class pylops.Symmetrize(N, dims=None, dir=0, dtype='float64')[source]

Symmetrize along an axis.

Symmetrize a multi-dimensional array along a specified direction dir.

N : int

Number of samples in model. Symmetric data has \(2N-1\) samples

dims : list, optional

Number of samples for each dimension (None if only one dimension is available)

dir : int, optional

Direction along which symmetrization is applied

dtype : str, optional

Type of elements in input array


The Symmetrize operator constructs a symmetric array given an input model in forward mode, by pre-pending the input model in reversed order.

For simplicity, given a one dimensional array, the forward operation can be expressed as:

\[\begin{split}y[i] = \begin{cases} x[i-N],& i\geq N\\ x[N-i],& \text{otherwise} \end{cases}\end{split}\]

for \(i=0,1,2,...,2N-2\), where \(N\) is the lenght of the input model.

In adjoint mode, the Symmetrize operator assigns the sums of the elements in position \(N-i\) and \(N+i\) to position \(i\) as follows:

\[\begin{multline} x[i] = y[N-i]+y[N+i] \quad \forall i=1,2,...,N-1 \end{multline}\]

apart from the central sample where \(x[0] = y[N]\).

shape : tuple

Operator shape

explicit : bool

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


__init__(N[, dims, dir, 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.
transpose() Transpose this linear operator.

Examples using pylops.Symmetrize