cblas_?her2k

Performs a Hermitian rank-2k update.

Syntax

void cblas_cher2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const float beta, void *c, const MKL_INT ldc);

void cblas_zher2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const double beta, void *c, const MKL_INT ldc);

Include Files

  • mkl.h

Description

The ?her2k routines perform a rank-2k matrix-matrix operation using general matrices A and B and a Hermitian matrix C. The operation is defined as

C := alpha*A*BH + conjg(alpha)*B*AH + beta*C,

or

C := alpha*AH*B + conjg(alpha)*BH*A + beta*C,

where:

alpha is a scalar and beta is a real scalar,

C is an n-by-n Hermitian matrix,

A and B are n-by-k matrices in the first case and k-by-n matrices in the second case.

Input Parameters

Layout

Specifies whether two-dimensional array storage is row-major (CblasRowMajor) or column-major (CblasColMajor).

uplo

Specifies whether the upper or lower triangular part of the array c is used.

If uplo = CblasUpper, then the upper triangular of the array c is used.

If uplo = CblasLower, then the low triangular of the array c is used.

trans

Specifies the operation:

if trans=CblasNoTrans, then C:=alpha*A*BH + alpha*B*AH + beta*C;

if trans=CblasConjTrans, then C:=alpha*AH*B + alpha*BH*A + beta*C.

n

Specifies the order of the matrix C. The value of n must be at least zero.

k

With trans=CblasNoTrans specifies the number of columns of the matrix A, and with trans=CblasConjTrans, k specifies the number of rows of the matrix A.

The value of k must be at least equal to zero.

alpha

Specifies the scalar alpha.

a
 

trans=CblasNoTrans

trans=CblasConjTrans

Layout = CblasColMajor

Array, size lda*k.

Before entry, the leading n-by-k part of the array a must contain the matrix A.

Array, size lda*n.

Before entry, the leading k-by-n part of the array a must contain the matrix A.

Layout = CblasRowMajor

Array, size lda*n.

Before entry, the leading k-by-n part of the array a must contain the matrix A.

Array, size lda*k.

Before entry, the leading n-by-k part of the array a must contain the matrix A.

lda

Specifies the leading dimension of a as declared in the calling (sub)program.

 

trans=CblasNoTrans

trans=CblasConjTrans

Layout = CblasColMajor

lda must be at least max(1, n).

lda must be at least max(1, k)

Layout = CblasRowMajor

lda must be at least max(1, k)

lda must be at least max(1, n).

beta

Specifies the scalar beta.

b
 

trans=CblasNoTrans

trans=CblasConjTrans

Layout = CblasColMajor

Array, size ldb*k.

Before entry, the leading n-by-k part of the array b must contain the matrix B.

Array, size ldb*n.

Before entry, the leading k-by-n part of the array b must contain the matrix B.

Layout = CblasRowMajor

Array, size lda*n.

Before entry, the leading k-by-n part of the array b must contain the matrix B.

Array, size lda*k.

Before entry, the leading n-by-k part of the array b must contain the matrix B.

ldb

Specifies the leading dimension of a as declared in the calling (sub)program.

 

trans=CblasNoTrans

trans=CblasConjTrans

Layout = CblasColMajor

ldb must be at least max(1, n).

ldb must be at least max(1, k)

Layout = CblasRowMajor

ldb must be at least max(1, k)

ldb must be at least max(1, n).

c

Array, size ldc by n.

Before entry with uplo = CblasUpper, the leading n-by-n upper triangular part of the array c must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of c is not referenced.

Before entry with uplo = CblasLower, the leading n-by-n lower triangular part of the array c must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of c is not referenced.

The imaginary parts of the diagonal elements need not be set, they are assumed to be zero.

ldc

Specifies the leading dimension of c as declared in the calling (sub)program. The value of ldc must be at least max(1, n).

Output Parameters

c

With uplo = CblasUpper, the upper triangular part of the array c is overwritten by the upper triangular part of the updated matrix.

With uplo = CblasLower, the lower triangular part of the array c is overwritten by the lower triangular part of the updated matrix.

The imaginary parts of the diagonal elements are set to zero.

For more complete information about compiler optimizations, see our Optimization Notice.
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