From 9219ceb2deab6bec34a3e4c2ab4eea44470904cb Mon Sep 17 00:00:00 2001 From: herjy Date: Fri, 17 Mar 2017 17:16:49 +0100 Subject: [PATCH] working version --- Examples/Test_SLIT.py | 70 +-- Examples/Test_SLIT_HR.py | 152 +++++++ Examples/Test_SLIT_MCA.py | 202 +++------ Examples/Test_sparsity.py | 104 +++++ Examples/alphas.fits | Bin 164160 -> 0 bytes Files/Galaxy.fits | Bin 0 -> 83520 bytes Files/Noise_levels_SLIT.fits | Bin 0 -> 483840 bytes Files/Noise_levels_SLIT_HR.fits | Bin 0 -> 2243520 bytes Files/Noise_levels_SLIT_MCA.fits | Bin 0 -> 483840 bytes Files/Source_HR.fits | Bin 0 -> 325440 bytes Files/kappa.fits | Bin 0 -> 325440 bytes SLIT/Lens.py | 84 +--- SLIT/SLIT.py | 734 +++++++++++++++---------------- build/lib/SLIT/Lens.py | 84 +--- build/lib/SLIT/SLIT.py | 734 +++++++++++++++---------------- dist/SLIT-0.1-py2.7.egg | Bin 20634 -> 17472 bytes 16 files changed, 1076 insertions(+), 1088 deletions(-) create mode 100644 Examples/Test_SLIT_HR.py create mode 100644 Examples/Test_sparsity.py delete mode 100644 Examples/alphas.fits create mode 100644 Files/Galaxy.fits create mode 100644 Files/Noise_levels_SLIT.fits create mode 100644 Files/Noise_levels_SLIT_HR.fits create mode 100644 Files/Noise_levels_SLIT_MCA.fits create mode 100644 Files/Source_HR.fits create mode 100644 Files/kappa.fits diff --git a/Examples/Test_SLIT.py b/Examples/Test_SLIT.py index 34112e2..4c40004 100644 --- a/Examples/Test_SLIT.py +++ b/Examples/Test_SLIT.py @@ -9,6 +9,13 @@ import warnings warnings.simplefilter("ignore") +#Example of a run of the SLIT algorithm on simulated images. +#Here the first part of the file shows how simulations are generated. +#For users intereseted only in seeing the code run, have a look at the running SLIT section. +#The command line that builds the Fkappa operator is also of outmost importance. + + +###############################Simulation############################### def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): kappa = np.zeros((n1,n2)) x,y = np.where(kappa == 0) @@ -25,78 +32,77 @@ def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): count += 1 return kappa - +#Source light profile newsource = pf.open('../Files/source.fits')[0].data ##N1,N2 are the numbers of pixels in the image plane. nt1= 100 nt2 = 100 +#Size ratio of the source to image number of pixels size = 1 -na1 = nt1 -na2 = nt2 +#PSF +PSF0 = pf.open('../Files/PSF.fits')[0].data +PSF = PSF0[1:,1:] +PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) +PSFconj=PSFconj/np.sum(PSFconj) +PSF = PSF/np.sum(PSF) + ## Lens mass distribution. b = 1.53/0.05 xc = 0.95 q = 0.71 betata = 2.1 thetata = 25.2 - -kappa = SIE(na1/2.+50,na2/2.+50,na1+100,na2+100,b,betata,q,xc, thetata) -theta = SLIT.Lens.F(kappa, nt1,nt2, size,na1/2.,na2/2.) - -x00 =3744 -y00 =2028 - - -PSF0 = pf.open('../Files/PSF.fits')[0].data -PSF = PSF0[1:,1:] -PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) -PSFconj=PSFconj/np.sum(PSFconj) -PSF = PSF/np.sum(PSF) +kappa = SIE(nt1/2.+50,nt2/2.+50,nt1+100,nt2+100,b,betata,q,xc, thetata) +#Mapping between lens and source IMPORTANT +Fkappa = SLIT.Lens.F(kappa, nt1,nt2, size,nt1/2.,nt2/2.) -I2 = SLIT.Lens.source_to_image(newsource, nt1 ,nt2 , theta) -PSF0 = np.abs(PSF0/np.sum(PSF0)) -PSF = np.abs(PSF/np.sum(PSF)) +#Generation of lensed source +I2 = SLIT.Lens.source_to_image(newsource, nt1 ,nt2 , Fkappa) +#Noise levels SNR = 500 sigma = np.sqrt(np.sum(I2**2)/SNR/(nt1*nt2*size**2)) - -I3 = np.copy(I2) +#Convolution by the PSF and generation of the final image I2 = scp.fftconvolve(I2, PSF, mode = 'same') + +#Final simulated image Image = I2+np.random.randn(nt1,nt2)*sigma + +################################Running SLIT############################ +#Parameters kmax = 5 niter =50 -pos_real = 1 -pos_wave = 0 -weight = [0] +levels = [0] +#Comment the following to have the level estimation routine run (takes more time) +levels = pf.open('../Files/Noise_levels_SLIT.fits')[0].data + +#Start clock start = time.clock() -sourcesl, Imsl = SLIT.SLIT(Image, theta, kmax, niter, size, mymy = 0, - pos = pos_real, posit = pos_wave, decrease = 0, soft =1, - weight = weight, PSF = PSF, PSFconj = PSFconj) +#Running SLIT +sourcesl, Imsl = SLIT.SLIT(Image, Fkappa, kmax, niter, size, PSF, PSFconj, levels = levels) +#Stop clock elapsed = (time.clock()-start) - print('execution time:', elapsed, 'seconds') +#Reconstruction goodness real_source = newsource - source_error = np.sum(np.abs(real_source[np.where(real_source!=0)] -sourcesl[np.where(real_source!=0)])**2 /real_source[np.where(real_source!=0)]**2)/(np.size( np.where(real_source!=0))/2.) - - image_chi2 = np.std(Image-Imsl)**2/sigma**2 print('Residuals in source space', source_error) print('Residuals in image space',image_chi2) - +#Display of results for i in [1]: plt.figure(2) # plt.suptitle('FISTA: error per pixel on the source: '+str(source_error)+' image chi2:'+str(image_chi2)) diff --git a/Examples/Test_SLIT_HR.py b/Examples/Test_SLIT_HR.py new file mode 100644 index 0000000..4ee2e7b --- /dev/null +++ b/Examples/Test_SLIT_HR.py @@ -0,0 +1,152 @@ +import pyfits as pf +import matplotlib.pyplot as plt +import numpy as np +import matplotlib.cm as cm +from scipy import signal as scp +import SLIT +import time +from scipy import signal as scp +import warnings +warnings.simplefilter("ignore") + +#Example of a run of the SLIT algorithm on simulated images. +#Here the first part of the file shows how simulations are generated. +#For users intereseted only in seeing the code run, have a look at the running SLIT section. +#The command line that builds the Fkappa operator is also of outmost importance. + + +###############################Simulation############################### +def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): + kappa = np.zeros((n1,n2)) + x,y = np.where(kappa == 0) + eps = (1-q**2)/(1+q**2) + up = b**(beta-1) + pre = up/(2*(1-eps)**((beta-1)/2)) + count = 0 + theta = theta*np.pi/180. + for i in x: + Xr = (x[count]-x0)*np.cos(theta)-(y[count]-y0)*np.sin(theta) + Yr = (x[count]-x0)*np.sin(theta)+(y[count]-y0)*np.cos(theta) + kappa[x[count],y[count]] = pre/((xc**2.)/(1.-eps)+(Xr)**2.+((Yr)**2.)/q**2.)**((beta-1.)/2.) + + count += 1 + return kappa + +#Source light profile +newsource = pf.open('../Files/Source_HR.fits')[0].data +##N1,N2 are the numbers of pixels in the image plane. +nt1= 100 +nt2 = 100 +#Size ratio of the source to image number of pixels +size = 2 + +#PSF +PSF0 = pf.open('../Files/PSF.fits')[0].data +PSF = PSF0[1:,1:] +PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) +PSFconj=PSFconj/np.sum(PSFconj) +PSF = PSF/np.sum(PSF) + +## Lens mass distribution. +b = 1.53/0.05 +xc = 0.95 +q = 0.71 +betata = 2.1 +thetata = 25.2 +kappa = SIE(nt1/2.+50,nt2/2.