?her2k

Perform a rank-2 update of a Hermitian matrix.

or .

alpha and beta are multiplication coefficients, and C is an n*n Hermitian matrix. For a first case, the matrix A and the matrix B are n*k, and in a second case, the matrix A and the matrix B are k*n.

Interface Definition

C interface:

void cblas_cher2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans, const BLASINT N, const BLASINT K, const void *alpha, const void *A, const BLASINT lda, const void *B, const BLASINT ldb, const float beta, void *C, const BLASINT ldc);

void cblas_zher2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans, const BLASINT N, const BLASINT K, const void *alpha, const void *A, const BLASINT lda, const void *B, const BLASINT ldb, const double beta, void *C, const BLASINT ldc);

Fortran interface:

CALL CHER2K(UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

CALL ZHER2K(UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

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 mode of matrix C	Input
Trans	Enumeration type CBLAS_TRANSPOSE	The matrices A and B are conventional matrices, transpose matrices, or conjugate matrices. When Trans = CblasNoTrans, . If Trans = CblasConjTrans, then .	Input
N	Integer	Row of matrix C	Input
K	Integer	The columns of matrix A and matrix B when Trans = CblasNoTrans. The rows of matrix A and matrix B when Trans = CblasConjTrans.	Input
alpha	For cher2k, alpha is of single-precision complex number type. For zher2k, alpha is of double-precision complex number type.	Multiplication coefficient	Input
A	For cher2k, A is of single-precision complex number type. For zher2k, A is of double-precision complex number type.	Matrix A (lda, ka). If Trans = CblasNoTrans, ka = k; otherwise, ka = n.	Input
lda	Integer	If the matrix is column store and Trans = CblasNoTrans, lda must be at least max(1, n); otherwise, lda must be at least max(1, k). If the matrix is column store and Trans = CblasNoTrans, lda must be at least max(1, k); otherwise, lda must be at least max(1, n).	Input
B	For cher2k, B is of single-precision complex number type. For zher2k, B is of double-precision complex number type.	Matrix B (ldb, kb). If Trans = CblasNoTrans, kb = k; otherwise, kb = n.	Input
ldb	Integer	If the matrix is column store and Trans = CblasNoTrans, ldb must be at least max(1, n); otherwise, ldb must be at least max(1, k). If the matrix is column store and Trans = CblasNoTrans, ldb must be at least max(1, k). Otherwise, ldb must be at least max(1, n).	Input
beta	For cher2k, beta is of single-precision complex number type. For zher2k, beta is of double-precision complex number type.	Multiplication coefficient	Input
C	For cher2k, C is of single-precision complex number type. For zher2k, C is of double-precision complex number type.	Matrix C (ldc, n)	Input/Output
ldc	Integer	The value of ldc is at least max(1, n).	Input

Dependencies

#include "kblas.h"

Examples

C interface:

    int n = 2, lda = 2, k = 2, ldb =3, ldc = 3; 
    float alpha[2] = {2.0, 1.0}, beta = 2.0; 
    /** 
     *                    | 4.0 1.0   1.0 2.0 | 
     *     A(2 * 2)    =  | 3.0 2.0   4.0 1.0 | 
     * 
     *     B(2 * 2)    =  | 2.0 1.0   3.0  2.0 | 
     *                    | 11.0 2.0 -2.0  1.0 | 
     * 
     *                    |  3.0 1.0  2.0  1.0 | 
     *     C(3 * 2)    =  | -1.0 1.0  -6.0 2.0 | 
     *                    |   .           .    | 
     */ 
    float a[8] = {4.0, 1.0, 3.0, 2.0, 1.0, 2.0, 4.0, 1.0}; 
    float b[8] = {2.0, 1.0, 11.0, 2.0, 3.0, 2.0, -2.0, 1.0}; 
    float c[12] = {3.0, 1.0, -1.0, 1.0, 0, 0, 2.0, 1.0, -6.0, 2.0, 0, 0}; 
 
    cblas_cher2k(CblasColMajor, CblasUpper, CblasConjTrans, n, k, alpha, a, lda, b, ldb, beta, c, ldc); 
    /** 
     * Output C 
     *                   | (218.0, 0.0)  (123.0, -27.0) | 
     *    C(3 * 2)    =  | (-1.0 1.0)    (46.0, 0.0)    | 
     *                   |   .                 .        | 
     * 
     */

Fortran interface:

      INTEGER :: N=2, K=2 
      INTEGER :: LDA=2, LDB=3, LDC=3 
      COMPLEX(4) :: ALPHA=(2.0, 1.0) 
      REAL(4) :: BETA=2.0 
      COMPLEX(4) :: A(2, 2), B(2, 2), C(3, 2) 
      DATA A/(4.0, 1.0), (3.0, 2.0), (1.0, 2.0), (4.0, 1.0)/ 
      DATA B/(2.0, 1.0), (11.0, 2.0), (3.0, 2.0), (-2.0, 1.0)/ 
      DATA C/(3.0, 1.0), (-1.0, 1.0), (0, 0), (2.0, 1.0), (-6.0, 2.0), 
     $       (0, 0)/ 
      EXTERNAL CHER2K 
      CALL CHER2K('U', 'C', N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC) 
 
*     Output C 
*                        | (218.0, 0.0)  (123.0, -27.0) | 
*         C(3 * 2)    =  | (-1.0 1.0)    (46.0, 0.0)    | 
*                        |   .                 .        |

Parent topic: KML_BLAS Level 3 Functions