def numerical_image_gradients(theta0, delta, scene=None, stamp=None):
dI_dp = []
for i, (p, dp) in enumerate(zip(theta0, delta)):
theta = theta0.copy()
imlo, _ = make_image(theta, scene, stamp)
theta[i] += dp
imhi, _ = make_image(theta, scene, stamp)
dI_dp.append((imhi - imlo) / (dp))
return np.array(dI_dp)
def test_image_gradients(ptrue, delta, scene=None, stamp=None):
delta = np.ones_like(ptrue) * 1e-6
#numerical
grad_num = numerical_image_gradients(ptrue, delta, scene, stamp)
image, grad = make_image(ptrue, scene, stamp)
fig, axes = pl.subplots(len(ptrue), 3, sharex=True, sharey=True)
for i in range(len(ptrue)):
g = grad[i, :].reshape(stamp.nx, stamp.ny)
c = axes[i, 0].imshow(grad_num[i, :, :].T, origin='lower')
fig.colorbar(c, ax=axes[i, 0])
c = axes[i, 1].imshow(g.T, origin='lower')
fig.colorbar(c, ax=axes[i, 1])
c = axes[i, 2].imshow((grad_num[i, :, :] - g).T, origin='lower')
fig.colorbar(c, ax=axes[i, 2])
axes[0, 0].set_title('Numerical')
axes[0, 1].set_title('Analytic')
axes[0, 2].set_title('N - A')
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
stamp = make_stamp(size, psfname=psfname)
# make the pixels tiny
#stamp.distortion = np.eye(2) * 8.0
oversample = 8
stamp.psf.covariances *= oversample**2
#stamp.psf.covariances[:, 0, 0] /= oversample
#stamp.psf.covariances[:, 1, 1] /= oversample
stamp.psf.means *= oversample
stamp.crpix = np.array([stamp.nx / 2., stamp.ny / 2.])
stamp.crval = np.zeros(2)
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()
sources = [Star()]
scene.sources = sources
# --- Get the mock image ----
label = ['flux', 'x', 'y']
theta = np.array([100., 0.0, 0.0])
ptrue = theta
stamp.pixel_values = make_image(ptrue, scene, stamp)[0]
fig, ax = pl.subplots()
ax.imshow(stamp.pixel_values.T, origin='lower')
pl.show()
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 add_noise:
noise = np.random.normal(0, err, size=(stamp.nx, stamp.ny))
stamp.pixel_values += noise
return scene, stamp, ptrue, label
if __name__ == "__main__":
# Get a scene and a stamp at some parameters
scene, stamp, ptrue, label = setup_scene(galaxy=True,
fwhm=2.0,
fudge=1.25,
add_noise=True)
true_image, partials = make_image(ptrue, scene, stamp)
# Set up likelihoods
nll = argfix(negative_lnlike_stamp, scene=scene, stamp=stamp)
nll_nograd = argfix(negative_lnlike_nograd, scene=scene, stamp=stamp)
# --- Chi2 on a grid ------
# needs to be debugged
if False:
mux = np.linspace(47, 53., 100)
muy = np.linspace(47, 53., 100)
flux = np.linspace(3000, 5000., 10)
chi2 = np.zeros([len(mux), len(muy), len(flux)])
for i, x in enumerate(mux):
for j, y in enumerate(muy):
if __name__ == "__main__":
# --- Get a postage stamp ----
psfname = os.path.join(paths.psfmixture, 'f090_ng6_em_random.p')
scene, stamp, ptrue, label = setup_scene(size=(50, 50),
psfname=psfname,
add_noise=True)
nll = argfix(negative_lnlike_stamp, scene=scene, stamp=stamp)
nll_nograd = argfix(negative_lnlike_nograd, scene=scene, stamp=stamp)
# --- Plot a model and gradients thereof ---
if False:
theta_init = ptrue * 1.05
image_init, partials_init = make_image(theta_init, scene, stamp)
fig, axes = pl.subplots(3, 2, sharex=True, sharey=True)
ax = axes.flat[0]
i = ax.imshow(stamp.pixel_values.T, origin='lower')
ax.text(0.1, 0.9, 'Mock Data', transform=ax.transAxes)
ax = axes.flat[1]
i = ax.imshow(image_init.T, origin='lower')
ax.text(0.1, 0.9, 'Initial Model', transform=ax.transAxes)
for i, ddtheta in enumerate(partials_init[scene.free_inds, :]):
ax = axes.flat[i + 2]
ax.imshow(ddtheta.reshape(stamp.nx, stamp.ny).T, origin='lower')
ax.text(0.1,
0.9,
'$\partial I/\partial {}$'.format(label[i]),
transform=ax.transAxes)
pl.show()
scene.sources = sources
label = ['flux', 'x', 'y']
nll = argfix(negative_lnlike_stamp, scene=scene, stamp=stamp)
nll_nograd = argfix(negative_lnlike_nograd, scene=scene, stamp=stamp)
# --- Initialize ---
theta_init = np.array([stamp.pixel_values.sum() * 1.0, ra_init, dec_init])
if inpixels:
world = np.array([ra_init, dec_init, 0])
hdr = fits.getheader(imname)
ast = apy_wcs.WCS(hdr)
center = ast.wcs_world2pix(world[None, :], 0)[0, :2] - stamp.lo
theta_init = np.array(
[stamp.pixel_values.sum() * 0.5, center[0], center[1]])
image_init, partials = make_image(theta_init, scene, stamp)
# --- Plot initial value ---
if True:
fig, axes = pl.subplots(3, 2, sharex=True, sharey=True)
ax = axes.flat[0]
i = ax.imshow(stamp.pixel_values.T, origin='lower')
ax.text(0.1, 0.9, 'Sim. Data', transform=ax.transAxes)
ax = axes.flat[1]
i = ax.imshow(image_init.T, origin='lower')
ax.text(0.1, 0.9, 'Initial Model', transform=ax.transAxes)
for i, ddtheta in enumerate(partials):
ax = axes.flat[i + 2]
ax.imshow(ddtheta.reshape(stamp.nx, stamp.ny).T, origin='lower')
ax.text(0.1,
0.9,