sgemv(3S)
SGEMV, DGEMV, CGEMV, ZGEMV - Multiplies a real or complex vector by a real or complex general matrix
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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, 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 * 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. 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) 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> 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 ALSO INTRO_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.