ZGERQF(3)                  MathKeisan LAPACK routine                 ZGERQF(3)



NAME
       ZGERQF - an RQ factorization of a complex M-by-N matrix A

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

           INTEGER        INFO, LDA, LWORK, M, N

           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       ZGERQF computes an RQ factorization of a complex 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) COMPLEX*16 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  unitary  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) COMPLEX*16 array, dimension (min(M,N))
               The  scalar  factors  of the elementary reflectors (see Further
               Details).

       WORK    (workspace/output) COMPLEX*16 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

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  complex  scalar, and v is a complex vector with v(n-
       k+i+1:n) = 0 and v(n-k+i) = 1; conjg(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 3.1)    November 2006                       ZGERQF(3)