dtzrqf.f(3) [centos man page]

dtzrqf.f(3)							      LAPACK							       dtzrqf.f(3)

NAME

       dtzrqf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dtzrqf (M, N, A, LDA, TAU, INFO)
	   DTZRQF

Function/Subroutine Documentation
   subroutine dtzrqf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, integerINFO)
       DTZRQF

       Purpose:

	    This routine is deprecated and has been replaced by routine DTZRZF.

	    DTZRQF 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.

       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 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

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

	   TAU

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

	   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:
	   November 2011

       Further Details:

	     The factorization is obtained by Householder's method.  The kth
	     transformation matrix, Z( k ), which is used to introduce zeros into
	     the ( m - k + 1 )th row of A, is given in the form

		Z( k ) = ( I	 0   ),
			 ( 0  T( k ) )

	     where

		T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
							      (   0    )
							      ( z( k ) )

	     tau is a scalar and z( k ) is an ( n - m ) element vector.
	     tau and z( k ) are chosen to annihilate the elements of the kth row
	     of X.

	     The scalar tau is returned in the kth element of TAU and the vector
	     u( k ) in the kth row of A, such that the elements of z( k ) are
	     in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
	     the upper triangular part of A.

	     Z is given by

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

       Definition at line 139 of file dtzrqf.f.

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

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

Check Out this Related Man Page

DTZRQF(l)								 )								 DTZRQF(l)

NAME

       DTZRQF - routine is deprecated and has been replaced by routine DTZRZF

SYNOPSIS

       SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO )

	   INTEGER	  INFO, LDA, M, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * )

PURPOSE

       This  routine is deprecated and has been replaced by routine DTZRZF.  DTZRQF 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.

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 >= M.

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

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

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

FURTHER DETAILS

       The factorization is obtained by Householder's method.  The kth transformation matrix, Z( k ), which is used to introduce zeros into the  (
       m - k + 1 )th row of A, is given in the form

	  Z( k ) = ( I	   0   ),
		   ( 0	T( k ) )

       where

	  T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
						      (   0    )
						      ( z( k ) )

       tau is a scalar and z( k ) is an ( n - m ) element vector.  tau and z( k ) are chosen to annihilate the elements of the kth row of X.

       The scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A, such that the elements of z( k ) are in	a(
       k, m + 1 ), ..., a( k, n ). The elements of R are returned in the upper triangular part of A.

       Z is given by

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

LAPACK version 3.0						   15 June 2000 							 DTZRQF(l)

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dtzrqf.f(3) [centos man page]

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