## SYNOPSIS

- SUBROUTINE CHFRK(
- TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,

- + C )

- REAL ALPHA, BETA

- INTEGER K, LDA, N

- CHARACTER TRANS, TRANSR, UPLO

- COMPLEX A( LDA, * ), C( * )

## PURPOSE

Level 3 BLAS like routine for C in RFP Format. CHFRK performs one of the Hermitian rank--k operationsC := 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 and A is an n--by--k matrix in the first case and a k--by--n matrix in the second case.

## ARGUMENTS

TRANSR - (input) CHARACTER. = 'N': The Normal Form of RFP A is stored;= 'C': The Conjugate-transpose Form of RFP A is stored.

- UPLO - (input) CHARACTER.
- On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced. Unchanged on exit.
- TRANS - (input) CHARACTER.
- On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*conjg( A' ) + beta*C. TRANS = 'C' or 'c' C := alpha*conjg( A' )*A + beta*C. Unchanged on exit.
- N - (input) INTEGER.
- On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit.
- K - (input) INTEGER.
- On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'C' or 'c', K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit.
- ALPHA - (input) REAL.
- On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
- A - (input) COMPLEX array of 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. Unchanged on exit.
- LDA - (input) INTEGER.
- On entry, LDA 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 ). Unchanged on exit.
- BETA - (input) REAL.
- On entry, BETA specifies the scalar beta. Unchanged on exit.
- C - (input/output) COMPLEX array, dimension ( N*(N+1)/2 ).
- On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero.

## ARGUMENTS