pylops.Symmetrize¶
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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.Parameters: 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 lenght 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__(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, 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. 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.
