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
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
|
*> \brief \b DGET51
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
* RESULT )
*
* .. Scalar Arguments ..
* INTEGER ITYPE, LDA, LDB, LDU, LDV, N
* DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), U( LDU, * ),
* $ V( LDV, * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGET51 generally checks a decomposition of the form
*>
*> A = U B V'
*>
*> where ' means transpose and U and V are orthogonal.
*>
*> Specifically, if ITYPE=1
*>
*> RESULT = | A - U B V' | / ( |A| n ulp )
*>
*> If ITYPE=2, then:
*>
*> RESULT = | A - B | / ( |A| n ulp )
*>
*> If ITYPE=3, then:
*>
*> RESULT = | I - UU' | / ( n ulp )
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] ITYPE
*> \verbatim
*> ITYPE is INTEGER
*> Specifies the type of tests to be performed.
*> =1: RESULT = | A - U B V' | / ( |A| n ulp )
*> =2: RESULT = | A - B | / ( |A| n ulp )
*> =3: RESULT = | I - UU' | / ( n ulp )
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The size of the matrix. If it is zero, DGET51 does nothing.
*> It must be at least zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA, N)
*> The original (unfactored) matrix.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A. It must be at least 1
*> and at least N.
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB, N)
*> The factored matrix.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of B. It must be at least 1
*> and at least N.
*> \endverbatim
*>
*> \param[in] U
*> \verbatim
*> U is DOUBLE PRECISION array, dimension (LDU, N)
*> The orthogonal matrix on the left-hand side in the
*> decomposition.
*> Not referenced if ITYPE=2
*> \endverbatim
*>
*> \param[in] LDU
*> \verbatim
*> LDU is INTEGER
*> The leading dimension of U. LDU must be at least N and
*> at least 1.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV, N)
*> The orthogonal matrix on the left-hand side in the
*> decomposition.
*> Not referenced if ITYPE=2
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of V. LDV must be at least N and
*> at least 1.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (2*N**2)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION
*> The values computed by the test specified by ITYPE. The
*> value is currently limited to 1/ulp, to avoid overflow.
*> Errors are flagged by RESULT=10/ulp.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET51( ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK,
$ RESULT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER ITYPE, LDA, LDB, LDU, LDV, N
DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), U( LDU, * ),
$ V( LDV, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TEN
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TEN = 10.0D0 )
* ..
* .. Local Scalars ..
INTEGER JCOL, JDIAG, JROW
DOUBLE PRECISION ANORM, ULP, UNFL, WNORM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE
EXTERNAL DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DGEMM, DLACPY
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, MAX, MIN
* ..
* .. Executable Statements ..
*
RESULT = ZERO
IF( N.LE.0 )
$ RETURN
*
* Constants
*
UNFL = DLAMCH( 'Safe minimum' )
ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
*
* Some Error Checks
*
IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
RESULT = TEN / ULP
RETURN
END IF
*
IF( ITYPE.LE.2 ) THEN
*
* Tests scaled by the norm(A)
*
ANORM = MAX( DLANGE( '1', N, N, A, LDA, WORK ), UNFL )
*
IF( ITYPE.EQ.1 ) THEN
*
* ITYPE=1: Compute W = A - UBV'
*
CALL DLACPY( ' ', N, N, A, LDA, WORK, N )
CALL DGEMM( 'N', 'N', N, N, N, ONE, U, LDU, B, LDB, ZERO,
$ WORK( N**2+1 ), N )
*
CALL DGEMM( 'N', 'C', N, N, N, -ONE, WORK( N**2+1 ), N, V,
$ LDV, ONE, WORK, N )
*
ELSE
*
* ITYPE=2: Compute W = A - B
*
CALL DLACPY( ' ', N, N, B, LDB, WORK, N )
*
DO 20 JCOL = 1, N
DO 10 JROW = 1, N
WORK( JROW+N*( JCOL-1 ) ) = WORK( JROW+N*( JCOL-1 ) )
$ - A( JROW, JCOL )
10 CONTINUE
20 CONTINUE
END IF
*
* Compute norm(W)/ ( ulp*norm(A) )
*
WNORM = DLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) )
*
IF( ANORM.GT.WNORM ) THEN
RESULT = ( WNORM / ANORM ) / ( N*ULP )
ELSE
IF( ANORM.LT.ONE ) THEN
RESULT = ( MIN( WNORM, N*ANORM ) / ANORM ) / ( N*ULP )
ELSE
RESULT = MIN( WNORM / ANORM, DBLE( N ) ) / ( N*ULP )
END IF
END IF
*
ELSE
*
* Tests not scaled by norm(A)
*
* ITYPE=3: Compute UU' - I
*
CALL DGEMM( 'N', 'C', N, N, N, ONE, U, LDU, U, LDU, ZERO, WORK,
$ N )
*
DO 30 JDIAG = 1, N
WORK( ( N+1 )*( JDIAG-1 )+1 ) = WORK( ( N+1 )*( JDIAG-1 )+
$ 1 ) - ONE
30 CONTINUE
*
RESULT = MIN( DLANGE( '1', N, N, WORK, N, WORK( N**2+1 ) ),
$ DBLE( N ) ) / ( N*ULP )
END IF
*
RETURN
*
* End of DGET51
*
END
|