+50,nt1+100,nt2+100,b,betata,q,xc, thetata) +#Mapping between lens and source IMPORTANT +Fkappa = SLIT.Lens.F(kappa, nt1,nt2, size,nt1/2.,nt2/2.) + + +#Generation of lensed source +I2 = SLIT.Lens.source_to_image(newsource, nt1 ,nt2 , Fkappa) + +#Noise levels +SNR = 500 +sigma = np.sqrt(np.sum(I2**2)/SNR/(nt1*nt2*size**2)) + +#Convolution by the PSF and generation of the final image +I2 = scp.fftconvolve(I2, PSF, mode = 'same') + +#Final simulated image +Image = I2+np.random.randn(nt1,nt2)*sigma + + +################################Running SLIT############################ +#Parameters +kmax = 5 +niter =50 +levels = [0] + +#Comment the following to have the level estimation routine run (takes more time) +levels = pf.open('../Files/Noise_levels_SLIT_HR.fits')[0].data + +#Start clock +start = time.clock() + +#Running SLIT +sourcesl, Imsl = SLIT.SLIT(Image, Fkappa, kmax, niter, size, PSF, PSFconj, levels = levels) + +#Stop clock +elapsed = (time.clock()-start) +print('execution time:', elapsed, 'seconds') + +#Reconstruction goodness +real_source = newsource +source_error = np.sum(np.abs(real_source[np.where(real_source!=0)] + -sourcesl[np.where(real_source!=0)])**2 + /real_source[np.where(real_source!=0)]**2)/(np.size( + np.where(real_source!=0))/2.) + +image_chi2 = np.std(Image-Imsl)**2/sigma**2 +print('Residuals in source space', source_error) +print('Residuals in image space',image_chi2) + +#Display of results +for i in [1]: + plt.figure(2) + # plt.suptitle('FISTA: error per pixel on the source: '+str(source_error)+' image chi2:'+str(image_chi2)) + # plt.subplot(2,3,1) + plt.title('Source from SLIT') + plt.imshow((sourcesl), vmin = np.min(real_source), vmax = np.max(real_source),cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() +# plt.subplot(2,3,2) + plt.figure(3) + plt.title('Original source') + plt.imshow(real_source, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,3) + plt.figure(4) + plt.title('Lensed source') + plt.imshow(Image, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + plt.figure(41) + plt.title('Reconstructed lensed source') + plt.imshow(Imsl, vmin = np.min(Image), vmax = np.max(Image), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,4) + plt.figure(5) + plt.title('relative difference') + diff = (real_source-sourcesl)/real_source + diff[np.where(real_source==0)] = 0 + diff[np.where(diff>1)]= np.log(0.) + plt.imshow(np.abs(diff), vmax = 1., vmin = 0., cmap = cm.gist_stern, interpolation = 'nearest' ) + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,5) + plt.figure(6) + plt.title('difference with reconstructed lensed image') + plt.imshow(Image-Imsl, vmin = -5*sigma, vmax = 5*sigma, cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() + # plt.subplot(2,3,6) + plt.figure(7) + plt.title('difference with true source') + plt.imshow((np.abs(real_source-sourcesl)), cmap = cm.gist_stern, interpolation = 'nearest') + plt.axis('off') + plt.colorbar() +plt.show() diff --git a/Examples/Test_SLIT_MCA.py b/Examples/Test_SLIT_MCA.py index 7ed074a..879fa38 100644 --- a/Examples/Test_SLIT_MCA.py +++ b/Examples/Test_SLIT_MCA.py @@ -1,18 +1,22 @@ - -import Lens_better as Lens +from SLIT import Lens import pyfits as pf import matplotlib.pyplot as plt import numpy as np import matplotlib.cm as cm from scipy import signal as scp -import gaussian as gs import SLIT as slit import time from scipy import signal as scp import warnings warnings.simplefilter("ignore") +#Example of a run of the SLIT_MCA algorithm on simulated images. +#Here the first part of the file shows how simulations are generated. +#For users intereseted only in seeing the code run, have a look at the running SLIT_MCA section. +#The command line that builds the Fkappa operator is also of outmost importance. + +###############################Simulation############################### def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): kappa = np.zeros((n1,n2)) x,y = np.where(kappa == 0) @@ -29,141 +33,73 @@ def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): count += 1 return kappa - -real_source = pf.open('/Users/remy/Desktop/These/MuSCADeT/HFF/Abell2744/Colour_images_recombined.fits')[0].data#pf.open('imp_lens.fits')[0].data +#Source light profile +newsource = pf.open('../Files/source.fits')[0].data ##N1,N2 are the numbers of pixels in the image plane. nt1= 100 nt2 = 100 +#Size ratio of the source to image number of pixels +size = 1 -na1 = nt1 -na2 = nt2 +#PSF +PSF0 = pf.open('../Files/PSF.fits')[0].data +PSF = PSF0[1:,1:] +PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) +PSFconj=PSFconj/np.sum(PSFconj) +PSF = PSF/np.sum(PSF) + ## Lens mass distribution. b = 1.53/0.05 xc = 0.95 q = 0.71 betata = 2.1 thetata = 25.2 +kappa = SIE(nt1/2.+50,nt2/2.+50,nt1+100,nt2+100,b,betata,q,xc, thetata) +#Mapping between lens and source IMPORTANT +Fkappa = slit.Lens.F(kappa, nt1,nt2, size,nt1/2.,nt2/2.) -gal0 = real_source[0,2871-nt1/2:2871+nt1/2,1878-nt2/2:1878+nt2/2]#gs.sersic(nt1,nt2,nt1/2.,nt2/2.,2,0.08,0.1,0.2,1) - -gal2 = gs.gaussian(nt1,nt2,nt1/2.+3,3-nt2/2.,4,0.05,0.12,0) - - - -#gal0[-3:,-3:] = 0 -#gal2[-3:,-3:]=0 -extra = 100 -kappa = SIE(na1/2.+extra/2.,na2/2.+extra/2.,na1+extra,na2+extra,b,betata,q,xc, thetata) -#kappa2 = SIE(na1/2.+extra/2.,na2/2.+extra/2.,na1+extra,na2+extra,b+0.1,betata,q,xc, thetata) -#kappa = barkana(na1/2.,na2/2.,na1,na2,b,betata,q,thetata) - -hdus = pf.PrimaryHDU(kappa) -lists = pf.HDUList([hdus]) -lists.writeto('kappa.fits', clobber=True) - -x00 =3743+1#4843-35 -y00 =2030-2#6420+15 -size = 1 -newsource =real_source[0,x00-nt1*size/2.:x00+nt1*size/2.,y00-nt2*size/2.:y00+nt2*size/2.] -s = wine.MCA.MAD(newsource) -newsource,c = wine.MCA.mr_filter(newsource, 20,5, s, lvl = 5) -gal0,c = wine.MCA.mr_filter(gal0, 20,7, s, lvl = 5) -gal0 = (gal0-np.min(gal0))*4 -newsource = newsource-np.min(newsource) - - - -plt.imshow(gal0, cmap = cm.gist_stern, interpolation = 'nearest') -plt.axis('off') -plt.title('Lens galaxy') -plt.colorbar(); plt.show() - -start = time.clock() -theta = Lens.F(kappa, nt1,nt2, size,na1/2.,na2/2.) -#theta2 = Lens.F(kappa2, nt1,nt2, size,na1/2.,na2/2.) -elapsed = (time.clock()-start) - - -npsf1 = 65. -npsf2 = 65. -PSF0 = pf.open('PSF.fits')[0].data#('HST_1430/psf1.fits')[0].data## -PSF = PSF0[1:,1:] -PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF0[:-1,:-1])))) -PSFconj=PSFconj/np.sum(PSFconj) -PSF = PSF/np.sum(PSF) - - -##PSF0 = gs.gaussian(npsf1,npsf2,33.,33.,1.,0.95,0.95,0) -##PSF = gs.gaussian(npsf1,npsf2,32.,32.,1.,0.95,0.95,0) -##PSF[npsf2-1,npsf1-2] = 0 -##PSF0[npsf2-1,npsf1-2] = 0 +#Lens galaxy light profile +gal0 = pf.open('../Files/Galaxy.fits')[0].data +#Generation of lensed source +I2 = slit.Lens.source_to_image(newsource, nt1 ,nt2 , Fkappa) -xt,yt = np.where(np.zeros((nt1,nt2))==0) -I2 = Lens.source_to_image(newsource, nt1 ,nt2 , theta) -PSF0 = np.abs(PSF0/np.sum(PSF0)) -PSF = np.abs(PSF/np.sum(PSF)) - -##PSFconj = np.real(np.fft.ifft2(np.conjugate(np.fft.fft2(PSF)))) - - -I3 = np.copy(I2) -I2 = scp.fftconvolve(I2, PSF, mode = 'same') +#Noise levels SNR = 500 sigma = np.sqrt(np.sum(I2**2)/SNR/(nt1*nt2*size**2)) -gal = np.copy(gal0) -gal = scp.fftconvolve(gal, PSF, mode = 'same') - -Image = I2+gal+np.random.randn(nt1,nt2)*sigma - -plt.imshow(Image, cmap = cm.gist_stern, interpolation = 'nearest') -plt.title('Lens system') -plt.axis('off') -plt.colorbar() -plt.show() - -plt.imshow(newsource, cmap = cm.gist_stern, interpolation = 'nearest') -plt.title('Background source') -plt.axis('off') -plt.colorbar() -plt.show() +#Convolution by the PSF and generation of the final image +I2 = scp.fftconvolve(I2, PSF, mode = 'same') -plt.imshow(kappa, cmap = cm.gist_stern, interpolation = 'nearest') -plt.title('surface mass density') -plt.axis('off') -plt.colorbar() -plt.show() +#Convolution of the observed image +simu = scp.fftconvolve(gal0.astype(float)+I2, PSF.astype(float), mode = 'same') +#Sotring the convolved lens light profile: +gal = scp.fftconvolve(gal0.astype(float), PSF.astype(float), mode = 'same') +#Final simulated image +Image = simu+np.random.randn(nt1,nt2)*sigma +################################Running SLIT############################ +#Parameters kmax = 5 -niter =500 -kinter = 6 -ninter = 1 -pos_real = 1 -pos_wave = 0 -weight = 1 -#PSF=[0,0] -riter =200 - -FB = 0 -soft = 1 -repeat = 1 -PD = 0 +niter =100 +riter =50 +levels = [0] +#Comment the following to have the level estimation routine run (takes more time) +levels = pf.open('../Files/Noise_levels_SLIT_MCA.fits')[0].data + +#Start clock start = time.clock() -sourcesl, Imsl, G = slit.SLIT_old(Image, theta, kmax, niter,riter, kinter, ninter, size, - pos = pos_real, posit = pos_wave, decrease = 1, soft =soft, FB = FB, - reweighting = weight, Ginit =0, PSF = PSF, PSFconj = PSFconj, repeat = repeat, mrfilter = PD) +#Running SLIT_MCA +sourcesl, Imsl, G = slit.SLIT_MCA(Image, Fkappa, kmax, niter,riter, size,PSF, PSFconj, levels = levels) +#Stop clock elapsed = (time.clock()-start) - print('execution time:', elapsed, 'seconds') -source = sourcesl -Im=Imsl real_source = newsource @@ -172,105 +108,83 @@ def SIE(x0,y0,n1,n2,b,beta,q,xc,theta): /real_source[np.where(real_source!=0)]**2)/(np.size( np.where(real_source!=0))/2.) -GSF = np.copy(G) - - image_chi2 = np.std(Image-Imsl-G)**2/sigma**2 print('Residuals in source space', source_error) print('Residuals in image space',image_chi2) -hdus = pf.PrimaryHDU(sourcesl) -lists = pf.HDUList([hdus]) -lists.writeto('Souce.fits', clobber=True) - -hdus = pf.PrimaryHDU(G) -lists = pf.HDUList([hdus]) -lists.writeto('Galaxy_SLIT.fits', clobber=True) - - -hdus = pf.PrimaryHDU(real_source-source) -lists = pf.HDUList([hdus]) -lists.writeto('Diff.fits', clobber=True) - for i in [1]: ###Source - # plt.suptitle('FISTA: error per pixel on the source: '+str(source_error)+' image chi2:'+str(image_chi2)) -# plt.subplot(4,3,2) + plt.figure(0) plt.title('Source from SLIT') plt.imshow((sourcesl), vmin = np.min(real_source), vmax = np.max(real_source), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,1) + plt.figure(1) plt.title('Original image of the source') plt.imshow(real_source, cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,3) + plt.figure(2) plt.title('relative difference') - diff = (real_source-sourcesl)#/real_source - # diff[np.where(real_source==0)] = 0 -# diff[np.where(diff>1)]= np.log(0.) + diff = (real_source-sourcesl) plt.imshow((np.abs(diff)), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() ####Lensed source - # plt.subplot(4,3,4) plt.figure(3) plt.title('Original lensed galaxy') plt.imshow(I2, cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,5) + plt.figure(4) plt.title('reconstructed lensed source') plt.imshow((Imsl), vmin = np.min(I2), vmax = np.max(I2), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,6) + plt.figure(5) plt.title('error on the source in image plane') plt.imshow((I2-Imsl), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() ###Galaxy - # plt.subplot(4,3,7) plt.figure(6) plt.title('Original galaxy') plt.imshow((gal0), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,8) + plt.figure(12) plt.title('Estimated Galaxy') plt.imshow((G), vmin = np.min(gal0), vmax = np.max(gal0), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,9) + plt.figure(7) plt.title('Error on the galaxy') plt.imshow((gal-G), cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() ###Image - # plt.subplot(4,3,10) plt.figure(8) plt.title('Image') plt.imshow(Image, cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,11) + plt.figure(9) plt.title('Reconstructed image') - plt.imshow(Imsl+GSF, cmap = cm.gist_stern, interpolation = 'nearest') + plt.imshow(Imsl+G, cmap = cm.gist_stern, interpolation = 'nearest') plt.axis('off') plt.colorbar() - # plt.subplot(4,3,12) + plt.figure(10) plt.title('difference with reconstructed image') - plt.imshow(Image-Imsl-GSF,cmap = cm.gist_stern, interpolation = 'nearest', vmin = -5*sigma, vmax = 5*sigma)#slit.fft_convolve(Im,PSF) + plt.imshow(Image-Imsl-G,cmap = cm.gist_stern, interpolation = 'nearest', vmin = -5*sigma, vmax = 5*sigma)#slit.fft_convolve(Im,PSF) plt.axis('off') plt.colorbar() diff --git a/Examples/Test_sparsity.py b/Examples/Test_sparsity.py new file mode 100644 index 0000000..7284ff6 --- /dev/null +++ b/Examples/Test_sparsity.py @@ -0,0 +1,104 @@ +from SLIT import Lens +import pyfits as pf +import matplotlib.pyplot as plt +import numpy as np +import matplotlib.cm as cm +from scipy import signal as scp +from SLIT import wave_transform as mw +import time +from scipy import signal as scp +import SLIT as slit +from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes +from mpl_toolkits.axes_grid1.inset_locator import mark_inset +import warnings +warnings.simplefilter("ignore") + + + +S = pf.open('../Files/source.fits')[0].data +G = pf.open('../Files/Galaxy.fits')[0].data +##Sizes in image and source planes +nt1= 100 +nt2 = 100 +size = 1 + +#Mass profile of the lens +kappa = pf.open('../Files/kappa.fits')[0].data +Fkappa = Lens.F(kappa, nt1,nt2, size,nt1/2.,nt2/2.) +lensed = slit.lens_one(Fkappa, nt1,nt2, size) + +#Starlet transforms of the lens and source in their respective planes +wG = mw.wave_transform(G, lvl = 6) +wS = mw.wave_transform(S, lvl = 6) +#Lensed source +FS = Lens.source_to_image(S, nt1, nt2,Fkappa) +#Unlensed lens +FG = Lens.image_to_source(G, size, Fkappa, lensed=lensed) +#Starlet transform of the unlensed lens +wFG = mw.wave_transform(FG, 6) +#Starlet transform of the lensed +wFS = mw.wave_transform(FS, 6) + +def mk_sort(X): + Y = np.sort(np.resize(np.abs(X), X.size)) + return Y[::-1] + +#Function that computes the reconstruction error from the p% highest coefficients +def error_rec_from(X, p, wave = 0): + Xcopy = np.copy(X) + Y = mk_sort(X) + + ymin = Y[p*Y.size/1000.] + Xcopy[np.abs(X)N$UJ#*CTE%r)2d`~7S`SBHfzPPP=vEXsfQ zSxPaXcn1gh1&3@3rGy1j<~uBPrG$og1^IY|`22_GlZUJwmby5s_>b%HOvPk9uaFS0 z?GzucFfU5j_RYTkd6ob5sPo(v4zA?xe|&!;vR=^EP3wF^D8YXJ_sRjAe1k#*f`dZ; z*CPMhZ~t>W!GBy&z~}#OPyB!R>;GI&`2X>GqW`!ag+l(%|LKqIilw&B^Zp;!Tl#;x z8in#d7yCbd*?(X0-yQhx4*Yiq{<{PJ-GTq^z<+n(|2I2;X>9@3TAT(bOh40-KPmsmpQ}*wDU+LK?+o=7QorJH0va}D?Ey!^p=q?k@{Y1T zwB(`})@=@hR@e0!dyg;BzVrOC>&Cy(N%t;yJT@M>L9f(HKHh?!_1=lqj_aYXayead zQ5y6=CXDu~`+%}4)Bo1d4p8oN_c$KC394aC?it$a#l zP3Zuw%I(s$NH-YJSj!V1FN48elW$)ao`yk}oBiUXouJ!q_ZWOE1A4)ZK({{=z?dkS zH2Ql67(P2zo+x?(2I#yJOGhxZ#)$+j_rToJ#{Rk86U_Sum~8q7u(a+!+Iu4%tU#~A zBgeOZRiS;PR^1zh(&b&pd&upAKYX$7Zx|jv7dW`|C=8!Oo-Qv-fRWs69~Zl)Fq(VW 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