SORMLQ  -  overwrite the general real M-by-N matrix C with
       SIDE = 'L' SIDE = 'R' TRANS = 'N'


SYNOPSIS

       SUBROUTINE SORMLQ( SIDE, TRANS, M, N, K, A, LDA,  TAU,  C,
                          LDC, WORK, LWORK, INFO )

           CHARACTER      SIDE, TRANS

           INTEGER        INFO, K, LDA, LDC, LWORK, M, N

           REAL           A(  LDA,  *  ),  C( LDC, * ), TAU( * ),
                          WORK( * )


PURPOSE

       SORMLQ overwrites the general real M-by-N  matrix  C  with
       SIDE  =  'L'  SIDE  = 'R' TRANS = 'N': Q * C C * Q TRANS =
       'T':      Q**T * C       C * Q**T

       where Q is a real orthogonal matrix defined as the product
       of k elementary reflectors

             Q = H(k) . . . H(2) H(1)

       as  returned  by SGELQF. Q is of order M if SIDE = 'L' and
       of order N if SIDE = 'R'.


ARGUMENTS

       SIDE    (input) CHARACTER*1
               = 'L': apply Q or Q**T from the Left;
               = 'R': apply Q or Q**T from the Right.

       TRANS   (input) CHARACTER*1
               = 'N':  No transpose, apply Q;
               = 'T':  Transpose, apply Q**T.

       M       (input) INTEGER
               The number of rows of the matrix C. M >= 0.

       N       (input) INTEGER
               The number of columns of the matrix C. N >= 0.

       K       (input) INTEGER
               The number of elementary reflectors whose  product
               defines the matrix Q.  If SIDE = 'L', M >= K >= 0;
               if SIDE = 'R', N >= K >= 0.

       A       (input) REAL array, dimension
               (LDA,M) if SIDE = 'L', (LDA,N) if SIDE =  'R'  The
               i-th row must contain the vector which defines the
               elementary reflector H(i), for i =  1,2,...,k,  as
               returned  by  SGELQF  in  the  first k rows of its

               but restored on exit.

       LDA     (input) INTEGER
               The  leading  dimension  of  the  array  A. LDA >=
               max(1,K).

       TAU     (input) REAL array, dimension (K)
               TAU(i) must contain the scalar factor of the  ele­
               mentary reflector H(i), as returned by SGELQF.

       C       (input/output) REAL array, dimension (LDC,N)
               On  entry,  the  M-by-N  matrix  C.  On exit, C is
               overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

       LDC     (input) INTEGER
               The leading dimension  of  the  array  C.  LDC  >=
               max(1,M).

       WORK    (workspace/output) REAL array, dimension (LWORK)
               On  exit, if INFO = 0, WORK(1) returns the optimal
               LWORK.

       LWORK   (input) INTEGER
               The dimension of the array WORK.  If SIDE  =  'L',
               LWORK  >=  max(1,N);  if  SIDE  =  'R',  LWORK  >=
               max(1,M).  For optimum performance LWORK  >=  N*NB
               if  SIDE  =  'L', and LWORK >= M*NB if SIDE = 'R',
               where NB is the optimal blocksize.

               If LWORK = -1, then a workspace query is  assumed;
               the  routine  only  calculates the optimal size of
               the WORK array, returns this value  as  the  first
               entry  of  the  WORK  array,  and no error message
               related to LWORK is issued by XERBLA.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


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