import numpy as np
from pylops import LinearOperator
[docs]class Flip(LinearOperator):
r"""Flip along an axis.
Flip a multi-dimensional array along a specified direction ``dir``.
Parameters
----------
N : :obj:`int`
Number of samples in model.
dims : :obj:`list`, optional
Number of samples for each dimension
(``None`` if only one dimension is available)
dir : :obj:`int`, optional
Direction along which flipping is applied.
dtype : :obj:`str`, optional
Type of elements in input array.
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved explicitly
(``True``) or not (``False``)
Notes
-----
The Flip operator flips the input model (and data) along any chosen
direction. For simplicity, given a one dimensional array,
in forward mode this is equivalent to:
.. math::
y[i] = x[N-1-i] \quad \forall i=0,1,2,\ldots,N-1
where :math:`N` is the lenght of the input model. As this operator is
self-adjoint, :math:`x` and :math:`y` in the equation above are simply
swapped in adjoint mode.
"""
def __init__(self, N, dims=None, dir=0, dtype="float64"):
self.N = N
self.dir = dir
if dims is None:
self.dims = (self.N,)
self.reshape = False
else:
if np.prod(dims) != self.N:
raise ValueError("product of dims must equal N")
else:
self.dims = dims
self.reshape = True
self.shape = (self.N, self.N)
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
if self.reshape:
x = np.reshape(x, self.dims)
y = np.flip(x, axis=self.dir)
if self.reshape:
y = y.ravel()
return y
def _rmatvec(self, x):
return self._matvec(x)