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?hpmv

Compute the product of a vector and a triangle-expanded Hermitian matrix, that is, .

alpha and beta are scaling coefficients, x and y are vectors including n elements, and A is a triangularly expanded Hermitian matrix.

Interface Definition

C interface:

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

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

Fortran interface:

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

CALL ZHPMV(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 chpmv, alpha is of single-precision complex number type.
  • For zhpmv, alpha is of double-precision complex number type.

Coefficient

Input

Ap
  • For chpmv, Ap is of single-precision complex number type.
  • For zhpmv, Ap is of double-precision complex number type.

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

Input

X
  • For chpmv, X is of single-precision complex number type.
  • For zhpmv, 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 chpmv, beta is of single-precision complex number type.
  • For zhpmv, beta is of double-precision complex number type.

Multiplication coefficient

Input

Y
  • For chpmv, Y is of single-precision complex number type.
  • For zhpmv, 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[2] = {1.0, 0}, beta[2] = {1.0, 0}; 
    int incx = 1, incy = 1; 
   /*             |  (1.0, 0)  (3.0, 3.0)  (3.0, -3.0) | 
    *       A =   | (3.0, -3.0)  (2.0, 0.0)  (3.0, -1.0) | 
    *             |  (3.0, 3.0)  (3.0, 1.0)   (3.0, 0.0) | 
    */ 
    float ap[12] = {1.0, 0, 3.0, -3.0, 3.0, 3.0, 2.0, 0, 3.0, 1.0, 3.0, 0}; 
    float x[6] = {3.0, 2.0, 1.0, 2.0, -1.0, 1.0}; 
    float y[6] = {1.0, 2.0, 3.0, 2.0, -1.0, 1.0}; 
 
    cblas_chpmv(CblasColMajor,CblasLower, n, alpha, ap, x, incx, beta, y, incy); 
   /* 
    * Output y = |1.000000, 19.000000, 18.000000, 7.000000,  0.000000, 26.000000| 
    */

Fortran interface:

      INTEGER :: N=3 
      COMPLEX(4) :: ALPHA=(1.0, 0) 
      COMPLEX(4) :: BETA=(1.0, 0) 
      INTEGER :: INCX=1 
      INTEGER :: INCY=1 
      COMPLEX(4) :: AP(6) 
      DATA AP/(1.0, 0), (3.0, -3.0), (3.0, 3.0), (2.0, 0), (3.0, 1.0), (3.0, 0)/ 
      COMPLEX(4) :: X(3), Y(3) 
      DATA X/(3.0, 2.0), (1.0, 2.0), (-1.0, 1.0)/ 
      DATA Y/(1.0, 2.0), (3.0, 2.0), (-1.0, 1.0)/ 
      EXTERNAL CHPMV 
      CALL CHPMV('L', N, ALPHA, AP, X, INCX, BETA, Y, INCY) 
 
*     Output Y = |(1.000000, 19.000000), (18.000000, 7.000000),  (0.000000, 26.000000)|