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SciPy Reference Guide, Release 0.8.dev
3.15.1 Sparse Linear Algebra
The submodules of sparse.linalg:
1. eigen: sparse eigenvalue problem solvers
2. isolve: iterative methods for solving linear systems
3. dsolve: direct factorization methods for solving linear systems
3.15.2 Examples
class 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.
See Also:
Parameters
shape : tuple
Matrix dimensions (M,N)
matvec : callable f(v)
Returns returns A * v.
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
>>> A.matvec( ones(2) )
array([ 2., 3.])
>>> A * ones(2)
array([ 2., 3.])
Methods
matmat(X) Matrix-matrix multiplication
matvec(x) Matrix-vector multiplication
392 Chapter 3. Reference