1: *> \brief \b DGEBAK
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGEBAK + 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/dgebak.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgebak.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGEBAK( 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( * ), V( LDV, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DGEBAK forms the right or left eigenvectors of a real general matrix
39: *> by backward transformation on the computed eigenvectors of the
40: *> balanced matrix output by DGEBAL.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] JOB
47: *> \verbatim
48: *> JOB is CHARACTER*1
49: *> Specifies the type of backward transformation required:
50: *> = 'N': do nothing, return immediately;
51: *> = 'P': do backward transformation for permutation only;
52: *> = 'S': do backward transformation for scaling only;
53: *> = 'B': do backward transformations for both permutation and
54: *> scaling.
55: *> JOB must be the same as the argument JOB supplied to DGEBAL.
56: *> \endverbatim
57: *>
58: *> \param[in] SIDE
59: *> \verbatim
60: *> SIDE is CHARACTER*1
61: *> = 'R': V contains right eigenvectors;
62: *> = 'L': V contains left eigenvectors.
63: *> \endverbatim
64: *>
65: *> \param[in] N
66: *> \verbatim
67: *> N is INTEGER
68: *> The number of rows of the matrix V. N >= 0.
69: *> \endverbatim
70: *>
71: *> \param[in] ILO
72: *> \verbatim
73: *> ILO is INTEGER
74: *> \endverbatim
75: *>
76: *> \param[in] IHI
77: *> \verbatim
78: *> IHI is INTEGER
79: *> The integers ILO and IHI determined by DGEBAL.
80: *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
81: *> \endverbatim
82: *>
83: *> \param[in] SCALE
84: *> \verbatim
85: *> SCALE is DOUBLE PRECISION array, dimension (N)
86: *> Details of the permutation and scaling factors, as returned
87: *> by DGEBAL.
88: *> \endverbatim
89: *>
90: *> \param[in] M
91: *> \verbatim
92: *> M is INTEGER
93: *> The number of columns of the matrix V. M >= 0.
94: *> \endverbatim
95: *>
96: *> \param[in,out] V
97: *> \verbatim
98: *> V is DOUBLE PRECISION array, dimension (LDV,M)
99: *> On entry, the matrix of right or left eigenvectors to be
100: *> transformed, as returned by DHSEIN or DTREVC.
101: *> On exit, V is overwritten by the transformed eigenvectors.
102: *> \endverbatim
103: *>
104: *> \param[in] LDV
105: *> \verbatim
106: *> LDV is INTEGER
107: *> The leading dimension of the array V. LDV >= max(1,N).
108: *> \endverbatim
109: *>
110: *> \param[out] INFO
111: *> \verbatim
112: *> INFO is INTEGER
113: *> = 0: successful exit
114: *> < 0: if INFO = -i, the i-th argument had an illegal value.
115: *> \endverbatim
116: *
117: * Authors:
118: * ========
119: *
120: *> \author Univ. of Tennessee
121: *> \author Univ. of California Berkeley
122: *> \author Univ. of Colorado Denver
123: *> \author NAG Ltd.
124: *
125: *> \ingroup doubleGEcomputational
126: *
127: * =====================================================================
128: SUBROUTINE DGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
129: $ INFO )
130: *
131: * -- LAPACK computational routine --
132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134: *
135: * .. Scalar Arguments ..
136: CHARACTER JOB, SIDE
137: INTEGER IHI, ILO, INFO, LDV, M, N
138: * ..
139: * .. Array Arguments ..
140: DOUBLE PRECISION SCALE( * ), V( LDV, * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE
147: PARAMETER ( ONE = 1.0D+0 )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL LEFTV, RIGHTV
151: INTEGER I, II, K
152: DOUBLE PRECISION S
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: EXTERNAL LSAME
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL DSCAL, DSWAP, XERBLA
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC MAX, MIN
163: * ..
164: * .. Executable Statements ..
165: *
166: * Decode and Test the input parameters
167: *
168: RIGHTV = LSAME( SIDE, 'R' )
169: LEFTV = LSAME( SIDE, 'L' )
170: *
171: INFO = 0
172: IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
173: $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
174: INFO = -1
175: ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
176: INFO = -2
177: ELSE IF( N.LT.0 ) THEN
178: INFO = -3
179: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
180: INFO = -4
181: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
182: INFO = -5
183: ELSE IF( M.LT.0 ) THEN
184: INFO = -7
185: ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
186: INFO = -9
187: END IF
188: IF( INFO.NE.0 ) THEN
189: CALL XERBLA( 'DGEBAK', -INFO )
190: RETURN
191: END IF
192: *
193: * Quick return if possible
194: *
195: IF( N.EQ.0 )
196: $ RETURN
197: IF( M.EQ.0 )
198: $ RETURN
199: IF( LSAME( JOB, 'N' ) )
200: $ RETURN
201: *
202: IF( ILO.EQ.IHI )
203: $ GO TO 30
204: *
205: * Backward balance
206: *
207: IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
208: *
209: IF( RIGHTV ) THEN
210: DO 10 I = ILO, IHI
211: S = SCALE( I )
212: CALL DSCAL( M, S, V( I, 1 ), LDV )
213: 10 CONTINUE
214: END IF
215: *
216: IF( LEFTV ) THEN
217: DO 20 I = ILO, IHI
218: S = ONE / SCALE( I )
219: CALL DSCAL( M, S, V( I, 1 ), LDV )
220: 20 CONTINUE
221: END IF
222: *
223: END IF
224: *
225: * Backward permutation
226: *
227: * For I = ILO-1 step -1 until 1,
228: * IHI+1 step 1 until N do --
229: *
230: 30 CONTINUE
231: IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
232: IF( RIGHTV ) THEN
233: DO 40 II = 1, N
234: I = II
235: IF( I.GE.ILO .AND. I.LE.IHI )
236: $ GO TO 40
237: IF( I.LT.ILO )
238: $ I = ILO - II
239: K = INT( SCALE( I ) )
240: IF( K.EQ.I )
241: $ GO TO 40
242: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
243: 40 CONTINUE
244: END IF
245: *
246: IF( LEFTV ) THEN
247: DO 50 II = 1, N
248: I = II
249: IF( I.GE.ILO .AND. I.LE.IHI )
250: $ GO TO 50
251: IF( I.LT.ILO )
252: $ I = ILO - II
253: K = INT( SCALE( I ) )
254: IF( K.EQ.I )
255: $ GO TO 50
256: CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
257: 50 CONTINUE
258: END IF
259: END IF
260: *
261: RETURN
262: *
263: * End of DGEBAK
264: *
265: END
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