -14,42 +14,29 @@ """ import os -from mpi4py import MPI import numpy as np -from collections import OrderedDict -from sympy import lambdify, Matrix - -from scipy.sparse.linalg import spsolve - -from sympde.calculus import dot -from sympde.topology import element_of -from sympde.expr.expr import LinearForm -from sympde.expr.expr import integral, Norm from sympde.topology import Derham -from psydac.api.settings import PSYDAC_BACKENDS -from psydac.feec.pull_push import pull_2d_hcurl -from psydac.feec.multipatch.api import discretize -from psydac.feec.multipatch.fem_linear_operators import IdLinearOperator -from psydac.feec.multipatch.operators import HodgeOperator +from psydac.api.discretization import discretize from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_solution_hcurl -from psydac.feec.multipatch.utils_conga_2d import DiagGrid, P0_phys, P1_phys, P2_phys, get_Vh_diags_for +from psydac.feec.multipatch.utils_conga_2d import P1_phys from psydac.feec.multipatch.utilities import time_count -from psydac.linalg.utilities import array_to_psydac +# from psydac.linalg.utilities import array_to_psydac from psydac.fem.basic import FemField -from psydac.feec.multipatch.non_matching_operators import construct_h1_conforming_projection, construct_hcurl_conforming_projection from psydac.api.postprocessing import OutputManager, PostProcessManager +from psydac.linalg.basic import IdentityOperator +from psydac.fem.projectors import get_dual_dofs +from psydac.linalg.solvers import inverse + def solve_hcurl_source_pbm( - nc=4, deg=4, domain_name='pretzel_f', backend_language=None, source_proj='P_geom', source_type='manu_J', + nc=4, deg=4, domain_name='pretzel_f', backend_language=None, source_proj='tilde_Pi', source_type='manu_J', eta=-10., mu=1., nu=1., gamma_h=10., - project_sol=False, plot_dir=None, - m_load_dir=None, -): + project_sol=True, plot_dir=None): """ solver for the problem: find u in H(curl), such that @@ -82,15 +69,11 @@ def solve_hcurl_source_pbm( :param source_proj: approximation operator (in V1h) for the source, possible values are - 'tilde_Pi': dual commuting projection, an L2 projection filtered by the adjoint conforming projection) :param source_type: must be implemented in get_source_and_solution() - :param m_load_dir: directory for matrix storage """ diags = {} degree = [deg, deg] - if m_load_dir is not None: - if not os.path.exists(m_load_dir): - os.makedirs(m_load_dir) print('---------------------------------------------------------------------------------------------------------') print('Starting solve_hcurl_source_pbm function with: ') @@ -107,9 +90,9 @@ def solve_hcurl_source_pbm( t_stamp = time_count() print(' .. multi-patch domain...') domain = build_multipatch_domain(domain_name=domain_name) - mappings = OrderedDict([(P.logical_domain, P.mapping) - for P in domain.interior]) - mappings_list = list(mappings.values()) + # mappings = OrderedDict([(P.logical_domain, P.mapping) + # for P in domain.interior]) + # mappings_list = list(mappings.values()) if isinstance(nc, int): ncells = [nc, nc] @@ -117,8 +100,6 @@ def solve_hcurl_source_pbm( ncells = {patch.name: [nc[i], nc[i]] for (i, patch) in enumerate(domain.interior)} - # for diagnosttics - diag_grid = DiagGrid(mappings=mappings, N_diag=100) t_stamp = time_count(t_stamp) print(' .. derham sequence...') @@ -134,14 +115,14 @@ def solve_hcurl_source_pbm( t_stamp = time_count(t_stamp) print(' .. commuting projection operators...') - nquads = [4 * (d + 1) for d in degree] + nquads = [10 * (d + 1) for d in degree] P0, P1, P2 = derham_h.projectors(nquads=nquads) t_stamp = time_count(t_stamp) print(' .. multi-patch spaces...') - V0h = derham_h.V0 - V1h = derham_h.V1 - V2h = derham_h.V2 + V0h, V1h, V2h = derham_h.spaces + mappings = derham_h.callable_mapping + print('dim(V0h) = {}'.format(V0h.nbasis)) print('dim(V1h) = {}'.format(V1h.nbasis)) print('dim(V2h) = {}'.format(V2h.nbasis)) @@ -151,101 +132,44 @@ def solve_hcurl_source_pbm( t_stamp = time_count(t_stamp) print(' .. Id operator and matrix...') - I1 = IdLinearOperator(V1h) - I1_m = I1.to_sparse_matrix() + I1 = IdentityOperator(V1h.coeff_space) t_stamp = time_count(t_stamp) print(' .. Hodge operators...') # multi-patch (broken) linear operators / matrices # other option: define as Hodge Operators: - H0 = HodgeOperator( - V0h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=0) - H1 = HodgeOperator( - V1h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=1) - H2 = HodgeOperator( - V2h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=2) - - t_stamp = time_count(t_stamp) - print(' .. Hodge matrix H0_m = M0_m ...') - H0_m = H0.to_sparse_matrix() - t_stamp = time_count(t_stamp) - print(' .. dual Hodge matrix dH0_m = inv_M0_m ...') - dH0_m = H0.get_dual_Hodge_sparse_matrix() - - t_stamp = time_count(t_stamp) - print(' .. Hodge matrix H1_m = M1_m ...') - H1_m = H1.to_sparse_matrix() - t_stamp = time_count(t_stamp) - print(' .. dual Hodge matrix dH1_m = inv_M1_m ...') - dH1_m = H1.get_dual_Hodge_sparse_matrix() + H0, H1, H2 = derham_h.hodge_operators(kind='linop', backend_language=backend_language) + dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True, backend_language=backend_language) - t_stamp = time_count(t_stamp) - print(' .. Hodge matrix H2_m = M2_m ...') - H2_m = H2.to_sparse_matrix() - dH2_m = H2.get_dual_Hodge_sparse_matrix() t_stamp = time_count(t_stamp) print(' .. conforming Projection operators...') # conforming Projections (should take into account the boundary conditions # of the continuous deRham sequence) - cP0_m = construct_h1_conforming_projection(V0h, hom_bc=True) - cP1_m = construct_hcurl_conforming_projection(V1h, hom_bc=True) + cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', hom_bc = True) + t_stamp = time_count(t_stamp) print(' .. broken differential operators...') # broken (patch-wise) differential operators - bD0, bD1 = derham_h.broken_derivatives_as_operators - bD0_m = bD0.to_sparse_matrix() - bD1_m = bD1.to_sparse_matrix() - - if plot_dir is not None and not os.path.exists(plot_dir): - os.makedirs(plot_dir) - - def lift_u_bc(u_bc): - if u_bc is not None: - print('lifting the boundary condition in V1h...') - # note: for simplicity we apply the full P1 on u_bc, but we only - # need to set the boundary dofs - uh_bc = P1_phys(u_bc, P1, domain, mappings_list) - ubc_c = uh_bc.coeffs.toarray() - # removing internal dofs (otherwise ubc_c may already be a very - # good approximation of uh_c ...) - ubc_c = ubc_c - cP1_m.dot(ubc_c) - else: - ubc_c = None - return ubc_c + bD0, bD1 = derham_h.derivatives(kind='linop') # Conga (projection-based) stiffness matrices # curl curl: t_stamp = time_count(t_stamp) print(' .. curl-curl stiffness matrix...') - print(bD1_m.shape, H2_m.shape) - pre_CC_m = bD1_m.transpose() @ H2_m @ bD1_m - # CC_m = cP1_m.transpose() @ pre_CC_m @ cP1_m # Conga stiffness matrix + pre_CC = bD1.T @ H2 @ bD1 # grad div: t_stamp = time_count(t_stamp) print(' .. grad-div stiffness matrix...') - pre_GD_m = - H1_m @ bD0_m @ cP0_m @ dH0_m @ cP0_m.transpose() @ bD0_m.transpose() @ H1_m - # GD_m = cP1_m.transpose() @ pre_GD_m @ cP1_m # Conga stiffness matrix + pre_GD = - H1 @ bD0 @ cP0 @ dH0 @ cP0.T @ bD0.T @ H1 # jump stabilization: t_stamp = time_count(t_stamp) print(' .. jump stabilization matrix...') - jump_penal_m = I1_m - cP1_m - JP_m = jump_penal_m.transpose() @ H1_m @ jump_penal_m + JS = (I1 - cP1).T @ H1 @ (I1 - cP1) + t_stamp = time_count(t_stamp) print(' .. full operator matrix...') @@ -254,69 +178,81 @@ def lift_u_bc(u_bc): print('nu = {}'.format(nu)) print('STABILIZATION: gamma_h = {}'.format(gamma_h)) # useful for the boundary condition (if present) - pre_A_m = cP1_m.transpose() @ (eta * H1_m + mu * pre_CC_m - nu * pre_GD_m) - A_m = pre_A_m @ cP1_m + gamma_h * JP_m + pre_A = eta * cP1.T @ H1 + if mu != 0: + pre_A += mu * cP1.T @ pre_CC + if nu != 0: + pre_A -= nu * cP1.T @ pre_GD + + A = pre_A @ cP1 + gamma_h * JS t_stamp = time_count(t_stamp) print() print(' -- getting source --') - f_vect, u_bc, u_ex, curl_u_ex, div_u_ex = get_source_and_solution_hcurl( - source_type=source_type, eta=eta, mu=mu, domain=domain, domain_name=domain_name,) + f_vect, u_bc, u_ex, curl_u_ex, div_u_ex = get_source_and_solution_hcurl(source_type=source_type, eta=eta, mu=mu, domain=domain, domain_name=domain_name,) # compute approximate source f_h t_stamp = time_count(t_stamp) # f_h = L2 projection of f_vect, with filtering if tilde_Pi - print(' .. projecting the source with ' + - source_proj +' projection...') - - tilde_f_c = derham_h.get_dual_dofs( - space='V1', - f=f_vect, - backend_language=backend_language, - return_format='numpy_array') + print(' .. projecting the source with ' + source_proj +' projection...') + + tilde_f = get_dual_dofs(Vh=V1h, f=f_vect, domain_h=domain_h, backend_language=backend_language) + if source_proj == 'tilde_Pi': - print(' .. filtering the discrete source with P0.T ...') - tilde_f_c = cP1_m.transpose() @ tilde_f_c + print(' .. filtering the discrete source with P1.T ...') + tilde_f = cP1.T @ tilde_f + + def lift_u_bc(u_bc): + if u_bc is not None: + ubc = P1_phys(u_bc, P1, domain).coeffs + ubc -= cP1.dot(ubc) + + else: + ubc = None + + return ubc - ubc_c = lift_u_bc(u_bc) - if ubc_c is not None: + ubc = lift_u_bc(u_bc) + + if ubc is not None: # modified source for the homogeneous pbm t_stamp = time_count(t_stamp) print(' .. modifying the source with lifted bc solution...') - tilde_f_c = tilde_f_c - pre_A_m.dot(ubc_c) + tilde_f -= pre_A.dot(ubc) # direct solve with scipy spsolve t_stamp = time_count(t_stamp) - print() - print(' -- solving source problem with scipy.spsolve...') - uh_c = spsolve(A_m, tilde_f_c) + print('solving source problem with conjugate gradient...') + solver = inverse(A, solver='cg', tol=1e-8) + u = solver.solve(tilde_f) # project the homogeneous solution on the conforming problem space + t_stamp = time_count(t_stamp) if project_sol: - t_stamp = time_count(t_stamp) print(' .. projecting the homogeneous solution on the conforming problem space...') - uh_c = cP1_m.dot(uh_c) - else: - print(' .. NOT projecting the homogeneous solution on the conforming problem space') + u = cP1.dot(u) - if ubc_c is not None: + if ubc is not None: # adding the lifted boundary condition t_stamp = time_count(t_stamp) print(' .. adding the lifted boundary condition...') - uh_c += ubc_c + u += ubc - uh = FemField(V1h, coeffs=array_to_psydac(uh_c, V1h.coeff_space)) + uh = FemField(V1h, coeffs=u) #need cp1 here? - f_c = dH1_m.dot(tilde_f_c) - jh = FemField(V1h, coeffs=array_to_psydac(f_c, V1h.coeff_space)) + f = dH1.dot(tilde_f) + jh = FemField(V1h, coeffs=f) t_stamp = time_count(t_stamp) print(' -- plots and diagnostics --') if plot_dir: + if not os.path.exists(plot_dir): + os.makedirs(plot_dir) + OM = OutputManager(plot_dir + '/spaces.yml', plot_dir + '/fields.h5') OM.add_spaces(V1h=V1h) OM.set_static() @@ -349,11 +285,12 @@ def lift_u_bc(u_bc): time_count(t_stamp) if u_ex: - u_ex_c = P1_phys(u_ex, P1, domain, mappings_list).coeffs.toarray() - err = u_ex_c - uh_c - l2_error = np.sqrt(np.dot(err, H1_m.dot(err)))/np.sqrt(np.dot(u_ex_c,H1_m.dot(u_ex_c))) + u_ex_p = P1_phys(u_ex, P1, domain).coeffs + + err = u_ex_p - u + print(err.inner(H1.dot(err))) + l2_error = np.sqrt( H1.dot_inner(err, err) / H1.dot_inner(u_ex_p, u_ex_p)) print(l2_error) - #return l2_error diags['err'] = l2_error return diags diff --git a/psydac/feec/multipatch/examples/hcurl_source_testcase.py b/psydac/feec/multipatch/examples/hcurl_source_testcase.py index 35aa79dd6..720fb75b5 100644 --- a/psydac/feec/multipatch/examples/hcurl_source_testcase.py +++ b/psydac/feec/multipatch/examples/hcurl_source_testcase.py @@ -94,9 +94,6 @@ diag_filename = plot_dir + '/' + \ diag_fn(source_type=source_type, source_proj=source_proj) - # to save and load matrices - m_load_dir = get_mat_dir(domain_name, nc, deg) - # to save the FEM sol print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') @@ -124,7 +121,6 @@ project_sol=project_sol, gamma_h=gamma_h, plot_dir=plot_dir, - m_load_dir=m_load_dir, ) # diff --git a/psydac/feec/multipatch/examples/ppc_test_cases.py b/psydac/feec/multipatch/examples/ppc_test_cases.py index 94b772f4d..f0f7d0f8c 100644 --- a/psydac/feec/multipatch/examples/ppc_test_cases.py +++ b/psydac/feec/multipatch/examples/ppc_test_cases.py @@ -1,24 +1,9 @@ # coding: utf-8 - -from sympy.functions.special.error_functions import erf -from mpi4py import MPI - import os import numpy as np from sympy import pi, cos, sin, Tuple, exp, atan, atan2 - -from sympde.topology import Derham - -from psydac.fem.basic import FemField -from psydac.feec.multipatch.api import discretize -from psydac.feec.multipatch.operators import HodgeOperator -from psydac.fem.plotting_utilities import get_plotting_grid, my_small_plot, my_small_streamplot -from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain - -comm = MPI.COMM_WORLD - - +from sympy.functions.special.error_functions import erf # todo [MCP, 12/02/2022]: add an 'equation' argument to be able to return # 'exact solution' diff --git a/psydac/feec/multipatch/examples/timedomain_maxwell.py b/psydac/feec/multipatch/examples/timedomain_maxwell.py index 9e772f3e5..f382f0111 100644 --- a/psydac/feec/multipatch/examples/timedomain_maxwell.py +++ b/psydac/feec/multipatch/examples/timedomain_maxwell.py @@ -30,25 +30,22 @@ from sympde.expr.expr import LinearForm from sympde.expr.expr import integral, Norm from sympde.topology import Derham +from psydac.linalg.basic import IdentityOperator from psydac.api.settings import PSYDAC_BACKENDS -from psydac.feec.pull_push import pull_2d_hcurl -from psydac.feec.multipatch.api import discretize -from psydac.feec.multipatch.fem_linear_operators import IdLinearOperator -from psydac.feec.multipatch.operators import HodgeOperator, get_K0_and_K0_inv, get_K1_and_K1_inv -# , write_field_to_diag_grid, +from psydac.api.discretization import discretize + from psydac.fem.plotting_utilities import plot_field_2d as plot_field from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -# , get_praxial_Gaussian_beam_E, get_easy_Gaussian_beam_E, get_easy_Gaussian_beam_B,get_easy_Gaussian_beam_E_2, get_easy_Gaussian_beam_B_2 + from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_solution_hcurl, get_div_free_pulse, get_curl_free_pulse, get_Delta_phi_pulse, get_Gaussian_beam from psydac.feec.multipatch.utils_conga_2d import DiagGrid, P0_phys, P1_phys, P2_phys, get_Vh_diags_for -from psydac.feec.multipatch.utilities import time_count # , export_sol, import_sol -from psydac.linalg.utilities import array_to_psydac +from psydac.feec.multipatch.utilities import time_count from psydac.fem.basic import FemField -from psydac.feec.multipatch.non_matching_operators import construct_hcurl_conforming_projection, construct_h1_conforming_projection from psydac.feec.multipatch.multipatch_domain_utilities import build_cartesian_multipatch_domain from psydac.api.postprocessing import OutputManager, PostProcessManager +from psydac.fem.projectors import get_dual_dofs def solve_td_maxwell_pbm(*, @@ -61,26 +58,13 @@ def solve_td_maxwell_pbm(*, backend='pyccel-gcc', source_type='zero', source_omega=None, - source_proj='P_geom', - conf_proj='BSP', - gamma_h=10., + source_proj='P_L2', project_sol=False, filter_source=True, - quad_param=1, - E0_type='zero', + E0_type='pulse_2', E0_proj='P_L2', - hide_plots=True, plot_dir=None, plot_time_ranges=None, - plot_source=False, - plot_divE=False, - diag_dt=None, - # diag_dtau = None, - cb_min_sol=None, - cb_max_sol=None, - m_load_dir=None, - th_sol_filename="", - source_is_harmonic=False, domain_lims=None ): """ @@ -145,16 +129,6 @@ def solve_td_maxwell_pbm(*, dual degrees of freedom. Change of basis from primal to dual (and vice versa) is obtained through multiplication with the proper Hodge matrix. - conf_proj : str {'BSP' | 'GSP'} - Kind of conforming projection operator. Choose 'BSP' for an operator - based on the spline coefficients, which has maximum data locality. - Choose 'GSP' for an operator based on the geometric degrees of freedom, - which requires a change of basis (from B-spline to geometric, and then - vice versa) on the patch interfaces. - - gamma_h : float - Jump penalization parameter. - project_sol : bool Whether the solution fields should be projected onto the corresponding conforming spaces before plotting them. @@ -163,23 +137,14 @@ def solve_td_maxwell_pbm(*, If True, the current source will be filtered with the conforming projector operator (or its dual, depending on which basis is used). - quad_param : int - Multiplicative factor for the number of quadrature points; set - `quad_param` > 1 if you suspect that the quadrature is not accurate. - - E0_type : str {'zero', 'th_sol', 'pulse'} - Initial conditions for the electric field. Choose 'zero' for E0=0, - 'th_sol' for a field obtained from the time-harmonic Maxwell solver - (must provide a time-harmonic current source and set `source_omega`), + E0_type : str {'zero', 'pulse'} + Initial conditions for the electric field. Choose 'zero' for E0=0 and 'pulse' for a non-zero field localized in a small region. E0_proj : str {'P_geom' | 'P_L2'} Name of the approximation operator for the initial electric field E0 (see source_proj for details). Only relevant if E0 is not zero. - hide_plots : bool - If True, no windows are opened to show the figures interactively. - plot_dir : str Path to the directory where the figures will be saved. @@ -187,33 +152,12 @@ def solve_td_maxwell_pbm(*, List of lists, of the form `[[start, end], dtp]`, where `[start, end]` is a time interval and `dtp` is the time between two successive plots. - plot_source : bool - If True, plot the discrete field that approximates the current source. - - plot_divE : bool - If True, compute and plot the (weak) divergence of the electric field. - - diag_dt : float - Time elapsed between two successive calculations of scalar diagnostic - quantities. - - cb_min_sol : float - Minimum value to be used in colorbars when visualizing the solution. - - cb_max_sol : float - Maximum value to be used in colorbars when visualizing the solution. - - m_load_dir : str - Path to directory for matrix storage. - - th_sol_filename : str - Path to file with time-harmonic solution (to be used in conjuction with - `source_is_harmonic = True` and `E0_type = 'th_sol'`). + domain_lims : list + If the domain_name is 'refined_square' or 'square_L_shape', this + parameter must be set to the list of the two intervals defining the + rectangular domain, i.e. `[[x_min, x_max], [y_min, y_max]]`. """ - diags = {} - - # ncells = [nc, nc] degree = [deg, deg] if source_omega is not None: @@ -225,18 +169,6 @@ def solve_td_maxwell_pbm(*, [[0, final_time], final_time] ] - if diag_dt is None: - diag_dt = 0.1 - - # if backend is None: - # if domain_name in ['pretzel', 'pretzel_f'] and nc > 8: - # backend = 'numba' - # else: - # backend = 'python' - # print('[note: using '+backend_language+ ' backends in discretize functions]') - if m_load_dir is not None: - if not os.path.exists(m_load_dir): - os.makedirs(m_load_dir) print('---------------------------------------------------------------------------------------------------------') print('Starting solve_td_maxwell_pbm function with: ') @@ -248,10 +180,8 @@ def solve_td_maxwell_pbm(*, print(' source_type = {}'.format(source_type)) print(' source_proj = {}'.format(source_proj)) print(' backend = {}'.format(backend)) - # TODO: print other parameters print('---------------------------------------------------------------------------------------------------------') - debug = False print() print(' -- building discrete spaces and operators --') @@ -267,10 +197,10 @@ def solve_td_maxwell_pbm(*, if isinstance(nc, int): ncells = [nc, nc] - elif ncells.ndim == 1: + elif nc.ndim == 1: ncells = {patch.name: [nc[i], nc[i]] for (i, patch) in enumerate(domain.interior)} - elif ncells.ndim == 2: + elif nc.ndim == 2: ncells = {patch.name: [nc[int(patch.name[2])][int(patch.name[4])], nc[int(patch.name[2])][int(patch.name[4])]] for patch in domain.interior} @@ -278,8 +208,6 @@ def solve_td_maxwell_pbm(*, for P in domain.interior]) mappings_list = list(mappings.values()) - # for diagnosttics - diag_grid = DiagGrid(mappings=mappings, N_diag=100) t_stamp = time_count(t_stamp) print(' .. derham sequence...') @@ -301,101 +229,37 @@ def solve_td_maxwell_pbm(*, t_stamp = time_count(t_stamp) print(' .. multi-patch spaces...') - V0h = derham_h.V0 - V1h = derham_h.V1 - V2h = derham_h.V2 - print('dim(V0h) = {}'.format(V0h.nbasis)) - print('dim(V1h) = {}'.format(V1h.nbasis)) - print('dim(V2h) = {}'.format(V2h.nbasis)) - diags['ndofs_V0'] = V0h.nbasis - diags['ndofs_V1'] = V1h.nbasis - diags['ndofs_V2'] = V2h.nbasis + V0h, V1h, V2h = derham_h.spaces t_stamp = time_count(t_stamp) print(' .. Id operator and matrix...') - I1 = IdLinearOperator(V1h) - I1_m = I1.to_sparse_matrix() + I1 = IdentityOperator(V1h.coeff_space) t_stamp = time_count(t_stamp) print(' .. Hodge operators...') - # multi-patch (broken) linear operators / matrices - # other option: define as Hodge Operators: - H0 = HodgeOperator( - V0h, - domain_h, - backend_language=backend, - load_dir=m_load_dir, - load_space_index=0) - H1 = HodgeOperator( - V1h, - domain_h, - backend_language=backend, - load_dir=m_load_dir, - load_space_index=1) - H2 = HodgeOperator( - V2h, - domain_h, - backend_language=backend, - load_dir=m_load_dir, - load_space_index=2) - - t_stamp = time_count(t_stamp) - print(' .. Hodge matrix H0_m = M0_m ...') - H0_m = H0.to_sparse_matrix() - t_stamp = time_count(t_stamp) - print(' .. dual Hodge matrix dH0_m = inv_M0_m ...') - dH0_m = H0.get_dual_Hodge_sparse_matrix() + H0, H1, H2 = derham_h.hodge_operators(kind='linop') + dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True) - t_stamp = time_count(t_stamp) - print(' .. Hodge matrix H1_m = M1_m ...') - H1_m = H1.to_sparse_matrix() - t_stamp = time_count(t_stamp) - print(' .. dual Hodge matrix dH1_m = inv_M1_m ...') - dH1_m = H1.get_dual_Hodge_sparse_matrix() - - t_stamp = time_count(t_stamp) - print(' .. Hodge matrix dH2_m = M2_m ...') - H2_m = H2.to_sparse_matrix() - print(' .. dual Hodge matrix dH2_m = inv_M2_m ...') - dH2_m = H2.get_dual_Hodge_sparse_matrix() t_stamp = time_count(t_stamp) print(' .. conforming Projection operators...') - cP0_m = construct_h1_conforming_projection(V0h, hom_bc=False) - cP1_m = construct_hcurl_conforming_projection(V1h, hom_bc=False) - - if conf_proj == 'GSP': - print(' [* GSP-conga: using Geometric Spline conf Projections ]') - K0, K0_inv = get_K0_and_K0_inv(V0h, uniform_patches=False) - cP0_m = K0_inv @ cP0_m @ K0 - K1, K1_inv = get_K1_and_K1_inv(V1h, uniform_patches=False) - cP1_m = K1_inv @ cP1_m @ K1 - elif conf_proj == 'BSP': - print(' [* BSP-conga: using B-Spline conf Projections ]') - else: - raise ValueError(conf_proj) + cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', p_moments = degree[0]+2, hom_bc = False) t_stamp = time_count(t_stamp) print(' .. broken differential operators...') - # broken (patch-wise) differential operators - bD0, bD1 = derham_h.broken_derivatives_as_operators - bD0_m = bD0.to_sparse_matrix() - bD1_m = bD1.to_sparse_matrix() + bD0, bD1 = derham_h.derivatives(kind='linop') + if plot_dir is not None and not os.path.exists(plot_dir): os.makedirs(plot_dir) - # Conga (projection-based) matrices - t_stamp = time_count(t_stamp) - dH1_m = dH1_m.tocsr() - H2_m = H2_m.tocsr() - cP1_m = cP1_m.tocsr() - bD1_m = bD1_m.tocsr() - print(' .. matrix of the primal curl (in primal bases)...') - C_m = bD1_m @ cP1_m + C = bD1 @ cP1 print(' .. matrix of the dual curl (also in primal bases)...') + dC = dH1 @ C.T @ H2 + + ### Silvermueller ABC from sympde.calculus import grad, dot, curl, cross from sympde.topology import NormalVector from sympde.expr.expr import BilinearForm @@ -408,37 +272,38 @@ def solve_td_maxwell_pbm(*, a = BilinearForm((u, v), integral(boundary, expr_b)) ah = discretize(a, domain_h, [V1h, V1h], backend=PSYDAC_BACKENDS[backend],) - A_eps = ah.assemble().tosparse() + A_eps = ah.assemble() + # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - dC_m = dH1_m @ C_m.transpose() @ H2_m # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Compute stable time step size based on max CFL and max dt - dt = compute_stable_dt(C_m=C_m, dC_m=dC_m, cfl_max=cfl_max, dt_max=dt_max) + dt = compute_stable_dt(C=C, dC=dC, cfl_max=cfl_max, dt_max=dt_max) # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - # Absorbing dC_m - CH2 = C_m.transpose() @ H2_m - H1A = H1_m + dt * A_eps - - H1A_csc = H1A.tocsc() - dC_m = sp.sparse.linalg.spsolve(H1A_csc, CH2.tocsc()) - dCH1_m = sp.sparse.linalg.spsolve(H1A_csc, H1_m.tocsc()) + # Absorbing dC + CH2 = C.T @ H2 + H1A = H1 + dt * A_eps + + # alternative inverse + # from psydac.linalg.solvers import inverse + # H1A_inv = inverse(H1A, solver='cg', tol=1e-8) + ### + M = H1A + from scipy.linalg import inv + from scipy.sparse import csr_matrix + from psydac.linalg.sparse import SparseMatrixLinearOperator + M_inv = inv(M.toarray()) + M_inv = csr_matrix(M_inv) + H1A_inv = SparseMatrixLinearOperator(M.codomain, M.domain, M_inv) + #### + + dC = H1A_inv @ CH2 + dCH1 = H1A_inv @ H1 print(' .. matrix of the dual div (still in primal bases)...') - div_m = dH0_m @ cP0_m.transpose() @ bD0_m.transpose() @ H1_m - - # jump stabilization (may not be needed) - t_stamp = time_count(t_stamp) - print(' .. jump stabilization matrix...') - jump_penal_m = I1_m - cP1_m - JP_m = jump_penal_m.transpose() * H1_m * jump_penal_m + D = dH0 @ cP0.T @ bD0.T @ H1 - # t_stamp = time_count(t_stamp) - # print(' .. full operator matrix...') - # print('STABILIZATION: gamma_h = {}'.format(gamma_h)) - # pre_A_m = cP1_m.transpose() @ ( eta * H1_m + mu * pre_CC_m - nu * pre_GD_m ) # useful for the boundary condition (if present) - # A_m = pre_A_m @ cP1_m + gamma_h * JP_m print(" Reduce time step to match the simulation final time:") Nt = int(np.ceil(final_time / dt)) @@ -447,8 +312,7 @@ def solve_td_maxwell_pbm(*, print(f" . Nb of time steps: Nt = {Nt}") # ... - def is_plotting_time(nt, *, dt=dt, Nt=Nt, - plot_time_ranges=plot_time_ranges): + def is_plotting_time(nt, *, dt=dt, Nt=Nt, plot_time_ranges=plot_time_ranges): if nt in [0, Nt]: return True for [start, end], dt_plots in plot_time_ranges: @@ -459,21 +323,11 @@ def is_plotting_time(nt, *, dt=dt, Nt=Nt, return False # ... - # Number of time step between two successive calculations of the scalar - # diagnostics - diag_nt = max(int(diag_dt // dt), 1) print(' ------ ------ ------ ------ ------ ------ ------ ------ ') print(' ------ ------ ------ ------ ------ ------ ------ ------ ') - print( - ' total nb of time steps: Nt = {}, final time: T = {:5.4f}'.format( - Nt, - final_time)) + print(' total nb of time steps: Nt = {}, final time: T = {:5.4f}'.format(Nt, final_time)) print(' ------ ------ ------ ------ ------ ------ ------ ------ ') - print(' plotting times: the solution will be plotted for...') - for nt in range(Nt + 1): - if is_plotting_time(nt): - print(' * nt = {}, t = {:5.4f}'.format(nt, dt * nt)) print(' ------ ------ ------ ------ ------ ------ ------ ------ ') print(' ------ ------ ------ ------ ------ ------ ------ ------ ') @@ -483,8 +337,10 @@ def is_plotting_time(nt, *, dt=dt, Nt=Nt, t_stamp = time_count(t_stamp) print() print(' -- getting source --') - f0_c = None - f0_harmonic_c = None + f0_h = None + f0_harmonic_h = None + rho0_h = None + if source_type == 'zero': f0 = None @@ -492,11 +348,11 @@ def is_plotting_time(nt, *, dt=dt, Nt=Nt, elif source_type == 'pulse': - f0 = get_div_free_pulse(x_0=1.0, y_0=1.0, domain=domain) + f0 = get_div_free_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) elif source_type == 'cf_pulse': - f0 = get_curl_free_pulse(x_0=1.0, y_0=1.0, domain=domain) + f0 = get_curl_free_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) elif source_type == 'Il_pulse': # Issautier-like pulse # source will be @@ -507,91 +363,60 @@ def is_plotting_time(nt, *, dt=dt, Nt=Nt, # rho = - sin(om*t)/om * Delta phi # and Gauss' law reads # div E = rho = - sin(om*t)/om * Delta phi - f0 = get_div_free_pulse( - x_0=1.0, y_0=1.0, domain=domain) # this is curl A - f0_harmonic = get_curl_free_pulse( - x_0=1.0, y_0=1.0, domain=domain) # this is grad phi - assert not source_is_harmonic - - rho0 = get_Delta_phi_pulse( - x_0=1.0, y_0=1.0, domain=domain) # this is Delta phi - tilde_rho0_c = derham_h.get_dual_dofs( - space='V0', - f=rho0, - backend_language=backend, - return_format='numpy_array') - tilde_rho0_c = cP0_m.transpose() @ tilde_rho0_c - rho0_c = dH0_m.dot(tilde_rho0_c) + f0 = get_div_free_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) # this is curl A + f0_harmonic = get_curl_free_pulse( x_0=np.pi/2, y_0=np.pi/2, domain=domain) # this is grad phi + + rho0 = get_Delta_phi_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) # this is Delta phi + tilde_rho0_h = get_dual_dofs(Vh=V0h, f=rho0, domain_h=domain_h, backend_language=backend) + tilde_rho0_h = cP0.T @ tilde_rho0_h + rho0_h = dH0.dot(tilde_rho0_h) else: - f0, u_bc, u_ex, curl_u_ex, div_u_ex = get_source_and_solution_hcurl( - source_type=source_type, domain=domain, domain_name=domain_name, - ) + f0, u_bc, u_ex, curl_u_ex, div_u_ex = get_source_and_solution_hcurl(source_type=source_type, domain=domain, domain_name=domain_name) assert u_bc is None # only homogeneous BC's for now - # f0_c = np.zeros(V1h.nbasis) if source_omega is not None: f0_harmonic = f0 f0 = None - if E0_type == 'th_sol': - # use source enveloppe for smooth transition from 0 to 1 - def source_enveloppe(tau): - return (special.erf((tau / 25) - 2) - special.erf(-2)) / 2 - else: - def source_enveloppe(tau): - return 1 + + def source_enveloppe(tau): + return 1 t_stamp = time_count(t_stamp) - tilde_f0_c = f0_c = None - tilde_f0_harmonic_c = f0_harmonic_c = None + tilde_f0_h = f0_h = None + tilde_f0_harmonic_h = f0_harmonic_h = None + if source_proj == 'P_geom': print(' .. projecting the source with commuting projection...') + if f0 is not None: - f0_h = P1_phys(f0, P1, domain, mappings_list) - f0_c = f0_h.coeffs.toarray() - tilde_f0_c = H1_m.dot(f0_c) + f0_h = P1_phys(f0, P1, domain).coeffs + tilde_f0_h = H1.dot(f0_h) + if f0_harmonic is not None: - f0_harmonic_h = P1_phys(f0_harmonic, P1, domain, mappings_list) - f0_harmonic_c = f0_harmonic_h.coeffs.toarray() - tilde_f0_harmonic_c = H1_m.dot(f0_harmonic_c) + f0_harmonic_h = P1_phys(f0_harmonic, P1, domain).coeffs + tilde_f0_harmonic_h = H1.dot(f0_harmonic_h) elif source_proj == 'P_L2': - # helper: save/load coefs + if f0 is not None: if source_type == 'Il_pulse': source_name = 'Il_pulse_f0' else: source_name = source_type - sdd_filename = m_load_dir + '/' + source_name + \ - '_dual_dofs_qp{}.npy'.format(quad_param) - if os.path.exists(sdd_filename): - print( - ' .. loading source dual dofs from file {}'.format(sdd_filename)) - tilde_f0_c = np.load(sdd_filename) - else: - print(' .. projecting the source f0 with L2 projection...') - tilde_f0_c = derham_h.get_dual_dofs( - space='V1', f=f0, backend_language=backend, return_format='numpy_array') - print(' .. saving source dual dofs to file {}'.format(sdd_filename)) - np.save(sdd_filename, tilde_f0_c) + + print(' .. projecting the source f0 with L2 projection...') + tilde_f0_h = get_dual_dofs(Vh=V1h, f=f0, domain_h=domain_h, backend_language=backend) + if f0_harmonic is not None: if source_type == 'Il_pulse': source_name = 'Il_pulse_f0_harmonic' else: source_name = source_type - sdd_filename = m_load_dir + '/' + source_name + \ - '_dual_dofs_qp{}.npy'.format(quad_param) - if os.path.exists(sdd_filename): - print( - ' .. loading source dual dofs from file {}'.format(sdd_filename)) - tilde_f0_harmonic_c = np.load(sdd_filename) - else: - print(' .. projecting the source f0_harmonic with L2 projection...') - tilde_f0_harmonic_c = derham_h.get_dual_dofs( - space='V1', f=f0_harmonic, backend_language=backend, return_format='numpy_array') - print(' .. saving source dual dofs to file {}'.format(sdd_filename)) - np.save(sdd_filename, tilde_f0_harmonic_c) + + print(' .. projecting the source f0_harmonic with L2 projection...') + tilde_f0_harmonic_h = get_dual_dofs(Vh=V1h, f=f0_harmonic, domain_h=domain_h, backend_language=backend) else: raise ValueError(source_proj) @@ -599,259 +424,23 @@ def source_enveloppe(tau): t_stamp = time_count(t_stamp) if filter_source: print(' .. filtering the source...') - if tilde_f0_c is not None: - tilde_f0_c = cP1_m.transpose() @ tilde_f0_c - if tilde_f0_harmonic_c is not None: - tilde_f0_harmonic_c = cP1_m.transpose() @ tilde_f0_harmonic_c - - if tilde_f0_c is not None: - f0_c = dH1_m.dot(tilde_f0_c) - - if debug: - title = 'f0 part of source' - params_str = 'omega={}_gamma_h={}_Pf={}'.format( - source_omega, gamma_h, source_proj) - plot_field(numpy_coeffs=f0_c, Vh=V1h, space_kind='hcurl', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + '_f0.pdf', - plot_type='components', cb_min=cb_min_sol, cb_max=cb_max_sol, hide_plot=hide_plots) - plot_field(numpy_coeffs=f0_c, Vh=V1h, space_kind='hcurl', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + '_f0_vf.pdf', - plot_type='vector_field', cb_min=None, cb_max=None, hide_plot=hide_plots) - divf0_c = div_m @ f0_c - title = 'div f0' - plot_field(numpy_coeffs=divf0_c, Vh=V0h, space_kind='h1', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + '_divf0.pdf', - plot_type='components', cb_min=cb_min_sol, cb_max=cb_max_sol, hide_plot=hide_plots) - - if tilde_f0_harmonic_c is not None: - f0_harmonic_c = dH1_m.dot(tilde_f0_harmonic_c) - - if debug: - title = 'f0_harmonic part of source' - params_str = 'omega={}_gamma_h={}_Pf={}'.format( - source_omega, gamma_h, source_proj) - plot_field(numpy_coeffs=f0_harmonic_c, Vh=V1h, space_kind='hcurl', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + '_f0_harmonic.pdf', - plot_type='components', cb_min=None, cb_max=None, hide_plot=hide_plots) - plot_field(numpy_coeffs=f0_harmonic_c, Vh=V1h, space_kind='hcurl', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + '_f0_harmonic_vf.pdf', - plot_type='vector_field', cb_min=None, cb_max=None, hide_plot=hide_plots) - divf0_c = div_m @ f0_harmonic_c - title = 'div f0_harmonic' - plot_field(numpy_coeffs=divf0_c, Vh=V0h, space_kind='h1', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + '_divf0_harmonic.pdf', - plot_type='components', cb_min=cb_min_sol, cb_max=cb_max_sol, hide_plot=hide_plots) - - # else: - # raise NotImplementedError - - if f0_c is None: - f0_c = np.zeros(V1h.nbasis) - - # if plot_source and plot_dir: - # plot_field(numpy_coeffs=f0_c, Vh=V1h, space_kind='hcurl', domain=domain, title='f0_h with P = '+source_proj, filename=plot_dir+'/f0h_'+source_proj+'.png', hide_plot=hide_plots) - # plot_field(numpy_coeffs=f0_c, Vh=V1h, plot_type='vector_field', space_kind='hcurl', domain=domain, title='f0_h with P = '+source_proj, filename=plot_dir+'/f0h_'+source_proj+'_vf.png', hide_plot=hide_plots) + if tilde_f0_h is not None: + tilde_f0_h = cP1.T @ tilde_f0_h - t_stamp = time_count(t_stamp) + if tilde_f0_harmonic_h is not None: + tilde_f0_harmonic_h = cP1.T @ tilde_f0_harmonic_h + + if tilde_f0_h is not None: + f0_h = dH1.dot(tilde_f0_h) + + if tilde_f0_harmonic_h is not None: + f0_harmonic_h = dH1.dot(tilde_f0_harmonic_h) - def plot_J_source_nPlusHalf(f_c, nt): - print(' .. plotting the source...') - title = r'source $J^{n+1/2}_h$ (amplitude)' + \ - ' for $\\omega = {}$, $n = {}$'.format(source_omega, nt) - params_str = 'omega={}_gamma_h={}_Pf={}'.format( - source_omega, gamma_h, source_proj) - plot_field(numpy_coeffs=f_c, Vh=V1h, space_kind='hcurl', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + - '_Jh_nt={}.pdf'.format(nt), - plot_type='amplitude', cb_min=cb_min_sol, cb_max=cb_max_sol, hide_plot=hide_plots) - title = r'source $J^{n+1/2}_h$' + \ - ' for $\\omega = {}$, $n = {}$'.format(source_omega, nt) - plot_field(numpy_coeffs=f_c, Vh=V1h, space_kind='hcurl', domain=domain, title=title, - filename=plot_dir + '/' + params_str + - '_Jh_vf_nt={}.pdf'.format(nt), - plot_type='vector_field', vf_skip=1, hide_plot=hide_plots) - - def plot_E_field(E_c, nt, project_sol=False, plot_divE=False): - - # only E for now - if plot_dir: - - plot_omega_normalized_sol = (source_omega is not None) - # project the homogeneous solution on the conforming problem space - if project_sol: - # t_stamp = time_count(t_stamp) - print( - ' .. projecting the homogeneous solution on the conforming problem space...') - Ep_c = cP1_m.dot(E_c) - else: - Ep_c = E_c - print( - ' .. NOT projecting the homogeneous solution on the conforming problem space') - if plot_omega_normalized_sol: - print(' .. plotting the E/omega field...') - u_c = (1 / source_omega) * Ep_c - title = r'$u_h = E_h/\omega$ (amplitude) for $\omega = {:5.4f}$, $t = {:5.4f}$'.format( - source_omega, dt * nt) - params_str = 'omega={:5.4f}_gamma_h={}_Pf={}_Nt_pp={}'.format( - source_omega, gamma_h, source_proj, Nt_pp) - else: - print(' .. plotting the E field...') - if E0_type == 'pulse': - title = r'$t = {:5.4f}$'.format(dt * nt) - else: - title = r'$E_h$ (amplitude) at $t = {:5.4f}$'.format( - dt * nt) - u_c = Ep_c - params_str = f'gamma_h={gamma_h}_dt={dt}' - - plot_field(numpy_coeffs=u_c, Vh=V1h, space_kind='hcurl', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + - '_Eh_nt={}.pdf'.format(nt), - plot_type='amplitude', cb_min=cb_min_sol, cb_max=cb_max_sol, hide_plot=hide_plots) - - if plot_divE: - params_str = f'gamma_h={gamma_h}_dt={dt}' - if source_type == 'Il_pulse': - plot_type = 'components' - rho_c = rho0_c * \ - np.sin(source_omega * dt * nt) / source_omega - rho_norm2 = np.dot(rho_c, H0_m.dot(rho_c)) - title = r'$\rho_h$ at $t = {:5.4f}, norm = {}$'.format( - dt * nt, np.sqrt(rho_norm2)) - plot_field(numpy_coeffs=rho_c, Vh=V0h, space_kind='h1', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + - '_rho_nt={}.pdf'.format(nt), - plot_type=plot_type, cb_min=None, cb_max=None, hide_plot=hide_plots) - else: - plot_type = 'amplitude' - - divE_c = div_m @ Ep_c - divE_norm2 = np.dot(divE_c, H0_m.dot(divE_c)) - if project_sol: - title = r'div $P^1_h E_h$ at $t = {:5.4f}, norm = {}$'.format( - dt * nt, np.sqrt(divE_norm2)) - else: - title = r'div $E_h$ at $t = {:5.4f}, norm = {}$'.format( - dt * nt, np.sqrt(divE_norm2)) - plot_field(numpy_coeffs=divE_c, Vh=V0h, space_kind='h1', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + - '_divEh_nt={}.pdf'.format(nt), - plot_type=plot_type, cb_min=None, cb_max=None, hide_plot=hide_plots) - - else: - print(' -- WARNING: unknown plot_dir !!') - - def plot_B_field(B_c, nt): - - if plot_dir: - - print(' .. plotting B field...') - params_str = f'gamma_h={gamma_h}_dt={dt}' - - title = r'$B_h$ (amplitude) for $t = {:5.4f}$'.format(dt * nt) - plot_field(numpy_coeffs=B_c, Vh=V2h, space_kind='l2', domain=domain, surface_plot=False, title=title, - filename=plot_dir + '/' + params_str + - '_Bh_nt={}.pdf'.format(nt), - plot_type='amplitude', cb_min=cb_min_sol, cb_max=cb_max_sol, hide_plot=hide_plots) - - else: - print(' -- WARNING: unknown plot_dir !!') - - def plot_time_diags(time_diag, E_norm2_diag, B_norm2_diag, divE_norm2_diag, nt_start, nt_end, - GaussErr_norm2_diag=None, GaussErrP_norm2_diag=None, - PE_norm2_diag=None, I_PE_norm2_diag=None, J_norm2_diag=None, skip_titles=True): - - nt_start = max(nt_start, 0) - nt_end = min(nt_end, Nt) - - td = time_diag[nt_start:nt_end + 1] - t_label = r'$t$' - - # norm || E || - fig, ax = plt.subplots() - ax.plot(td, - np.sqrt(E_norm2_diag[nt_start:nt_end + 1]), - '-', - ms=7, - mfc='None', - mec='k') # , label='||E||', zorder=10) - if skip_titles: - title = '' - else: - title = r'$||E_h(t)||$ vs ' + t_label - ax.set_xlabel(t_label, fontsize=16) - ax.set_title(title, fontsize=18) - fig.tight_layout() - diag_fn = plot_dir + \ - f'/diag_E_norm_gamma={gamma_h}_dt={dt}_trange=[{dt*nt_start}, {dt*nt_end}].pdf' - print(f"saving plot for '{title}' in figure '{diag_fn}") - fig.savefig(diag_fn) - - # energy - fig, ax = plt.subplots() - E_energ = .5 * E_norm2_diag[nt_start:nt_end + 1] - B_energ = .5 * B_norm2_diag[nt_start:nt_end + 1] - ax.plot(td, E_energ, '-', ms=7, mfc='None', c='k', - label=r'$\frac{1}{2}||E||^2$') # , zorder=10) - ax.plot(td, B_energ, '-', ms=7, mfc='None', c='g', - label=r'$\frac{1}{2}||B||^2$') # , zorder=10) - ax.plot(td, E_energ + B_energ, '-', ms=7, mfc='None', c='b', - label=r'$\frac{1}{2}(||E||^2+||B||^2)$') # , zorder=10) - ax.legend(loc='best') - if skip_titles: - title = '' - else: - title = r'energy vs ' + t_label - if E0_type == 'pulse': - ax.set_ylim([0, 5]) - ax.set_xlabel(t_label, fontsize=16) - ax.set_title(title, fontsize=18) - fig.tight_layout() - diag_fn = plot_dir + \ - f'/diag_energy_gamma={gamma_h}_dt={dt}_trange=[{dt*nt_start},{dt*nt_end}].pdf' - print(f"saving plot for '{title}' in figure '{diag_fn}") - fig.savefig(diag_fn) - - # One curve per plot from now on. - # Collect information in a list where each item is of the form [tag, - # data, title] - time_diagnostics = [] - - if project_sol: - time_diagnostics += [['divPE', divE_norm2_diag, - r'$||div_h P^1_h E_h(t)||$ vs ' + t_label]] - else: - time_diagnostics += [['divE', divE_norm2_diag, - r'$||div_h E_h(t)||$ vs ' + t_label]] - - time_diagnostics += [ - ['I_PE', I_PE_norm2_diag, r'$||(I-P^1)E_h(t)||$ vs ' + t_label], - ['PE', PE_norm2_diag, r'$||(I-P^1)E_h(t)||$ vs ' + t_label], - ['GaussErr', GaussErr_norm2_diag, - r'$||(\rho_h - div_h E_h)(t)||$ vs ' + t_label], - ['GaussErrP', GaussErrP_norm2_diag, - r'$||(\rho_h - div_h E_h)(t)||$ vs ' + t_label], - ['J_norm', J_norm2_diag, r'$||J_h(t)||$ vs ' + t_label], - ] - for tag, data, title in time_diagnostics: - if data is None: - continue - fig, ax = plt.subplots() - ax.plot(td, - np.sqrt(I_PE_norm2_diag[nt_start:nt_end + 1]), - '-', - ms=7, - mfc='None', - mec='k') # , label='||E||', zorder=10) - diag_fn = plot_dir + \ - f'/diag_{tag}_gamma={gamma_h}_dt={dt}_trange=[{dt*nt_start},{dt*nt_end}].pdf' - ax.set_xlabel(t_label, fontsize=16) - if not skip_titles: - ax.set_title(title, fontsize=18) - fig.tight_layout() - print(f"saving plot for '{title}' in figure '{diag_fn}") - fig.savefig(diag_fn) + if f0_h is None: + f0_h = V1h.coeff_space.zeros() + + t_stamp = time_count(t_stamp) # diags arrays E_norm2_diag = np.zeros(Nt + 1) @@ -874,114 +463,73 @@ def plot_time_diags(time_diag, E_norm2_diag, B_norm2_diag, divE_norm2_diag, nt_s print(' .. initial solution ..') # initial B sol - B_c = np.zeros(V2h.nbasis) + B_h = V2h.coeff_space.zeros() + E_h = V1h.coeff_space.zeros() # initial E sol - if E0_type == 'th_sol': - - if os.path.exists(th_sol_filename): - print( - ' .. loading time-harmonic solution from file {}'.format(th_sol_filename)) - E_c = source_omega * np.load(th_sol_filename) - assert len(E_c) == V1h.nbasis - else: - print( - ' .. Error: time-harmonic solution file given {}, but not found'.format(th_sol_filename)) - raise ValueError(th_sol_filename) - - elif E0_type == 'zero': - E_c = np.zeros(V1h.nbasis) + if E0_type == 'zero': + E_h = V1h.coeff_space.zeros() elif E0_type == 'pulse': - E0 = get_div_free_pulse(x_0=1.0, y_0=1.0, domain=domain) + E0 = get_div_free_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) if E0_proj == 'P_geom': print(' .. projecting E0 with commuting projection...') - E0_h = P1_phys(E0, P1, domain, mappings_list) - E_c = E0_h.coeffs.toarray() + E0_h = P1_phys(E0, P1, domain) + E_h = E0_h.coeffs elif E0_proj == 'P_L2': - # helper: save/load coefs - E0dd_filename = m_load_dir + \ - '/E0_pulse_dual_dofs_qp{}.npy'.format(quad_param) - if os.path.exists(E0dd_filename): - print(' .. loading E0 dual dofs from file {}'.format(E0dd_filename)) - tilde_E0_c = np.load(E0dd_filename) - else: - print(' .. projecting E0 with L2 projection...') - tilde_E0_c = derham_h.get_dual_dofs( - space='V1', f=E0, backend_language=backend, return_format='numpy_array') - print(' .. saving E0 dual dofs to file {}'.format(E0dd_filename)) - np.save(E0dd_filename, tilde_E0_c) - E_c = dH1_m.dot(tilde_E0_c) - elif E0_type == 'pulse_2': - # E0 = get_praxial_Gaussian_beam_E(x_0=3.14, y_0=3.14, domain=domain) + print(' .. projecting E0 with L2 projection...') + tilde_E0_h = get_dual_dofs(Vh=V1h, f=E0, domain_h=domain_h, backend_language=backend) + E_h = dH1.dot(tilde_E0_h) - # E0 = get_easy_Gaussian_beam_E_2(x_0=0.05, y_0=0.05, domain=domain) - # B0 = get_easy_Gaussian_beam_B_2(x_0=0.05, y_0=0.05, domain=domain) + elif E0_type == 'pulse_2': - E0, B0 = get_Gaussian_beam(y_0=3.14, x_0=3.14, domain=domain) - # B0 = get_easy_Gaussian_beam_B(x_0=3.14, y_0=0.05, domain=domain) + E0, B0 = get_Gaussian_beam(y_0=np.pi/2, x_0=np.pi/2, domain=domain) if E0_proj == 'P_geom': print(' .. projecting E0 with commuting projection...') - E0_h = P1_phys(E0, P1, domain, mappings_list) - E_c = E0_h.coeffs.toarray() + E0_h = P1_phys(E0, P1, domain) + E_h = E0_h.coeffs - # B_c = np.real( - 1j * C_m @ E_c) - # E_c = np.real(E_c) - B0_h = P2_phys(B0, P2, domain, mappings_list) - B_c = B0_h.coeffs.toarray() + B0_h = P2_phys(B0, P2, domain) + B_h = B0_h.coeffs elif E0_proj == 'P_L2': - # helper: save/load coefs - E0dd_filename = m_load_dir + \ - '/E0_pulse_dual_dofs_qp{}.npy'.format(quad_param) - if False: # os.path.exists(E0dd_filename): - print(' .. loading E0 dual dofs from file {}'.format(E0dd_filename)) - tilde_E0_c = np.load(E0dd_filename) - else: - print(' .. projecting E0 with L2 projection...') - - tilde_E0_c = derham_h.get_dual_dofs( - space='V1', f=E0, backend_language=backend, return_format='numpy_array') - print(' .. saving E0 dual dofs to file {}'.format(E0dd_filename)) - # np.save(E0dd_filename, tilde_E0_c) + + print(' .. projecting E0 with L2 projection...') + tilde_E0_h = get_dual_dofs(Vh=V1h, f=E0, domain_h=domain_h, backend_language=backend) + E_h = dH1.dot(tilde_E0_h) - E_c = dH1_m.dot(tilde_E0_c) - dH2_m = H2.get_dual_sparse_matrix() - tilde_B0_c = derham_h.get_dual_dofs( - space='V2', f=B0, backend_language=backend, return_format='numpy_array') - B_c = dH2_m.dot(tilde_B0_c) + tilde_B0_h = get_dual_dofs(Vh=V2h, f=B0, domain_h=domain_h, backend_language=backend) + B_h = dH2.dot(tilde_B0_h) - # B_c = np.real( - C_m @ E_c) - # E_c = np.real(E_c) else: raise ValueError(E0_type) # ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- # time loop - def compute_diags(E_c, B_c, J_c, nt): + def compute_diags(E_h, B_h, J_h, nt): time_diag[nt] = (nt) * dt - PE_c = cP1_m.dot(E_c) - I_PE_c = E_c - PE_c - E_norm2_diag[nt] = np.dot(E_c, H1_m.dot(E_c)) - PE_norm2_diag[nt] = np.dot(PE_c, H1_m.dot(PE_c)) - I_PE_norm2_diag[nt] = np.dot(I_PE_c, H1_m.dot(I_PE_c)) - J_norm2_diag[nt] = np.dot(J_c, H1_m.dot(J_c)) - B_norm2_diag[nt] = np.dot(B_c, H2_m.dot(B_c)) - divE_c = div_m @ E_c - divE_norm2_diag[nt] = np.dot(divE_c, H0_m.dot(divE_c)) - if source_type == 'Il_pulse': - rho_c = rho0_c * np.sin(source_omega * nt * dt) / omega - GaussErr = rho_c - divE_c - GaussErrP = rho_c - div_m @ PE_c - GaussErr_norm2_diag[nt] = np.dot(GaussErr, H0_m.dot(GaussErr)) - GaussErrP_norm2_diag[nt] = np.dot(GaussErrP, H0_m.dot(GaussErrP)) + PE_h = cP1.dot(E_h) + I_PE_h = E_h - PE_h + E_norm2_diag[nt] = E_h.inner(H1.dot(E_h)) + PE_norm2_diag[nt] = PE_h.inner(H1.dot(PE_h)) + I_PE_norm2_diag[nt] = I_PE_h.inner(H1.dot(I_PE_h)) + J_norm2_diag[nt] = J_h.inner(H1.dot(J_h)) + B_norm2_diag[nt] = B_h.inner(H2.dot(B_h)) + divE_h = D @ E_h + divE_norm2_diag[nt] = divE_h.inner(H0.dot(divE_h)) + if source_type == 'Il_pulse' and source_omega is not None: + rho_h = rho0_h * np.sin(source_omega * nt * dt) / omega + GaussErr = rho_h - divE_h + GaussErrP = rho_h - D @ PE_h + GaussErr_norm2_diag[nt] = GaussErr.inner(H0.dot(GaussErr)) + GaussErrP_norm2_diag[nt] = GaussErrP.inner(H0.dot(GaussErrP)) if plot_dir: OM1 = OutputManager(plot_dir + '/spaces1.yml', plot_dir + '/fields1.h5') @@ -992,206 +540,85 @@ def compute_diags(E_c, B_c, J_c, nt): OM2.add_spaces(V2h=V2h) OM2.export_space_info() - stencil_coeffs_E = array_to_psydac(cP1_m @ E_c, V1h.coeff_space) - Eh = FemField(V1h, coeffs=stencil_coeffs_E) + Eh = FemField(V1h, coeffs=cP1 @ E_h) OM1.add_snapshot(t=0, ts=0) OM1.export_fields(Eh=Eh) - stencil_coeffs_B = array_to_psydac(B_c, V2h.coeff_space) - Bh = FemField(V2h, coeffs=stencil_coeffs_B) + Bh = FemField(V2h, coeffs=B_h) OM2.add_snapshot(t=0, ts=0) OM2.export_fields(Bh=Bh) - # PM = PostProcessManager(domain=domain, space_file=plot_dir+'/spaces1.yml', fields_file=plot_dir+'/fields1.h5' ) - # PM.export_to_vtk(plot_dir+"/Eh",grid=None, npts_per_cell=[6]*2, snapshots='all', fields='vh' ) - - # OM1.close() - # PM.close() - - # plot_E_field(E_c, nt=0, project_sol=project_sol, plot_divE=plot_divE) - # plot_B_field(B_c, nt=0) - f_c = np.copy(f0_c) + f_h = f0_h.copy() for nt in range(Nt): print(' .. nt+1 = {}/{}'.format(nt + 1, Nt)) # 1/2 faraday: Bn -> Bn+1/2 - B_c[:] -= (dt / 2) * C_m @ E_c + B_h -= (dt / 2) * C @ E_h # ampere: En -> En+1 - if f0_harmonic_c is not None: - f_harmonic_c = f0_harmonic_c * (np.sin(source_omega * (nt + 1) * dt) - np.sin( - source_omega * (nt) * dt)) / (dt * source_omega) # * source_enveloppe(omega*(nt+1/2)*dt) - f_c[:] = f0_c + f_harmonic_c + if f0_harmonic_h is not None and source_omega is not None: + f_harmonic_h = f0_harmonic_h * (np.sin(source_omega * (nt + 1) * dt) - np.sin(source_omega * (nt) * dt)) / (dt * source_omega) # * source_enveloppe(omega*(nt+1/2)*dt) + f_h = f0_h + f_harmonic_h - if nt == 0: - if plot_dir: - plot_J_source_nPlusHalf(f_c, nt=0) - compute_diags(E_c, B_c, f_c, nt=0) - - E_c[:] = dCH1_m @ E_c + dt * (dC_m @ B_c - f_c) - - # if abs(gamma_h) > 1e-10: - # E_c[:] -= dt * gamma_h * JP_m @ E_c + E_h = dCH1 @ E_h + dt * (dC @ B_h - f_h) # 1/2 faraday: Bn+1/2 -> Bn+1 - B_c[:] -= (dt / 2) * C_m @ E_c + B_h -= (dt / 2) * C @ E_h # diags: - compute_diags(E_c, B_c, f_c, nt=nt + 1) - - # PE_c = cP1_m.dot(E_c) - # I_PE_c = E_c-PE_c - # E_norm2_diag[nt+1] = np.dot(E_c,H1_m.dot(E_c)) - # PE_norm2_diag[nt+1] = np.dot(PE_c,H1_m.dot(PE_c)) - # I_PE_norm2_diag[nt+1] = np.dot(I_PE_c,H1_m.dot(I_PE_c)) - # B_norm2_diag[nt+1] = np.dot(B_c,H2_m.dot(B_c)) - # time_diag[nt+1] = (nt+1)*dt - - # diags: div - # if project_sol: - # Ep_c = PE_c # = cP1_m.dot(E_c) - # else: - # Ep_c = E_c - # divE_c = div_m @ Ep_c - # divE_norm2 = np.dot(divE_c, H0_m.dot(divE_c)) - # # print('in diag[{}]: divE_norm = {}'.format(nt+1, np.sqrt(divE_norm2))) - # divE_norm2_diag[nt+1] = divE_norm2 - - # if source_type == 'Il_pulse': - # rho_c = rho0_c * np.sin(omega*dt*(nt+1))/omega - # GaussErr = rho_c - div_m @ E_c - # GaussErrP = rho_c - div_m @ (cP1_m.dot(E_c)) - # GaussErr_norm2_diag[nt+1] = np.dot(GaussErr, H0_m.dot(GaussErr)) - # GaussErrP_norm2_diag[nt+1] = np.dot(GaussErrP, H0_m.dot(GaussErrP)) - - if debug: - divCB_c = div_m @ dC_m @ B_c - divCB_norm2 = np.dot(divCB_c, H0_m.dot(divCB_c)) - print('-- [{}]: dt*|| div CB || = {}'.format(nt + - 1, dt * np.sqrt(divCB_norm2))) - - divf_c = div_m @ f_c - divf_norm2 = np.dot(divf_c, H0_m.dot(divf_c)) - print('-- [{}]: dt*|| div f || = {}'.format(nt + - 1, dt * np.sqrt(divf_norm2))) - - divE_c = div_m @ E_c - divE_norm2 = np.dot(divE_c, H0_m.dot(divE_c)) - print('-- [{}]: || div E || = {}'.format(nt + 1, np.sqrt(divE_norm2))) + compute_diags(E_h, B_h, f_h, nt=nt + 1) + + if is_plotting_time(nt + 1) and plot_dir: - print("Plot Stuff") - # plot_E_field(E_c, nt=nt+1, project_sol=True, plot_divE=False) - # plot_B_field(B_c, nt=nt+1) - # plot_J_source_nPlusHalf(f_c, nt=nt) + print("Plot fields") - stencil_coeffs_E = array_to_psydac(cP1_m @ E_c, V1h.coeff_space) - Eh = FemField(V1h, coeffs=stencil_coeffs_E) + Eh = FemField(V1h, coeffs=cP1 @ E_h) OM1.add_snapshot(t=nt * dt, ts=nt) OM1.export_fields(Eh=Eh) - stencil_coeffs_B = array_to_psydac(B_c, V2h.coeff_space) - Bh = FemField(V2h, coeffs=stencil_coeffs_B) + Bh = FemField(V2h, coeffs=B_h) OM2.add_snapshot(t=nt * dt, ts=nt) OM2.export_fields(Bh=Bh) - # if (nt+1) % diag_nt == 0: - # plot_time_diags(time_diag, E_norm2_diag, B_norm2_diag, divE_norm2_diag, nt_start=(nt+1)-diag_nt, nt_end=(nt+1), - # PE_norm2_diag=PE_norm2_diag, I_PE_norm2_diag=I_PE_norm2_diag, J_norm2_diag=J_norm2_diag, - # GaussErr_norm2_diag=GaussErr_norm2_diag, - # GaussErrP_norm2_diag=GaussErrP_norm2_diag) + if plot_dir: OM1.close() - print("Do some PP") + print("Post process fields") PM = PostProcessManager( domain=domain, - space_file=plot_dir + - '/spaces1.yml', - fields_file=plot_dir + - '/fields1.h5') + space_file=plot_dir + '/spaces1.yml', + fields_file=plot_dir + '/fields1.h5') PM.export_to_vtk( plot_dir + "/Eh", grid=None, - npts_per_cell=2, + npts_per_cell=4, snapshots='all', fields='Eh') PM.close() PM = PostProcessManager( domain=domain, - space_file=plot_dir + - '/spaces2.yml', - fields_file=plot_dir + - '/fields2.h5') + space_file=plot_dir + '/spaces2.yml', + fields_file=plot_dir + '/fields2.h5') PM.export_to_vtk( plot_dir + "/Bh", grid=None, - npts_per_cell=2, + npts_per_cell=4, snapshots='all', fields='Bh') PM.close() - # plot_time_diags(time_diag, E_norm2_diag, B_norm2_diag, divE_norm2_diag, nt_start=0, nt_end=Nt, - # PE_norm2_diag=PE_norm2_diag, I_PE_norm2_diag=I_PE_norm2_diag, J_norm2_diag=J_norm2_diag, - # GaussErr_norm2_diag=GaussErr_norm2_diag, - # GaussErrP_norm2_diag=GaussErrP_norm2_diag) - - # Eh = FemField(V1h, coeffs=array_to_stencil(E_c, V1h.coeff_space)) - # t_stamp = time_count(t_stamp) - - # if sol_filename: - # raise NotImplementedError - # print(' .. saving final solution coeffs to file {}'.format(sol_filename)) - # np.save(sol_filename, E_c) - - # time_count(t_stamp) - - # print() - # print(' -- plots and diagnostics --') - - # # diagnostics: errors - # err_diags = diag_grid.get_diags_for(v=uh, space='V1') - # for key, value in err_diags.items(): - # diags[key] = value - # if u_ex is not None: - # check_diags = get_Vh_diags_for(v=uh, v_ref=uh_ref, M_m=H1_m, msg='error between Ph(u_ex) and u_h') - # diags['norm_Pu_ex'] = check_diags['sol_ref_norm'] - # diags['rel_l2_error_in_Vh'] = check_diags['rel_l2_error'] - # if curl_u_ex is not None: - # print(' .. diag on curl_u:') - # curl_uh_c = bD1_m @ cP1_m @ uh_c - # title = r'curl $u_h$ (amplitude) for $\eta = $'+repr(eta) - # params_str = 'eta={}_mu={}_nu={}_gamma_h={}_Pf={}'.format(eta, mu, nu, gamma_h, source_proj) - # plot_field(numpy_coeffs=curl_uh_c, Vh=V2h, space_kind='l2', domain=domain, surface_plot=False, title=title, filename=plot_dir+'/'+params_str+'_curl_uh.png', - # plot_type='amplitude', cb_min=None, cb_max=None, hide_plot=hide_plots) - - # curl_uh = FemField(V2h, coeffs=array_to_stencil(curl_uh_c, V2h.coeff_space)) - # curl_diags = diag_grid.get_diags_for(v=curl_uh, space='V2') - # diags['curl_error (to be checked)'] = curl_diags['rel_l2_error'] - - # title = r'div_h $u_h$ (amplitude) for $\eta = $'+repr(eta) - # params_str = 'eta={}_mu={}_nu={}_gamma_h={}_Pf={}'.format(eta, mu, nu, gamma_h, source_proj) - # plot_field(numpy_coeffs=div_uh_c, Vh=V0h, space_kind='h1', domain=domain, surface_plot=False, title=title, filename=plot_dir+'/'+params_str+'_div_uh.png', - # plot_type='amplitude', cb_min=None, cb_max=None, hide_plot=hide_plots) - - # div_uh = FemField(V0h, coeffs=array_to_stencil(div_uh_c, V0h.coeff_space)) - # div_diags = diag_grid.get_diags_for(v=div_uh, space='V0') - # diags['div_error (to be checked)'] = div_diags['rel_l2_error'] - - return diags - - -# def compute_stable_dt(cfl_max, dt_max, C_m, dC_m, V1_dim): -def compute_stable_dt(*, C_m, dC_m, cfl_max, dt_max=None): +def compute_stable_dt(*, C, dC, cfl_max, dt_max=None): """ Compute a stable time step size based on the maximum CFL parameter in the domain. To this end we estimate the operator norm of - `dC_m @ C_m: V1h -> V1h`, + `dC @ C: V1h -> V1h`, find the largest stable time step compatible with Strang splitting, and rescale it by the provided `cfl_max`. Setting `cfl_max = 1` would run the @@ -1204,10 +631,10 @@ def compute_stable_dt(*, C_m, dC_m, cfl_max, dt_max=None): Parameters ---------- - C_m : scipy.sparse.spmatrix + C : LinearOperator Matrix of the Curl operator. - dC_m : scipy.sparse.spmatrix + dC : LinearOperator Matrix of the dual Curl operator. cfl_max : float @@ -1227,36 +654,37 @@ def compute_stable_dt(*, C_m, dC_m, cfl_max, dt_max=None): print(" .. compute_stable_dt by estimating the operator norm of ") print(" .. dC_m @ C_m: V1h -> V1h ") - print(" .. with dim(V1h) = {} ...".format(C_m.shape[1])) + print(" .. with dim(V1h) = {} ...".format(C.domain.dimension)) if not (0 < cfl_max < 1): print(' ****** ****** ****** ****** ****** ****** ') print(' WARNING !!! cfl = {} '.format(cfl)) print(' ****** ****** ****** ****** ****** ****** ') - def vect_norm_2(vv): - return np.sqrt(np.dot(vv, vv)) - t_stamp = time_count() - vv = np.random.random(C_m.shape[1]) - norm_vv = vect_norm_2(vv) + V = C.domain + from psydac.linalg.utilities import array_to_psydac + vv = array_to_psydac(np.random.rand(V.dimension), V) + + norm_vv = np.sqrt(vv.inner(vv)) + max_ncfl = 500 ncfl = 0 spectral_rho = 1 conv = False - CC_m = dC_m @ C_m + CC = dC @ C while not (conv or ncfl > max_ncfl): - vv[:] = (1. / norm_vv) * vv + vv *= (1. / norm_vv) ncfl += 1 - vv[:] = CC_m.dot(vv) + CC.dot(vv, out=vv) - norm_vv = vect_norm_2(vv) + norm_vv = np.sqrt(vv.inner(vv)) old_spectral_rho = spectral_rho - spectral_rho = vect_norm_2(vv) # approximation + spectral_rho = norm_vv # approximation conv = abs((spectral_rho - old_spectral_rho) / spectral_rho) < 0.001 - print(" ... spectral radius iteration: spectral_rho( dC_m @ C_m ) ~= {}".format(spectral_rho)) + print(" ... spectral radius iteration: spectral_rho( dC @ C ) ~= {}".format(spectral_rho)) t_stamp = time_count(t_stamp) norm_op = np.sqrt(spectral_rho) @@ -1269,11 +697,8 @@ def vect_norm_2(vv): dt = min(dt, dt_max) print(" Time step dt computed for Maxwell solver:") - print( - f" Based on cfl_max = {cfl_max} and dt_max = {dt_max}, we set dt = {dt}") - print( - f" -- note that c*Dt = {light_c*dt} and c_dt_max = {c_dt_max}, thus c * dt / c_dt_max = {light_c*dt/c_dt_max}") - print( - f" -- and spectral_radius((c*dt)**2* dC_m @ C_m ) = {(light_c * dt * norm_op)**2} (should be < 4).") + print(f" Based on cfl_max = {cfl_max} and dt_max = {dt_max}, we set dt = {dt}") + print(f" -- note that c*Dt = {light_c*dt} and c_dt_max = {c_dt_max}, thus c * dt / c_dt_max = {light_c*dt/c_dt_max}") + print(f" -- and spectral_radius((c*dt)**2* dC @ C ) = {(light_c * dt * norm_op)**2} (should be < 4).") return dt diff --git a/psydac/feec/multipatch/examples/timedomain_maxwell_testcase.py b/psydac/feec/multipatch/examples/timedomain_maxwell_testcase.py index 19c1e13d6..e17c70b4a 100644 --- a/psydac/feec/multipatch/examples/timedomain_maxwell_testcase.py +++ b/psydac/feec/multipatch/examples/timedomain_maxwell_testcase.py @@ -5,22 +5,15 @@ import numpy as np from psydac.feec.multipatch.examples.timedomain_maxwell import solve_td_maxwell_pbm -from psydac.feec.multipatch.utilities import time_count, FEM_sol_fn, get_run_dir, get_plot_dir, get_mat_dir, get_sol_dir, diag_fn -from psydac.feec.multipatch.utils_conga_2d import write_diags_to_file - -t_stamp_full = time_count() +from psydac.feec.multipatch.utilities import get_run_dir, get_plot_dir # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- # -# main test-cases and parameters used for the ppc paper: - -test_case = 'E0_pulse_no_source' # used in paper -# test_case = 'Issautier_like_source' # used in paper -# test_case = 'transient_to_harmonic' # actually, not used in paper +test_case = 'E0_pulse_no_source' +# test_case = 'Issautier_like_source' # J_proj_case = 'P_geom' J_proj_case = 'P_L2' -# J_proj_case = 'tilde Pi_1' # # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- @@ -34,62 +27,21 @@ # domain_name = 'pretzel_f' # non-conf domains -domain = [[0, 2 * np.pi], [0, 2 * np.pi]] # interval in x- and y-direction +domain = [[0, np.pi], [0, np.pi]] # interval in x- and y-direction domain_name = 'refined_square' # use isotropic meshes (probably with a square domain) # 4x8= 64 patches # care for the transpose -ncells = np.array([[16, 16], - [16, 16]]) - -# ncells = np.array([[8,8,16,8], -# [8,8,16,8], -# [8,8,16,8], -# [8,8,16,8]]) -# ncells = np.array([[8,8,8,8], -# [8,8,8,8], -# [8,8,8,8], -# [8,8,8,8]]) -# ncells = np.array([[8,8,16,8,8,8], -# [8,8,16,8,8,8], -# [8,8,16,8,8,8], -# [8,8,16,8,8,8]]) - -# ncells = np.array([[4, 4, 4], -# [4, 8, 4], -# [8, 16, 8], -# [4, 8, 4], -# [4, 4, 4]]) -# ncells = np.array([[4, 4, 4, 4], -# [4, 8, 8, 4], -# [8, 16, 16, 8], -# [4, 8, 8, 4], -# [4, 4, 4, 4]]).transpose() -# ncells = np.array([[4, 4, 4, 4], -# [4, 4, 4, 4], -# [4, 8, 8, 4], -# [8, 16, 16, 8], -# [8, 16, 16, 8], -# [4, 8, 8, 4], -# [4, 4, 4, 4], -# [4, 4, 4, 4]]) - +ncells = np.array([[10, 10, 10], + [10, 20, 10], + [10, 10, 10]]) cfl_max = 0.8 + # 'P_geom' # projection used for initial E0 (B0 = 0 in all cases) -E0_proj = 'P_geom' +E0_proj = 'P_L2' backend = 'pyccel-gcc' project_sol = True # whether cP1 E_h is plotted instead of E_h -# multiplicative parameter for quadrature order in (bi)linear forms -# discretizaion -quad_param = 4 -gamma_h = 0 # jump dissipation parameter (not used in paper) -# 'BSP' # type of conforming projection operators (averaging B-spline or Geometric-splines coefficients) -conf_proj = 'GSP' -hide_plots = True -plot_divE = True -# time interval between scalar diagnostics (if None, compute every time step) -diag_dt = None # Parameters that depend on test case if test_case == 'E0_pulse_no_source': @@ -97,9 +49,8 @@ E0_type = 'pulse_2' # non-zero initial conditions source_type = 'zero' # no current source source_omega = None - final_time = 9.02 # wave transit time in domain is > 4 + final_time = 2 # wave transit time in domain is > 4 dt_max = None - plot_source = False plot_a_lot = True if plot_a_lot: @@ -110,9 +61,6 @@ [[final_time - 1, final_time], 0.1], ] - cb_min_sol = 0 - cb_max_sol = 5 - # TODO: check elif test_case == 'Issautier_like_source': @@ -120,9 +68,9 @@ source_type = 'Il_pulse' source_omega = None final_time = 20 - plot_source = True dt_max = None - if deg_s == [3] and final_time == 20: + + if deg == 3 and final_time == 20: plot_time_ranges = [ [[1.9, 2], 0.1], @@ -131,36 +79,6 @@ [[19.9, 20], 0.1], ] - # plot_time_ranges = [ - # ] - # if nc_s == [8]: - # Nt_pp = 10 - - cb_min_sol = 0 # None - cb_max_sol = 0.3 # None - -# TODO: check -elif test_case == 'transient_to_harmonic': - - E0_type = 'th_sol' - source_type = 'elliptic_J' - source_omega = np.sqrt(50) # source time pulsation - plot_source = True - - source_period = 2 * np.pi / source_omega - nb_t_periods = 100 - Nt_pp = 20 - - dt_max = source_period / Nt_pp - final_time = nb_t_periods * source_period - - plot_time_ranges = [ - [[(nb_t_periods - 2) * source_period, final_time], dt_max] - ] - - cb_min_sol = 0 - cb_max_sol = 1 - else: raise ValueError(test_case) @@ -181,8 +99,8 @@ else: raise ValueError(J_proj_case) -case_dir = 'nov14_' + test_case + '_J_proj=' + \ - J_proj_case + '_qp{}'.format(quad_param) +case_dir = 'tdmaxwell_' + test_case + '_J_proj=' + J_proj_case + if filter_source: case_dir += '_Jfilter' else: @@ -198,32 +116,17 @@ # # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- -common_diag_filename = './' + case_dir + '_diags.txt' - - run_dir = get_run_dir( domain_name, sum(ncells), deg, source_type=source_type, - conf_proj=conf_proj) + conf_proj="") + plot_dir = get_plot_dir(case_dir, run_dir) -diag_filename = plot_dir + '/' + \ - diag_fn(source_type=source_type, source_proj=source_proj) - -# to save and load matrices -m_load_dir = get_mat_dir(domain_name, sum(ncells), deg, quad_param=quad_param) - -if E0_type == 'th_sol': - # initial E0 will be loaded from time-harmonic FEM solution - th_case_dir = 'maxwell_hom_eta=50' - th_sol_dir = get_sol_dir(th_case_dir, domain_name, sum(ncells), deg) - th_sol_filename = th_sol_dir + '/' + \ - FEM_sol_fn(source_type=source_type, source_proj=source_proj) -else: - # no initial solution to load - th_sol_filename = '' + +# params = { 'nc': ncells, 'deg': deg, @@ -235,23 +138,12 @@ 'source_type': source_type, 'source_omega': source_omega, 'source_proj': source_proj, - 'conf_proj': conf_proj, - 'gamma_h': gamma_h, 'project_sol': project_sol, 'filter_source': filter_source, - 'quad_param': quad_param, 'E0_type': E0_type, 'E0_proj': E0_proj, - 'hide_plots': hide_plots, 'plot_dir': plot_dir, 'plot_time_ranges': plot_time_ranges, - 'plot_source': plot_source, - 'plot_divE': plot_divE, - 'diag_dt': diag_dt, - 'cb_min_sol': cb_min_sol, - 'cb_max_sol': cb_max_sol, - 'm_load_dir': m_load_dir, - 'th_sol_filename': th_sol_filename, 'domain_lims': domain } @@ -259,17 +151,4 @@ print(' Calling solve_td_maxwell_pbm() with params = {}'.format(params)) print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') -diags = solve_td_maxwell_pbm(**params) - -write_diags_to_file( - diags, - script_filename=__file__, - diag_filename=diag_filename, - params=params) -write_diags_to_file( - diags, - script_filename=__file__, - diag_filename=common_diag_filename, - params=params) - -time_count(t_stamp_full, msg='full program') +solve_td_maxwell_pbm(**params) diff --git a/psydac/feec/multipatch/fem_linear_operators.py b/psydac/feec/multipatch/fem_linear_operators.py deleted file mode 100644 index aafb77931..000000000 --- a/psydac/feec/multipatch/fem_linear_operators.py +++ /dev/null @@ -1,218 +0,0 @@ -# coding: utf-8 - -from mpi4py import MPI - -from scipy.sparse import eye as sparse_id - -from psydac.linalg.basic import LinearOperator -from psydac.fem.basic import FemField - -#=============================================================================== -class FemLinearOperator( LinearOperator ): - """ - Linear operators with an additional Fem layer - """ - - def __init__( self, fem_domain=None, fem_codomain=None, matrix=None, sparse_matrix=None): - """ - we may store the matrix of the linear operator with different formats - :param matrix: stencil format - :param sparse_matrix: scipy sparse format - """ - assert fem_domain - self._fem_domain = fem_domain - if fem_codomain: - self._fem_codomain = fem_codomain - else: - self._fem_codomain = fem_domain - self._domain = self._fem_domain.coeff_space - self._codomain = self._fem_codomain.coeff_space - - self._matrix = matrix - self._sparse_matrix = sparse_matrix - - @property - def domain( self ): - return self._domain - - @property - def codomain( self ): - return self._codomain - - @property - def fem_domain( self ): - return self._fem_domain - - @property - def fem_codomain( self ): - return self._fem_codomain - - @property - def matrix( self ): - return self._matrix - - @property - def T(self): - return self.transpose() - - @property - def dtype( self ): - return self.domain.dtype - - def toarray(self): - return self._matrix.toarray() - #raise NotImplementedError('toarray() is not defined for FEMLinearOperators.') - - def tosparse(self): - return self._matrix.tosparse() - #raise NotImplementedError('tosparse() is not defined for FEMLinearOperators.') - - # ... - def transpose(self, conjugate=False): - raise NotImplementedError('Class does not provide a transpose() method') - - # ... - def to_sparse_matrix( self , **kwargs): - if self._sparse_matrix is not None: - return self._sparse_matrix - elif self._matrix is not None: - return self._matrix.tosparse() - else: - raise NotImplementedError('Class does not provide a get_sparse_matrix() method without a matrix') - - # ... - def __call__( self, f ): - if self._matrix is not None: - coeffs = self._matrix.dot(f.coeffs) - return FemField(self.fem_codomain, coeffs=coeffs) - else: - raise NotImplementedError('Class does not provide a __call__ method without a matrix') - - # ... - def dot( self, f_coeffs, out=None ): - # coeffs layer - if self._matrix is not None: - f = FemField(self.fem_domain, coeffs=f_coeffs) - return self(f).coeffs - else: - raise NotImplementedError('Class does not provide a dot method without a matrix') - - # ... - def __mul__(self, c): - return MultLinearOperator(c, self) - - # ... - def __add__(self, C): - assert isinstance(C, FemLinearOperator) - return SumLinearOperator(C, self) - - # ... - def __sub__(self, C): - assert isinstance(C, FemLinearOperator) - return SumLinearOperator(C, -self) - - # ... - def __neg__(self): - return MultLinearOperator(-1, self) - - -#============================================================================== -class ComposedLinearOperator( FemLinearOperator ): - """ - operator L = L_1 .. L_n - with L_i = self._operators[i-1] - (so, the last one is applied first, like in a product) - """ - def __init__( self, operators ): - n = len(operators) - assert all([isinstance(operators[i], FemLinearOperator) for i in range(n)]) - assert all([operators[i].fem_domain == operators[i+1].fem_codomain for i in range(n-1)]) - FemLinearOperator.__init__( - self, fem_domain=operators[-1].fem_domain, fem_codomain=operators[0].fem_codomain - ) - self._operators = operators - self._n = n - - # matrix not defined by matrix product because it could break the Stencil Matrix structure - - def to_sparse_matrix( self, **kwargs): - mat = self._operators[-1].to_sparse_matrix() - for i in range(2, self._n+1): - mat = self._operators[-i].to_sparse_matrix() * mat - return mat - - def __call__( self, f ): - v = self._operators[-1](f) - for i in range(2, self._n+1): - v = self._operators[-i](v) - return v - - def dot( self, f_coeffs, out=None ): - v_coeffs = self._operators[-1].dot(f_coeffs) - for i in range(2, self._n+1): - v_coeffs = self._operators[-i].dot(v_coeffs) - return v_coeffs - - -#============================================================================== -class IdLinearOperator( FemLinearOperator ): - - def __init__( self, V ): - FemLinearOperator.__init__(self, fem_domain=V) - - def to_sparse_matrix( self , **kwargs): - return sparse_id( self.fem_domain.nbasis ) - - def __call__( self, f ): - return f - - def dot( self, f_coeffs, out=None ): - return f_coeffs - -#============================================================================== -class SumLinearOperator( FemLinearOperator ): - - def __init__( self, B, A ): - assert isinstance(A, FemLinearOperator) - assert isinstance(B, FemLinearOperator) - assert B.fem_domain == A.fem_domain - assert B.fem_codomain == A.fem_codomain - FemLinearOperator.__init__( - self, fem_domain=A.fem_domain, fem_codomain=A.fem_codomain - ) - self._A = A - self._B = B - - def to_sparse_matrix( self, **kwargs): - return self._A.to_sparse_matrix() + self._B.to_sparse_matrix() - - def __call__( self, f ): - # fem layer - return self._B(f) + self._A(f) - - def dot( self, f_coeffs, out=None ): - # coeffs layer - return self._B.dot(f_coeffs) + self._A.dot(f_coeffs) - -#============================================================================== -class MultLinearOperator( FemLinearOperator ): - - def __init__( self, c, A ): - assert isinstance(A, FemLinearOperator) - FemLinearOperator.__init__( - self, fem_domain=A.fem_domain, fem_codomain=A.fem_codomain - ) - self._A = A - self._c = c - - def to_sparse_matrix( self, **kwargs): - return self._c * self._A.to_sparse_matrix() - - def __call__( self, f ): - # fem layer - return self._c * self._A(f) - - def dot( self, f_coeffs, out=None ): - # coeffs layer - return self._c * self._A.dot(f_coeffs) - diff --git a/psydac/feec/multipatch/operators.py b/psydac/feec/multipatch/operators.py deleted file mode 100644 index 0ee00210c..000000000 --- a/psydac/feec/multipatch/operators.py +++ /dev/null @@ -1,1248 +0,0 @@ -# coding: utf-8 - -# Conga operators on piecewise (broken) de Rham sequences - -from sympy import Tuple -from mpi4py import MPI -import os -import numpy as np - -from scipy.sparse import save_npz, load_npz -from scipy.sparse import kron, block_diag -from scipy.sparse.linalg import inv - -from sympde.topology import Boundary, Interface, Union -from sympde.topology import element_of, elements_of -from sympde.topology.space import ScalarFunction -from sympde.calculus import grad, dot, inner, rot, div -from sympde.calculus import laplace, bracket, convect -from sympde.calculus import jump, avg, Dn, minus, plus -from sympde.expr.expr import LinearForm, BilinearForm -from sympde.expr.expr import integral - -from psydac.core.bsplines import collocation_matrix, histopolation_matrix - -from psydac.api.discretization import discretize -from psydac.api.essential_bc import apply_essential_bc_stencil -from psydac.api.settings import PSYDAC_BACKENDS -from psydac.linalg.block import BlockVectorSpace, BlockVector, BlockLinearOperator -from psydac.linalg.stencil import StencilVector, StencilMatrix, StencilInterfaceMatrix -from psydac.linalg.solvers import inverse -from psydac.fem.basic import FemField - - -from psydac.feec.global_projectors import Projector_H1, Projector_Hcurl, Projector_L2 -from psydac.feec.derivatives import Gradient_2D, ScalarCurl_2D -from psydac.feec.multipatch.fem_linear_operators import FemLinearOperator - - -def get_patch_index_from_face(domain, face): - """ Return the patch index of subdomain/boundary - - Parameters - ---------- - domain : - The Symbolic domain - - face : - A patch or a boundary of a patch - - Returns - ------- - i : - The index of a subdomain/boundary in the multipatch domain - """ - - if domain.mapping: - domain = domain.logical_domain - if face.mapping: - face = face.logical_domain - - domains = domain.interior.args - if isinstance(face, Interface): - raise NotImplementedError( - "This face is an interface, it has several indices -- I am a machine, I cannot choose. Help.") - elif isinstance(face, Boundary): - i = domains.index(face.domain) - else: - i = domains.index(face) - return i - - -def get_interface_from_corners(corner1, corner2, domain): - """ Return the interface between two corners from two different patches that correspond to a single (physical) vertex. - - Parameters - ---------- - corner1 : - The first corner of the 2D interface - - corner2 : - The second corner of the 2D interface - - domain : - The Symbolic domain - - Returns - ------- - interface: - The interface between two vertices - - """ - - interface = [] - interfaces = domain.interfaces - - if not isinstance(interfaces, Union): - interfaces = (interfaces,) - - for i in interfaces: - if i.plus.domain in [corner1.domain, corner2.domain]: - if i.minus.domain in [corner1.domain, corner2.domain]: - interface.append(i) - - bd1 = corner1.boundaries - bd2 = corner2.boundaries - - new_interface = [] - - for i in interface: - if i.minus in bd1 + bd2: - if i.plus in bd2 + bd1: - new_interface.append(i) - - if len(new_interface) == 1: - return new_interface[0] - if len(new_interface) > 1: - raise ValueError( - 'found more than one interface for the corners {} and {}'.format( - corner1, corner2)) - return None - - -def get_row_col_index(corner1, corner2, interface, axis, V1, V2): - """ Return the row and column index of a corner in the StencilInterfaceMatrix - for dofs of H1 type spaces - - Parameters - ---------- - corner1 : - The first corner of the 2D interface - - corner2 : - The second corner of the 2D interface - - interface : - The interface between the two corners - - axis : - Axis of the interface - - V1 : - Test Space - - V2 : - Trial Space - - Returns - ------- - index: - The StencilInterfaceMatrix index of the corner, it has the form (i1, i2, k1, k2) in 2D, - where (i1, i2) identifies