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zlatrz.f(3) LAPACK zlatrz.f(3)

zlatrz.f -


subroutine zlatrz (M, N, L, A, LDA, TAU, WORK)
 
ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.
Purpose:
 ZLATRZ 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
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
L
          L is INTEGER
          The number of columns of the matrix A containing the
          meaningful part of the Householder vectors. N-M >= L >= 0.
A
          A is 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 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*16 array, dimension (M)
          The scalar factors of the elementary reflectors.
WORK
          WORK is COMPLEX*16 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 zlatrz.f.

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Sat Nov 16 2013 Version 3.4.2

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