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

Block-diagonal operator.

Create a block-diagonal operator from N linear operators.

ops : list

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

dtype : str, optional

Type of elements in input array.


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

\[\begin{split}\begin{bmatrix} \mathbf{L_1} & \mathbf{0} & ... & \mathbf{0} \\ \mathbf{0} & \mathbf{L_2} & ... & \mathbf{0} \\ ... & ... & ... & ... \\ \mathbf{0} & \mathbf{0} & ... & \mathbf{L_N} \end{bmatrix} \begin{bmatrix} \mathbf{x}_{1} \\ \mathbf{x}_{2} \\ ... \\ \mathbf{x}_{N} \end{bmatrix} = \begin{bmatrix} \mathbf{L_1} \mathbf{x}_{1} \\ \mathbf{L_2} \mathbf{x}_{2} \\ ... \\ \mathbf{L_N} \mathbf{x}_{N} \end{bmatrix}\end{split}\]

while its application in adjoint mode leads to

\[\begin{split}\begin{bmatrix} \mathbf{L_1}^H \quad \mathbf{0} \quad ... \quad \mathbf{0} \\ \mathbf{0} \quad \mathbf{L_2}^H \quad ... \quad \mathbf{0} \\ ... \quad ... \quad ... \quad ... \\ \mathbf{0} \quad \mathbf{0} \quad ... \quad \mathbf{L_N}^H \end{bmatrix} \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ ... \\ \mathbf{y}_{N} \end{bmatrix} = \begin{bmatrix} \mathbf{L_1}^H \mathbf{y}_{1} \\ \mathbf{L_2}^H \mathbf{y}_{2} \\ ... \\ \mathbf{L_N}^H \mathbf{y}_{N} \end{bmatrix}\end{split}\]
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.
apply_columns(self, cols) Apply subset of columns of operator
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.
rmatmat(self, X) Adjoint matrix-matrix multiplication.
rmatvec(self, x) Adjoint matrix-vector multiplication.
todense(self) Return dense matrix.
transpose(self) Transpose this linear operator.

Examples using pylops.BlockDiag