ZHER2K  performs one of the hermitian rank 2k operations


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


 or


    C := alpha*A**H*B + conjg( alpha )*B**H*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.

UPLO

          UPLO is 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.

TRANS

          TRANS is CHARACTER*1


           On entry,  TRANS  specifies the operation to be performed as


           follows:


              TRANS = 'N' or 'n'    C := alpha*A*B**H          +


                                         conjg( alpha )*B*A**H +


                                         beta*C.


              TRANS = 'C' or 'c'    C := alpha*A**H*B          +


                                         conjg( alpha )*B**H*A +


                                         beta*C.

N

          N is INTEGER


           On entry,  N specifies the order of the matrix C.  N must be


           at least zero.

K

          K is 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.

ALPHA

          ALPHA is COMPLEX*16 .


           On entry, ALPHA specifies the scalar alpha.

A

          A is COMPLEX*16 array, 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.

LDA

          LDA is 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 ).

B

          B is COMPLEX*16 array, 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.

LDB

          LDB is 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

          BETA is DOUBLE PRECISION .


           On entry, BETA specifies the scalar beta.

C

          C is COMPLEX*16 array, 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

          LDC is 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 ).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  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.


  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.


     Ed Anderson, Cray Research Inc.