1: SUBROUTINE ZGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
2: $ LDV, INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER JOB, SIDE
11: INTEGER IHI, ILO, INFO, LDV, M, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION LSCALE( * ), RSCALE( * )
15: COMPLEX*16 V( LDV, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZGGBAK forms the right or left eigenvectors of a complex generalized
22: * eigenvalue problem A*x = lambda*B*x, by backward transformation on
23: * the computed eigenvectors of the balanced pair of matrices output by
24: * ZGGBAL.
25: *
26: * Arguments
27: * =========
28: *
29: * JOB (input) CHARACTER*1
30: * Specifies the type of backward transformation required:
31: * = 'N': do nothing, return immediately;
32: * = 'P': do backward transformation for permutation only;
33: * = 'S': do backward transformation for scaling only;
34: * = 'B': do backward transformations for both permutation and
35: * scaling.
36: * JOB must be the same as the argument JOB supplied to ZGGBAL.
37: *
38: * SIDE (input) CHARACTER*1
39: * = 'R': V contains right eigenvectors;
40: * = 'L': V contains left eigenvectors.
41: *
42: * N (input) INTEGER
43: * The number of rows of the matrix V. N >= 0.
44: *
45: * ILO (input) INTEGER
46: * IHI (input) INTEGER
47: * The integers ILO and IHI determined by ZGGBAL.
48: * 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
49: *
50: * LSCALE (input) DOUBLE PRECISION array, dimension (N)
51: * Details of the permutations and/or scaling factors applied
52: * to the left side of A and B, as returned by ZGGBAL.
53: *
54: * RSCALE (input) DOUBLE PRECISION array, dimension (N)
55: * Details of the permutations and/or scaling factors applied
56: * to the right side of A and B, as returned by ZGGBAL.
57: *
58: * M (input) INTEGER
59: * The number of columns of the matrix V. M >= 0.
60: *
61: * V (input/output) COMPLEX*16 array, dimension (LDV,M)
62: * On entry, the matrix of right or left eigenvectors to be
63: * transformed, as returned by ZTGEVC.
64: * On exit, V is overwritten by the transformed eigenvectors.
65: *
66: * LDV (input) INTEGER
67: * The leading dimension of the matrix V. LDV >= max(1,N).
68: *
69: * INFO (output) INTEGER
70: * = 0: successful exit.
71: * < 0: if INFO = -i, the i-th argument had an illegal value.
72: *
73: * Further Details
74: * ===============
75: *
76: * See R.C. Ward, Balancing the generalized eigenvalue problem,
77: * SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
78: *
79: * =====================================================================
80: *
81: * .. Local Scalars ..
82: LOGICAL LEFTV, RIGHTV
83: INTEGER I, K
84: * ..
85: * .. External Functions ..
86: LOGICAL LSAME
87: EXTERNAL LSAME
88: * ..
89: * .. External Subroutines ..
90: EXTERNAL XERBLA, ZDSCAL, ZSWAP
91: * ..
92: * .. Intrinsic Functions ..
93: INTRINSIC MAX
94: * ..
95: * .. Executable Statements ..
96: *
97: * Test the input parameters
98: *
99: RIGHTV = LSAME( SIDE, 'R' )
100: LEFTV = LSAME( SIDE, 'L' )
101: *
102: INFO = 0
103: IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
104: $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
105: INFO = -1
106: ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
107: INFO = -2
108: ELSE IF( N.LT.0 ) THEN
109: INFO = -3
110: ELSE IF( ILO.LT.1 ) THEN
111: INFO = -4
112: ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
113: INFO = -4
114: ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
115: $ THEN
116: INFO = -5
117: ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
118: INFO = -5
119: ELSE IF( M.LT.0 ) THEN
120: INFO = -8
121: ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
122: INFO = -10
123: END IF
124: IF( INFO.NE.0 ) THEN
125: CALL XERBLA( 'ZGGBAK', -INFO )
126: RETURN
127: END IF
128: *
129: * Quick return if possible
130: *
131: IF( N.EQ.0 )
132: $ RETURN
133: IF( M.EQ.0 )
134: $ RETURN
135: IF( LSAME( JOB, 'N' ) )
136: $ RETURN
137: *
138: IF( ILO.EQ.IHI )
139: $ GO TO 30
140: *
141: * Backward balance
142: *
143: IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
144: *
145: * Backward transformation on right eigenvectors
146: *
147: IF( RIGHTV ) THEN
148: DO 10 I = ILO, IHI
149: CALL ZDSCAL( M, RSCALE( I ), V( I, 1 ), LDV )
150: 10 CONTINUE
151: END IF
152: *
153: * Backward transformation on left eigenvectors
154: *
155: IF( LEFTV ) THEN
156: DO 20 I = ILO, IHI
157: CALL ZDSCAL( M, LSCALE( I ), V( I, 1 ), LDV )
158: 20 CONTINUE
159: END IF
160: END IF
161: *
162: * Backward permutation
163: *
164: 30 CONTINUE
165: IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
166: *
167: * Backward permutation on right eigenvectors
168: *
169: IF( RIGHTV ) THEN
170: IF( ILO.EQ.1 )
171: $ GO TO 50
172: DO 40 I = ILO - 1, 1, -1
173: K = RSCALE( I )
174: IF( K.EQ.I )
175: $ GO TO 40
176: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
177: 40 CONTINUE
178: *
179: 50 CONTINUE
180: IF( IHI.EQ.N )
181: $ GO TO 70
182: DO 60 I = IHI + 1, N
183: K = RSCALE( I )
184: IF( K.EQ.I )
185: $ GO TO 60
186: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
187: 60 CONTINUE
188: END IF
189: *
190: * Backward permutation on left eigenvectors
191: *
192: 70 CONTINUE
193: IF( LEFTV ) THEN
194: IF( ILO.EQ.1 )
195: $ GO TO 90
196: DO 80 I = ILO - 1, 1, -1
197: K = LSCALE( I )
198: IF( K.EQ.I )
199: $ GO TO 80
200: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
201: 80 CONTINUE
202: *
203: 90 CONTINUE
204: IF( IHI.EQ.N )
205: $ GO TO 110
206: DO 100 I = IHI + 1, N
207: K = LSCALE( I )
208: IF( K.EQ.I )
209: $ GO TO 100
210: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
211: 100 CONTINUE
212: END IF
213: END IF
214: *
215: 110 CONTINUE
216: *
217: RETURN
218: *
219: * End of ZGGBAK
220: *
221: END
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