org.nd4j.linalg.api.blas.impl

Class SparseBaseLapack

java.lang.Object

org.nd4j.linalg.api.blas.impl.SparseBaseLapack

All Implemented Interfaces:

Lapack

public class SparseBaseLapack
extends Object
implements Lapack

Author:

Audrey Loeffel

Constructor Summary

Constructors

Constructor and Description
SparseBaseLapack()

Method Summary

Modifier and Type	Method and Description
void	geqrf(INDArray A, INDArray R) QR decomposiiton of a matrix Factorize a matrix A such that A = QR The matrix A is overwritten by the Q component (i.e.
void	gesvd(INDArray A, INDArray S, INDArray U, INDArray VT) SVD decomposiiton of a matrix Factorize a matrix into its singular vectors and eigenvalues The decomposition is such that: A = U x S x VT gesvd = singular value decomposition (SVD) of a general matrix (GE)
INDArray	getLFactor(INDArray A) extracts the L (lower triangular) matrix from the LU factor result L will be the same dimensions as A
INDArray	getPFactor(int M, INDArray ipiv) This method takes one of the ipiv returns from LAPACK and creates the permutation matrix.
INDArray	getrf(INDArray A) LU decomposiiton of a matrix Factorize a matrix A The matrix A is overridden by the L & U combined.
void	getri(int N, INDArray A, int lda, int[] IPIV, INDArray WORK, int lwork, int INFO) Generate inverse ggiven LU decomp
INDArray	getUFactor(INDArray A) extracts the U (upper triangular) matrix from the LU factor result U will be n x n matrix where n = num cols in A
void	potrf(INDArray A, boolean lower) Triangular decomposiiton of a positive definite matrix ( cholesky ) Factorize a matrix A such that A = LL* (assuming lower==true) or A = U*U (a * represents conjugate i.e.
int	syev(char jobz, char uplo, INDArray A, INDArray V) Caclulate the eigenvalues and vectors of a symmetric matrix.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SparseBaseLapack

public SparseBaseLapack()

Method Detail

getrf

public INDArray getrf(INDArray A)

Description copied from interface: Lapack

LU decomposiiton of a matrix Factorize a matrix A The matrix A is overridden by the L & U combined. The permutation results are returned directly as a vector. To create the permutation matrix use getPFactor method To split out the L & U matrix use getLFactor and getUFactor methods getrf = triangular factorization (TRF) of a general matrix (GE)

Specified by:

getrf in interface Lapack

Parameters:

A - the input matrix, it will be overwritten with the factors

getPFactor

public INDArray getPFactor(int M,
                           INDArray ipiv)

Description copied from interface: Lapack

This method takes one of the ipiv returns from LAPACK and creates the permutation matrix. When factorizing, it is useful to avoid underflows and overflows by reordering rows/and or columns of the input matrix (mostly these methods solve simultaneous equations, so order is not important). The ipiv method assumes that only row ordering is done ( never seen column ordering done )

Specified by:

getPFactor in interface Lapack

Parameters:

M - - the size of the permutation matrix ( usu. the # rows in factored matrix )

ipiv - - the vector returned from a refactoring

getLFactor

public INDArray getLFactor(INDArray A)

Description copied from interface: Lapack

extracts the L (lower triangular) matrix from the LU factor result L will be the same dimensions as A

Specified by:

getLFactor in interface Lapack

Parameters:

A - - the combined L & U matrices returned from factorization

getUFactor

public INDArray getUFactor(INDArray A)

Description copied from interface: Lapack

extracts the U (upper triangular) matrix from the LU factor result U will be n x n matrix where n = num cols in A

Specified by:

getUFactor in interface Lapack

Parameters:

A - - the combined L & U matrices returned from factorization

getri

public void getri(int N,
                  INDArray A,
                  int lda,
                  int[] IPIV,
                  INDArray WORK,
                  int lwork,
                  int INFO)

Description copied from interface: Lapack

Generate inverse ggiven LU decomp

Specified by:

getri in interface Lapack

geqrf

public void geqrf(INDArray A,
                  INDArray R)

Description copied from interface: Lapack

QR decomposiiton of a matrix Factorize a matrix A such that A = QR The matrix A is overwritten by the Q component (i.e. destroyed) geqrf = QR factorization of a general matrix (GE) into an orthogonal matrix Q and an upper triangular R matrix

Specified by:

geqrf in interface Lapack

Parameters:

A - the input matrix, it will be overwritten with the factors

potrf

public void potrf(INDArray A,
                  boolean lower)

Description copied from interface: Lapack

Triangular decomposiiton of a positive definite matrix ( cholesky ) Factorize a matrix A such that A = LL* (assuming lower==true) or A = U*U (a * represents conjugate i.e. if matrix is real U* is a transpose) The matrix A is overridden by the L (or U). potrf = LU factorization of a positive definite matrix (PO) into a lower L ( or upper U ) triangular matrix

Specified by:

potrf in interface Lapack

Parameters:

A - the input matrix, it will be overwritten with the factors

syev

public int syev(char jobz,
                char uplo,
                INDArray A,
                INDArray V)

Description copied from interface: Lapack

Caclulate the eigenvalues and vectors of a symmetric matrix. The symmetric matrix means the results are guaranteed to be real (not complex) The matrix A is overridden by the eigenvectors. The eigenvalues are returned separately

Specified by:

syev in interface Lapack

A - the input matrix, it will be overwritten with the eigenvectors

V - the resulting eigenvalues

gesvd

public void gesvd(INDArray A,
                  INDArray S,
                  INDArray U,
                  INDArray VT)

Description copied from interface: Lapack

SVD decomposiiton of a matrix Factorize a matrix into its singular vectors and eigenvalues The decomposition is such that: A = U x S x VT gesvd = singular value decomposition (SVD) of a general matrix (GE)

Specified by:

gesvd in interface Lapack

Parameters:

A - the input matrix

S - the eigenvalues as a vector

U - the left singular vectors as a matrix. Maybe null if no S required

VT - the right singular vectors as a (transposed) matrix. Maybe null if no V required