def linear_operator_from_mesh(mesh_coord, mesh_triangles, mask=None, offset=0,
weights=None):
"""Generates the linear operator for the total variation Nesterov function
from a mesh.
Parameters
----------
mesh_coord : Numpy array [n, 3] of float.
mesh_triangles : Numpy array, n_triangles-by-3. The (integer) indices of
the three nodes forming the triangle.
mask : Numpy array (shape (n,)) of integers/boolean. Non-null values
correspond to columns of X. Groups may be defined using different
values in the mask. TV will be applied within groups of the same
value in the mask.
offset : Non-negative integer. The index of the first column, variable,
where TV applies. This is different from penalty_start which
define where the penalty applies. The offset defines where TV
applies within the penalised variables.
Example: X := [Intercept, Age, Weight, Image]. Intercept is
not penalized, TV does not apply on Age and Weight but only on
Image. Thus: penalty_start = 1, offset = 2 (skip Age and
Weight).
weights : Numpy array. The weight put on the gradient of every point.
Default is weight 1 for each point, or equivalently, no weight. The
weights is a numpy array of the same shape as mask.
Returns
-------
out1 : List or sparse matrices. Linear operator for the total variation
Nesterov function computed over a mesh.
out2 : Integer. The number of compacts.
Examples
--------
>>> import numpy as np
>>> import parsimony.functions.nesterov.l1tv as tv_helper
>>> mesh_coord = np.array([[0, 0], [1, 0], [0, 1], [1, 1], [0, 2], [1, 2]])
>>> mesh_triangles = np.array([[0 ,1, 3], [0, 2 ,3], [2, 3, 5], [2, 4, 5]])
>>> A = tv_helper.linear_operator_from_mesh(mesh_coord,mesh_triangles)
"""
Atv = tv.linear_operator_from_mesh(mesh_coord=mesh_coord,
mesh_triangles=mesh_triangles,
mask=mask, offset=offset,
weights=weights)
num_variables = mask.sum() if not mask is None else mesh_coord.shape[0]
Al1 = l1.linear_operator_from_variables(num_variables,
penalty_start=offset)
A = LinearOperator(Al1[0], *Atv)
return A
def linear_operator_from_shape(shape, num_variables, penalty_start=0):
"""Generates the linear operator for the total variation Nesterov function
from the shape of a 3D image.
Parameters
----------
shape : List or tuple with 1, 2 or 3 elements. The shape of the 1D, 2D or
3D image. shape has the form (Z, Y, X), where Z is the number of
"layers", Y is the number of rows and X is the number of columns.
The shape does not involve any intercept variables.
num_variables : Positive integer. The total number of variables, including
the intercept variable(s).
penalty_start : Non-negative integer. The number of variables to exempt
from penalisation. Equivalently, the first index to be penalised.
Default is 0, all variables are included.
"""
Atv = tv.linear_operator_from_shape(shape)
Al1 = l1.linear_operator_from_variables(num_variables, penalty_start=penalty_start)
A = LinearOperator(Al1[0], *Atv)
return A
