pylops.Symmetrize¶

class pylops.Symmetrize(dims, axis=-1, dtype='float64', name='S')[source]¶

Symmetrize along an axis.

Symmetrize a multi-dimensional array along axis.

Parameters:

dimslist or int: Number of samples for each dimension (None if only one dimension is available)
axisint, optional: Added in version 2.0.0.

Axis along which model is symmetrized.
dtypestr, optional: Type of elements in input array
namestr, optional: Added in version 2.0.0.

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

Attributes:

nsymint

Number of samples along the symmetrized axis.

dimstuple

Shape of the array after the adjoint, but before flattening.

For example, x_reshaped = (Op.H * y.ravel()).reshape(Op.dims).

dimsdtuple

Shape of the array after the forward, but before flattening.

For example, y_reshaped = (Op * x.ravel()).reshape(Op.dimsd).

shapetuple

Operator shape.

Notes

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:

\[\begin{split}y[i] = \begin{cases} x[i-N+1],& i\geq N\\ x[N-1-i],& \text{otherwise} \end{cases}\end{split}\]

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

In adjoint mode, the Symmetrize operator assigns the sums of the elements in position \(N-1-i\) and \(N-1+i\) to position \(i\) as follows:

\[\begin{multline} x[i] = y[N-1-i]+y[N-1+i] \quad \forall i=0,2,\ldots,N-1 \end{multline}\]

apart from the central sample where \(x[0] = y[N-1]\).

Methods

`__init__`(dims[, axis, dtype, name])
`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`()

Examples using `pylops.Symmetrize`¶