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CHERK(l)BLAS routine CHERK(l)CHERK - perform one of the hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C,NAMESUBROUTINE CHERK ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC ) CHARACTER*1 UPLO, TRANS INTEGER N, K, LDA, LDC REAL ALPHA, BETA COMPLEX A( LDA, * ), C( LDC, * )SYNOPSISCHERK performs one of the hermitian rank k operations 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.PURPOSEUPLO - CHARACTER*1. 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 - CHARACTER*1. 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 - INTEGER. On entry, N specifies the order of the matrix C. N must be at least zero. Unchanged on exit. K - 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 - REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - 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 lead- ing 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 - 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 - REAL . On entry, BETA specifies the scalar beta. Unchanged on exit. C - COMPLEX array of 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. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. 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. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. Note that the imagi- nary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero. LDC - INTEGER. On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ). Unchanged on exit. Level 3 Blas routine.PARAMETERSWritten on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd.--BLAS routine16 October 1992 CHERK(l)

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