import numpy as np
from pylops import LinearOperator
[docs]class Pad(LinearOperator):
r"""Pad operator.
Zero-pad model in forward model and extract non-zero subsequence
in adjoint. Padding can be performed in one or multiple directions to any
multi-dimensional input arrays.
Parameters
----------
dims : :obj:`int` or :obj:`tuple`
Number of samples for each dimension
pad : :obj:`tuple`
Number of samples to pad. If ``dims`` is a scalar, ``pad`` is a single
tuple ``(pad_in, pad_end)``. If ``dims`` is a tuple,
``pad`` is a tuple of tuples where each inner tuple contains
the number of samples to pad in each dimension
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``)
Raises
------
ValueError
If any element of ``pad`` is negative.
Notes
-----
Given an array of size :math:`N`, the *Pad* operator simply adds
:math:`pad_{in}` at the start and :math:`pad_{end}` at the end in forward mode:
.. math::
y_{i} = x_{i-pad_{in}} \quad \forall
i=pad_{in},pad_{in}+1,...,pad_{in}+N-1
and :math:`y_i = 0 \quad \forall
i=0,...,pad_{in}-1, pad_{in}+N-1,...,N+pad_{in}+pad_{end}`
In adjoint mode, values from :math:`pad_{in}` to :math:`N-pad_{end}` are
extracted from the data:
.. math::
x_{i} = y_{pad_{in}+i} \quad \forall i=0, N-1
"""
def __init__(self, dims, pad, dtype='float64'):
if np.any(np.array(pad) < 0):
raise ValueError('Padding must be positive or zero')
self.dims = dims
self.pad = pad
self.reshape = False if isinstance(self.dims, int) else True
if self.reshape:
self.dimsd = [dim + p[0] + p[1] for dim, p in zip(dims, pad)]
else:
self.dimsd = dims + pad[0] + pad[1]
self.shape = (np.prod(np.array(self.dimsd)),
np.prod(np.array(self.dims)))
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
if self.reshape:
y = x.reshape(self.dims)
y = np.pad(y, self.pad, mode='constant')
else:
y = np.pad(x, self.pad, mode='constant')
return y.flatten()
def _rmatvec(self, x):
if self.reshape:
y = x.reshape(self.dimsd)
for ax, pad in enumerate(self.pad):
y = np.take(y, np.arange(pad[0], pad[0] + self.dims[ax]),
axis=ax)
else:
y = x[self.pad[0]:self.pad[0]+self.dims]
return y.flatten()