pylops.Block#
- class pylops.Block(ops, nproc=1, dtype=None)[source]#
Block operator.
Create a block operator from N lists of M linear operators each.
- Parameters
- ops
list List of lists of operators to be combined in block fashion. Alternatively,
numpy.ndarrayorscipy.sparsematrices 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. Ifnproc=1, work in serial mode.- dtype
str, optional Type of elements in input array.
- ops
Notes
In mathematics, a block or a partitioned matrix is a matrix that is interpreted as being broken into sections called blocks or submatrices. Similarly a block operator is composed of N sets of M linear operators each such that its application in forward mode leads to
\[\begin{split}\begin{bmatrix} \mathbf{L}_{1,1} & \mathbf{L}_{1,2} & \ldots & \mathbf{L}_{1,M} \\ \mathbf{L}_{2,1} & \mathbf{L}_{2,2} & \ldots & \mathbf{L}_{2,M} \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{L}_{N,1} & \mathbf{L}_{N,2} & \ldots & \mathbf{L}_{N,M} \end{bmatrix} \begin{bmatrix} \mathbf{x}_{1} \\ \mathbf{x}_{2} \\ \vdots \\ \mathbf{x}_{M} \end{bmatrix} = \begin{bmatrix} \mathbf{L}_{1,1} \mathbf{x}_{1} + \mathbf{L}_{1,2} \mathbf{x}_{2} + \mathbf{L}_{1,M} \mathbf{x}_{M} \\ \mathbf{L}_{2,1} \mathbf{x}_{1} + \mathbf{L}_{2,2} \mathbf{x}_{2} + \mathbf{L}_{2,M} \mathbf{x}_{M} \\ \vdots \\ \mathbf{L}_{N,1} \mathbf{x}_{1} + \mathbf{L}_{N,2} \mathbf{x}_{2} + \mathbf{L}_{N,M} \mathbf{x}_{M} \end{bmatrix}\end{split}\]while its application in adjoint mode leads to
\[\begin{split}\begin{bmatrix} \mathbf{L}_{1,1}^H & \mathbf{L}_{2,1}^H & \ldots & \mathbf{L}_{N,1}^H \\ \mathbf{L}_{1,2}^H & \mathbf{L}_{2,2}^H & \ldots & \mathbf{L}_{N,2}^H \\ \vdots & \vdots & \ddots & \vdots \\ \mathbf{L}_{1,M}^H & \mathbf{L}_{2,M}^H & \ldots & \mathbf{L}_{N,M}^H \end{bmatrix} \begin{bmatrix} \mathbf{y}_{1} \\ \mathbf{y}_{2} \\ \vdots \\ \mathbf{y}_{N} \end{bmatrix} = \begin{bmatrix} \mathbf{L}_{1,1}^H \mathbf{y}_{1} + \mathbf{L}_{2,1}^H \mathbf{y}_{2} + \mathbf{L}_{N,1}^H \mathbf{y}_{N} \\ \mathbf{L}_{1,2}^H \mathbf{y}_{1} + \mathbf{L}_{2,2}^H \mathbf{y}_{2} + \mathbf{L}_{N,2}^H \mathbf{y}_{N} \\ \vdots \\ \mathbf{L}_{1,M}^H \mathbf{y}_{1} + \mathbf{L}_{2,M}^H \mathbf{y}_{2} + \mathbf{L}_{N,M}^H \mathbf{y}_{N} \end{bmatrix}\end{split}\]- Attributes
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()
