Annotation of rpl/lapack/lapack/zgebak.f, revision 1.8
1.8 ! bertrand 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
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgebak.f">
! 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: * =====================================================================
1.1 bertrand 131: SUBROUTINE ZGEBAK( JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV,
132: $ INFO )
133: *
1.8 ! bertrand 134: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 135: * -- LAPACK is a software package provided by Univ. of Tennessee, --
136: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 137: * November 2011
1.1 bertrand 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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