org.nd4j.linalg.api.blas.impl

Class BaseLapack

java.lang.Object

org.nd4j.linalg.api.blas.impl.BaseLapack

All Implemented Interfaces:

Lapack

public abstract class BaseLapack
extends Object
implements Lapack

Base lapack define float and double versions.

Author:

Adam Gibson, rcorbish

Constructor Summary

Constructors

Constructor and Description
BaseLapack()

Method Summary

Modifier and Type	Method and Description
abstract void	dgeqrf(int M, int N, INDArray A, INDArray R, INDArray INFO)
abstract void	dgesvd(byte jobu, byte jobvt, int M, int N, INDArray A, INDArray S, INDArray U, INDArray VT, INDArray INFO)
abstract void	dgetrf(int M, int N, INDArray A, INDArray IPIV, INDArray INFO)
abstract void	dpotrf(byte uplo, int N, INDArray A, INDArray INFO)
abstract int	dsyev(char jobz, char uplo, int N, INDArray A, INDArray R)
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.
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.
abstract void	sgeqrf(int M, int N, INDArray A, INDArray R, INDArray INFO) Float/Double versions of QR decomp.
abstract void	sgesvd(byte jobu, byte jobvt, int M, int N, INDArray A, INDArray S, INDArray U, INDArray VT, INDArray INFO)
abstract void	sgetrf(int M, int N, INDArray A, INDArray IPIV, INDArray INFO) Float/Double versions of LU decomp.
abstract void	spotrf(byte uplo, int N, INDArray A, INDArray INFO) Float/Double versions of cholesky decomp for positive definite matrices A = LL*
abstract int	ssyev(char jobz, char uplo, int N, INDArray A, INDArray R) Float/Double versions of eigen value/vector calc.
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

Methods inherited from interface org.nd4j.linalg.api.blas.Lapack

getri

Constructor Detail

BaseLapack

public BaseLapack()

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

sgetrf

public abstract void sgetrf(int M,
                            int N,
                            INDArray A,
                            INDArray IPIV,
                            INDArray INFO)

Float/Double versions of LU decomp. This is the official LAPACK interface (in case you want to call this directly) See getrf for full details on LU Decomp

Parameters:

M - the number of rows in the matrix A

N - the number of cols in the matrix A

A - the matrix to factorize - data must be in column order ( create with 'f' ordering )

IPIV - an output array for the permutations ( must be int based storage )

INFO - error details 1 int array, a positive number (i) implies row i cannot be factored, a negative value implies paramtere i is invalid

dgetrf

public abstract void dgetrf(int M,
                            int N,
                            INDArray A,
                            INDArray IPIV,
                            INDArray INFO)

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

spotrf

public abstract void spotrf(byte uplo,
                            int N,
                            INDArray A,
                            INDArray INFO)

Float/Double versions of cholesky decomp for positive definite matrices A = LL*

Parameters:

uplo - which factor to return L or U

A - the matrix to factorize - data must be in column order ( create with 'f' ordering )

INFO - error details 1 int array, a positive number (i) implies row i cannot be factored, a negative value implies paramtere i is invalid

dpotrf

public abstract void dpotrf(byte uplo,
                            int N,
                            INDArray A,
                            INDArray INFO)

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

sgeqrf

public abstract void sgeqrf(int M,
                            int N,
                            INDArray A,
                            INDArray R,
                            INDArray INFO)

Float/Double versions of QR decomp. This is the official LAPACK interface (in case you want to call this directly) See geqrf for full details on LU Decomp

Parameters:

M - the number of rows in the matrix A

N - the number of cols in the matrix A

A - the matrix to factorize - data must be in column order ( create with 'f' ordering )

R - an output array for other part of factorization

INFO - error details 1 int array, a positive number (i) implies row i cannot be factored, a negative value implies paramtere i is invalid

dgeqrf

public abstract void dgeqrf(int M,
                            int N,
                            INDArray A,
                            INDArray R,
                            INDArray INFO)

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

ssyev

public abstract int ssyev(char jobz,
                          char uplo,
                          int N,
                          INDArray A,
                          INDArray R)

Float/Double versions of eigen value/vector calc.

Parameters:

jobz - 'N' - no eigen vectors, 'V' - return eigenvectors

uplo - upper or lower part of symmetric matrix to use

N - the number of rows & cols in the matrix A

A - the matrix to calculate eigenvectors

R - an output array for eigenvalues ( may be null )

dsyev

public abstract int dsyev(char jobz,
                          char uplo,
                          int N,
                          INDArray A,
                          INDArray R)

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

sgesvd

public abstract void sgesvd(byte jobu,
                            byte jobvt,
                            int M,
                            int N,
                            INDArray A,
                            INDArray S,
                            INDArray U,
                            INDArray VT,
                            INDArray INFO)

dgesvd

public abstract void dgesvd(byte jobu,
                            byte jobvt,
                            int M,
                            int N,
                            INDArray A,
                            INDArray S,
                            INDArray U,
                            INDArray VT,
                            INDArray INFO)

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