DSYRK - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C,

SUBROUTINE DSYRK

( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC )

CHARACTER*1 UPLO, TRANS

INTEGER N, K, LDA, LDC

DOUBLE PRECISION ALPHA, BETA

DOUBLE PRECISION A( LDA, * ), C( LDC, * )

DSYRK performs one of the symmetric rank k operations

or

C := alpha*A'*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

UPLO - 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*A' + beta*C.

TRANS = 'T' or 't' C := alpha*A'*A + beta*C.

TRANS = 'C' or 'c' C := alpha*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 = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrix A. K must be at least zero. Unchanged on exit.

ALPHA - DOUBLE PRECISION.

On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

A - DOUBLE PRECISION 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 - 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 - DOUBLE PRECISION.

On entry, BETA specifies the scalar beta. Unchanged on exit.

C - DOUBLE PRECISION 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 symmetric 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 symmetric 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.

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.

-- Written 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.