def im_backproject(im, rot_matrices):
"""
Backproject images along rotation
:param im: An L-by-L-by-n array of images to backproject.
:param rot_matrices: An 3-by-3-by-n array of rotation matrices corresponding to viewing directions.
:return: An L-by-L-by-L volumes corresponding to the sum of the backprojected images.
"""
L, _, n = im.shape
ensure(L == im.shape[1], "im must be LxLxK")
ensure(n == rot_matrices.shape[2],
"No. of rotation matrices must match the number of images")
pts_rot = rotated_grids(L, rot_matrices)
pts_rot = m_reshape(pts_rot, (3, -1))
im_f = centered_fft2(im) / (L**2)
if L % 2 == 0:
im_f[0, :, :] = 0
im_f[:, 0, :] = 0
im_f = m_flatten(im_f)
plan = Plan(sz=(L, L, L), fourier_pts=pts_rot)
vol = np.real(plan.adjoint(im_f)) / L
return vol
def vec_to_symmat(vec):
"""
Convert packed lower triangular vector to symmetric matrix
:param vec: A vector of size N*(N+1)/2-by-... describing a symmetric (or Hermitian) matrix.
:return: An array of size N-by-N-by-... which indexes symmetric/Hermitian matrices that occupy the first two
dimensions. The lower triangular parts of these matrices consists of the corresponding vectors in vec.
"""
# TODO: Handle complex values in vec
if np.iscomplex(vec).any():
raise NotImplementedError('Coming soon')
# M represents N(N+1)/2
M = vec.shape[0]
N = int(round(np.sqrt(2 * M + 0.25) - 0.5))
ensure((M == 0.5 * N * (N + 1)) and N != 0,
"Vector must be of size N*(N+1)/2 for some N>0.")
vec, sz_roll = unroll_dim(vec, 2)
index_matrix = np.empty((N, N))
i_upper = np.triu_indices_from(index_matrix)
index_matrix[i_upper] = np.arange(
M) # Incrementally populate upper triangle in row major order
index_matrix.T[i_upper] = index_matrix[i_upper] # Copy to lower triangle
mat = vec[index_matrix.flatten('F').astype('int')]
mat = m_reshape(mat, (N, N) + mat.shape[1:])
mat = roll_dim(mat, sz_roll)
return mat
def __init__(self, size, ell_max=None):
d = len(size)
ensure(d == 3, 'Only three-dimensional basis functions are supported.')
ensure(len(set(size)) == 1, 'Only cubic domains are supported.')
super().__init__(size, ell_max)
def __init__(self, xfer_fn_array):
"""
A Filter corresponding to the filter with the specified transfer function.
:param xfer_fn_array: The transfer function of the filter in the form of an array of one or two dimensions.
"""
dim = xfer_fn_array.ndim
ensure(dim in (1, 2), "Only dimensions 1 and 2 supported.")
super().__init__(dim=dim, radial=False)
