1: *> \brief \b DGGBAK
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGGBAK + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dggbak.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
22: * LDV, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOB, SIDE
26: * INTEGER IHI, ILO, INFO, LDV, M, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DGGBAK forms the right or left eigenvectors of a real generalized
39: *> eigenvalue problem A*x = lambda*B*x, by backward transformation on
40: *> the computed eigenvectors of the balanced pair of matrices output by
41: *> DGGBAL.
42: *> \endverbatim
43: *
44: * Arguments:
45: * ==========
46: *
47: *> \param[in] JOB
48: *> \verbatim
49: *> JOB is CHARACTER*1
50: *> Specifies the type of backward transformation required:
51: *> = 'N': do nothing, return immediately;
52: *> = 'P': do backward transformation for permutation only;
53: *> = 'S': do backward transformation for scaling only;
54: *> = 'B': do backward transformations for both permutation and
55: *> scaling.
56: *> JOB must be the same as the argument JOB supplied to DGGBAL.
57: *> \endverbatim
58: *>
59: *> \param[in] SIDE
60: *> \verbatim
61: *> SIDE is CHARACTER*1
62: *> = 'R': V contains right eigenvectors;
63: *> = 'L': V contains left eigenvectors.
64: *> \endverbatim
65: *>
66: *> \param[in] N
67: *> \verbatim
68: *> N is INTEGER
69: *> The number of rows of the matrix V. N >= 0.
70: *> \endverbatim
71: *>
72: *> \param[in] ILO
73: *> \verbatim
74: *> ILO is INTEGER
75: *> \endverbatim
76: *>
77: *> \param[in] IHI
78: *> \verbatim
79: *> IHI is INTEGER
80: *> The integers ILO and IHI determined by DGGBAL.
81: *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
82: *> \endverbatim
83: *>
84: *> \param[in] LSCALE
85: *> \verbatim
86: *> LSCALE is DOUBLE PRECISION array, dimension (N)
87: *> Details of the permutations and/or scaling factors applied
88: *> to the left side of A and B, as returned by DGGBAL.
89: *> \endverbatim
90: *>
91: *> \param[in] RSCALE
92: *> \verbatim
93: *> RSCALE is DOUBLE PRECISION array, dimension (N)
94: *> Details of the permutations and/or scaling factors applied
95: *> to the right side of A and B, as returned by DGGBAL.
96: *> \endverbatim
97: *>
98: *> \param[in] M
99: *> \verbatim
100: *> M is INTEGER
101: *> The number of columns of the matrix V. M >= 0.
102: *> \endverbatim
103: *>
104: *> \param[in,out] V
105: *> \verbatim
106: *> V is DOUBLE PRECISION array, dimension (LDV,M)
107: *> On entry, the matrix of right or left eigenvectors to be
108: *> transformed, as returned by DTGEVC.
109: *> On exit, V is overwritten by the transformed eigenvectors.
110: *> \endverbatim
111: *>
112: *> \param[in] LDV
113: *> \verbatim
114: *> LDV is INTEGER
115: *> The leading dimension of the matrix V. LDV >= max(1,N).
116: *> \endverbatim
117: *>
118: *> \param[out] INFO
119: *> \verbatim
120: *> INFO is INTEGER
121: *> = 0: successful exit.
122: *> < 0: if INFO = -i, the i-th argument had an illegal value.
123: *> \endverbatim
124: *
125: * Authors:
126: * ========
127: *
128: *> \author Univ. of Tennessee
129: *> \author Univ. of California Berkeley
130: *> \author Univ. of Colorado Denver
131: *> \author NAG Ltd.
132: *
133: *> \ingroup doubleGBcomputational
134: *
135: *> \par Further Details:
136: * =====================
137: *>
138: *> \verbatim
139: *>
140: *> See R.C. Ward, Balancing the generalized eigenvalue problem,
141: *> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
142: *> \endverbatim
143: *>
144: * =====================================================================
145: SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
146: $ LDV, INFO )
147: *
148: * -- LAPACK computational routine --
149: * -- LAPACK is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151: *
152: * .. Scalar Arguments ..
