# pylops.BlockDiag#

class pylops.BlockDiag(ops, nproc=1, dtype=None)[source]#

Block-diagonal operator.

Create a block-diagonal operator from N linear operators.

Parameters
opslist

Linear operators to be stacked. Alternatively, numpy.ndarray or scipy.sparse matrices can be passed in place of one or more operators.

nprocint, optional

Number of processes used to evaluate the N operators in parallel using multiprocessing. If nproc=1, work in serial mode.

dtypestr, optional

Type of elements in input array.

Notes

A block-diagonal operator composed of N linear operators is created such as its application in forward mode leads to

$\begin{split}\begin{bmatrix} \mathbf{L}_1 & \mathbf{0} & \ldots & \mathbf{0} \\ \mathbf{0} & \mathbf{L}_2 & \ldots & \mathbf{0} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{0} & \mathbf{0} & \ldots & \mathbf{L}_N \end{bmatrix} \begin{bmatrix} \mathbf{x}_{1} \\ \mathbf{x}_{2} \\ \vdots \\ \mathbf{x}_{N} \end{bmatrix} = \begin{bmatrix} \mathbf{L}_1 \mathbf{x}_{1} \\ \mathbf{L}_2 \mathbf{x}_{2} \\ \vdots \\ \mathbf{L}_N \mathbf{x}_{N} \end{bmatrix}\end{split}$

$\begin{split}\begin{bmatrix} \mathbf{L}_1^H & \mathbf{0} & \ldots & \mathbf{0} \\ \mathbf{0} & \mathbf{L}_2^H & \ldots & \mathbf{0} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{0} & \mathbf{0} & \ldots & \mathbf{L}_N^H \end{bmatrix} \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ \vdots \\ \mathbf{y}_{N} \end{bmatrix} = \begin{bmatrix} \mathbf{L}_1^H \mathbf{y}_{1} \\ \mathbf{L}_2^H \mathbf{y}_{2} \\ \vdots \\ \mathbf{L}_N^H \mathbf{y}_{N} \end{bmatrix}\end{split}$
Attributes
shapetuple

Operator shape

explicitbool

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

Methods

 __init__(ops[, nproc, dtype]) 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.BlockDiag#

Operators concatenation

Operators concatenation

Operators with Multiprocessing

Operators with Multiprocessing