the row and (k1, k2) the diagonal. - """ - start = V1.coeff_space.starts - end = V1.coeff_space.ends - degree = V2.degree - start_end = (start, end) - - row = [None] * len(start) - col = [0] * len(start) - - assert corner1.boundaries[0].axis == corner2.boundaries[0].axis - - for bd in corner1.boundaries: - row[bd.axis] = start_end[(bd.ext + 1) // 2][bd.axis] - - if interface is None and corner1.domain != corner2.domain: - bd = [i for i in corner1.boundaries if i.axis == axis][0] - if bd.ext == 1: - row[bd.axis] = degree[bd.axis] - - if interface is None: - return row + col - - axis = interface.axis - - if interface.minus.domain == corner1.domain: - if interface.minus.ext == -1: - row[axis] = 0 - else: - row[axis] = degree[axis] - else: - if interface.plus.ext == -1: - row[axis] = 0 - else: - row[axis] = degree[axis] - - if interface.minus.ext == interface.plus.ext: - pass - elif interface.minus.domain == corner1.domain: - if interface.minus.ext == -1: - col[axis] = degree[axis] - else: - col[axis] = -degree[axis] - else: - if interface.plus.ext == -1: - col[axis] = degree[axis] - else: - col[axis] = -degree[axis] - - return row + col - - -# =============================================================================== -def allocate_interface_matrix(corners, test_space, trial_space): - """ Allocate the interface matrix for a vertex shared by two patches - - Parameters - ---------- - corners: - The patch corners corresponding to the common shared vertex - - test_space: - The test space - - trial_space: - The trial space - - Returns - ------- - mat: - The interface matrix shared by two patches - """ - bi, bj = list(zip(*corners)) - permutation = np.arange(bi[0].domain.dim) - - flips = [] - k = 0 - while k < len(bi): - c1 = np.array(bi[k].coordinates) - c2 = np.array(bj[k].coordinates)[permutation] - flips.append( - np.array([-1 if d1 != d2 else 1 for d1, d2 in zip(c1, c2)])) - - if np.sum(abs(flips[0] - flips[-1])) != 0: - prod = [f1 * f2 for f1, f2 in zip(flips[0], flips[-1])] - while -1 in prod: - i1 = prod.index(-1) - if -1 in prod[i1 + 1:]: - i2 = i1 + 1 + prod[i1 + 1:].index(-1) - prod = prod[i2 + 1:] - permutation[i1], permutation[i2] = permutation[i2], permutation[i1] - k = -1 - flips = [] - else: - break - - k += 1 - - assert all(abs(flips[0] - i).sum() == 0 for i in flips) - cs = list(zip(*[i.coordinates for i in bi])) - axis = [all(i[0] == j for j in i) for i in cs].index(True) - ext = 1 if cs[axis][0] == 1 else -1 - s = test_space.get_assembly_grids( - )[axis].spans[-1 if ext == 1 else 0] - test_space.degree[axis] - - mat = StencilInterfaceMatrix( - trial_space.coeff_space, - test_space.coeff_space, - s, - s, - axis, - flip=flips[0], - permutation=list(permutation)) - return mat - -# =============================================================================== -# The following operators are not compatible with the changes in the Stencil format -# and their datatype does not allow for non-matching interfaces, but they might be -# useful for future implementations -# =============================================================================== - - -class ConformingProjection_V0(FemLinearOperator): - """ - Conforming projection from global broken V0 space to conforming global V0 space - Defined by averaging of interface dofs - - Parameters - ---------- - V0h: - The discrete space - - domain_h: - The discrete domain of the projector - - hom_bc : - Apply homogenous boundary conditions if True - - backend_language: - The backend used to accelerate the code - - storage_fn: - filename to store/load the operator sparse matrix - """ - # todo (MCP, 16.03.2021): - # - avoid discretizing a bilinear form - # - allow case without interfaces (single or multipatch) - - def __init__( - self, - V0h, - domain_h, - hom_bc=False, - backend_language='python', - storage_fn=None): - - FemLinearOperator.__init__(self, fem_domain=V0h) - - V0 = V0h.symbolic_space - domain = V0.domain - self.symbolic_domain = domain - - if storage_fn and os.path.exists(storage_fn): - print( - "[ConformingProjection_V0] loading operator sparse matrix from " + - storage_fn) - self._sparse_matrix = load_npz(storage_fn) - - else: - # assemble the operator matrix - u, v = elements_of(V0, names='u, v') - expr = u * v # dot(u,v) - - Interfaces = domain.interfaces # note: interfaces does not include the boundary - # this penalization is for an H1-conforming space - expr_I = (plus(u) - minus(u)) * (plus(v) - minus(v)) - - a = BilinearForm((u, v), integral(domain, expr) + - integral(Interfaces, expr_I)) - # print('[[ forcing python backend for ConformingProjection_V0]] ') - # backend_language = 'python' - ah = discretize( - a, domain_h, [ - V0h, V0h], backend=PSYDAC_BACKENDS[backend_language]) - - # self._A = ah.assemble() - self._A = ah.forms[0]._matrix - - spaces = self._A.domain.spaces - - if isinstance(Interfaces, Interface): - Interfaces = (Interfaces, ) - - for b1 in self._A.blocks: - for A in b1: - if A is None: - continue - A[:, :, :, :] = 0 - - indices = [slice(None, None)] * domain.dim + [0] * domain.dim - - for i in range(len(self._A.blocks)): - self._A[i, i][tuple(indices)] = 1 - - for I in Interfaces: - - axis = I.axis - i_minus = get_patch_index_from_face(domain, I.minus) - i_plus = get_patch_index_from_face(domain, I.plus) - - sp_minus = spaces[i_minus] - sp_plus = spaces[i_plus] - - s_minus = sp_minus.starts[axis] - e_minus = sp_minus.ends[axis] - - s_plus = sp_plus.starts[axis] - e_plus = sp_plus.ends[axis] - - d_minus = V0h.spaces[i_minus].degree[axis] - d_plus = V0h.spaces[i_plus].degree[axis] - - indices = [slice(None, None)] * domain.dim + [0] * domain.dim - - minus_ext = I.minus.ext - plus_ext = I.plus.ext - - if minus_ext == 1: - indices[axis] = e_minus - else: - indices[axis] = s_minus - self._A[i_minus, i_minus][tuple(indices)] = 1 / 2 - - if plus_ext == 1: - indices[axis] = e_plus - else: - indices[axis] = s_plus - - self._A[i_plus, i_plus][tuple(indices)] = 1 / 2 - - if plus_ext == minus_ext: - if minus_ext == 1: - indices[axis] = d_minus - else: - indices[axis] = s_minus - - self._A[i_minus, i_plus][tuple(indices)] = 1 / 2 - - if plus_ext == 1: - indices[axis] = d_plus - else: - indices[axis] = s_plus - - self._A[i_plus, i_minus][tuple(indices)] = 1 / 2 - - else: - if minus_ext == 1: - indices[axis] = d_minus - else: - indices[axis] = s_minus - - if plus_ext == 1: - indices[domain.dim + axis] = d_plus - else: - indices[domain.dim + axis] = -d_plus - - self._A[i_minus, i_plus][tuple(indices)] = 1 / 2 - - if plus_ext == 1: - indices[axis] = d_plus - else: - indices[axis] = s_plus - - if minus_ext == 1: - indices[domain.dim + axis] = d_minus - else: - indices[domain.dim + axis] = -d_minus - - self._A[i_plus, i_minus][tuple(indices)] = 1 / 2 - - domain = domain.logical_domain - corner_blocks = {} - for c in domain.corners: - for b1 in c.corners: - i = get_patch_index_from_face(domain, b1.domain) - for b2 in c.corners: - j = get_patch_index_from_face(domain, b2.domain) - if (i, j) in corner_blocks: - corner_blocks[i, j] += [(b1, b2)] - else: - corner_blocks[i, j] = [(b1, b2)] - - for c in domain.corners: - if len(c) == 2: - continue - for b1 in c.corners: - i = get_patch_index_from_face(domain, b1.domain) - for b2 in c.corners: - j = get_patch_index_from_face(domain, b2.domain) - interface = get_interface_from_corners(b1, b2, domain) - axis = None - if self._A[i, j] is None: - self._A[i, j] = allocate_interface_matrix( - corner_blocks[i, j], V0h.spaces[i], V0h.spaces[j]) - - if i != j and self._A[i, j]: - axis = self._A[i, j]._dim - index = get_row_col_index( - b1, b2, interface, axis, V0h.spaces[i], V0h.spaces[j]) - self._A[i, j][tuple(index)] = 1 / len(c) - - if hom_bc: - for bn in domain.boundary: - self.set_homogenous_bc(bn) - - self._matrix = self._A - self._sparse_matrix = self._matrix.tosparse() # self._sparse_matrix - - if storage_fn: - print( - "[ConformingProjection_V0] storing operator sparse matrix in " + - storage_fn) - save_npz(storage_fn, self._sparse_matrix) - - def set_homogenous_bc(self, boundary, rhs=None): - domain = self.symbolic_domain - Vh = self.fem_domain - if domain.mapping: - domain = domain.logical_domain - if boundary.mapping: - boundary = boundary.logical_domain - - corners = domain.corners - i = get_patch_index_from_face(domain, boundary) - if rhs: - apply_essential_bc_stencil( - rhs[i], axis=boundary.axis, ext=boundary.ext, order=0) - for j in range(len(domain)): - if self._A[i, j] is None: - continue - apply_essential_bc_stencil( - self._A[i, j], axis=boundary.axis, ext=boundary.ext, order=0) - - for c in corners: - faces = [f for b in c.corners for f in b.boundaries] - if len(c) == 2: - continue - if boundary in faces: - for b1 in c.corners: - i = get_patch_index_from_face(domain, b1.domain) - for b2 in c.corners: - j = get_patch_index_from_face(domain, b2.domain) - interface = get_interface_from_corners(b1, b2, domain) - axis = None - if i != j: - axis = self._A[i, j].dim - index = get_row_col_index( - b1, b2, interface, axis, Vh.spaces[i], Vh.spaces[j]) - self._A[i, j][tuple(index)] = 0. - - if i == j and rhs: - rhs[i][tuple(index[:2])] = 0. - -# =============================================================================== - - -class ConformingProjection_V1(FemLinearOperator): - """ - Conforming projection from global broken V1 space to conforming V1 global space - - proj.dot(v) returns the conforming projection of v, computed by solving linear system - - Parameters - ---------- - V1h: - The discrete space - - domain_h: - The discrete domain of the projector - - hom_bc : - Apply homogenous boundary conditions if True - - backend_language: - The backend used to accelerate the code - - storage_fn: - filename to store/load the operator sparse matrix - """ - # todo (MCP, 16.03.2021): - # - avoid discretizing a bilinear form - # - allow case without interfaces (single or multipatch) - - def __init__( - self, - V1h, - domain_h, - hom_bc=False, - backend_language='python', - storage_fn=None): - - FemLinearOperator.__init__(self, fem_domain=V1h) - - V1 = V1h.symbolic_space - domain = V1.domain - self.symbolic_domain = domain - - if storage_fn and os.path.exists(storage_fn): - print( - "[ConformingProjection_V1] loading operator sparse matrix from " + - storage_fn) - self._sparse_matrix = load_npz(storage_fn) - - else: - # assemble the operator matrix - u, v = elements_of(V1, names='u, v') - expr = dot(u, v) - # - Interfaces = domain.interfaces # note: interfaces does not include the boundary - # this penalization is for an H1-conforming space - expr_I = dot(plus(u) - minus(u), plus(v) - minus(v)) - - a = BilinearForm((u, v), integral(domain, expr) + - integral(Interfaces, expr_I)) - # print('[[ forcing python backend for ConformingProjection_V1]] ') - # backend_language = 'python' - ah = discretize( - a, domain_h, [ - V1h, V1h], backend=PSYDAC_BACKENDS[backend_language]) - # - # # self._A = ah.assemble() - self._A = ah.forms[0]._matrix - # C1 = V1h.coeff_space - # self._A = BlockLinearOperator(C1, C1) - - for b1 in self._A.blocks: - for b2 in b1: - if b2 is None: - continue - for b3 in b2.blocks: - for A in b3: - if A is None: - continue - A[:, :, :, :] = 0 - - spaces = self._A.domain.spaces - - if isinstance(Interfaces, Interface): - Interfaces = (Interfaces, ) - - indices = [slice(None, None)] * domain.dim + [0] * domain.dim - - for i in range(len(self._A.blocks)): - self._A[i, i][0, 0][tuple(indices)] = 1 - self._A[i, i][1, 1][tuple(indices)] = 1 - - # empty list if no interfaces ? - if Interfaces is not None: - - for I in Interfaces: - - i_minus = get_patch_index_from_face(domain, I.minus) - i_plus = get_patch_index_from_face(domain, I.plus) - - indices = [slice(None, None)] * \ - domain.dim + [0] * domain.dim - - sp1 = spaces[i_minus] - sp2 = spaces[i_plus] - - s11 = sp1.spaces[0].starts[I.axis] - e11 = sp1.spaces[0].ends[I.axis] - s12 = sp1.spaces[1].starts[I.axis] - e12 = sp1.spaces[1].ends[I.axis] - - s21 = sp2.spaces[0].starts[I.axis] - e21 = sp2.spaces[0].ends[I.axis] - s22 = sp2.spaces[1].starts[I.axis] - e22 = sp2.spaces[1].ends[I.axis] - - d11 = V1h.spaces[i_minus].spaces[0].degree[I.axis] - d12 = V1h.spaces[i_minus].spaces[1].degree[I.axis] - - d21 = V1h.spaces[i_plus].spaces[0].degree[I.axis] - d22 = V1h.spaces[i_plus].spaces[1].degree[I.axis] - - s_minus = [s11, s12] - e_minus = [e11, e12] - - s_plus = [s21, s22] - e_plus = [e21, e22] - - d_minus = [d11, d12] - d_plus = [d21, d22] - - minus_ext = I.minus.ext - plus_ext = I.plus.ext - - axis = I.axis - for k in range(domain.dim): - if k == I.axis: - continue - - if minus_ext == 1: - indices[axis] = e_minus[k] - else: - indices[axis] = s_minus[k] - self._A[i_minus, i_minus][k, k][tuple(indices)] = 1 / 2 - - if plus_ext == 1: - indices[axis] = e_plus[k] - else: - indices[axis] = s_plus[k] - - self._A[i_plus, i_plus][k, k][tuple(indices)] = 1 / 2 - - if plus_ext == minus_ext: - if minus_ext == 1: - indices[axis] = d_minus[k] - else: - indices[axis] = s_minus[k] - - self._A[i_minus, i_plus][k, k][tuple( - indices)] = 1 / 2 * I.direction - - if plus_ext == 1: - indices[axis] = d_plus[k] - else: - indices[axis] = s_plus[k] - - self._A[i_plus, i_minus][k, k][tuple( - indices)] = 1 / 2 * I.direction - - else: - if minus_ext == 1: - indices[axis] = d_minus[k] - else: - indices[axis] = s_minus[k] - - if plus_ext == 1: - indices[domain.dim + axis] = d_plus[k] - else: - indices[domain.dim + axis] = -d_plus[k] - - self._A[i_minus, i_plus][k, k][tuple( - indices)] = 1 / 2 * I.direction - - if plus_ext == 1: - indices[axis] = d_plus[k] - else: - indices[axis] = s_plus[k] - - if minus_ext == 1: - indices[domain.dim + axis] = d_minus[k] - else: - indices[domain.dim + axis] = -d_minus[k] - - self._A[i_plus, i_minus][k, k][tuple( - indices)] = 1 / 2 * I.direction - - if hom_bc: - for bn in domain.boundary: - self.set_homogenous_bc(bn) - - self._matrix = self._A - self._sparse_matrix = self._matrix.tosparse() - - if storage_fn: - print( - "[ConformingProjection_V1] storing operator sparse matrix in " + - storage_fn) - save_npz(storage_fn, self._sparse_matrix) - - def set_homogenous_bc(self, boundary): - domain = self.symbolic_domain - Vh = self.fem_domain - - i = get_patch_index_from_face(domain, boundary) - axis = boundary.axis - ext = boundary.ext - for j in range(len(domain)): - if self._A[i, j] is None: - continue - apply_essential_bc_stencil( - self._A[i, j][1 - axis, 1 - axis], axis=axis, ext=ext, order=0) - - -# =============================================================================== -def get_K0_and_K0_inv(V0h, uniform_patches=False): - """ - Compute the change of basis matrices K0 and K0^{-1} in V0h. - - With - K0_ij = sigma^0_i(B_j) = B_jx(n_ix) * B_jy(n_iy) - where sigma_i is the geometric (interpolation) dof - and B_j is the tensor-product B-spline - """ - if uniform_patches: - print(' [[WARNING -- hack in get_K0_and_K0_inv: using copies of 1st-patch matrices in every patch ]] ') - - V0 = V0h.symbolic_space # VOh is FemSpace - domain = V0.domain - K0_blocks = [] - K0_inv_blocks = [] - for k, D in enumerate(domain.interior): - if uniform_patches and k > 0: - K0_k = K0_blocks[0].copy() - K0_inv_k = K0_inv_blocks[0].copy() - - else: - V0_k = V0h.spaces[k] # fem space on patch k: (TensorFemSpace) - K0_k_factors = [None, None] - for d in [0, 1]: - # 1d fem space alond dim d (SplineSpace) - V0_kd = V0_k.spaces[d] - K0_k_factors[d] = collocation_matrix( - knots=V0_kd.knots, - degree=V0_kd.degree, - periodic=V0_kd.periodic, - normalization=V0_kd.basis, - xgrid=V0_kd.greville - ) - K0_k = kron(*K0_k_factors) - K0_k.eliminate_zeros() - K0_inv_k = inv(K0_k.tocsc()) - K0_inv_k.eliminate_zeros() - - K0_blocks.append(K0_k) - K0_inv_blocks.append(K0_inv_k) - K0 = block_diag(K0_blocks) - K0_inv = block_diag(K0_inv_blocks) - return K0, K0_inv - - -# =============================================================================== -def get_K1_and_K1_inv(V1h, uniform_patches=False): - """ - Compute the change of basis matrices K1 and K1^{-1} in Hcurl space V1h. - - With - K1_ij = sigma^1_i(B_j) = int_{e_ix}(M_jx) * B_jy(n_iy) - if i = horizontal edge [e_ix, n_iy] and j = (M_jx o B_jy) x-oriented MoB spline - or - = B_jx(n_ix) * int_{e_iy}(M_jy) - if i = vertical edge [n_ix, e_iy] and j = (B_jx o M_jy) y-oriented BoM spline - (above, 'o' denotes tensor-product for functions) - """ - if uniform_patches: - print(' [[WARNING -- hack in get_K1_and_K1_inv: using copies of 1st-patch matrices in every patch ]] ') - - V1 = V1h.symbolic_space # V1h is FemSpace - domain = V1.domain - K1_blocks = [] - K1_inv_blocks = [] - for k, D in enumerate(domain.interior): - if uniform_patches and k > 0: - K1_k = K1_blocks[0].copy() - K1_inv_k = K1_inv_blocks[0].copy() - - else: - # fem space on patch k: - V1_k = V1h.spaces[k] - K1_k_blocks = [] - for c in [0, 1]: # dim of component - # fem space for comp. dc (TensorFemSpace) - V1_kc = V1_k.spaces[c] - K1_kc_factors = [None, None] - for d in [0, 1]: # dim of variable - # 1d fem space for comp c alond dim d (SplineSpace) - V1_kcd = V1_kc.spaces[d] - if c == d: - K1_kc_factors[d] = histopolation_matrix( - knots=V1_kcd.knots, - degree=V1_kcd.degree, - periodic=V1_kcd.periodic, - normalization=V1_kcd.basis, - xgrid=V1_kcd.ext_greville - ) - else: - K1_kc_factors[d] = collocation_matrix( - knots=V1_kcd.knots, - degree=V1_kcd.degree, - periodic=V1_kcd.periodic, - normalization=V1_kcd.basis, - xgrid=V1_kcd.greville - ) - K1_kc = kron(*K1_kc_factors) - K1_kc.eliminate_zeros() - K1_k_blocks.append(K1_kc) - K1_k = block_diag(K1_k_blocks) - K1_k.eliminate_zeros() - K1_inv_k = inv(K1_k.tocsc()) - K1_inv_k.eliminate_zeros() - - K1_blocks.append(K1_k) - K1_inv_blocks.append(K1_inv_k) - - K1 = block_diag(K1_blocks) - K1_inv = block_diag(K1_inv_blocks) - return K1, K1_inv - - -# #=============================================================================== -# def get_M_and_M_inv(Vh, subdomains_h, is_scalar, backend_language='python'): -# """ -# compute the mass matrix M and M^{-1} in multipatch space Vh -# DOES NOT WORK -- SHOULD WE HAVE THE POSSIBILITY OF DOING THAT ? -# """ -# from pprint import pprint -# -# V = Vh.symbolic_space # VOh is FemSpace -# domain = V.domain -# M_blocks = [] -# M_inv_blocks = [] -# -# # print('type(domain_h) = ', type(domain_h)) -# # -# # print('type(domain_h._patches) = ', type(domain_h._patches)) -# # print('len(domain_h._patches) = ', len(domain_h._patches)) -# # -# # mappings = domain_h.mappings -# # print('type(mappings) = ', type(mappings)) -# # print('len(mappings) = ', len(mappings)) -# # -# # mappings_list = list(mappings.values()) -# # print('len(mappings_list) = ', len(mappings_list)) -# # -# # print('type(mappings_list[0]) = ', type(mappings_list[0])) -# -# for k, Dh_k in enumerate(subdomains_h): -# -# print('k = ', k) -# print('type(Dh_k) = ', type(Dh_k)) -# # print('Dh = ', Dh) -# D_k = domain.interior[k] -# -# # exit() -# -# # for k, D in enumerate(domain.interior): -# -# V_k = V.spaces[k] -# Vh_k = Vh.spaces[k] -# -# # print(type(domain_h)) -# # -# # pprint(dir(domain_h)) -# # -# # -# # print(len(domain_h._patches)) -# # exit() -# # Dh_k = domain_h.spaces[k] # fem space on patch k: (TensorFemSpace) -# u, v = elements_of(V_k, names='u, v') -# if is_scalar: -# expr = u*v -# else: -# expr = dot(u,v) -# a_k = BilinearForm((u,v), integral(D_k, expr)) -# a_kh = discretize(a_k, Dh_k, [Vh_k, Vh_k], backend=PSYDAC_BACKENDS[backend_language]) # 'pyccel-gcc']) -# -# M_k = a_kh.assemble().toarray() -# M_k.eliminate_zeros() -# M_inv_k = inv(M_k.tocsc()) -# M_inv_k.eliminate_zeros() -# -# M_blocks.append(M_k) -# M_inv_blocks.append(M_inv_k) -# M = block_diag(M_blocks) -# M_inv = block_diag(M_inv_blocks) -# return M, M_inv - -# =============================================================================== -class HodgeOperator(FemLinearOperator): - """ - Change of basis operator: dual basis -> primal basis - - self._matrix: matrix of the primal Hodge = this is the mass matrix ! - self.dual_Hodge_matrix: this is the INVERSE mass matrix - - Parameters - ---------- - Vh: - The discrete space - - domain_h: - The discrete domain of the projector - - metric : - the metric of the de Rham complex - - backend_language: - The backend used to accelerate the code - - load_dir: - storage files for the primal and dual Hodge sparse matrice - - load_space_index: - the space index in the derham sequence - - Notes - ----- - Either we use a storage, or these matrices are only computed on demand - # todo: we compute the sparse matrix when to_sparse_matrix is called -- but never the stencil matrix (should be fixed...) - We only support the identity metric, this implies that the dual Hodge is the inverse of the primal one. - # todo: allow for non-identity metrics - """ - - def __init__( - self, - Vh, - domain_h, - metric='identity', - backend_language='python', - load_dir=None, - load_space_index=''): - - FemLinearOperator.__init__(self, fem_domain=Vh) - self._domain_h = domain_h - self._backend_language = backend_language - self._dual_Hodge_sparse_matrix = None - - assert metric == 'identity' - self._metric = metric - - if load_dir and isinstance(load_dir, str): - if not os.path.exists(load_dir): - os.makedirs(load_dir) - assert str(load_space_index) in ['0', '1', '2', '3'] - primal_Hodge_storage_fn = load_dir + \ - '/H{}_m.npz'.format(load_space_index) - dual_Hodge_storage_fn = load_dir + \ - '/dH{}_m.npz'.format(load_space_index) - - primal_Hodge_is_stored = os.path.exists(primal_Hodge_storage_fn) - dual_Hodge_is_stored = os.path.exists(dual_Hodge_storage_fn) - if dual_Hodge_is_stored: - assert primal_Hodge_is_stored - print( - " ... loading dual Hodge sparse matrix from " + - dual_Hodge_storage_fn) - self._dual_Hodge_sparse_matrix = load_npz( - dual_Hodge_storage_fn) - print( - "[HodgeOperator] loading primal Hodge sparse matrix from " + - primal_Hodge_storage_fn) - self._sparse_matrix = load_npz(primal_Hodge_storage_fn) - else: - assert not primal_Hodge_is_stored - print( - "[HodgeOperator] assembling both sparse matrices for storage...") - self.assemble_primal_Hodge_matrix() - print( - "[HodgeOperator] storing primal Hodge sparse matrix in " + - primal_Hodge_storage_fn) - save_npz(primal_Hodge_storage_fn, self._sparse_matrix) - self.assemble_dual_Hodge_matrix() - print( - "[HodgeOperator] storing dual Hodge sparse matrix in " + - dual_Hodge_storage_fn) - save_npz(dual_Hodge_storage_fn, self._dual_Hodge_sparse_matrix) - else: - # matrices are not stored, we will probably compute them later - pass - - def to_sparse_matrix(self): - """ - the Hodge matrix is the patch-wise multi-patch mass matrix - it is not stored by default but assembled on demand - """ - - if (self._sparse_matrix is not None) or (self._matrix is not None): - return FemLinearOperator.to_sparse_matrix(self) - - self.assemble_primal_Hodge_matrix() - - return self._sparse_matrix - - def assemble_primal_Hodge_matrix(self): - """ - the Hodge matrix is the patch-wise multi-patch mass matrix - it is not stored by default but assembled on demand - """ - - if self._matrix is None: - Vh = self.fem_domain - assert Vh == self.fem_codomain - - V = Vh.symbolic_space - domain = V.domain - # domain_h = V0h.domain: would be nice... - u, v = elements_of(V, names='u, v') - - if isinstance(u, ScalarFunction): - expr = u * v - else: - expr = dot(u, v) - - a = BilinearForm((u, v), integral(domain, expr)) - ah = discretize(a, self._domain_h, [ - Vh, Vh], backend=PSYDAC_BACKENDS[self._backend_language]) - - self._matrix = ah.assemble() # Mass matrix in stencil format - self._sparse_matrix = self._matrix.tosparse() - - def get_dual_Hodge_sparse_matrix(self): - if self._dual_Hodge_sparse_matrix is None: - self.assemble_dual_Hodge_matrix() - - return self._dual_Hodge_sparse_matrix - - def assemble_dual_Hodge_matrix(self): - """ - the dual Hodge matrix is the patch-wise inverse of the multi-patch mass matrix - it is not stored by default but computed on demand, by local (patch-wise) inversion of the mass matrix - """ - - if self._dual_Hodge_sparse_matrix is None: - if not self._matrix: - self.assemble_primal_Hodge_matrix() - - M = self._matrix # mass matrix of the (primal) basis - nrows = M.n_block_rows - ncols = M.n_block_cols - - inv_M_blocks = [] - for i in range(nrows): - Mii = M[i, i].tosparse() - inv_Mii = inv(Mii.tocsc()) - inv_Mii.eliminate_zeros() - inv_M_blocks.append(inv_Mii) - - inv_M = block_diag(inv_M_blocks) - self._dual_Hodge_sparse_matrix = inv_M - -# ============================================================================== - - -class BrokenGradient_2D(FemLinearOperator): - - def __init__(self, V0h, V1h): - - FemLinearOperator.__init__(self, fem_domain=V0h, fem_codomain=V1h) - - D0s = [Gradient_2D(V0, V1) for V0, V1 in zip(V0h.spaces, V1h.spaces)] - - self._matrix = BlockLinearOperator(self.domain, self.codomain, blocks={ - (i, i): D0i._matrix for i, D0i in enumerate(D0s)}) - - def transpose(self, conjugate=False): - # todo (MCP): define as the dual differential operator - return BrokenTransposedGradient_2D(self.fem_domain, self.fem_codomain) - -# ============================================================================== - - -class BrokenTransposedGradient_2D(FemLinearOperator): - - def __init__(self, V0h, V1h): - - FemLinearOperator.