Contents

Indexes:

Purpose

=======

DSYR2K performs one of the symmetric rank 2k operations

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

or

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

where alpha and beta are scalars, C is an n by n symmetric matrix

and A and B are n by k matrices in the first case and k by n

matrices in the second case.

Parameters

==========

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*B' + alpha*B*A' +

beta*C.

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

beta*C.

TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*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 matrices A and B, and on entry with

TRANS = 'T' or 't' or 'C' or 'c', K specifies the number

of rows of the matrices A and B. 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.

B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb 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 B must contain the matrix B, otherwise

the leading k by n part of the array B must contain the

matrix B.

Unchanged on exit.

LDB - INTEGER.

On entry, LDB specifies the first dimension of B as declared

in the calling (sub) program. When TRANS = 'N' or 'n'

then LDB must be at least max( 1, n ), otherwise LDB 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.