def __init__(self, *args):
'''
MogParams(amp, mean, var)
or
MogParams(a0,a1,a2, mx0,my0,mx1,my1,mx2,my2,
vxx0,vyy0,vxy0, vxx1,vyy1,vxy1, vxx2,vyy2,vxy2)
amp: np array (size K) of Gaussian amplitudes
mean: np array (size K,2) of means
var: np array (size K,2,2) of variances
'''
from tractor import mixture_profiles as mp
if len(args) == 3:
amp, mean, var = args
else:
assert (len(args) % 6 == 0)
K = len(args) // 6
amp = np.array(args[:K])
mean = np.array(args[K:3 * K]).reshape((K, 2))
args = args[3 * K:]
var = np.zeros((K, 2, 2))
var[:, 0, 0] = args[::3]
var[:, 1, 1] = args[1::3]
var[:, 0, 1] = var[:, 1, 0] = args[2::3]
self.mog = mp.MixtureOfGaussians(amp, mean, var)
K = self.mog.K
assert (self.mog.D == 2)
super(MogParams, self).__init__()
# drop the ParamList storage
del self.vals
self._set_param_names(K)
def getCircularMog(amps, sigmas):
K = len(amps)
amps = np.array(amps).astype(np.float32)
means = np.zeros((K, 2), np.float32)
vars = np.zeros((K, 2, 2), np.float32)
for k in range(K):
vars[k, 0, 0] = vars[k, 1, 1] = sigmas[k]**2
return mp.MixtureOfGaussians(amps, means, vars, quick=True)
def getMixtureOfGaussians(self, px=None, py=None):
K = len(self.myweights)
amps = np.array(self.myweights)
means = np.zeros((K, 2))
vars = np.zeros((K, 2, 2))
for k in range(K):
vars[k, 0, 0] = vars[k, 1, 1] = self.mysigmas[k]**2
return mp.MixtureOfGaussians(amps, means, vars)
class GaussianGalaxy(HoggGalaxy):
nre = 6.
profile = mp.MixtureOfGaussians(np.array([1.]), np.zeros((1, 2)),
np.array([[[1., 0.], [0., 1.]]]))
profile.normalize()
def __init__(self, *args, **kwargs):
self.nre = GaussianGalaxy.nre
super(GaussianGalaxy, self).__init__(*args, **kwargs)
def getName(self):
return 'GaussianGalaxy'
def getProfile(self):
return GaussianGalaxy.profile
def _realGetUnitFluxModelPatch(self, img, px, py, minval, modelMask=None):
if modelMask is not None:
x0, y0 = modelMask.x0, modelMask.y0
else:
# choose the patch size
halfsize = self._getUnitFluxPatchSize(img,
px=px,
py=py,
minval=minval)
# find overlapping pixels to render
(outx,
inx) = get_overlapping_region(int(np.floor(px - halfsize)),
int(np.ceil(px + halfsize + 1)), 0,
img.getWidth())
(outy,
iny) = get_overlapping_region(int(np.floor(py - halfsize)),
int(np.ceil(py + halfsize + 1)), 0,
img.getHeight())
if inx == [] or iny == []:
# no overlap
return None
x0, x1 = outx.start, outx.stop
y0, y1 = outy.start, outy.stop
psf = img.getPsf()
# We have two methods of rendering profile galaxies: If the
# PSF can be represented as a mixture of Gaussians, then we do
# the analytic Gaussian convolution, producing a larger
# mixture of Gaussians, and we render that. Otherwise
# (pixelized PSFs), we FFT the PSF, multiply by the analytic
# FFT of the galaxy, and IFFT back to get the rendered
# profile.
# The "HybridPSF" class is just a marker to indicate whether this
# code should treat the PSF as a hybrid.
from tractor.psf import HybridPSF
hybrid = isinstance(psf, HybridPSF)
def run_mog(amix=None, mm=None):
''' This runs the mixture-of-Gaussians convolution method.
