linear_operators.operators.EigendecompositionOperator

Class EigendecompositionOperator

object --+ | interface.LinearOperator --+ | SymmetricOperator --+ | EigendecompositionOperator

Define a SymmetricOperator from the eigendecomposition of another SymmetricOperator. This can be used as an approximation for the operator. Inputs ------- A: LinearOperator (default: None) The LinearOperator to approximate. v: 2d ndarray (default: None) The eigenvectors as given by arpack.eigsh w: 1d ndarray (default: None) The eigenvalues as given by arpack.eigsh **kwargs: keyword arguments Passed to the arpack.eigsh function. You need to specify either A or v and w. Returns ------- An EigendecompositionOperator instance, which is a subclass of the SymmetricOperator. Notes ----- This is really a wrapper for scipy.sparse.linalg.eigen.arpack.eigsh

Instance Methods

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__init__(self, A=None, v=None, w=None, **kwargs)
Returns a SymmetricOperator of given shape and matvec function.

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det(self)
Output an approximation of the determinant from the eigenvalues.

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logdet(self)
Output the log of the determinant.

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__pow__(self, n)
Raising an eigendecomposition to an integer power requires only raising the eigenvalues to this power.

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inv(self)
Returns the pseudo-inverse of the operator.

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trace(self)

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cond(self)
Output an approximation of the condition number by taking the ratio of the maximum over the minimum eigenvalues, removing the zeros.

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Inherited from interface.LinearOperator: __add__, __iadd__, __imul__, __isub__, __mul__, __neg__, __radd__, __repr__, __rmul__, __rsub__, __sub__, matmat, matvec, todense

Inherited from interface.LinearOperator (private): _matmat

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __str__, __subclasshook__

Properties

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Inherited from interface.LinearOperator: T

Inherited from object: __class__

init(self, A=None, v=None, w=None, **kwargs)
(Constructor)

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Returns a SymmetricOperator of given shape and matvec
function.

Parameters
----------

shape : length 2 tuple
    The shape of the operator. Should be square.

matvec : function
    The matrix-vector operation.

Returns
-------
A SymmetricOperator instance.

Overrides: object.__init__: (inherited documentation)

logdet(self)

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Output the log of the determinant. Useful as the determinant of large matrices can exceed floating point capabilities.

pow(self, n)

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Raising an eigendecomposition to an integer power requires only raising the eigenvalues to this power.

Overrides: interface.LinearOperator.__pow__

cond(self)

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Output an approximation of the condition number by taking the ratio of the maximum over the minimum eigenvalues, removing the zeros.

For better approximation of the condition number, one should consider generating the eigendecomposition with the keyword which='BE', in order to have a correct estimate of the small eigenvalues.

Class EigendecompositionOperator

__init__(self, A=None, v=None, w=None, **kwargs) (Constructor)

logdet(self)

__pow__(self, n)

cond(self)

init(self, A=None, v=None, w=None, **kwargs)
(Constructor)

pow(self, n)