Contains prototypes for BLAS level 1, 2, 3 and Lapack routines. More...

#include "gurls++/blas_lapack.hpp"

Include dependency graph for blas_lapack.h:

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Classes
class	gurls::BlasUtils
	BlasUtils is a convenience class to interface with Blas. More...
Namespaces
namespace	gurls
	The main namespace of GURLS++.
Enumerations
enum	gurls::CBLAS_DIAG { CblasNonUnit = 5, CblasUnit = 6 }
	Diagonal options (unit, non unit)
enum	gurls::CBLAS_ORDER { CblasRowMajor = 9, CblasColMajor = 10 }
	Matrix Order (row major or column major)
enum	gurls::CBLAS_SIDE { CblasLeft = 7, CblasRight = 8 }
	Side options (left, right)
enum	gurls::CBLAS_TRANSPOSE { CblasNoTrans = 0, CblasTrans = 1, CblasConjTrans = 2 }
	Transposition options (no transpose, transpose, conjugate transpose)
enum	gurls::CBLAS_UPLO { CblasUpper = 3, CblasLower = 4 }
	Upper/lower options (upper, lower)
Functions
void	daxpy_ (int n, double alpha, double x, int incx, double y, int incy)
	Prototype for Blas DAXPY.
void	dcopy_ (int n, double x, int incx, double y, int *incy)
	Prototype for Blas DCOPY.
double	ddot_ (int n, double x, int incx, double y, int *incy)
	Prototype for Blas DDOT.
int	dgeev_ (char jobvl, char jobvr, int n, double a, int lda, double wr, double wi, double vl, int ldvl, double vr, int ldvr, double work, int lwork, int info)
	Prototype for Lapack DGEEV.
int	dgelss_ (int m, int n, int nrhs, double a, int lda, double b, int ldb, double s, double rcond, int rank, double work, int lwork, int *info)
	Prototype for Lapack DGELSS.
void	dgemm_ (char transa, char transb, int m, int n, int k, double alpha, double a, int lda, double b, int ldb, double beta, double c, int *ldc)
	Prototype for Blas DGEMM.
void	dgemv_ (char trans, int m, int n, double alpha, double a, int lda, double x, int incx, double beta, double y, int *incy)
	Prototype for Blas DGEMV.
void	dgeqp3_ (int m, int n, double A, int lda, int jpvt, double tau, double work, int lwork, int *info)
	Prototype for Lapack DGEQP3.
int	dgesvd_ (char jobu, char jobvt, int m, int n, double a, int lda, double s, double u, int ldu, double vt, int ldvt, double work, int lwork, int info)
	Prototype for Lapack DGESVD.
double	dnrm2_ (int n, double x, int *incx)
	Prototype for Blas DNRM2.
void	dorgqr_ (int m, int n, int k, double a, int lda, double tau, double work, int lwork, int *info)
	Prototype for Lapack DORGQR.
int	dpotrf_ (char UPLO, int n, double a, int lda, int *info)
	Prototype for Lapack DPOTRF.
void	dscal_ (int n, double a, double x, int incx)
	Prototype for Blas DSCAL.
void	dswap_ (int n, double sx, int incx, double sy, int *incy)
	Prototype for Blas DSWAP.
int	dsyev_ (char jobz, char uplo, int n, double a, int lda, double w, double work, int lwork, int *info)
	Prototype for Lapack DSYEV.
void	dtrsm_ (char side, char uplo, char transa, char diag, int m, int n, double alpha, double a, int lda, double b, int *ldb)
	Prototype for Blas DTRSM.
void	saxpy_ (int n, float alpha, float x, int incx, float y, int incy)
	Prototype for Blas SAXPY.
void	scopy_ (int n, float x, int incx, float y, int *incy)
	Prototype for Blas SCOPY.
float	sdot_ (int n, float x, int incx, float y, int *incy)
	Prototype for Blas SDOT.
int	sgeev_ (char jobvl, char jobvr, int n, float a, int lda, float wr, float wi, float vl, int ldvl, float vr, int ldvr, float work, int lwork, int info)
	Prototype for Lapack SGEEV.
int	sgelss_ (int m, int n, int nrhs, float a, int lda, float b, int ldb, float s, float rcond, int rank, float work, int lwork, int *info)
	Prototype for Lapack SGELSS.
void	sgemm_ (char transa, char transb, int m, int n, int k, float alpha, float a, int lda, float b, int ldb, float beta, float c, int *ldc)
	Prototype for Blas SGEMM.
void	sgemv_ (char trans, int m, int n, float alpha, float a, int lda, float x, int incx, float beta, float y, int *incy)
	Prototype for Blas SGEMV.
void	sgeqp3_ (int m, int n, float A, int lda, int jpvt, float tau, float work, int lwork, int *info)
	Prototype for Lapack SGEQP3.
int	sgesvd_ (char jobu, char jobvt, int m, int n, float a, int lda, float s, float u, int ldu, float vt, int ldvt, float work, int lwork, int info)
	Prototype for Lapack SGESVD.
int	sgetrf_ (int m, int n, float a, int lda, int ipiv, int info)
	Prototype for Lapack SGETRF.
int	sgetri_ (int n, float a, int lda, int ipiv, float work, int lwork, int *info)
	Prototype for Lapack SGETRI.
float	snrm2_ (int n, float x, int *incx)
	Prototype for Blas SNRM2.
void	sorgqr_ (int m, int n, int k, float a, int lda, float tau, float work, int lwork, int *info)
	Prototype for Lapack SORGQR.
int	spotrf_ (char UPLO, int n, float a, int lda, int *info)
	Prototype for Lapack SPOTRF.
void	sscal_ (int n, float a, float x, int incx)
	Prototype for Blas SSCAL.
void	sswap_ (int n, float sx, int incx, float sy, int *incy)
	Prototype for Blas SSWAP.
int	ssyev_ (char jobz, char uplo, int n, float a, int lda, float w, float work, int lwork, int *info)
	Prototype for Lapack SSYEV.
void	strsm_ (char side, char uplo, char transa, char diag, int m, int n, float alpha, float a, int lda, float b, int *ldb)
	Prototype for Blas STRSM.

