Blas.h File Reference

#include "./cimpl.h"
#include <cmath>

Go to the source code of this file.

Namespaces
namespace	Blas
Functions
float	Asum (Vector< float > &x)
	|x(0)|+...+|x(n)|
double	Asum (Vector< double > &x)
float	Asum (Vector< ComplexFloat > &x)
double	Asum (Vector< ComplexDouble > &x)
void	Axpy (float alpha, Vector< float > &x, Vector< float > &y)
	y += alpha*x
void	Axpy (double alpha, Vector< double > &x, Vector< double > &y)
void	Axpy (ComplexFloat alpha, Vector< ComplexFloat > &x, Vector< ComplexFloat > &y)
void	Axpy (ComplexDouble alpha, Vector< ComplexDouble > &x, Vector< ComplexDouble > &y)
void	Copy (Vector< float > &x, Vector< float > &y)
	y = x
void	Copy (Vector< double > &x, Vector< double > &y)
void	Copy (Vector< ComplexFloat > &x, Vector< ComplexFloat > &y)
void	Copy (Vector< ComplexDouble > &x, Vector< ComplexDouble > &y)
float	Dot (Vector< float > &x, Vector< float > &y)
	Dot product of x and y.
double	Dot (Vector< double > &x, Vector< double > &y)
ComplexFloat	Dot (Vector< ComplexFloat > &x, Vector< ComplexFloat > &y, bool conjugated)
ComplexDouble	Dot (Vector< ComplexDouble > &x, Vector< ComplexDouble > &y, bool conjugated)
ComplexFloat	Dot (Vector< ComplexFloat > &x, Vector< ComplexFloat > &y)
ComplexDouble	Dot (Vector< ComplexDouble > &x, Vector< ComplexDouble > &y)
float	Nrm2 (Vector< float > &x)
double	Nrm2 (Vector< double > &x)
float	Nrm2 (Vector< ComplexFloat > &x)
double	Nrm2 (Vector< ComplexDouble > &x)
void	Rot (Vector< float > &x, Vector< float > &y, const float c, const float s)
void	Rot (Vector< double > &x, Vector< double > &y, const double c, const double s)
void	Rot (Vector< ComplexFloat > &x, Vector< ComplexFloat > &y, const float c, const float s)
void	Rot (Vector< ComplexDouble > &x, Vector< ComplexDouble > &y, const double c, const double s)
void	Rotg (float &a, float &b, float &c, float &s)
	Generate elements for a givens plane rotation.
void	Rotg (double &a, double &b, double &c, double &s)
void	Rotg (ComplexFloat &a, ComplexFloat &b, float &c, ComplexFloat &s)
void	Rotg (ComplexDouble &a, ComplexDouble &b, double &c, ComplexDouble &s)
void	Rotm (Vector< float > &x, Vector< float > &y, float *param)
	Apply modified givens transformation.
void	Rotm (Vector< double > &x, Vector< double > &y, double *param)
void	Rotmg (float &d1, float &d2, float &b1, float &b2, float *param)
	Generate elements for a modified Givens transform.
void	Rotmg (double &d1, double &d2, double &b1, double &b2, double *param)
void	Scal (float alpha, Vector< float > &x)
	x *= alpha
void	Scal (double alpha, Vector< double > &x)
void	Scal (float alpha, Vector< ComplexFloat > &x)
void	Scal (double alpha, Vector< ComplexDouble > &x)
void	Scal (ComplexFloat alpha, Vector< ComplexFloat > &x)
void	Scal (ComplexDouble alpha, Vector< ComplexDouble > &x)
void	Swap (Vector< float > &x, Vector< float > &y)
	Swap elements of two vectors.
void	Swap (Vector< double > &x, Vector< double > &y)
void	Swap (Vector< ComplexFloat > &x, Vector< ComplexFloat > &y)
void	Swap (Vector< ComplexDouble > &x, Vector< ComplexDouble > &y)
