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Merged
ilyamandel merged 3 commits into from
Aug 20, 2026
+29 −10
Merged

2-detector selection effects in Matlab post-processing #1483

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1a9b00a
Integrator partial changes
Jul 6, 2026
65e2393
Changing detection probability calculation to use two detectors
Aug 10, 2026
1df89e5
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Aug 10, 2026
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39 changes: 29 additions & 10 deletions compas_matlab_utils/CosmicHistoryIntegrator.m
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Original file line number Diff line number Diff line change
Expand Up @@ -331,37 +331,56 @@
Fplus=1/2*(1+costh.^2).*cos(2*phi).*cos(2*psi)-costh.*sin(2*phi).*sin(2*psi);
Fcross=1/2*(1+costh.^2).*cos(2*phi).*sin(2*psi)+costh.*sin(2*phi).*cos(2*psi);
Theta=1/2*sqrt(Fplus.^2.*(1+cosiota.^2).^2+4*Fcross.^2.*cosiota.^2);
Thetas=sort(Theta);

alpha=13.6*pi/180; %angle between z axes, https://labcit.ligo.caltech.edu/~ajw/bursts/protect/T030215cor.pdf
alpha=20*pi/180;
cosalpha=cos(alpha); sinalpha=sin(alpha);
costh2=costh*cosalpha-sinth*sinalpha;
phi2=phi+2*alpha;
psi2=psi+2*alpha;
%the transformations below are very approximate
Fplus2=1/2*(1+costh2.^2).*cos(2*phi2).*cos(2*psi2)-costh2.*sin(2*phi2).*sin(2*psi2);
Fcross2=1/2*(1+costh2.^2).*cos(2*phi2).*sin(2*psi2)+costh2.*sin(2*phi2).*cos(2*psi2);
Theta2=1/2*sqrt(Fplus2.^2.*(1+cosiota.^2).^2+4*Fcross2.^2.*cosiota.^2);

Thetas=sort(sqrt(Theta.^2+Theta2.^2));


%save time by not doing calculations beyond maximum redshifted total
%mass corresponding to detection redshift threshold
Mtzlistdetection=1:1:ceil(max(Mtlist)*(1+max(zlistdetection)));
%the masses are probably too discrete; consider relative discretisation
%of mass and redshift grids for smooth detection curves, or maybe move
%masses to a uniform-in-log grid?
SNRat1Mpc=zeros(length(Mtzlistdetection),length(etalist));
for(i=1:length(Mtzlistdetection)),
for(j=1:length(etalist)),
[h,Am,psi]=IMRSAWaveform(f, Mtzlistdetection(i), etalist(j), 0, 0, 0, 1, flow);
integral=sum(4*Am.^2./Sf*df);
integral=sum(4*Am.*conj(Am)./Sf*df);
SNRat1Mpc(i,j)=sqrt(integral);
end;
end;

SNR=zeros(length(zlistdetection),length(Mtlist),length(etalist));
%optimal SNR for face-on, overhead source
SNRopt=zeros(length(zlistdetection),length(Mtlist),length(etalist));

for(i=1:length(zlistdetection)),
for(j=1:length(Mtlist)),
SNR(i,j,:)=SNRat1Mpc(ceil(Mtlist(j)*(zlistdetection(i)+1)),:)./Dl(i);
SNRopt(i,j,:)=SNRat1Mpc(ceil(Mtlist(j)*(zlistdetection(i)+1)),:)./Dl(i);
end;
end;

SNR8pre=1:0.01:100;
theta=1./SNR8pre;
pdetect=1-interp1([0,Thetas,1],[(0:Ntheta)/Ntheta,1],theta);
pdetect(1)=0; %set of measure zero to exceed threshold, but enforce just in case
%Compute detection probability as a function of the ratio of SNRopt to SNRthreshold
SNRratio=0.01:0.01:100; %for convenience, no chance of detection below 1/max(Thetas)~1/sqrt(2)
%find indices of first values larger than SNRthreshold/SNRopt in Thetas
idx=discretize(1./SNRratio, Thetas);
pdetect=1-idx/Ntheta;
pdetect(isnan(pdetect))=0;

SNR8=SNR/8;
SNRtothreshold=SNRopt/8; %should really be 10 for network,
% but 8 matches Reed's calculations more closely according to Michael Fulgoni
pdetection=zeros(length(zlistdetection),length(Mtlist),length(etalist));
pdetection=pdetect(max(min(floor((SNR8-1)*100),length(pdetect)),1));
pdetection=pdetect(max(min(ceil(SNRtothreshold*100),length(pdetect)),1));
end %end of DetectionProbability

%Make a set of default plots
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