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LAPACK version 3.0
zgerq2(3)

PURPOSE
  ZGERQ2 - compute an RQ factorization of a complex m by n matrix A

SYNTAX
  SUBROUTINE ZGERQ2( M, N, A, LDA, TAU, WORK, INFO )

      INTEGER	     INFO, LDA, M, N

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

DESCRIPTION
  ZGERQ2 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 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) COMPLEX*16 array, dimension (M)

  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).