def compare_subsampled(S,
s,
ps,
psf,
pixpsf,
Gmine,
v,
w,
gal_sigma,
psf_sigma,
cd,
get_ffts=False,
eval_psf=integrate_gaussian):
print()
print('Subsample', s)
print()
step = 1. / s
sz = s * (S - 1) + 1
#x = np.arange(0, S, step)[:sz+1]
x = np.arange(0, S, step)[:sz]
#y = np.arange(0, S, step)[:sz+1]
# Create pixelized PSF (Gaussian)
sx = x - 0.5 + step / 2.
subpixpsf = eval_psf(psf, sx, sx)
binned = bin_image(subpixpsf, s)
bh, bw = binned.shape
pixpsf1 = pixpsf[:bh, :bw]
ph, pw = pixpsf.shape
binned = binned[:ph, :pw]
print('Binned PSF:')
measure(binned)
print('Pix PSF:')
measure(pixpsf)
# Recompute my convolution using the binned PSF
P, FG, Gmine, v, w = galaxy_psf_convolution(gal_sigma,
0.,
0.,
GaussianGalaxy,
cd,
0.,
0.,
binned,
debug=True)
xx, yy = np.meshgrid(x, x)
# plt.clf()
#
# plt.subplot(2,2,1)
# dimshow(subpixpsf)
# plt.title('subpix psf')
# plt.colorbar()
#
# plt.subplot(2,2,2)
# dimshow(binned)
# plt.title('binned subpix psf')
# plt.colorbar()
#
# plt.subplot(2,2,3)
# dimshow(pixpsf1)
# plt.title('pix psf')
# plt.colorbar()
#
# plt.subplot(2,2,4)
# dimshow(pixpsf1 - binned)
# plt.title('pix - binned')
# plt.colorbar()
# plt.suptitle('subsample %i' % s)
# ps.savefig()
# Create pixelized galaxy image
#gxx,gyy = xx + step/2., yy + step/2.
gxx, gyy = xx, yy
#gxx,gyy = xx - step, yy - step
#gxx,gyy = xx - step/2., yy - step/2.
center = S / 2
subpixgal = np.exp(-0.5 * ((gxx - center)**2 + (gyy - center)**2) /
gal_sigma**2)
sh, sw = subpixpsf.shape
subpixgal = subpixgal[:sh, :sw]
print('Subpix psf, gal', subpixpsf.shape, subpixgal.shape)
print('Subpix PSF:')
measure(subpixpsf)
print('Subpix gal:')
measure(subpixgal)
# FFT convolution
Fpsf = np.fft.rfft2(subpixpsf)
spg = np.fft.ifftshift(subpixgal)
# plt.clf()
# for i in range(len(w)):
# plt.plot(v, Fpsf[i,:], 'c-')
# for i in range(len(v)):
# plt.plot(w, Fpsf[:,i], 'm-')
# plt.title('PSF Fourier transform')
# ps.savefig()
#
# IV = np.argsort(v)
# IW = np.argsort(w)
# plt.clf()
# for i in range(len(w)):
# plt.plot(v[IV], np.abs(Fpsf[i,IV]), 'c-')
# for i in range(len(v)):
# plt.plot(w[IW], np.abs(Fpsf[IW,i]), 'm-')
# plt.title('abs PSF Fourier transform')
# ps.savefig()
#
# plt.yscale('log')
# ps.savefig()
# plt.clf()
# dimshow(spg)
# plt.title('spg')
# ps.savefig()
Fgal = np.fft.rfft2(spg)
if get_ffts:
return Fpsf, Fgal
Fconv = Fpsf * Fgal
subpixfft = np.fft.irfft2(Fconv, s=subpixpsf.shape)
print('Shapes:', 'subpixpsf', subpixpsf.shape, 'Fpsf', Fpsf.shape)
print('spg', spg.shape, 'Fgal', Fgal.shape, 'Fconv', Fconv.shape,
'subpixfft', subpixfft.shape)
print('Subpix conv', subpixfft.shape)
binned = bin_image(subpixfft, s)
binned /= np.sum(binned)
print('Binned', binned.shape)
print('Mine:', Gmine.shape)
print('Mine:')
measure(Gmine)
print('Binned subpix FFT:')
measure(binned)
mh, mw = Gmine.shape
binned = binned[:mh, :mw]
plt.clf()
plt.subplot(2, 3, 1)
dimshow(subpixpsf)
plt.title('subpix psf')
plt.colorbar()
plt.subplot(2, 3, 2)
dimshow(subpixgal)
plt.title('subpix galaxy')
plt.colorbar()
plt.subplot(2, 3, 3)
dimshow(subpixfft)
plt.title('subpix FFT conv')
plt.colorbar()
plt.subplot(2, 3, 4)
dimshow(np.log10(np.maximum(binned / np.max(binned), 1e-12)))
plt.title('log binned FFT conv')
plt.colorbar()
plt.subplot(2, 3, 5)
dimshow(np.log10(np.maximum(Gmine / np.max(Gmine), 1e-12)))
#dimshow(Gmine)
plt.title('log my conv')
plt.colorbar()
gh, gw = Gmine.shape
binned = binned[:gh, :gw]
bh, bw = binned.shape
Gmine = Gmine[:bh, :bw]
diff = Gmine - binned
plt.subplot(2, 3, 6)
dimshow(diff)
plt.title('mine - FFT')
plt.colorbar()
plt.suptitle('PSF %g, Gal %g, subsample %i' % (psf_sigma, gal_sigma, s))
ps.savefig()
rmsdiff = np.sqrt(np.mean(diff**2))
return rmsdiff
plt.colorbar()
plt.title('subpix Gal real')
plt.subplot(2, 4, 8)
dimshow(Fsubgal.imag)
plt.colorbar()
plt.title('subpix Gal imag')
ps.savefig()
pixconv = np.fft.irfft2(Fpsf * Fgal, s=pixpsf.shape)
subpixconv = np.fft.irfft2(Fsub * Fsubgal, s=subpixpsf.shape)
# my convolution
pixscale = 1.
cd = pixscale * np.eye(2) / 3600.