__init__(self, fem_domain=V1h, fem_codomain=V0h) - - D0s = [Gradient_2D(V0, V1) for V0, V1 in zip(V0h.spaces, V1h.spaces)] - - self._matrix = BlockLinearOperator(self.domain, self.codomain, blocks={ - (i, i): D0i._matrix.T for i, D0i in enumerate(D0s)}) - - def transpose(self, conjugate=False): - # todo (MCP): discard - return BrokenGradient_2D(self.fem_codomain, self.fem_domain) - - -# ============================================================================== -class BrokenScalarCurl_2D(FemLinearOperator): - def __init__(self, V1h, V2h): - - FemLinearOperator.__init__(self, fem_domain=V1h, fem_codomain=V2h) - - D1s = [ScalarCurl_2D(V1, V2) for V1, V2 in zip(V1h.spaces, V2h.spaces)] - - self._matrix = BlockLinearOperator(self.domain, self.codomain, blocks={ - (i, i): D1i._matrix for i, D1i in enumerate(D1s)}) - - def transpose(self, conjugate=False): - return BrokenTransposedScalarCurl_2D( - V1h=self.fem_domain, V2h=self.fem_codomain) - - -# ============================================================================== -class BrokenTransposedScalarCurl_2D(FemLinearOperator): - - def __init__(self, V1h, V2h): - - FemLinearOperator.__init__(self, fem_domain=V2h, fem_codomain=V1h) - - D1s = [ScalarCurl_2D(V1, V2) for V1, V2 in zip(V1h.spaces, V2h.spaces)] - - self._matrix = BlockLinearOperator(self.domain, self.codomain, blocks={ - (i, i): D1i._matrix.T for i, D1i in enumerate(D1s)}) - - def transpose(self, conjugate=False): - return BrokenScalarCurl_2D(V1h=self.fem_codomain, V2h=self.fem_domain) - - -# ============================================================================== - -# def multipatch_Moments_Hcurl(f, V1h, domain_h): - -def ortho_proj_Hcurl(EE, V1h, domain_h, M1, backend_language='python'): - """ - return orthogonal projection of E on V1h, given M1 the mass matrix - """ - assert isinstance(EE, Tuple) - V1 = V1h.symbolic_space - v = element_of(V1, name='v') - l = LinearForm(v, integral(V1.domain, dot(v, EE))) - lh = discretize( - l, - domain_h, - V1h, - backend=PSYDAC_BACKENDS[backend_language]) - b = lh.assemble() - M1_inv = inverse(M1.mat(), 'pcg', pc='jacobi', tol=1e-10) - sol_coeffs = M1_inv @ b - - return FemField(V1h, coeffs=sol_coeffs) - -# ============================================================================== - - -class Multipatch_Projector_H1: - """ - to apply the H1 projection (2D) on every patch - """ - - def __init__(self, V0h): - - self._P0s = [Projector_H1(V) for V in V0h.spaces] - self._V0h = V0h # multipatch Fem Space - - def __call__(self, funs_log): - """ - project a list of functions given in the logical domain - """ - u0s = [P(fun) for P, fun, in zip(self._P0s, funs_log)] - - u0_coeffs = BlockVector(self._V0h.coeff_space, - blocks=[u0j.coeffs for u0j in u0s]) - - return FemField(self._V0h, coeffs=u0_coeffs) - -# ============================================================================== - - -class Multipatch_Projector_Hcurl: - - """ - to apply the Hcurl projection (2D) on every patch - """ - - def __init__(self, V1h, nquads=None): - - self._P1s = [Projector_Hcurl(V, nquads=nquads) for V in V1h.spaces] - self._V1h = V1h # multipatch Fem Space - - def __call__(self, funs_log): - """ - project a list of functions given in the logical domain - """ - E1s = [P(fun) for P, fun, in zip(self._P1s, funs_log)] - - E1_coeffs = BlockVector(self._V1h.coeff_space, - blocks=[E1j.coeffs for E1j in E1s]) - - return FemField(self._V1h, coeffs=E1_coeffs) - -# ============================================================================== - - -class Multipatch_Projector_L2: - - """ - to apply the L2 projection (2D) on every patch - """ - - def __init__(self, V2h, nquads=None): - - self._P2s = [Projector_L2(V, nquads=nquads) for V in V2h.spaces] - self._V2h = V2h # multipatch Fem Space - - def __call__(self, funs_log): - """ - project a list of functions given in the logical domain - """ - B2s = [P(fun) for P, fun, in zip(self._P2s, funs_log)] - - B2_coeffs = BlockVector(self._V2h.coeff_space, - blocks=[B2j.coeffs for B2j in B2s]) - - return FemField(self._V2h, coeffs=B2_coeffs) diff --git a/psydac/feec/multipatch/tests/test_feec_maxwell_multipatch_2d.py b/psydac/feec/multipatch/tests/test_feec_maxwell_multipatch_2d.py index bb1b09004..3986aabb2 100644 --- a/psydac/feec/multipatch/tests/test_feec_maxwell_multipatch_2d.py +++ b/psydac/feec/multipatch/tests/test_feec_maxwell_multipatch_2d.py @@ -1,13 +1,13 @@ # coding: utf-8 import numpy as np +import pytest from psydac.feec.multipatch.examples.hcurl_source_pbms_conga_2d import solve_hcurl_source_pbm from psydac.feec.multipatch.examples.hcurl_eigen_pbms_conga_2d import hcurl_solve_eigen_pbm from psydac.feec.multipatch.examples.hcurl_eigen_pbms_dg_2d import hcurl_solve_eigen_pbm_dg from psydac.feec.multipatch.examples.timedomain_maxwell import solve_td_maxwell_pbm - def test_time_harmonic_maxwell_pretzel_f(): nc = 4 deg = 2 @@ -29,8 +29,7 @@ def test_time_harmonic_maxwell_pretzel_f(): source_proj=source_proj, backend_language='pyccel-gcc') - assert abs(diags["err"] - 0.007201508128407582) < 1e-10 - + assert abs(diags["err"] - 0.0072015081402929445) < 1e-10 def test_time_harmonic_maxwell_pretzel_f_nc(): deg = 2 @@ -54,8 +53,7 @@ def test_time_harmonic_maxwell_pretzel_f_nc(): source_proj=source_proj, backend_language='pyccel-gcc') - assert abs(diags["err"] - 0.004849165663310541) < 1e-10 - + assert abs(diags["err"] - 0.004849225522124346) < 5e-7 def test_maxwell_eigen_curved_L_shape(): domain_name = 'curved_L_shape' @@ -88,7 +86,6 @@ def test_maxwell_eigen_curved_L_shape(): nb_eigs_plot=nb_eigs_plot, domain_name=domain_name, domain=domain, backend_language='pyccel-gcc', - plot_dir='./plots/eigen_maxell', ) error = 0 @@ -97,8 +94,7 @@ def test_maxwell_eigen_curved_L_shape(): error += (eigenvalues[k] - ref_sigmas[k])**2 error = np.sqrt(error) - assert abs(error - 0.01291539899483907) < 1e-10 - + assert abs(error - 0.012915398994855902) < 1e-10 def test_maxwell_eigen_curved_L_shape_nc(): domain_name = 'curved_L_shape' @@ -133,7 +129,6 @@ def test_maxwell_eigen_curved_L_shape_nc(): nb_eigs_plot=nb_eigs_plot, domain_name=domain_name, domain=domain, backend_language='pyccel-gcc', - plot_dir='./plots/eigen_maxell_nc', ) error = 0 @@ -142,8 +137,7 @@ def test_maxwell_eigen_curved_L_shape_nc(): error += (eigenvalues[k] - ref_sigmas[k])**2 error = np.sqrt(error) - assert abs(error - 0.010504876643873904) < 1e-10 - + assert abs(error - 0.010504876643886937) < 1e-10 def test_maxwell_eigen_curved_L_shape_dg(): domain_name = 'curved_L_shape' @@ -176,7 +170,6 @@ def test_maxwell_eigen_curved_L_shape_dg(): nb_eigs_plot=nb_eigs_plot, domain_name=domain_name, domain=domain, backend_language='pyccel-gcc', - plot_dir='./plots/eigen_maxell_dg', ) error = 0 @@ -184,9 +177,8 @@ def test_maxwell_eigen_curved_L_shape_dg(): for k in range(n_errs): error += (eigenvalues[k] - ref_sigmas[k])**2 error = np.sqrt(error) - - assert abs(error - 0.035139029534570064) < 1e-10 + assert abs(error - 0.035139029534592255) < 1e-10 def test_maxwell_timedomain(): solve_td_maxwell_pbm(nc = 4, deg = 2, final_time = 2, domain_name = 'square_2') diff --git a/psydac/feec/multipatch/tests/test_feec_poisson_multipatch_2d.py b/psydac/feec/multipatch/tests/test_feec_poisson_multipatch_2d.py index 7a0d94cbb..2804fba2d 100644 --- a/psydac/feec/multipatch/tests/test_feec_poisson_multipatch_2d.py +++ b/psydac/feec/multipatch/tests/test_feec_poisson_multipatch_2d.py @@ -2,7 +2,6 @@ from psydac.feec.multipatch.examples.h1_source_pbms_conga_2d import solve_h1_source_pbm - def test_poisson_pretzel_f(): source_type = 'manu_poisson_2' @@ -19,7 +18,7 @@ def test_poisson_pretzel_f(): backend_language='pyccel-gcc', plot_dir=None) - assert abs(l2_error - 1.0585687717792318e-05) < 1e-10 + assert abs(l2_error - 1.1016888403643595e-05) < 5e-8 def test_poisson_pretzel_f_nc(): @@ -39,7 +38,7 @@ def test_poisson_pretzel_f_nc(): backend_language='pyccel-gcc', plot_dir=None) - assert abs(l2_error - 6.051557012306659e-06) < 1e-10 + assert abs(l2_error - 7.079666478120528e-06) < 5e-8 # ============================================================================== diff --git a/psydac/feec/multipatch/utils_conga_2d.py b/psydac/feec/multipatch/utils_conga_2d.py index 351511d5e..b457f0232 100644 --- a/psydac/feec/multipatch/utils_conga_2d.py +++ b/psydac/feec/multipatch/utils_conga_2d.py @@ -5,70 +5,41 @@ from sympy import lambdify from sympde.topology import Derham +from sympde.topology.callable_mapping import BasicCallableMapping from psydac.api.settings import PSYDAC_BACKENDS from psydac.feec.pull_push import pull_2d_h1, pull_2d_hcurl, pull_2d_l2 -from psydac.feec.multipatch.api import discretize -from psydac.feec.multipatch.utilities import time_count # , export_sol, import_sol +from psydac.api.discretization import discretize +from psydac.feec.multipatch.utilities import time_count from psydac.linalg.utilities import array_to_psydac from psydac.fem.basic import FemField from psydac.fem.plotting_utilities import get_plotting_grid, get_grid_quad_weights, get_grid_vals +from scipy.sparse import kron, block_diag +from psydac.core.bsplines import collocation_matrix, histopolation_matrix +from psydac.linalg.solvers import inverse -# commuting projections on the physical domain (should probably be in the -# interface) -def P0_phys(f_phys, P0, domain, mappings_list): - f = lambdify(domain.coordinates, f_phys) - f_log = [pull_2d_h1(f, m.get_callable_mapping()) for m in mappings_list] - return P0(f_log) - - -def P1_phys(f_phys, P1, domain, mappings_list): - f_x = lambdify(domain.coordinates, f_phys[0]) - f_y = lambdify(domain.coordinates, f_phys[1]) - f_log = [pull_2d_hcurl([f_x, f_y], m.get_callable_mapping()) - for m in mappings_list] - return P1(f_log) - - -def P2_phys(f_phys, P2, domain, mappings_list): - f = lambdify(domain.coordinates, f_phys) - f_log = [pull_2d_l2(f, m.get_callable_mapping()) for m in mappings_list] - return P2(f_log) # commuting projections on the physical domain (should probably be in the # interface) - - -def P_phys_h1(f_phys, P0, domain, mappings_list): +def P0_phys(f_phys, P0, domain): f = lambdify(domain.coordinates, f_phys) - if len(mappings_list) == 1: - m = mappings_list[0] - f_log = pull_2d_h1(f, m) - else: - f_log = [pull_2d_h1(f, m) for m in mappings_list] - return P0(f_log) + return P0(f) -def P_phys_hcurl(f_phys, P1, domain, mappings_list): - f_x = lambdify(domain.coordinates, f_phys[0]) - f_y = lambdify(domain.coordinates, f_phys[1]) - f_log = [pull_2d_hcurl([f_x, f_y], m) for m in mappings_list] - return P1(f_log) - -def P_phys_hdiv(f_phys, P1, domain, mappings_list): +def P1_phys(f_phys, P1, domain): f_x = lambdify(domain.coordinates, f_phys[0]) f_y = lambdify(domain.coordinates, f_phys[1]) - f_log = [pull_2d_hdiv([f_x, f_y], m) for m in mappings_list] - return P1(f_log) + + return P1([f_x, f_y]) -def P_phys_l2(f_phys, P2, domain, mappings_list): +def P2_phys(f_phys, P2, domain): f = lambdify(domain.coordinates, f_phys) - f_log = [pull_2d_l2(f, m) for m in mappings_list] - return P2(f_log) + + return P2(f) def get_kind(space='V*'): @@ -83,6 +54,142 @@ def get_kind(space='V*'): raise ValueError(space) return kind +# =============================================================================== +def get_K0_and_K0_inv(V0h, uniform_patches=False): + """ + Compute the change of basis matrices K0 and K0^{-1} in V0h. + + With + K0_ij = sigma^0_i(B_j) = B_jx(n_ix) * B_jy(n_iy) + where sigma_i is the geometric (interpolation) dof + and B_j is the tensor-product B-spline + """ + if uniform_patches: + print(' [[WARNING -- hack in get_K0_and_K0_inv: using copies of 1st-patch matrices in every patch ]] ') + + V0 = V0h.symbolic_space # VOh is FemSpace + domain = V0.domain + K0_blocks = [] + K0_inv_blocks = [] + for k, D in enumerate(domain.interior): + if uniform_patches and k > 0: + K0_k = K0_blocks[0].copy() + K0_inv_k = K0_inv_blocks[0].copy() + + else: + V0_k = V0h.spaces[k] # fem space on patch k: (TensorFemSpace) + K0_k_factors = [None, None] + for d in [0, 1]: + # 1d fem space alond dim d (SplineSpace) + V0_kd = V0_k.spaces[d] + K0_k_factors[d] = collocation_matrix( + knots=V0_kd.knots, + degree=V0_kd.degree, + periodic=V0_kd.periodic, + normalization=V0_kd.basis, + xgrid=V0_kd.greville + ) + K0_k = kron(*K0_k_factors) + K0_k.eliminate_zeros() + K0_inv_k = inv(K0_k.tocsc()) + K0_inv_k.eliminate_zeros() + + K0_blocks.append(K0_k) + K0_inv_blocks.append(K0_inv_k) + K0 = block_diag(K0_blocks) + K0_inv = block_diag(K0_inv_blocks) + return K0, K0_inv + + +# =============================================================================== +def get_K1_and_K1_inv(V1h, uniform_patches=False): + """ + Compute the change of basis matrices K1 and K1^{-1} in Hcurl space V1h. + + With + K1_ij = sigma^1_i(B_j) = int_{e_ix}(M_jx) * B_jy(n_iy) + if i = horizontal edge [e_ix, n_iy] and j = (M_jx o B_jy) x-oriented MoB spline + or + = B_jx(n_ix) * int_{e_iy}(M_jy) + if i = vertical edge [n_ix, e_iy] and j = (B_jx o M_jy) y-oriented BoM spline + (above, 'o' denotes tensor-product for functions) + """ + if uniform_patches: + print(' [[WARNING -- hack in get_K1_and_K1_inv: using copies of 1st-patch matrices in every patch ]] ') + + V1 = V1h.symbolic_space # V1h is FemSpace + domain = V1.domain + K1_blocks = [] + K1_inv_blocks = [] + for k, D in enumerate(domain.interior): + if uniform_patches and k > 0: + K1_k = K1_blocks[0].copy() + K1_inv_k = K1_inv_blocks[0].copy() + + else: + # fem space on patch k: + V1_k = V1h.spaces[k] + K1_k_blocks = [] + for c in [0, 1]: # dim of component + # fem space for comp. dc (TensorFemSpace) + V1_kc = V1_k.spaces[c] + K1_kc_factors = [None, None] + for d in [0, 1]: # dim of variable + # 1d fem space for comp c alond dim d (SplineSpace) + V1_kcd = V1_kc.spaces[d] + if c == d: + K1_kc_factors[d] = histopolation_matrix( + knots=V1_kcd.knots, + degree=V1_kcd.degree, + periodic=V1_kcd.periodic, + normalization=V1_kcd.basis, + xgrid=V1_kcd.ext_greville + ) + else: + K1_kc_factors[d] = collocation_matrix( + knots=V1_kcd.knots, + degree=V1_kcd.degree, + periodic=V1_kcd.periodic, + normalization=V1_kcd.basis, + xgrid=V1_kcd.greville + ) + K1_kc = kron(*K1_kc_factors) + K1_kc.eliminate_zeros() + K1_k_blocks.append(K1_kc) + K1_k = block_diag(K1_k_blocks) + K1_k.eliminate_zeros() + K1_inv_k = inv(K1_k.tocsc()) + K1_inv_k.eliminate_zeros() + + K1_blocks.append(K1_k) + K1_inv_blocks.append(K1_inv_k) + + K1 = block_diag(K1_blocks) + K1_inv = block_diag(K1_inv_blocks) + return K1, K1_inv + +# =============================================================================== + + +def ortho_proj_Hcurl(EE, V1h, domain_h, M1, backend_language='python'): + """ + return orthogonal projection of E on V1h, given M1 the mass matrix + """ + assert isinstance(EE, Tuple) + V1 = V1h.symbolic_space + v = element_of(V1, name='v') + l = LinearForm(v, integral(V1.domain, dot(v, EE))) + lh = discretize( + l, + domain_h, + V1h, + backend=PSYDAC_BACKENDS[backend_language]) + b = lh.assemble() + M1_inv = inverse(M1.mat(), 'pcg', pc='jacobi', tol=1e-10) + sol_coeffs = M1_inv @ b + + return FemField(V1h, coeffs=sol_coeffs) + # =============================================================================== class DiagGrid(): diff --git a/psydac/feec/tests/test_axis_projection.py b/psydac/feec/tests/test_axis_projection.py index 61e1dfb4f..7a81f0953 100644 --- a/psydac/feec/tests/test_axis_projection.py +++ b/psydac/feec/tests/test_axis_projection.py @@ -1,6 +1,6 @@ -from sympde.topology import Square, Derham, element_of -from sympde.expr.expr import BilinearForm, integral -from psydac.feec.multipatch.api import discretize +from sympde.topology import Square, Derham, element_of +from sympde.expr.expr import BilinearForm, integral +from psydac.api.discretization import discretize from psydac.api.settings import PSYDAC_BACKENDS def test_axis_projection(): diff --git a/psydac/feec/tests/test_commuting_projections.py b/psydac/feec/tests/test_commuting_projections.py index 38881220f..b038fbc25 100644 --- a/psydac/feec/tests/test_commuting_projections.py +++ b/psydac/feec/tests/test_commuting_projections.py @@ -3,13 +3,17 @@ import numpy as np import pytest -from psydac.feec.global_projectors import Projector_H1, Projector_L2, Projector_Hcurl, Projector_Hdiv +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorH1 +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorL2 +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHcurl +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHdiv + from psydac.fem.tensor import TensorFemSpace, SplineSpace from psydac.fem.vector import VectorFemSpace from psydac.core.bsplines import make_knots -from psydac.feec.derivatives import Derivative_1D, Gradient_2D, Gradient_3D -from psydac.feec.derivatives import ScalarCurl_2D, VectorCurl_2D, Curl_3D -from psydac.feec.derivatives import Divergence_2D, Divergence_3D +from psydac.feec.derivatives import Derivative1D, Gradient2D, Gradient3D +from psydac.feec.derivatives import ScalarCurl2D, VectorCurl2D, Curl3D +from psydac.feec.derivatives import Divergence2D, Divergence3D from psydac.ddm.cart import DomainDecomposition from psydac.linalg.solvers import inverse from psydac.linalg.basic import IdentityOperator @@ -57,13 +61,13 @@ def test_3d_commuting_pro_1(Nel, Nq, p, bc, m): Hcurl = VectorFemSpace(*spaces) # create an instance of the H1 projector class - P0 = Projector_H1(H1) + P0 = GlobalGeometricProjectorH1(H1) # Build linear operators on stencil arrays - grad = Gradient_3D(H1, Hcurl) + grad = Gradient3D(H1, Hcurl) # create an instance of the projector class - P1 = Projector_Hcurl(Hcurl, Nq) + P1 = GlobalGeometricProjectorHcurl(Hcurl, Nq) #------------------------------------- # Projections and discrete derivatives #------------------------------------- @@ -150,11 +154,11 @@ def test_3d_commuting_pro_2(Nel, Nq, p, bc, m): Hdiv = VectorFemSpace(*spaces) # Build linear operators on stencil arrays - curl = Curl_3D(Hcurl, Hdiv) + curl = Curl3D(Hcurl, Hdiv) # create an instance of the projector class - P1 = Projector_Hcurl(Hcurl, Nq) - P2 = Projector_Hdiv(Hdiv, Nq) + P1 = GlobalGeometricProjectorHcurl(Hcurl, Nq) + P2 = GlobalGeometricProjectorHdiv(Hdiv, Nq) #------------------------------------- # Projections and discrete derivatives @@ -232,11 +236,11 @@ def test_3d_commuting_pro_3(Nel, Nq, p, bc, m): # create an instance of the H1 projector class # Build linear operators on stencil arrays - div = Divergence_3D(Hdiv, L2) + div = Divergence3D(Hdiv, L2) # create an instance of the projector class - P2 = Projector_Hdiv(Hdiv, Nq) - P3 = Projector_L2(L2, Nq) + P2 = GlobalGeometricProjectorHdiv(Hdiv, Nq) + P3 = GlobalGeometricProjectorL2(L2, Nq) #------------------------------------- # Projections and discrete derivatives @@ -307,13 +311,13 @@ def test_2d_commuting_pro_1(Nel, Nq, p, bc, m): Hcurl = VectorFemSpace(*spaces) # create an instance of the H1 projector class - P0 = Projector_H1(H1) + P0 = GlobalGeometricProjectorH1(H1) # Build linear operators on stencil arrays - grad = Gradient_2D(H1, Hcurl) + grad = Gradient2D(H1, Hcurl) # create an instance of the projector class - P1 = Projector_Hcurl(Hcurl, Nq) + P1 = GlobalGeometricProjectorHcurl(Hcurl, Nq) #------------------------------------- # Projections and discrete derivatives #------------------------------------- @@ -380,13 +384,13 @@ def test_2d_commuting_pro_2(Nel, Nq, p, bc, m): Hdiv = VectorFemSpace(*spaces) # create an instance of the H1 projector class - P0 = Projector_H1(H1) + P0 = GlobalGeometricProjectorH1(H1) # Linear operator: 2D vector curl - curl = VectorCurl_2D(H1, Hdiv) + curl = VectorCurl2D(H1, Hdiv) # create an instance of the projector class - P1 = Projector_Hdiv(Hdiv, Nq) + P1 = GlobalGeometricProjectorHdiv(Hdiv, Nq) #------------------------------------- # Projections and discrete derivatives #------------------------------------- @@ -461,11 +465,11 @@ def test_2d_commuting_pro_3(Nel, Nq, p, bc, m): # create an instance of the H1 projector class # Build linear operators on stencil arrays - div = Divergence_2D(Hdiv, L2) + div = Divergence2D(Hdiv, L2) # create an instance of the projector class - P2 = Projector_Hdiv(Hdiv, Nq) - P3 = Projector_L2(L2, Nq) + P2 = GlobalGeometricProjectorHdiv(Hdiv, Nq) + P3 = GlobalGeometricProjectorL2(L2, Nq) #------------------------------------- # Projections and discrete derivatives @@ -541,11 +545,11 @@ def test_2d_commuting_pro_4(Nel, Nq, p, bc, m): # create an instance of the H1 projector class # Build linear operators on stencil arrays - curl = ScalarCurl_2D(Hcurl, L2) + curl = ScalarCurl2D(Hcurl, L2) # create an instance of the projector class - P1 = Projector_Hcurl(Hcurl, Nq) - P2 = Projector_L2(L2, Nq) + P1 = GlobalGeometricProjectorHcurl(Hcurl, Nq) + P2 = GlobalGeometricProjectorL2(L2, Nq) #------------------------------------- # Projections and discrete derivatives @@ -610,13 +614,13 @@ def test_1d_commuting_pro_1(Nel, Nq, p, bc, m): L2 = H1.reduce_degree(axes=[0], basis='M') # create an instance of the H1 projector class - P0 = Projector_H1(H1) + P0 = GlobalGeometricProjectorH1(H1) # Build linear operators on stencil arrays - grad = Derivative_1D(H1, L2) + grad = Derivative1D(H1, L2) # create an instance of the projector class - P1 = Projector_L2(L2, Nq) + P1 = GlobalGeometricProjectorL2(L2, Nq) #------------------------------------- # Projections and discrete derivatives #------------------------------------- diff --git a/psydac/feec/tests/test_commuting_projections_dual.py b/psydac/feec/tests/test_commuting_projections_dual.py index 944915bc4..9057ba1ff 100644 --- a/psydac/feec/tests/test_commuting_projections_dual.py +++ b/psydac/feec/tests/test_commuting_projections_dual.py @@ -1,6 +1,6 @@ -from psydac.feec.derivatives import Gradient_3D -from psydac.feec.derivatives import Curl_3D -from psydac.feec.derivatives import Divergence_3D +from psydac.feec.derivatives import Gradient3D +from psydac.feec.derivatives import Curl3D +from psydac.feec.derivatives import Divergence3D from sympde.expr import LinearForm, integral from sympde.topology import Derham, element_of, Cube from psydac.api.discretization import discretize @@ -39,7 +39,7 @@ def test_transpose_div_3d(Nel, Nq, p, bc, m): v2 = element_of(derham.V2, name='v2') v3 = element_of(derham.V3, name='v3') - div = Divergence_3D(derham_h.V2, derham_h.V3) + div = Divergence3D(derham_h.V2, derham_h.V3) f2 = LinearForm(v2, integral(domain, D1fun1(*domain.coordinates)*v2[0] + D2fun1(*domain.coordinates)*v2[1] + D3fun1(*domain.coordinates)*v2[2])) f3 = LinearForm(v3, integral(domain, fun1(*domain.coordinates) * v3)) @@ -47,7 +47,7 @@ def test_transpose_div_3d(Nel, Nq, p, bc, m): u2 = discretize(f2, domain_h, derham_h.V2, nquads=Nq, backend=PSYDAC_BACKENDS['pyccel-gcc']).assemble() u3 = discretize(f3, domain_h, derham_h.V3, nquads=Nq, backend=PSYDAC_BACKENDS['pyccel-gcc']).assemble() - divT_u3 = - div.matrix.T.dot(u3) + divT_u3 = - div.linop.T.dot(u3) error = abs((u2-divT_u3).toarray()).max() assert error < 2e-10 @@ -97,7 +97,7 @@ def test_transpose_curl_3d(Nel, Nq, p, bc, m): v1 = element_of(derham.V1, name='v1') v2 = element_of(derham.V2, name='v2') - curl = Curl_3D(derham_h.V1, derham_h.V2) + curl = Curl3D(derham_h.V1, derham_h.V2) f1 = LinearForm(v1, integral(domain, cf1(*domain.coordinates)*v1[0] + cf2(*domain.coordinates)*v1[1] + cf3(*domain.coordinates)*v1[2])) f2 = LinearForm(v2, integral(domain, fun1(*domain.coordinates)*v2[0] + fun2(*domain.coordinates)*v2[1] + fun3(*domain.coordinates)*v2[2])) @@ -105,7 +105,7 @@ def test_transpose_curl_3d(Nel, Nq, p, bc, m): u1 = discretize(f1, domain_h, derham_h.V1, nquads=Nq, backend=PSYDAC_BACKENDS['pyccel-gcc']).assemble() u2 = discretize(f2, domain_h, derham_h.V2, nquads=Nq, backend=PSYDAC_BACKENDS['pyccel-gcc']).assemble() - curlT_u2 = curl.matrix.T.dot(u2) + curlT_u2 = curl.linop.T.dot(u2) error = abs((u1-curlT_u2).toarray()).max() assert error < 2e-9 @@ -144,7 +144,7 @@ def test_transpose_grad_3d(Nel, Nq, p, bc, m): v0 = element_of(derham.V0, name='v0') v1 = element_of(derham.V1, name='v1') - grad = Gradient_3D(derham_h.V0, derham_h.V1) + grad = Gradient3D(derham_h.V0, derham_h.V1) f0 = LinearForm(v0, integral(domain, (D1fun1(*domain.coordinates) + D2fun2(*domain.coordinates) + D3fun3(*domain.coordinates))*v0)) f1 = LinearForm(v1, integral(domain, fun1(*domain.coordinates)*v1[0] + fun2(*domain.coordinates)*v1[1] + fun3(*domain.coordinates)*v1[2])) @@ -152,7 +152,7 @@ def test_transpose_grad_3d(Nel, Nq, p, bc, m): u0 = discretize(f0, domain_h, derham_h.V0, nquads=Nq, backend=PSYDAC_BACKENDS['pyccel-gcc']).assemble() u1 = discretize(f1, domain_h, derham_h.V1, nquads=Nq, backend=PSYDAC_BACKENDS['pyccel-gcc']).assemble() - gradT_u1 = -grad.matrix.T.dot(u1) + gradT_u1 = -grad.linop.T.dot(u1) error = abs((u0-gradT_u1).toarray()).max() assert error < 5e-10 diff --git a/psydac/feec/tests/test_differentiation_matrices.py