pylops.BlockDiag

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

Block-diagonal operator.

Create a block-diagonal operator from N linear operators.

Parameters:
ops : list

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

nproc : int, optional

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

dtype : str, 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

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

while its application in adjoint mode leads to

\[\begin{split}\begin{bmatrix} \mathbf{L}_1^H & \mathbf{0} & \ldots & \mathbf{0} \\ \mathbf{0} & \mathbf{L}_2^H & \ldots & \mathbf{0} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{0} & \mathbf{0} & \ldots & \mathbf{L}_N^H \end{bmatrix} \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ \vdots \\ \mathbf{y}_{N} \end{bmatrix} = \begin{bmatrix} \mathbf{L}_1^H \mathbf{y}_{1} \\ \mathbf{L}_2^H \mathbf{y}_{2} \\ \vdots \\ \mathbf{L}_N^H \mathbf{y}_{N} \end{bmatrix}\end{split}\]
Attributes:
shape : tuple

Operator shape

explicit : bool

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

Methods

__init__(ops[, nproc, 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.
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() Transpose this linear operator.