def _solve_(self, L, x, b):
if 'FIPY_VERBOSE_SOLVER' in os.environ:
verbosity = True
else:
verbosity = False
return solve(L.matrix, b, verb=verbosity, tol=self.tolerance)
def _call_solver (self):
"""Solves the linear system (self._A)x = self._b and returns the solution vector.
@return: The solution to the linear system.
"""
import pyamg
x = pyamg.solve ( self._A, self._b, verb=True, tol=1e-8, maxiter=800 )
return x, 0
def poisson_blend(artwork_img, selfie_img, mask_img):
# this function works only for 500x500 images (input adjustment needeed)
# kudos to https://github.com/fbessho/PyPoi
mask_img = mask_img[0:500, 0:500]
mask_img[mask_img == 0] = False
mask_img[mask_img != False] = True
# create coefficient matrix
A = scipy.sparse.identity(np.prod((500,500)), format='lil')
for y in range(0,500):
for x in range(0,500):
if mask_img[y, x]:
index = x + y * 500
A[index, index] = 4
if index + 1 < np.prod((500,500)):
A[index, index + 1] = -1
if index - 1 >= 0:
A[index, index - 1] = -1
if index + 500 < np.prod((500,500)):
A[index, index + 500] = -1
if index - 500 >= 0:
A[index, index - 500] = -1
A = A.tocsr() # Returns a copy of this matrix in Compressed Sparse Row format
# create poisson matrix for b
P = pyamg.gallery.poisson(mask_img.shape)
# for each layer (ex. RGB)
for channel in range(artwork_img.shape[2]):
t = artwork_img[0:500, 0:500, channel]
s = selfie_img[0:500, 0:500, channel]
t = t.flatten() # Returns a copy of the array collapsed into one dimension.
s = s.flatten()
# create b
b = P * s
for y in range(0,500):
for x in range(0,500):
if not mask_img[y, x]:
index = x + y * 500
b[index] = t[index]
# solve Ax = b
x = pyamg.solve(A, b, verb=False, tol=1e-10)
# assign x to target image
x = np.reshape(x, (500,500))
x[x > 255] = 255
x[x < 0] = 0
x = np.array(x, artwork_img.dtype)
artwork_img[0:500, 0:500, channel] = x
return artwork_img
def apply_inverse(op,
V,
options=None,
least_squares=False,
check_finite=True,
default_solver='pyamg_solve'):
"""Solve linear equation system.
Applies the inverse of `op` to the vectors in `rhs` using PyAMG.
Parameters
----------
op
The linear, non-parametric |Operator| to invert.
rhs
|VectorArray| of right-hand sides for the equation system.
options
The |solver_options| to use (see :func:`solver_options`).
least_squares
Must be `False`.
check_finite
Test if solution only contains finite values.
default_solver
Default solver to use (pyamg_solve, pyamg_rs, pyamg_sa).
Returns
-------
|VectorArray| of the solution vectors.
"""
assert V in op.range
if least_squares:
raise NotImplementedError
if isinstance(op, NumpyMatrixOperator):
matrix = op.matrix
else:
from pymor.algorithms.to_matrix import to_matrix
matrix = to_matrix(op)
options = _parse_options(options, solver_options(), default_solver,
None, least_squares)
V = V.to_numpy()
promoted_type = np.promote_types(matrix.dtype, V.dtype)
R = np.empty((len(V), matrix.shape[1]), dtype=promoted_type)
if options['type'] == 'pyamg_solve':
if len(V) > 0:
V_iter = iter(enumerate(V))
R[0], ml = pyamg.solve(matrix,
next(V_iter)[1],
tol=options['tol'],
maxiter=options['maxiter'],
return_solver=True)
for i, VV in V_iter:
R[i] = pyamg.solve(matrix,
VV,
tol=options['tol'],
maxiter=options['maxiter'],
existing_solver=ml)
elif options['type'] == 'pyamg_rs':
ml = pyamg.ruge_stuben_solver(
matrix,
strength=options['strength'],
CF=options['CF'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
coarse_solver=options['coarse_solver'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'] == 'pyamg_sa':
ml = pyamg.smoothed_aggregation_solver(
matrix,
symmetry=options['symmetry'],
strength=options['strength'],
aggregate=options['aggregate'],
smooth=options['smooth'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
improve_candidates=options['improve_candidates'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
diagonal_dominance=options['diagonal_dominance'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
else:
raise ValueError('Unknown solver type')
if check_finite:
if not np.isfinite(np.sum(R)):
raise InversionError('Result contains non-finite values')
return op.source.from_numpy(R)
def PoissonBlending(src, tar, mask):
H, W = tar.shape[:2]
blending_mask = mask
fill_mask = np.ones_like(mask, dtype=bool)
loc = blending_mask.nonzero()
loc_map = {} # mapping from coordinate to variable
for i_loc, (j, i) in enumerate(zip(loc[0], loc[1])):
loc_map[(j, i)] = i_loc
#w_l, w_r = BlendingWeights(src_mask, tar_mask, src_img.shape[0])
N = np.count_nonzero(blending_mask)
y_min = np.min(loc[0])
y_max = np.max(loc[0])
x_min = np.min(loc[1])
x_max = np.max(loc[1])
res = np.zeros((N, 3))
size = np.prod((y_max - y_min + 1, x_max - x_min + 1))
print('solving...N: {}'.format(N))
stride = x_max - x_min + 1
A = scipy.sparse.identity(N, format='lil')
b = np.zeros((N, 3), dtype=np.float32)
for (j, i) in zip(loc[0], loc[1]):
alpha = 0.0 #w_l[j, i]
cur_ptr = loc_map[(j, i)]
if (blending_mask[j, i]):
N_p = 0.0
v_pq = np.zeros((1, 3), dtype=np.float32)
f_p = tar[j, i, :].astype(np.float32)
g_p = src[j, i, :].astype(np.float32)
if (j > 0):
if (fill_mask[j - 1, i]): #upper neighbor exists
f_q = tar[j - 1, i, :].astype(np.float32)
g_q = src[j - 1, i, :].astype(np.float32)
if (blending_mask[j - 1, i]): # in the omega
v_pq += np.dot([alpha, 1 - alpha],
np.array([(f_p - f_q), (g_p - g_q)]))
A[cur_ptr, loc_map[(j - 1, i)]] = -1.0
else: # on the boundary
# known function f*_p + v_pq
# here we choose gradient image of original image with its
# pixel value exists.
v_pq += tar[j - 1,
i, :].astype(np.float32) #+ (f_p-f_q)
N_p += 1.0
if (j < H - 1):
if (fill_mask[j + 1, i]): #lower neighbor exists
f_q = tar[j + 1, i, :].astype(np.float32)
g_q = src[j + 1, i, :].astype(np.float32)
if (blending_mask[j + 1, i]): # in the omega
v_pq += np.dot([alpha, 1 - alpha],
np.array([(f_p - f_q), (g_p - g_q)]))
A[cur_ptr, loc_map[(j + 1, i)]] = -1.0
else: # on the boundary
v_pq += tar[j + 1,
i, :].astype(np.float32) #+ (f_p-f_q)
N_p += 1.0
if (fill_mask[j, i - 1]): #left neighbor exists
f_q = tar[j, i - 1, :].astype(np.float32)
g_q = src[j, i - 1, :].astype(np.float32)
if (blending_mask[j, i - 1]): # in the omega
v_pq += np.dot([alpha, 1 - alpha],
np.array([(f_p - f_q), (g_p - g_q)]))
A[cur_ptr, loc_map[(j, i - 1)]] = -1.0
else: # on the boundary
v_pq += tar[j, i - 1, :].astype(np.float32) #+ (f_p-f_q)
N_p += 1.0
if (fill_mask[j, i + 1]): #right neighbor exists
f_q = tar[j, i + 1, :].astype(np.float32)
g_q = src[j, i + 1, :].astype(np.float32)
if (blending_mask[j, i + 1]): # in the omega
v_pq += np.dot([alpha, 1 - alpha],
np.array([(f_p - f_q), (g_p - g_q)]))
A[cur_ptr, loc_map[(j, i + 1)]] = -1.0
else: # on the boundary
v_pq += tar[j, i + 1, :].astype(np.float32) #+ (f_p-f_q)
N_p += 1.0
A[cur_ptr, cur_ptr] = N_p
b[cur_ptr, :] = v_pq.astype(np.float32)
else: # not in blending region
raise Exception('Illegal image!!')
gc.collect()
A = A.tocsr()
for c in range(3):
x = pyamg.solve(A, b[:, c], verb=True, tol=1e-5)
x = np.clip(x, 0, 255)
res[:, c] = x.astype('uint8')
tar = tar.copy()
tar[blending_mask, :] = res
return tar
from scipy import rand from numpy import arange, array from pyamg import solve from pyamg.gallery import poisson from pyamg.util.linalg import norm # Run solve(...) with the verbose option n = 100 A = poisson((n,n),format='csr') b = array(arange(A.shape[0]), dtype=float) x = solve(A,b,verb=True) ## # Return the solver generated by solve(...) so that it can be used again (x,ml) = solve(A,b,verb=True,return_solver=True,tol=1e-8) # run for a new right-hand-side b2 = rand(b.shape[0],) x2 = solve(A,b2,verb=True,existing_solver=ml,tol=1e-8)
def apply_inverse(matrix, U, options=None):
"""Solve linear equation system.
Applies the inverse of `matrix` to the row vectors in `U`.
See :func:`sparse_options` for documentation of all possible options for
sparse matrices.
Parameters
----------
matrix
The |NumPy| matrix to invert.
U
2-dimensional |NumPy array| containing as row vectors
the right-hand sides of the linear equation systems to
solve.
options
|invert_options| to use. (See :func:`invert_options`.)
Returns
-------
|NumPy array| of the solution vectors.
