ZHER2K(3)       BLAS routine of NEC Numeric Library Collection       ZHER2K(3)



NAME
       ZHER2K  -  perform  one  of  the  hermitian  rank  2k operations   C :=
       alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' )  +  beta*C,    C  :=
       alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C


SYNOPSIS
       SUBROUTINE ZHER2K( UPLO,  TRANS,  N, K, ALPHA, A, LDA, B, LDB, BETA, C,
                          LDC )

           CHARACTER*1    UPLO, TRANS

           INTEGER        N, K, LDA, LDB, LDC

           DOUBLE         PRECISION BETA

           COMPLEX*16     ALPHA

           COMPLEX*16     A( LDA, * ), B( LDB, * ), C( LDC, * )

PURPOSE
       ZHER2K  performs one of the hermitian rank 2k operations

          C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C or

          C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C,

       where  alpha and beta  are scalars with  beta  real,  C is an  n  by  n
       hermitian  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*conjg( B' )          + conjg(
              alpha )*B*conjg( A' ) + beta*C.

              TRANS = 'C' or 'c'    C := alpha*conjg( A' )*B          + conjg(
              alpha )*conjg( 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 =
              '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  - COMPLEX*16      .
              On  entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       A      - COMPLEX*16       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      - COMPLEX*16       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      - COMPLEX*16       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 tri-
              angular part  of the  hermitian matrix  and the  strictly  lower
              triangular part of C is not referenced.  On exit, the upper tri-
              angular part of the array  C is overwritten by the upper  trian-
              gular  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  hermi-
              tian 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 imaginary 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.

              --  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                      ZHER2K(3)