Gmine = galaxy_psf_convolution(gal_re, 0., 0., gal, cd, 0., 0., pixpsf)
pixconv /= np.sum(pixconv)
subpixconv /= np.sum(subpixconv)
subpixconv *= scale**2
Gmine /= np.sum(Gmine)
plt.clf()
plt.subplot(1, 3, 1)
plt.imshow(pixconv, interpolation='nearest', origin='lower')
plt.subplot(1, 3, 2)
plt.imshow(subpixconv, interpolation='nearest', origin='lower')
plt.subplot(1, 3, 3)
plt.imshow(Gmine, interpolation='nearest', origin='lower')
ps.savefig()
def main():
ps = PlotSequence('conv')
S = 51
center = S / 2
print('Center', center)
#for psf_sigma in [2., 1.5, 1.]:
for psf_sigma in [2.]:
rms2 = []
x = np.arange(S)
y = np.arange(S)
xx, yy = np.meshgrid(x, y)
scale = 1.5 / psf_sigma
pixpsf = render_airy((scale, center), x, y)
psf = (scale, center)
eval_psf = render_airy
plt.clf()
plt.subplot(2, 1, 1)
plt.plot(x, pixpsf[center, :], 'b-')
plt.plot(x, pixpsf[:, center], 'r-')
plt.subplot(2, 1, 2)
plt.plot(x, np.maximum(1e-16, pixpsf[center, :]), 'b-')
plt.plot(x, np.maximum(1e-16, pixpsf[:, center]), 'r-')
plt.yscale('log')
ps.savefig()
plt.clf()
plt.imshow(pixpsf, interpolation='nearest', origin='lower')
ps.savefig()
plt.clf()
plt.imshow(np.log10(np.maximum(1e-16, pixpsf)),
interpolation='nearest',
origin='lower')
plt.colorbar()
plt.title('log PSF')
ps.savefig()
# psf
#psf = scipy.stats.norm(loc=center + 0.5, scale=psf_sigma)
# plt.clf()
# plt.imshow(Pcdf, interpolation='nearest', origin='lower')
# ps.savefig()
# #Pcdf = psf.cdf(xx) * psf.cdf(yy)
# #pixpsf = integrate_gaussian(psf, xx, yy)
#
# padpsf = np.zeros((S*2-1, S*2-1))
# ph,pw = pixpsf.shape
# padpsf[S/2:S/2+ph, S/2:S/2+pw] = pixpsf
# Fpsf = np.fft.rfft2(padpsf)
#
# padh,padw = padpsf.shape
# v = np.fft.rfftfreq(padw)
# w = np.fft.fftfreq(padh)
# fmax = max(max(np.abs(v)), max(np.abs(w)))
# cut = fmax / 2. * 1.000001
# #print('Frequence cut:', cut)
# Ffiltpsf = Fpsf.copy()
# #print('Ffiltpsf', Ffiltpsf.shape)
# #print((np.abs(w) < cut).shape)
# #print((np.abs(v) < cut).shape)
# Ffiltpsf[np.abs(w) > cut, :] = 0.
# Ffiltpsf[:, np.abs(v) > cut] = 0.
# #print('pad v', v)
# #print('pad w', w)
#
# filtpsf = np.fft.irfft2(Ffiltpsf, s=(padh,padw))
#
# print('filtered PSF real', np.max(np.abs(filtpsf.real)))
# print('filtered PSF imag', np.max(np.abs(filtpsf.imag)))
#
# plt.clf()
# plt.subplot(2,3,1)
# dimshow(Fpsf.real)
# plt.colorbar()
# plt.title('Padded PSF real')
# plt.subplot(2,3,4)
# dimshow(Fpsf.imag)
# plt.colorbar()
# plt.title('Padded PSF imag')
#
# plt.subplot(2,3,2)
# dimshow(Ffiltpsf.real)
# plt.colorbar()
# plt.title('Filt PSF real')
# plt.subplot(2,3,5)
# dimshow(Ffiltpsf.imag)
# plt.colorbar()
# plt.title('Filt PSF imag')
#
# plt.subplot(2,3,3)
# dimshow(filtpsf.real)
# plt.title('PSF real')
# plt.colorbar()
#
# plt.subplot(2,3,6)
# dimshow(filtpsf.imag)
# plt.title('PSF imag')
# plt.colorbar()
#
# ps.savefig()
#
#
# pixpsf = filtpsf
gal_sigmas = [2, 1, 0.5, 0.25]
for gal_sigma in gal_sigmas:
# plt.clf()
# plt.imshow(Gcdf, interpolation='nearest', origin='lower')
# plt.savefig('dcdf.png')
# plt.clf()
# plt.imshow(np.exp(-0.5 * ((xx-center)**2 + (yy-center)**2)/2.**2),
# interpolation='nearest', origin='lower')
# plt.savefig('g.png')
# my convolution
pixscale = 1.
cd = pixscale * np.eye(2) / 3600.