"""
default_options = invert_options(matrix)
if options is None:
options = default_options.values()[0]
elif isinstance(options, str):
if options == 'least_squares':
for k, v in default_options.iteritems():
if k.startswith('least_squares'):
options = v
break
assert not isinstance(options, str)
else:
options = default_options[options]
else:
assert 'type' in options and options['type'] in default_options \
and options.viewkeys() <= default_options[options['type']].viewkeys()
user_options = options
options = default_options[user_options['type']]
options.update(user_options)
R = np.empty((len(U), matrix.shape[1]))
if options['type'] == 'solve':
for i, UU in enumerate(U):
try:
R[i] = np.linalg.solve(matrix, UU)
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
elif options['type'] == 'least_squares_lstsq':
for i, UU in enumerate(U):
try:
R[i], _, _, _ = np.linalg.lstsq(matrix, UU, rcond=options['rcond'])
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
elif options['type'] == 'bicgstab':
for i, UU in enumerate(U):
R[i], info = bicgstab(matrix, UU, tol=options['tol'], maxiter=options['maxiter'])
if info != 0:
if info > 0:
raise InversionError('bicgstab failed to converge after {} iterations'.format(info))
else:
raise InversionError('bicgstab failed with error code {} (illegal input or breakdown)'.
format(info))
elif options['type'] == 'bicgstab_spilu':
ilu = spilu(matrix, drop_tol=options['spilu_drop_tol'], fill_factor=options['spilu_fill_factor'],
drop_rule=options['spilu_drop_rule'], permc_spec=options['spilu_permc_spec'])
precond = LinearOperator(matrix.shape, ilu.solve)
for i, UU in enumerate(U):
R[i], info = bicgstab(matrix, UU, tol=options['tol'], maxiter=options['maxiter'], M=precond)
if info != 0:
if info > 0:
raise InversionError('bicgstab failed to converge after {} iterations'.format(info))
else:
raise InversionError('bicgstab failed with error code {} (illegal input or breakdown)'.
format(info))
elif options['type'] == 'spsolve':
for i, UU in enumerate(U):
R[i] = spsolve(matrix, UU, permc_spec=options['permc_spec'])
elif options['type'] == 'lgmres':
for i, UU in enumerate(U):
R[i], info = lgmres(matrix, UU.copy(i),
tol=options['tol'],
maxiter=options['maxiter'],
inner_m=options['inner_m'],
outer_k=options['outer_k'])
if info > 0:
raise InversionError('lgmres failed to converge after {} iterations'.format(info))
assert info == 0
elif options['type'] == 'least_squares_lsmr':
for i, UU in enumerate(U):
R[i], info, itn, _, _, _, _, _ = lsmr(matrix, UU.copy(i),
damp=options['damp'],
atol=options['atol'],
btol=options['btol'],
conlim=options['conlim'],
maxiter=options['maxiter'],
show=options['show'])
assert 0 <= info <= 7
if info == 7:
raise InversionError('lsmr failed to converge after {} iterations'.format(itn))
elif options['type'] == 'least_squares_lsqr':
for i, UU in enumerate(U):
R[i], info, itn, _, _, _, _, _, _, _ = lsqr(matrix, UU.copy(i),
damp=options['damp'],
atol=options['atol'],
btol=options['btol'],
conlim=options['conlim'],
iter_lim=options['iter_lim'],
show=options['show'])
assert 0 <= info <= 7
if info == 7:
raise InversionError('lsmr failed to converge after {} iterations'.format(itn))
elif options['type'] == 'pyamg':
if len(U) > 0:
U_iter = iter(enumerate(U))
R[0], ml = pyamg.solve(matrix, next(U_iter)[1],
tol=options['tol'],
maxiter=options['maxiter'],
return_solver=True)
for i, UU in U_iter:
R[i] = pyamg.solve(matrix, UU,
tol=options['tol'],
maxiter=options['maxiter'],
existing_solver=ml)
elif options['type'] == 'pyamg-rs':
ml = pyamg.ruge_stuben_solver(matrix,
strength=options['strength'],
CF=options['CF'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
coarse_solver=options['coarse_solver'])
for i, UU in enumerate(U):
R[i] = ml.solve(UU,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'] == 'pyamg-sa':
ml = pyamg.smoothed_aggregation_solver(matrix,
symmetry=options['symmetry'],
strength=options['strength'],
aggregate=options['aggregate'],
smooth=options['smooth'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
improve_candidates=options['improve_candidates'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
diagonal_dominance=options['diagonal_dominance'])
for i, UU in enumerate(U):
R[i] = ml.solve(UU,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'].startswith('generic') or options['type'].startswith('least_squares_generic'):
logger = getLogger('pymor.la.numpysolvers.apply_inverse')
logger.warn('You have selected a (potentially slow) generic solver for a NumPy matrix operator!')
from pymor.operators.basic import NumpyMatrixOperator
from pymor.la import NumpyVectorArray
return genericsolvers.apply_inverse(NumpyMatrixOperator(matrix),
NumpyVectorArray(U, copy=False),
options=options).data
else:
raise ValueError('Unknown solver type')
return R
def apply_inverse(op, V, options=None, least_squares=False, check_finite=True, default_solver='pyamg_solve'):
"""Solve linear equation system.
Applies the inverse of `op` to the vectors in `rhs` using PyAMG.
Parameters
----------
op
The linear, non-parametric |Operator| to invert.
rhs
|VectorArray| of right-hand sides for the equation system.
options
The |solver_options| to use (see :func:`solver_options`).
check_finite
Test if solution only containes finite values.
default_solver
Default solver to use (pyamg_solve, pyamg_rs, pyamg_sa).
Returns
-------
|VectorArray| of the solution vectors.
"""
assert V in op.range
if isinstance(op, NumpyMatrixOperator):
matrix = op._matrix
else:
from pymor.algorithms.to_matrix import to_matrix
matrix = to_matrix(op)
options = _parse_options(options, solver_options(), default_solver, None, least_squares)
V = V.data
promoted_type = np.promote_types(matrix.dtype, V.dtype)
R = np.empty((len(V), matrix.shape[1]), dtype=promoted_type)
if options['type'] == 'pyamg_solve':
if len(V) > 0:
V_iter = iter(enumerate(V))
R[0], ml = pyamg.solve(matrix, next(V_iter)[1],
tol=options['tol'],
maxiter=options['maxiter'],
return_solver=True)
for i, VV in V_iter:
R[i] = pyamg.solve(matrix, VV,
tol=options['tol'],
maxiter=options['maxiter'],
existing_solver=ml)
elif options['type'] == 'pyamg_rs':
ml = pyamg.ruge_stuben_solver(matrix,
strength=options['strength'],
CF=options['CF'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
coarse_solver=options['coarse_solver'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'] == 'pyamg_sa':
ml = pyamg.smoothed_aggregation_solver(matrix,
symmetry=options['symmetry'],
strength=options['strength'],
aggregate=options['aggregate'],
smooth=options['smooth'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
improve_candidates=options['improve_candidates'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
diagonal_dominance=options['diagonal_dominance'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
else:
raise ValueError('Unknown solver type')
if check_finite:
if not np.isfinite(np.sum(R)):
raise InversionError('Result contains non-finite values')
return op.source.from_data(R)
def diffuse_inprob(inprobs, paths, segs, imgs):
#inprobs is a list of inside probability for superpixels
init_prob = []
id2index = []
index = 0
n_last = len(np.unique(segs[-1]))
for i in range(len(inprobs)):
id2index.append({})
for (jj, j) in enumerate(inprobs[i]):
init_prob.append(j)
id2index[i][jj] = index
index += 1
dist = []
row_index = []
col_index = []
rgbs = np.zeros((len(init_prob), 3))
n_frames = len(imgs)
for (i, id) in enumerate(paths.keys()):
frame = paths[id].frame
rows = paths[id].rows
cols = paths[id].cols
unique_frame = np.unique(frame)
for f in unique_frame:
if f == n_frames - 1: continue
r1 = rows[frame == f]
c1 = cols[frame == f]
index1 = id2index[f][segs[f][r1[0], c1[0]]]
rgb1 = np.mean(imgs[f][r1, c1], axis=0)
rgbs[index1] = rgb1
for f2 in unique_frame:
if f >= f2: continue
if f2 == n_frames - 1: continue
r2 = rows[frame == f2]
c2 = cols[frame == f2]
rgb2 = np.mean(imgs[f2][r2, c2], axis=0)
index2 = id2index[f2][segs[f2][r2[0], c2[0]]]
rgbs[index2] = rgb2
d = np.linalg.norm(rgb1 - rgb2)**2
row_index.append(index1)
row_index.append(index2)
col_index.append(index2)
col_index.append(index1)
dist.append(d)
dist.append(d)
adjs = sp_adj(segs)
for i in range(n_frames - 1):
for j in range(adjs[i].shape[0]):
index1 = id2index[i][j]
rgb1 = rgbs[index1]
row_index.append(index1)
col_index.append(index1)
dist.append(0)
for k in np.nonzero(adjs[i][j])[0]:
if j > k: continue
index2 = id2index[i][k]
rgb2 = rgbs[index2]
d = np.linalg.norm(rgb1 - rgb2)**2
row_index.append(index1)
row_index.append(index2)
col_index.append(index2)
col_index.append(index1)
dist.append(d)
dist.append(d)
sigma = 30
values2 = np.exp(-np.array(dist) / (2 * sigma**2))
from scipy.sparse import csr_matrix, spdiags
n_node = len(init_prob)
W = csr_matrix((values2, (row_index, col_index)), shape=(n_node, n_node))
inv_D = spdiags(1.0 / ((W.sum(axis=1)).flatten()), 0, W.shape[0],
W.shape[1])
D = spdiags(W.sum(axis=1).flatten(), 0, W.shape[0], W.shape[1])
lam = 10
lhs = D + lam * (D - W)
from scipy.sparse import eye
from scipy.sparse.linalg import spsolve, lsmr
# diffused_prob = spsolve(lhs, D.dot(np.array(init_prob)))
diffused_prob = solve(lhs, D.dot(np.array(init_prob)))
diffused_probs = []
count = 0
for i in range(len(inprobs)):
diffused_probs.append(diffused_prob[count:len(inprobs[i]) + count])
count += len(inprobs[i])
return diffused_probs
def _apply_inverse(matrix, V, options=None):
"""Solve linear equation system.
Applies the inverse of `matrix` to the row vectors in `V`.
See :func:`dense_options` for documentation of all possible options for
sparse matrices.
See :func:`sparse_options` for documentation of all possible options for
sparse matrices.
This method is called by :meth:`pymor.core.NumpyMatrixOperator.apply_inverse`
and usually should not be used directly.
Parameters
----------
matrix
The |NumPy| matrix to invert.
V
2-dimensional |NumPy array| containing as row vectors
the right-hand sides of the linear equation systems to
solve.
options
The solver options to use. (See :func:`_options`.)
Returns
-------
|NumPy array| of the solution vectors.
