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
|
*> \brief \b DGEBAK
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DGEBAK + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgebak.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgebak.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgebak.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOB, SIDE
* INTEGER IHI, ILO, INFO, LDV, M, N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION SCALE( * ), V( LDV, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGEBAK forms the right or left eigenvectors of a real general matrix
*> by backward transformation on the computed eigenvectors of the
*> balanced matrix output by DGEBAL.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] JOB
*> \verbatim
*> JOB is CHARACTER*1
*> Specifies the type of backward transformation required:
*> = 'N', do nothing, return immediately;
*> = 'P', do backward transformation for permutation only;
*> = 'S', do backward transformation for scaling only;
*> = 'B', do backward transformations for both permutation and
*> scaling.
*> JOB must be the same as the argument JOB supplied to DGEBAL.
*> \endverbatim
*>
*> \param[in] SIDE
*> \verbatim
*> SIDE is CHARACTER*1
*> = 'R': V contains right eigenvectors;
*> = 'L': V contains left eigenvectors.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows of the matrix V. N >= 0.
*> \endverbatim
*>
*> \param[in] ILO
*> \verbatim
*> ILO is INTEGER
*> \endverbatim
*>
*> \param[in] IHI
*> \verbatim
*> IHI is INTEGER
*> The integers ILO and IHI determined by DGEBAL.
*> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
*> \endverbatim
*>
*> \param[in] SCALE
*> \verbatim
*> SCALE is DOUBLE PRECISION array, dimension (N)
*> Details of the permutation and scaling factors, as returned
*> by DGEBAL.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of columns of the matrix V. M >= 0.
*> \endverbatim
*>
*> \param[in,out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension (LDV,M)
*> On entry, the matrix of right or left eigenvectors to be
*> transformed, as returned by DHSEIN or DTREVC.
*> On exit, V is overwritten by the transformed eigenvectors.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*> LDV is INTEGER
*> The leading dimension of the array V. LDV >= max(1,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 doubleGEcomputational
*
* =====================================================================
SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
$ 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 JOB, SIDE
INTEGER IHI, ILO, INFO, LDV, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION SCALE( * ), V( LDV, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LEFTV, RIGHTV
INTEGER I, II, K
DOUBLE PRECISION S
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DSCAL, DSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Decode and Test the input parameters
*
RIGHTV = LSAME( SIDE, 'R' )
LEFTV = LSAME( SIDE, 'L' )
*
INFO = 0
IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
$ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
INFO = -1
ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
INFO = -5
ELSE IF( M.LT.0 ) THEN
INFO = -7
ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGEBAK', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
IF( M.EQ.0 )
$ RETURN
IF( LSAME( JOB, 'N' ) )
$ RETURN
*
IF( ILO.EQ.IHI )
$ GO TO 30
*
* Backward balance
*
IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
*
IF( RIGHTV ) THEN
DO 10 I = ILO, IHI
S = SCALE( I )
CALL DSCAL( M, S, V( I, 1 ), LDV )
10 CONTINUE
END IF
*
IF( LEFTV ) THEN
DO 20 I = ILO, IHI
S = ONE / SCALE( I )
CALL DSCAL( M, S, V( I, 1 ), LDV )
20 CONTINUE
END IF
*
END IF
*
* Backward permutation
*
* For I = ILO-1 step -1 until 1,
* IHI+1 step 1 until N do --
*
30 CONTINUE
IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
IF( RIGHTV ) THEN
DO 40 II = 1, N
I = II
IF( I.GE.ILO .AND. I.LE.IHI )
$ GO TO 40
IF( I.LT.ILO )
$ I = ILO - II
K = SCALE( I )
IF( K.EQ.I )
$ GO TO 40
CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
40 CONTINUE
END IF
*
IF( LEFTV ) THEN
DO 50 II = 1, N
I = II
IF( I.GE.ILO .AND. I.LE.IHI )
$ GO TO 50
IF( I.LT.ILO )
$ I = ILO - II
K = SCALE( I )
IF( K.EQ.I )
$ GO TO 50
CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
50 CONTINUE
END IF
END IF
*
RETURN
*
* End of DGEBAK
*
END
|
