def pb_thomson_lo(data, in_map, u, mask=None):
"""Defines thomson scattering linear operator"""
# data coefs
data_coefs = _pb_data_coef(data).flatten()
O = lo.diag(data_coefs)
# map coefs
map_coefs = _pb_map_coef(in_map, u).flatten()
M = lo.diag(map_coefs)
# projection
P = siddon_lo(data.header, in_map.header, obstacle="sun", mask=mask)
# thomson lo
T = O * P * M
return T
def smoothness_prior(my_map, height_prior=False):
"""
Defines a smoothness prior.
"""
D = [lo.diff(my_map.shape, axis=i) for i in xrange(my_map.ndim)]
if height_prior:
r = _radius_map(my_map)
R = lo.diag(r.ravel())
D = [Di * R for Di in D]
return D
def irls(A0, x0, tol1=1e-5, maxiter1=10, p=1, optimizer=spl.cgs, **kargs):
""" Iteratively Reweighted Least Square
"""
A0 = lo.aslinearoperator(A0)
out = A0.T * x0
tol1 /= np.sum(np.abs(x0 - A0 * out) ** p)
for i in xrange(maxiter1):
print("\n outer loop " + str(i + 1) + "\n")
w = np.abs(x0 - A0 * out) ** (p - 2)
A = A0.T * lo.diag(w) * A0
x = A0.T * (w * x0)
out, t = optimizer(A, x, **kargs)
if np.sum(np.abs(x0 - A0 * out) ** p) < tol1:
break
return out
def irls(A0, x0, tol1=1e-5, maxiter1=10, p=1, optimizer=spl.cgs, **kargs):
""" Iteratively Reweighted Least Square
"""
A0 = lo.aslinearoperator(A0)
out = A0.T * x0
tol1 /= np.sum(np.abs(x0 - A0 * out) ** p)
for i in xrange(maxiter1):
print("\n outer loop " + str(i + 1) + "\n")
w = np.abs(x0 - A0 * out) ** (p - 2)
A = A0.T * lo.diag(w) * A0
x = A0.T * (w * x0)
out, t = optimizer(A, x, **kargs)
if np.sum(np.abs(x0 - A0 * out) ** p) < tol1:
break
return out
def rirls(M, y, Ds=[], tol1=1e-5, maxiter1=10, p=1, optimizer=spl.cgs, **kargs):
""" Regularized Iteratively Reweighted Least Square
"""
M = lo.aslinearoperator(M)
Ds = [lo.aslinearoperator(D) for D in Ds]
x0 = M.T * y
x = copy(x0)
r = M * x - y
tol1 /= np.sum(np.abs(r) ** p)
for i in xrange(maxiter1):
print("\n outer loop " + str(i + 1) + "\n")
A = M.T * M
for D in Ds:
rd = D * x
w = np.abs(rd) ** (p - 2)
w[np.where(1 - np.isfinite(w))] = 0 # inf
A += D.T * lo.diag(w) * D
x, t = optimizer(A, x0, **kargs)
if np.sum(np.abs(y - M * x) ** p) < tol1:
break
r = M * x - y
return x
def rirls(M, y, Ds=[], tol1=1e-5, maxiter1=10, p=1, optimizer=spl.cgs, **kargs):
""" Regularized Iteratively Reweighted Least Square
"""
M = lo.aslinearoperator(M)
Ds = [lo.aslinearoperator(D) for D in Ds]
x0 = M.T * y
x = copy(x0)
r = M * x - y
tol1 /= np.sum(np.abs(r) ** p)
for i in xrange(maxiter1):
print("\n outer loop " + str(i + 1) + "\n")
A = M.T * M
for D in Ds:
rd = D * x
w = np.abs(rd) ** (p - 2)
w[np.where(1 - np.isfinite(w))] = 0 # inf
A += D.T * lo.diag(w) * D
x, t = optimizer(A, x0, **kargs)
if np.sum(np.abs(y - M * x) ** p) < tol1:
break
r = M * x - y
return x
model = masking * projection
# remove drift
tod = tm.filter_median(tod, length=999)
model = masking * projection
# naive map
backmap = model.transpose(tod)
# coverage map
weights = model.transpose(tod.ones(tod.shape))
# mask on map
mask = weights == 0
M = lo.mask(mask)
# preconditionner
iweights = 1 / weights
iweights[np.where(np.isfinite(iweights) == 0)] = 0.
M0 = lo.diag(iweights.flatten())
# transform to lo
P = lo.aslinearoperator(model.aslinearoperator())
# priors
Dx = lo.diff(backmap.shape, axis=0)
Dy = lo.diff(backmap.shape, axis=1)
# inversion
y = (masking.T * tod).flatten()
# algos
algos = [spl.cg, spl.cgs, spl.bicg, spl.bicgstab]
models = [P.T * P, P.T * P + Dx.T * Dx + Dy.T * Dy,]
n_iterations = []
resid = []
for algo in algos:
for A in models:
for is_masked in (False, True):
model = masking * projection
# remove drift
tod = tm.filter_median(tod, length=999)
model = masking * projection
# naive map
backmap = model.transpose(tod)
# coverage map
weights = model.transpose(tod.ones(tod.shape))
# mask on map
mask = weights == 0
M = lo.mask(mask)
# preconditionner
iweights = 1 / weights
iweights[np.where(np.isfinite(iweights) == 0)] = 0.
M0 = lo.diag(iweights.flatten())
# transform to lo
P = lo.aslinearoperator(model.aslinearoperator())
# priors
Dx = lo.diff(backmap.shape, axis=0)
Dy = lo.diff(backmap.shape, axis=1)
# inversion
y = (masking.T * tod).flatten()
# algos
algos = [spl.cg, spl.cgs, spl.bicg, spl.bicgstab]
models = [
P.T * P,
P.T * P + Dx.T * Dx + Dy.T * Dy,
]
n_iterations = []
resid = []