int	IAmax (Vector< float > &x)
	index of the maximum element (First element is indexed as 1)
int	IAmax (Vector< double > &x)
int	IAmax (Vector< ComplexFloat > &x)
int	IAmax (Vector< ComplexDouble > &x)
int	IAmin (Vector< float > &x)
	index of the minimum element (First element is indexed as 1)
int	IAmin (Vector< double > &x)
int	IAmin (Vector< ComplexFloat > &x)
int	IAmin (Vector< ComplexDouble > &x)
Vector< float >	Gemv (Matrix< float > &A, Vector< float > &x)
	m*v for general matrix
Vector< double >	Gemv (Matrix< double > &A, Vector< double > &x)
Vector< ComplexFloat >	Gemv (Matrix< ComplexFloat > &A, Vector< ComplexFloat > &x)
Vector< ComplexDouble >	Gemv (Matrix< ComplexDouble > &A, Vector< ComplexDouble > &x)
void	Ger (float alpha, Vector< float > &x, Vector< float > &y, Matrix< float > &A)
void	Ger (double alpha, Vector< double > &x, Vector< double > &y, Matrix< double > &A)
void	Ger (ComplexFloat alpha, Vector< ComplexFloat > &x, Vector< ComplexFloat > &y, Matrix< ComplexFloat > &A)
void	Ger (ComplexDouble alpha, Vector< ComplexDouble > &x, Vector< ComplexDouble > &y, Matrix< ComplexDouble > &A)
void	Ger (ComplexFloat alpha, Vector< ComplexFloat > x, Vector< ComplexFloat > y, Matrix< ComplexFloat > &A, bool conjugated)
void	Ger (ComplexDouble alpha, Vector< ComplexDouble > &x, Vector< ComplexDouble > &y, Matrix< ComplexDouble > &A, bool conjugated)
Vector< float >	Symv (Matrix< float > &A, Vector< float > x)
	Symv, Hemv: m*v for symmetric or hermitian matrix.
Vector< double >	Symv (Matrix< double > &A, Vector< double > x)
Vector< ComplexFloat >	Hemv (Matrix< ComplexFloat > &A, Vector< ComplexFloat > &x)
Vector< ComplexDouble >	Hemv (Matrix< ComplexDouble > &A, Vector< ComplexDouble > &x)
void	Syr (float alpha, Vector< float > &x, Matrix< float > &A)
void	Syr (double alpha, Vector< double > &x, Matrix< double > &A)
void	Her (float alpha, Vector< ComplexFloat > &x, Matrix< ComplexFloat > &A)
void	Her (double alpha, Vector< ComplexDouble > &x, Matrix< ComplexDouble > &A)
void	Syr2 (float alpha, Vector< float > &x, Vector< float > &y, Matrix< float > &A)
void	Syr2 (double alpha, Vector< double > &x, Vector< double > &y, Matrix< double > &A)
void	Her2 (ComplexFloat alpha, Vector< ComplexFloat > &x, Vector< ComplexFloat > &y, Matrix< ComplexFloat > &A)
void	Her2 (ComplexDouble alpha, Vector< ComplexDouble > &x, Vector< ComplexDouble > &y, Matrix< ComplexDouble > &A)
Vector< float >	Trmv (Matrix< float > &A, Vector< float > &x)
	Trmv: m*v for triangular matrix.
Vector< double >	Trmv (Matrix< double > &A, Vector< double > &x)
Vector< ComplexFloat >	Trmv (Matrix< ComplexFloat > &A, Vector< ComplexFloat > &x)
Vector< ComplexDouble >	Trmv (Matrix< ComplexDouble > &A, Vector< ComplexDouble > &x)
Vector< float >	Trsv (Matrix< float > &A, Vector< float > &b)
	Trsv: Solver of a system of linear equations with a triangular matrix.
Vector< double >	Trsv (Matrix< double > &A, Vector< double > &b)
Vector< ComplexFloat >	Trsv (Matrix< ComplexFloat > &A, Vector< ComplexFloat > &b)
Vector< ComplexDouble >	Trsv (Matrix< ComplexDouble > &A, Vector< ComplexDouble > &b)