P, FG, Gmine, v, w = galaxy_psf_convolution(gal_sigma,
0.,
0.,
GaussianGalaxy,
cd,
0.,
0.,
pixpsf,
debug=True)
#print('v:', v)
#print('w:', w)
#print('P:', P.shape)
print()
print('PSF %g, Gal %g' % (psf_sigma, gal_sigma))
rmax = np.argmax(np.abs(w))
cmax = np.argmax(np.abs(v))
l2_rmax = np.sqrt(np.sum(P[rmax, :].real**2 + P[rmax, :].imag**2))
l2_cmax = np.sqrt(np.sum(P[:, cmax].real**2 + P[:, cmax].imag**2))
print('PSF L_2 in highest-frequency rows & cols:', l2_rmax,
l2_cmax)
l2_rmax = np.sqrt(np.sum(FG[rmax, :].real**2 +
FG[rmax, :].imag**2))
l2_cmax = np.sqrt(np.sum(FG[:, cmax].real**2 +
FG[:, cmax].imag**2))
print('Gal L_2 in highest-frequency rows & cols:', l2_rmax,
l2_cmax)
C = P * FG
l2_rmax = np.sqrt(np.sum(C[rmax, :].real**2 + C[rmax, :].imag**2))
l2_cmax = np.sqrt(np.sum(C[:, cmax].real**2 + C[:, cmax].imag**2))
print('PSF*Gal L_2 in highest-frequency rows & cols:', l2_rmax,
l2_cmax)
print()
Fpsf, Fgal = compare_subsampled(S,
1,
ps,
psf,
pixpsf,
Gmine,
v,
w,
gal_sigma,
psf_sigma,
cd,
get_ffts=True,
eval_psf=eval_psf)
plt.clf()
plt.subplot(2, 4, 1)
dimshow(P.real)
plt.colorbar()
plt.title('PSF real')
plt.subplot(2, 4, 5)
dimshow(P.imag)
plt.colorbar()
plt.title('PSF imag')
plt.subplot(2, 4, 2)
dimshow(FG.real)
plt.colorbar()
plt.title('Gal real')
plt.subplot(2, 4, 6)
dimshow(FG.imag)
plt.colorbar()
plt.title('Gal imag')
plt.subplot(2, 4, 3)
dimshow((P * FG).real)
plt.colorbar()
plt.title('P*Gal real')
plt.subplot(2, 4, 7)
dimshow((P * FG).imag)
plt.colorbar()
plt.title('P*Gal imag')
plt.subplot(2, 4, 4)
dimshow((Fgal).real)
plt.colorbar()
plt.title('pixGal real')
plt.subplot(2, 4, 8)
dimshow((Fgal).imag)
plt.colorbar()
plt.title('pixGal imag')
plt.suptitle('PSF %g, Gal %g' % (psf_sigma, gal_sigma))
ps.savefig()
subsample = [1, 2, 4]
rms1 = []
for s in subsample:
rms = compare_subsampled(S,
s,
ps,
psf,
pixpsf,
Gmine,
v,
w,
gal_sigma,
psf_sigma,
cd,
eval_psf=eval_psf)
rms1.append(rms)
rms2.append(rms1)
print()
print('PSF sigma =', psf_sigma)
print('RMSes:')
for rms1, gal_sigma in zip(rms2, gal_sigmas):
print('Gal sigma', gal_sigma, 'rms:',
', '.join(['%.3g' % r for r in rms1]))
def compare(ph, pw, psf_sigma, gal_sigma, ps, subsample):
pixscale = 1.
cd = pixscale * np.eye(2) / 3600.
cx,cy = pw/2, ph/2
xx,yy = np.meshgrid(np.arange(pw), np.arange(ph))
# Create pixelized PSF (Gaussian)
pixpsf = np.exp(-0.5 * ((xx-cx)**2 + (yy-cy)**2) / psf_sigma**2)
plt.clf()
plt.imshow(pixpsf, interpolation='nearest', origin='lower', cmap='gray')
plt.title('PSF')
plt.colorbar()
ps.savefig()
#Gmine = galaxy_psf_convolution(gal_sigma, 0., 0., GaussianGalaxy, cd,
# 0., 0., pixpsf)
P,FG,Gmine,v,w = galaxy_psf_convolution(gal_sigma, 0., 0., GaussianGalaxy,
cd, 0., 0., pixpsf, debug=True)
Gmine /= Gmine.sum()
plt.clf()
plt.imshow(Gmine, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Mine')
plt.colorbar()
ps.savefig()
print('Mine:')
measure(Gmine)
# Create pixelized PSF (x) Gaussian
gal_psf_sigma = np.hypot(psf_sigma, gal_sigma)
Gana = np.exp(-0.5 * ((xx-cx)**2 + (yy-cy)**2) / gal_psf_sigma**2)
Gana /= Gana.sum()
print('Pixelized, analytic:')
measure(Gana)
gal = galsim.Gaussian(flux=1., sigma=gal_sigma)
psf = galsim.Gaussian(flux=1., sigma=psf_sigma)
final = galsim.Convolve([gal, psf])
print('Final:', final)
image = galsim.ImageF(pw,ph)
final.drawImage(image, offset=(0.5, 0.5), scale=pixscale, method='sb')
Ggs = image.array
Ggs /= Ggs.sum()
print('Galsim shifted:')
measure(Ggs)
plt.clf()
plt.imshow(Ggs, interpolation='nearest', origin='lower', cmap='gray')
plt.title('GalSim analytic')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Ggs - Gana, 'GalSim Analytic - Analytic')
plt.colorbar()
ps.savefig()
plt.clf()
plt.imshow(Gana, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Analytic')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gmine - Gana, 'Mine - Analytic')
plt.colorbar()
ps.savefig()
r = np.hypot(xx - cx, yy - cy)
plt.clf()
plt.subplot(2,1,1)
plt.loglog(r.ravel(), Gmine.ravel(), 'b.')
plt.loglog(r.ravel(), Gana.ravel(), 'g.')
plt.ylim(1e-20, 1.)
plt.ylabel('mine(b) analytic(g)')
plt.subplot(2,1,2)
plt.plot(r.ravel(), (Gmine-Gana).ravel(), 'r.')