'''
if amix is None:
amix = self._getAffineProfile(img, px, py)
if mm is None:
mm = modelMask
# now convolve with the PSF, analytically
# (note that the psf's center is *not* set to px,py; that's just
# the position to use for spatially-varying PSFs)
psfmix = psf.getMixtureOfGaussians(px=px, py=py)
cmix = amix.convolve(psfmix)
if mm is None:
#print('Mixture to patch: amix', amix, 'psfmix', psfmix, 'cmix', cmix)
return mp.mixture_to_patch(cmix, x0, x1, y0, y1, minval)
# The convolved mixture *already* has the px,py offset added
# (via px,py to amix) so set px,py=0,0 in this call.
if mm.mask is not None:
p = cmix.evaluate_grid_masked(mm.x0, mm.y0, mm.mask, 0., 0.)
else:
p = cmix.evaluate_grid(mm.x0, mm.x1, mm.y0, mm.y1, 0., 0.)
assert (p.shape == mm.shape)
return p
if hasattr(psf, 'getMixtureOfGaussians') and not hybrid:
return run_mog(mm=modelMask)
# Otherwise, FFT:
imh, imw = img.shape
if modelMask is None:
# Avoid huge galaxies -> huge halfsize in a tiny image (blob)
imsz = max(imh, imw)
halfsize = min(halfsize, imsz)
# FIXME -- should take some kind of combination of
# modelMask, PSF, and Galaxy sizes!
else:
# ModelMask sets the sizes.
mh, mw = modelMask.shape
x1 = x0 + mw
y1 = y0 + mh
halfsize = max(mh / 2., mw / 2.)
# How far from the source center to furthest modelMask edge?
# FIXME -- add 1 for Lanczos margin?
halfsize = max(
halfsize,
max(max(1 + px - x0, 1 + x1 - px), max(1 + py - y0,
1 + y1 - py)))
psfh, psfw = psf.shape
halfsize = max(halfsize, max(psfw / 2., psfh / 2.))
#print('Halfsize:', halfsize)
# is the source center outside the modelMask?
sourceOut = (px < x0 or px > x1 - 1 or py < y0 or py > y1 - 1)
# print('mh,mw', mh,mw, 'sourceout?', sourceOut)
if sourceOut:
if hybrid:
return run_mog(mm=modelMask)
# Super Yuck -- FFT, modelMask, source is outside the
# box.
neardx, neardy = 0., 0.
if px < x0:
neardx = x0 - px
if px > x1:
neardx = px - x1
if py < y0:
neardy = y0 - py
if py > y1:
neardy = py - y1
nearest = np.hypot(neardx, neardy)
#print('Nearest corner:', nearest, 'vs radius', self.getRadius())
if nearest > self.getRadius():
return None
# how far is the furthest point from the source center?
farw = max(abs(x0 - px), abs(x1 - px))
farh = max(abs(y0 - py), abs(y1 - py))
bigx0 = int(np.floor(px - farw))
bigx1 = int(np.ceil(px + farw))
bigy0 = int(np.floor(py - farh))
bigy1 = int(np.ceil(py + farh))
bigw = 1 + bigx1 - bigx0
bigh = 1 + bigy1 - bigy0
boffx = x0 - bigx0
boffy = y0 - bigy0
assert (bigw >= mw)
assert (bigh >= mh)
assert (boffx >= 0)
assert (boffy >= 0)
bigMask = np.zeros((bigh, bigw), bool)
if modelMask.mask is not None:
bigMask[boffy:boffy + mh,
boffx:boffx + mw] = modelMask.mask
else:
bigMask[boffy:boffy + mh, boffx:boffx + mw] = True
bigMask = ModelMask(bigx0, bigy0, bigMask)
# print('Recursing:', self, ':', (mh,mw), 'to', (bigh,bigw))
bigmodel = self._realGetUnitFluxModelPatch(img,
px,
py,
minval,
modelMask=bigMask)
return Patch(
x0, y0, bigmodel.patch[boffy:boffy + mh, boffx:boffx + mw])
# print('Getting Fourier transform of PSF at', px,py)
# print('Tim shape:', img.shape)
P, (cx, cy), (pH, pW), (v,
w) = psf.getFourierTransform(px, py, halfsize)
dx = px - cx
dy = py - cy
if modelMask is not None:
# the Patch we return *must* have this origin.
ix0 = x0
iy0 = y0
# the difference that we have to handle by shifting the model image
mux = dx - ix0
muy = dy - iy0
# we will handle the integer portion by computing a shifted image
# and copying it into the result
sx = int(np.round(mux))
sy = int(np.round(muy))
# the subpixel portion will be handled with a Lanczos interpolation
mux -= sx
muy -= sy
else:
# Put the integer portion of the offset into Patch x0,y0
ix0 = int(np.round(dx))
iy0 = int(np.round(dy))
# the subpixel portion will be handled with a Lanczos interpolation
mux = dx - ix0
muy = dy - iy0
# At this point, mux,muy are both in [-0.5, 0.5]
assert (np.abs(mux) <= 0.5)
assert (np.abs(muy) <= 0.5)
amix = self._getShearedProfile(img, px, py)
fftmix = amix
mogmix = None
#print('Galaxy affine profile:', amix)
if hybrid:
# Split "amix" into terms that we will evaluate using MoG
# vs FFT.
vv = amix.var[:, 0, 0] + amix.var[:, 1, 1]
nsigma = 3.
