SGERQ2  -  compute  an  RQ  factorization of a real m by n
       matrix A


SYNOPSIS

       SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, LDA, M, N

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


PURPOSE

       SGERQ2 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 trape­
               zoidal matrix R; the remaining elements, with  the
               array  TAU, represent the orthogonal matrix Q as a
               product  of  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) REAL array, dimension (M)

       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).


          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).


Man(1) output converted with man2html