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
|
*> \brief \b SQRT11
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* REAL FUNCTION SQRT11( M, K, A, LDA, TAU, WORK, LWORK )
*
* .. Scalar Arguments ..
* INTEGER K, LDA, LWORK, M
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SQRT11 computes the test ratio
*>
*> || Q'*Q - I || / (eps * m)
*>
*> where the orthogonal matrix Q is represented as a product of
*> elementary transformations. Each transformation has the form
*>
*> H(k) = I - tau(k) v(k) v(k)'
*>
*> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
*> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
*> in A(k+1:m,k).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of columns of A whose subdiagonal entries
*> contain information about orthogonal transformations.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is REAL array, dimension (LDA,K)
*> The (possibly partial) output of a QR reduction routine.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL array, dimension (K)
*> The scaling factors tau for the elementary transformations as
*> computed by the QR factorization routine.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= M*M + M.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup single_lin
*
* =====================================================================
REAL FUNCTION SQRT11( M, K, A, 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 K, LDA, LWORK, M
* ..
* .. Array Arguments ..
REAL A( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER INFO, J
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE
EXTERNAL SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SLASET, SORM2R, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL
* ..
* .. Local Arrays ..
REAL RDUMMY( 1 )
* ..
* .. Executable Statements ..
*
SQRT11 = ZERO
*
* Test for sufficient workspace
*
IF( LWORK.LT.M*M+M ) THEN
CALL XERBLA( 'SQRT11', 7 )
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 )
$ RETURN
*
CALL SLASET( 'Full', M, M, ZERO, ONE, WORK, M )
*
* Form Q
*
CALL SORM2R( 'Left', 'No transpose', M, M, K, A, LDA, TAU, WORK,
$ M, WORK( M*M+1 ), INFO )
*
* Form Q'*Q
*
CALL SORM2R( 'Left', 'Transpose', M, M, K, A, LDA, TAU, WORK, M,
$ WORK( M*M+1 ), INFO )
*
DO 10 J = 1, M
WORK( ( J-1 )*M+J ) = WORK( ( J-1 )*M+J ) - ONE
10 CONTINUE
*
SQRT11 = SLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) /
$ ( REAL( M )*SLAMCH( 'Epsilon' ) )
*
RETURN
*
* End of SQRT11
*
END
|