Detailed Description

Definition in file blas_lapack.h.

Function Documentation

void daxpy_	(	int *	n,
		double *	alpha,
		double *	x,
		int *	incx,
		double *	y,
		int *	incy
	)

Constant times a vector plus a vector

void dcopy_	(	int *	n,
		double *	x,
		int *	incx,
		double *	y,
		int *	incy
	)

Copies a vector x to a vector y

double ddot_	(	int *	n,
		double *	x,
		int *	incx,
		double *	y,
		int *	incy
	)

Dot product of two double precision vectors

int dgeev_	(	char *	jobvl,
		char *	jobvr,
		int *	n,
		double *	a,
		int *	lda,
		double *	wr,
		double *	wi,
		double *	vl,
		int *	ldvl,
		double *	vr,
		int *	ldvr,
		double *	work,
		int *	lwork,
		int *	info
	)

Computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. The right eigenvector v(j) of A satisfies

$A v(j) = \lambda (j) v(j)$

where $\lambda (j)$ is its eigenvalue. The left eigenvector $u(j)$ of $A$ satisfies

$u(j)^T A = \lambda (j) u(j)^T$

where $u(j)^T$ denotes the transpose of $u(j)$ . The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.

int dgelss_	(	int *	m,
		int *	n,
		int *	nrhs,
		double *	a,
		int *	lda,
		double *	b,
		int *	ldb,
		double *	s,
		double *	rcond,
		int *	rank,
		double *	work,
		int *	lwork,
		int *	info
	)

Computes the minimum norm solution to a real linear least squares problem:

Minimize $||(| b - Ax |)||_2$ .

Using the singular value decomposition (SVD) of $A$ . $A$ is an M-by-N matrix which may be rank-deficient.

Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix $B$ and the N-by-NRHS solution matrix $X$ .

The effective rank of $A$ is determined by treating as zero those singular values which are less than RCOND times the largest singular value.

void dgemm_	(	char *	transa,
		char *	transb,
		int *	m,
		int *	n,
		int *	k,
		double *	alpha,
		double *	a,
		int *	lda,
		double *	b,
		int *	ldb,
		double *	beta,
		double *	c,
		int *	ldc
	)

Performs one of the matrix-matrix operations:

$C = \alpha op(A) op(B) + \beta C,$

where $op(X)$ is one of $op(X) = X$ or $op(X) = X^T$ , $\alpha$ and $\beta$ are scalars, and $A$ , $B$ and $C$ are matrices, with $op(A)$ an m by k matrix, $op(B)$ a k by n matrix and $C$ an m by n matrix

void dgemv_	(	char *	trans,
		int *	m,
		int *	n,
		double *	alpha,
		double *	a,
		int *	lda,
		double *	x,
		int *	incx,
		double *	beta,
		double *	y,
		int *	incy
	)

Performs one of the matrix-vector operations

$y = \alpha A x + \beta y$

or

$y = \alpha A^T x + \beta y$

where $\alpha$ and $\beta$ are scalars, $x$ and $y$ are vectors and $A$ is an m by n matrix.

void dgeqp3_	(	int *	m,
		int *	n,
		double *	A,
		int *	lda,
		int *	jpvt,
		double *	tau,
		double *	work,
		int *	lwork,
		int *	info
	)

Computes a QR factorization with column pivoting of a matrix $A$ : $A P = Q R$ using Level 3 BLAS.