Matrix< float >	Gemm (Matrix< float > &A, Matrix< float > &B)
Matrix< double >	Gemm (Matrix< double > &A, Matrix< double > &B)
Matrix< ComplexFloat >	Gemm (Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B)
Matrix< ComplexDouble >	Gemm (Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B)
Matrix< float >	Symm (Matrix< float > &A, Matrix< float > &B)
	C = A*B or C = B*A.
Matrix< double >	Symm (Matrix< double > &A, Matrix< double > &B)
Matrix< ComplexFloat >	Symm (Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B)
Matrix< ComplexDouble >	Symm (Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B)
Matrix< float >	Symm (Matrix< float > &A, Matrix< float > &B, bool orderReversed)
Matrix< double >	Symm (Matrix< double > &A, Matrix< double > &B, bool orderReversed)
Matrix< ComplexFloat >	Symm (Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B, bool orderReversed)
Matrix< ComplexDouble >	Symm (Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B, bool orderReversed)
Matrix< ComplexFloat >	Hemm (Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B)
Matrix< ComplexDouble >	Hemm (Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B)
Matrix< ComplexFloat >	Hemm (Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B, bool orderReversed)
Matrix< ComplexDouble >	Hemm (Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B, bool orderReversed)
void	Syrk (float alpha, Matrix< float > &A, Matrix< float > &C)
void	Syrk (double alpha, Matrix< double > &A, Matrix< double > &C)
void	Syrk (ComplexFloat alpha, Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &C)
void	Syrk (ComplexDouble alpha, Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &C)
void	Syr2k (float alpha, Matrix< float > &A, Matrix< float > &B, Matrix< float > &C)
void	Syr2k (double alpha, Matrix< double > &A, Matrix< double > &B, Matrix< double > &C)
void	Syr2k (ComplexFloat alpha, Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B, Matrix< ComplexFloat > &C)
void	Syr2k (ComplexDouble alpha, Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B, Matrix< ComplexDouble > &C)
void	Herk (float alpha, Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &C)
void	Herk (double alpha, Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &C)
void	Her2k (ComplexFloat alpha, Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B, Matrix< ComplexFloat > &C)
void	Her2k (ComplexDouble alpha, Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B, Matrix< ComplexDouble > &C)
Matrix< float >	Trmm (Matrix< float > &A, Matrix< float > &B)
	C = A*B.
Matrix< double >	Trmm (Matrix< double > &A, Matrix< double > &B)
Matrix< ComplexFloat >	Trmm (Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B)
Matrix< ComplexDouble >	Trmm (Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B)
Matrix< float >	Trsm (Matrix< float > &A, Matrix< float > &B)
	Solve AX=B for X.
Matrix< double >	Trsm (Matrix< double > &A, Matrix< double > &B)
Matrix< ComplexFloat >	Trsm (Matrix< ComplexFloat > &A, Matrix< ComplexFloat > &B)
Matrix< ComplexDouble >	Trsm (Matrix< ComplexDouble > &A, Matrix< ComplexDouble > &B)