"""
default_options = _options(matrix)
if options is None:
options = default_options.values()[0]
elif isinstance(options, str):
if options == "least_squares":
for k, v in default_options.iteritems():
if k.startswith("least_squares"):
options = v
break
assert not isinstance(options, str)
else:
options = default_options[options]
else:
assert (
"type" in options
and options["type"] in default_options
and options.viewkeys() <= default_options[options["type"]].viewkeys()
)
user_options = options
options = default_options[user_options["type"]]
options.update(user_options)
R = np.empty((len(V), matrix.shape[1]), dtype=np.promote_types(matrix.dtype, V.dtype))
if options["type"] == "solve":
for i, VV in enumerate(V):
try:
R[i] = np.linalg.solve(matrix, VV)
except np.linalg.LinAlgError as e:
raise InversionError("{}: {}".format(str(type(e)), str(e)))
elif options["type"] == "least_squares_lstsq":
for i, VV in enumerate(V):
try:
R[i], _, _, _ = np.linalg.lstsq(matrix, VV, rcond=options["rcond"])
except np.linalg.LinAlgError as e:
raise InversionError("{}: {}".format(str(type(e)), str(e)))
elif options["type"] == "bicgstab":
for i, VV in enumerate(V):
R[i], info = bicgstab(matrix, VV, tol=options["tol"], maxiter=options["maxiter"])
if info != 0:
if info > 0:
raise InversionError("bicgstab failed to converge after {} iterations".format(info))
else:
raise InversionError("bicgstab failed with error code {} (illegal input or breakdown)".format(info))
elif options["type"] == "bicgstab_spilu":
ilu = spilu(
matrix,
drop_tol=options["spilu_drop_tol"],
fill_factor=options["spilu_fill_factor"],
drop_rule=options["spilu_drop_rule"],
permc_spec=options["spilu_permc_spec"],
)
precond = LinearOperator(matrix.shape, ilu.solve)
for i, VV in enumerate(V):
R[i], info = bicgstab(matrix, VV, tol=options["tol"], maxiter=options["maxiter"], M=precond)
if info != 0:
if info > 0:
raise InversionError("bicgstab failed to converge after {} iterations".format(info))
else:
raise InversionError("bicgstab failed with error code {} (illegal input or breakdown)".format(info))
elif options["type"] == "spsolve":
try:
if scipy.version.version >= "0.14":
if hasattr(matrix, "factorization"):
R = matrix.factorization.solve(V.T).T
elif options["keep_factorization"]:
matrix.factorization = splu(matrix, permc_spec=options["permc_spec"])
R = matrix.factorization.solve(V.T).T
else:
R = spsolve(matrix, V.T, permc_spec=options["permc_spec"]).T
else:
if hasattr(matrix, "factorization"):
for i, VV in enumerate(V):
R[i] = matrix.factorization.solve(VV)
elif options["keep_factorization"]:
matrix.factorization = splu(matrix, permc_spec=options["permc_spec"])
for i, VV in enumerate(V):
R[i] = matrix.factorization.solve(VV)
elif len(V) > 1:
factorization = splu(matrix, permc_spec=options["permc_spec"])
for i, VV in enumerate(V):
R[i] = factorization.solve(VV)
else:
R = spsolve(matrix, V.T, permc_spec=options["permc_spec"]).reshape((1, -1))
except RuntimeError as e:
raise InversionError(e)
elif options["type"] == "lgmres":
for i, VV in enumerate(V):
R[i], info = lgmres(
matrix,
VV.copy(i),
tol=options["tol"],
maxiter=options["maxiter"],
inner_m=options["inner_m"],
outer_k=options["outer_k"],
)
if info > 0:
raise InversionError("lgmres failed to converge after {} iterations".format(info))
assert info == 0
elif options["type"] == "least_squares_lsmr":
for i, VV in enumerate(V):
R[i], info, itn, _, _, _, _, _ = lsmr(
matrix,
VV.copy(i),
damp=options["damp"],
atol=options["atol"],
btol=options["btol"],
conlim=options["conlim"],
maxiter=options["maxiter"],
show=options["show"],
)
assert 0 <= info <= 7
if info == 7:
raise InversionError("lsmr failed to converge after {} iterations".format(itn))
elif options["type"] == "least_squares_lsqr":
for i, VV in enumerate(V):
R[i], info, itn, _, _, _, _, _, _, _ = lsqr(
matrix,
VV.copy(i),
damp=options["damp"],
atol=options["atol"],
btol=options["btol"],
conlim=options["conlim"],
iter_lim=options["iter_lim"],
show=options["show"],
)
assert 0 <= info <= 7
if info == 7:
raise InversionError("lsmr failed to converge after {} iterations".format(itn))
elif options["type"] == "pyamg":
if len(V) > 0:
V_iter = iter(enumerate(V))
R[0], ml = pyamg.solve(
matrix, next(V_iter)[1], tol=options["tol"], maxiter=options["maxiter"], return_solver=True
)
for i, VV in V_iter:
R[i] = pyamg.solve(matrix, VV, tol=options["tol"], maxiter=options["maxiter"], existing_solver=ml)
elif options["type"] == "pyamg-rs":
ml = pyamg.ruge_stuben_solver(
matrix,
strength=options["strength"],
CF=options["CF"],
presmoother=options["presmoother"],
postsmoother=options["postsmoother"],
max_levels=options["max_levels"],
max_coarse=options["max_coarse"],
coarse_solver=options["coarse_solver"],
)
for i, VV in enumerate(V):
R[i] = ml.solve(
VV, tol=options["tol"], maxiter=options["maxiter"], cycle=options["cycle"], accel=options["accel"]
)
elif options["type"] == "pyamg-sa":
ml = pyamg.smoothed_aggregation_solver(
matrix,
symmetry=options["symmetry"],
strength=options["strength"],
aggregate=options["aggregate"],
smooth=options["smooth"],
presmoother=options["presmoother"],
postsmoother=options["postsmoother"],
improve_candidates=options["improve_candidates"],
max_levels=options["max_levels"],
max_coarse=options["max_coarse"],
diagonal_dominance=options["diagonal_dominance"],
)
for i, VV in enumerate(V):
R[i] = ml.solve(
VV, tol=options["tol"], maxiter=options["maxiter"], cycle=options["cycle"], accel=options["accel"]
)
elif options["type"].startswith("generic") or options["type"].startswith("least_squares_generic"):
logger = getLogger("pymor.operators.numpy._apply_inverse")
logger.warn("You have selected a (potentially slow) generic solver for a NumPy matrix operator!")
from pymor.operators.numpy import NumpyMatrixOperator
from pymor.vectorarrays.numpy import NumpyVectorArray
return genericsolvers.apply_inverse(
NumpyMatrixOperator(matrix), NumpyVectorArray(V, copy=False), options=options
).data
else:
raise ValueError("Unknown solver type")
return R
def blend(img_target, img_source, img_mask, offset, center):
# compute regions to be blended
# clip and normalize mask image
# create coefficient matrix
if (img_target.shape != img_source.shape):
img_source = cv2.resize(img_source,
(img_target.shape[1], img_target.shape[0]))
img_mask = cv2.resize(img_mask,
(img_target.shape[1], img_target.shape[0]))
img_source = np.roll(img_source, offset[1], axis=0)
img_source = np.roll(img_source, offset[0], axis=1)
img_mask = np.roll(img_mask, offset[1], axis=0)
img_mask = np.roll(img_mask, offset[0], axis=1)
img_mask = rgb2gray(img_mask)
zeros = np.nonzero(img_mask)
sizeofzero = zeros[0].shape[0] / img_mask.shape[
0] #ratio of white to black features
erosion = int(sizeofzero * (80 / 120))
SE = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,
(erosion + 50, erosion + 50))
if (erosion - 40 < 0):
SE = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,
(erosion + 35, erosion + 35))
SE2 = cv2.getStructuringElement(cv2.MORPH_RECT,
(erosion + 9, erosion + 9))
else:
SE2 = cv2.getStructuringElement(cv2.MORPH_RECT,
(erosion - 30, erosion - 5))
#img_mask[0:int(center[0]),::]=binary_erosion(img_mask[0:int(center[0]),::],SE)
#img_mask[int(center[0]):img_mask.shape[0],::]=binary_erosion( img_mask[int(center[0]):img_mask.shape[0],::],SE2)
img_mask = binary_erosion(img_mask, SE)
img_mask = binary_dilation(img_mask, SE2)
show_images([img_mask])
#img_mask=binary_dilation(img_mask,SE1)
#SE=np.ones(())
A = scipy.sparse.identity(img_mask.shape[0] * img_mask.shape[1],
format='lil')
for j in range(img_mask.shape[0]):
for i in range(img_mask.shape[1]):
if img_mask[j][i] != 0:
index = i + j * img_mask.shape[1]
A[index, index] = 4
if index + 1 < (img_mask.shape[0] * img_mask.shape[1]):
A[index, index + 1] = -1
if index - 1 >= 0:
A[index, index - 1] = -1
if index + img_mask.shape[
1] < img_mask.shape[0] * img_mask.shape[1]:
A[index, index + img_mask.shape[1]] = -1
if index - img_mask.shape[1] >= 0:
A[index, index - img_mask.shape[1]] = -1
A = A.tocsr()
# create poisson matrix for b
P = pyamg.gallery.poisson(img_mask.shape)
# for each layer (ex. RGB)
for RGB in range(3):
# get subimages
t = img_target[:, :, RGB]
s = img_source[:, :, RGB]
t = t.flatten()
s = s.flatten()
# create b
b = P * s
laplace = np.abs(np.reshape(b, img_mask.shape))
F2 = np.array([[0, 1, 0], [1, -4, 1], [0, 1, 0]])
filter1 = np.abs(convolve2d(in1=img_source[:, :, RGB], in2=F2))
show_images([laplace, filter1], ["poisson", "LOG"])
for y in range(img_mask.shape[0]):
for x in range(img_mask.shape[1]):
if img_mask[y][x] == 0:
index = x + y * img_mask.shape[1]
b[index] = t[index]
# solve Ax = b
x = pyamg.solve(A, b, verb=False, tol=1e-10)
# assign x to target image
x = np.reshape(x, img_mask.shape)
x[x > 255] = 255
x[x < 0] = 0
x = np.array(x, img_target.dtype)
img_target[:, :, RGB] = x
return img_target
def _apply_inverse(matrix, V, options=None):
"""Solve linear equation system.
