SSFRK(3)       LAPACK routine of NEC Numeric Library Collection       SSFRK(3)



NAME
       SSFRK

SYNOPSIS
       SUBROUTINE SSFRK (TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C)



PURPOSE
            Level 3 BLAS like routine for C in RFP Format.

            SSFRK 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.




ARGUMENTS
           TRANSR    (input)
                     TRANSR is CHARACTER*1
                     = 'N':  The Normal Form of RFP A is stored;
                     = 'T':  The Transpose Form of RFP A is stored.

           UPLO      (input)
                     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     (input)
                     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         (input)
                     N is INTEGER
                      On entry, N specifies the order of the matrix C. N must be
                      at least zero.
                      Unchanged on exit.

           K         (input)
                     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     (input)
                     ALPHA is REAL
                      On entry, ALPHA specifies the scalar alpha.
                      Unchanged on exit.

           A         (input)
                     A is REAL 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       (input)
                     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      (input)
                     BETA is REAL
                      On entry, BETA specifies the scalar beta.
                      Unchanged on exit.

           C         (input/output)
                     C is REAL 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.



LAPACK routine                  31 October 2017                       SSFRK(3)