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
|
*> \brief \b CTREXC
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CTREXC + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctrexc.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctrexc.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctrexc.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
*
* .. Scalar Arguments ..
* CHARACTER COMPQ
* INTEGER IFST, ILST, INFO, LDQ, LDT, N
* ..
* .. Array Arguments ..
* COMPLEX Q( LDQ, * ), T( LDT, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTREXC reorders the Schur factorization of a complex matrix
*> A = Q*T*Q**H, so that the diagonal element of T with row index IFST
*> is moved to row ILST.
*>
*> The Schur form T is reordered by a unitary similarity transformation
*> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
*> postmultplying it with Z.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> COMPQ is CHARACTER*1
*> = 'V': update the matrix Q of Schur vectors;
*> = 'N': do not update Q.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix T. N >= 0.
*> If N == 0 arguments ILST and IFST may be any value.
*> \endverbatim
*>
*> \param[in,out] T
*> \verbatim
*> T is COMPLEX array, dimension (LDT,N)
*> On entry, the upper triangular matrix T.
*> On exit, the reordered upper triangular matrix.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*> Q is COMPLEX array, dimension (LDQ,N)
*> On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
*> On exit, if COMPQ = 'V', Q has been postmultiplied by the
*> unitary transformation matrix Z which reorders T.
*> If COMPQ = 'N', Q is not referenced.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= 1, and if
*> COMPQ = 'V', LDQ >= max(1,N).
*> \endverbatim
*>
*> \param[in] IFST
*> \verbatim
*> IFST is INTEGER
*> \endverbatim
*>
*> \param[in] ILST
*> \verbatim
*> ILST is INTEGER
*>
*> Specify the reordering of the diagonal elements of T:
*> The element with row index IFST is moved to row ILST by a
*> sequence of transpositions between adjacent elements.
*> 1 <= IFST <= N; 1 <= ILST <= N.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
*
* -- LAPACK computational 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 ..
CHARACTER COMPQ
INTEGER IFST, ILST, INFO, LDQ, LDT, N
* ..
* .. Array Arguments ..
COMPLEX Q( LDQ, * ), T( LDT, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL WANTQ
INTEGER K, M1, M2, M3
REAL CS
COMPLEX SN, T11, T22, TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CLARTG, CROT, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX
* ..
* .. Executable Statements ..
*
* Decode and test the input parameters.
*
INFO = 0
WANTQ = LSAME( COMPQ, 'V' )
IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
INFO = -6
ELSE IF(( IFST.LT.1 .OR. IFST.GT.N ).AND.( N.GT.0 )) THEN
INFO = -7
ELSE IF(( ILST.LT.1 .OR. ILST.GT.N ).AND.( N.GT.0 )) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTREXC', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 .OR. IFST.EQ.ILST )
$ RETURN
*
IF( IFST.LT.ILST ) THEN
*
* Move the IFST-th diagonal element forward down the diagonal.
*
M1 = 0
M2 = -1
M3 = 1
ELSE
*
* Move the IFST-th diagonal element backward up the diagonal.
*
M1 = -1
M2 = 0
M3 = -1
END IF
*
DO 10 K = IFST + M1, ILST + M2, M3
*
* Interchange the k-th and (k+1)-th diagonal elements.
*
T11 = T( K, K )
T22 = T( K+1, K+1 )
*
* Determine the transformation to perform the interchange.
*
CALL CLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP )
*
* Apply transformation to the matrix T.
*
IF( K+2.LE.N )
$ CALL CROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
$ SN )
CALL CROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS, CONJG( SN ) )
*
T( K, K ) = T22
T( K+1, K+1 ) = T11
*
IF( WANTQ ) THEN
*
* Accumulate transformation in the matrix Q.
*
CALL CROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
$ CONJG( SN ) )
END IF
*
10 CONTINUE
*
RETURN
*
* End of CTREXC
*
END
|