Applies the inverse of `matrix` to the row vectors in `V`.
See :func:`dense_options` for documentation of all possible options for
sparse matrices.
See :func:`sparse_options` for documentation of all possible options for
sparse matrices.
This method is called by :meth:`pymor.core.NumpyMatrixOperator.apply_inverse`
and usually should not be used directly.
Parameters
----------
matrix
The |NumPy| matrix to invert.
V
2-dimensional |NumPy array| containing as row vectors
the right-hand sides of the linear equation systems to
solve.
options
The solver options to use. (See :func:`_options`.)
Returns
-------
|NumPy array| of the solution vectors.
"""
default_options = _options(matrix)
if options is None:
options = next(iter(default_options.values()))
elif isinstance(options, str):
if options == 'least_squares':
for k, v in default_options.items():
if k.startswith('least_squares'):
options = v
break
assert not isinstance(options, str)
else:
options = default_options[options]
else:
assert 'type' in options and options['type'] in default_options \
and options.keys() <= default_options[options['type']].keys()
user_options = options
options = default_options[user_options['type']]
options.update(user_options)
promoted_type = np.promote_types(matrix.dtype, V.dtype)
R = np.empty((len(V), matrix.shape[1]), dtype=promoted_type)
if options['type'] == 'solve':
for i, VV in enumerate(V):
try:
R[i] = np.linalg.solve(matrix, VV)
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
elif options['type'] == 'least_squares_lstsq':
for i, VV in enumerate(V):
try:
R[i], _, _, _ = np.linalg.lstsq(matrix,
VV,
rcond=options['rcond'])
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
elif options['type'] == 'bicgstab':
for i, VV in enumerate(V):
R[i], info = bicgstab(matrix,
VV,
tol=options['tol'],
maxiter=options['maxiter'])
if info != 0:
if info > 0:
raise InversionError(
'bicgstab failed to converge after {} iterations'.
format(info))
else:
raise InversionError(
'bicgstab failed with error code {} (illegal input or breakdown)'
.format(info))
elif options['type'] == 'bicgstab_spilu':
# workaround for https://github.com/pymor/pymor/issues/171
try:
ilu = spilu(matrix,
drop_tol=options['spilu_drop_tol'],
fill_factor=options['spilu_fill_factor'],
drop_rule=options['spilu_drop_rule'],
permc_spec=options['spilu_permc_spec'])
except TypeError as t:
logger = getLogger('pymor.operators.numpy._apply_inverse')
logger.error("ignoring drop_rule in ilu factorization")
ilu = spilu(matrix,
drop_tol=options['spilu_drop_tol'],
fill_factor=options['spilu_fill_factor'],
permc_spec=options['spilu_permc_spec'])
precond = LinearOperator(matrix.shape, ilu.solve)
for i, VV in enumerate(V):
R[i], info = bicgstab(matrix,
VV,
tol=options['tol'],
maxiter=options['maxiter'],
M=precond)
if info != 0:
if info > 0:
raise InversionError(
'bicgstab failed to converge after {} iterations'.
format(info))
else:
raise InversionError(
'bicgstab failed with error code {} (illegal input or breakdown)'
.format(info))
elif options['type'] == 'spsolve':
try:
# maybe remove unusable factorization:
if hasattr(matrix, 'factorization'):
fdtype = matrix.factorizationdtype
if not np.can_cast(V.dtype, fdtype, casting='safe'):
del matrix.factorization
if list(map(int, scipy.version.version.split('.'))) >= [0, 14, 0]:
if hasattr(matrix, 'factorization'):
# we may use a complex factorization of a real matrix to
# apply it to a real vector. In that case, we downcast
# the result here, removing the imaginary part,
# which should be zero.
R = matrix.factorization.solve(V.T).T.astype(promoted_type,
copy=False)
elif options['keep_factorization']:
# the matrix is always converted to the promoted type.
# if matrix.dtype == promoted_type, this is a no_op
matrix.factorization = splu(
matrix_astype_nocopy(matrix, promoted_type),
permc_spec=options['permc_spec'])
matrix.factorizationdtype = promoted_type
R = matrix.factorization.solve(V.T).T
else:
# the matrix is always converted to the promoted type.
# if matrix.dtype == promoted_type, this is a no_op
R = spsolve(matrix_astype_nocopy(matrix, promoted_type),
V.T,
permc_spec=options['permc_spec']).T
else:
# see if-part for documentation
if hasattr(matrix, 'factorization'):
for i, VV in enumerate(V):
R[i] = matrix.factorization.solve(VV).astype(
promoted_type, copy=False)
elif options['keep_factorization']:
matrix.factorization = splu(
matrix_astype_nocopy(matrix, promoted_type),
permc_spec=options['permc_spec'])
matrix.factorizationdtype = promoted_type
for i, VV in enumerate(V):
R[i] = matrix.factorization.solve(VV)
elif len(V) > 1:
factorization = splu(matrix_astype_nocopy(
matrix, promoted_type),
permc_spec=options['permc_spec'])
for i, VV in enumerate(V):
R[i] = factorization.solve(VV)
else:
R = spsolve(matrix_astype_nocopy(matrix, promoted_type),
V.T,
permc_spec=options['permc_spec']).reshape(
(1, -1))
except RuntimeError as e:
raise InversionError(e)
elif options['type'] == 'lgmres':
for i, VV in enumerate(V):
R[i], info = lgmres(matrix,
VV.copy(i),
tol=options['tol'],
maxiter=options['maxiter'],
inner_m=options['inner_m'],
outer_k=options['outer_k'])
if info > 0:
raise InversionError(
'lgmres failed to converge after {} iterations'.format(
info))
assert info == 0
elif options['type'] == 'least_squares_lsmr':
for i, VV in enumerate(V):
R[i], info, itn, _, _, _, _, _ = lsmr(matrix,
VV.copy(i),
damp=options['damp'],
atol=options['atol'],
btol=options['btol'],
conlim=options['conlim'],
maxiter=options['maxiter'],
show=options['show'])
assert 0 <= info <= 7
if info == 7:
raise InversionError(
'lsmr failed to converge after {} iterations'.format(itn))
elif options['type'] == 'least_squares_lsqr':
for i, VV in enumerate(V):
R[i], info, itn, _, _, _, _, _, _, _ = lsqr(
matrix,
VV.copy(i),
damp=options['damp'],
atol=options['atol'],
btol=options['btol'],
conlim=options['conlim'],
iter_lim=options['iter_lim'],
show=options['show'])
assert 0 <= info <= 7
if info == 7:
raise InversionError(
'lsmr failed to converge after {} iterations'.format(itn))
elif options['type'] == 'pyamg':
if len(V) > 0:
V_iter = iter(enumerate(V))
R[0], ml = pyamg.solve(matrix,
next(V_iter)[1],
tol=options['tol'],
maxiter=options['maxiter'],
return_solver=True)
for i, VV in V_iter:
R[i] = pyamg.solve(matrix,
VV,
tol=options['tol'],
maxiter=options['maxiter'],
existing_solver=ml)
elif options['type'] == 'pyamg-rs':
ml = pyamg.ruge_stuben_solver(matrix,
strength=options['strength'],
CF=options['CF'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
coarse_solver=options['coarse_solver'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'] == 'pyamg-sa':
ml = pyamg.smoothed_aggregation_solver(
matrix,
symmetry=options['symmetry'],
strength=options['strength'],
aggregate=options['aggregate'],
smooth=options['smooth'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
improve_candidates=options['improve_candidates'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
diagonal_dominance=options['diagonal_dominance'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'].startswith('generic') or options['type'].startswith(
'least_squares_generic'):
logger = getLogger('pymor.operators.numpy._apply_inverse')
logger.warn(
'You have selected a (potentially slow) generic solver for a NumPy matrix operator!'