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Function Documentation

double Blas::Asum (  Vector< ComplexDouble > &  x  )

Definition at line 84 of file Blas1.cpp.

float Blas::Asum (  Vector< ComplexFloat > &  x  )

Definition at line 79 of file Blas1.cpp.

double Blas::Asum (  Vector< double > &  x  )

Definition at line 74 of file Blas1.cpp.

float Blas::Asum (  Vector< float > &  x  )

|x(0)|+...+|x(n)| Definition at line 69 of file Blas1.cpp.

void Blas::Axpy (  ComplexDouble  alpha, Vector< ComplexDouble > &  x, Vector< ComplexDouble > &  y )

Definition at line 123 of file Blas1.cpp.

void Blas::Axpy (  ComplexFloat  alpha, Vector< ComplexFloat > &  x, Vector< ComplexFloat > &  y )

Definition at line 113 of file Blas1.cpp.

void Blas::Axpy (  double  alpha, Vector< double > &  x, Vector< double > &  y )

Definition at line 103 of file Blas1.cpp.

void Blas::Axpy (  float  alpha, Vector< float > &  x, Vector< float > &  y )

y += alpha*x Definition at line 93 of file Blas1.cpp.

void Blas::Copy (  Vector< ComplexDouble > &  x, Vector< ComplexDouble > &  y )

Definition at line 169 of file Blas1.cpp.

void Blas::Copy (  Vector< ComplexFloat > &  x, Vector< ComplexFloat > &  y )

Definition at line 159 of file Blas1.cpp.

void Blas::Copy (  Vector< double > &  x, Vector< double > &  y )

Definition at line 149 of file Blas1.cpp.

void Blas::Copy (  Vector< float > &  x, Vector< float > &  y )

y = x Definition at line 139 of file Blas1.cpp.

ComplexDouble Blas::Dot (  Vector< ComplexDouble > &  x, Vector< ComplexDouble > &  y )

Definition at line 248 of file Blas1.cpp.

ComplexFloat Blas::Dot (  Vector< ComplexFloat > &  x, Vector< ComplexFloat > &  y )

Definition at line 243 of file Blas1.cpp.

ComplexDouble Blas::Dot (  Vector< ComplexDouble > &  x, Vector< ComplexDouble > &  y, bool  conjugated )

Definition at line 223 of file Blas1.cpp.

ComplexFloat Blas::Dot (  Vector< ComplexFloat > &  x, Vector< ComplexFloat > &  y, bool  conjugated )

Definition at line 203 of file Blas1.cpp.

double Blas::Dot (  Vector< double > &  x, Vector< double > &  y )

Definition at line 193 of file Blas1.cpp.

float Blas::Dot (  Vector< float > &  x, Vector< float > &  y )

Dot product of x and y. Definition at line 183 of file Blas1.cpp.

Matrix< ComplexDouble > Blas::Gemm (  Matrix< ComplexDouble > &  A, Matrix< ComplexDouble > &  B )

Definition at line 109 of file Blas3.cpp.

Matrix< ComplexFloat > Blas::Gemm (  Matrix< ComplexFloat > &  A, Matrix< ComplexFloat > &  B )

Definition at line 96 of file Blas3.cpp.

Matrix< double > Blas::Gemm (  Matrix< double > &  A, Matrix< double > &  B )

Definition at line 84 of file Blas3.cpp.

Matrix< float > Blas::Gemm (  Matrix< float > &  A, Matrix< float > &  B )

Gemm: General m*m C = A*B A is an m by k matrix, B is a k by n matrix, and C is an m by n matrix. Definition at line 72 of file Blas3.cpp.

Vector< ComplexDouble > Blas::Gemv (  Matrix< ComplexDouble > &  A, Vector< ComplexDouble > &  x )

Definition at line 105 of file Blas2.cpp.

Vector< ComplexFloat > Blas::Gemv (  Matrix< ComplexFloat > &  A, Vector< ComplexFloat > &  x )

Definition at line 92 of file Blas2.cpp.

Vector< double > Blas::Gemv (  Matrix< double > &  A, Vector< double > &  x )

Definition at line 80 of file Blas2.cpp.

