clatrz-f(3)

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 M-by-(M+L) complex upper trapezoidal matrix
 [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+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 M-by-M upper triangular matrices.

Parameters:

 M is INTEGER
 The number of rows of the matrix A. M >= 0.

 N is INTEGER
 The number of columns of the matrix A. N >= 0.

 L is INTEGER
 The number of columns of the matrix A containing the
 meaningful part of the Householder vectors. N-M >= L >= 0.

 A is COMPLEX 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 N-L+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

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

TAU

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

WORK

 WORK 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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