1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
|
*> \brief \b DRZT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DRZT01( M, N, A, AF, LDA, TAU, WORK,
* LWORK )
*
* .. Scalar Arguments ..
* INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DRZT01 returns
*> || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with DTZRZF.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> The original upper trapezoidal M by N matrix A.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is DOUBLE PRECISION array, dimension (LDA,N)
*> The output of DTZRZF for input matrix A.
*> The lower triangle is not referenced.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A and AF.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION array, dimension (M)
*> Details of the Householder transformations as returned by
*> DTZRZF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= m*n + m*nb.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_lin
*
* =====================================================================
DOUBLE PRECISION FUNCTION DRZT01( M, N, A, AF, LDA, TAU, WORK,
$ LWORK )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
DOUBLE PRECISION NORMA
* ..
* .. Local Arrays ..
DOUBLE PRECISION RWORK( 1 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE
EXTERNAL DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DLASET, DORMRZ, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX
* ..
* .. Executable Statements ..
*
DRZT01 = ZERO
*
IF( LWORK.LT.M*N+M ) THEN
CALL XERBLA( 'DRZT01', 8 )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
NORMA = DLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
* Copy upper triangle R
*
CALL DLASET( 'Full', M, N, ZERO, ZERO, WORK, M )
DO 20 J = 1, M
DO 10 I = 1, J
WORK( ( J-1 )*M+I ) = AF( I, J )
10 CONTINUE
20 CONTINUE
*
* R = R * P(1) * ... *P(m)
*
CALL DORMRZ( 'Right', 'No tranpose', M, N, M, N-M, AF, LDA, TAU,
$ WORK, M, WORK( M*N+1 ), LWORK-M*N, INFO )
*
* R = R - A
*
DO 30 I = 1, N
CALL DAXPY( M, -ONE, A( 1, I ), 1, WORK( ( I-1 )*M+1 ), 1 )
30 CONTINUE
*
DRZT01 = DLANGE( 'One-norm', M, N, WORK, M, RWORK )
*
DRZT01 = DRZT01 / ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) )
IF( NORMA.NE.ZERO )
$ DRZT01 = DRZT01 / NORMA
*
RETURN
*
* End of DRZT01
*
END
|
