ZGEQRF(3)                  MathKeisan LAPACK routine                 ZGEQRF(3)



NAME
       ZGEQRF - a QR factorization of a complex M-by-N matrix A

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

           INTEGER        INFO, LDA, LWORK, M, N

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

PURPOSE
       ZGEQRF  computes a QR factorization of a complex M-by-N matrix A: A = Q
       * R.


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, the  elements  on  and
               above the diagonal of the array contain the min(M,N)-by-N upper
               trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
               elements  below the diagonal, 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,N).  For opti-
               mum  performance  LWORK >= N*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(1:i-1)
       = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau  in
       TAU(i).




 LAPACK routine (version 3.1)    November 2006                       ZGEQRF(3)