class pylops.Pad(dims, pad, dtype='float64', name='P')[source]

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.

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.

name : str, optional

New in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)


If any element of pad is negative.


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:

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

Operator shape

explicit : bool

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


__init__(dims, pad[, dtype, name]) 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, densesolver]) 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.
reset_count() Reset counters
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