int dgesvd_	(	char *	jobu,
		char *	jobvt,
		int *	m,
		int *	n,
		double *	a,
		int *	lda,
		double *	s,
		double *	u,
		int *	ldu,
		double *	vt,
		int *	ldvt,
		double *	work,
		int *	lwork,
		int *	info
	)

Computes the singular value decomposition (SVD) of a real M-by-N matrix $A$ , optionally computing the left and/or right singular vectors. The SVD is written

$A = U \Sigma V^T$

where $\Sigma$ is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, $U$ is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of $\Sigma$ are the singular values of $A$ ; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of $U$ and $V$ are the left and right singular vectors of $A$ . Note that the routine returns $V^T$ , not $V$ .

double dnrm2_	(	int *	n,
		double *	x,
		int *	incx
	)

Returns the euclidean norm of a vector via the function name, so that $SNRM2 = \sqrt{(x^T x)}$

void dorgqr_	(	int *	m,
		int *	n,
		int *	k,
		double *	a,
		int *	lda,
		double *	tau,
		double *	work,
		int *	lwork,
		int *	info
	)

Generates an M-by-N real matrix $Q$ with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M

$Q = H(1) H(2) . . . H(k)$

as returned by SGEQRF.

int dpotrf_	(	char *	UPLO,
		int *	n,
		double *	a,
		int *	lda,
		int *	info
	)

Computes the Cholesky factorization of a real symmetric positive definite matrix A.

The factorization has the form

$A = U^T U$

, if UPLO = 'U', or

$A = L L^T$

, if UPLO = 'L', where $U$ is an upper triangular matrix and $L$ is lower triangular

void dscal_	(	int *	n,
		double *	a,
		double *	x,
		int *	incx
	)

Scales a vector by a constant

void dswap_	(	int *	n,
		double *	sx,
		int *	incx,
		double *	sy,
		int *	incy
	)

Interchanges two vectors. Uses unrolled loops for increments equal to 1.

int dsyev_	(	char *	jobz,
		char *	uplo,
		int *	n,
		double *	a,
		int *	lda,
		double *	w,
		double *	work,
		int *	lwork,
		int *	info
	)

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void dtrsm_	(	char *	side,
		char *	uplo,
		char *	transa,
		char *	diag,
		int *	m,
		int *	n,
		double *	alpha,
		double *	a,
		int *	lda,
		double *	b,
		int *	ldb
	)

Solves one of the matrix equations

$op(A) X = \alpha B$

or

$X op(A) = \alpha B$

, where $\alpha$ is a scalar, $X$ and $B$ are m by n matrices, $A$ is a unit, or non-unit, upper or lower triangular matrix and $op(A)$ is one of $ op(A) = A$ or $op(A) = A^T$ . The matrix $X$ is overwritten on $B$ .

void saxpy_	(	int *	n,
		float *	alpha,
		float *	x,
		int *	incx,
		float *	y,
		int *	incy
	)

Constant times a vector plus a vector

void scopy_	(	int *	n,
		float *	x,
		int *	incx,
		float *	y,
		int *	incy
	)

Copies a vector x to a vector y

float sdot_	(	int *	n,
		float *	x,
		int *	incx,
		float *	y,
		int *	incy
	)

Dot product of two single precision vectors

int sgeev_	(	char *	jobvl,
		char *	jobvr,
		int *	n,
		float *	a,
		int *	lda,
		float *	wr,
		float *	wi,
		float *	vl,
		int *	ldvl,
		float *	vr,
		int *	ldvr,
		float *	work,
		int *	lwork,
		int *	info
	)

Computes for an N-by-N real nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. The right eigenvector v(j) of A satisfies

$A v(j) = \lambda (j) v(j)$

where $\lambda (j)$ is its eigenvalue. The left eigenvector $u(j)$ of $A$ satisfies

$u(j)^T A = \lambda (j) u(j)^T$

where $u(j)^T$ denotes the transpose of $u(j)$ . The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.

int sgelss_	(	int *	m,
		int *	n,
		int *	nrhs,
		float *	a,
		int *	lda,
		float *	b,
		int *	ldb,
		float *	s,
		float *	rcond,
		int *	rank,
		float *	work,
		int *	lwork,
		int *	info
	)

Computes the minimum norm solution to a real linear least squares problem:

Minimize $||(| b - Ax |)||_2$ .

Using the singular value decomposition (SVD) of $A$ . $A$ is an M-by-N matrix which may be rank-deficient.

Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix $B$ and the N-by-NRHS solution matrix $X$ .

