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
|
*> \brief \b CGET36
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* .. Scalar Arguments ..
* INTEGER KNT, LMAX, NIN, NINFO
* REAL RMAX
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGET36 tests CTREXC, a routine for reordering diagonal entries of a
*> matrix in complex Schur form. Thus, CLAEXC computes a unitary matrix
*> Q such that
*>
*> Q' * T1 * Q = T2
*>
*> and where one of the diagonal blocks of T1 (the one at row IFST) has
*> been moved to position ILST.
*>
*> The test code verifies that the residual Q'*T1*Q-T2 is small, that T2
*> is in Schur form, and that the final position of the IFST block is
*> ILST.
*>
*> The test matrices are read from a file with logical unit number NIN.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is REAL
*> Value of the largest test ratio.
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*> LMAX is INTEGER
*> Example number where largest test ratio achieved.
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER
*> Number of examples where INFO is nonzero.
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*>
*> \param[in] NIN
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex_eig
*
* =====================================================================
SUBROUTINE CGET36( RMAX, LMAX, NINFO, KNT, NIN )
*
* -- LAPACK test routine (version 3.1) --
* -- 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 KNT, LMAX, NIN, NINFO
REAL RMAX
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
INTEGER LDT, LWORK
PARAMETER ( LDT = 10, LWORK = 2*LDT*LDT )
* ..
* .. Local Scalars ..
INTEGER I, IFST, ILST, INFO1, INFO2, J, N
REAL EPS, RES
COMPLEX CTEMP
* ..
* .. Local Arrays ..
REAL RESULT( 2 ), RWORK( LDT )
COMPLEX DIAG( LDT ), Q( LDT, LDT ), T1( LDT, LDT ),
$ T2( LDT, LDT ), TMP( LDT, LDT ), WORK( LWORK )
* ..
* .. External Functions ..
REAL SLAMCH
EXTERNAL SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CCOPY, CHST01, CLACPY, CLASET, CTREXC
* ..
* .. Executable Statements ..
*
EPS = SLAMCH( 'P' )
RMAX = ZERO
LMAX = 0
KNT = 0
NINFO = 0
*
* Read input data until N=0
*
10 CONTINUE
READ( NIN, FMT = * )N, IFST, ILST
IF( N.EQ.0 )
$ RETURN
KNT = KNT + 1
DO 20 I = 1, N
READ( NIN, FMT = * )( TMP( I, J ), J = 1, N )
20 CONTINUE
CALL CLACPY( 'F', N, N, TMP, LDT, T1, LDT )
CALL CLACPY( 'F', N, N, TMP, LDT, T2, LDT )
RES = ZERO
*
* Test without accumulating Q
*
CALL CLASET( 'Full', N, N, CZERO, CONE, Q, LDT )
CALL CTREXC( 'N', N, T1, LDT, Q, LDT, IFST, ILST, INFO1 )
DO 40 I = 1, N
DO 30 J = 1, N
IF( I.EQ.J .AND. Q( I, J ).NE.CONE )
$ RES = RES + ONE / EPS
IF( I.NE.J .AND. Q( I, J ).NE.CZERO )
$ RES = RES + ONE / EPS
30 CONTINUE
40 CONTINUE
*
* Test with accumulating Q
*
CALL CLASET( 'Full', N, N, CZERO, CONE, Q, LDT )
CALL CTREXC( 'V', N, T2, LDT, Q, LDT, IFST, ILST, INFO2 )
*
* Compare T1 with T2
*
DO 60 I = 1, N
DO 50 J = 1, N
IF( T1( I, J ).NE.T2( I, J ) )
$ RES = RES + ONE / EPS
50 CONTINUE
60 CONTINUE
IF( INFO1.NE.0 .OR. INFO2.NE.0 )
$ NINFO = NINFO + 1
IF( INFO1.NE.INFO2 )
$ RES = RES + ONE / EPS
*
* Test for successful reordering of T2
*
CALL CCOPY( N, TMP, LDT+1, DIAG, 1 )
IF( IFST.LT.ILST ) THEN
DO 70 I = IFST + 1, ILST
CTEMP = DIAG( I )
DIAG( I ) = DIAG( I-1 )
DIAG( I-1 ) = CTEMP
70 CONTINUE
ELSE IF( IFST.GT.ILST ) THEN
DO 80 I = IFST - 1, ILST, -1
CTEMP = DIAG( I+1 )
DIAG( I+1 ) = DIAG( I )
DIAG( I ) = CTEMP
80 CONTINUE
END IF
DO 90 I = 1, N
IF( T2( I, I ).NE.DIAG( I ) )
$ RES = RES + ONE / EPS
90 CONTINUE
*
* Test for small residual, and orthogonality of Q
*
CALL CHST01( N, 1, N, TMP, LDT, T2, LDT, Q, LDT, WORK, LWORK,
$ RWORK, RESULT )
RES = RES + RESULT( 1 ) + RESULT( 2 )
*
* Test for T2 being in Schur form
*
DO 110 J = 1, N - 1
DO 100 I = J + 1, N
IF( T2( I, J ).NE.CZERO )
$ RES = RES + ONE / EPS
100 CONTINUE
110 CONTINUE
IF( RES.GT.RMAX ) THEN
RMAX = RES
LMAX = KNT
END IF
GO TO 10
*
* End of CGET36
*
END
|