?herk

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?herk

Performs a Hermitian rank-k update.

Syntax

call cherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)

call zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)

call herk(a, c [,uplo] [, trans] [,alpha][,beta])

Include Files

mkl.fi, blas.f90

Description

The ?herk routines perform a rank-k matrix-matrix operation using a general matrix A and a Hermitian matrix C. The operation is defined as:

C := alpha*A*A^H + beta*C,

C := alpha*A^H*A + beta*C,

where:

alpha and beta are real scalars,

C is an n-by-n Hermitian matrix,

A is an n-by-k matrix in the first case and a k-by-n matrix in the second case.

Input Parameters

uplo

CHARACTER*1. Specifies whether the upper or lower triangular part of the array c is used.

If uplo = 'U' or 'u' , then the upper triangular part of the array c is used.

If uplo = 'L' or 'l' , then the low triangular part of the array c is used.

trans

CHARACTER*1. Specifies the operation:

if trans= 'N' or 'n', then C := alpha*A*A^H + beta*C;

if trans= 'C' or 'c', then C := alpha*A^H*A + beta*C.

n

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

k

INTEGER. Withtrans= 'N' or 'n', k specifies the number of columns of the matrix A, and with trans= 'C' or 'c', k specifies the number of rows of the matrix A.

The value of k must be at least zero.

alpha

REAL for cherk

DOUBLE PRECISION for zherk

Specifies the scalar alpha.

a

COMPLEX for cherk

DOUBLE COMPLEX for zherk

Array, size (lda, ka), where ka is k when trans= 'N' or 'n', and is n otherwise. Before entry with trans= 'N' or 'n', the leading n-by-k part of the array a must contain the matrix a, otherwise the leading k-by-n part of the array a must contain the matrix A.

lda

INTEGER. Specifies the leading dimension of a as declared in the calling (sub)program. When trans= 'N' or 'n', then lda must be at least max(1, n), otherwise lda must be at least max(1, k).

beta

REAL for cherk

DOUBLE PRECISION for zherk

Specifies the scalar beta.

c

COMPLEX for cherk

DOUBLE COMPLEX for zherk

Array, size ldc by n.

Before entry with uplo = 'U' or 'u' , 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 = 'L' or 'l' , 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

INTEGER. 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 = 'U' or 'u' , the upper triangular part of the array c is overwritten by the upper triangular part of the updated matrix.

With uplo = 'L' or 'l' , 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.

BLAS 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see BLAS 95 Interface Conventions.

Specific details for the routine herk interface are the following:

a

Holds the matrix A of size (ma,ka) where

ka = k if trans='N',

ka = n otherwise,

ma = n if trans='N',

ma = k otherwise.

c

Holds the matrix C of size (n,n).

uplo

Must be 'U' or 'L'. The default value is 'U'.

trans

Must be 'N' or 'C'. The default value is 'N'.

alpha

The default value is 1.

beta

The default value is 0.

Parent topic: BLAS Level 3 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?herk