plt.ylabel('mine - analytic')
plt.xlabel('radius (pix)')
ps.savefig()
plt.clf()
plt.subplot(1,2,1)
plt.imshow(np.log10(np.maximum(Gana, 1e-16)),
interpolation='nearest', origin='lower', cmap='gray')
plt.title('Log Analytic')
plt.colorbar()
plt.subplot(1,2,2)
plt.imshow(np.log10(np.maximum(Gmine, 1e-16)),
interpolation='nearest', origin='lower', cmap='gray')
plt.title('Log Mine')
plt.colorbar()
ps.savefig()
# Create pixelized galaxy
gx,gy = cx,cy
pixgal = np.exp(-0.5 * ((xx-gx)**2 + (yy-gy)**2) / gal_sigma**2)
pixgal /= np.sum(pixgal)
# FFT convolution
Fpsf = np.fft.rfft2(pixpsf)
print('Fpsf:', Fpsf.shape, Fpsf.dtype)
spg = np.fft.ifftshift(pixgal)
Fgal = np.fft.rfft2(spg)
#Fgal = np.fft.rfft2(pixgal)
print('Fgal:', Fgal.shape, Fgal.dtype)
plt.clf()
plt.subplot(1,2,1)
plt.imshow(Fpsf.real, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('Fpsf.real')
plt.subplot(1,2,2)
plt.imshow(Fpsf.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('Fpsf.imag')
ps.savefig()
print('P:', P.shape, P.dtype)
plt.clf()
plt.subplot(1,2,1)
plt.imshow(P.real, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('P.real')
plt.subplot(1,2,2)
plt.imshow(P.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('P.imag')
ps.savefig()
psf2 = np.fft.irfft2(Fpsf)
plt.clf()
plt.imshow(psf2 - pixpsf, interpolation='nearest', origin='lower', cmap='gray')
plt.title('ifft(fft(psf)) - psf')
plt.colorbar()
ps.savefig()
plt.clf()
plt.subplot(1,2,1)
plt.imshow(Fgal.real, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fgal.real [%.2g,%.2g]' % (Fgal.real.min(), Fgal.real.max()))
plt.colorbar()
plt.subplot(1,2,2)
plt.imshow(Fgal.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fgal.imag [%.2g,%.2g]' % (Fgal.imag.min(), Fgal.imag.max()))
plt.colorbar()
ps.savefig()
print('FG:', FG.shape, FG.dtype)
plt.clf()
plt.subplot(1,2,1)
plt.imshow(FG.real, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('FG.real [%.2g,%.2g]' % (FG.real.min(), FG.real.max()))
plt.subplot(1,2,2)
plt.imshow(FG.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('FG.imag [%.2g,%.2g]' % (FG.imag.min(), FG.imag.max()))
ps.savefig()
Fconv = Fpsf * Fgal
plt.clf()
plt.subplot(1,2,1)
plt.imshow(Fconv.real, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fconv.real')
plt.colorbar()
plt.subplot(1,2,2)
plt.imshow(Fconv.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fconv.imag')
plt.colorbar()
ps.savefig()
Fconvmine = P * FG
plt.clf()
plt.subplot(1,2,1)
plt.imshow(Fconvmine.real, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fconvmine.real')
plt.colorbar()
plt.subplot(1,2,2)
plt.imshow(Fconvmine.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fconvmine.imag')
plt.colorbar()
ps.savefig()
Fgal.imag[:,:] = 0.
Gfft = np.fft.irfft2(Fpsf * Fgal)
#Gfft = np.fft.ifftshift(Gfft)
print('Gfft:', Gfft.shape, Gfft.dtype)
Gfft /= Gfft.sum()
print('Pixelized (fft):')
measure(Gfft)
plt.clf()
plt.imshow(Gfft, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Pixelized convolution')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gfft - Gana, 'Pixelized - Analytic')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gmine - Gfft, 'Mine - Pixelized')
plt.colorbar()
ps.savefig()
for s in subsample:
step = 1./s
#xx,yy = np.meshgrid(-step/2. + np.arange(0, pw, step),
# -step/2. + np.arange(0, ph, step))
xx,yy = np.meshgrid(-0.5 + step/2. + np.arange(0, pw, step),
-0.5 + step/2. + np.arange(0, ph, step))
# Create pixelized PSF (Gaussian)
#pixpsf = np.exp(-0.5 * ((xx-cx)**2 + (yy-cy)**2) / psf_sigma**2)
subpixpsf = np.repeat(np.repeat(pixpsf, s, axis=0), s, axis=1)
gxx,gyy = np.meshgrid(np.arange(0, pw*s),
np.arange(0, ph*s))
gx,gy = pw*s/2, ph*s/2
pixgal = np.exp(-0.5 * ((gxx-gx)**2 + (gyy-gy)**2) / (gal_sigma*s)**2)
#gx,gy = cx - step/2., cy - step/2.
#pixgal = np.exp(-0.5 * ((xx-gx)**2 + (yy-gy)**2) / gal_sigma**2)
# FFT convolution
Fpsf = np.fft.rfft2(subpixpsf)
print('Fpsf:', Fpsf.shape, Fpsf.dtype)
Fgal = np.fft.rfft2(pixgal)
print('Fgal:', Fgal.shape, Fgal.dtype)
Gfft = np.fft.irfft2(Fpsf * Fgal)
Gfft = np.fft.ifftshift(Gfft)
print('Gfft:', Gfft.shape, Gfft.dtype)
Gfft /= Gfft.sum()
print('Subsampled, pixelized:')
measure(Gfft)
plt.clf()
plt.imshow(Gfft, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Subsampled convolution')
plt.colorbar()
ps.savefig()
# Bin down s x s
Gbin = np.zeros((ph, pw))
for i in range(s):
for j in range(s):
Gbin += Gfft[i::s, j::s]
Gfft = Gbin
Gfft /= Gfft.sum()
print('Subsampled, pixelized:')
measure(Gfft)
plt.clf()
plt.imshow(Gfft, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Subsampled & binned convolution')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gfft - Gana, 'Sub-Pixelized - Analytic')
plt.colorbar()
ps.savefig()
def compare(ph, pw, psf_sigma, gal_sigma, ps, subsample):
pixscale = 1.
cd = pixscale * np.eye(2) / 3600.
