sspmv(3S)
SSPMV, DSPMV, CSPMV, ZSPMV - Multiplies a real or complex symmetric packed matrix by a real or complex vector
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NAME SSPMV, DSPMV, CSPMV, ZSPMV - Multiplies a real or complex symmetric packed matrix by a real or complex vector SYNOPSIS Single precision Fortran: CALL SSPMV (uplo, n, alpha, ap, x, incx, beta, y, incy) C/C++: #include <scsl_blas.h> void sspmv (char *uplo, int n, float alpha, float *ap, float *x, int incx, float beta, float *y, int incy); Double precision Fortran: CALL DSPMV (uplo, n, alpha, ap, x, incx, beta, y, incy) C/C++: #include <scsl_blas.h> void dspmv (char *uplo, int n, double alpha, double *ap, double *x, int incx, double beta, double *y, int incy); Single precision complex Fortran: CALL CSPMV (uplo, n, alpha, ap, x, incx, beta, y, incy) C/C++: #include <scsl_blas.h> void cspmv (char *uplo, int n, scsl_complex *alpha, scsl_complex *ap, scsl_complex *x, int incx, scsl_complex *beta, scsl_complex *y, int incy); C++ STL: #include <complex.h> #include <scsl_blas.h> void cspmv (char *uplo, int n, complex<float> *alpha, complex<float> *ap, complex<float> *x, int incx, complex<float> *beta, complex<float> *y, int incy); Double precision complex Fortran: CALL ZSPMV (uplo, n, alpha, ap, x, incx, beta, y, incy) C/C++: #include <scsl_blas.h> void zspmv (char *uplo, int n, scsl_zomplex *alpha, scsl_zomplex *ap, scsl_zomplex *x, int incx, scsl_zomplex *beta, scsl_zomplex *y, int incy); C++ STL: #include <complex.h> #include <scsl_blas.h> void zspmv (char *uplo, int n, complex<float> *alpha, complex<float> *ap, complex<float> *x, int incx, complex<float> *beta, complex<float> *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 These routines perform the following matrix-vector operation: y <-alpha Ax + beta y where alpha and beta are scalars, x and y are n-element vectors, and A is an n-by-n symmetric packed matrix. 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: uplo Character. (input) Specifies whether the upper or lower triangular part of matrix A is packed into the array argument ap, as follows: uplo= 'U' or 'u': the upper triangular part of A is being supplied in the argument ap. uplo= 'L' or 'l': the lower triangular part of A is being supplied in the argument ap. For C/C++, a pointer to this character is passed. n Integer. (input) Specifies the order of matrix A. n >= 0. alpha Scalar alpha. (input) SSPMV: Single precision. DSPMV: Double precision. CSPMV: Single precision complex. ZSPMV: Double precision complex. For C/C++, a pointer to this scalar is passed when alpha is complex; otherwise, alpha is passed by value. ap Array of dimension (n(n+1))/2 (input) SSPMV: Single precision array. DSPMV: Double precision array. CSPMV: Single precision complex array. ZSPMV: Double precision complex array. Before entry with uplo = 'U' or 'u', array ap must contain the upper triangular part of the symmetric matrix packed sequentially, column-by-column, so that ap(1) contains A(1,1), ap(2) contains A(1,2), ap(3) contains A(2,2), and so on. Before entry with uplo = 'L' or 'l', array ap must contain the lower triangular part of the symmetric matrix packed sequentially, column-by-column, so that ap(1) contains A(1,1), ap(2) contains A(2,1), ap(3) contains A(3,1), and so on. x Array of dimension 1+(n-1) * |incx|. (input) SSPMV: Single precision array. DSPMV: Double precision array. CSPMV: Single precision omplex array. ZSPMV: Double precision complex array. Contains vector x. incx Integer. (input) Specifies the increment for the elements of x. incx must not be 0. beta Scalar beta. (input) SSPMV: Single precision. DSPMV: Double precision. CSPMV: Single precision complex. ZSPMV: Double precision complex. If 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+(n-1) * |incy|. (input and output) SSPMV: Single precision array. DSPMV: Double precision array. CSPMV: Single precision complex array. ZSPMV: Double precision complex array. Contains vector y. 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 SSPMV/DSPMV is a Level 2 Basic Linear Algebra Subprogram (Level 2 BLAS). CSPMV/ZSPMV is an extension to 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) 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] 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] 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), CHPMV(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.