)
from pymor.operators.numpy import NumpyMatrixOperator
from pymor.vectorarrays.numpy import NumpyVectorArray
return genericsolvers.apply_inverse(NumpyMatrixOperator(matrix),
NumpyVectorArray(V, copy=False),
options=options).data
else:
raise ValueError('Unknown solver type')
return R
def poisson_blend(img_source, dest_img, img_mask, offset=(0, 0)):
# http://opencv.jp/opencv2-x-samples/poisson-blending
img_target = np.copy(dest_img)
import pyamg
# compute regions to be blended
region_source = (
max(-offset[0], 0),
max(-offset[1], 0),
min(img_target.shape[0] - offset[0], img_source.shape[0]),
min(img_target.shape[1] - offset[1], img_source.shape[1]))
region_target = (
max(offset[0], 0),
max(offset[1], 0),
min(img_target.shape[0], img_source.shape[0] + offset[0]),
min(img_target.shape[1], img_source.shape[1] + offset[1]))
region_size = (region_source[2] - region_source[0],
region_source[3] - region_source[1])
# clip and normalize mask image
img_mask = img_mask[region_source[0]:region_source[2],
region_source[1]:region_source[3]]
# create coefficient matrix
coff_mat = scipy.sparse.identity(np.prod(region_size), format='lil')
for y in range(region_size[0]):
for x in range(region_size[1]):
if img_mask[y, x]:
index = x + y * region_size[1]
coff_mat[index, index] = 4
if index + 1 < np.prod(region_size):
coff_mat[index, index + 1] = -1
if index - 1 >= 0:
coff_mat[index, index - 1] = -1
if index + region_size[1] < np.prod(region_size):
coff_mat[index, index + region_size[1]] = -1
if index - region_size[1] >= 0:
coff_mat[index, index - region_size[1]] = -1
coff_mat = coff_mat.tocsr()
# create poisson matrix for b
poisson_mat = pyamg.gallery.poisson(img_mask.shape)
# for each layer (ex. RGB)
for num_layer in range(img_target.shape[2]):
# get subimages
t = img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer]
s = img_source[region_source[0]:region_source[2],
region_source[1]:region_source[3], num_layer]
t = t.flatten()
s = s.flatten()
# create b
b = poisson_mat * s
for y in range(region_size[0]):
for x in range(region_size[1]):
if not img_mask[y, x]:
index = x + y * region_size[1]
b[index] = t[index]
# solve Ax = b
x = pyamg.solve(coff_mat, b, verb=False, tol=1e-10)
# assign x to target image
x = np.reshape(x, region_size)
x[x > 255] = 255
x[x < 0] = 0
x = np.array(x, img_target.dtype)
img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer] = x
return img_target
def blend(img_target, img_source, img_mask, offset=(0, 0), mode=0):
# modes:
# 0 — standard
# 1 — mixing
# 2 — average
# compute regions to be blended
region_source = (max(-offset[0], 0), max(-offset[1], 0),
min(img_target.shape[0] - offset[0], img_source.shape[0]),
min(img_target.shape[1] - offset[1], img_source.shape[1]))
region_target = (max(offset[0], 0), max(offset[1], 0),
min(img_target.shape[0], img_source.shape[0] + offset[0]),
min(img_target.shape[1], img_source.shape[1] + offset[1]))
region_size = (region_source[2] - region_source[0],
region_source[3] - region_source[1])
# clip and normalize mask image
img_mask = img_mask[region_source[0]:region_source[2],
region_source[1]:region_source[3]]
img_mask = prepare_mask(img_mask)
#img_mask[img_mask==0] = False
#img_mask[img_mask!=False] = True
# create coefficient matrix
A = scipy.sparse.identity(np.prod(region_size), format='lil')
for y in range(region_size[0]):
for x in range(region_size[1]):
if img_mask[y, x] != 0:
index = x + y * region_size[1]
Np = 0
if index + 1 < np.prod(region_size):
A[index, index + 1] = -1
Np += 1
if index - 1 >= 0:
A[index, index - 1] = -1
Np += 1
if index + region_size[1] < np.prod(region_size):
A[index, index + region_size[1]] = -1
Np += 1
if index - region_size[1] >= 0:
A[index, index - region_size[1]] = -1
Np += 1
A[index, index] = Np
A = A.tocsr()
# create poisson matrix for b
P = pyamg.gallery.poisson(img_mask.shape)
# for each layer (ex. RGB)
N = 1 if len(img_target.shape) < 3 else img_target.shape[2]
for num_layer in range(N):
# get subimages
if N == 1:
tar = img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3]]
sour = img_source[region_source[0]:region_source[2],
region_source[1]:region_source[3]]
else:
tar = img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer]
sour = img_source[region_source[0]:region_source[2],
region_source[1]:region_source[3], num_layer]
t = tar.flatten()
s = sour.flatten()
# create b
B = P * s
for y in range(region_size[0]):
for x in range(region_size[1]):
if img_mask[y, x] == 0:
index = x + y * region_size[1]
#B[index] = t[index]
#b = scipy.sparse.lil_matrix((np.prod(region_size)))
b = np.zeros(np.prod(region_size))
for y in range(region_size[0]):
for x in range(region_size[1]):
index = x + y * region_size[1]
if img_mask[y, x] != 0:
sum = 0
neighbors = [[1, 0], [0, 1], [0, -1], [-1, 0]]
checkIfOutOfRange = lambda ind: ind[0] >= 0 and ind[
1] >= 0 and ind[0] < region_size[0] and ind[
1] < region_size[1]
for nb in neighbors:
p2 = tuple(np.array([y, x]) + np.array(nb))
if checkIfOutOfRange(p2) and img_mask[p2] != 0:
s1 = int(sour[y, x]) - int(sour[p2])
s2 = int(tar[y, x]) - int(tar[p2])
if mode == 0: #standard
sum += s1
elif mode == 1: #mixing
sum += s1 if abs(s1) >= abs(s2) else s2
elif mode == 2: #average
sum += (1.0 * (s1 + s2)) / 2
elif mode == -1:
pass
b[index] = sum
else:
pass
b[index] = t[index]
# solve Ax = b
x = pyamg.solve(A, b, verb=False, tol=1e-10)
#print time.time() - start
#print region_target
#x = seidel(A,b, 1e-10)
# assign x to target image
x = np.reshape(x, region_size)
x[x > 255] = 255
x[x < 0] = 0
x = np.array(x, img_target.dtype)
#print x.shape
if N == 1:
img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3]] = x
else:
img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer] = x
return img_target
def poisson_blend(img_source, dest_img, img_mask, offset=(0, 0)):
# http://opencv.jp/opencv2-x-samples/poisson-blending
img_target = np.copy(dest_img)
import pyamg
# compute regions to be blended
region_source = (max(-offset[0], 0), max(-offset[1], 0),
min(img_target.shape[0] - offset[0], img_source.shape[0]),
min(img_target.shape[1] - offset[1], img_source.shape[1]))
region_target = (max(offset[0], 0), max(offset[1], 0),
min(img_target.shape[0], img_source.shape[0] + offset[0]),
min(img_target.shape[1], img_source.shape[1] + offset[1]))
region_size = (region_source[2] - region_source[0],
region_source[3] - region_source[1])
# clip and normalize mask image
img_mask = img_mask[region_source[0]:region_source[2],
region_source[1]:region_source[3]]
# create coefficient matrix
coff_mat = scipy.sparse.identity(np.prod(region_size), format='lil')
for y in range(region_size[0]):
for x in range(region_size[1]):
if img_mask[y, x]:
index = x + y * region_size[1]
coff_mat[index, index] = 4
if index + 1 < np.prod(region_size):
coff_mat[index, index + 1] = -1
if index - 1 >= 0:
coff_mat[index, index - 1] = -1
if index + region_size[1] < np.prod(region_size):
coff_mat[index, index + region_size[1]] = -1
if index - region_size[1] >= 0:
coff_mat[index, index - region_size[1]] = -1
coff_mat = coff_mat.tocsr()
# create poisson matrix for b
poisson_mat = pyamg.gallery.poisson(img_mask.shape)
# for each layer (ex. RGB)
for num_layer in range(img_target.shape[2]):
# get subimages
t = img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer]
s = img_source[region_source[0]:region_source[2],
region_source[1]:region_source[3], num_layer]
t = t.flatten()
s = s.flatten()
# create b
b = poisson_mat * s
for y in range(region_size[0]):
for x in range(region_size[1]):
if not img_mask[y, x]:
index = x + y * region_size[1]
b[index] = t[index]
# solve Ax = b
x = pyamg.solve(coff_mat, b, verb=False, tol=1e-10)
# assign x to target image
x = np.reshape(x, region_size)
x[x > 255] = 255
x[x < 0] = 0
x = np.array(x, img_target.dtype)
img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer] = x
return img_target
def blend(img_target, img_source, img_mask, offset=(0, 0)):
# compute regions to be blended
region_source = (max(-offset[0], 0), max(-offset[1], 0),
min(img_target.shape[0] - offset[0], img_source.shape[0]),
min(img_target.shape[1] - offset[1], img_source.shape[1]))
region_target = (max(offset[0], 0), max(offset[1], 0),
min(img_target.shape[0], img_source.shape[0] + offset[0]),
min(img_target.shape[1], img_source.shape[1] + offset[1]))
region_size = (region_source[2] - region_source[0],
region_source[3] - region_source[1])
# clip and normalize mask image
img_mask = img_mask[region_source[0]:region_source[2],
region_source[1]:region_source[3]]
img_mask = prepare_mask(img_mask)
img_mask[img_mask == 0] = False
img_mask[img_mask != False] = True
# create coefficient matrix
A = scipy.sparse.identity(np.prod(region_size), format='lil')
for y in range(region_size[0]):
for x in range(region_size[1]):
if img_mask[y, x]:
index = x + y * region_size[1]
A[index, index] = 4
if index + 1 < np.prod(region_size):
A[index, index + 1] = -1
if index - 1 >= 0:
A[index, index - 1] = -1
if index + region_size[1] < np.prod(region_size):
A[index, index + region_size[1]] = -1
if index - region_size[1] >= 0:
A[index, index - region_size[1]] = -1
A = A.tocsr()
# create poisson matrix for b
P = pyamg.gallery.poisson(img_mask.shape)
# for each layer (ex. RGB)
for num_layer in range(img_target.shape[2]):
# get subimages
t = img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer]
s = img_source[region_source[0]:region_source[2],
region_source[1]:region_source[3], num_layer]
t = t.flatten()
s = s.flatten()
# create b
b = P * s
for y in range(region_size[0]):
for x in range(region_size[1]):
if not img_mask[y, x]:
index = x + y * region_size[1]
b[index] = t[index]
# solve Ax = b
x = pyamg.solve(A, b, verb=False, tol=1e-10)
# assign x to target image
x = np.reshape(x, region_size)
x[x > 255] = 255
x[x < 0] = 0
x = np.array(x, img_target.dtype)
img_target[region_target[0]:region_target[2],
region_target[1]:region_target[3], num_layer] = x
return img_target
handle an arbitrary matrix.
"""
from scipy import rand
from numpy import arange, array
from pyamg import solve
from pyamg.gallery import poisson
from pyamg.util.linalg import norm
if __name__ == '__main__':
##
# Run solve(...) with the verbose option
n = 100
A = poisson((n,n),format='csr')
b = array(arange(A.shape[0]), dtype=float)
print ""
x = solve(A,b,verb=True)
##
# Return the solver generated by solve(...) so that it can be used again
print ""
(x,ml) = solve(A,b,verb=True,return_solver=True,tol=1e-8)
# run for a new right-hand-side
b2 = rand(b.shape[0],)
print ""
x2 = solve(A,b2,verb=True,existing_solver=ml,tol=1e-8)
print ""
def _apply_inverse(matrix, V, options=None):
"""Solve linear equation system.
Applies the inverse of `matrix` to the row vectors in `V`.
See :func:`dense_options` for documentation of all possible options for
sparse matrices.
See :func:`sparse_options` for documentation of all possible options for
sparse matrices.
This method is called by :meth:`pymor.core.NumpyMatrixOperator.apply_inverse`
and usually should not be used directly.
Parameters
----------
matrix
The |NumPy| matrix to invert.
V
2-dimensional |NumPy array| containing as row vectors
the right-hand sides of the linear equation systems to
solve.
options
The solver options to use. (See :func:`_options`.)
Returns
-------
|NumPy array| of the solution vectors.
