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
|
*> \brief \b CPPT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER N
* REAL RESID
* ..
* .. Array Arguments ..
* REAL RWORK( * )
* COMPLEX A( * ), AFAC( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CPPT01 reconstructs a Hermitian positive definite packed matrix A
*> from its L*L' or U'*U factorization and computes the residual
*> norm( L*L' - A ) / ( N * norm(A) * EPS ) or
*> norm( U'*U - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon, L' is the conjugate transpose of
*> L, and U' is the conjugate transpose of U.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> Hermitian matrix A is stored:
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX array, dimension (N*(N+1)/2)
*> The original Hermitian matrix A, stored as a packed
*> triangular matrix.
*> \endverbatim
*>
*> \param[in,out] AFAC
*> \verbatim
*> AFAC is COMPLEX array, dimension (N*(N+1)/2)
*> On entry, the factor L or U from the L*L' or U'*U
*> factorization of A, stored as a packed triangular matrix.
*> Overwritten with the reconstructed matrix, and then with the
*> difference L*L' - A (or U'*U - A).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is REAL
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex_lin
*
* =====================================================================
SUBROUTINE CPPT01( UPLO, N, A, AFAC, RWORK, RESID )
*
* -- 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 ..
CHARACTER UPLO
INTEGER N
REAL RESID
* ..
* .. Array Arguments ..
REAL RWORK( * )
COMPLEX A( * ), AFAC( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, K, KC
REAL ANORM, EPS, TR
COMPLEX TC
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANHP, SLAMCH
COMPLEX CDOTC
EXTERNAL LSAME, CLANHP, SLAMCH, CDOTC
* ..
* .. External Subroutines ..
EXTERNAL CHPR, CSCAL, CTPMV
* ..
* .. Intrinsic Functions ..
INTRINSIC AIMAG, REAL
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = SLAMCH( 'Epsilon' )
ANORM = CLANHP( '1', UPLO, N, A, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Check the imaginary parts of the diagonal elements and return with
* an error code if any are nonzero.
*
KC = 1
IF( LSAME( UPLO, 'U' ) ) THEN
DO 10 K = 1, N
IF( AIMAG( AFAC( KC ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
KC = KC + K + 1
10 CONTINUE
ELSE
DO 20 K = 1, N
IF( AIMAG( AFAC( KC ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
KC = KC + N - K + 1
20 CONTINUE
END IF
*
* Compute the product U'*U, overwriting U.
*
IF( LSAME( UPLO, 'U' ) ) THEN
KC = ( N*( N-1 ) ) / 2 + 1
DO 30 K = N, 1, -1
*
* Compute the (K,K) element of the result.
*
TR = CDOTC( K, AFAC( KC ), 1, AFAC( KC ), 1 )
AFAC( KC+K-1 ) = TR
*
* Compute the rest of column K.
*
IF( K.GT.1 ) THEN
CALL CTPMV( 'Upper', 'Conjugate', 'Non-unit', K-1, AFAC,
$ AFAC( KC ), 1 )
KC = KC - ( K-1 )
END IF
30 CONTINUE
*
* Compute the difference L*L' - A
*
KC = 1
DO 50 K = 1, N
DO 40 I = 1, K - 1
AFAC( KC+I-1 ) = AFAC( KC+I-1 ) - A( KC+I-1 )
40 CONTINUE
AFAC( KC+K-1 ) = AFAC( KC+K-1 ) - REAL( A( KC+K-1 ) )
KC = KC + K
50 CONTINUE
*
* Compute the product L*L', overwriting L.
*
ELSE
KC = ( N*( N+1 ) ) / 2
DO 60 K = N, 1, -1
*
* Add a multiple of column K of the factor L to each of
* columns K+1 through N.
*
IF( K.LT.N )
$ CALL CHPR( 'Lower', N-K, ONE, AFAC( KC+1 ), 1,
$ AFAC( KC+N-K+1 ) )
*
* Scale column K by the diagonal element.
*
TC = AFAC( KC )
CALL CSCAL( N-K+1, TC, AFAC( KC ), 1 )
*
KC = KC - ( N-K+2 )
60 CONTINUE
*
* Compute the difference U'*U - A
*
KC = 1
DO 80 K = 1, N
AFAC( KC ) = AFAC( KC ) - REAL( A( KC ) )
DO 70 I = K + 1, N
AFAC( KC+I-K ) = AFAC( KC+I-K ) - A( KC+I-K )
70 CONTINUE
KC = KC + N - K + 1
80 CONTINUE
END IF
*
* Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
RESID = CLANHP( '1', UPLO, N, AFAC, RWORK )
*
RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
*
RETURN
*
* End of CPPT01
*
END
|