# sz is assigned before we do anything with xfer_fn_array
self.sz = xfer_fn_array.shape
# The following code, though superficially different from the MATLAB code it's copied from,
# results in the same behavior.
# TODO: This could use documentation - very unintuitive!
if dim == 1:
# If we have a vector of even length, then append the first element to the last
if xfer_fn_array.shape[0] % 2 == 0:
xfer_fn_array = np.concatenate((xfer_fn_array, np.array([xfer_fn_array[0]])))
elif dim == 2:
# If we have a 2d array with an even no. of rows, append the first row reversed at the bottom
if xfer_fn_array.shape[0] % 2 == 0:
xfer_fn_array = np.vstack((xfer_fn_array, xfer_fn_array[0, ::-1]))
# If we have a 2d array with an even no. of columns, append the first column reversed at the right
if xfer_fn_array.shape[1] % 2 == 0:
xfer_fn_array = np.hstack((xfer_fn_array, xfer_fn_array[::-1, 0][:, np.newaxis]))
self.xfer_fn_array = xfer_fn_array
def process_micrograph(self,
filepath,
return_centers=True,
return_img=False,
show_progress=True,
create_jpg=False):
ensure(not all([return_centers, return_img]),
"Cannot specify both return_centers and return_img")
ensure(filepath.endswith('.mrc'),
f"Input file doesn't seem to be in MRC format! ({filepath})")
picker = Picker(self.particle_size, self.max_particle_size,
self.min_particle_size, self.query_image_size,
self.tau1, self.tau2, self.minimum_overlap_amount,
self.container_size, filepath, self.output_dir)
logger.info('Computing scores for query images')
score = picker.query_score(
show_progress=show_progress
) # compute score using normalized cross-correlations
while True:
logger.info(
f'Running svm with tau1={picker.tau1}, tau2={picker.tau2}')
# train SVM classifier and classify all windows in micrograph
segmentation = picker.run_svm(score)
# If all windows are classified identically, update tau_1 or tau_2
if np.all(segmentation):
picker.tau2 += 500
elif not np.any(segmentation):
picker.tau1 += 500
else:
break
logger.info('Discarding suspected artifacts')
segmentation = picker.morphology_ops(segmentation)
logger.info('Getting particle centers')
centers = picker.extract_particles(segmentation)
particle_image = None
if create_jpg and self.output_dir is not None:
particle_image = self.particle_image(picker.original_im,
picker.particle_size, centers)
misc.imsave(
os.path.join(
self.output_dir,
os.path.splitext(os.path.basename(picker.filename))[0] +
'_result.jpg'), particle_image)
if return_centers:
return centers
elif return_img:
if particle_image is not None:
return particle_image
else:
return self.particle_image(picker.original_im,
picker.particle_size, centers)
def unique_coords_nd(N, ndim):
"""
Generate unique polar coordinates from 2D or 3D rectangular coordinates.
:param N: length size of a square or cube.
:param ndim: number of dimension, 2 or 3.
:return: The unique polar coordinates in 2D or 3D
"""
ensure(ndim in (2, 3),
'Only two- or three-dimensional basis functions are supported.')
ensure(N > 0, 'Number of grid points should be greater than 0.')
if ndim == 2:
grid = grid_2d(N)
mask = grid['r'] <= 1
# Minor differences in r/theta/phi values are unimportant for the purpose
# of this function, so round off before proceeding
# TODO: numpy boolean indexing will return a 1d array (like MATLAB)
# However, it always searches in row-major order, unlike MATLAB (column-major),
# with no options to change the search order. The results we'll be getting back are thus not comparable.
# We transpose the appropriate ndarrays before applying the mask to obtain the same behavior as MATLAB.
r = grid['r'].T[mask].round(5)
phi = grid['phi'].T[mask].round(5)
r_unique, r_idx = np.unique(r, return_inverse=True)
ang_unique, ang_idx = np.unique(phi, return_inverse=True)
else:
grid = grid_3d(N)
mask = grid['r'] <= 1
# In Numpy, elements in the indexed array are always iterated and returned in row-major (C-style) order.
# To emulate a behavior where iteration happens in Fortran order, we swap axes 0 and 2 of both the array
# being indexed (r/theta/phi), as well as the mask itself.
# TODO: This is only for the purpose of getting the same behavior as MATLAB while porting the code, and is
# likely not needed in the final version.
# Minor differences in r/theta/phi values are unimportant for the purpose of this function,
# so we round off before proceeding.
mask_ = np.swapaxes(mask, 0, 2)
r = np.swapaxes(grid['r'], 0, 2)[mask_].round(5)
theta = np.swapaxes(grid['theta'], 0, 2)[mask_].round(5)
phi = np.swapaxes(grid['phi'], 0, 2)[mask_].round(5)
r_unique, r_idx = np.unique(r, return_inverse=True)
ang_unique, ang_idx = np.unique(np.vstack([theta, phi]),
axis=1,
return_inverse=True)
return {
'r_unique': r_unique,
'ang_unique': ang_unique,
'r_idx': r_idx,
'ang_idx': ang_idx,
'mask': mask
}
def vec_to_im(X):
"""
Unroll vectors to images
:param X: N^2-by-... array.
:return: An N-by-N-by-... array.
"""
shape = X.shape
N = round(shape[0]**(1 / 2))
ensure(N**2 == shape[0], "First dimension of X must be square")
return m_reshape(X, (N, N) + (shape[1:]))
def vec_to_vol(X):
"""
Unroll vectors to volumes
:param X: N^3-by-... array.
:return: An N-by-N-by-N-by-... array.
"""
shape = X.shape
N = round(shape[0]**(1 / 3))
ensure(N**3 == shape[0], "First dimension of X must be cubic")
return m_reshape(X, (N, N, N) + (shape[1:]))
def transform(self, signal):
ensure(signal.shape == self.sz,
f'Signal to be transformed must have shape {self.sz}')
self._plan.f_hat = signal.astype('complex64')
f = self._plan.trafo()
if signal.dtype == np.float32:
f = f.astype('complex64')
return f
def vol_to_vec(X):
"""
Roll up volumes into vectors
:param X: N-by-N-by-N-by-... array.
