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ztzrzf.f(3)				      LAPACK				      ztzrzf.f(3)

NAME
       ztzrzf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine ztzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
	   ZTZRZF

Function/Subroutine Documentation
   subroutine ztzrzf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA,
       complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerLWORK, integerINFO)
       ZTZRZF

       Purpose:

	    ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
	    to upper triangular form by means of unitary transformations.

	    The upper trapezoidal matrix A is factored as

	       A = ( R	0 ) * Z,

	    where Z is an N-by-N unitary matrix and R is an M-by-M upper
	    triangular matrix.

       Parameters:
	   M

		     M is INTEGER
		     The number of rows of the matrix A.  M >= 0.

	   N

		     N is INTEGER
		     The number of columns of the matrix A.  N >= M.

	   A

		     A is COMPLEX*16 array, dimension (LDA,N)
		     On entry, the leading M-by-N upper trapezoidal part of the
		     array A must contain the matrix to be factorized.
		     On exit, the leading M-by-M upper triangular part of A
		     contains the upper triangular matrix R, and elements M+1 to
		     N of the first M rows of A, with the array TAU, represent the
		     unitary matrix Z as a product of M elementary reflectors.

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,M).

	   TAU

		     TAU is COMPLEX*16 array, dimension (M)
		     The scalar factors of the elementary reflectors.

	   WORK

		     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.  LWORK >= max(1,M).
		     For optimum performance LWORK >= M*NB, where NB is
		     the optimal blocksize.

		     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

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   April 2012

       Contributors:
	   A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       Further Details:

	     The N-by-N matrix Z can be computed by

		Z =  Z(1)*Z(2)* ... *Z(M)

	     where each N-by-N Z(k) is given by

		Z(k) = I - tau(k)*v(k)*v(k)**H

	     with v(k) is the kth row vector of the M-by-N matrix

		V = ( I   A(:,M+1:N) )

	     I is the M-by-M identity matrix, A(:,M+1:N)
	     is the output stored in A on exit from DTZRZF,
	     and tau(k) is the kth element of the array TAU.

       Definition at line 152 of file ztzrzf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      ztzrzf.f(3)
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