cx, cy = pw / 2, ph / 2
xx, yy = np.meshgrid(np.arange(pw), np.arange(ph))
# Create pixelized PSF (Gaussian)
pixpsf = np.exp(-0.5 * ((xx - cx)**2 + (yy - cy)**2) / psf_sigma**2)
plt.clf()
plt.imshow(pixpsf, interpolation='nearest', origin='lower', cmap='gray')
plt.title('PSF')
plt.colorbar()
ps.savefig()
#Gmine = galaxy_psf_convolution(gal_sigma, 0., 0., GaussianGalaxy, cd,
# 0., 0., pixpsf)
P, FG, Gmine, v, w = galaxy_psf_convolution(gal_sigma,
0.,
0.,
GaussianGalaxy,
cd,
0.,
0.,
pixpsf,
debug=True)
Gmine /= Gmine.sum()
plt.clf()
plt.imshow(Gmine, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Mine')
plt.colorbar()
ps.savefig()
print('Mine:')
measure(Gmine)
# Create pixelized PSF (x) Gaussian
gal_psf_sigma = np.hypot(psf_sigma, gal_sigma)
Gana = np.exp(-0.5 * ((xx - cx)**2 + (yy - cy)**2) / gal_psf_sigma**2)
Gana /= Gana.sum()
print('Pixelized, analytic:')
measure(Gana)
gal = galsim.Gaussian(flux=1., sigma=gal_sigma)
psf = galsim.Gaussian(flux=1., sigma=psf_sigma)
final = galsim.Convolve([gal, psf])
print('Final:', final)
image = galsim.ImageF(pw, ph)
final.drawImage(image, offset=(0.5, 0.5), scale=pixscale, method='sb')
Ggs = image.array
Ggs /= Ggs.sum()
print('Galsim shifted:')
measure(Ggs)
plt.clf()
plt.imshow(Ggs, interpolation='nearest', origin='lower', cmap='gray')
plt.title('GalSim analytic')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Ggs - Gana, 'GalSim Analytic - Analytic')
plt.colorbar()
ps.savefig()
plt.clf()
plt.imshow(Gana, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Analytic')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gmine - Gana, 'Mine - Analytic')
plt.colorbar()
ps.savefig()
r = np.hypot(xx - cx, yy - cy)
plt.clf()
plt.subplot(2, 1, 1)
plt.loglog(r.ravel(), Gmine.ravel(), 'b.')
plt.loglog(r.ravel(), Gana.ravel(), 'g.')
plt.ylim(1e-20, 1.)
plt.ylabel('mine(b) analytic(g)')
plt.subplot(2, 1, 2)
plt.plot(r.ravel(), (Gmine - Gana).ravel(), 'r.')
plt.ylabel('mine - analytic')
plt.xlabel('radius (pix)')
ps.savefig()
plt.clf()
plt.subplot(1, 2, 1)
plt.imshow(np.log10(np.maximum(Gana, 1e-16)),
interpolation='nearest',
origin='lower',
cmap='gray')
plt.title('Log Analytic')
plt.colorbar()
plt.subplot(1, 2, 2)
plt.imshow(np.log10(np.maximum(Gmine, 1e-16)),
interpolation='nearest',
origin='lower',
cmap='gray')
plt.title('Log Mine')
plt.colorbar()
ps.savefig()
# Create pixelized galaxy
gx, gy = cx, cy
pixgal = np.exp(-0.5 * ((xx - gx)**2 + (yy - gy)**2) / gal_sigma**2)
pixgal /= np.sum(pixgal)
# FFT convolution
Fpsf = np.fft.rfft2(pixpsf)
print('Fpsf:', Fpsf.shape, Fpsf.dtype)
spg = np.fft.ifftshift(pixgal)
Fgal = np.fft.rfft2(spg)
#Fgal = np.fft.rfft2(pixgal)
print('Fgal:', Fgal.shape, Fgal.dtype)
plt.clf()
plt.subplot(1, 2, 1)
plt.imshow(Fpsf.real, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('Fpsf.real')
plt.subplot(1, 2, 2)
plt.imshow(Fpsf.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('Fpsf.imag')
ps.savefig()
print('P:', P.shape, P.dtype)
plt.clf()
plt.subplot(1, 2, 1)
plt.imshow(P.real, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('P.real')
plt.subplot(1, 2, 2)
plt.imshow(P.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('P.imag')
ps.savefig()
psf2 = np.fft.irfft2(Fpsf)
plt.clf()
plt.imshow(psf2 - pixpsf,
interpolation='nearest',
origin='lower',
cmap='gray')
plt.title('ifft(fft(psf)) - psf')
plt.colorbar()
ps.savefig()
plt.clf()
plt.subplot(1, 2, 1)
plt.imshow(Fgal.real, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fgal.real [%.2g,%.2g]' % (Fgal.real.min(), Fgal.real.max()))
plt.colorbar()
plt.subplot(1, 2, 2)
plt.imshow(Fgal.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Fgal.imag [%.2g,%.2g]' % (Fgal.imag.min(), Fgal.imag.max()))
plt.colorbar()
ps.savefig()
print('FG:', FG.shape, FG.dtype)
plt.clf()
plt.subplot(1, 2, 1)
plt.imshow(FG.real, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('FG.real [%.2g,%.2g]' % (FG.real.min(), FG.real.max()))
plt.subplot(1, 2, 2)
plt.imshow(FG.imag, interpolation='nearest', origin='lower', cmap='gray')
plt.colorbar()
plt.title('FG.imag [%.2g,%.2g]' % (FG.imag.min(), FG.imag.max()))
ps.savefig()
Fconv = Fpsf * Fgal
plt.clf()
plt.subplot(1, 2, 1)
plt.imshow(Fconv.real,
interpolation='nearest',
origin='lower',
cmap='gray')
plt.title('Fconv.real')
plt.colorbar()
plt.subplot(1, 2, 2)
plt.imshow(Fconv.imag,
interpolation='nearest',
origin='lower',
cmap='gray')
plt.title('Fconv.imag')
plt.colorbar()
ps.savefig()
Fconvmine = P * FG
plt.clf()
plt.subplot(1, 2, 1)
plt.imshow(Fconvmine.real,
interpolation='nearest',
origin='lower',
cmap='gray')
plt.title('Fconvmine.real')
plt.colorbar()
plt.subplot(1, 2, 2)
plt.imshow(Fconvmine.imag,
interpolation='nearest',
origin='lower',
cmap='gray')
plt.title('Fconvmine.imag')
plt.colorbar()
ps.savefig()
Fgal.imag[:, :] = 0.
