class pylops.VStack(ops, dtype=None)[source]

Vertical stacking.

Stack a set of N linear operators vertically.

ops : list

Linear operators to be stacked

dtype : str, optional

Type of elements in input array.


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

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

while its application in adjoint mode leads to

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

Operator shape

explicit : bool

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


__init__(self, ops[, dtype]) Initialize this LinearOperator.
adjoint(self) Hermitian adjoint.
cond(self, \*\*kwargs_eig) Condition number of linear operator.
conj(self) Complex conjugate operator
div(self, y[, niter]) Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(self, x) Matrix-matrix or matrix-vector multiplication.
eigs(self[, neigs, symmetric, niter]) Most significant eigenvalues of linear operator.
matmat(self, X) Matrix-matrix multiplication.
matvec(self, x) Matrix-vector multiplication.
rmatvec(self, x) Adjoint matrix-vector multiplication.
transpose(self) Transpose this linear operator.

Examples using pylops.VStack