# ?herk

Performs a rank-n update of a Hermitian matrix.

## Syntax

FORTRAN 77:

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

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

Fortran 95:

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

## Description

The ?herk routines perform a matrix-matrix operation using Hermitian matrices. The operation is defined as
`C := alpha*A*conjg(A') + beta*C,`

or
`C := alpha*conjg(A')*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 is used.

trans

  CHARACTER*1. Specifies the operation:

  if `trans = 'N'` or `'n'`, then `C:= alpha*A*conjg(A')+beta*C`;

  if `trans = 'C'` or `'c'`, then `C:= alpha*conjg(A')*A+beta*C`.

n

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

k

  INTEGER. With `trans = '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, 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 first 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, DIMENSION (ldc,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 first 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.

## Fortran 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 Fortran 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 `transa= 'N'`,

  `ka = n` otherwise,

  `ma = n` if `transa= '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 1.

Parent topic: BLAS Level 3 Routines