:return: An N^3-by-... array.
"""
shape = X.shape
ensure(X.ndim >= 3, "Array should have at least 3 dimensions")
ensure(shape[0] == shape[1] == shape[2], "Array should have first 3 dimensions identical")
return m_reshape(X, (shape[0]**3,) + (shape[3:]))
def im_to_vec(im):
"""
Roll up images into vectors
:param im: An N-by-N-by-... array.
:return: An N^2-by-... array.
"""
shape = im.shape
ensure(im.ndim >= 2, "Array should have at least 2 dimensions")
ensure(shape[0] == shape[1], "Array should have first 2 dimensions identical")
return m_reshape(im, (shape[0]**2,) + (shape[2:]))
def set_max_resolution(self, max_L):
ensure(
max_L <= self.L,
"Max desired resolution should be less than the current resolution"
)
self.L = max_L
ds_factor = self._L / max_L
self.filters.scale(ds_factor)
self.offsets /= ds_factor
# Invalidate images
self._im = None
def acorr(x, y, axes=None):
"""
Calculate array correlation along given axes
:param x: An array of arbitrary shape
:param y: An array of same shape as x
:param axes: The axis along which to compute the correlation. If None, the correlation is calculated along all axes.
:return: The correlation of x along specified axes.
"""
ensure(x.shape == y.shape, "The shapes of the inputs have to match")
if axes is None:
axes = range(x.ndim)
return ainner(x, y, axes) / (anorm(x, axes) * anorm(y, axes))
def ainner(x, y, axes=None):
"""
Calculate array inner product along given axes
:param x: An array of arbitrary shape
:param y: An array of same shape as x
:param axes: The axis along which to compute the inner product. If None, the product is calculated along all axes.
:return:
"""
ensure(x.shape == y.shape, "The shapes of the inputs have to match")
if axes is None:
axes = range(x.ndim)
return np.tensordot(x, y, axes=(axes, axes))
def eval_clustering(self, vol_idx):
"""
Evaluate clustering estimation
:param vol_idx: Indexes of the volumes determined (0-indexed)
:return: Accuracy [0-1] in terms of proportion of correctly assigned labels
"""
ensure(
len(vol_idx) == self.n,
f'Need {self.n} vol indexes to evaluate clustering')
# Remember that `states` is 1-indexed while vol_idx is 0-indexed
correctly_classified = np.sum(self.states - 1 == vol_idx)
return correctly_classified / self.n
def vec_to_mat(vec, is_symmat=False):
"""
Converts a vectorized matrix into a matrix
:param vec: The vectorized representations. If the matrix is non-symmetric, this array has the dimensions
N^2-by-..., but if the matrix is symmetric, the dimensions are N*(N+1)/2-by-... .
:param is_symmat: True if the vectors represent symmetric matrices (default False)
:return: The array of size N-by-N-by-... representing the matrices.
"""
if not is_symmat:
sz = vec.shape
N = int(round(np.sqrt(sz[0])))
ensure(sz[0] == N**2, "Vector must represent square matrix.")
return m_reshape(vec, (N, N) + sz[1:])
else:
return vec_to_symmat(vec)
def __call__(self, im, start=0, num=None):
ensure(
im.ndim == 3,
"A SourceFilter can only be called for a 3d volume representing a stack of images"
)
end = self.n
if num is not None:
end = min(start + num, self.n)
all_idx = np.arange(start, end)
unique_filters = np.unique(self.indices[all_idx]).astype('int')
for k in unique_filters:
idx_k = np.where(self.indices[all_idx] == k)[0]
im[:, :, idx_k] = im_filter(im[:, :, idx_k], self.filters[k])
return im
def mat_to_vec(mat, is_symmat=False):
"""
Converts a matrix into vectorized form
:param mat: An array of size N-by-N-by-... containing the matrices to be vectorized.
:param is_symmat: Specifies whether the matrices are symmetric/Hermitian, in which case they are stored in packed
form using symmat_to_vec (default False).
:return: The vectorized form of the matrices, with dimension N^2-by-... or N*(N+1)/2-by-... depending on the value
of is_symmat.
