![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zlaein.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack|
Return to zlaein.f CVS log | Up to [local] / rpl / lapack / lapack |
1.1 bertrand 1: SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK,
2: $ EPS3, SMLNUM, INFO )
3: *
4: * -- LAPACK auxiliary 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: LOGICAL NOINIT, RIGHTV
11: INTEGER INFO, LDB, LDH, N
12: DOUBLE PRECISION EPS3, SMLNUM
13: COMPLEX*16 W
14: * ..
15: * .. Array Arguments ..
16: DOUBLE PRECISION RWORK( * )
17: COMPLEX*16 B( LDB, * ), H( LDH, * ), V( * )
18: * ..
19: *
20: * Purpose
21: * =======
22: *
23: * ZLAEIN uses inverse iteration to find a right or left eigenvector
24: * corresponding to the eigenvalue W of a complex upper Hessenberg
25: * matrix H.
26: *
27: * Arguments
28: * =========
29: *
30: * RIGHTV (input) LOGICAL
31: * = .TRUE. : compute right eigenvector;
32: * = .FALSE.: compute left eigenvector.
33: *
34: * NOINIT (input) LOGICAL
35: * = .TRUE. : no initial vector supplied in V
36: * = .FALSE.: initial vector supplied in V.
37: *
38: * N (input) INTEGER
39: * The order of the matrix H. N >= 0.
40: *
41: * H (input) COMPLEX*16 array, dimension (LDH,N)
42: * The upper Hessenberg matrix H.
43: *
44: * LDH (input) INTEGER
45: * The leading dimension of the array H. LDH >= max(1,N).
46: *
47: * W (input) COMPLEX*16
48: * The eigenvalue of H whose corresponding right or left
49: * eigenvector is to be computed.
50: *
51: * V (input/output) COMPLEX*16 array, dimension (N)
52: * On entry, if NOINIT = .FALSE., V must contain a starting
53: * vector for inverse iteration; otherwise V need not be set.
54: * On exit, V contains the computed eigenvector, normalized so
55: * that the component of largest magnitude has magnitude 1; here
56: * the magnitude of a complex number (x,y) is taken to be
57: * |x| + |y|.
58: *
59: * B (workspace) COMPLEX*16 array, dimension (LDB,N)
60: *
61: * LDB (input) INTEGER
62: * The leading dimension of the array B. LDB >= max(1,N).
63: *
64: * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
65: *
66: * EPS3 (input) DOUBLE PRECISION
67: * A small machine-dependent value which is used to perturb
68: * close eigenvalues, and to replace zero pivots.
69: *
70: * SMLNUM (input) DOUBLE PRECISION
71: * A machine-dependent value close to the underflow threshold.
72: *
73: * INFO (output) INTEGER
74: * = 0: successful exit
75: * = 1: inverse iteration did not converge; V is set to the
76: * last iterate.
77: *
78: * =====================================================================
79: *
80: * .. Parameters ..
81: DOUBLE PRECISION ONE, TENTH
82: PARAMETER ( ONE = 1.0D+0, TENTH = 1.0D-1 )
83: COMPLEX*16 ZERO
84: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
85: * ..
86: * .. Local Scalars ..
87: CHARACTER NORMIN, TRANS
88: INTEGER I, IERR, ITS, J
89: DOUBLE PRECISION GROWTO, NRMSML, ROOTN, RTEMP, SCALE, VNORM
90: COMPLEX*16 CDUM, EI, EJ, TEMP, X
91: * ..
92: * .. External Functions ..
93: INTEGER IZAMAX
94: DOUBLE PRECISION DZASUM, DZNRM2
95: COMPLEX*16 ZLADIV
96: EXTERNAL IZAMAX, DZASUM, DZNRM2, ZLADIV
97: * ..
98: * .. External Subroutines ..
99: EXTERNAL ZDSCAL, ZLATRS
100: * ..
101: * .. Intrinsic Functions ..
102: INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT
103: * ..
104: * .. Statement Functions ..
105: DOUBLE PRECISION CABS1
106: * ..
107: * .. Statement Function definitions ..
108: CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
109: * ..
110: * .. Executable Statements ..
111: *
112: INFO = 0
113: *
114: * GROWTO is the threshold used in the acceptance test for an
115: * eigenvector.
116: *
117: ROOTN = SQRT( DBLE( N ) )
118: GROWTO = TENTH / ROOTN
119: NRMSML = MAX( ONE, EPS3*ROOTN )*SMLNUM
120: *
121: * Form B = H - W*I (except that the subdiagonal elements are not
122: * stored).
123: *
124: DO 20 J = 1, N
125: DO 10 I = 1, J - 1
126: B( I, J ) = H( I, J )
127: 10 CONTINUE
128: B( J, J ) = H( J, J ) - W
129: 20 CONTINUE
130: *
131: IF( NOINIT ) THEN
132: *
133: * Initialize V.