b/psydac/feec/tests/test_differentiation_matrices.py index a60cbae36..609799dd3 100644 --- a/psydac/feec/tests/test_differentiation_matrices.py +++ b/psydac/feec/tests/test_differentiation_matrices.py @@ -8,11 +8,9 @@ from psydac.fem.vector import VectorFemSpace from psydac.feec.derivatives import DirectionalDerivativeOperator -from psydac.feec.derivatives import Derivative_1D, Gradient_2D, Gradient_3D -from psydac.feec.derivatives import ScalarCurl_2D, VectorCurl_2D, Curl_3D -from psydac.feec.derivatives import Divergence_2D, Divergence_3D - -from psydac.feec.global_projectors import Projector_H1 +from psydac.feec.derivatives import Derivative1D, Gradient2D, Gradient3D +from psydac.feec.derivatives import ScalarCurl2D, VectorCurl2D, Curl3D +from psydac.feec.derivatives import Divergence2D, Divergence3D from psydac.ddm.cart import DomainDecomposition from mpi4py import MPI @@ -352,7 +350,7 @@ def test_directional_derivative_operator_3d_par(domain, ncells, degree, periodic @pytest.mark.parametrize('seed', [1,3]) @pytest.mark.parametrize('multiplicity', [1,2]) -def test_Derivative_1D(domain, ncells, degree, periodic, seed, multiplicity): +def test_Derivative1D(domain, ncells, degree, periodic, seed, multiplicity): # determinize tests np.random.seed(seed) @@ -372,7 +370,7 @@ def test_Derivative_1D(domain, ncells, degree, periodic, seed, multiplicity): u0 = FemField(V0) # Linear operator: 1D derivative - grad = Derivative_1D(V0, V1) + grad = Derivative1D(V0, V1) # Create random field in V0 s, = V0.coeff_space.starts @@ -401,7 +399,7 @@ def test_Derivative_1D(domain, ncells, degree, periodic, seed, multiplicity): @pytest.mark.parametrize('seed', [1,3]) @pytest.mark.parametrize('multiplicity', [(1, 1), (1, 2), (2, 2)]) -def test_Gradient_2D(domain, ncells, degree, periodic, seed, multiplicity): +def test_Gradient2D(domain, ncells, degree, periodic, seed, multiplicity): # determinize tests np.random.seed(seed) @@ -421,7 +419,7 @@ def test_Gradient_2D(domain, ncells, degree, periodic, seed, multiplicity): V1 = VectorFemSpace(DxNy, NxDy) # Linear operator: 2D gradient - grad = Gradient_2D(V0, V1) + grad = Gradient2D(V0, V1) # Create random field in V0 u0 = FemField(V0) @@ -463,7 +461,7 @@ def test_Gradient_2D(domain, ncells, degree, periodic, seed, multiplicity): @pytest.mark.parametrize('seed', [1,3]) @pytest.mark.parametrize('multiplicity', [(1, 1, 1), (1, 2, 2), (2, 2, 2)]) -def test_Gradient_3D(domain, ncells, degree, periodic, seed, multiplicity): +def test_Gradient3D(domain, ncells, degree, periodic, seed, multiplicity): if any([ncells[d] <= degree[d] and periodic[d] for d in range(3)]): return @@ -489,7 +487,7 @@ def test_Gradient_3D(domain, ncells, degree, periodic, seed, multiplicity): V1 = VectorFemSpace(DxNyNz, NxDyNz, NxNyDz) # Linear operator: 3D gradient - grad = Gradient_3D(V0, V1) + grad = Gradient3D(V0, V1) # Create random field in V0 u0 = FemField(V0) @@ -530,7 +528,7 @@ def test_Gradient_3D(domain, ncells, degree, periodic, seed, multiplicity): @pytest.mark.parametrize('multiplicity', [(1, 1), (1, 2), (2, 2)]) -def test_ScalarCurl_2D(domain, ncells, degree, periodic, seed, multiplicity): +def test_ScalarCurl2D(domain, ncells, degree, periodic, seed, multiplicity): # determinize tests np.random.seed(seed) @@ -555,7 +553,7 @@ def test_ScalarCurl_2D(domain, ncells, degree, periodic, seed, multiplicity): V2 = DxDy # Linear operator: curl - curl = ScalarCurl_2D(V1, V2) + curl = ScalarCurl2D(V1, V2) # ... # Create random field in V1 @@ -605,7 +603,7 @@ def eval_curl(fx, fy, *eta): @pytest.mark.parametrize('seed', [1,3]) @pytest.mark.parametrize('multiplicity', [(1, 1), (1, 2), (2, 2)]) -def test_VectorCurl_2D(domain, ncells, degree, periodic, seed, multiplicity): +def test_VectorCurl2D(domain, ncells, degree, periodic, seed, multiplicity): # determinize tests np.random.seed(seed) @@ -625,7 +623,7 @@ def test_VectorCurl_2D(domain, ncells, degree, periodic, seed, multiplicity): V1 = VectorFemSpace(NxDy, DxNy) # Linear operator: 2D vector curl - curl = VectorCurl_2D(V0, V1) + curl = VectorCurl2D(V0, V1) # Create random field in V0 u0 = FemField(V0) @@ -671,7 +669,7 @@ def eval_curl(f, *eta): @pytest.mark.parametrize('seed', [1,3]) @pytest.mark.parametrize('multiplicity', [(1, 1, 1), (1, 2, 2), (2, 2, 2)]) -def test_Curl_3D(domain, ncells, degree, periodic, seed, multiplicity): +def test_Curl3D(domain, ncells, degree, periodic, seed, multiplicity): if any([ncells[d] <= degree[d] and periodic[d] for d in range(3)]): return @@ -703,7 +701,7 @@ def test_Curl_3D(domain, ncells, degree, periodic, seed, multiplicity): V2 = VectorFemSpace(NxDyDz, DxNyDz, DxDyNz) # Linear operator: curl - curl = Curl_3D(V1, V2) + curl = Curl3D(V1, V2) # ... # Create random field in V1 @@ -763,7 +761,7 @@ def eval_curl(fx, fy, fz, *eta): @pytest.mark.parametrize('seed', [1,3]) @pytest.mark.parametrize('multiplicity', [(1, 1), (1, 2), (2, 2)]) -def test_Divergence_2D(domain, ncells, degree, periodic, seed, multiplicity): +def test_Divergence2D(domain, ncells, degree, periodic, seed, multiplicity): # determinize tests np.random.seed(seed) @@ -787,7 +785,7 @@ def test_Divergence_2D(domain, ncells, degree, periodic, seed, multiplicity): V2 = V0.reduce_degree(axes=[0, 1], basis='M') # Linear operator: divergence - div = Divergence_2D(V1, V2) + div = Divergence2D(V1, V2) # ... # Create random field in V1 @@ -839,7 +837,7 @@ def eval_div(fx, fy, *eta): @pytest.mark.parametrize('seed', [1,3]) @pytest.mark.parametrize('multiplicity', [(1, 1, 1), (1, 2, 2), (2, 2, 2)]) -def test_Divergence_3D(domain, ncells, degree, periodic, seed, multiplicity): +def test_Divergence3D(domain, ncells, degree, periodic, seed, multiplicity): # determinize tests np.random.seed(seed) @@ -865,7 +863,7 @@ def test_Divergence_3D(domain, ncells, degree, periodic, seed, multiplicity): V3 = V0.reduce_degree(axes=[0, 1, 2], basis='M') # Linear operator: divergence - div = Divergence_3D(V2, V3) + div = Divergence3D(V2, V3) # ... # Create random field in V2 @@ -915,11 +913,11 @@ def eval_div(fx, fy, fz, *eta): #============================================================================== if __name__ == '__main__': - test_Derivative_1D(domain=[0, 1], ncells=3, degree=3, periodic=False, seed=1, multiplicity=1) - test_Derivative_1D(domain=[0, 1], ncells=12, degree=3, periodic=True, seed=1, multiplicity=1) + test_Derivative1D(domain=[0, 1], ncells=3, degree=3, periodic=False, seed=1, multiplicity=1) + test_Derivative1D(domain=[0, 1], ncells=12, degree=3, periodic=True, seed=1, multiplicity=1) - test_Gradient_2D( + test_Gradient2D( domain = ([0, 1], [0, 1]), ncells = (10, 15), degree = (3, 2), @@ -927,7 +925,7 @@ def eval_div(fx, fy, fz, *eta): seed = 1 ) - test_Gradient_3D( + test_Gradient3D( domain = ([0, 1], [0, 1], [0, 1]), ncells = (5, 8, 4), degree = (3, 2, 3), @@ -935,7 +933,7 @@ def eval_div(fx, fy, fz, *eta): seed = 1 ) - test_ScalarCurl_2D( + test_ScalarCurl2D( domain = ([0, 1], [0, 1]), ncells = (10, 15), degree = (3, 2), @@ -943,7 +941,7 @@ def eval_div(fx, fy, fz, *eta): seed = 1 ) - test_VectorCurl_2D( + test_VectorCurl2D( domain = ([0, 1], [0, 1]), ncells = (10, 15), degree = (3, 2), @@ -951,7 +949,7 @@ def eval_div(fx, fy, fz, *eta): seed = 1 ) - test_Curl_3D( + test_Curl3D( domain = ([0, 1], [0, 1], [0, 1]), ncells = (5, 8, 4), degree = (3, 2, 3), @@ -959,7 +957,7 @@ def eval_div(fx, fy, fz, *eta): seed = 1 ) - test_Divergence_2D( + test_Divergence2D( domain = ([0, 1], [0, 1]), ncells = (10, 15), degree = (3, 2), @@ -967,7 +965,7 @@ def eval_div(fx, fy, fz, *eta): seed = 1 ) - test_Divergence_3D( + test_Divergence3D( domain = ([0, 1], [0, 1], [0, 1]), ncells = (5, 8, 4), degree = (3, 2, 3), diff --git a/psydac/feec/multipatch/tests/test_feec_conf_projectors_cart_2d.py b/psydac/feec/tests/test_feec_conf_projectors_cart_2d.py similarity index 54% rename from psydac/feec/multipatch/tests/test_feec_conf_projectors_cart_2d.py rename to psydac/feec/tests/test_feec_conf_projectors_cart_2d.py index 3d0dd85ff..01a0dd38e 100644 --- a/psydac/feec/multipatch/tests/test_feec_conf_projectors_cart_2d.py +++ b/psydac/feec/tests/test_feec_conf_projectors_cart_2d.py @@ -2,16 +2,16 @@ from collections import OrderedDict import numpy as np -from sympy import Tuple +from sympy import Tuple, lambdify from scipy.sparse.linalg import norm as sp_norm +from scipy.sparse.linalg import inv from sympde.topology.domain import Domain from sympde.topology import Derham, Square, IdentityMapping -from psydac.feec.multipatch.api import discretize -from psydac.feec.multipatch.operators import HodgeOperator -from psydac.feec.multipatch.non_matching_operators import construct_h1_conforming_projection, construct_hcurl_conforming_projection -from psydac.feec.multipatch.utils_conga_2d import P_phys_l2, P_phys_hdiv, P_phys_hcurl, P_phys_h1 +from psydac.api.discretization import discretize + +from psydac.fem.projectors import get_dual_dofs def get_polynomial_function(degree, hom_bc_axes, domain): @@ -37,7 +37,10 @@ def get_polynomial_function(degree, hom_bc_axes, domain): # else: g0_y = (y - 0.75)**degree[1] - return g0_x * g0_y + expr = g0_x * g0_y + callable_function = lambdify(domain.coordinates, expr) + + return expr, callable_function # ============================================================================== @@ -46,10 +49,10 @@ def get_polynomial_function(degree, hom_bc_axes, domain): @pytest.mark.parametrize('nc', [5]) @pytest.mark.parametrize('reg', [0]) @pytest.mark.parametrize('hom_bc', [False, True]) -@pytest.mark.parametrize('domain_name', ["4patch_nc", "2patch_nc"]) +@pytest.mark.parametrize('domain_name', ["1patch", "4patch_nc", "2patch_nc"]) @pytest.mark.parametrize("nonconforming, full_mom_pres", [(True, True), (False, True)]) -# NOTE (MCP march 2025): momentum conservation fails for nc = 4 and degree = 3, why? + def test_conf_projectors_2d( V1_type, degree, @@ -60,8 +63,12 @@ def test_conf_projectors_2d( domain_name, nonconforming ): + if domain_name == '1patch': + log_domain = Square('Omega', bounds1=(0, 1), bounds2=(0, 1)) + mapping = IdentityMapping('M1', dim=2) + domain = mapping(log_domain) - if domain_name == '2patch_nc': + elif domain_name == '2patch_nc': A = Square('A', bounds1=(0, 0.5), bounds2=(0, 1)) B = Square('B', bounds1=(0.5, 1.), bounds2=(0, 1)) @@ -95,8 +102,10 @@ def test_conf_projectors_2d( ((0, 1, 1), (2, 1, -1), 1), ((1, 1, 1), (3, 1, -1), 1)], name='domain') + if domain_name == '1patch': + ncells_h = {domain.name: [nc, nc]} - if nonconforming: + elif nonconforming: if len(domain) == 2: ncells_h = { 'M1(A)': [nc, nc], @@ -115,24 +124,14 @@ def test_conf_projectors_2d( for k, D in enumerate(domain.interior): ncells_h[D.name] = [nc, nc] - derham = Derham(domain, ["H1", "Hcurl", "L2"]) domain_h = discretize(domain, ncells=ncells_h) # Vh space - derham_h = discretize(derham, domain_h, degree=degree) - V0h = derham_h.V0 - V1h = derham_h.V1 - V2h = derham_h.V2 - - mappings = OrderedDict([(P.logical_domain, P.mapping) - for P in domain.interior]) - mappings_list = [m.get_callable_mapping() for m in mappings.values()] - p_derham = Derham(domain, ["H1", V1_type, "L2"]) + derham = Derham(domain, ["H1", V1_type, "L2"]) nquads = [(d + 1) for d in degree] - p_derham_h = discretize(p_derham, domain_h, degree=degree) - p_V0h = p_derham_h.V0 - p_V1h = p_derham_h.V1 - p_V2h = p_derham_h.V2 + derham_h = discretize(derham, domain_h, degree=degree) + V0h, V1h, V2h = derham_h.spaces + # full moment preservation only possible if enough interior functions in a # patch (<=> enough cells) @@ -145,38 +144,26 @@ def test_conf_projectors_2d( # moment preservation... # geometric projections (operators) - p_geomP0, p_geomP1, p_geomP2 = p_derham_h.projectors(nquads=nquads) + geomP0, geomP1, geomP2 = derham_h.projectors(nquads=nquads) # conforming projections (scipy matrices) - cP0 = construct_h1_conforming_projection(V0h, reg, mom_pres, hom_bc) - cP1 = construct_hcurl_conforming_projection(V1h, reg, mom_pres, hom_bc) - cP2 = construct_h1_conforming_projection(V2h, reg - 1, mom_pres, hom_bc) + cP0, cP1, cP2 = derham_h.conforming_projectors(p_moments=mom_pres, hom_bc=hom_bc) + cP0, cP1, cP2 = (m.tosparse() for m in (cP0, cP1, cP2)) + + M0, M1, M2 = derham_h.hodge_operators() + M0, M1, M2 = (m.tosparse().tocsc() for m in (M0, M1, M2)) - HOp0 = HodgeOperator(p_V0h, domain_h) - M0 = HOp0.to_sparse_matrix() # mass matrix - M0_inv = HOp0.get_dual_Hodge_sparse_matrix() # inverse mass matrix + M0_inv, M1_inv, M2_inv = (inv(m) for m in (M0, M1, M2)) - HOp1 = HodgeOperator(p_V1h, domain_h) - M1 = HOp1.to_sparse_matrix() # mass matrix - M1_inv = HOp1.get_dual_Hodge_sparse_matrix() # inverse mass matrix + bD0, bD1 = derham_h.derivatives() + bD0, bD1 = (m.tosparse() for m in (bD0, bD1)) - HOp2 = HodgeOperator(p_V2h, domain_h) - M2 = HOp2.to_sparse_matrix() # mass matrix - M2_inv = HOp2.get_dual_Hodge_sparse_matrix() # inverse mass matrix - - bD0, bD1 = p_derham_h.broken_derivatives_as_operators - - bD0 = bD0.to_sparse_matrix() # broken grad - bD1 = bD1.to_sparse_matrix() # broken curl or div D0 = bD0 @ cP0 # Conga grad D1 = bD1 @ cP1 # Conga curl or div - assert np.allclose(sp_norm(cP0 - cP0 @ cP0), 0, 1e-12, - 1e-12) # cP0 is a projection - assert np.allclose(sp_norm(cP1 - cP1 @ cP1), 0, 1e-12, - 1e-12) # cP1 is a projection - assert np.allclose(sp_norm(cP2 - cP2 @ cP2), 0, 1e-12, - 1e-12) # cP2 is a projection + assert np.allclose(sp_norm(cP0 - cP0 @ cP0), 0, 1e-12, 1e-12) # cP0 is a projection + assert np.allclose(sp_norm(cP1 - cP1 @ cP1), 0, 1e-12, 1e-12) # cP1 is a projection + assert np.allclose(sp_norm(cP2 - cP2 @ cP2), 0, 1e-12, 1e-12) # cP2 is a projection # D0 maps in the conforming V1 space (where cP1 coincides with Id) assert np.allclose(sp_norm(D0 - cP1 @ D0), 0, 1e-12, 1e-12) @@ -186,14 +173,11 @@ def test_conf_projectors_2d( # comparing projections of polynomials which should be exact # tests on cP0: - g0 = get_polynomial_function( - degree=degree, hom_bc_axes=[ - hom_bc, hom_bc], domain=domain) - g0h = P_phys_h1(g0, p_geomP0, domain, mappings_list) + g0, g0_fun = get_polynomial_function(degree=degree, hom_bc_axes=[hom_bc, hom_bc], domain=domain) + g0h = geomP0(g0_fun) g0_c = g0h.coeffs.toarray() - tilde_g0_c = p_derham_h.get_dual_dofs( - space='V0', f=g0, return_format='numpy_array') + tilde_g0_c = get_dual_dofs(Vh=V0h, f=g0, domain_h = domain_h, return_format='numpy_array') g0_L2_c = M0_inv @ tilde_g0_c # (P0_geom - P0_L2) polynomial = 0 @@ -206,46 +190,27 @@ def test_conf_projectors_2d( # the following projection should be exact for polynomials of proper degree (no bc) # conf_P0* : L2 -> V0 defined by := # for all phi in V0 - g0 = get_polynomial_function(degree=degree, hom_bc_axes=[ - False, False], domain=domain) - g0h = P_phys_h1(g0, p_geomP0, domain, mappings_list) + g0, g0_fun = get_polynomial_function(degree=degree, hom_bc_axes=[False, False], domain=domain) + g0h = geomP0(g0_fun) g0_c = g0h.coeffs.toarray() - tilde_g0_c = p_derham_h.get_dual_dofs( - space='V0', f=g0, return_format='numpy_array') + tilde_g0_c = get_dual_dofs(Vh=V0h, f=g0, domain_h = domain_h, return_format='numpy_array') + g0_star_c = M0_inv @ cP0.transpose() @ tilde_g0_c # (P10_geom - P0_star) polynomial = 0 assert np.allclose(g0_c, g0_star_c, 1e-12, 1e-12) # tests on cP1: + G1_x, G1_x_fun = get_polynomial_function(degree=[degree[0] - 1,degree[1]], hom_bc_axes=[False, hom_bc], domain=domain) + G1_y, G1_y_fun = get_polynomial_function(degree=[degree[0], degree[1] - 1], hom_bc_axes=[hom_bc, False], domain=domain) + + G1 = Tuple(G1_x, G1_y) + G1_fun = [G1_x_fun, G1_y_fun] - G1 = Tuple( - get_polynomial_function( - degree=[ - degree[0] - 1, - degree[1]], - hom_bc_axes=[ - False, - hom_bc], - domain=domain), - get_polynomial_function( - degree=[ - degree[0], - degree[1] - 1], - hom_bc_axes=[ - hom_bc, - False], - domain=domain) - ) - - if V1_type == "Hcurl": - G1h = P_phys_hcurl(G1, p_geomP1, domain, mappings_list) - elif V1_type == "Hdiv": - G1h = P_phys_hdiv(G1, p_geomP1, domain, mappings_list) - + G1h = geomP1(G1_fun) G1_c = G1h.coeffs.toarray() - tilde_G1_c = p_derham_h.get_dual_dofs( - space='V1', f=G1, return_format='numpy_array') + tilde_G1_c = get_dual_dofs(Vh=V1h, f=G1, domain_h=domain_h, return_format='numpy_array') + G1_L2_c = M1_inv @ tilde_G1_c assert np.allclose(G1_c, G1_L2_c, 1e-12, 1e-12) @@ -254,48 +219,29 @@ def test_conf_projectors_2d( if full_mom_pres: # as above - G1 = Tuple( - get_polynomial_function( - degree=[ - degree[0] - 1, - degree[1]], - hom_bc_axes=[ - False, - False], - domain=domain), - get_polynomial_function( - degree=[ - degree[0], - degree[1] - 1], - hom_bc_axes=[ - False, - False], - domain=domain) - ) - - G1h = P_phys_hcurl(G1, p_geomP1, domain, mappings_list) - G1_c = G1h.coeffs.toarray() - - tilde_G1_c = p_derham_h.get_dual_dofs( - space='V1', f=G1, return_format='numpy_array') - G1_star_c = M1_inv @ cP1.transpose() @ tilde_G1_c - # (P1_geom - P1_star) polynomial = 0 - assert np.allclose(G1_c, G1_star_c, 1e-12, 1e-12) + G1_x, G1_x_fun = get_polynomial_function(degree=[degree[0] - 1,degree[1]], hom_bc_axes=[False, False], domain=domain) + G1_y, G1_y_fun = get_polynomial_function(degree=[degree[0], degree[1] - 1], hom_bc_axes=[False, False], domain=domain) + + G1 = Tuple(G1_x, G1_y) + G1_fun = [G1_x_fun, G1_y_fun] + + G1h = geomP1(G1_fun) + G1_c = G1h.coeffs.toarray() + + G1h = geomP1(G1_fun) + G1_c = G1h.coeffs.toarray() + + tilde_G1_c = get_dual_dofs(Vh=V1h, f=G1, domain_h=domain_h, return_format='numpy_array') + G1_star_c = M1_inv @ cP1.transpose() @ tilde_G1_c + # (P1_geom - P1_star) polynomial = 0 + assert np.allclose(G1_c, G1_star_c, 1e-12, 1e-12) # tests on cP2 (non trivial for reg = 1): - g2 = get_polynomial_function( - degree=[ - degree[0] - 1, - degree[1] - 1], - hom_bc_axes=[ - False, - False], - domain=domain) - g2h = P_phys_l2(g2, p_geomP2, domain, mappings_list) + g2, g2_fun = get_polynomial_function(degree=[degree[0] - 1, degree[1] - 1], hom_bc_axes=[False, False], domain=domain) + g2h = geomP2(g2_fun) g2_c = g2h.coeffs.toarray() - tilde_g2_c = p_derham_h.get_dual_dofs( - space='V2', f=g2, return_format='numpy_array') + tilde_g2_c = get_dual_dofs(Vh=V2h, f=g2, domain_h=domain_h, return_format='numpy_array') g2_L2_c = M2_inv @ tilde_g2_c # (P2_geom - P2_L2) polynomial = 0 @@ -305,7 +251,6 @@ def test_conf_projectors_2d( if full_mom_pres: # as above, here with same degree and bc as - # tilde_g2_c = p_derham_h.get_dual_dofs(space='V2', f=g2, return_format='numpy_array', nquads=nquads) g2_star_c = M2_inv @ cP2.transpose() @ tilde_g2_c # (P2_geom - P2_star) polynomial = 0 assert np.allclose(g2_c, g2_star_c, 1e-12, 1e-12) diff --git a/psydac/feec/tests/test_global_projectors.py b/psydac/feec/tests/test_global_projectors.py index 1d1f64282..c1389f17f 100644 --- a/psydac/feec/tests/test_global_projectors.py +++ b/psydac/feec/tests/test_global_projectors.py @@ -1,11 +1,13 @@ import numpy as np import pytest -from psydac.core.bsplines import make_knots -from psydac.fem.basic import FemField -from psydac.fem.splines import SplineSpace -from psydac.fem.tensor import TensorFemSpace -from psydac.feec.global_projectors import Projector_H1, Projector_L2 +from psydac.core.bsplines import make_knots +from psydac.fem.basic import FemField +from psydac.fem.splines import SplineSpace +from psydac.fem.tensor import TensorFemSpace +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorH1 +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorL2 + from psydac.ddm.cart import DomainDecomposition from sympde.topology import Square, Cube from psydac.api.discretization import discretize @@ -33,7 +35,7 @@ def test_H1_projector_1d(domain, ncells, degree, periodic, multiplicity): V0 = TensorFemSpace(domain_decomposition, N) # Projector onto H1 space (1D interpolation) - P0 = Projector_H1(V0) + P0 = GlobalGeometricProjectorH1(V0) # Function to project f = lambda xi1 : np.sin( xi1 + 0.5 ) @@ -79,7 +81,7 @@ def test_L2_projector_1d(domain, ncells, degree, periodic, nquads, multiplicity) V1 = V0.reduce_degree(axes=[0], basis='M') # Projector onto L2 space (1D histopolation) - P1 = Projector_L2(V1, nquads=[nquads]) + P1 = GlobalGeometricProjectorL2(V1, nquads=[nquads]) # Function to project f = lambda xi1 : np.sin( xi1 + 0.5 ) diff --git a/psydac/feec/tests/test_projections_parallel.py b/psydac/feec/tests/test_projections_parallel.py index 034287bd1..a4cad1cdc 100644 --- a/psydac/feec/tests/test_projections_parallel.py +++ b/psydac/feec/tests/test_projections_parallel.py @@ -9,9 +9,13 @@ from psydac.fem.splines import SplineSpace from psydac.fem.tensor import TensorFemSpace from psydac.fem.vector import VectorFemSpace -from psydac.feec.global_projectors import Projector_H1, Projector_L2, Projector_Hcurl, Projector_Hdiv from psydac.ddm.cart import DomainDecomposition +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorH1 +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorL2 +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHcurl +from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHdiv + def run_projection_comparison(domain, ncells, degree, periodic, funcs, reduce): @@ -19,45 +23,45 @@ def run_projection_comparison(domain, ncells, degree, periodic, funcs, reduce): if len(domain) == 1: if reduce == 0: opV = lambda V0: V0 - opP = Projector_H1 + opP = GlobalGeometricProjectorH1 else: opV = lambda V0: V0.reduce_degree(axes=[0], basis='M') - opP = Projector_L2 + opP = GlobalGeometricProjectorL2 elif len(domain) == 2: if reduce == 0: opV = lambda V0: V0 - opP = Projector_H1 + opP = GlobalGeometricProjectorH1 elif reduce == 1: opV = lambda V0: VectorFemSpace(V0.reduce_degree(axes=[0], basis='M'), V0.reduce_degree(axes=[1], basis='M')) - opP = Projector_Hcurl + opP = GlobalGeometricProjectorHcurl elif reduce == 2: # (note: this would be more instructive, if the index was 1 as well...) opV = lambda V0: VectorFemSpace(V0.reduce_degree(axes=[1], basis='M'), V0.reduce_degree(axes=[0], basis='M')) - opP = Projector_Hdiv + opP = GlobalGeometricProjectorHdiv else: opV = lambda V0: V0.reduce_degree(axes=[0,1], basis='M') - opP = Projector_L2 + opP = GlobalGeometricProjectorL2 elif len(domain) == 3: if reduce == 0: opV = lambda V0: V0 - opP = Projector_H1 + opP = GlobalGeometricProjectorH1 elif reduce == 1: opV = lambda V0: VectorFemSpace(V0.reduce_degree(axes=[0], basis='M'), V0.reduce_degree(axes=[1], basis='M'), V0.reduce_degree(axes=[2], basis='M')) - opP = Projector_Hcurl + opP = GlobalGeometricProjectorHcurl elif reduce == 2: opV = lambda V0: VectorFemSpace(V0.reduce_degree(axes=[1,2], basis='M'), V0.reduce_degree(axes=[0,2], basis='M'), V0.reduce_degree(axes=[0,1], basis='M')) - opP = Projector_Hdiv + opP = GlobalGeometricProjectorHdiv else: opV = lambda V0: V0.reduce_degree(axes=[0,1,2], basis='M') - opP = Projector_L2 + opP = GlobalGeometricProjectorL2 # Choose number of quadrature points nquads = None if reduce == 0 else [d + 1 for d in degree] diff --git a/psydac/fem/basic.py b/psydac/fem/basic.py index 09a1466fb..090243205 100644 --- a/psydac/fem/basic.py +++ b/psydac/fem/basic.py @@ -7,9 +7,9 @@ """ from abc import ABCMeta, abstractmethod -from psydac.linalg.basic import Vector +from psydac.linalg.basic import Vector, LinearOperator -__all__ = ('FemSpace', 'FemField') +__all__ = ('FemSpace', 'FemField', 'FemLinearOperator') #=============================================================================== # ABSTRACT BASE CLASS: FINITE ELEMENT SPACE @@ -380,3 +380,86 @@ def __isub__(self, other): assert self._space is other._space self._coeffs -= other._coeffs return self + +#=============================================================================== +# CONCRETE CLASS: Linear Operator acting on a FEM field +#=============================================================================== +class FemLinearOperator: + """ + Linear operators with an additional FEM layer. + There is also a shorthand access to sparse matrices as they are sometimes + used in the FEEC interfaces. + Parameters + ---------- + fem_domain : psydac.fem.basic.FemSpace + The discrete space of the domain + + fem_codomain : psydac.fem.basic.FemSpace + The discrete space of the codomain + + linop : + Linear Operator. + + """ + + def __init__(self, fem_domain, fem_codomain, *, linop=None): + assert isinstance(fem_domain, FemSpace) + assert isinstance(fem_codomain, FemSpace) + if linop is not None: + assert isinstance(linop, LinearOperator) + + self._fem_domain = fem_domain + self._fem_codomain = fem_codomain + + self._linop_domain = fem_domain.coeff_space + self._linop_codomain = fem_codomain.coeff_space + + self._linop = linop + + @property + def fem_domain(self): + return self._fem_domain + + @property + def fem_codomain(self): + return self._fem_codomain + + @property + def linop_domain(self): + return self._linop_domain + + @property + def linop_codomain(self): + return self._linop_codomain + + @property + def linop(self): + return self._linop + + def toarray(self): + return self._linop.toarray() + + def tosparse(self): + return