

DTZRQF(l) ) DTZRQF(l) NAME DTZRQF  routine is deprecated and has been replaced by routine DTZRZF SYNOPSIS SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO ) INTEGER INFO, LDA, M, N DOUBLE PRECISION A( LDA, * ), TAU( * ) PURPOSE This routine is deprecated and has been replaced by routine DTZRZF.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 byN ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthog onal transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an NbyN orthogonal matrix and R is an MbyM 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 MbyN upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading MbyM 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 ith 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)