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?spmv

Compute the product of a vector and a packed symmetric matrix, that is, .

Where alpha and beta are scaling coefficients, x and y are vectors including n elements, and A is an n-order compression symmetric matrix.

Interface Definition

C interface:

void cblas_sspmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const float alpha, const float *Ap, const float *X, const BLASINT incX, const float beta, float *Y, const BLASINT incY);

void cblas_dspmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const BLASINT N, const double alpha, const double *Ap, const double *X, const BLASINT incX, const double beta, double *Y, const BLASINT incY);

Fortran interface:

CALL SSPMV(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)

CALL DSPMV(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)

Parameters

Parameter

Type

Description

Input/Output

order

Enumeration type CBLAS_ORDER

Indicates whether the matrix is in row- or column-major order.

Input

Uplo

Enumeration type CBLAS_UPLO

Storage expansion mode of matrix A (upper triangle or lower triangle)

  • If Uplo = CblasUpper, the upper triangle of A is used for expansion.
  • If Uplo = CblasLower, the lower triangle of A is used for expansion.

Input

N

Integer

Order of the matrix A. N must be greater than or equal to zero.

Input

alpha
  • For sspmv, alpha is of single-precision complex number type.
  • For dspmv, alpha is of double-precision complex number type.

Multiplication coefficient

Input

Ap
  • For sspmv, Ap is of single-precision complex number type.
  • For dspmv, Ap is of double-precision complex number type.

The size of a compressed symmetric matrix is at least (n*(n+1)/2).

Input

X
  • For sspmv, X is of single-precision complex number type.
  • For dspmv, X is of double-precision complex number type.

Vector X. The vector scale is at least (1+(N-1)*abs(incX)).

Input

incX

Integer

Increment for elements in X. The value cannot be 0.

Input

beta
  • For sspmv, beta is of single-precision complex number type.
  • For dspmv, beta is of double-precision complex number type.

Multiplication coefficient

Input

Y
  • For sspmv, Y is of single-precision complex number type.
  • For dspmv, Y is of double-precision complex number type.

Vector Y. The vector scale is at least (1+(N-1)*abs(incY)).

Input/Output

incY

Integer

Increment for elements in Y. The value cannot be 0.

Input

Dependencies

#include "kblas.h"

Examples

C interface:

    int n = 3; 
    float alpha = 1.0, beta = 1.0; 
    int incx = 1, incy = 1; 
    /* 
     * A =  | 2.0  1.0  3.0 | 
     *      | 1.0  6.0  9.0 | 
     *      | 3.0  9.0  2.0 | 
     */ 
    float a[6] = {2.0, 1.0, 3.0, 6.0, 9.0, 2.0}; 
    float x[3] = {1.0, 1.0, 1.0}; 
    float y[3] = {3.0, 2.0, 2.0}; 
 
    cblas_sspmv(CblasColMajor,CblasLower, n, alpha, a, x, incx, beta, y, incy); 
    /* 
     * Output y = |9.0, 18.0, 16.0| 
     */

Fortran interface:

      INTEGER :: N=3 
      REAL(4) :: ALPHA=2.0 
      REAL(4) :: BETA=1.0 
      REAL(4) :: A(6), X(3), Y(3) 
      DATA A/2.0, 1.0, 3.0, 6.0, 9.0, 2.0/ 
      DATA X/1.0, 1.0, 1.0/ 
      DATA Y/3.0, 2.0, 2.0/ 
      EXTERNAL SSPMV 
      CALL SSPMV('L', N, ALPHA, A, X, INCX, BETA, Y, INCY) 
 
*     Output Y = |9.0, 18.0, 16.0|