SORGQR - generate an M-by-N real matrix Q with orthonormal
       columns,


SYNOPSIS

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

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

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


PURPOSE

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

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

       as returned by SGEQRF.


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. M >= N >=
               0.

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

       A       (input/output) REAL array, dimension (LDA,N)
               On  entry, the i-th column must contain the vector
               which defines the elementary reflector H(i), for i
               =  1,2,...,k, as returned by SGEQRF in the first k
               columns 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 SGEQRF.

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

               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,N).   For optimum performance LWORK >= N*NB,
               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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