org.nd4j.linalg.api.blas

Interface Lapack

All Known Implementing Classes:

BaseLapack

public interface Lapack

Lapack interface

Author:

Adam Gibson, rcorbish

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.

Method Detail

getrf

INDArray getrf(INDArray A)

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)

Parameters:

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

Throws:

Error - - with a message to indicate failure (usu. bad params)

geqrf

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. destroyed) geqrf = QR factorization of a general matrix (GE) into an orthogonal matrix Q and an upper triangular R matrix

Parameters:

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

The - R array if null R is not returned

Throws:

Error - - with a message to indicate failure (usu. bad params)

potrf

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. 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

Parameters:

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

whether - to return the upper (false) or lower factor

Throws:

Error - - with a message to indicate failure (usu. bad params)

syev

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

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

Parameters:

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

V - the resulting eigenvalues

Throws:

Error - - with a message to indicate failure (usu. bad params)

gesvd

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)

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

Throws:

Error - - with a message to indicate failure (usu. bad params)

getPFactor

INDArray getPFactor(int M,
                    INDArray ipiv)

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 )

Parameters:

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

ipiv - - the vector returned from a refactoring

getLFactor

INDArray getLFactor(INDArray A)

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

Parameters:

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

getUFactor

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

Parameters:

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

getri

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

Generate inverse ggiven LU decomp

Parameters:

N -

A -

lda -

IPIV -

WORK -

lwork -

INFO -