Vector< float > Blas::Gemv (  Matrix< float > &  A, Vector< float > &  x )

m*v for general matrix Definition at line 68 of file Blas2.cpp.

void Blas::Ger (  ComplexDouble  alpha, Vector< ComplexDouble > &  x, Vector< ComplexDouble > &  y, Matrix< ComplexDouble > &  A, bool  conjugated )

Definition at line 182 of file Blas2.cpp.

void Blas::Ger (  ComplexFloat  alpha, Vector< ComplexFloat >  x, Vector< ComplexFloat >  y, Matrix< ComplexFloat > &  A, bool  conjugated )

Definition at line 164 of file Blas2.cpp.

void Blas::Ger (  ComplexDouble  alpha, Vector< ComplexDouble > &  x, Vector< ComplexDouble > &  y, Matrix< ComplexDouble > &  A )

Definition at line 153 of file Blas2.cpp.

void Blas::Ger (  ComplexFloat  alpha, Vector< ComplexFloat > &  x, Vector< ComplexFloat > &  y, Matrix< ComplexFloat > &  A )

Definition at line 142 of file Blas2.cpp.

void Blas::Ger (  double  alpha, Vector< double > &  x, Vector< double > &  y, Matrix< double > &  A )

Definition at line 132 of file Blas2.cpp.

void Blas::Ger (  float  alpha, Vector< float > &  x, Vector< float > &  y, Matrix< float > &  A )

Rank one update, general matrix A += alpha*x*transp(y) A += alpha*x*conjug_transp(y) if conjugate == true Definition at line 122 of file Blas2.cpp.

Matrix< ComplexDouble > Blas::Hemm (  Matrix< ComplexDouble > &  A, Matrix< ComplexDouble > &  B, bool  orderReversed )

Definition at line 394 of file Blas3.cpp.

Matrix< ComplexFloat > Blas::Hemm (  Matrix< ComplexFloat > &  A, Matrix< ComplexFloat > &  B, bool  orderReversed )

Definition at line 361 of file Blas3.cpp.

Matrix< ComplexDouble > Blas::Hemm (  Matrix< ComplexDouble > &  A, Matrix< ComplexDouble > &  B )

Definition at line 214 of file Blas3.cpp.

Matrix< ComplexFloat > Blas::Hemm (  Matrix< ComplexFloat > &  A, Matrix< ComplexFloat > &  B )

Definition at line 196 of file Blas3.cpp.

Vector< ComplexDouble > Blas::Hemv (  Matrix< ComplexDouble > &  A, Vector< ComplexDouble > &  x )

Definition at line 255 of file Blas2.cpp.

Vector< ComplexFloat > Blas::Hemv (  Matrix< ComplexFloat > &  A, Vector< ComplexFloat > &  x )

Definition at line 237 of file Blas2.cpp.

void Blas::Her (  double  alpha, Vector< ComplexDouble > &  x, Matrix< ComplexDouble > &  A )

Definition at line 326 of file Blas2.cpp.

void Blas::Her (  float  alpha, Vector< ComplexFloat > &  x, Matrix< ComplexFloat > &  A )

Definition at line 311 of file Blas2.cpp.

void Blas::Her2 (  ComplexDouble  alpha, Vector< ComplexDouble > &  x, Vector< ComplexDouble > &  y, Matrix< ComplexDouble > &  A )

Definition at line 395 of file Blas2.cpp.

void Blas::Her2 (  ComplexFloat  alpha, Vector< ComplexFloat > &  x, Vector< ComplexFloat > &  y, Matrix< ComplexFloat > &  A )

Definition at line 379 of file Blas2.cpp.

void Blas::Her2k (  ComplexDouble  alpha, Matrix< ComplexDouble > &  A, Matrix< ComplexDouble > &  B, Matrix< ComplexDouble > &  C )

Definition at line 619 of file Blas3.cpp.

void Blas::Her2k (  ComplexFloat  alpha, Matrix< ComplexFloat > &  A, Matrix< ComplexFloat > &  B, Matrix< ComplexFloat > &  C )

C += alpha*A*conjug_transp(B) + alpha*B*conjug_transp(A) A and B are of size n by k Definition at line 604 of file Blas3.cpp.

void Blas::Herk (  double  alpha, Matrix< ComplexDouble > &