DArray: Add SVD algorithm

[jpsamaroo]

Written by Claude Opus and Sonnet

[github-actions]

Dagger benchmarks: dirty vs master

	master	dirty	master / dirty
array/dagger/N=1024 (block 512)/add (X + X)	8.7 ± 0.22 ms	8.94 ± 1.6 ms	0.974 ± 0.17
array/dagger/N=1024 (block 512)/alloc (rand)	3.5 ± 0.45 ms	3.26 ± 0.65 ms	1.07 ± 0.26
array/dagger/N=1024 (block 512)/broadcast (X .+ 1)	6.7 ± 1 ms	6.16 ± 0.38 ms	1.09 ± 0.18
array/dagger/N=1024 (block 512)/map (sin.(X))	8.99 ± 1.1 ms	8.62 ± 1.5 ms	1.04 ± 0.23
array/dagger/N=1024 (block 512)/norm	3.46 ± 0.17 ms	3.41 ± 0.16 ms	1.01 ± 0.067
array/dagger/N=1024 (block 512)/reduce (sum)	7.63 ± 1.3 ms	6.49 ± 0.42 ms	1.18 ± 0.21
array/dagger/N=1024 (block 512)/transpose (permutedims)	5.59 ± 0.76 ms	5.57 ± 0.12 ms	1 ± 0.14
array/dagger/N=256 (block 256)/add (X + X)	2.98 ± 0.19 ms	3.05 ± 0.2 ms	0.976 ± 0.09
array/dagger/N=256 (block 256)/alloc (rand)	1.2 ± 0.067 ms	1.24 ± 0.026 ms	0.969 ± 0.058
array/dagger/N=256 (block 256)/broadcast (X .+ 1)	2.71 ± 0.33 ms	3.48 ± 2.5 ms	0.779 ± 0.56
array/dagger/N=256 (block 256)/map (sin.(X))	3.03 ± 0.21 ms	3.13 ± 0.28 ms	0.967 ± 0.11
array/dagger/N=256 (block 256)/norm	1.94 ± 0.21 ms	1.92 ± 0.14 ms	1.01 ± 0.13
array/dagger/N=256 (block 256)/reduce (sum)	4.7 ± 1.4 ms	3.54 ± 0.35 ms	1.33 ± 0.42
array/dagger/N=256 (block 256)/transpose (permutedims)	2.32 ± 0.27 ms	2.38 ± 0.19 ms	0.975 ± 0.14
linalg/dagger/N=1024 (block 512)/cholesky	0.0339 ± 0.0063 s	26.5 ± 3.8 ms	1.28 ± 0.3
linalg/dagger/N=1024 (block 512)/lu	6.54 s	6.6 s	0.991
linalg/dagger/N=1024 (block 512)/matmul (A*A)	0.0338 ± 0.00076 s	0.0412 ± 0.0055 s	0.82 ± 0.11
linalg/dagger/N=1024 (block 512)/matvec (A*x)	8.12 ± 0.62 ms	8.44 ± 1.1 ms	0.962 ± 0.15
linalg/dagger/N=1024 (block 512)/qr	0.209 ± 0.0042 s	0.224 ± 0.0092 s	0.934 ± 0.043
linalg/dagger/N=1024 (block 512)/solve (A\b via lu)	9.46 s	9.31 s	1.02
linalg/dagger/N=1024 (block 512)/syrk (A'*A)	31.6 ± 29 ms	0.0339 ± 0.0026 s	0.932 ± 0.86
linalg/dagger/N=256 (block 256)/cholesky	6.05 ± 0.11 ms	6.15 ± 1.8 ms	0.983 ± 0.29
linalg/dagger/N=256 (block 256)/lu	1.16 ± 0.0095 s	1.14 ± 0.028 s	1.01 ± 0.026
linalg/dagger/N=256 (block 256)/matmul (A*A)	3.84 ± 0.079 ms	3.66 ± 0.24 ms	1.05 ± 0.072
