zher2k

ZHER2K(l)                        BLAS routine                        ZHER2K(l)



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

       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
              triangular part  of the  hermitian 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
              hermitian 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(l)