scipy.sparse.linalg.LinearOperator

class scipy.sparse.linalg.LinearOperator(shape, matvec, rmatvec=None, matmat=None, dtype=None)

Common interface for performing matrix vector products

Many iterative methods (e.g. cg, gmres) do not need to know the individual entries of a matrix to solve a linear system A*x=b. Such solvers only require the computation of matrix vector products, A*v where v is a dense vector. This class serves as an abstract interface between iterative solvers and matrix-like objects.

Parameters :

shape : tuple

Matrix dimensions (M,N)

matvec : callable f(v)

Returns returns A * v.

Other Parameters:  

rmatvec : callable f(v)

Returns A^H * v, where A^H is the conjugate transpose of A.

matmat : callable f(V)

Returns A * V, where V is a dense matrix with dimensions (N,K).

dtype : dtype

Data type of the matrix.

See also

aslinearoperator

Construct LinearOperators

Notes

The user-defined matvec() function must properly handle the case where v has shape (N,) as well as the (N,1) case. The shape of the return type is handled internally by LinearOperator.

Examples

>>> from scipy.sparse.linalg import LinearOperator
>>> from scipy import *
>>> def mv(v):
...     return array([ 2*v[0], 3*v[1]])
...
>>> A = LinearOperator( (2,2), matvec=mv )
>>> A
<2x2 LinearOperator with unspecified dtype>
>>> A.matvec( ones(2) )
array([ 2.,  3.])
>>> A * ones(2)
array([ 2.,  3.])

Methods

matmat(X)	Matrix-matrix multiplication
matvec(x)	Matrix-vector multiplication