redhat man page for ztzrqf

ZTZRQF(l)								 )								 ZTZRQF(l)

NAME
       ZTZRQF - routine is deprecated and has been replaced by routine ZTZRZF

SYNOPSIS
       SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO )

	   INTEGER	  INFO, LDA, M, N

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

PURPOSE
       This  routine is deprecated and has been replaced by routine ZTZRZF.  ZTZRQF 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.

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

       TAU     (output) COMPLEX*16 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 ), whose conjugate transpose is used to intro-
       duce 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 							 ZTZRQF(l)