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NAME
     sgerqf - compute an RQ factorization of a real M-by-N matrix
     A

SYNOPSIS
     SUBROUTINE SGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

     INTEGER INFO, LDA, LWORK, M, N

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



     #include <sunperf.h>

     void sgerqf(int m, int n, float *sa, int  lda,  float  *tau,
               int *info) ;

PURPOSE
     SGERQF computes an RQ factorization of a real M-by-N  matrix
     A:  A = R * Q.


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

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

     A         (input/output) REAL array, dimension (LDA,N)
               On entry, the M-by-N matrix A.  On exit, if  m  <=
               n,  the  upper  triangle  of the subarray A(1:m,n-
               m+1:n) contains the M-by-M upper triangular matrix
               R;  if  m  >= n, the elements on and above the (m-
               n)-th subdiagonal contain the  M-by-N  upper  tra-
               pezoidal  matrix  R;  the remaining elements, with
               the array TAU, represent the orthogonal  matrix  Q
               as  a  product  of  min(m,n) elementary reflectors
               (see Further Details).   LDA      (input)  INTEGER
               The  leading  dimension  of  the  array A.  LDA >=
               max(1,M).

     TAU       (output) REAL array, dimension (min(M,N))
               The scalar factors of  the  elementary  reflectors
               (see Further Details).

     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   >=
               max(1,M).   For optimum performance LWORK >= M*NB,
               where NB is the optimal blocksize.

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

FURTHER DETAILS
     The matrix Q is  represented  as  a  product  of  elementary
     reflectors

        Q = H(1) H(2) . . . H(k), where k = min(m,n).

     Each H(i) has the form

        H(i) = I - tau * v * v'

     where tau is a real scalar, and v is a real vector with
     v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on
     exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

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