SSPMV(3S)SSPMV(3S)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
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SSPMV(3S)SSPMV(3S)
*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.
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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.
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SSPMV(3S)SSPMV(3S)
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])
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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 ALSOINTRO_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.
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