scipy.sparse.linalg.LinearOperator¶

class
scipy.sparse.linalg.
LinearOperator
(dtype, shape)[source]¶ 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 matrixlike objects.
To construct a concrete LinearOperator, either pass appropriate callables to the constructor of this class, or subclass it.
A subclass must implement either one of the methods
_matvec
and_matmat
, and the attributes/propertiesshape
(pair of integers) anddtype
(may be None). It may call the__init__
on this class to have these attributes validated. Implementing_matvec
automatically implements_matmat
(using a naive algorithm) and viceversa.Optionally, a subclass may implement
_rmatvec
or_adjoint
to implement the Hermitian adjoint (conjugate transpose). As with_matvec
and_matmat
, implementing either_rmatvec
or_adjoint
implements the other automatically. Implementing_adjoint
is preferable;_rmatvec
is mostly there for backwards compatibility. Parameters
 shapetuple
Matrix dimensions (M, N).
 matveccallable f(v)
Returns returns A * v.
 rmatveccallable f(v)
Returns A^H * v, where A^H is the conjugate transpose of A.
 matmatcallable f(V)
Returns A * V, where V is a dense matrix with dimensions (N, K).
 dtypedtype
Data type of the matrix.
 rmatmatcallable f(V)
Returns A^H * V, where V is a dense matrix with dimensions (M, K).
See also
aslinearoperator
Construct LinearOperators
Notes
The userdefined 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.
LinearOperator instances can also be multiplied, added with each other and exponentiated, all lazily: the result of these operations is always a new, composite LinearOperator, that defers linear operations to the original operators and combines the results.
More details regarding how to subclass a LinearOperator and several examples of concrete LinearOperator instances can be found in the external project PyLops.
Examples
>>> import numpy as np >>> from scipy.sparse.linalg import LinearOperator >>> def mv(v): ... return np.array([2*v[0], 3*v[1]]) ... >>> A = LinearOperator((2,2), matvec=mv) >>> A <2x2 _CustomLinearOperator with dtype=float64> >>> A.matvec(np.ones(2)) array([ 2., 3.]) >>> A * np.ones(2) array([ 2., 3.])
 Attributes
 argstuple
For linear operators describing products etc. of other linear operators, the operands of the binary operation.
Methods
__call__
(self, x)Call self as a function.
adjoint
(self)Hermitian adjoint.
dot
(self, x)Matrixmatrix or matrixvector multiplication.
matmat
(self, X)Matrixmatrix multiplication.
matvec
(self, x)Matrixvector multiplication.
rmatmat
(self, X)Adjoint matrixmatrix multiplication.
rmatvec
(self, x)Adjoint matrixvector multiplication.
transpose
(self)Transpose this linear operator.
__mul__