134: *
135: DO 30 I = 1, N
136: V( I ) = EPS3
137: 30 CONTINUE
138: ELSE
139: *
140: * Scale supplied initial vector.
141: *
142: VNORM = DZNRM2( N, V, 1 )
143: CALL ZDSCAL( N, ( EPS3*ROOTN ) / MAX( VNORM, NRMSML ), V, 1 )
144: END IF
145: *
146: IF( RIGHTV ) THEN
147: *
148: * LU decomposition with partial pivoting of B, replacing zero
149: * pivots by EPS3.
150: *
151: DO 60 I = 1, N - 1
152: EI = H( I+1, I )
153: IF( CABS1( B( I, I ) ).LT.CABS1( EI ) ) THEN
154: *
155: * Interchange rows and eliminate.
156: *
157: X = ZLADIV( B( I, I ), EI )
158: B( I, I ) = EI
159: DO 40 J = I + 1, N
160: TEMP = B( I+1, J )
161: B( I+1, J ) = B( I, J ) - X*TEMP
162: B( I, J ) = TEMP
163: 40 CONTINUE
164: ELSE
165: *
166: * Eliminate without interchange.
167: *
168: IF( B( I, I ).EQ.ZERO )
169: $ B( I, I ) = EPS3
170: X = ZLADIV( EI, B( I, I ) )
171: IF( X.NE.ZERO ) THEN
172: DO 50 J = I + 1, N
173: B( I+1, J ) = B( I+1, J ) - X*B( I, J )
174: 50 CONTINUE
175: END IF
176: END IF
177: 60 CONTINUE
178: IF( B( N, N ).EQ.ZERO )
179: $ B( N, N ) = EPS3
180: *
181: TRANS = 'N'
182: *
183: ELSE
184: *
185: * UL decomposition with partial pivoting of B, replacing zero
186: * pivots by EPS3.
187: *
188: DO 90 J = N, 2, -1
189: EJ = H( J, J-1 )
190: IF( CABS1( B( J, J ) ).LT.CABS1( EJ ) ) THEN
191: *
192: * Interchange columns and eliminate.
193: *
194: X = ZLADIV( B( J, J ), EJ )
195: B( J, J ) = EJ
196: DO 70 I = 1, J - 1
197: TEMP = B( I, J-1 )
198: B( I, J-1 ) = B( I, J ) - X*TEMP
199: B( I, J ) = TEMP
200: 70 CONTINUE
201: ELSE
202: *
203: * Eliminate without interchange.
204: *
205: IF( B( J, J ).EQ.ZERO )
206: $ B( J, J ) = EPS3
207: X = ZLADIV( EJ, B( J, J ) )
208: IF( X.NE.ZERO ) THEN
209: DO 80 I = 1, J - 1
210: B( I, J-1 ) = B( I, J-1 ) - X*B( I, J )
211: 80 CONTINUE
212: END IF
213: END IF
214: 90 CONTINUE
215: IF( B( 1, 1 ).EQ.ZERO )
216: $ B( 1, 1 ) = EPS3
217: *
218: TRANS = 'C'
219: *
220: END IF
221: *
222: NORMIN = 'N'
223: DO 110 ITS = 1, N
224: *
225: * Solve U*x = scale*v for a right eigenvector
226: * or U'*x = scale*v for a left eigenvector,
227: * overwriting x on v.
228: *
229: CALL ZLATRS( 'Upper', TRANS, 'Nonunit', NORMIN, N, B, LDB, V,
230: $ SCALE, RWORK, IERR )
231: NORMIN = 'Y'
232: *
233: * Test for sufficient growth in the norm of v.
234: *
235: VNORM = DZASUM( N, V, 1 )
236: IF( VNORM.GE.GROWTO*SCALE )
237: $ GO TO 120
238: *
239: * Choose new orthogonal starting vector and try again.
240: *
241: RTEMP = EPS3 / ( ROOTN+ONE )
242: V( 1 ) = EPS3
243: DO 100 I = 2, N
244: V( I ) = RTEMP
245: 100 CONTINUE
246: V( N-ITS+1 ) = V( N-ITS+1 ) - EPS3*ROOTN
247: 110 CONTINUE
248: *
249: * Failure to find eigenvector in N iterations.
250: *
251: INFO = 1
252: *
253: 120 CONTINUE
254: *
255: * Normalize eigenvector.
256: *
257: I = IZAMAX( N, V, 1 )
258: CALL ZDSCAL( N, ONE / CABS1( V( I ) ), V, 1 )
259: *
260: RETURN
261: *
262: * End of ZLAEIN
263: *
264: END