?hfrk

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?hfrk

Performs a Hermitian rank-k operation for matrix in RFP format.

Syntax

call chfrk(transr, uplo, trans, n, k, alpha, a, lda, beta, c)

call zhfrk(transr, uplo, trans, n, k, alpha, a, lda, beta, c)

Include Files

mkl.fi

Description

The ?hfrk routines perform a matrix-matrix operation using Hermitian matrices. 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 in RFP format,

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

Input Parameters

transr

CHARACTER*1.

if transr = 'N' or 'n', the normal form of RFP C is stored;

if transr = 'C' or 'c', the conjugate-transpose form of RFP C is stored.

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. On entry with trans = 'N' or 'n', k specifies the number of columns of the matrix a, and on entry with trans = 'T' or 't' or 'C' or 'c', k specifies the number of rows of the matrix a.

The value of k must be at least zero.

alpha

COMPLEX for chfrk

DOUBLE COMPLEX for zhfrk

Specifies the scalar alpha.

a

COMPLEX for chfrk

DOUBLE COMPLEX for zhfrk

Array, DIMENSION(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

COMPLEX for chfrk

DOUBLE COMPLEX for zhfrk

Specifies the scalar beta.

c

COMPLEX for chfrk

DOUBLE COMPLEX for zhfrk

Array, size (n*(n+1)/2 ). Before entry contains the Hermitian matrix C in in RFP format.

Output Parameters

c

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

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

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hfrk