linalg/dagger/N=256 (block 256)/matvec (A*x)	3.04 ± 0.06 ms	3.08 ± 0.16 ms	0.987 ± 0.054
linalg/dagger/N=256 (block 256)/qr	8.77 ± 0.53 ms	8.53 ± 0.9 ms	1.03 ± 0.13
linalg/dagger/N=256 (block 256)/solve (A\b via lu)	1.92 ± 0.011 s	1.94 ± 0.015 s	0.989 ± 0.0095
linalg/dagger/N=256 (block 256)/syrk (A'*A)	5.88 ± 0.15 ms	5.6 ± 0.47 ms	1.05 ± 0.092
stencil/dagger/N=1024 (block 512)/alloc (neighbors Wrap)	0.0756 ± 0.015 s	0.047 ± 0.0015 s	1.61 ± 0.31
stencil/dagger/N=1024 (block 512)/assign (const)	3.47 ± 0.036 ms	3.6 ± 0.22 ms	0.963 ± 0.059
stencil/dagger/N=1024 (block 512)/multi-expr	9.8 ± 0.34 ms	8.96 ± 0.29 ms	1.09 ± 0.052
stencil/dagger/N=1024 (block 512)/neighbors (Clamp)	0.0756 ± 0.012 s	0.0467 ± 0.0016 s	1.62 ± 0.27
stencil/dagger/N=1024 (block 512)/neighbors (Pad)	0.0727 ± 0.014 s	0.0749 ± 0.018 s	0.971 ± 0.3
stencil/dagger/N=1024 (block 512)/neighbors (Reflect)	0.041 ± 0.0058 s	0.0444 ± 0.0047 s	0.925 ± 0.16
stencil/dagger/N=1024 (block 512)/neighbors (Wrap)	0.047 ± 0.0017 s	0.0439 ± 0.0069 s	1.07 ± 0.17
stencil/dagger/N=1024 (block 512)/update (+)	6.39 ± 0.38 ms	5.89 ± 0.35 ms	1.08 ± 0.091
stencil/dagger/N=256 (block 256)/alloc (neighbors Wrap)	13.9 ± 0.41 ms	12.5 ± 0.7 ms	1.11 ± 0.07
stencil/dagger/N=256 (block 256)/assign (const)	2.54 ± 0.28 ms	2.35 ± 0.058 ms	1.08 ± 0.12
stencil/dagger/N=256 (block 256)/multi-expr	4.34 ± 0.061 ms	4.66 ± 0.33 ms	0.931 ± 0.067
stencil/dagger/N=256 (block 256)/neighbors (Clamp)	13.5 ± 0.66 ms	12.1 ± 0.19 ms	1.11 ± 0.057
stencil/dagger/N=256 (block 256)/neighbors (Pad)	13.5 ± 0.37 ms	13.3 ± 0.63 ms	1.02 ± 0.056
stencil/dagger/N=256 (block 256)/neighbors (Reflect)	12.1 ± 0.84 ms	13.1 ± 1.8 ms	0.924 ± 0.14
stencil/dagger/N=256 (block 256)/neighbors (Wrap)	12.5 ± 1.4 ms	11.9 ± 1.9 ms	1.05 ± 0.2
stencil/dagger/N=256 (block 256)/update (+)	2.54 ± 0.57 ms	2.75 ± 0.2 ms	0.925 ± 0.22
time_to_load	0.896 ± 0.006 s	0.893 ± 0.018 s	1 ± 0.022

Plots

⚠️ Regressions (> 25.0%)

• array/dagger/N=256 (block 256)/broadcast (X .+ 1): +28.4%

Improvements (> 25.0% faster)

• stencil/dagger/N=1024 (block 512)/neighbors (Clamp): -38.3%
• stencil/dagger/N=1024 (block 512)/alloc (neighbors Wrap): -37.8%

Full results and plots (download the benchmark-results artifact).