"""
if not is_symmat:
sz = mat.shape
N = sz[0]
ensure(sz[1] == N, "Matrix must be square")
return m_reshape(mat, (N**2, ) + sz[2:])
else:
return symmat_to_vec(mat)
def convolve_volume_matrix(self, x):
"""
Convolve volume matrix with kernel
:param x: An N-by-...-by-N (6 dimensions) volume matrix to be convolved.
:return: The original volume matrix convolved by the kernel with the same dimensions as before.
"""
shape = x.shape
N = shape[0]
kernel_f = self.kernel
ensure(
len(set(shape[i] for i in range(5))) == 1,
"Volume matrix must be cubic and square")
# TODO from MATLAB code: Deal with rolled dimensions
is_singleton = len(shape) == 6
N_ker = kernel_f.shape[0]
# Note from MATLAB code:
# Order is important here. It's about 20% faster to run from 1 through 6 compared with 6 through 1.
# TODO: Experiment with scipy order; try overwrite_x argument
x = fft(x, N_ker, 0, overwrite_x=True)
x = fft(x, N_ker, 1, overwrite_x=True)
x = fft(x, N_ker, 2, overwrite_x=True)
x = fft(x, N_ker, 3, overwrite_x=True)
x = fft(x, N_ker, 4, overwrite_x=True)
x = fft(x, N_ker, 5, overwrite_x=True)
x *= kernel_f
x = ifft(x, None, 5, overwrite_x=True)
x = x[:, :, :, :, :, :N]
x = ifft(x, None, 4, overwrite_x=True)
x = x[:, :, :, :, :N, :]
x = ifft(x, None, 3, overwrite_x=True)
x = x[:, :, :, :N, :, :]
x = ifft(x, None, 2, overwrite_x=True)
x = x[:, :, :N, :, :, :]
x = ifft(x, None, 1, overwrite_x=True)
x = x[:, :N, :, :, :, :]
x = ifft(x, None, 0, overwrite_x=True)
x = x[:N, :, :, :, :, :]
x = np.real(x)
return x
def process_micrograph(self,
filepath,
return_centers=True,
show_progress=True):
ensure(filepath.endswith('.mrc'),
f"Input file doesn't seem to be an MRC format! ({filepath})")
picker = Picker(self.particle_size, self.max_particle_size,
self.min_particle_size, self.query_image_size,
self.tau1, self.tau2, self.minimum_overlap_amount,
self.container_size, filepath, self.output_dir)
logger.info('Reading MRC file')
im = picker.read_mrc()
logger.info('Computing scores for query images')
score = picker.query_score(
im, show_progress=show_progress
) # compute score using normalized cross-correlations
while True:
logger.info(
f'Running svm with tau1={picker.tau1}, tau2={picker.tau2}')
# train SVM classifier and classify all windows in micrograph
segmentation = picker.run_svm(im, score)
# If all windows are classified identically, update tau_1 or tau_2
if np.all(segmentation):
picker.tau2 += 500
elif not np.any(segmentation):
picker.tau1 += 500
else:
break
logger.info('Discarding suspected artifacts')
segmentation = picker.morphology_ops(segmentation)
logger.info('Getting particle centers')
centers = picker.extract_particles(segmentation, self.create_jpg)
if return_centers:
return centers
def _shrink(self, covar_b_coeff, noise_variance, method=None):
"""
Shrink covariance matrix
:param covar_b_coeff: Outer products of the mean-subtracted images
:param noise_variance: Noise variance
:param method: One of None/'frobenius_norm'/'operator_norm'/'soft_threshold'
:return: Shrunk covariance matrix
"""
ensure(
method
in (None, 'frobenius_norm', 'operator_norm', 'soft_threshold'),
'Unsupported shrink method')
An = self.basis.mat_evaluate_t(self.mean_kernel.toeplitz())
if method is None:
covar_b_coeff -= noise_variance * An
else:
raise NotImplementedError('Only default shrink method supported.')
return covar_b_coeff
def symmat_to_vec(mat):
"""
Packs a symmetric matrix into a lower triangular vector
:param mat: An array of size N-by-N-by-... where the first two dimensions constitute symmetric or
Hermitian matrices.
:return: A vector of size N*(N+1)/2-by-... consisting of the lower triangular part of each matrix.
Note that a lot of acrobatics happening here (swapaxes/triu instead of tril etc.) are so that we can get
column-major ordering of elements (to get behavior consistent with MATLAB), since masking in numpy only returns
data in row-major order.
