Level 3 BLAS like routine for C in RFP Format.


 DSFRK performs one of the symmetric rank--k operations


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


 or


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


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


 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;


          = 'T':  The 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**T + beta*C.


              TRANS = 'T' or 't'   C := alpha*A**T*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 = 'T'


           or 't', 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 DOUBLE PRECISION 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.


           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 DOUBLE PRECISION array, dimension (NT)


           NT = N*(N+1)/2. On entry, the symmetric matrix C in RFP


           Format. RFP Format is described by TRANSR, UPLO and N.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016