1: *> \brief \b ZGEBAK
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGEBAK + dependencies
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11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgebak.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgebak.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
22: * INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOB, SIDE
26: * INTEGER IHI, ILO, INFO, LDV, M, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION SCALE( * )
30: * COMPLEX*16 V( LDV, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZGEBAK forms the right or left eigenvectors of a complex general
40: *> matrix by backward transformation on the computed eigenvectors of the
41: *> balanced matrix output by ZGEBAL.
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 ZGEBAL.
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 ZGEBAL.
81: *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
82: *> \endverbatim
83: *>
84: *> \param[in] SCALE
85: *> \verbatim
86: *> SCALE is DOUBLE PRECISION array, dimension (N)
87: *> Details of the permutation and scaling factors, as returned
88: *> by ZGEBAL.
89: *> \endverbatim
90: *>
91: *> \param[in] M
92: *> \verbatim
93: *> M is INTEGER
94: *> The number of columns of the matrix V. M >= 0.
95: *> \endverbatim
96: *>
97: *> \param[in,out] V
98: *> \verbatim
99: *> V is COMPLEX*16 array, dimension (LDV,M)
100: *> On entry, the matrix of right or left eigenvectors to be
101: *> transformed, as returned by ZHSEIN or ZTREVC.
102: *> On exit, V is overwritten by the transformed eigenvectors.
103: *> \endverbatim
104: *>
105: *> \param[in] LDV
106: *> \verbatim
107: *> LDV is INTEGER
108: *> The leading dimension of the array V. LDV >= max(1,N).
109: *> \endverbatim
110: *>
111: *> \param[out] INFO
112: *> \verbatim
113: *> INFO is INTEGER
114: *> = 0: successful exit
115: *> < 0: if INFO = -i, the i-th argument had an illegal value.
116: *> \endverbatim
117: *
118: * Authors:
119: * ========
120: *
121: *> \author Univ. of Tennessee
122: *> \author Univ. of California Berkeley
123: *> \author Univ. of Colorado Denver
124: *> \author NAG Ltd.
125: *
126: *> \date November 2011
127: *
128: *> \ingroup complex16GEcomputational
129: *
130: * =====================================================================
131: SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
132: $ INFO )
133: *
134: * -- LAPACK computational routine (version 3.4.0) --
135: * -- LAPACK is a software package provided by Univ. of Tennessee, --
136: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137: * November 2011
138: *
139: * .. Scalar Arguments ..
140: CHARACTER JOB, SIDE
141: INTEGER IHI, ILO, INFO, LDV, M, N
142: * ..
143: * .. Array Arguments ..
144: DOUBLE PRECISION SCALE( * )
145: COMPLEX*16 V( LDV, * )
146: * ..
147: *
148: * =====================================================================
149: *
150: * .. Parameters ..
151: DOUBLE PRECISION ONE
152: PARAMETER ( ONE = 1.0D+0 )
153: * ..
154: * .. Local Scalars ..
155: LOGICAL LEFTV, RIGHTV
156: INTEGER I, II, K
157: DOUBLE PRECISION S
158: * ..
159: * .. External Functions ..
160: LOGICAL LSAME
161: EXTERNAL LSAME
162: * ..
163: * .. External Subroutines ..
164: EXTERNAL XERBLA, ZDSCAL, ZSWAP
165: * ..
166: * .. Intrinsic Functions ..
167: INTRINSIC MAX, MIN
168: * ..
169: * .. Executable Statements ..
170: *
171: * Decode and Test the input parameters
172: *
173: RIGHTV = LSAME( SIDE, 'R' )
174: LEFTV = LSAME( SIDE, 'L' )
175: *
176: INFO = 0
177: IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
178: $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
179: INFO = -1
180: ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
181: INFO = -2
182: ELSE IF( N.LT.0 ) THEN
183: INFO = -3
184: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
185: INFO = -4
186: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
187: INFO = -5
188: ELSE IF( M.LT.0 ) THEN
189: INFO = -7
190: ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
191: INFO = -9
192: END IF
193: IF( INFO.NE.0 ) THEN
194: CALL XERBLA( 'ZGEBAK', -INFO )
195: RETURN
196: END IF
197: *
198: * Quick return if possible
199: *
200: IF( N.EQ.0 )
201: $ RETURN
202: IF( M.EQ.0 )
203: $ RETURN
204: IF( LSAME( JOB, 'N' ) )
205: $ RETURN
206: *
207: IF( ILO.EQ.IHI )
208: $ GO TO 30
209: *
210: * Backward balance
211: *
212: IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
213: *
214: IF( RIGHTV ) THEN
215: DO 10 I = ILO, IHI
216: S = SCALE( I )
217: CALL ZDSCAL( M, S, V( I, 1 ), LDV )
218: 10 CONTINUE
219: END IF
220: *
221: IF( LEFTV ) THEN
222: DO 20 I = ILO, IHI
223: S = ONE / SCALE( I )
224: CALL ZDSCAL( M, S, V( I, 1 ), LDV )
225: 20 CONTINUE
226: END IF
227: *
228: END IF
229: *
230: * Backward permutation
231: *
232: * For I = ILO-1 step -1 until 1,
233: * IHI+1 step 1 until N do --
234: *
235: 30 CONTINUE
236: IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
237: IF( RIGHTV ) THEN
238: DO 40 II = 1, N
239: I = II
240: IF( I.GE.ILO .AND. I.LE.IHI )
241: $ GO TO 40
242: IF( I.LT.ILO )
243: $ I = ILO - II
244: K = SCALE( I )
245: IF( K.EQ.I )
246: $ GO TO 40
247: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
248: 40 CONTINUE
249: END IF
250: *
251: IF( LEFTV ) THEN
252: DO 50 II = 1, N
253: I = II
254: IF( I.GE.ILO .AND. I.LE.IHI )
255: $ GO TO 50
256: IF( I.LT.ILO )
257: $ I = ILO - II
258: K = SCALE( I )
259: IF( K.EQ.I )
260: $ GO TO 50
261: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
262: 50 CONTINUE
263: END IF
264: END IF
265: *
266: RETURN
267: *
268: * End of ZGEBAK
269: *
270: END
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