"""
N = mat.shape[0]
ensure(mat.shape[1] == N, "Matrix must be square")
mat, sz_roll = unroll_dim(mat, 3)
triu_indices = np.triu_indices(N)
vec = mat.swapaxes(0, 1)[triu_indices]
vec = roll_dim(vec, sz_roll)
return vec
def evaluate(self, omega):
"""
Evaluate the filter at specified frequencies.
:param omega: An array of size 2-by-n representing the spatial frequencies at which the filter
is to be evaluated. These are normalized so that pi is equal to the Nyquist frequency.
:return: The value of the filter at the specified frequencies.
"""
ensure(omega.shape[0] == self.dim, f'Omega must be of size {self.dim} x n')
if self.radial:
omega = np.sqrt(np.sum(omega ** 2, axis=0))
omega, idx = np.unique(omega, return_inverse=True)
omega = np.vstack((omega, np.zeros_like(omega)))
h = self._evaluate(omega)
if self.power != 1:
h = h ** self.power
if self.radial:
h = np.take(h, idx)
return h
def im_translate(im, shifts):
"""
Translate image by shifts
:param im: An array of size L-by-L-by-n containing images to be translated.
:param shifts: An array of size 2-by-n specifying the shifts in pixels.
Alternatively, it can be a column vector of length 2, in which case the same shifts is applied to each image.
:return: The images translated by the shifts, with periodic boundaries.
"""
n_im = im.shape[-1]
n_shifts = shifts.shape[-1]
ensure(shifts.shape[0] == 2, "shifts must be 2xn")
ensure(n_shifts == 1 or n_shifts == n_im,
"no. of shifts must be 1 or match the no. of images")
ensure(im.shape[0] == im.shape[1], "images must be square")
L = im.shape[0]
im_f = fft2(im, axes=(0, 1))
grid_1d = ifftshift(np.ceil(np.arange(-L / 2, L / 2))) * 2 * np.pi / L
om_x, om_y = np.meshgrid(grid_1d, grid_1d, indexing='ij')
phase_shifts_x = np.broadcast_to(-shifts[0, :], (L, L, n_shifts))
phase_shifts_y = np.broadcast_to(-shifts[1, :], (L, L, n_shifts))
phase_shifts = (om_x[:, :, np.newaxis] *
phase_shifts_x) + (om_y[:, :, np.newaxis] * phase_shifts_y)
mult_f = np.exp(-1j * phase_shifts)
im_translated_f = im_f * mult_f
im_translated = ifft2(im_translated_f, axes=(0, 1))
im_translated = np.real(im_translated)
return im_translated
def convolve_volume(self, x):
"""
Convolve volume with kernel
:param x: An N-by-N-by-N-by-... array of volumes to be convolved.
:return: The original volumes convolved by the kernel with the same dimensions as before.
"""
N = x.shape[0]
kernel_f = self.kernel
N_ker = kernel_f.shape[0]
x, sz_roll = unroll_dim(x, 4)
ensure(x.shape[0] == x.shape[1] == x.shape[2] == N,
"Volumes in x must be cubic")
ensure(kernel_f.ndim == 3, "Convolution kernel must be cubic")
ensure(
len(set(kernel_f.shape)) == 1, "Convolution kernel must be cubic")
is_singleton = x.ndim == 3
if is_singleton:
x = fftn(x, (N_ker, N_ker, N_ker))
else:
raise NotImplementedError('not yet')
x = x * kernel_f
if is_singleton:
x = np.real(ifftn(x))
x = x[:N, :N, :N]
else:
raise NotImplementedError('not yet')
x = roll_dim(x, sz_roll)
return x
def expand(self, x):
"""
Obtain expansion coefficients in Fourier Bessel basis from those in standard 3D coordinate basis.
This is a similar function to evaluate_t but with more accuracy by using the cg optimizing of linear
equation, Ax=b.
:param x: An array whose first three dimensions are to be expanded in FB basis.
These dimensions must equal `self.sz`.
:return : The coefficients of `v` expanded in FB basis. The first dimension of `v` is with size of `basis_count`
and the second and higher dimensions of the return value correspond to those higher dimensions of `x`.