"""
default_options = _options(matrix)
if options is None:
options = default_options.values()[0]
elif isinstance(options, str):
if options == 'least_squares':
for k, v in default_options.iteritems():
if k.startswith('least_squares'):
options = v
break
assert not isinstance(options, str)
else:
options = default_options[options]
else:
assert 'type' in options and options['type'] in default_options \
and options.viewkeys() <= default_options[options['type']].viewkeys()
user_options = options
options = default_options[user_options['type']]
options.update(user_options)
promoted_type = np.promote_types(matrix.dtype, V.dtype)
R = np.empty((len(V), matrix.shape[1]), dtype=promoted_type)
if options['type'] == 'solve':
for i, VV in enumerate(V):
try:
R[i] = np.linalg.solve(matrix, VV)
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
elif options['type'] == 'least_squares_lstsq':
for i, VV in enumerate(V):
try:
R[i], _, _, _ = np.linalg.lstsq(matrix, VV, rcond=options['rcond'])
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
elif options['type'] == 'bicgstab':
for i, VV in enumerate(V):
R[i], info = bicgstab(matrix, VV, tol=options['tol'], maxiter=options['maxiter'])
if info != 0:
if info > 0:
raise InversionError('bicgstab failed to converge after {} iterations'.format(info))
else:
raise InversionError('bicgstab failed with error code {} (illegal input or breakdown)'.
format(info))
elif options['type'] == 'bicgstab_spilu':
ilu = spilu(matrix, drop_tol=options['spilu_drop_tol'], fill_factor=options['spilu_fill_factor'],
drop_rule=options['spilu_drop_rule'], permc_spec=options['spilu_permc_spec'])
precond = LinearOperator(matrix.shape, ilu.solve)
for i, VV in enumerate(V):
R[i], info = bicgstab(matrix, VV, tol=options['tol'], maxiter=options['maxiter'], M=precond)
if info != 0:
if info > 0:
raise InversionError('bicgstab failed to converge after {} iterations'.format(info))
else:
raise InversionError('bicgstab failed with error code {} (illegal input or breakdown)'.
format(info))
elif options['type'] == 'spsolve':
try:
# maybe remove unusable factorization:
if hasattr(matrix, 'factorization'):
fdtype = matrix.factorizationdtype
if not np.can_cast(V.dtype, fdtype, casting='safe'):
del matrix.factorization
if map(int, scipy.version.version.split('.')) >= [0, 14, 0]:
if hasattr(matrix, 'factorization'):
# we may use a complex factorization of a real matrix to
# apply it to a real vector. In that case, we downcast
# the result here, removing the imaginary part,
# which should be zero.
R = matrix.factorization.solve(V.T).T.astype(promoted_type, copy=False)
elif options['keep_factorization']:
# the matrix is always converted to the promoted type.
# if matrix.dtype == promoted_type, this is a no_op
matrix.factorization = splu(matrix_astype_nocopy(matrix, promoted_type), permc_spec=options['permc_spec'])
matrix.factorizationdtype = promoted_type
R = matrix.factorization.solve(V.T).T
else:
# the matrix is always converted to the promoted type.
# if matrix.dtype == promoted_type, this is a no_op
R = spsolve(matrix_astype_nocopy(matrix, promoted_type), V.T, permc_spec=options['permc_spec']).T
else:
# see if-part for documentation
if hasattr(matrix, 'factorization'):
for i, VV in enumerate(V):
R[i] = matrix.factorization.solve(VV).astype(promoted_type, copy=False)
elif options['keep_factorization']:
matrix.factorization = splu(matrix_astype_nocopy(matrix, promoted_type), permc_spec=options['permc_spec'])
matrix.factorizationdtype = promoted_type
for i, VV in enumerate(V):
R[i] = matrix.factorization.solve(VV)
elif len(V) > 1:
factorization = splu(matrix_astype_nocopy(matrix, promoted_type), permc_spec=options['permc_spec'])
for i, VV in enumerate(V):
R[i] = factorization.solve(VV)
else:
R = spsolve(matrix_astype_nocopy(matrix, promoted_type), V.T, permc_spec=options['permc_spec']).reshape((1, -1))
except RuntimeError as e:
raise InversionError(e)
elif options['type'] == 'lgmres':
for i, VV in enumerate(V):
R[i], info = lgmres(matrix, VV.copy(i),
tol=options['tol'],
maxiter=options['maxiter'],
inner_m=options['inner_m'],
outer_k=options['outer_k'])
if info > 0:
raise InversionError('lgmres failed to converge after {} iterations'.format(info))
assert info == 0
elif options['type'] == 'least_squares_lsmr':
for i, VV in enumerate(V):
R[i], info, itn, _, _, _, _, _ = lsmr(matrix, VV.copy(i),
damp=options['damp'],
atol=options['atol'],
btol=options['btol'],
conlim=options['conlim'],
maxiter=options['maxiter'],
show=options['show'])
assert 0 <= info <= 7
if info == 7:
raise InversionError('lsmr failed to converge after {} iterations'.format(itn))
elif options['type'] == 'least_squares_lsqr':
for i, VV in enumerate(V):
R[i], info, itn, _, _, _, _, _, _, _ = lsqr(matrix, VV.copy(i),
damp=options['damp'],
atol=options['atol'],
btol=options['btol'],
conlim=options['conlim'],
iter_lim=options['iter_lim'],
show=options['show'])
assert 0 <= info <= 7
if info == 7:
raise InversionError('lsmr failed to converge after {} iterations'.format(itn))
elif options['type'] == 'pyamg':
if len(V) > 0:
V_iter = iter(enumerate(V))
R[0], ml = pyamg.solve(matrix, next(V_iter)[1],
tol=options['tol'],
maxiter=options['maxiter'],
return_solver=True)
for i, VV in V_iter:
R[i] = pyamg.solve(matrix, VV,
tol=options['tol'],
maxiter=options['maxiter'],
existing_solver=ml)
elif options['type'] == 'pyamg-rs':
ml = pyamg.ruge_stuben_solver(matrix,
strength=options['strength'],
CF=options['CF'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
coarse_solver=options['coarse_solver'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'] == 'pyamg-sa':
ml = pyamg.smoothed_aggregation_solver(matrix,
symmetry=options['symmetry'],
strength=options['strength'],
aggregate=options['aggregate'],
smooth=options['smooth'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
improve_candidates=options['improve_candidates'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
diagonal_dominance=options['diagonal_dominance'])
for i, VV in enumerate(V):
R[i] = ml.solve(VV,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'].startswith('generic') or options['type'].startswith('least_squares_generic'):
logger = getLogger('pymor.operators.numpy._apply_inverse')
logger.warn('You have selected a (potentially slow) generic solver for a NumPy matrix operator!')
from pymor.operators.numpy import NumpyMatrixOperator
from pymor.vectorarrays.numpy import NumpyVectorArray
return genericsolvers.apply_inverse(NumpyMatrixOperator(matrix),
NumpyVectorArray(V, copy=False),
options=options).data
else:
raise ValueError('Unknown solver type')
return R
def poisson(img_bgr, M, mask):
rows, cols, ch = img_bgr[0].shape
# Handling panorama boudaries
x_max = cols
y_min = 0
y_max = rows
position = []
warp_mask = []
### calculate img size of output
### d_size is current img border after homography
for i in range(1, len(img_bgr)):
# Define d_size for output img
x = np.array([[0, cols], [0, cols]])
y = np.array([[0, 0], [rows, rows]])
d_size_x = x*M[i-1][0,0] + y*M[i-1][0,1] + 1*M[i-1][0,2]
d_size_y = x*M[i-1][1,0] + y*M[i-1][1,1] + 1*M[i-1][1,2]
d_size_x = d_size_x.astype(int)
d_size_y = d_size_y.astype(int)
if max(d_size_x[0,1], d_size_x[1,1]) > x_max:
x_max = max(d_size_x[0,1], d_size_x[1,1])
if min(d_size_y[0,0], d_size_y[0,1]) < y_min:
y_min = min(d_size_y[0,0], d_size_y[0,1])
if max(d_size_y[1,0], d_size_y[1,1]) > y_max:
y_max = max(d_size_y[1,0], d_size_y[1,1])
### panorama is initialized with full size
panorama = np.zeros((y_max-y_min+1, x_max+1, 3))
### process each image
### no image is pasted at this step
### only calculate refined homography and mask
for i in range(len(img_bgr)):
print 'processing img', i
### calculate borders
x = np.array([[0, cols-1], [0, cols-1]])
y = np.array([[0, 0], [rows-1, rows-1]])
if i == 0:
#panorama[-y_min:rows-y_min, 0:cols, :] += img_bgr[i]
position.append([-y_min, rows-y_min-1, 0, cols-1])
warp_mask.append(mask)
continue
if i > 0:
### again d_size is the border of current image on absolute coordinate
d_size_x = x*M[i-1][0,0] + y*M[i-1][0,1] + 1*M[i-1][0,2]
d_size_y = x*M[i-1][1,0] + y*M[i-1][1,1] + 1*M[i-1][1,2]
y_begin = int(min(d_size_y[0,0], d_size_y[0,1]) - y_min)
y_end = int(max(d_size_y[1,0], d_size_y[1,1]) - y_min)
x_begin = int(min(d_size_x[0,0], d_size_x[1,0]))
x_end = int(max(d_size_x[0,1], d_size_x[1,1]))
position.append([y_begin, y_end, x_begin, x_end])
### this is to match cv2.warpPerspective
### move the image after homography to top-left and corp to desired size
H = np.copy(M[i-1])