Gfft = np.fft.irfft2(Fpsf * Fgal)
#Gfft = np.fft.ifftshift(Gfft)
print('Gfft:', Gfft.shape, Gfft.dtype)
Gfft /= Gfft.sum()
print('Pixelized (fft):')
measure(Gfft)
plt.clf()
plt.imshow(Gfft, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Pixelized convolution')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gfft - Gana, 'Pixelized - Analytic')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gmine - Gfft, 'Mine - Pixelized')
plt.colorbar()
ps.savefig()
for s in subsample:
step = 1. / s
#xx,yy = np.meshgrid(-step/2. + np.arange(0, pw, step),
# -step/2. + np.arange(0, ph, step))
xx, yy = np.meshgrid(-0.5 + step / 2. + np.arange(0, pw, step),
-0.5 + step / 2. + np.arange(0, ph, step))
# Create pixelized PSF (Gaussian)
#pixpsf = np.exp(-0.5 * ((xx-cx)**2 + (yy-cy)**2) / psf_sigma**2)
subpixpsf = np.repeat(np.repeat(pixpsf, s, axis=0), s, axis=1)
gxx, gyy = np.meshgrid(np.arange(0, pw * s), np.arange(0, ph * s))
gx, gy = pw * s / 2, ph * s / 2
pixgal = np.exp(-0.5 * ((gxx - gx)**2 + (gyy - gy)**2) /
(gal_sigma * s)**2)
#gx,gy = cx - step/2., cy - step/2.
#pixgal = np.exp(-0.5 * ((xx-gx)**2 + (yy-gy)**2) / gal_sigma**2)
# FFT convolution
Fpsf = np.fft.rfft2(subpixpsf)
print('Fpsf:', Fpsf.shape, Fpsf.dtype)
Fgal = np.fft.rfft2(pixgal)
print('Fgal:', Fgal.shape, Fgal.dtype)
Gfft = np.fft.irfft2(Fpsf * Fgal)
Gfft = np.fft.ifftshift(Gfft)
print('Gfft:', Gfft.shape, Gfft.dtype)
Gfft /= Gfft.sum()
print('Subsampled, pixelized:')
measure(Gfft)
plt.clf()
plt.imshow(Gfft, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Subsampled convolution')
plt.colorbar()
ps.savefig()
# Bin down s x s
Gbin = np.zeros((ph, pw))
for i in range(s):
for j in range(s):
Gbin += Gfft[i::s, j::s]
Gfft = Gbin
Gfft /= Gfft.sum()
print('Subsampled, pixelized:')
measure(Gfft)
plt.clf()
plt.imshow(Gfft, interpolation='nearest', origin='lower', cmap='gray')
plt.title('Subsampled & binned convolution')
plt.colorbar()
ps.savefig()
plt.clf()
imshow_diff(Gfft - Gana, 'Sub-Pixelized - Analytic')
plt.colorbar()
ps.savefig()
def compare_subsampled(S, s, ps, psf, pixpsf, Gmine,v,w, gal_sigma, psf_sigma,
cd,
get_ffts=False, eval_psf=integrate_gaussian):
print()
print('Subsample', s)
print()
step = 1./s
sz = s * (S-1) + 1
#x = np.arange(0, S, step)[:sz+1]
x = np.arange(0, S, step)[:sz]
#y = np.arange(0, S, step)[:sz+1]
# Create pixelized PSF (Gaussian)
sx = x - 0.5 + step/2.
subpixpsf = eval_psf(psf, sx, sx)
binned = bin_image(subpixpsf, s)
bh,bw = binned.shape
pixpsf1 = pixpsf[:bh,:bw]
ph,pw = pixpsf.shape
binned = binned[:ph,:pw]
print('Binned PSF:')
measure(binned)
print('Pix PSF:')
measure(pixpsf)
# Recompute my convolution using the binned PSF
P,FG,Gmine,v,w = galaxy_psf_convolution(
gal_sigma, 0., 0., GaussianGalaxy, cd,
0., 0., binned, debug=True)
xx,yy = np.meshgrid(x,x)
# plt.clf()
#
# plt.subplot(2,2,1)
# dimshow(subpixpsf)
# plt.title('subpix psf')
# plt.colorbar()
#
# plt.subplot(2,2,2)
# dimshow(binned)
# plt.title('binned subpix psf')
# plt.colorbar()
#
# plt.subplot(2,2,3)
# dimshow(pixpsf1)
# plt.title('pix psf')
# plt.colorbar()
#
# plt.subplot(2,2,4)
# dimshow(pixpsf1 - binned)
# plt.title('pix - binned')
# plt.colorbar()
# plt.suptitle('subsample %i' % s)
# ps.savefig()
# Create pixelized galaxy image
#gxx,gyy = xx + step/2., yy + step/2.
gxx,gyy = xx,yy
#gxx,gyy = xx - step, yy - step
#gxx,gyy = xx - step/2., yy - step/2.
