ZTZRQF - Online Linux Manual Page

Section : 1
Updated : November 2008
Source : LAPACK routine (version 3.2)
Note : LAPACK routine (version 3.2)
NAMEZTZRQF - routine i deprecated and has been replaced by routine ZTZRZF
SYNOPSISSUBROUTINE ZTZRQF(  M, N, A, LDA, TAU, INFO )  INTEGER INFO, LDA, M, N  COMPLEX*16 A( LDA, * ), TAU( * )
PURPOSEThis routine is deprecated and has been replaced by routine ZTZRZF.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.
ARGUMENTSM (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 DETAILSThe factorization is obtained by Householder's method. The kth transformation matrix, Z( k ), whose conjugate transpose 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 ).
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