H[0,2] -= min(d_size_x[0,0], d_size_x[1,0])
H[1,2] -= min(d_size_y[0,0], d_size_y[0,1])
d_size = (x_end-x_begin+1, y_end-y_begin+1)
warp_mask.append(cv2.warpPerspective(mask, H, d_size, None, cv2.INTER_NEAREST))
mask_xor = [] ### mask for current image, starting from img0
mask_and = [] ### mask for image overlay, starting from img1(overlay with 0)
for i in range(len(img_bgr)):
if i != len(img_bgr)-1:
### calculate coordinate of overlay area
if( position[i][0] > position[i+1][0] ):
y_begin = 0
ny_begin = position[i][0] - position[i+1][0]
else:
y_begin = position[i+1][0] - position[i][0]
ny_begin = 0
if( position[i][1] > position[i+1][1] ):
y_end = position[i+1][1] - position[i][0]
ny_end = position[i+1][1] - position[i+1][0]
else:
y_end = position[i][1] - position[i][0]
ny_end = position[i][1] - position[i+1][0]
x_begin = position[i+1][2] - position[i][2]
x_end = position[i][3] - position[i][2]
nx_begin = 0
nx_end = position[i][3] - position[i+1][2]
### calculate masks
tmp_mask = np.copy(warp_mask[i]) ### mask for current image
ntmp_mask = np.zeros((warp_mask[i+1].shape)) ### overlay mask for next image(relative to next image)
ntmp_mask[ny_begin:ny_end, nx_begin:nx_end] = warp_mask[i+1][ny_begin:ny_end, nx_begin:nx_end] \
* tmp_mask[y_begin:y_end, x_begin:x_end]
mask_and.append(ntmp_mask)
if i != 0:
### first image has no previous
tmp_mask -= mask_and[i-1]
#tmp_mask[y_begin:y_end, x_begin:x_end] -= ntmp_mask[ny_begin:ny_end, nx_begin:nx_end]
mask_xor.append(tmp_mask)
else:
### last image has no next image
tmp_mask = np.copy(warp_mask[i])
tmp_mask -= mask_and[i-1]
mask_xor.append(tmp_mask)
### image blending
pwarp_img_bgr = np.zeros(mask_xor[0].shape, dtype='float64')
for i in range(len(img_bgr)):
y_begin, y_end, x_begin, x_end = position[i]
### directly paste first image
if i == 0:
panorama[y_begin:y_end+1, x_begin:x_end+1, 0] = img_bgr[i][:, :, 0] * mask_xor[0]
panorama[y_begin:y_end+1, x_begin:x_end+1, 1] = img_bgr[i][:, :, 1] * mask_xor[0]
panorama[y_begin:y_end+1, x_begin:x_end+1, 2] = img_bgr[i][:, :, 2] * mask_xor[0]
pwarp_img_bgr = img_bgr[i]
pwarp_img_bgr = pwarp_img_bgr.astype('float64')
continue
### d_size is the desired corp size
d_size_x = x*M[i-1][0,0] + y*M[i-1][0,1] + 1*M[i-1][0,2]
d_size_y = x*M[i-1][1,0] + y*M[i-1][1,1] + 1*M[i-1][1,2]
H = np.copy(M[i-1])
H[0,2] -= min(d_size_x[0,0], d_size_x[1,0])
H[1,2] -= min(d_size_y[0,0], d_size_y[0,1])
d_size = (x_end-x_begin+1, y_end-y_begin+1)
print 'warp img size:', d_size
warp_img_bgr = np.zeros((y_end-y_begin+1, x_end-x_begin+1, 3))
warp_img_bgr[:,:,0] = cv2.warpPerspective(img_bgr[i][:,:,0], H, d_size, None, cv2.INTER_NEAREST)
warp_img_bgr[:,:,1] = cv2.warpPerspective(img_bgr[i][:,:,1], H, d_size, None, cv2.INTER_NEAREST)
warp_img_bgr[:,:,2] = cv2.warpPerspective(img_bgr[i][:,:,2], H, d_size, None, cv2.INTER_NEAREST)
### directly paste image to panorama first
panorama[y_begin:y_end+1, x_begin:x_end+1, 0] += warp_img_bgr[:, :, 0] * mask_xor[i]
panorama[y_begin:y_end+1, x_begin:x_end+1, 1] += warp_img_bgr[:, :, 1] * mask_xor[i]
panorama[y_begin:y_end+1, x_begin:x_end+1, 2] += warp_img_bgr[:, :, 2] * mask_xor[i]
### calculate coordinate of overlay area
### no_prefix: current image
### p : panorama
if( position[i-1][0] > position[i][0] ):
py_begin = 0
y_begin = position[i-1][0] - position[i][0]
oy_begin = position[i-1][0]
else:
py_begin = position[i][0] - position[i-1][0]
y_begin = 0
oy_begin = position[i][0]
if( position[i-1][1] > position[i][1] ):
py_end = position[i][1] - position[i-1][0]
y_end = position[i][1] - position[i][0]
oy_end = position[i][1]
else:
py_end = position[i-1][1] -position[i-1][0]
y_end = position[i-1][1] - position[i][0]
oy_end = position[i-1][1]
px_begin = position[i][2] - position[i-1][2]
px_end = position[i-1][3] - position[i-1][2]
x_begin = 0
x_end = position[i-1][3] - position[i][2]
ox_begin = position[i][2]
ox_end = position[i-1][3]
### poisson blending
### first cut the overlay block
overlay_bgr = warp_img_bgr[y_begin:y_end, x_begin:x_end, :]
poverlay_bgr = panorama[oy_begin:oy_end, ox_begin:ox_end, :]
mask_overlay = mask_and[i-1][y_begin:y_end, x_begin:x_end]
### performed on 3 channel seperately
for c in range(3):
overlay = overlay_bgr[:, :, c]
poverlay = poverlay_bgr[:, :, c]
rows = len(overlay)
cols = len(overlay[0])
### fill in Ax = b and solve x
print 'size'
print rows, cols
A = scipy.sparse.identity(rows*cols, format='lil')
B = np.zeros(rows*cols)
### fill in A
for row in range(rows):
for col in range(cols):
### print progress
print "\r",
print str(c) + " " + str(int((row*cols+col)/float(rows*cols)*100)),
Vpq = 0
Np = 0 ### neighbor count
neighbor = [0, 0, 0, 0] ### up, down, right, left
if(mask_overlay[row, col]):
fp = overlay[row, col]
gp = poverlay[row, col]
### inside mask
### get difference that is larger
if( row>0 ):
### has up neighbor
fq = overlay[row-1, col]
gq = poverlay[row-1, col]
if( mask_overlay[row-1, col] ):
Vpq += gp-gq
else:
Vpq += (fp-fq, gp-gq)[col<(cols/2)]
neighbor[0] = -1
Np += 1
if( row<rows-1 ):
### has down neighbor
fq = overlay[row+1, col]
gq = poverlay[row+1, col]
if( mask_overlay[row+1, col] ):
Vpq += gp-gq
else:
Vpq += (fp-fq, gp-gq)[col<(cols/2)]
neighbor[1] = -1
Np += 1
if( col<cols-1 ):
### has right neighbor
fq = overlay[row, col+1]
gq = poverlay[row, col+1]
if( mask_overlay[row, col+1] ):
Vpq += gp-gq
else:
Vpq += (fp-fq, gp-gq)[col<(cols/2)]
neighbor[2] = -1
Np += 1
if( col>0 ):
### has left neighbor
fq = overlay[row, col-1]
gq = poverlay[row, col-1]
if( mask_overlay[row, col-1] ):
Vpq += gp-gq
else:
Vpq += (fp-fq, gp-gq)[col<(cols/2)]
neighbor[3] = -1
Np += 1
### fill the coefficients
line = row*cols+col
A[line, row*cols+col] = Np
A[line, (row-1)*cols+col] += neighbor[0]
A[line, (row+1)*cols+col] += neighbor[1]
A[line, row*cols+col+1] += neighbor[2]
A[line, row*cols+col-1] += neighbor[3]
B[row*cols+col] = Vpq
else:
### not inside mask
B[row*cols+col] = (poverlay[row, col], overlay[row, col])[col>(cols/2)]
print 'solving'
A = A.tocsr()
result = pyamg.solve(A, B, verb=False, tol=1e-10)
result[result>255] = 255
result[result<0] = 0
panorama[oy_begin:oy_end, ox_begin:ox_end, c] *= (1-mask_overlay)
panorama[oy_begin:oy_end, ox_begin:ox_end, c] += mask_overlay * np.reshape(result, (rows, cols))
pwarp_img_bgr = warp_img_bgr
cv2.imwrite('panorama'+str(i)+'.jpg', panorama)
cv2.imwrite('panorama.jpg', panorama)
return panorama
def blend(img_target, img_source, img_mask, offset=(0, 0)):
# compute regions to be blended
region_source = (
max(-offset[0], 0),
max(-offset[1], 0),
min(img_target.shape[0]-offset[0], img_source.shape[0]),
min(img_target.shape[1]-offset[1], img_source.shape[1]))
region_target = (
max(offset[0], 0),
max(offset[1], 0),
min(img_target.shape[0], img_source.shape[0]+offset[0]),
min(img_target.shape[1], img_source.shape[1]+offset[1]))
region_size = (region_source[2]-region_source[0], region_source[3]-region_source[1])
# clip and normalize mask image
img_mask = img_mask[region_source[0]:region_source[2], region_source[1]:region_source[3]]
img_mask[img_mask==0] = False
img_mask[img_mask!=False] = True
# create coefficient matrix
A = scipy.sparse.identity(np.prod(region_size), format='lil')
for y in range(region_size[0]):
for x in range(region_size[1]):
if img_mask[y,x]:
index = x+y*region_size[1]
A[index, index] = 4
if index+1 < np.prod(region_size):
A[index, index+1] = -1
if index-1 >= 0:
A[index, index-1] = -1
if index+region_size[1] < np.prod(region_size):
A[index, index+region_size[1]] = -1
if index-region_size[1] >= 0:
A[index, index-region_size[1]] = -1
A = A.tocsr()
# create poisson matrix for b
P = pyamg.gallery.poisson(img_mask.shape)
# for each layer (ex. RGB)
for num_layer in range(img_target.shape[2]):
# get subimages
t = img_target[region_target[0]:region_target[2],region_target[1]:region_target[3],num_layer]
s = img_source[region_source[0]:region_source[2], region_source[1]:region_source[3],num_layer]
t = t.flatten()
s = s.flatten()
# create b
b = P * s
for y in range(region_size[0]):
for x in range(region_size[1]):
if not img_mask[y,x]:
index = x+y*region_size[1]
b[index] = t[index]
# solve Ax = b
x = pyamg.solve(A,b,verb=False,tol=1e-10)
# assign x to target image
x = np.reshape(x, region_size)
x[x>255] = 255
x[x<0] = 0
x = np.array(x, img_target.dtype)
img_target[region_target[0]:region_target[2],region_target[1]:region_target[3],num_layer] = x
return img_target
def solve_withPyAMG(self, delfineVar, parameter):
"""Solves the equation system with pyAMG.
