def setup_scene(galaxy=False,
fudge=1.0,
fwhm=1.0,
offset=0.0,
size=(30, 30),
add_noise=False):
stamp = make_stamp(size, fwhm, offset=offset)
# --- Get a Source and Scene -----
if galaxy:
source = Galaxy()
source.ngauss = 1
source.radii = np.arange(source.ngauss) * 0.5 + 1.0
source.q = 0.5
source.pa = np.deg2rad(30.)
theta = [100., 10., 10., 0.5, np.deg2rad(10.)]
label = ['$\psi$', '$x$', '$y$', '$q$', '$\\varphi$']
bounds = [(0, 1e4), (0., 30), (0, 30), (0, 1), (0, np.pi / 2)]
else:
source = Star()
theta = [100., 10., 10.]
label = ['$\psi$', '$x$', '$y$']
bounds = [(-1e6, 1e6), (-1e5, 1e5), (-1e5, 1e5)]
scene = Scene(galaxy=galaxy)
scene.sources = [source]
# --- Generate mock and add to stamp ---
ptrue = np.array(theta) * fudge
true_image, partials = make_image(ptrue, scene, stamp)
stamp.pixel_values = true_image.copy()
err = stamp.pixel_values.max() * 1e-2
#err = np.sqrt(stamp.pixel_values.flatten())
stamp.ierr = np.ones(stamp.npix) / err
if add_noise:
noise = np.random.normal(0, err, size=(stamp.nx, stamp.ny))
stamp.pixel_values += noise
return scene, stamp, ptrue, label
def setup_scene(psfname='', size=(100, 100), fudge=1.0, add_noise=False):
# --- Get a postage stamp ----
stamp = make_stamp(size, psfname=psfname)
# --- get the Scene ---
scene = Scene(galaxy=False)
sources = [Star()]
scene.sources = sources
# --- Get the mock image ----
label = ['flux', 'x', 'y']
theta = np.array([100., stamp.nx / 2., stamp.ny / 2.])
ptrue = theta * fudge
stamp.pixel_values = make_image(ptrue, scene, stamp)[0]
err = stamp.pixel_values.max() * 1e-2
#err = np.sqrt(stamp.pixel_values.flatten())
stamp.ierr = np.ones(stamp.npix) / err
if add_noise:
noise = np.random.normal(0, err, size=(stamp.nx, stamp.ny))
stamp.pixel_values += noise
return scene, stamp, ptrue, label
#ra_init, dec_init = 53.115299, -27.803508
# keep in mind 1pixel ~ 1e-5 degrees
ra_init, dec_init = 53.115295, -27.803501
pos_init = (ra_init, dec_init)
stamps = [make_stamp(im, pos_init, center_type='celestial', size=(100, 100), psfname=psfname)
for im in imnames]
# override the psf to reflect in both directions
T = -1.0 * np.eye(2)
for s in stamps:
s.psf.covariances = np.matmul(T, np.matmul(s.psf.covariances, T.T))
s.psf.means = np.matmul(s.psf.means, T)
# --- get the Scene ---
scene = Scene()
sources = [Star()]
sources[0].id = 0
scene.sources = sources
label = ['flux', 'alpha', 'delta']
nll = argfix(negative_lnlike_multistamp, scene=scene, stamps=stamps)
# --- Initialize ---
theta_init = np.array([ra_init, dec_init, stamps[0].pixel_values.sum() * 1.0])
# --- Optimization ---
if True:
def callback(x):
#nf += 1
print(x, nll(x))
def fit_source(ra=53.115325, dec=-27.803518, imname='', psfname=None,
stamp_size=(100, 100), use_grad=True,
err_expand=1.0, jitter=0.0, gain=np.inf):
"""
"""
# --- Build the postage stamp ----
stamp = make_stamp(imname, (ra, dec), stamp_size,
psfname=psfname, center_type='celestial')
stamp.snr = stamp.pixel_values * stamp.ierr
stamp.ierr = stamp.ierr.flatten() / err_expand
counts = stamp.pixel_values.flatten() - stamp.pixel_values.min()
stamp.ierr = 1.0 / np.sqrt(1/stamp.ierr**2 + jitter**2 + counts/gain)
# override the WCS so coordinates are in pixels
# The scale matrix D
stamp.scale = np.eye(2)
# The sky coordinates of the reference pixel
stamp.crval = np.zeros([2])
# The pixel coordinates of the reference pixel
stamp.crpix = np.zeros([2])
# Rotate the PSF by 180 degrees
T = -1.0 * np.eye(2)
stamp.psf.covariances = np.matmul(T, np.matmul(stamp.psf.covariances, T.T))
stamp.psf.means = np.matmul(stamp.psf.means, T)
# --- get the Scene ---
scene = Scene(galaxy=False)
sources = [Star()]
scene.sources = sources
# ---- Optimization ------
if use_grad:
nll = argfix(negative_lnlike_stamp, scene=scene, stamp=stamp)
else:
nll = argfix(negative_lnlike_nograd, scene=scene, stamp=stamp)
if False:
nll = argfix(chi_vector, scene=scene, stamp=stamp)
method = 'lm'
use_grad = False
if True:
def callback(x):
#nf += 1
print(x, nll(x))
callback = None
# Initial and bounds
p0 = np.array([stamp.pixel_values.sum(), stamp.nx/2, stamp.ny/2])
p0 += np.random.normal(0., [0.1 * p0[0], 0.5, 0.5])
bounds = [(1, 1e4), (0., stamp_size[0]), (0, stamp_size[1])]
bounds = None
# Optimize
from scipy.optimize import minimize
lbfgsb_opt = {'ftol': 1e-20, 'gtol': 1e-12, 'disp':True, 'iprint': -1, 'maxcor': 20}
result = minimize(nll, p0, jac=use_grad, bounds=None, callback=callback,
options=lbfgsb_opt)
# plot results
resid, partials = make_image(result.x, scene, stamp)
dim = stamp.pixel_values
mim = resid
chi = (dim - mim) * stamp.ierr.reshape(stamp.nx, stamp.ny)
fig, axes = pl.subplots(1, 4, sharex=True, sharey=True, figsize=(14.75, 3.25))
images = [dim, mim, dim-mim, chi]
labels = ['Data', 'Model', 'Data-Model', '$\chi$']
for k, ax in enumerate(axes):
c = ax.imshow(images[k].T, origin='lower')
pl.colorbar(c, ax=ax)
ax.set_title(labels[k])
return result, (fig, axes), nll(result.x), stamp, scene
if m < M:
return a.reshape((m, M / m, n, N / n)).mean(3).mean(1)
else:
return np.repeat(np.repeat(a, m / M, axis=0), n / N, axis=1)
def compare(x, y, source, native, oversampled):
image = get_image(x, y, source, native)
oimage = get_image(x, y, source, oversampled)
rimage = rebin(oimage, image.shape) * oversample**2
if __name__ == "__main__":
source = Star()
use = slice(0, 3)
# FWHM in native pixels
fwhm = 1.0
sigma = fwhm / 2.355
# native resolution
native = get_stamp(30)
native.psf.covariances = np.array([np.eye(2) * sigma**2])
native.crpix = np.array([15, 15])
# oversampled image
oversample = 8
dx = 1. / oversample
oversampled = get_stamp(int(30 / dx), dx)