pylops.Pad

class pylops.Pad(dims, pad, dtype='float64')

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 : int or tuple

Number of samples for each dimension

pad : 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 : str, optional

Type of elements in input array.

Raises:

ValueError

If any element of pad is negative.

Notes

Given an array of size \(N\), the Pad operator simply adds \(\text{pad}_\text{in}\) at the start and \(\text{pad}_\text{end}\) at the end in forward mode:

\[y_{i} = x_{i-\text{pad}_\text{in}} \quad \forall i=\text{pad}_\text{in},\ldots,\text{pad}_\text{in}+N-1\]

and \(y_i = 0 \quad \forall i=0,\ldots,\text{pad}_\text{in}-1, \text{pad}_\text{in}+N-1,\ldots,N+\text{pad}_\text{in}+\text{pad}_\text{end}\)

In adjoint mode, values from \(\text{pad}_\text{in}\) to \(N-\text{pad}_\text{end}\) are extracted from the data:

\[x_{i} = y_{\text{pad}_\text{in}+i} \quad \forall i=0, N-1\]

Attributes:

shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

__init__(dims, pad[, dtype])	Initialize this LinearOperator.
adjoint()	Hermitian adjoint.
apply_columns(cols)	Apply subset of columns of operator
cond([uselobpcg])	Condition number of linear operator.
conj()	Complex conjugate operator
div(y[, niter])	Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x)	Matrix-matrix or matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg])	Most significant eigenvalues of linear operator.
matmat(X)	Matrix-matrix multiplication.
matvec(x)	Matrix-vector multiplication.
rmatmat(X)	Matrix-matrix multiplication.
rmatvec(x)	Adjoint matrix-vector multiplication.
todense([backend])	Return dense matrix.
toimag([forw, adj])	Imag operator
toreal([forw, adj])	Real operator
tosparse()	Return sparse matrix.
trace([neval, method, backend])	Trace of linear operator.
transpose()	Transpose this linear operator.

Examples using pylops.Pad

Padding