153: CHARACTER JOB, SIDE
154: INTEGER IHI, ILO, INFO, LDV, M, N
155: * ..
156: * .. Array Arguments ..
157: DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * )
158: * ..
159: *
160: * =====================================================================
161: *
162: * .. Local Scalars ..
163: LOGICAL LEFTV, RIGHTV
164: INTEGER I, K
165: * ..
166: * .. External Functions ..
167: LOGICAL LSAME
168: EXTERNAL LSAME
169: * ..
170: * .. External Subroutines ..
171: EXTERNAL DSCAL, DSWAP, XERBLA
172: * ..
173: * .. Intrinsic Functions ..
174: INTRINSIC MAX, INT
175: * ..
176: * .. Executable Statements ..
177: *
178: * Test the input parameters
179: *
180: RIGHTV = LSAME( SIDE, 'R' )
181: LEFTV = LSAME( SIDE, 'L' )
182: *
183: INFO = 0
184: IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
185: $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
186: INFO = -1
187: ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
188: INFO = -2
189: ELSE IF( N.LT.0 ) THEN
190: INFO = -3
191: ELSE IF( ILO.LT.1 ) THEN
192: INFO = -4
193: ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
194: INFO = -4
195: ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
196: $ THEN
197: INFO = -5
198: ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
199: INFO = -5
200: ELSE IF( M.LT.0 ) THEN
201: INFO = -8
202: ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
203: INFO = -10
204: END IF
205: IF( INFO.NE.0 ) THEN
206: CALL XERBLA( 'DGGBAK', -INFO )
207: RETURN
208: END IF
209: *
210: * Quick return if possible
211: *
212: IF( N.EQ.0 )
213: $ RETURN
214: IF( M.EQ.0 )
215: $ RETURN
216: IF( LSAME( JOB, 'N' ) )
217: $ RETURN
218: *
219: IF( ILO.EQ.IHI )
220: $ GO TO 30
221: *
222: * Backward balance
223: *
224: IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
225: *
226: * Backward transformation on right eigenvectors
227: *
228: IF( RIGHTV ) THEN
229: DO 10 I = ILO, IHI
230: CALL DSCAL( M, RSCALE( I ), V( I, 1 ), LDV )
231: 10 CONTINUE
232: END IF
233: *
234: * Backward transformation on left eigenvectors
235: *
236: IF( LEFTV ) THEN
237: DO 20 I = ILO, IHI
238: CALL DSCAL( M, LSCALE( I ), V( I, 1 ), LDV )
239: 20 CONTINUE
240: END IF
241: END IF
242: *
243: * Backward permutation
244: *
245: 30 CONTINUE
246: IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
247: *
248: * Backward permutation on right eigenvectors
249: *
250: IF( RIGHTV ) THEN
251: IF( ILO.EQ.1 )
252: $ GO TO 50
253: *
254: DO 40 I = ILO - 1, 1, -1
255: K = INT(RSCALE( I ))
256: IF( K.EQ.I )
257: $ GO TO 40
258: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
259: 40 CONTINUE
260: *
261: 50 CONTINUE
262: IF( IHI.EQ.N )
263: $ GO TO 70
264: DO 60 I = IHI + 1, N
265: K = INT(RSCALE( I ))
266: IF( K.EQ.I )
267: $ GO TO 60
268: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
269: 60 CONTINUE
270: END IF
271: *
272: * Backward permutation on left eigenvectors
273: *
274: 70 CONTINUE
275: IF( LEFTV ) THEN
276: IF( ILO.EQ.1 )
277: $ GO TO 90
278: DO 80 I = ILO - 1, 1, -1
279: K = INT(LSCALE( I ))
280: IF( K.EQ.I )
281: $ GO TO 80
282: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
283: 80 CONTINUE
284: *
285: 90 CONTINUE
286: IF( IHI.EQ.N )
287: $ GO TO 110
288: DO 100 I = IHI + 1, N
289: K = INT(LSCALE( I ))
290: IF( K.EQ.I )
291: $ GO TO 100
292: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
293: 100 CONTINUE
294: END IF
295: END IF
296: *
297: 110 CONTINUE
298: *
299: RETURN
300: *
301: * End of DGGBAK
302: *
303: END
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