The effective rank of $A$ is determined by treating as zero those singular values which are less than RCOND times the largest singular value.

void sgemm_	(	char *	transa,
		char *	transb,
		int *	m,
		int *	n,
		int *	k,
		float *	alpha,
		float *	a,
		int *	lda,
		float *	b,
		int *	ldb,
		float *	beta,
		float *	c,
		int *	ldc
	)

Performs one of the matrix-matrix operations:

$C = \alpha op(A) op(B) + \beta C,$

where $op(X)$ is one of $op(X) = X$ or $op(X) = X^T$ , $\alpha$ and $\beta$ are scalars, and $A$ , $B$ and $C$ are matrices, with $op(A)$ an m by k matrix, $op(B)$ a k by n matrix and $C$ an m by n matrix

void sgemv_	(	char *	trans,
		int *	m,
		int *	n,
		float *	alpha,
		float *	a,
		int *	lda,
		float *	x,
		int *	incx,
		float *	beta,
		float *	y,
		int *	incy
	)

Performs one of the matrix-vector operations

$y = \alpha A x + \beta y$

or

$y = \alpha A^T x + \beta y$

where $\alpha$ and $\beta$ are scalars, $x$ and $y$ are vectors and $A$ is an m by n matrix.

void sgeqp3_	(	int *	m,
		int *	n,
		float *	A,
		int *	lda,
		int *	jpvt,
		float *	tau,
		float *	work,
		int *	lwork,
		int *	info
	)

Computes a QR factorization with column pivoting of a matrix $A$ : $A P = Q R$ using Level 3 BLAS.

int sgesvd_	(	char *	jobu,
		char *	jobvt,
		int *	m,
		int *	n,
		float *	a,
		int *	lda,
		float *	s,
		float *	u,
		int *	ldu,
		float *	vt,
		int *	ldvt,
		float *	work,
		int *	lwork,
		int *	info
	)

Computes the singular value decomposition (SVD) of a real M-by-N matrix $A$ , optionally computing the left and/or right singular vectors. The SVD is written

$A = U \Sigma V^T$

where $\Sigma$ is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, $U$ is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of $\Sigma$ are the singular values of $A$ ; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of $U$ and $V$ are the left and right singular vectors of $A$ . Note that the routine returns $V^T$ , not $V$ .

int sgetrf_	(	int *	m,
		int *	n,
		float *	a,
		int *	lda,
		int *	ipiv,
		int *	info
	)

Computes an LU factorization of a general M-by-N matrix $A$ using partial pivoting with row interchanges. The factorization has the form

$A = P L U$

where $P$ is a permutation matrix, $L$ is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and $U$ is upper triangular (upper trapezoidal if m < n)

int sgetri_	(	int *	n,
		float *	a,
		int *	lda,
		int *	ipiv,
		float *	work,
		int *	lwork,
		int *	info
	)

Computes the inverse of a matrix using the LU factorization computed by SGETRF.

This method inverts $U$ and then computes $A^{-1}$ by solving the system $A^{-1} L = U^{-1}$ for $A^{-1}$ .

float snrm2_	(	int *	n,
		float *	x,
		int *	incx
	)

Returns the euclidean norm of a vector via the function name, so that $SNRM2 = \sqrt{(x^T x)}$

void sorgqr_	(	int *	m,
		int *	n,
		int *	k,
		float *	a,
		int *	lda,
		float *	tau,
		float *	work,
		int *	lwork,
		int *	info
	)

Generates an M-by-N real matrix $Q$ with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M

$Q = H(1) H(2) . . . H(k)$

as returned by SGEQRF.

int spotrf_	(	char *	UPLO,
		int *	n,
		float *	a,
		int *	lda,
		int *	info
	)

Computes the Cholesky factorization of a real symmetric positive definite matrix A.

The factorization has the form

$A = U^T U$

, if UPLO = 'U', or

$A = L L^T$

, if UPLO = 'L', where $U$ is an upper triangular matrix and $L$ is lower triangular

void sscal_	(	int *	n,
		float *	a,
		float *	x,
		int *	incx
	)

Scales a vector by a constant

void sswap_	(	int *	n,
		float *	sx,
		int *	incx,
		float *	sy,
		int *	incy
	)

Interchanges two vectors. Uses unrolled loops for increments equal to 1.

int ssyev_	(	char *	jobz,
		char *	uplo,
		int *	n,
		float *	a,
		int *	lda,
		float *	w,
		float *	work,
		int *	lwork,
		int *	info
	)

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

void strsm_	(	char *	side,
		char *	uplo,
		char *	transa,
		char *	diag,
		int *	m,
		int *	n,
		float *	alpha,
		float *	a,
		int *	lda,
		float *	b,
		int *	ldb
	)

Solves one of the matrix equations

$op(A) X = \alpha B$

or

$X op(A) = \alpha B$

, where $\alpha$ is a scalar, $X$ and $B$ are m by n matrices, $A$ is a unit, or non-unit, upper or lower triangular matrix and $op(A)$ is one of $ op(A) = A$ or $op(A) = A^T$ . The matrix $X$ is overwritten on $B$ .

Classes

Namespaces

Enumerations

Functions

Detailed Description

Function Documentation