self._linop.tosparse() + + #-------------------------------------------------------------------------- + def __call__(self, u, *, out=None): + assert isinstance(u, FemField) + assert u.space == self.fem_domain + + if self._linop is not None: + coeffs = self._linop.dot(u.coeffs) + else: + raise NotImplementedError('Class does not provide a __call__ method without a linear operator') + + return FemField(self.fem_codomain, coeffs=coeffs) + + def dot(self, f_coeffs, *, out=None): + assert isinstance(f_coeffs, Vector) + assert f_coeffs.space is self._linop_domain + + if self._linop is not None: + f = FemField(self.fem_domain, coeffs=f_coeffs) + return self(f).coeffs + else: + raise NotImplementedError('Class does not provide a dot method without a linear operator') diff --git a/psydac/fem/projectors.py b/psydac/fem/projectors.py index d40db6a8c..e13185051 100644 --- a/psydac/fem/projectors.py +++ b/psydac/fem/projectors.py @@ -1,8 +1,17 @@ import numpy as np -from psydac.linalg.kron import KroneckerDenseMatrix -from psydac.core.bsplines import hrefinement_matrix -from psydac.linalg.stencil import StencilVectorSpace +from sympde.topology import element_of +from sympde.topology.space import ScalarFunction +from sympde.topology.mapping import Mapping +from sympde.calculus import dot +from sympde.expr.expr import LinearForm, integral + +from psydac.api.settings import PSYDAC_BACKENDS + +from psydac.linalg.kron import KroneckerDenseMatrix +from psydac.core.bsplines import hrefinement_matrix +from psydac.linalg.stencil import StencilVectorSpace +from psydac.fem.basic import FemSpace __all__ = ('knots_to_insert', 'knot_insertion_projection_operator') @@ -100,3 +109,52 @@ def knot_insertion_projection_operator(domain, codomain): ops.append(np.eye(d.nbasis)) return KroneckerDenseMatrix(domain.coeff_space, codomain.coeff_space, *ops) + + +def get_dual_dofs(Vh, f, domain_h, backend_language="python", return_format='stencil_array'): + """ + return the dual dofs tilde_sigma_i(f) = < Lambda_i, f >_{L2} i = 1, .. dim(Vh)) of a given function f, as a stencil array or numpy array + + Parameters + ---------- + Vh : FemSpace + The discrete space for the dual dofs + + f : + The function used for evaluation + + domain_h : + The discrete domain corresponding to Vh + + backend_language: + The backend used to accelerate the code + + return_format: + The format of the dofs, can be 'stencil_array' or 'numpy_array' + + Returns + ------- + tilde_f: + The dual dofs + """ + + from psydac.api.discretization import discretize + + assert isinstance(Vh, FemSpace) + + V = Vh.symbolic_space + v = element_of(V, name='v') + + if Vh.is_vector_valued: + expr = dot(f,v) + else: + expr = f*v + + l = LinearForm(v, integral( V.domain, expr)) + lh = discretize(l, domain_h, Vh, backend=PSYDAC_BACKENDS[backend_language]) + tilde_f = lh.assemble() + + if return_format == 'numpy_array': + return tilde_f.toarray() + else: + return tilde_f diff --git a/psydac/linalg/basic.py b/psydac/linalg/basic.py index a6a02f68a..ba8ca3663 100644 --- a/psydac/linalg/basic.py +++ b/psydac/linalg/basic.py @@ -720,11 +720,10 @@ def set_scalar(self, c): self._scalar = c def toarray(self): - return self._scalar*self._operator.toarray() + return self._scalar * self._operator.toarray() def tosparse(self): - from scipy.sparse import csr_matrix - return self._scalar*csr_matrix(self._operator.toarray()) + return self._scalar * self._operator.tosparse().tocsr() def transpose(self, conjugate=False): return ScaledLinearOperator(domain=self.codomain, codomain=self.domain, c=self._scalar if not conjugate else np.conjugate(self._scalar), A=self._operator.transpose(conjugate=conjugate)) @@ -1326,7 +1325,7 @@ def dot(self, v, out=None, **kwargs): self._dot(v, out=out, **kwargs) else: # provided dot product does not take an out argument: we simply copy the result into out - self._dot(v).copy(out=out, **kwargs) + self._dot(v, **kwargs).copy(out=out) return out diff --git a/psydac/linalg/sparse.py b/psydac/linalg/sparse.py new file mode 100644 index 000000000..71fa29fed --- /dev/null +++ b/psydac/linalg/sparse.py @@ -0,0 +1,114 @@ +# coding: utf-8 + +from scipy.sparse import sparray, csr_array, bsr_array +from scipy.sparse import spmatrix, csr_matrix, bsr_matrix + +from psydac.linalg.basic import LinearOperator +from psydac.linalg.basic import VectorSpace, Vector, LinearOperator +from psydac.linalg.stencil import StencilVector +from psydac.linalg.block import BlockVector + +__all__ = ( + 'SparseMatrixLinearOperator', +) + +class SparseMatrixLinearOperator(LinearOperator): + """ + LinearOperator representation of a sparse matrix. + + Parameters + ---------- + domain : VectorSpace + The domain of the operator. + + codomain : VectorSpace + The codomain of the operator. + + sparse_matrix : scipy.sparse.sparray | scipy.sparse.spmatrix + The sparse SciPy matrix representing the operator. Recommended formats are + CSR and BSR. Any other format will be converted to CSR (csr_array). + """ + + def __init__(self, domain, codomain, sparse_matrix): + + assert isinstance(domain, VectorSpace) + assert isinstance(codomain, VectorSpace) + assert isinstance(sparse_matrix, (sparray, spmatrix)) + + if not isinstance(sparse_matrix, + (csr_array, csr_matrix, + bsr_array, bsr_matrix)): + sparse_matrix = sparse_matrix.tocsr() + + if domain.parallel: + raise NotImplementedError('Parallel SparseMatrixLinearOperator not supported yet.') + + self._domain = domain + self._codomain = codomain + self._matrix = sparse_matrix + + @property + def domain(self): + return self._domain + + @property + def codomain(self): + return self._codomain + + @property + def dtype(self): + return self._matrix.dtype + + def toarray(self): + return self._matrix.toarray() + + def tosparse(self): + return self._matrix + + def transpose(self, conjugate=False): + if conjugate: + return SparseMatrixLinearOperator(self.codomain, self.domain, self._matrix.getH().tocsr()) + else: + return SparseMatrixLinearOperator(self.codomain, self.domain, self._matrix.T.tocsr()) + + def dot(self, v, out=None): + assert isinstance(v, Vector) + assert v.space is self.domain + + if out is not None: + assert isinstance(out, Vector) + assert out.space is self.codomain + out *= 0 + else: + out = self.codomain.zeros() + + self._dot_recursive(v, out=out) + + return out + + def _dot_recursive(self, v, out, ind_V=0, ind_W=0): + V = v.space + W = out.space + + if isinstance(v, StencilVector): + index_global_W = tuple(slice(s, e+1) for s, e in zip(W.starts, W.ends)) + index_global_V = tuple(slice(s, e+1) for s, e in zip(V.starts, V.ends)) + + dim_W = W.dimension + dim_V = V.dimension + + out[index_global_W].flat += self._matrix[ind_W:ind_W+dim_W, ind_V:ind_V+dim_V] @ v[index_global_V].flat + + elif isinstance(v, BlockVector): + + offset_i = ind_W + for (i, Wi) in enumerate(W.spaces): + + offset_j = ind_V + for (j, Vj) in enumerate(V.spaces): + + self._dot_recursive(v[j], out[i], ind_V=offset_j, ind_W=offset_i) + + offset_j += Vj.dimension + + offset_i += Wi.dimension diff --git a/psydac/linalg/tests/test_block.py b/psydac/linalg/tests/test_block.py index ff3bf1e6c..23a53046a 100644 --- a/psydac/linalg/tests/test_block.py +++ b/psydac/linalg/tests/test_block.py @@ -10,6 +10,7 @@ from psydac.linalg.block import BlockVectorSpace, BlockVector from psydac.linalg.block import BlockLinearOperator from psydac.linalg.utilities import array_to_psydac, petsc_to_psydac +from psydac.linalg.sparse import SparseMatrixLinearOperator from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL from psydac.ddm.cart import DomainDecomposition, CartDecomposition @@ -727,6 +728,87 @@ def test_block_linear_operator_serial_dot( dtype, n1, n2, p1, p2, P1, P2 ): @pytest.mark.parametrize( 'dtype', [float, complex] ) @pytest.mark.parametrize( 'n1', [8, 16] ) @pytest.mark.parametrize( 'n2', [8, 12] ) +@pytest.mark.parametrize( 'p1', [1, 3] ) +@pytest.mark.parametrize( 'p2', [1, 2] ) +@pytest.mark.parametrize( 'P1', [True, False] ) +@pytest.mark.parametrize( 'P2', [True] ) + +def test_sparse_matrix_linear_operator_serial_dot( dtype, n1, n2, p1, p2, P1, P2 ): + # set seed for reproducibility + seed(n1*n2*p1*p2) + + D = DomainDecomposition([n1,n2], periods=[P1,P2]) + + # Partition the points + npts = [n1,n2] + global_starts, global_ends = compute_global_starts_ends(D, npts) + + cart = CartDecomposition(D, npts, global_starts, global_ends, pads=[p1,p2], shifts=[1,1]) + + # Create vector spaces, stencil matrices, and stencil vectors + V = StencilVectorSpace( cart, dtype=dtype ) + M1 = StencilMatrix( V, V) + M2 = StencilMatrix( V, V ) + M3 = StencilMatrix( V, V ) + x1 = StencilVector( V ) + x2 = StencilVector( V ) + + # Fill in stencil matrices based on diagonal index + if dtype==complex: + f=lambda k1,k2: 10j*k1+k2 + else: + f=lambda k1,k2: 10*k1+k2 + + for k1 in range(-p1,p1+1): + for k2 in range(-p2,p2+1): + M1[:,:,k1,k2] = f(k1,k2) + M2[:,:,k1,k2] = f(k1,k2)+2. + M3[:,:,k1,k2] = f(k1,k2)+5. + + M1.remove_spurious_entries() + M2.remove_spurious_entries() + M3.remove_spurious_entries() + + # Fill in vector with random values, then update ghost regions + for i1 in range(n1): + for i2 in range(n2): + x1[i1,i2] = 2.0*random() - 1.0 + x2[i1,i2] = 5.0*random() - 1.0 + x1.update_ghost_regions() + x2.update_ghost_regions() + + W = BlockVectorSpace(V, V) + + # Construct a BlockLinearOperator object containing M1, M2, M, using 3 ways + # |M1 M2| + # L = | | + # |M3 0 | + + dict_blocks = {(0,0):M1, (0,1):M2, (1,0):M3} + + L = BlockLinearOperator( W, W, blocks=dict_blocks ) + Lm = SparseMatrixLinearOperator(W, W, L.tosparse().tocsr()) + + # Construct a BlockVector object containing x1 and x2 + # |x1| + # X = | | + # |x2| + + X = BlockVector(W) + X[0] = x1 + X[1] = x2 + + # Compute BlockLinearOperator product + Y = L.dot(X) + + Ym = Lm.dot(X) + + # Check data in 1D array + assert np.allclose( Ym.toarray(), Y.toarray(), rtol=1e-12, atol=1e-12 ) +#=============================================================================== +@pytest.mark.parametrize( 'dtype', [float, complex] ) +@pytest.mark.parametrize( 'n1', [8, 16] ) +@pytest.mark.parametrize( 'n2', [8, 12] ) @pytest.mark.parametrize( 'p1', [1, 2] ) @pytest.mark.parametrize( 'p2', [1, 3] ) @pytest.mark.parametrize( 'P1', [True, False] ) diff --git a/psydac/linalg/utilities.py b/psydac/linalg/utilities.py index 57a9a6b86..fb13a2e6d 100644 --- a/psydac/linalg/utilities.py +++ b/psydac/linalg/utilities.py @@ -4,14 +4,14 @@ from math import sqrt from psydac.linalg.basic import Vector -from psydac.linalg.stencil import StencilVectorSpace, StencilVector +from psydac.linalg.stencil import StencilVector, StencilVectorSpace from psydac.linalg.block import BlockVector, BlockVectorSpace from psydac.linalg.topetsc import petsc_local_to_psydac, get_npts_per_block __all__ = ( 'array_to_psydac', 'petsc_to_psydac', - '_sym_ortho' + '_sym_ortho', ) #============================================================================== From ccbd6e3b029bf8e978780c73a643b7b1186b0942 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Wed, 1 Oct 2025 06:25:42 +0200 Subject: [PATCH 16/23] Allow `mpi_dims_mask` with geometry file (#526) Add the optional parameter `mpi_dims_mask` to the constructor of class `Geometry`, as well as its class methods `from_discrete_mapping` and `from_topological_domain`. Add unit tests to verify that the domain is correctly decomposed. --------- Co-authored-by: Alisa Kirkinskaia Co-authored-by: Alisa Kirkinskaia --- psydac/api/discretization.py | 2 +- psydac/cad/geometry.py | 18 +++--- psydac/cad/tests/test_geometry.py | 97 ++++++++++++++++++++++++++++++- 3 files changed, 108 insertions(+), 9 deletions(-) diff --git a/psydac/api/discretization.py b/psydac/api/discretization.py index bedec470e..d98ba1a51 100644 --- a/psydac/api/discretization.py +++ b/psydac/api/discretization.py @@ -575,7 +575,7 @@ def discretize_domain(domain, *, filename=None, ncells=None, periodic=None, comm raise ValueError("Cannot provide both 'filename' and 'ncells'") elif filename: - return Geometry(filename=filename, comm=comm) + return Geometry(filename=filename, comm=comm, mpi_dims_mask=mpi_dims_mask) elif ncells: return Geometry.from_topological_domain(domain, ncells, periodic=periodic, comm=comm, mpi_dims_mask=mpi_dims_mask) diff --git a/psydac/cad/geometry.py b/psydac/cad/geometry.py index 066dc8231..58d3dc3ba 100644 --- a/psydac/cad/geometry.py +++ b/psydac/cad/geometry.py @@ -30,7 +30,7 @@ from sympde.topology.basic import Union #============================================================================== -class Geometry( object ): +class Geometry: """ Distributed discrete geometry that works for single and multiple patches. The Geometry object can be created in two ways: @@ -75,7 +75,7 @@ def __init__(self, domain=None, ncells=None, periodic=None, mappings=None, # ... read the geometry if the filename is given if filename is not None: - self.read(filename, comm=comm) + self.read(filename, comm=comm, mpi_dims_mask=mpi_dims_mask) elif domain is not None: assert isinstance(domain, Domain) @@ -122,7 +122,7 @@ def __init__(self, domain=None, ncells=None, periodic=None, mappings=None, # Option [2]: from a discrete mapping #-------------------------------------------------------------------------- @classmethod - def from_discrete_mapping(cls, mapping, comm=None, name=None): + def from_discrete_mapping(cls, mapping, *, comm=None, mpi_dims_mask=None, name=None): """Create a geometry from one discrete mapping. Parameters @@ -132,7 +132,11 @@ def from_discrete_mapping(cls, mapping, comm=None, name=None): comm : MPI.Comm MPI intra-communicator. - + + mpi_dims_mask: list of bool + True if the dimension is to be used in the domain decomposition (=default for each dimension). + If mpi_dims_mask[i]=False, the i-th dimension will not be decomposed. + name : string Optional name for the Mapping that will be created. Needed to avoid conflicts in case several mappings are created @@ -150,7 +154,7 @@ def from_discrete_mapping(cls, mapping, comm=None, name=None): ncells = {domain.name: mapping.space.domain_decomposition.ncells} periodic = {domain.name: mapping.space.domain_decomposition.periods} - return Geometry(domain=domain, ncells=ncells, periodic=periodic, mappings=mappings, comm=comm) + return Geometry(domain=domain, ncells=ncells, periodic=periodic, mappings=mappings, comm=comm, mpi_dims_mask=mpi_dims_mask) #-------------------------------------------------------------------------- @@ -223,7 +227,7 @@ def mappings(self): def __len__(self): return len(self.domain) - def read( self, filename, comm=None ): + def read(self, filename, comm=None, mpi_dims_mask=None): # ... check extension of the file basename, ext = os.path.splitext(filename) if not(ext == '.h5'): @@ -287,7 +291,7 @@ def read( self, filename, comm=None ): self._cart = None if n_patches == 1: - self._ddm = DomainDecomposition(ncells[domain.name], periodic[domain.name], comm=comm) + self._ddm = DomainDecomposition(ncells[domain.name], periodic[domain.name], comm=comm, mpi_dims_mask=mpi_dims_mask) ddms = [self._ddm] else: ncells_ = [ncells[itr.name] for itr in interiors] diff --git a/psydac/cad/tests/test_geometry.py b/psydac/cad/tests/test_geometry.py index 0f0f1a93d..458fc8f50 100644 --- a/psydac/cad/tests/test_geometry.py +++ b/psydac/cad/tests/test_geometry.py @@ -17,6 +17,8 @@ from psydac.utilities.utils import refine_array_1d from psydac.ddm.cart import DomainDecomposition +from mpi4py import MPI + base_dir = os.path.dirname(os.path.realpath(__file__)) #============================================================================== def test_geometry_2d_1(): @@ -169,6 +171,99 @@ def test_geometry_2d_4(): # export it geo.export('circle.h5') +#============================================================================== +@pytest.mark.parallel +def test_geometry_with_mpi_dims_mask(): + + comm = MPI.COMM_WORLD + rank = comm.rank + size = comm.size + mpi_dims_mask = [False, True, False] # We will verify that this has an effect + ncells = [4, 2*size, 8] # Each process should have two cells along x2 + degree = [2, 2, 2] + + expected_starts = (0, 2 * rank, 0) + expected_ends = (3, 2 * rank + 1, 7) + + # create an identity mapping + mapping = discrete_mapping('identity', ncells=ncells, degree=degree) + + # create a topological domain + F = Mapping('F', dim=3) + domain = F(Cube(name='Omega')) + + # associate the mapping to the topological domain + mappings = {domain.name: mapping} + + # Define d_ncells as a dict + d_ncells = {domain.name: ncells} + + # Create a geometry from a topological domain and the dict of mappings + # Here we allow for any distribution of the domain: mpi_dims_mask is not passed + geo = Geometry(domain=domain, ncells=d_ncells, mappings=mappings, comm=comm) + geo.export('geo_mpi_dims.h5') + + # Read geometry file in parallel, but using mpi_dims_mask + geo_from_file = Geometry(filename='geo_mpi_dims.h5', comm=comm, mpi_dims_mask=mpi_dims_mask) + + # Verify that the domain is distributed as expected + assert geo_from_file.ddm.starts == expected_starts + assert geo_from_file.ddm.ends == expected_ends + + # Safely remove the file + comm.Barrier() + if rank == 0: + os.remove('geo_mpi_dims.h5') + + +# ============================================================================== +@pytest.mark.parallel +def test_from_discrete_mapping(): + + comm = MPI.COMM_WORLD + rank = comm.rank + size = comm.size + mpi_dims_mask = [False, False, True] # We swill verify that this has an effect + ncells = [4, 8, 2 * size] # Each process should have two cells along x3 + degree = [3, 3, 3] + + expected_starts = (0, 0, 2 * rank) + expected_ends = (3, 7, 2 * rank + 1) + + # Create a mapping + mapping = discrete_mapping('identity', ncells=ncells, degree=degree) + + # Create geometry from the mapping using mpi_dims_mask + geo_from_mapping = Geometry.from_discrete_mapping(mapping, comm=comm, mpi_dims_mask=mpi_dims_mask) + + # Verify that the domain is distributed as expected + assert geo_from_mapping.ddm.starts == expected_starts + assert geo_from_mapping.ddm.ends == expected_ends + +# ============================================================================== +@pytest.mark.parallel +def test_from_topological_domain(): + + comm = MPI.COMM_WORLD + rank = comm.rank + size = comm.size + mpi_dims_mask = [False, True, False] # We will verify that this has an effect + ncells = [4, 2 * size, 8] # Each process should have two cells along x2 + + expected_starts = (0, 2 * rank, 0) + expected_ends = (3, 2 * rank + 1, 7) + + # Create a topological domain + F = Mapping('F', dim=3) + domain = F(Cube(name='Omega')) + + # Create geometry from topological domain using mpi_dims_mask + geo_from_domain = Geometry.from_topological_domain(domain, ncells, comm=comm, mpi_dims_mask=mpi_dims_mask) + + # Verify that the domain is distributed as expected + assert geo_from_domain.ddm.starts == expected_starts + assert geo_from_domain.ddm.ends == expected_ends + #============================================================================== @pytest.mark.parametrize( 'ncells', [[8,8], [12,12], [14,14]] ) @pytest.mark.parametrize( 'degree', [[2,2], [3,2], [2,3], [3,3], [4,4]] ) @@ -289,7 +384,7 @@ def teardown_module(): 'quart_circle_1.h5', 'circle.h5', 'pipe.h5', - 'L_shaped.h5' + 'L_shaped.h5', ] for fname in filenames: if os.path.exists(fname): From c531d986c6d15dd4d83e3bb7dc4146913400a957 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Mon, 13 Oct 2025 22:43:22 +0200 Subject: [PATCH 17/23] Fix the parallel low-level 2D Poisson example (#528) Fix `examples/poisson_2d_mapping.py`: - Use renamed method `get_assembly_grids` (formerly `get_quadrature_grids`) of class `TensorFemSpace` - Add missing definition of `Vnew` variable in the case of distributed visualization - Avoid string warnings --- examples/poisson_2d_mapping.py | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/examples/poisson_2d_mapping.py b/examples/poisson_2d_mapping.py index 602b9f34c..74fb620d3 100644 --- a/examples/poisson_2d_mapping.py +++ b/examples/poisson_2d_mapping.py @@ -57,7 +57,7 @@ def __call__(self, phi): #============================================================================== class Poisson2D: - """ + r""" Exact solution to the 2D Poisson equation with Dirichlet boundary conditions, to be employed for the method of manufactured solutions. @@ -77,7 +77,7 @@ def __init__(self, domain, periodic, mapping, phi, rho, O_point=False): # ... @staticmethod def new_square(mx=1, my=1): - """ + r""" Solve Poisson's equation on the unit square. : code @@ -103,7 +103,7 @@ def new_square(mx=1, my=1): # ... @staticmethod def new_annulus(rmin=0.5, rmax=1.0): - """ + r""" Solve Poisson's equation on an annulus centered at (x,y)=(0,0), with logical coordinates (r,theta): @@ -143,7 +143,7 @@ def new_annulus(rmin=0.5, rmax=1.0): # ... @staticmethod def new_circle(): - """ + r""" Solve Poisson's equation on a unit circle centered at (x,y)=(0,0), with logical coordinates (r,theta): @@ -401,7 +401,7 @@ def assemble_matrices(V, mapping, kernel, *, nquads): [p1, p2] = V.coeff_space.pads # Quadrature data - quad_grids = V.get_quadrature_grids(*nquads) + quad_grids = V.get_assembly_grids(*nquads) [ nk1, nk2] = [g.num_elements for g in quad_grids] [ nq1, nq2] = [g.num_quad_pts for g in quad_grids] [ spans_1, spans_2] = [g.spans for g in quad_grids] @@ -483,7 +483,7 @@ def assemble_rhs(V, mapping, f, *, nquads): [p1, p2] = V.coeff_space.pads # Quadrature data - quad_grids = V.get_quadrature_grids(*nquads) + quad_grids = V.get_assembly_grids(*nquads) [ nk1, nk2] = [g.num_elements for g in quad_grids] [ nq1, nq2] = [g.num_quad_pts for g in quad_grids] [ spans_1, spans_2] = [g.spans for g in quad_grids] @@ -803,6 +803,9 @@ def main(*, test_case, ncells, degree, nquads, # Import solution vector into new serial field phi, = Vnew.import_fields( 'fields.h5', 'phi' ) + else: + Vnew = V + # Compute numerical solution (and error) on refined logical grid [sk1, sk2], [ek1, ek2] = Vnew.local_domain From c97f2652eb2fb77bb57ef08849a49e5674bdbb08 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Tue, 21 Oct 2025 13:41:19 +0200 Subject: [PATCH 18/23] Fix method `plot_2d_decomposition` of `TensorFemSpace` (#529) Fix bug in method `plot_2d_decomposition` of `TensorFemSpace`, which was failing when run in parallel with a distributed spline mapping. - Create a new test file `psydac/fem/tests/test_tensor.py` with a unit test which fails on the `devel` branch. This compares the generated PNG images with "reference" ones which are known to be correct, within a 2 % relative tolerance on each of the RGB channels. - Only evaluate mapping in local subdomain owned by process - Gather global mapping information on root process - Add optional parameters `fig`, `ax`, and `mpi_root` - Add docstring - Update `examples/poisson_2d_mapping.py` to pass the correct mapping (i.e. also a distributed spline mapping if that is used in the computations) to `plot_2d_decomposition`. --- .github/workflows/testing.yml | 2 +- examples/poisson_2d_mapping.py | 3 +- psydac/fem/tensor.py | 125 ++++++++-- .../tests/data/decomp_analytical_1_procs.png | Bin 0 -> 56846 bytes .../tests/data/decomp_analytical_4_procs.png | Bin 0 -> 59285 bytes .../fem/tests/data/decomp_spline_1_procs.png | Bin 0 -> 56851 bytes .../fem/tests/data/decomp_spline_4_procs.png | Bin 0 -> 59379 bytes psydac/fem/tests/test_tensor.py | 220 ++++++++++++++++++ pyproject.toml | 3 +- 9 files changed, 334 insertions(+), 19 deletions(-) create mode 100644 psydac/fem/tests/data/decomp_analytical_1_procs.png create mode 100644 psydac/fem/tests/data/decomp_analytical_4_procs.png create mode 100644 psydac/fem/tests/data/decomp_spline_1_procs.png create mode 100644 psydac/fem/tests/data/decomp_spline_4_procs.png create mode 100644 psydac/fem/tests/test_tensor.py diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml index d8ff30b1c..c3c2da8a4 100644 --- a/.github/workflows/testing.yml +++ b/.github/workflows/testing.yml @@ -195,7 +195,7 @@ jobs: - name: Run coverage tests on macOS if: matrix.os == 'macos-14' working-directory: ./pytest - run: >- + run: >- python -m pytest -n auto --cov psydac --cov-config $GITHUB_WORKSPACE/pyproject.toml diff --git a/examples/poisson_2d_mapping.py b/examples/poisson_2d_mapping.py index 74fb620d3..79e84b843 100644 --- a/examples/poisson_2d_mapping.py +++ b/examples/poisson_2d_mapping.py @@ -781,7 +781,8 @@ def main(*, test_case, ncells, degree, nquads, ########## # Plot domain decomposition (master only) - V.plot_2d_decomposition(model.mapping, refine=N) + fig = V.plot_2d_decomposition(mapping, refine=N) + fig.show() # Perform other visualization using master or all processes if not distribute_viz: diff --git a/psydac/fem/tensor.py b/psydac/fem/tensor.py index 644f08cc4..9bc6678e4 100644 --- a/psydac/fem/tensor.py +++ b/psydac/fem/tensor.py @@ -1184,24 +1184,77 @@ def set_refined_space(self, ncells, new_space): self._refined_space[tuple(ncells)] = new_space # ... - def plot_2d_decomposition(self, mapping=None, refine=10): + def plot_2d_decomposition(self, mapping=None, *, refine=10, fig=None, ax=None, mpi_root=0): + """ + Plot decomposition of 2D TensorFemSpace w/ mapping to 2D physical space + + Plot the domain decomposition across MPI processes of a 2D + TensorFemSpace with a mapping between 2D logical and 2D physical spaces. + This function must be called collectively, and only the root process will make + the plot. On non-root processes the arguments `fig` and `ax` must be None. + + Parameters + ---------- + mapping : BasicCallableMapping + Mapping from (eta1, eta2) to (x1, x2). + + refine : int, default=10 + Cell refinement along the logical dimensions eta1 and eta2. + + fig : plt.Figure, optional + Figure where the plot should be made. Must be None on non-root processes. + ax : plt.Axes, optional + Axes where the plot should be made. Must be None on non-root processes. + + mpi_root: int, default=0 + The rank of the MPI root process which should create the plot. + + Returns + ------- + plt.Figure + Figure where the plot was made. Coincides with `fig` if provided. + """ import matplotlib.pyplot as plt from matplotlib.patches import Polygon, Patch + from sympde.topology.mapping import BasicCallableMapping from psydac.utilities.utils import refine_array_1d + # Sanity check + assert self.ldim == 2, "Function only works in 2D" + + # Check mapping if mapping is None: mapping = lambda eta: eta else: - assert mapping.ldim == self.ldim == 2 - assert mapping.pdim == self.ldim == 2 + assert isinstance(mapping, BasicCallableMapping) + assert mapping.ldim == 2, "Domain of argument `mapping` must be 2D" + assert mapping.pdim == 2, "Codomain of argument `mapping` must be 2D" - assert refine >= 1 - N = int(refine) - V1, V2 = self.spaces + # Check refine argument + assert isinstance(refine, int), f"Argument `refine` must be int, got {type(refine)} instead" + assert refine >= 1, f"Argument `refine` must be >= 1, got {refine} instead" + # Extract information about MPI communicator mpi_comm = self.coeff_space.cart.comm mpi_rank = mpi_comm.rank + mpi_size = mpi_comm.size + + # Check mpi_root argument + assert isinstance(mpi_root, int), f"Argument `mpi_root` must be int, got {type(mpi_root)} instead" + assert mpi_root >= 0, f"Argument `mpi_root` must be >= 0, got {mpi_root} instead" + assert mpi_root < mpi_size, f"Argument `mpi_root` must be smaller than communicator size ({mpi_size}), got {mpi_root} instead" + + # Check fig and ax arguments + if mpi_rank == mpi_root: + assert isinstance(fig, plt.Figure) or fig is None, f"Argument `fig` must be matplotlib Figure, got {type(fig)} instead" + assert isinstance(ax, plt.Axes) or ax is None, f"Argument `ax` must be matplotlib Axes, got {type(ax)} instead" + else: + assert fig is None, f"Argument `fig` must be None on non-root process with rank {mpi_rank}" + assert ax is None, f"Argument `ax` must be None on non-root process with rank {mpi_rank}" + + N = refine + V1, V2 = self.spaces # Local grid, refined [sk1, sk2], [ek1, ek2] = self.local_domain @@ -1218,23 +1271,62 @@ def plot_2d_decomposition(self, mapping=None, refine=10): poly = Polygon(xy, edgecolor='None') # Gather polygons on master process - polys = mpi_comm.gather(poly) + polys = mpi_comm.gather(poly, root=mpi_root) + + # Gather (s1, s2, e1, e2) on root + if mpi_rank == mpi_root: + s1_all = np.empty(mpi_size, dtype=int) + s2_all = np.empty(mpi_size, dtype=int) + e1_all = np.empty(mpi_size, dtype=int) + e2_all = np.empty(mpi_size, dtype=int) + else: + s1_all = None + s2_all = None + e1_all = None + e2_all = None + + mpi_comm.Gather(sk1 * N, s1_all, root=mpi_root) + mpi_comm.Gather(sk2 * N, s2_all, root=mpi_root) + mpi_comm.Gather((ek1 + 1) * N, e1_all, root=mpi_root) + mpi_comm.Gather((ek2 + 1) * N, e2_all, root=mpi_root) + + # Gather pcoords on root + # TODO: use Gatherv, and NumPy arrays as buffers + gathered_pcoords = mpi_comm.gather(pcoords, root=mpi_root) #------------------------------- # Non-master processes stop here - if mpi_rank != 0: + if mpi_rank != mpi_root: return #------------------------------- - # Global grid, refined - eta1 = refine_array_1d(V1.breaks, N) - eta2 = refine_array_1d(V2.breaks, N) - pcoords = np.array([[mapping(e1, e2) for e2 in eta2] for e1 in eta1]) - xx = pcoords[:, :, 0] - yy = pcoords[:, :, 1] + # Reconstruct global grid (refined) on root process + global_shape = ((V1.breaks.size - 1) * N + 1, + (V2.breaks.size - 1) * N + 1, + 2) + pcoords_global = np.empty(global_shape) + + for rank in range(mpi_comm.size): + s1 = s1_all[rank] + e1 = e1_all[rank] + s2 = s2_all[rank] + e2 = e2_all[rank] + pcoords_global[s1:e1+1, s2:e2+1, :] = gathered_pcoords[rank] + + xx = pcoords_global[:, :, 0] + yy = pcoords_global[:, :, 1] + + # If fig or ax are given, get one from the other. Otherwise create new ones + if fig and ax: + assert ax in fig.axes, "Argument `ax` must be in `fig.axes`" + elif fig: + ax = fig.gca() + elif ax: + fig = ax.figure + else: + fig, ax = plt.subplots(1, 1) # Plot decomposed domain - fig, ax = plt.subplots(1, 1) colors = itertools.cycle(plt.rcParams['axes.prop_cycle'].by_key()['color']) handles = [] for i, (poly, color) in enumerate(zip(polys, colors)): @@ -1253,7 +1345,8 @@ def plot_2d_decomposition(self, mapping=None, refine=10): ax.set_aspect('equal') ax.legend(handles=handles, bbox_to_anchor=(1.05, 1), loc=2) fig.tight_layout() - fig.show() + + return fig # ... def __str__(self): diff --git a/psydac/fem/tests/data/decomp_analytical_1_procs.png b/psydac/fem/tests/data/decomp_analytical_1_procs.png new file mode 100644 index 0000000000000000000000000000000000000000..f4066700f4b9d6fe9810766c17e86d2b867ddb97 GIT binary patch literal 56846 zcmb5WWmr~i)Ghjef`AetNQ;OPN(j7kiZn_JNTYOjry_!+goIK8ijvX|($do1-Q9KO 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za&iXxITKmBg|H?~DDSyUm4}uq{d{ufNgqm z<~V3$lZw*z5CV`$ z*tobVnDq9x1Ub5Zp`15hHuxEuv1ozdnL#A-8Xd5{^Yqjv_9;F&@~}VE*VmImic<&s zNa0@zC?PCBwrSR9MDqJ}{Snfw<6i;gx08%@3dVy(((kC0tVf{o{{h1Pd58bT6G-Cn Y8NKK&eB(4-!-FqF17rRBlv6?f0DGx9Hvj+t literal 0 HcmV?d00001 diff --git a/psydac/fem/tests/test_tensor.py b/psydac/fem/tests/test_tensor.py new file mode 100644 index 000000000..cc0dc8200 --- /dev/null +++ b/psydac/fem/tests/test_tensor.py @@ -0,0 +1,220 @@ +import os +import contextlib +from pathlib import Path + +import pytest +import numpy as np +import matplotlib as mpl +import matplotlib.pyplot as plt +from PIL import Image +from mpi4py import MPI + +from sympde.topology.domain import Square +from sympde.topology.space import ScalarFunctionSpace +from sympde.topology.analytical_mapping import TargetMapping + +from psydac.mapping.discrete_gallery import discrete_mapping +from psydac.api.discretization import discretize + + +#============================================================================== +# Machinery for comparing a PNG image with a reference on the root MPI process +#============================================================================== + +def similar_images(file1, file2, tolerance=0.01): + """ + Compare two PNG images and check if they are similar within tolerance. + + Parameters + ---------- + file1 : str + Path to first PNG file. + file2 : str + Path to second PNG file. + tolerance: float + Maximum allowed average difference between pixel values (0-1). + + Returns + ------- + bool : + True if images are similar enough, False otherwise. + """ + # Load images and convert to numpy arrays + img1 = np.array(Image.open(file1)).astype(float) + img2 = np.array(Image.open(file2)).astype(float) + + # Check dimensions match + if img1.shape != img2.shape: + return False + + # Normalize pixel values to 0-1 + img1 = img1 / 255.0 + img2 = img2 / 255.0 + + # Calculate mean absolute difference + diff = np.mean(np.abs(img1 - img2)) + + return diff <= tolerance + + +@contextlib.contextmanager +def consistent_png_rendering(): + """ + Context manager for consistent Matplotlib rendering across platforms. + """ + # Store original settings + orig_backend = mpl.get_backend() + orig_settings = { + 'text.usetex': mpl.rcParams['text.usetex'], + 'font.family': mpl.rcParams['font.family'], + } + + try: + # Use Agg backend (pure python, no GUI) + mpl.use('Agg') + # Configure settings for consistent rendering + mpl.rcParams.update({ + 'text.usetex': False, + 'font.family': 'DejaVu Sans', + }) + yield # Control returns to the with block + finally: + # Restore original settings + mpl.use(orig_backend) + mpl.rcParams.update(orig_settings) + + +def compare_figure_to_reference(fig, filename, *, dpi, tol, folder, comm, root): + """ + Compare a matplotlib figure to a reference PNG file on the root MPI process. + + Parameters + ---------- + fig : matplotlib.figure.Figure + The figure to compare with the reference image. + filename : str + Name of the PNG file to save and compare. + dpi : int + Dots per inch resolution for saving the figure. + tol : float + Tolerance for image comparison (between 0 and 1). + folder : str + Name of the folder containing reference images. + comm : mpi4py.MPI.Comm + MPI communicator object. + root : int + Rank of the MPI process that should perform the comparison. + + Returns + ------- + bool + True if the images are similar enough within the tolerance, + False otherwise. The result is broadcast to all MPI processes. + + Notes + ----- + The function saves the figure to a temporary file, compares it with + the reference image, and then removes the temporary file. Only the + root process performs the actual comparison, but the result is + broadcast to all processes. + """ + if comm.rank == root: + test_dir = Path(__file__).parent.absolute() + file1 = test_dir / filename + file2 = test_dir / folder / filename + with consistent_png_rendering(): + fig.savefig(file1, dpi=dpi) + close_enough = similar_images(file1, file2, tol) + # Clean up the temporary file + os.remove(file1) + else: + close_enough = None + + # Broadcast the boolean result from the root process to all others + close_enough = comm.bcast(close_enough, root=root) + + # All MPI processes return the same result + return close_enough + +#============================================================================== +# Unit tests +#============================================================================== +@pytest.mark.parallel +@pytest.mark.parametrize('root', ['first', 'last']) +@pytest.mark.parametrize('kind', ['spline', 'analytical']) +def test_plot_2d_decomposition(kind, root): + + # MPI communicator + mpi_comm = MPI.COMM_WORLD + mpi_size = mpi_comm.size + mpi_rank = mpi_comm.rank + + # MPI rank which should make the plot + if root == 'first': + mpi_root = 0 + elif root == 'last': + mpi_root = mpi_size - 1 + else: + raise ValueError(f'root argument has wrong value {root}') + + # Parameters of tensor-product 2D spline space + ncells = (6, 9) + degree = (2, 2) + + if kind == 'spline': + # 2D spline mapping and tensor FEM space (distributed) + F, Vh = discrete_mapping('target', ncells=ncells, degree=degree, + comm=mpi_comm, return_space=True) + elif kind == 'analytical': + Omega = Square('Omega', bounds1=(0, 1), bounds2=(0, 2 * np.pi)) + params = dict(c1=0, c2=0, k=0.3, D=0.2) + M = TargetMapping('M', dim=2, **params) + domain = M(Omega) + V = ScalarFunctionSpace('V', domain) + + # 2D Geometry object + domain_h = discretize(domain, ncells=ncells, periodic=(False, True), + comm=mpi_comm) + + # 2D spline tensor FEM space (distributed) + Vh = discretize(V, domain_h, degree=degree) + + # 2D callable mapping (analytical) + F = M.get_callable_mapping() + else: + raise ValueError(f'kind argument has wrong value {kind}') + + # Name of temporary image file to be compared with reference one + filename = f'decomp_{kind}_{mpi_size}_procs.png' + + # Relative tolerance for image comparison + RTOL = 0.02 + + # Plot 2D decomposition + # [1] Run without passing (fig, ax) + fig = Vh.plot_2d_decomposition(F, refine=5, mpi_root=mpi_root) + assert compare_figure_to_reference(fig, filename, folder='data', dpi=100, + tol=RTOL, comm=mpi_comm, root=mpi_root) + + # [2] Run with given (fig, ax), compatible + fig2, ax2 = plt.subplots(1, 1) if mpi_rank == mpi_root else (None, None) + Vh.plot_2d_decomposition(F, refine=5, fig=fig2, ax=ax2, mpi_root=mpi_root) + assert compare_figure_to_reference(fig2, filename, folder='data', dpi=100, + tol=RTOL, comm=mpi_comm, root=mpi_root) + + # [3] Run with given (fig, ax), incompatible + if mpi_rank == mpi_root: + fig3, ax3 = plt.subplots(1, 1) + with pytest.raises(AssertionError) as excinfo: + Vh.plot_2d_decomposition(F, refine=5, fig=fig2, ax=ax3, mpi_root=mpi_root) + assert "Argument `ax` must be in `fig.axes`" in str(excinfo.value) + plt.close(fig3) + else: + Vh.plot_2d_decomposition(F, refine=5, fig=None, ax=None, mpi_root=mpi_root) + +#============================================================================== +if __name__ == '__main__': + + test_plot_2d_decomposition('spline', 'first') + test_plot_2d_decomposition('analytical', 'last') + plt.show() diff --git a/pyproject.toml b/pyproject.toml index c20cf49d3..a8df91d59 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -60,6 +60,7 @@ test = [ "pytest-cov >= 5.0.0", 'pytest >= 4.5', 'pytest-xdist >= 1.16', + 'Pillow', # Python Imaging Library (PIL) fork ] [project.urls] @@ -76,7 +77,7 @@ exclude = ["*__psydac__*"] namespaces = false [tool.setuptools.package-data] -"*" = ["*.txt"] +"*" = ["*.txt", "**/tests/data/*.png"] [tool.coverage.run] branch = true From b6d4d5d3cb816b86252c327dcd4970451a717d64 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Thu, 30 Oct 2025 16:53:41 +0100 Subject: [PATCH 19/23] Describe library name in README.md (#535) Add a NOTE block with the meaning of the PSYDAC acronym, as well as its pronounciation. --- README.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/README.md b/README.md index d218c17cb..819214681 100644 --- a/README.md +++ b/README.md @@ -12,6 +12,10 @@ PSYDAC automatically generates Python code for the assembly of user-defined func This Python code is then accelerated to C/Fortran speed using [Pyccel](https://github.com/pyccel/pyccel). The library also enables large parallel computations on distributed-memory supercomputers using [MPI](https://en.wikipedia.org/wiki/Message_Passing_Interface) and [OpenMP](https://en.wikipedia.org/wiki/OpenMP). +> [!NOTE] +> The name PSYDAC stands for "Python Spline librarY for Differential equations with Automatic Code generation". +> It is pronounced like the famous Pokémon character, from which the developers draw inspiration for its psychic powers. + ## Citing If PSYDAC has been significant in your research, and you would like to acknowledge the project in your academic publication, we would ask that you cite the following paper: From c7ca428704c8f99a86882b6738ea146d9c7a394b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Fri, 7 Nov 2025 00:22:18 +0100 Subject: [PATCH 20/23] Fix parallelization bug in polar splines (#539) --- examples/poisson_2d_mapping.py | 5 +++-- psydac/polar/dense.py | 6 +++++- 2 files changed, 8 insertions(+), 3 deletions(-) diff --git a/examples/poisson_2d_mapping.py b/examples/poisson_2d_mapping.py index 79e84b843..cd69c2b47 100644 --- a/examples/poisson_2d_mapping.py +++ b/examples/poisson_2d_mapping.py @@ -780,9 +780,10 @@ def main(*, test_case, ncells, degree, nquads, N = 10 ########## - # Plot domain decomposition (master only) + # Plot domain decomposition (collective call, master creates a figure) fig = V.plot_2d_decomposition(mapping, refine=N) - fig.show() + if fig: + fig.show() # Perform other visualization using master or all processes if not distribute_viz: diff --git a/psydac/polar/dense.py b/psydac/polar/dense.py index 302e0a529..da26bedc0 100644 --- a/psydac/polar/dense.py +++ b/psydac/polar/dense.py @@ -3,6 +3,7 @@ # Copyright 2018 Yaman Güçlü import numpy as np +from mpi4py import MPI from scipy.sparse import coo_matrix from psydac.linalg.basic import VectorSpace, Vector, LinearOperator @@ -177,12 +178,15 @@ def inner(self, x, y): assert x.space is self assert y.space is self + # 1. Local dot product res = np.dot(x._data, y._data) V = self if V.parallel: - if V.radial_comm.rank == V.radial_root: + # 2. MPI_ALLREDUCE operation on the M-2 dimensional tensor subcomm. + if (V.tensor_comm != MPI.COMM_NULL) and (V.radial_comm.rank == V.radial_root): res = V.tensor_comm.allreduce(res) + # 3. MPI_BCAST operation on the 1D radial subcommunicator res = V.radial_comm.bcast(res, root=V.radial_root) return res From 153055f6c21bf5382ea6230d698a99037cc750e0 Mon Sep 17 00:00:00 2001 From: Stefan Possanner Date: Fri, 7 Nov 2025 07:59:54 +0100 Subject: [PATCH 21/23] change version to 2.6.0.dev0 --- pyproject.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pyproject.toml b/pyproject.toml index 5b460fb16..080d99941 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -4,7 +4,7 @@ build-backend = "setuptools.build_meta" [project] name = "psydac" -version = "2.5.0.dev0" +version = "2.6.0.dev0" description = "Python package for isogeometric analysis (IGA)" readme = "README.md" requires-python = ">= 3.10" From a4ca280d0288c6cfef844e24171dbdc486d914bc Mon Sep 17 00:00:00 2001 From: Stefan Possanner Date: Fri, 7 Nov 2025 08:44:33 +0100 Subject: [PATCH 22/23] remove test_tensor.py --- psydac/fem/tests/test_tensor.py | 220 -------------------------------- 1 file changed, 220 deletions(-) delete mode 100644 psydac/fem/tests/test_tensor.py diff --git a/psydac/fem/tests/test_tensor.py b/psydac/fem/tests/test_tensor.py deleted file mode 100644 index cc0dc8200..000000000 --- a/psydac/fem/tests/test_tensor.py +++ /dev/null @@ -1,220 +0,0 @@ -import os -import contextlib -from pathlib import Path - -import pytest -import numpy as np -import matplotlib as mpl -import matplotlib.pyplot as plt -from PIL import Image -from mpi4py import MPI - -from sympde.topology.domain import Square -from sympde.topology.space import ScalarFunctionSpace -from sympde.topology.analytical_mapping import TargetMapping - -from psydac.mapping.discrete_gallery import discrete_mapping -from psydac.api.discretization import discretize - - -#============================================================================== -# Machinery for comparing a PNG image with a reference on the root MPI process -#============================================================================== - -def similar_images(file1, file2, tolerance=0.01): - """ - Compare two PNG images and check if they are similar within tolerance. - - Parameters - ---------- - file1 : str - Path to first PNG file. - file2 : str - Path to second PNG file. - tolerance: float - Maximum allowed average difference between pixel values (0-1). - - Returns - ------- - bool : - True if images are similar enough, False otherwise. - """ - # Load images and convert to numpy arrays - img1 = np.array(Image.open(file1)).astype(float) - img2 = np.array(Image.open(file2)).astype(float) - - # Check dimensions match - if img1.shape != img2.shape: - return False - - # Normalize pixel values to 0-1 - img1 = img1 / 255.0 - img2 = img2 / 255.0 - - # Calculate mean absolute difference - diff = np.mean(np.abs(img1 - img2)) - - return diff <= tolerance - - -@contextlib.contextmanager -def consistent_png_rendering(): - """ - Context manager for consistent Matplotlib rendering across platforms. - """ - # Store original settings - orig_backend = mpl.get_backend() - orig_settings = { - 'text.usetex': mpl.rcParams['text.usetex'], - 'font.family': mpl.rcParams['font.family'], - } - - try: - # Use Agg backend (pure python, no GUI) - mpl.use('Agg') - # Configure settings for consistent rendering - mpl.rcParams.update({ - 'text.usetex': False, - 'font.family': 'DejaVu Sans', - }) - yield # Control returns to the with block - finally: - # Restore original settings - mpl.use(orig_backend) - mpl.rcParams.update(orig_settings) - - -def compare_figure_to_reference(fig, filename, *, dpi, tol, folder, comm, root): - """ - Compare a matplotlib figure to a reference PNG file on the root MPI process. - - Parameters - ---------- - fig : matplotlib.figure.Figure - The figure to compare with the reference image. - filename : str - Name of the PNG file to save and compare. - dpi : int - Dots per inch resolution for saving the figure. - tol : float - Tolerance for image comparison (between 0 and 1). - folder : str - Name of the folder containing reference images. - comm : mpi4py.MPI.Comm - MPI communicator object. - root : int - Rank of the MPI process that should perform the comparison. - - Returns - ------- - bool - True if the images are similar enough within the tolerance, - False otherwise. The result is broadcast to all MPI processes. - - Notes - ----- - The function saves the figure to a temporary file, compares it with - the reference image, and then removes the temporary file. Only the - root process performs the actual comparison, but the result is - broadcast to all processes. - """ - if comm.rank == root: - test_dir = Path(__file__).parent.absolute() - file1 = test_dir / filename - file2 = test_dir / folder / filename - with consistent_png_rendering(): - fig.savefig(file1, dpi=dpi) - close_enough = similar_images(file1, file2, tol) - # Clean up the temporary file - os.remove(file1) - else: - close_enough = None - - # Broadcast the boolean result from the root process to all others - close_enough = comm.bcast(close_enough, root=root) - - # All MPI processes return the same result - return close_enough - -#============================================================================== -# Unit tests -#============================================================================== -@pytest.mark.parallel -@pytest.mark.parametrize('root', ['first', 'last']) -@pytest.mark.parametrize('kind', ['spline', 'analytical']) -def test_plot_2d_decomposition(kind, root): - - # MPI communicator - mpi_comm = MPI.COMM_WORLD - mpi_size = mpi_comm.size - mpi_rank = mpi_comm.rank - - # MPI rank which should make the plot - if root == 'first': - mpi_root = 0 - elif root == 'last': - mpi_root = mpi_size - 1 - else: - raise ValueError(f'root argument has wrong value {root}') - - # Parameters of tensor-product 2D spline space - ncells = (6, 9) - degree = (2, 2) - - if kind == 'spline': - # 2D spline mapping and tensor FEM space (distributed) - F, Vh = discrete_mapping('target', ncells=ncells, degree=degree, - comm=mpi_comm, return_space=True) - elif kind == 'analytical': - Omega = Square('Omega', bounds1=(0, 1), bounds2=(0, 2 * np.pi)) - params = dict(c1=0, c2=0, k=0.3, D=0.2) - M = TargetMapping('M', dim=2, **params) - domain = M(Omega) - V = ScalarFunctionSpace('V', domain) - - # 2D Geometry object - domain_h = discretize(domain, ncells=ncells, periodic=(False, True), - comm=mpi_comm) - - # 2D spline tensor FEM space (distributed) - Vh = discretize(V, domain_h, degree=degree) - - # 2D callable mapping (analytical) - F = M.get_callable_mapping() - else: - raise ValueError(f'kind argument has wrong value {kind}') - - # Name of temporary image file to be compared with reference one - filename = f'decomp_{kind}_{mpi_size}_procs.png' - - # Relative tolerance for image comparison - RTOL = 0.02 - - # Plot 2D decomposition - # [1] Run without passing (fig, ax) - fig = Vh.plot_2d_decomposition(F, refine=5, mpi_root=mpi_root) - assert compare_figure_to_reference(fig, filename, folder='data', dpi=100, - tol=RTOL, comm=mpi_comm, root=mpi_root) - - # [2] Run with given (fig, ax), compatible - fig2, ax2 = plt.subplots(1, 1) if mpi_rank == mpi_root else (None, None) - Vh.plot_2d_decomposition(F, refine=5, fig=fig2, ax=ax2, mpi_root=mpi_root) - assert compare_figure_to_reference(fig2, filename, folder='data', dpi=100, - tol=RTOL, comm=mpi_comm, root=mpi_root) - - # [3] Run with given (fig, ax), incompatible - if mpi_rank == mpi_root: - fig3, ax3 = plt.subplots(1, 1) - with pytest.raises(AssertionError) as excinfo: - Vh.plot_2d_decomposition(F, refine=5, fig=fig2, ax=ax3, mpi_root=mpi_root) - assert "Argument `ax` must be in `fig.axes`" in str(excinfo.value) - plt.close(fig3) - else: - Vh.plot_2d_decomposition(F, refine=5, fig=None, ax=None, mpi_root=mpi_root) - -#============================================================================== -if __name__ == '__main__': - - test_plot_2d_decomposition('spline', 'first') - test_plot_2d_decomposition('analytical', 'last') - plt.show() From 750721a4343489638a530f13258672bd05931948 Mon Sep 17 00:00:00 2001 From: Stefan Possanner Date: Fri, 7 Nov 2025 16:50:03 +0100 Subject: [PATCH 23/23] install struohy from 108-psydac-change-renaming-of-globalpojector --- .github/workflows/test-struphy.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.github/workflows/test-struphy.yml b/.github/workflows/test-struphy.yml index 807fd0220..3fef4e200 100644 --- a/.github/workflows/test-struphy.yml +++ b/.github/workflows/test-struphy.yml @@ -58,6 +58,7 @@ jobs: echo "Psydac location for this branch" pip show psydac pip uninstall psydac -y + git checkout 108-psydac-change-renaming-of-globalpojector python -m pip install ".[phys]" --no-cache-dir echo "Psydac location after installing struphy" pip show psydac

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