Level 3 BLAS like routine for C in RFP Format.


 ZHFRK performs one of the Hermitian rank--k operations


    C := alpha*A*A**H + beta*C,


 or


    C := alpha*A**H*A + beta*C,


 where alpha and beta are real scalars, C is an n--by--n Hermitian


 matrix and A is an n--by--k matrix in the first case and a k--by--n


 matrix in the second case.

TRANSR

          TRANSR is CHARACTER*1


          = 'N':  The Normal Form of RFP A is stored;


          = 'C':  The Conjugate-transpose Form of RFP A is stored.

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.


           Unchanged on exit.

TRANS

          TRANS is CHARACTER*1


           On entry,  TRANS  specifies the operation to be performed as


           follows:


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


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


           Unchanged on exit.

N

          N is INTEGER


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


           at least zero.


           Unchanged on exit.

K

          K is INTEGER


           On entry with  TRANS = 'N' or 'n',  K  specifies  the number


           of  columns   of  the   matrix   A,   and  on   entry   with


           TRANS = 'C' or 'c',  K  specifies  the number of rows of the


           matrix A.  K must be at least zero.


           Unchanged on exit.

ALPHA

          ALPHA is DOUBLE PRECISION


           On entry, ALPHA specifies the scalar alpha.


           Unchanged on exit.

A

          A is 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

          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 ).


           Unchanged on exit.

BETA

          BETA is DOUBLE PRECISION


           On entry, BETA specifies the scalar beta.


           Unchanged on exit.

C

          C is COMPLEX*16 array, dimension (N*(N+1)/2)


           On entry, the matrix A in RFP Format. RFP Format is


           described by TRANSR, UPLO and N. 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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012