1STZRQF(1) LAPACK routine (version 3.2) STZRQF(1)
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6 STZRQF - routine i deprecated and has been replaced by routine STZRZF
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9 SUBROUTINE STZRQF( M, N, A, LDA, TAU, INFO )
10 INTEGER INFO, LDA, M, N
12 REAL A( LDA, * ), TAU( * )
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16 This routine is deprecated and has been replaced by routine STZRZF.
17 STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to
18 upper triangular form by means of orthogonal transformations. The
19 upper trapezoidal matrix A is factored as
20 A = ( R 0 ) * Z,
21 where Z is an N-by-N orthogonal matrix and R is an M-by-M upper trian‐
22 gular matrix.
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25 M (input) INTEGER
26 The number of rows of the matrix A. M >= 0.
27 N (input) INTEGER
29 The number of columns of the matrix A. N >= M.
30 A (input/output) REAL array, dimension (LDA,N)
32 On entry, the leading M-by-N upper trapezoidal part of the
33 array A must contain the matrix to be factorized. On exit, the
34 leading M-by-M upper triangular part of A contains the upper
35 triangular matrix R, and elements M+1 to N of the first M rows
36 of A, with the array TAU, represent the orthogonal matrix Z as
37 a product of M elementary reflectors.
38 LDA (input) INTEGER
40 The leading dimension of the array A. LDA >= max(1,M).
41 TAU (output) REAL array, dimension (M)
43 The scalar factors of the elementary reflectors.
44 INFO (output) INTEGER
46 = 0: successful exit
47 < 0: if INFO = -i, the i-th argument had an illegal value
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50 The factorization is obtained by Householder's method. The kth trans‐
51 formation matrix, Z( k ), which is used to introduce zeros into the ( m
52 - k + 1 )th row of A, is given in the form
53 Z( k ) = ( I 0 ),
54 ( 0 T( k ) )
55 where
56 T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
57 ( 0 )
58 ( z( k ) ) tau is a
59 scalar and z( k ) is an ( n - m ) element vector. tau and z( k ) are
60 chosen to annihilate the elements of the kth row of X.
61 The scalar tau is returned in the kth element of TAU and the vector u(
62 k ) in the kth row of A, such that the elements of z( k ) are in a( k,
63 m + 1 ), ..., a( k, n ). The elements of R are returned in the upper
64 triangular part of A.
65 Z is given by
66 Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
67 LAPACK routine (version 3.2) November 2008 STZRQF(1)