clatrz (3)  Linux Manuals
NAME
clatrz.f 
SYNOPSIS
Functions/Subroutines
subroutine clatrz (M, N, L, A, LDA, TAU, WORK)
CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.
Function/Subroutine Documentation
subroutine clatrz (integerM, integerN, integerL, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK)
CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.
Purpose:

CLATRZ factors the Mby(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,NL+1:N) ] as ( R 0 ) * Z by means of unitary transformations, where Z is an (M+L)by(M+L) unitary matrix and, R and A1 are MbyM upper triangular matrices.
Parameters:

M
M is INTEGER The number of rows of the matrix A. M >= 0.
NN is INTEGER The number of columns of the matrix A. N >= 0.
LL is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder vectors. NM >= L >= 0.
AA is COMPLEX 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 NL+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.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAUTAU is COMPLEX array, dimension (M) The scalar factors of the elementary reflectors.
WORKWORK is COMPLEX array, dimension (M)
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Contributors:
 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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 )**H, u( k ) = ( 1 ), ( 0 ) ( z( k ) ) tau is a scalar and z( k ) is an l element vector. tau and z( k ) are chosen to annihilate the elements of the kth row of A2. The scalar tau is returned in the kth element of TAU and the vector u( k ) in the kth row of A2, such that the elements of z( k ) are in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in the upper triangular part of A1. Z is given by Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
Definition at line 141 of file clatrz.f.
Author
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