?hfrk

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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

chfrk zhfrk hfrk

The ?hfrk routines perform a matrix-matrix operation using Hermitian matrices. The operation is defined as

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

C := alpha * A^:code:`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) .
a: Array, size max(1,lda*ka) , where ka is in the following table: Col_major Row_major trans = ‘N’ kntrans = ‘T’ nk 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: Specifies the leading dimension of a as declared in the calling (sub)program. lda is defined by the following table: Col_major Row_major trans = ‘N’ max(1,n)max(1,k)trans = ‘T’ max(1,k)max(1,n)
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 ;

Return Values

No return value.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hfrk

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values