"""
# TODO: this is function could be move to base class if all standard and fast versions of 2d and 3d are using
# the same data structures of x and v.
ensure(x.shape[:self.d] == self.sz,
f'First {self.d} dimensions of x must match {self.sz}.')
operator = LinearOperator(
shape=(self.basis_count, self.basis_count),
matvec=lambda v: self.evaluate_t(self.evaluate(v)))
# TODO: (from MATLAB implementation) - Check that this tolerance make sense for multiple columns in v
tol = 10 * np.finfo(x.dtype).eps
logger.info('Expanding array in basis')
# number of image samples
n_data = np.size(x, self.d)
v = np.zeros((self.basis_count, n_data), dtype=x.dtype)
for isample in range(0, n_data):
b = self.evaluate_t(x[..., isample])
# TODO: need check the initial condition x0 can improve the results or not.
v[..., isample], info = cg(operator, b, tol=tol)
if info != 0:
raise RuntimeError('Unable to converge!')
# return v coefficients with the first dimension of self.basis_count
return v
def expand(self, v):
"""
Expand array in basis
If `v` is a matrix of size `basis.ct`-by-..., `B` is the change-of-basis matrix of this basis, and `x` is a
matrix of size `self.sz`-by-..., the function calculates
v = (B' * B)^(-1) * B' * x
where the rows of `B` and columns of `x` are read as vectorized arrays.
:param v: An array whose first few dimensions are to be expanded in this basis.
These dimensions must equal `self.sz`.
:return: The coefficients of `v` expanded in this basis. If more than one array of size `self.sz` is found in
`v`, the second and higher dimensions of the return value correspond to those higher dimensions of `v`.
.. seealso:: evaluate
"""
ensure(v.shape[:self.d] == self.sz,
f'First {self.d} dimensions of v must match {self.sz}.')
v, sz_roll = unroll_dim(v, self.d + 1)
b = self.evaluate_t(v)
operator = LinearOperator(
shape=(self.basis_count, self.basis_count),
matvec=lambda x: self.evaluate_t(self.evaluate(x)))
# TODO: (from MATLAB implementation) - Check that this tolerance make sense for multiple columns in v
tol = 10 * np.finfo(v.dtype).eps
logger.info('Expanding array in basis')
v, info = cg(operator, b, tol=tol)
if info != 0:
raise RuntimeError('Unable to converge!')
v = roll_dim(v, sz_roll)
return v
def transform(self, signal):
ensure(signal.shape == self.sz,
f'Signal to be transformed must have shape {self.sz}')
epsilon = max(self.epsilon, np.finfo(signal.dtype).eps)
# Forward transform functions in finufftpy have signatures of the form:
# (x, y, z, c, isign, eps, f, ...)
# (x, y c, isign, eps, f, ...)
# (x, c, isign, eps, f, ...)
# Where f is a Fortran-order ndarray of the appropriate dimensions
# We form these function signatures here by tuple-unpacking
result = np.zeros(self.num_pts).astype('complex128')
result_code = self.transform_function(*self.fourier_pts, result, -1,
epsilon, signal)
if result_code != 0:
raise RuntimeError(
f'FINufft transform failed. Result code {result_code}')
return result
def __init__(self, filters, indices=None, n=None):
"""
:param filters: An iterable of Filter objects.
:param indices: An iterable of indices representing the 0-indexed indices of an image stack
on which to apply the filters. If unspecified, `n` must be supplied, and individual filters are applied
randomly.
:param n: An integer representing the depth of the image stack on which this SourceFilter is applied.
Not needed if `indices` are supplied.
"""
if indices is None:
ensure(n is not None,
"Either indices or n must be supplied for a SourceFilter")
# Assign filters randomly.
# For Matlab compatibility, randi returns numbers in the range [1, iMax] decrement by one for our purposes
indices = randi(len(filters), n, seed=0) - 1
else:
ensure(n is None,
"Cannot supply both indices and n for a SourceFilter")
n = len(indices)
self.filters = filters
self.indices = indices
self.n = n
def expand_t(self, v):
ensure(v.shape[0] == self.basis_count,
f'First dimension of v must be {self.basis_count}')
v, sz_roll = unroll_dim(v, 2)
b = im_to_vec(self.evaluate(v))
operator = LinearOperator(
shape=(self.N**2, self.N**2),
matvec=lambda x: im_to_vec(
self.evaluate(self.evaluate_t(vec_to_im(x)))))
# TODO: (from MATLAB implementation) - Check that this tolerance make sense for multiple columns in v
tol = 10 * np.finfo(v.dtype).eps
logger.info('Expanding array in dual basis')
v, info = cg(operator, b, tol=tol)
if info != 0:
raise RuntimeError('Unable to converge!')
v = roll_dim(v, sz_roll)
x = vec_to_im(v)
return x