Input:
elliptic = AssembleElliptic() [AssembleElliptic.py]
"""
# Reads solver data
# Alternatives: CG (with or without PreCond) | GMRES (w/ or w/o PC)
# | LU (still pending))
solverType = parameter.num.pressSolv.type
tolerance = parameter.num.pressSolv.tolerance
maxStep = parameter.num.pressSolv.maxNumSteps
# Reads type of preconditioner
# Alternatives: AMG | ILU | None
preCondType = parameter.num.pressSolv.preConditioning.type
# Getting data from elliptic eq. assembler
A = delfineVar.A
rhs = delfineVar.rhs
# Get sparse matrix data
(row,col,data) = A.data()
n = A.size(0)
# It was commented the line 126 and 129 of the file compressed.py
# of the scipy package located in /usr/local/lib/python2.6/dist-packages
# /scipy/sparse in order to avoid some annoying warning messages.
# If some strange behaviour takes place in this solver routine, this
# information may be important for debugging
Asp = csr_matrix( (data,col.view(),row.view()), shape=(n,n))
# Get right-hand side vector(rhs) data
b = rhs.data()
residuals = []
# Solves equation system
if (solverType == 'blackbox'):
# Uses PyAMG blackbox solver, which implies that the program detect automatically
# the best solver parameters for the case. Very useful for debugging and
# "difficult" to converge cases. Does not allow to set max. iterations or this kind
# of stuff.
x = solve(Asp, b, verb=True,tol=tolerance)
else:
if (preCondType == "amg"):
# Using AMG Solver as preconditioner with 'solverType' (cg,gmres) as
# accelerator. If ilu is defined as solver, it will use pure AMG without
# accelaration.
nCoarse = parameter.num.pressSolv.preConditioning.numCoarseLevel
ml = smoothed_aggregation_solver(Asp, max_levels=nCoarse, max_coarse=1)
if ((solverType == "cg") | (solverType == "gmres")):
# Use CG or GMRES acceleration
x = ml.solve(b,tol=tolerance, maxiter=maxStep, cycle='V', accel=solverType,residuals=residuals)
elif(solverType == "none"):
# No accelaration (stand-alone AMG)
x = ml.solve(b,tol=tolerance, maxiter=maxStep, cycle='V', residuals=residuals)
elif (solverType == "lu"):
# Trying to use a direct LU solver with amg, but it is not coherent
print "Error(7):"
print "Direct solver not compatible with amg"
print "You can try: amg+cg,amg+gmres,amg+none,"
print " none+cg,none+gmres,none+lu,"
print " ilu+cg,ilu+gmres"
print " "
sys.exit(1)
print ml
####################################
# Print customized spectrum of multigrid operator
# This function is efficient just for a small n (max=32)
#from pyamg.util.utils import hierarchy_spectrum
#hierarchy_spectrum(ml, filter=True, plot=True)
####################################
elif (preCondType == "none") :
# Iterate without preconditioner
if (solverType == "cg"):
# Using conventional Conjugate Gradients Solver
(x, flag) = cg(Asp,b, maxiter=maxStep, tol=tolerance, residuals=residuals)
elif (solverType == "gmres"):
# Using conventional Generalized Minimum Residual Method Solver
(x, flag) = gmres(Asp,b, maxiter=maxStep, tol=tolerance, residuals=residuals)
elif (solverType == "lu"):
# Using a direct LU solver
# (still pending, to be done with dolfin solver schema, not pyamg)
print "Error(8):"
print "Direct solver still not available, use cg or gmres instead"
print " "
sys.exit(1)
elif (solverType == "none"):
# Using a direct LU solver
# (still pending, to be done with dolfin solver schema, not pyamg)
print "Error(9):"
print "Invalid solver + preconditioner option!"
print "You can try: amg+cg,amg+gmres,amg+none,"
print " none+cg,none+gmres,none+lu,"
print " ilu+cg,ilu+gmres"
print " "
sys.exit(1)
elif (preCondType == "ilu"):
# Using a ILU preconditioner
# (still pending, to be done with dolfin solver schema, not pyamg)
print "Error(10):"
print "ILU Preconditioner still not available, use amg or none instead"
print " "
sys.exit(1)
# Print residuals history
if (solverType != 'blackbox'):
pass
#residuals = residuals/residuals[0]
# Define return parameters
delfineVar.x = x
delfineVar.residuals = residuals
def apply_inverse(self, U, ind=None, mu=None, options=None):
default_options = self.invert_options
if options is None:
options = default_options.values()[0]
elif isinstance(options, str):
options = default_options[options]
else:
assert 'type' in options and options['type'] in default_options \
and options.viewkeys() <= default_options[options['type']].viewkeys()
user_options = options
options = default_options[user_options['type']]
options.update(user_options)
assert isinstance(U, NumpyVectorArray)
assert self.dim_range == U.dim
U = U._array[:U._len] if ind is None else U._array[ind]
if U.shape[1] == 0:
return NumpyVectorArray(U)
R = np.empty((len(U), self.dim_source))
if self.sparse:
if options['type'] == 'bicgstab':
for i, UU in enumerate(U):
R[i], info = bicgstab(self._matrix, UU, tol=options['tol'], maxiter=options['maxiter'])
if info != 0:
if info > 0:
raise InversionError('bicgstab failed to converge after {} iterations'.format(info))
else:
raise InversionError('bicgstab failed with error code {} (illegal input or breakdown)'.
format(info))
elif options['type'] == 'bicgstab-spilu':
ilu = spilu(self._matrix, drop_tol=options['spilu_drop_tol'], fill_factor=options['spilu_fill_factor'],
drop_rule=options['spilu_drop_rule'], permc_spec=options['spilu_permc_spec'])
precond = LinearOperator(self._matrix.shape, ilu.solve)
for i, UU in enumerate(U):
R[i], info = bicgstab(self._matrix, UU, tol=options['tol'], maxiter=options['maxiter'], M=precond)
if info != 0:
if info > 0:
raise InversionError('bicgstab failed to converge after {} iterations'.format(info))
else:
raise InversionError('bicgstab failed with error code {} (illegal input or breakdown)'.
format(info))
elif options['type'] == 'spsolve':
for i, UU in enumerate(U):
R[i] = spsolve(self._matrix, UU, permc_spec=options['permc_spec'])
elif options['type'] == 'pyamg':
if len(U) > 0:
U_iter = iter(enumerate(U))
R[0], ml = pyamg.solve(self._matrix, next(U_iter)[1],
tol=options['tol'],
maxiter=options['maxiter'],
return_solver=True)
for i, UU in U_iter:
R[i] = pyamg.solve(self._matrix, UU,
tol=options['tol'],
maxiter=options['maxiter'],
existing_solver=ml)
elif options['type'] == 'pyamg-rs':
ml = pyamg.ruge_stuben_solver(self._matrix,
strength=options['strength'],
CF=options['CF'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
coarse_solver=options['coarse_solver'])
for i, UU in enumerate(U):
R[i] = ml.solve(UU,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
elif options['type'] == 'pyamg-sa':
ml = pyamg.smoothed_aggregation_solver(self._matrix,
symmetry=options['symmetry'],
strength=options['strength'],
aggregate=options['aggregate'],
smooth=options['smooth'],
presmoother=options['presmoother'],
postsmoother=options['postsmoother'],
improve_candidates=options['improve_candidates'],
max_levels=options['max_levels'],
max_coarse=options['max_coarse'],
diagonal_dominance=options['diagonal_dominance'])
for i, UU in enumerate(U):
R[i] = ml.solve(UU,
tol=options['tol'],
maxiter=options['maxiter'],
cycle=options['cycle'],
accel=options['accel'])
else:
raise ValueError('Unknown solver type')
else:
for i, UU in enumerate(U):
try:
R[i] = np.linalg.solve(self._matrix, UU)
except np.linalg.LinAlgError as e:
raise InversionError('{}: {}'.format(str(type(e)), str(e)))
return NumpyVectorArray(R)
def diffuse_inprob(inprobs, paths, segs, imgs):
#inprobs is a list of inside probability for superpixels
init_prob = []
id2index = []
index = 0
n_last = len(np.unique(segs[-1]))
for i in range(len(inprobs)):
id2index.append({})
for (jj,j) in enumerate(inprobs[i]):
init_prob.append(j)
id2index[i][jj] = index
index += 1
dist = []
row_index = []
col_index = []
rgbs = np.zeros((len(init_prob),3))
n_frames = len(imgs)
for (i,id) in enumerate(paths.keys()):
frame = paths[id].frame
rows = paths[id].rows
cols = paths[id].cols
unique_frame = np.unique(frame)
for f in unique_frame:
if f == n_frames-1: continue
r1 = rows[frame == f]
c1 = cols[frame == f]
index1 = id2index[f][segs[f][r1[0],c1[0]]]
rgb1 = np.mean(imgs[f][r1,c1],axis=0)
rgbs[index1] = rgb1
for f2 in unique_frame:
if f >= f2: continue
if f2 == n_frames-1: continue
r2 = rows[frame == f2]
c2 = cols[frame == f2]
rgb2 = np.mean(imgs[f2][r2,c2],axis=0)
index2 = id2index[f2][segs[f2][r2[0],c2[0]]]
rgbs[index2] = rgb2
d = np.linalg.norm(rgb1-rgb2) **2
row_index.append(index1)
row_index.append(index2)
col_index.append(index2)
col_index.append(index1)
dist.append(d)
dist.append(d)
adjs = sp_adj(segs)
for i in range(n_frames-1):
for j in range(adjs[i].shape[0]):
index1 = id2index[i][j]
rgb1 = rgbs[index1]
row_index.append(index1)
col_index.append(index1)
dist.append(0)
for k in np.nonzero(adjs[i][j])[0]:
if j > k: continue
index2 = id2index[i][k]
rgb2 = rgbs[index2]
d = np.linalg.norm(rgb1-rgb2) **2
row_index.append(index1)
row_index.append(index2)
col_index.append(index2)
col_index.append(index1)
dist.append(d)
dist.append(d)
sigma = 30
values2 = np.exp(-np.array(dist) / (2*sigma**2))
from scipy.sparse import csr_matrix, spdiags
n_node = len(init_prob)
W = csr_matrix((values2, (row_index, col_index)), shape=(n_node, n_node))
inv_D =spdiags(1.0/((W.sum(axis=1)).flatten()), 0, W.shape[0], W.shape[1])
D =spdiags(W.sum(axis=1).flatten(), 0, W.shape[0], W.shape[1])
lam = 10
lhs = D + lam * (D - W)
from scipy.sparse import eye
from scipy.sparse.linalg import spsolve,lsmr
# diffused_prob = spsolve(lhs, D.dot(np.array(init_prob)))
diffused_prob = solve(lhs, D.dot(np.array(init_prob)))
diffused_probs = []
count = 0
for i in range(len(inprobs)):
diffused_probs.append(diffused_prob[count:len(inprobs[i])+count])
count += len(inprobs[i])
return diffused_probs
