1SLATRZ(1)                LAPACK routine (version 3.2)                SLATRZ(1)
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NAME

6       SLATRZ - factors the M-by-(M+L) real 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  orthogonal
8       transformations
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SYNOPSIS

11       SUBROUTINE SLATRZ( M, N, L, A, LDA, TAU, WORK )
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13           INTEGER        L, LDA, M, N
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15           REAL           A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

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

24       M       (input) INTEGER
25               The number of rows of the matrix A.  M >= 0.
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27       N       (input) INTEGER
28               The number of columns of the matrix A.  N >= 0.
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30       L       (input) INTEGER
31               The number of columns of the matrix A containing the meaningful
32               part of the Householder vectors. N-M >= L >= 0.
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34       A       (input/output) REAL array, dimension (LDA,N)
35               On  entry,  the  leading  M-by-N  upper trapezoidal part of the
36               array A must contain the matrix to be factorized.  On exit, the
37               leading  M-by-M  upper  triangular part of A contains the upper
38               triangular matrix R, and elements N-L+1 to N  of  the  first  M
39               rows  of A, with the array TAU, represent the orthogonal matrix
40               Z as a product of M elementary reflectors.
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42       LDA     (input) INTEGER
43               The leading dimension of the array A.  LDA >= max(1,M).
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45       TAU     (output) REAL array, dimension (M)
46               The scalar factors of the elementary reflectors.
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48       WORK    (workspace) REAL array, dimension (M)
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FURTHER DETAILS

51       Based on contributions by
52         A. Petitet, Computer Science Dept., Univ. of  Tenn.,  Knoxville,  USA
53       The  factorization is obtained by Householder's method.  The kth trans‐
54       formation matrix, Z( k ), which is used to introduce zeros into the ( m
55       - k + 1 )th row of A, is given in the form
56          Z( k ) = ( I     0   ),
57                   ( 0  T( k ) )
58       where
59          T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
60                                                      (   0    )
61                                                      (  z(  k  )  )  tau is a
62       scalar and z( k ) is an l element vector. tau and z( k ) are chosen  to
63       annihilate  the  elements  of  the  kth  row  of A2.  The scalar tau is
64       returned in the kth element of TAU and the vector u( k ) in the kth row
65       of  A2, such that the elements of z( k ) are in  a( k, l + 1 ), ..., a(
66       k, n ). The elements of R are returned in the upper triangular part  of
67       A1.
68       Z is given by
69          Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
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73 LAPACK routine (version 3.2)    November 2008                       SLATRZ(1)
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