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dtzrzf.f(3)				      LAPACK				      dtzrzf.f(3)

       dtzrzf.f -

       subroutine dtzrzf (M, N, A, LDA, TAU, WORK, LWORK, INFO)

Function/Subroutine Documentation
   subroutine dtzrzf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA,
       double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerLWORK,


	    DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
	    to upper triangular form by means of orthogonal transformations.

	    The upper trapezoidal matrix A is factored as

	       A = ( R	0 ) * Z,

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


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


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


		     A is DOUBLE PRECISION 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
		     orthogonal matrix Z as a product of M elementary reflectors.


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


		     TAU is DOUBLE PRECISION array, dimension (M)
		     The scalar factors of the elementary reflectors.


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


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

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   April 2012

	   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)**T

	     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 dtzrzf.f.

       Generated automatically by Doxygen for LAPACK from the source code.

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