import numpy as np
import numpy.ma as np_ma
from pylops import LinearOperator
[docs]class Restriction(LinearOperator):
r"""Restriction (or sampling) operator.
Extract subset of values from input vector at locations ``iava``
in forward mode and place those values at locations ``iava``
in an otherwise zero vector in adjoint mode.
Parameters
----------
M : :obj:`int`
Number of samples in model.
iava : :obj:`list` or :obj:`numpy.ndarray`
Integer indices of available samples for data selection.
dims : :obj:`list`
Number of samples for each dimension
(``None`` if only one dimension is available)
dir : :obj:`int`, optional
Direction along which restriction is applied.
dtype : :obj:`str`, optional
Type of elements in input array.
inplace : :obj:`bool`, optional
Work inplace (``True``) or make a new copy (``False``). By default,
data is a reference to the model (in forward) and model is a reference
to the data (in adjoint).
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved
explicitly (``True``) or not (``False``)
See Also
--------
pylops.signalprocessing.Interp : Interpolation operator
Notes
-----
Extraction (or *sampling*) of a subset of :math:`N` values at locations
``iava`` from an input (or model) vector :math:`\mathbf{x}` of size
:math:`M` can be expressed as:
.. math::
y_i = x_{l_i} \quad \forall i=1,2,...,M
where :math:`\mathbf{l}=[l_1, l_2,..., l_M]` is a vector containing the indeces
of the original array at which samples are taken.
Conversely, in adjoint mode the available values in the data vector
:math:`\mathbf{y}` are placed at locations
:math:`\mathbf{l}=[l_1, l_2,..., l_M]` in the model vector:
.. math::
x_{l_i} = y_i \quad \forall i=1,2,...,M
and :math:`x_{j}=0 j \neq l_i` (i.e., at all other locations in input
vector).
"""
def __init__(self, M, iava, dims=None, dir=0,
dtype='float64', inplace=True):
self.M = M
self.dir = dir
self.iava = iava
if dims is None:
self.N = len(iava)
self.dims = (self.M, )
self.reshape = False
else:
if np.prod(dims) != self.M:
raise ValueError('product of dims must equal M!')
else:
self.dims = dims # model dimensions
self.dimsd = list(dims) # data dimensions
self.dimsd[self.dir] = len(iava)
self.iavareshape = [1] * self.dir + [len(self.iava)] + \
[1] * (len(self.dims) - self.dir - 1)
self.N = np.prod(self.dimsd)
self.reshape = True
self.inplace = inplace
self.shape = (self.N, self.M)
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
if not self.inplace: x = x.copy()
if not self.reshape:
y = x[self.iava]
else:
x = np.reshape(x, self.dims)
y = np.take(x, self.iava, axis=self.dir)
return y
def _rmatvec(self, x):
if not self.inplace: x = x.copy()
if not self.reshape:
y = np.zeros(self.dims, dtype=self.dtype)
y[self.iava] = x
else:
x = np.reshape(x, self.dimsd)
y = np.zeros(self.dims, dtype=self.dtype)
np.put_along_axis(y, np.reshape(self.iava, self.iavareshape),
x, axis=self.dir)
return y
[docs] def mask(self, x):
"""Apply mask to input signal returning a signal of same size with
values at ``iava`` locations and ``0`` at other locations
Parameters
----------
x : :obj:`numpy.ndarray`
Input array (can be either flattened or not)
Returns
----------
y : :obj:`numpy.ma.core.MaskedArray`
Masked array.
"""
y = np_ma.array(np.zeros(self.dims), mask=np.ones(self.dims),
dtype=self.dtype)
if self.reshape:
x = np.reshape(x, self.dims)
x = np.swapaxes(x, self.dir, 0)
y = np.swapaxes(y, self.dir, 0)
y.mask[self.iava] = False
y[self.iava] = x[self.iava]
if self.reshape:
y = np.swapaxes(y, 0, self.dir)
return y