dsyrk

DSYRK(l)                         BLAS routine                         DSYRK(l)



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

SYNOPSIS
       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, * )

PURPOSE
       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.


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*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.







BLAS routine                    16 October 1992                       DSYRK(l)