


DGERQF(3f)         LAPACK routine (version 3.1)        DGERQF(3f)


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

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

           INTEGER        INFO, LDA, LWORK, M, N

           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       DGERQF  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) DOUBLE PRECISION 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 trapezoidal
               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) DOUBLE PRECISION array, dimension (min(M,N))
               The  scalar  factors  of the elementary reflectors (see Further
               Details).

       WORK    (workspace/output) DOUBLE PRECISION array, dimension
       (MAX(1,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 opti-
               mum performance LWORK >= M*NB, where NB is the  optimal  block-
               size.

               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 illegal value




 LAPACK routine (version 3November 2006                         1





DGERQF(3f)         LAPACK routine (version 3.1)        DGERQF(3f)


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).













































 LAPACK routine (version 3November 2006                         2


