dsyr2k

DSYR2K(1)                        BLAS routine                        DSYR2K(1)



NAME
       DSYR2K - performs one of the symmetric rank 2k operations   C :=
       alpha*A*B' + alpha*B*A' + beta*C,

SYNOPSIS
       SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)

           DOUBLE                                                     PRECISION
                                                                      ALPHA,BETA

           INTEGER                                                    K,LDA,LDB,LDC,N

           CHARACTER                                                  TRANS,UPLO

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

PURPOSE
       DSYR2K  performs one of the symmetric rank 2k operations

       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.


ARGUMENTS
       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.

FURTHER DETAILS
       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                     November 2008                       DSYR2K(1)