# Terms that will wrap-around significantly...
I = ((vv * nsigma**2) > (pW**2))
if np.any(I):
# print('Evaluating', np.sum(I), 'terms as MoGs')
mogmix = mp.MixtureOfGaussians(
amix.amp[I],
amix.mean[I, :] + np.array([px, py])[np.newaxis, :],
amix.var[I, :, :],
quick=True)
I = np.logical_not(I)
if np.any(I):
# print('Evaluating', np.sum(I), 'terms with FFT')
fftmix = mp.MixtureOfGaussians(amix.amp[I],
amix.mean[I, :],
amix.var[I, :, :],
quick=True)
else:
fftmix = None
if fftmix is not None:
Fsum = fftmix.getFourierTransform(v, w, zero_mean=True)
# In Intel's mkl_fft library, the irfftn code path is faster than irfft2
# (the irfft2 version sets args (to their default values) which triggers padding
# behavior, changing the FFT size and copying behavior)
#G = np.fft.irfft2(Fsum * P, s=(pH, pW))
G = np.fft.irfftn(Fsum * P)
assert (G.shape == (pH, pW))
# FIXME -- we could try to be sneaky and Lanczos-interp
# after cutting G down to nearly its final size... tricky
# tho
# Lanczos-3 interpolation in ~the same way we do for
# pixelized PSFs.
from tractor.psf import lanczos_shift_image
G = G.astype(np.float32)
lanczos_shift_image(G, mux, muy, inplace=True)
else:
G = np.zeros((pH, pW), np.float32)
if modelMask is not None:
gh, gw = G.shape
if sx != 0 or sy != 0:
yi, yo = get_overlapping_region(-sy, -sy + mh - 1, 0, gh - 1)
xi, xo = get_overlapping_region(-sx, -sx + mw - 1, 0, gw - 1)
# shifted
# FIXME -- are yo,xo always the whole image? If so, optimize
shG = np.zeros((mh, mw), G.dtype)
shG[yo, xo] = G[yi, xi]
if debug_ps is not None:
_fourier_galaxy_debug_plots(G, shG, xi, yi, xo, yo, P,
Fsum, pW, pH, psf)
G = shG
if gh > mh or gw > mw:
G = G[:mh, :mw]
assert (G.shape == modelMask.shape)
else:
# Clip down to suggested "halfsize"
if x0 > ix0:
G = G[:, x0 - ix0:]
ix0 = x0
if y0 > iy0:
G = G[y0 - iy0:, :]
iy0 = y0
gh, gw = G.shape
if gw + ix0 > x1:
G = G[:, :x1 - ix0]
if gh + iy0 > y1:
G = G[:y1 - iy0, :]
if mogmix is not None:
if modelMask is not None:
mogpatch = run_mog(amix=mogmix, mm=modelMask)
else:
gh, gw = G.shape
mogpatch = run_mog(amix=mogmix, mm=ModelMask(ix0, iy0, gw, gh))
assert (mogpatch.patch.shape == G.shape)
G += mogpatch.patch
return Patch(ix0, iy0, G)
plt.clf() plt.subplot(2,2,2) dimshow(np.log10(np.maximum(floor, patch2.patch)), **ima) plt.subplot(2,2,3) dimshow(dx2.patch) plt.subplot(2,2,4) dimshow(dy2.patch) ps.savefig() sys.exit(0) mg = mp.MixtureOfGaussians([1.], [0.,0.], np.array([1.])) x = mg.evaluate(np.array([0,0])) x = mg.evaluate(np.array([0.,1.])) x = mg.evaluate(np.array([-3.,2.])) x = mg.evaluate(np.array([[-3.,2.], [-17,4], [4,-2]])) mg = mp.MixtureOfGaussians([1.], [0.,1.], np.array([2.])) x = mg.evaluate(np.array([0.,1.])) x = mg.evaluate(np.array([0,0])) x = mg.evaluate(np.array([-3.,2.])) x = mg.evaluate(np.array([[-3.,2.], [-17,4], [4,-2]])) mg = mp.MixtureOfGaussians([1.], [0.,1.], np.array([ [[1.3, 0.1],[0.1,3.1]], ])) x = mg.evaluate(np.array([0.,1.])) x = mg.evaluate(np.array([0,0])) x = mg.evaluate(np.array([-3.,2.]))
