pylops.VStack#

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

Vertical stacking.

Stack a set of N linear operators vertically.

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.
forceflatbool, optional: New in version 2.2.0.

Force an array to be flattened after rmatvec.
dtypestr, optional: Type of elements in input array.

Raises

ValueError: If ops have different number of rows

Notes

A vertical stack of N linear operators is created such as its application in forward mode leads to

\[\begin{split}\begin{bmatrix} \mathbf{L}_{1} \\ \mathbf{L}_{2} \\ \vdots \\ \mathbf{L}_{N} \end{bmatrix} \mathbf{x} = \begin{bmatrix} \mathbf{L}_{1} \mathbf{x} \\ \mathbf{L}_{2} \mathbf{x} \\ \vdots \\ \mathbf{L}_{N} \mathbf{x} \end{bmatrix} = \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ \vdots \\ \mathbf{y}_{N} \end{bmatrix}\end{split}\]

while its application in adjoint mode leads to

\[\begin{split}\begin{bmatrix} \mathbf{L}_{1}^H & \mathbf{L}_{2}^H & \ldots & \mathbf{L}_{N}^H \end{bmatrix} \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ \vdots \\ \mathbf{y}_{N} \end{bmatrix} = \mathbf{L}_{1}^H \mathbf{y}_1 + \mathbf{L}_{2}^H \mathbf{y}_2 + \ldots + \mathbf{L}_{N}^H \mathbf{y}_N\end{split}\]

Attributes

shapetuple: Operator shape
explicitbool: Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

`__init__`(ops[, nproc, forceflat, 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`()