Annotation of rpl/lapack/lapack/zggbak.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZGGBAK
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGGBAK + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggbak.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggbak.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggbak.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGGBAK( 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( * )
! 30: * COMPLEX*16 V( LDV, * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> ZGGBAK forms the right or left eigenvectors of a complex generalized
! 40: *> eigenvalue problem A*x = lambda*B*x, by backward transformation on
! 41: *> the computed eigenvectors of the balanced pair of matrices output by
! 42: *> ZGGBAL.
! 43: *> \endverbatim
! 44: *
! 45: * Arguments:
! 46: * ==========
! 47: *
! 48: *> \param[in] JOB
! 49: *> \verbatim
! 50: *> JOB is CHARACTER*1
! 51: *> Specifies the type of backward transformation required:
! 52: *> = 'N': do nothing, return immediately;
! 53: *> = 'P': do backward transformation for permutation only;
! 54: *> = 'S': do backward transformation for scaling only;
! 55: *> = 'B': do backward transformations for both permutation and
! 56: *> scaling.
! 57: *> JOB must be the same as the argument JOB supplied to ZGGBAL.
! 58: *> \endverbatim
! 59: *>
! 60: *> \param[in] SIDE
! 61: *> \verbatim
! 62: *> SIDE is CHARACTER*1
! 63: *> = 'R': V contains right eigenvectors;
! 64: *> = 'L': V contains left eigenvectors.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] N
! 68: *> \verbatim
! 69: *> N is INTEGER
! 70: *> The number of rows of the matrix V. N >= 0.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] ILO
! 74: *> \verbatim
! 75: *> ILO is INTEGER
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] IHI
! 79: *> \verbatim
! 80: *> IHI is INTEGER
! 81: *> The integers ILO and IHI determined by ZGGBAL.
! 82: *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] LSCALE
! 86: *> \verbatim
! 87: *> LSCALE is DOUBLE PRECISION array, dimension (N)
! 88: *> Details of the permutations and/or scaling factors applied
! 89: *> to the left side of A and B, as returned by ZGGBAL.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[in] RSCALE
! 93: *> \verbatim
! 94: *> RSCALE is DOUBLE PRECISION array, dimension (N)
! 95: *> Details of the permutations and/or scaling factors applied
! 96: *> to the right side of A and B, as returned by ZGGBAL.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[in] M
! 100: *> \verbatim
! 101: *> M is INTEGER
! 102: *> The number of columns of the matrix V. M >= 0.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[in,out] V
! 106: *> \verbatim
! 107: *> V is COMPLEX*16 array, dimension (LDV,M)
! 108: *> On entry, the matrix of right or left eigenvectors to be
! 109: *> transformed, as returned by ZTGEVC.
! 110: *> On exit, V is overwritten by the transformed eigenvectors.
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in] LDV
! 114: *> \verbatim
! 115: *> LDV is INTEGER
! 116: *> The leading dimension of the matrix V. LDV >= max(1,N).
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[out] INFO
! 120: *> \verbatim
! 121: *> INFO is INTEGER
! 122: *> = 0: successful exit.
! 123: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 124: *> \endverbatim
! 125: *
! 126: * Authors:
! 127: * ========
! 128: *
! 129: *> \author Univ. of Tennessee
! 130: *> \author Univ. of California Berkeley
! 131: *> \author Univ. of Colorado Denver
! 132: *> \author NAG Ltd.
! 133: *
! 134: *> \date November 2011
! 135: *
! 136: *> \ingroup complex16GBcomputational
! 137: *
! 138: *> \par Further Details:
! 139: * =====================
! 140: *>
! 141: *> \verbatim
! 142: *>
! 143: *> See R.C. Ward, Balancing the generalized eigenvalue problem,
! 144: *> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
! 145: *> \endverbatim
! 146: *>
! 147: * =====================================================================
1.1 bertrand 148: SUBROUTINE ZGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
149: $ LDV, INFO )
150: *
1.8 ! bertrand 151: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 152: * -- LAPACK is a software package provided by Univ. of Tennessee, --
153: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 154: * November 2011
1.1 bertrand 155: *
156: * .. Scalar Arguments ..
157: CHARACTER JOB, SIDE
158: INTEGER IHI, ILO, INFO, LDV, M, N
159: * ..
160: * .. Array Arguments ..
161: DOUBLE PRECISION LSCALE( * ), RSCALE( * )
162: COMPLEX*16 V( LDV, * )
163: * ..
164: *
165: * =====================================================================
166: *
167: * .. Local Scalars ..
168: LOGICAL LEFTV, RIGHTV
169: INTEGER I, K
170: * ..
171: * .. External Functions ..
172: LOGICAL LSAME
173: EXTERNAL LSAME
174: * ..