center = S/2
subpixgal = np.exp(-0.5 * ((gxx-center)**2 + (gyy-center)**2)/gal_sigma**2)
sh,sw = subpixpsf.shape
subpixgal = subpixgal[:sh,:sw]
print('Subpix psf, gal', subpixpsf.shape, subpixgal.shape)
print('Subpix PSF:')
measure(subpixpsf)
print('Subpix gal:')
measure(subpixgal)
# FFT convolution
Fpsf = np.fft.rfft2(subpixpsf)
spg = np.fft.ifftshift(subpixgal)
# plt.clf()
# for i in range(len(w)):
# plt.plot(v, Fpsf[i,:], 'c-')
# for i in range(len(v)):
# plt.plot(w, Fpsf[:,i], 'm-')
# plt.title('PSF Fourier transform')
# ps.savefig()
#
# IV = np.argsort(v)
# IW = np.argsort(w)
# plt.clf()
# for i in range(len(w)):
# plt.plot(v[IV], np.abs(Fpsf[i,IV]), 'c-')
# for i in range(len(v)):
# plt.plot(w[IW], np.abs(Fpsf[IW,i]), 'm-')
# plt.title('abs PSF Fourier transform')
# ps.savefig()
#
# plt.yscale('log')
# ps.savefig()
# plt.clf()
# dimshow(spg)
# plt.title('spg')
# ps.savefig()
Fgal = np.fft.rfft2(spg)
if get_ffts:
return Fpsf, Fgal
Fconv = Fpsf * Fgal
subpixfft = np.fft.irfft2(Fconv, s=subpixpsf.shape)
print('Shapes:', 'subpixpsf', subpixpsf.shape, 'Fpsf', Fpsf.shape)
print('spg', spg.shape, 'Fgal', Fgal.shape, 'Fconv', Fconv.shape,
'subpixfft', subpixfft.shape)
print('Subpix conv', subpixfft.shape)
binned = bin_image(subpixfft, s)
binned /= np.sum(binned)
print('Binned', binned.shape)
print('Mine:', Gmine.shape)
print('Mine:')
measure(Gmine)
print('Binned subpix FFT:')
measure(binned)
mh,mw = Gmine.shape
binned = binned[:mh,:mw]
plt.clf()
plt.subplot(2,3,1)
dimshow(subpixpsf)
plt.title('subpix psf')
plt.colorbar()
plt.subplot(2,3,2)
dimshow(subpixgal)
plt.title('subpix galaxy')
plt.colorbar()
plt.subplot(2,3,3)
dimshow(subpixfft)
plt.title('subpix FFT conv')
plt.colorbar()
plt.subplot(2,3,4)
dimshow(np.log10(np.maximum(binned / np.max(binned), 1e-12)))
plt.title('log binned FFT conv')
plt.colorbar()
plt.subplot(2,3,5)
dimshow(np.log10(np.maximum(Gmine / np.max(Gmine), 1e-12)))
#dimshow(Gmine)
plt.title('log my conv')
plt.colorbar()
gh,gw = Gmine.shape
binned = binned[:gh,:gw]
bh,bw = binned.shape
Gmine = Gmine[:bh,:bw]
diff = Gmine - binned
plt.subplot(2,3,6)
dimshow(diff)
plt.title('mine - FFT')
plt.colorbar()
plt.suptitle('PSF %g, Gal %g, subsample %i' % (psf_sigma, gal_sigma, s))
ps.savefig()
rmsdiff = np.sqrt(np.mean(diff**2))
return rmsdiff
def main():
ps = PlotSequence('conv')
S = 51
center = S/2
print('Center', center)
#for psf_sigma in [2., 1.5, 1.]:
for psf_sigma in [2.]:
rms2 = []
x = np.arange(S)
y = np.arange(S)
xx,yy = np.meshgrid(x, y)
scale = 1.5 / psf_sigma
pixpsf = render_airy((scale, center), x, y)
psf = (scale,center)
eval_psf = render_airy
plt.clf()
plt.subplot(2,1,1)
plt.plot(x, pixpsf[center,:], 'b-')
plt.plot(x, pixpsf[:,center], 'r-')
plt.subplot(2,1,2)
plt.plot(x, np.maximum(1e-16, pixpsf[center,:]), 'b-')
plt.plot(x, np.maximum(1e-16, pixpsf[:,center]), 'r-')
plt.yscale('log')
ps.savefig()
plt.clf()
plt.imshow(pixpsf, interpolation='nearest', origin='lower')
ps.savefig()
plt.clf()
plt.imshow(np.log10(np.maximum(1e-16, pixpsf)),
interpolation='nearest', origin='lower')
plt.colorbar()
plt.title('log PSF')
ps.savefig()
# psf
#psf = scipy.stats.norm(loc=center + 0.5, scale=psf_sigma)
