SORGLQ - generate an M-by-N real matrix Q with orthonormal
       rows,


SYNOPSIS

       SUBROUTINE SORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO
                          )

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

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


PURPOSE

       SORGLQ  generates an M-by-N real matrix Q with orthonormal
       rows, which is defined as the first M rows of a product of
       K elementary reflectors of order N

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

       as returned by SGELQF.


ARGUMENTS

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

       N       (input) INTEGER
               The number of columns of the matrix Q. N >= M.

       K       (input) INTEGER
               The  number of elementary reflectors whose product
               defines the matrix Q. M >= K >= 0.

       A       (input/output) REAL array, dimension (LDA,N)
               On entry, 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 array argument A.  On exit, the M-by-N
               matrix Q.

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

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

       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.  LWORK  >=

               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 has an ille­
               gal value


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