175: * .. External Subroutines ..
176: EXTERNAL XERBLA, ZDSCAL, ZSWAP
177: * ..
178: * .. Intrinsic Functions ..
179: INTRINSIC MAX
180: * ..
181: * .. Executable Statements ..
182: *
183: * Test the input parameters
184: *
185: RIGHTV = LSAME( SIDE, 'R' )
186: LEFTV = LSAME( SIDE, 'L' )
187: *
188: INFO = 0
189: IF( .NOT.LSAME( JOB, 'N' ) .AND. .NOT.LSAME( JOB, 'P' ) .AND.
190: $ .NOT.LSAME( JOB, 'S' ) .AND. .NOT.LSAME( JOB, 'B' ) ) THEN
191: INFO = -1
192: ELSE IF( .NOT.RIGHTV .AND. .NOT.LEFTV ) THEN
193: INFO = -2
194: ELSE IF( N.LT.0 ) THEN
195: INFO = -3
196: ELSE IF( ILO.LT.1 ) THEN
197: INFO = -4
198: ELSE IF( N.EQ.0 .AND. IHI.EQ.0 .AND. ILO.NE.1 ) THEN
199: INFO = -4
200: ELSE IF( N.GT.0 .AND. ( IHI.LT.ILO .OR. IHI.GT.MAX( 1, N ) ) )
201: $ THEN
202: INFO = -5
203: ELSE IF( N.EQ.0 .AND. ILO.EQ.1 .AND. IHI.NE.0 ) THEN
204: INFO = -5
205: ELSE IF( M.LT.0 ) THEN
206: INFO = -8
207: ELSE IF( LDV.LT.MAX( 1, N ) ) THEN
208: INFO = -10
209: END IF
210: IF( INFO.NE.0 ) THEN
211: CALL XERBLA( 'ZGGBAK', -INFO )
212: RETURN
213: END IF
214: *
215: * Quick return if possible
216: *
217: IF( N.EQ.0 )
218: $ RETURN
219: IF( M.EQ.0 )
220: $ RETURN
221: IF( LSAME( JOB, 'N' ) )
222: $ RETURN
223: *
224: IF( ILO.EQ.IHI )
225: $ GO TO 30
226: *
227: * Backward balance
228: *
229: IF( LSAME( JOB, 'S' ) .OR. LSAME( JOB, 'B' ) ) THEN
230: *
231: * Backward transformation on right eigenvectors
232: *
233: IF( RIGHTV ) THEN
234: DO 10 I = ILO, IHI
235: CALL ZDSCAL( M, RSCALE( I ), V( I, 1 ), LDV )
236: 10 CONTINUE
237: END IF
238: *
239: * Backward transformation on left eigenvectors
240: *
241: IF( LEFTV ) THEN
242: DO 20 I = ILO, IHI
243: CALL ZDSCAL( M, LSCALE( I ), V( I, 1 ), LDV )
244: 20 CONTINUE
245: END IF
246: END IF
247: *
248: * Backward permutation
249: *
250: 30 CONTINUE
251: IF( LSAME( JOB, 'P' ) .OR. LSAME( JOB, 'B' ) ) THEN
252: *
253: * Backward permutation on right eigenvectors
254: *
255: IF( RIGHTV ) THEN
256: IF( ILO.EQ.1 )
257: $ GO TO 50
258: DO 40 I = ILO - 1, 1, -1
259: K = RSCALE( I )
260: IF( K.EQ.I )
261: $ GO TO 40
262: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
263: 40 CONTINUE
264: *
265: 50 CONTINUE
266: IF( IHI.EQ.N )
267: $ GO TO 70
268: DO 60 I = IHI + 1, N
269: K = RSCALE( I )
270: IF( K.EQ.I )
271: $ GO TO 60
272: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
273: 60 CONTINUE
274: END IF
275: *
276: * Backward permutation on left eigenvectors
277: *
278: 70 CONTINUE
279: IF( LEFTV ) THEN
280: IF( ILO.EQ.1 )
281: $ GO TO 90
282: DO 80 I = ILO - 1, 1, -1
283: K = LSCALE( I )
284: IF( K.EQ.I )
285: $ GO TO 80
286: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
287: 80 CONTINUE
288: *
289: 90 CONTINUE
290: IF( IHI.EQ.N )
291: $ GO TO 110
292: DO 100 I = IHI + 1, N
293: K = LSCALE( I )
294: IF( K.EQ.I )
295: $ GO TO 100
296: CALL ZSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
297: 100 CONTINUE
298: END IF
299: END IF
300: *
301: 110 CONTINUE
302: *
303: RETURN
304: *
305: * End of ZGGBAK
306: *
307: END
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