linear_operators.operators

Module operators

Definition of specialized LinearOperator subclasses. Classes ------- - SymmetricOperator : Enforces matvec = rmatvec and square shape. - IdentityOperator : Identity operator. - HomotheticOperator : Homothetic operators : i.e. of the form a * I. - DiagonalOperator : Diagonal operator. - MaskOperator : Diagonal operator with ones and zeros on the diagonal. - ShiftOperator : Shift the input vector values. - PermutationOperator : Perform permutations of the input vector values. - FftOperator : Perform one-dimensional Fast-Fourier Transform (np.fft.fft) - ReplicationOperator : Replicates the input vector n times. - SliceOperator : Performs slicing on an array. - TridiagonalOperator : A tridiagonal matrix a 3 1d arrays. - SymmetricTridiagonal : A symmetric tridiagonal matrix a 2 1d arrays. - BandOperator : A band matrix using lapack storage scheme. - SymmetricBandOperator : A symmetric band matrix using lapack storage scheme. - LoweTriangularOperator : A special case of band operator with only subdiagonal bands. - UpperTriangularOperator : A special case of band operator with only superdiagonal bands. - EigendecompositionOperator : A class storing eigenpairs of another operator. Functions --------- Functions generate instances of the associated classes. The following are available : - identity - homothetic - diagonal - mask - shift - permutation - fft - replication - slice_operator - tridiagonal - band_approximation : Generate a BandOperator from a dense matrix. - symmetric_band_approximation : Generate a BandOperator from a dense matrix.

Classes

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SymmetricOperator
Subclass of LinearOperator for the definition of symmetric operators, i.e.

IdentityOperator
SymmetricOperator with identity matvec (lambda x: x).

HomotheticOperator
Generate a SymmetricOperator performing an homothety, i.e.

DiagonalOperator
An operator which mimics a diagonal matrix.

MaskOperator
A subclass of DiagonalOperator with a boolean diagonal.

ShiftOperator
A LinearOperator corresponding to a shift matrix

PermutationOperator
Perform permutations to the vector elements.

FftOperator
Generate an Operator performing Fast Fourier Transform.

ReplicationOperator
Generate an operator which replicates the input vector n times.

SliceOperator
Perform slicing on the input vector.

TridiagonalOperator
Store a tridiagonal operator in the form of 3 arrays

SymmetricTridiagonal

BandOperator
Store a band matrix in ab format as defined in LAPACK documentation.

LowerTriangularOperator

UpperTriangularOperator

SymmetricBandOperator

EigendecompositionOperator
Define a SymmetricOperator from the eigendecomposition of another SymmetricOperator.

Functions

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_band_diag(ku, i=0)
Return a slice to get the i-th line of a band operator

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identity(shape, **kwargs)
Parameters: shape : the shape of the operator Output: I : identity LinearOperator

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homothetic(shape, coef, **kwargs)

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diagonal(d, **kwargs)

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diag(d, **kwargs)

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mask(mask, **kwargs)

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shift(shape, s, **kwargs)

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permutation(p, **kwargs)

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fft(shape, **kwargs)

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replication(shape, n, **kwargs)

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slice_operator(shape, slice, **kwargs)

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tridiagonal(shape, diag, subdiag, superdiag, **kwargs)

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symmetric_tridiagonal(shape, diag, subdiag, **kwargs)

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band_operator(shape, ab, kl, ku, **kwargs)

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symmetric_band_operator(shape, ab, lower=True, **kwargs)

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band_approximation(mat, kl=0, ku=0)
Approximate a dense matrix as a BandOperator.

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symmetric_band_approximation(mat, k=0)
Approximate a symmetrix matrix as a SymmetricBandOperator.

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Variables

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__package__ = 'linear_operators'

Function Details

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identity(shape, **kwargs)

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Parameters: shape : the shape of the operator Output: I : identity LinearOperator

Exemple: >>> I = identity((16, 16), dtype=float32)