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
- dims
list
orint
Number of samples for each dimension (
None
if only one dimension is available)- axis
int
, optional New in version 2.0.0.
Axis along which model is symmetrized.
- 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
)
- dims
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 \(x[0] = y[N-1]\).
- Attributes
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
()