SGEMV(3S)SGEMV(3S)NAME
SGEMV, DGEMV, CGEMV, ZGEMV - Multiplies a real or complex vector by a
real or complex general matrix
SYNOPSIS
Single precision
Fortran:
CALL SGEMV (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
C/C++:
#include <scsl_blas.h>
void sgemv (char *trans, int m, int n, float alpha, float *a,
int lda, float *x, int incx, float beta, float *y, int incy);
Double precision
Fortran:
CALL DGEMV (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
C/C++:
#include <scsl_blas.h>
void dgemv (char *trans, int m, int n, double alpha, double *a,
int lda, double *x, int incx, double beta, double *y, int
incy);
Single precision complex
Fortran:
CALL CGEMV (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
C/C++:
#include <scsl_blas.h>
void cgemv (char *trans, int m, int n, scsl_complex *alpha,
scsl_complex *a, int lda, scsl_complex *x, int incx,
scsl_complex *beta, scsl_complex *y, int incy);
C++ STL:
#include <complex.h>
#include <scsl_blas.h>
void cgemv (char *trans, int m, int n, complex<float> *alpha,
complex<float> *a, int lda, complex<float> *x, int incx,
complex<float> *beta, complex<float> *y, int incy);
Double precision complex
Fortran:
CALL ZGEMV (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
C/C++:
#include <scsl_blas.h>
void zgemv (char *trans, int m, int n, scsl_zomplex *alpha,
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scsl_zomplex *a, int lda, scsl_zomplex *x, int incx,
scsl_zomplex *beta, scsl_zomplex *y, int incy);
C++ STL:
#include <complex.h>
#include <scsl_blas.h>
void zgemv (char *trans, int m, int n, complex<double> *alpha,
complex<double> *a, int lda, complex<double> *x, int incx,
complex<double> *beta, complex<double> *y, int incy);
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
The C and C++ prototypes shown above are appropriate for the 4-byte
integer version of SCSL. When using the 8-byte integer version, the
variables of type int become long long and the <scsl_blas_i8.h> header
file should be included.
DESCRIPTION
SGEMV and DGEMV multiply a real vector by a real general matrix.
CGEMV and ZGEMV multiply a complex vector by a complex general matrix.
These routines perform one of the following matrix-vector operations:
y <- alpha Ax + beta y
y <- alpha ATx + beta y
y <- alpha AHx + beta y
where
* alpha and beta are scalars,
* x and y are vectors
* A is an m-by-n general matrix
* AT is the transpose of A
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* AH is the conjugate transpose of A
See the NOTES section of this man page for information about the
interpretation of the data types described in the following arguments.
These routines have the following arguments:
trans Character. (input)
Specifies the operation to be performed:
trans = 'N' or 'n': y <- alpha Ax + beta y
trans = 'T' or 't': y <- alpha ATx + beta y
trans = 'C' or 'c': y <- alpha ATx + beta y (SGEMV, DGEMV), or
y <- alpha AHx + beta y (CGEMV, ZGEMV)
For C/C++, a pointer to this character is passed.
m Integer. (input)
Specifies the number of rows in matrix A. m >= 0.
n Integer. (input)
Specifies the number of columns in matrix A. n >= 0.
alpha Scalar alpha. (input)
SGEMV: Single precision.
DGEMV: Double precision.
CGEMV: Single precision complex.
ZGEMV: Double precision complex.
For C/C++, a pointer to this scalar is passed when alpha is
complex; otherwise, alpha is passed by value.
a array of dimension (lda,n). (input)
SGEMV: Single precision array.
DGEMV: Double precision array.
CGEMV: Single precision complex array.
ZGEMV: Double precision complex array.
Before entry, the leading m-by-n part of array a must contain
the matrix of coefficients.
lda Integer. (input)
Specifies the first dimension of a as declared in the calling
program. lda >= MAX(1,m).
x Array of dimension 1+(kx-1) * |incx|. (input)
SGEMV: Single precision array.
DGEMV: Double precision array.
CGEMV: Single precision complex array.
ZGEMV: Double precision complex array.
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SGEMV(3S)SGEMV(3S)
Contains the vector x. When trans = 'N' or 'n', kx is n;
otherwise, it is m.
incx Integer. (input)
Specifies the increment for the elements of x. incx must not
be 0.
beta Scalar beta. (input)
SGEMV: Single precision.
DGEMV: Double precision.
CGEMV: Single precision complex.
ZGEMV: Double precision complex.
When beta is supplied as 0, y need not be set on input.
For C/C++, a pointer to this scalar is passed when beta is
complex; otherwise, beta is passed by value.
y Array of dimension 1+(ky-1) * |incy|. (input and output)
SGEMV: Single precision array.
DGEMV: Double precision array.
CGEMV: Single precision complex array.
ZGEMV: Double precision complex array.
Contains the vector y. When trans = 'N' or 'n', ky is m;
otherwise, it is n. When beta is supplied as 0, y need not be
set on input. On exit, the updated vector overwrites array y.
incy Integer. (input)
Specifies the increment for the elements of y. incy must not
be 0.
NOTES
SGEMV, DGEMV and CGEMV, ZGEMV are Level 2 Basic Linear Algebra
Subprograms (Level 2 BLAS).
When working backward (incx < 0 or incy < 0), each routine starts at the
end of the vector and moves backward, as follows:
x(1-incx * (n-1)), x(1-incx * (n-2)) , ..., x(1)
y(1-incy * (n-1)), y(1-incy * (n-2)) , ..., y(1)
Data Types
The following data types are described in this documentation:
Term Used Data type
Fortran:
Array dimensioned n x(n)
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SGEMV(3S)SGEMV(3S)
Array of dimensions (m,n) x(m,n)
Character CHARACTER
Integer INTEGER (INTEGER*8 for -lscs_i8[_mp])
Single precision REAL
Double precision DOUBLE PRECISION
Single precision complex COMPLEX
Double precision complex DOUBLE COMPLEX
C/C++:
Array dimensioned n x[n]
Array of dimensions (m,n) x[m*n]
Character char
Integer int (long long for -lscs_i8[_mp])
Single precision float
Double precision double
Single precision complex scsl_complex
Double precision complex scsl_zomplex
C++ STL:
Array dimensioned n x[n]
Array of dimensions (m,n) x[m*n]
Character char
Integer int (long long for -lscs_i8[_mp])
Single precision float
Double precision double
Single precision complex complex<float>
Double precision complex complex<double>
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SGEMV(3S)SGEMV(3S)
Note that you can explicitly declare multidimensional C/C++ arrays
provided that the array dimensions are swapped with respect to the
Fortran declaration (e.g., x[n][m] in C/C++ versus x(m,n) in Fortran).
To avoid a compiler type mismatch error in C++ (or a compiler warning
message in C), however, the array should be cast to a pointer of the
appropriate type when passed as an argument to a SCSL routine.
SEE ALSOINTRO_SCSL(3S), INTRO_BLAS2(3S)INTRO_CBLAS(3S) for information about using the C interface to Fortran 77
Basic Linear Algebra Subprograms (legacy BLAS) set forth by the Basic
Linear Algebra Subprograms Technical Forum.
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