1ZLATRZ(1)                LAPACK routine (version 3.1)                ZLATRZ(1)
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NAME

6       ZLATRZ  - the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [
7       A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of  unitary  trans‐
8       formations,  where  Z is an (M+L)-by-(M+L) unitary matrix and, R and A1
9       are M-by-M upper triangular matrices
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SYNOPSIS

12       SUBROUTINE ZLATRZ( M, N, L, A, LDA, TAU, WORK )
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14           INTEGER        L, LDA, M, N
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16           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

19       ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix [ A1  A2
20       ]  =  [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R  0 ) * Z by means of unitary
21       transformations, where  Z is an (M+L)-by-(M+L) unitary  matrix  and,  R
22       and A1 are M-by-M upper triangular matrices.
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ARGUMENTS

26       M       (input) INTEGER
27               The number of rows of the matrix A.  M >= 0.
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29       N       (input) INTEGER
30               The number of columns of the matrix A.  N >= 0.
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32       L       (input) INTEGER
33               The number of columns of the matrix A containing the meaningful
34               part of the Householder vectors. N-M >= L >= 0.
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36       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
37               On entry, the leading M-by-N  upper  trapezoidal  part  of  the
38               array A must contain the matrix to be factorized.  On exit, the
39               leading M-by-M upper triangular part of A  contains  the  upper
40               triangular  matrix  R,  and  elements N-L+1 to N of the first M
41               rows of A, with the array TAU, represent the unitary  matrix  Z
42               as a product of M elementary reflectors.
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44       LDA     (input) INTEGER
45               The leading dimension of the array A.  LDA >= max(1,M).
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47       TAU     (output) COMPLEX*16 array, dimension (M)
48               The scalar factors of the elementary reflectors.
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50       WORK    (workspace) COMPLEX*16 array, dimension (M)
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FURTHER DETAILS

53       Based on contributions by
54         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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56       The  factorization is obtained by Householder's method.  The kth trans‐
57       formation matrix, Z( k ), which is used to introduce zeros into the ( m
58       - k + 1 )th row of A, is given in the form
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60          Z( k ) = ( I     0   ),
61                   ( 0  T( k ) )
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63       where
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65          T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
66                                                      (   0    )
67                                                      ( z( k ) )
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69       tau  is  a scalar and z( k ) is an l element vector. tau and z( k ) are
70       chosen to annihilate the elements of the kth row of A2.
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72       The scalar tau is returned in the kth element of TAU and the vector  u(
73       k  )  in the kth row of A2, such that the elements of z( k ) are in  a(
74       k, l + 1 ), ..., a( k, n ). The elements of R are returned in the upper
75       triangular part of A1.
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77       Z is given by
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79          Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
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84 LAPACK routine (version 3.1)    November 2006                       ZLATRZ(1)
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