# plt.clf()
# plt.imshow(Pcdf, interpolation='nearest', origin='lower')
# ps.savefig()
# #Pcdf = psf.cdf(xx) * psf.cdf(yy)
# #pixpsf = integrate_gaussian(psf, xx, yy)
#
# padpsf = np.zeros((S*2-1, S*2-1))
# ph,pw = pixpsf.shape
# padpsf[S/2:S/2+ph, S/2:S/2+pw] = pixpsf
# Fpsf = np.fft.rfft2(padpsf)
#
# padh,padw = padpsf.shape
# v = np.fft.rfftfreq(padw)
# w = np.fft.fftfreq(padh)
# fmax = max(max(np.abs(v)), max(np.abs(w)))
# cut = fmax / 2. * 1.000001
# #print('Frequence cut:', cut)
# Ffiltpsf = Fpsf.copy()
# #print('Ffiltpsf', Ffiltpsf.shape)
# #print((np.abs(w) < cut).shape)
# #print((np.abs(v) < cut).shape)
# Ffiltpsf[np.abs(w) > cut, :] = 0.
# Ffiltpsf[:, np.abs(v) > cut] = 0.
# #print('pad v', v)
# #print('pad w', w)
#
# filtpsf = np.fft.irfft2(Ffiltpsf, s=(padh,padw))
#
# print('filtered PSF real', np.max(np.abs(filtpsf.real)))
# print('filtered PSF imag', np.max(np.abs(filtpsf.imag)))
#
# plt.clf()
# plt.subplot(2,3,1)
# dimshow(Fpsf.real)
# plt.colorbar()
# plt.title('Padded PSF real')
# plt.subplot(2,3,4)
# dimshow(Fpsf.imag)
# plt.colorbar()
# plt.title('Padded PSF imag')
#
# plt.subplot(2,3,2)
# dimshow(Ffiltpsf.real)
# plt.colorbar()
# plt.title('Filt PSF real')
# plt.subplot(2,3,5)
# dimshow(Ffiltpsf.imag)
# plt.colorbar()
# plt.title('Filt PSF imag')
#
# plt.subplot(2,3,3)
# dimshow(filtpsf.real)
# plt.title('PSF real')
# plt.colorbar()
#
# plt.subplot(2,3,6)
# dimshow(filtpsf.imag)
# plt.title('PSF imag')
# plt.colorbar()
#
# ps.savefig()
#
#
# pixpsf = filtpsf
gal_sigmas = [2, 1, 0.5, 0.25]
for gal_sigma in gal_sigmas:
# plt.clf()
# plt.imshow(Gcdf, interpolation='nearest', origin='lower')
# plt.savefig('dcdf.png')
# plt.clf()
# plt.imshow(np.exp(-0.5 * ((xx-center)**2 + (yy-center)**2)/2.**2),
# interpolation='nearest', origin='lower')
# plt.savefig('g.png')
# my convolution
pixscale = 1.
cd = pixscale * np.eye(2) / 3600.
P,FG,Gmine,v,w = galaxy_psf_convolution(
gal_sigma, 0., 0., GaussianGalaxy, cd,
0., 0., pixpsf, debug=True)
#print('v:', v)
#print('w:', w)
#print('P:', P.shape)
print()
print('PSF %g, Gal %g' % (psf_sigma, gal_sigma))
rmax = np.argmax(np.abs(w))
cmax = np.argmax(np.abs(v))
l2_rmax = np.sqrt(np.sum(P[rmax,:].real**2 + P[rmax,:].imag**2))
l2_cmax = np.sqrt(np.sum(P[:,cmax].real**2 + P[:,cmax].imag**2))
print('PSF L_2 in highest-frequency rows & cols:', l2_rmax, l2_cmax)
l2_rmax = np.sqrt(np.sum(FG[rmax,:].real**2 + FG[rmax,:].imag**2))
l2_cmax = np.sqrt(np.sum(FG[:,cmax].real**2 + FG[:,cmax].imag**2))
print('Gal L_2 in highest-frequency rows & cols:', l2_rmax, l2_cmax)
C = P * FG
l2_rmax = np.sqrt(np.sum(C[rmax,:].real**2 + C[rmax,:].imag**2))
l2_cmax = np.sqrt(np.sum(C[:,cmax].real**2 + C[:,cmax].imag**2))
print('PSF*Gal L_2 in highest-frequency rows & cols:', l2_rmax, l2_cmax)
print()
Fpsf, Fgal = compare_subsampled(
S, 1, ps, psf, pixpsf, Gmine,v,w,
gal_sigma, psf_sigma, cd, get_ffts=True, eval_psf=eval_psf)
plt.clf()
plt.subplot(2,4,1)
dimshow(P.real)
plt.colorbar()
plt.title('PSF real')
plt.subplot(2,4,5)
dimshow(P.imag)
plt.colorbar()
plt.title('PSF imag')
plt.subplot(2,4,2)
dimshow(FG.real)
plt.colorbar()
plt.title('Gal real')
plt.subplot(2,4,6)
dimshow(FG.imag)
plt.colorbar()
plt.title('Gal imag')
plt.subplot(2,4,3)
dimshow((P * FG).real)
plt.colorbar()
plt.title('P*Gal real')
plt.subplot(2,4,7)
dimshow((P * FG).imag)
plt.colorbar()
plt.title('P*Gal imag')
plt.subplot(2,4,4)
dimshow((Fgal).real)
plt.colorbar()
plt.title('pixGal real')
plt.subplot(2,4,8)
dimshow((Fgal).imag)
plt.colorbar()
plt.title('pixGal imag')
plt.suptitle('PSF %g, Gal %g' % (psf_sigma, gal_sigma))
ps.savefig()
subsample = [1,2,4]
rms1 = []
for s in subsample:
rms = compare_subsampled(S, s, ps, psf, pixpsf, Gmine,v,w, gal_sigma, psf_sigma, cd, eval_psf=eval_psf)
rms1.append(rms)
rms2.append(rms1)
print()
print('PSF sigma =', psf_sigma)
print('RMSes:')
for rms1,gal_sigma in zip(rms2, gal_sigmas):
print('Gal sigma', gal_sigma, 'rms:',
', '.join(['%.3g' % r for r in rms1]))
plt.title('subpix Gal real')
plt.subplot(2,4,8)
dimshow(Fsubgal.imag)
plt.colorbar()
plt.title('subpix Gal imag')
ps.savefig()
pixconv = np.fft.irfft2(Fpsf * Fgal, s=pixpsf.shape)
subpixconv = np.fft.irfft2(Fsub * Fsubgal, s=subpixpsf.shape)
# my convolution
pixscale = 1.
cd = pixscale * np.eye(2) / 3600.
Gmine = galaxy_psf_convolution(gal_re, 0., 0., gal, cd,
0., 0., pixpsf)
pixconv /= np.sum(pixconv)
subpixconv /= np.sum(subpixconv)
subpixconv *= scale**2
Gmine /= np.sum(Gmine)
plt.clf()
plt.subplot(1,3,1)
plt.imshow(pixconv, interpolation='nearest', origin='lower')
plt.subplot(1,3,2)
plt.imshow(subpixconv, interpolation='nearest', origin='lower')
plt.subplot(1,3,3)
plt.imshow(Gmine, interpolation='nearest', origin='lower')
ps.savefig()
