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Mon Jan 27 09:28:27 2014 UTC (10 years, 3 months ago) by
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1: *> \brief <b> DSTEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSTEV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstev.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstev.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstev.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER JOBZ
25: * INTEGER INFO, LDZ, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DSTEV computes all eigenvalues and, optionally, eigenvectors of a
38: *> real symmetric tridiagonal matrix A.
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] JOBZ
45: *> \verbatim
46: *> JOBZ is CHARACTER*1
47: *> = 'N': Compute eigenvalues only;
48: *> = 'V': Compute eigenvalues and eigenvectors.
49: *> \endverbatim
50: *>
51: *> \param[in] N
52: *> \verbatim
53: *> N is INTEGER
54: *> The order of the matrix. N >= 0.
55: *> \endverbatim
56: *>
57: *> \param[in,out] D
58: *> \verbatim
59: *> D is DOUBLE PRECISION array, dimension (N)
60: *> On entry, the n diagonal elements of the tridiagonal matrix
61: *> A.
62: *> On exit, if INFO = 0, the eigenvalues in ascending order.
63: *> \endverbatim
64: *>
65: *> \param[in,out] E
66: *> \verbatim
67: *> E is DOUBLE PRECISION array, dimension (N-1)
68: *> On entry, the (n-1) subdiagonal elements of the tridiagonal
69: *> matrix A, stored in elements 1 to N-1 of E.
70: *> On exit, the contents of E are destroyed.
71: *> \endverbatim
72: *>
73: *> \param[out] Z
74: *> \verbatim
75: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
76: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
77: *> eigenvectors of the matrix A, with the i-th column of Z
78: *> holding the eigenvector associated with D(i).
79: *> If JOBZ = 'N', then Z is not referenced.
80: *> \endverbatim
81: *>
82: *> \param[in] LDZ
83: *> \verbatim
84: *> LDZ is INTEGER
85: *> The leading dimension of the array Z. LDZ >= 1, and if
86: *> JOBZ = 'V', LDZ >= max(1,N).
87: *> \endverbatim
88: *>
89: *> \param[out] WORK
90: *> \verbatim
91: *> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2))
92: *> If JOBZ = 'N', WORK is not referenced.
93: *> \endverbatim
94: *>
95: *> \param[out] INFO
96: *> \verbatim
97: *> INFO is INTEGER
98: *> = 0: successful exit
99: *> < 0: if INFO = -i, the i-th argument had an illegal value
100: *> > 0: if INFO = i, the algorithm failed to converge; i
101: *> off-diagonal elements of E did not converge to zero.
102: *> \endverbatim
103: *
104: * Authors:
105: * ========
106: *
107: *> \author Univ. of Tennessee
108: *> \author Univ. of California Berkeley
109: *> \author Univ. of Colorado Denver
110: *> \author NAG Ltd.
111: *
112: *> \date November 2011
113: *
114: *> \ingroup doubleOTHEReigen
115: *
116: * =====================================================================
117: SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
118: *
119: * -- LAPACK driver routine (version 3.4.0) --
120: * -- LAPACK is a software package provided by Univ. of Tennessee, --
121: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
122: * November 2011
123: *
124: * .. Scalar Arguments ..
125: CHARACTER JOBZ
126: INTEGER INFO, LDZ, N
127: * ..
128: * .. Array Arguments ..
129: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE PRECISION ZERO, ONE
136: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
137: * ..
138: * .. Local Scalars ..
139: LOGICAL WANTZ
140: INTEGER IMAX, ISCALE
141: DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
142: $ TNRM
143: * ..
144: * .. External Functions ..
145: LOGICAL LSAME
146: DOUBLE PRECISION DLAMCH, DLANST
147: EXTERNAL LSAME, DLAMCH, DLANST
148: * ..
149: * .. External Subroutines ..
150: EXTERNAL DSCAL, DSTEQR, DSTERF, XERBLA
151: * ..
152: * .. Intrinsic Functions ..
153: INTRINSIC SQRT
154: * ..
155: * .. Executable Statements ..
156: *
157: * Test the input parameters.
158: *
159: WANTZ = LSAME( JOBZ, 'V' )
160: *
161: INFO = 0
162: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
163: INFO = -1
164: ELSE IF( N.LT.0 ) THEN
165: INFO = -2
166: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
167: INFO = -6
168: END IF
169: *
170: IF( INFO.NE.0 ) THEN
171: CALL XERBLA( 'DSTEV ', -INFO )
172: RETURN
173: END IF
174: *
175: * Quick return if possible
176: *
177: IF( N.EQ.0 )
178: $ RETURN
179: *
180: IF( N.EQ.1 ) THEN
181: IF( WANTZ )
182: $ Z( 1, 1 ) = ONE
183: RETURN
184: END IF
185: *
186: * Get machine constants.
187: *
188: SAFMIN = DLAMCH( 'Safe minimum' )
189: EPS = DLAMCH( 'Precision' )
190: SMLNUM = SAFMIN / EPS
191: BIGNUM = ONE / SMLNUM
192: RMIN = SQRT( SMLNUM )
193: RMAX = SQRT( BIGNUM )
194: *
195: * Scale matrix to allowable range, if necessary.
196: *
197: ISCALE = 0
198: TNRM = DLANST( 'M', N, D, E )
199: IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
200: ISCALE = 1
201: SIGMA = RMIN / TNRM
202: ELSE IF( TNRM.GT.RMAX ) THEN
203: ISCALE = 1
204: SIGMA = RMAX / TNRM
205: END IF
206: IF( ISCALE.EQ.1 ) THEN
207: CALL DSCAL( N, SIGMA, D, 1 )
208: CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
209: END IF
210: *
211: * For eigenvalues only, call DSTERF. For eigenvalues and
212: * eigenvectors, call DSTEQR.
213: *
214: IF( .NOT.WANTZ ) THEN
215: CALL DSTERF( N, D, E, INFO )
216: ELSE
217: CALL DSTEQR( 'I', N, D, E, Z, LDZ, WORK, INFO )
218: END IF
219: *
220: * If matrix was scaled, then rescale eigenvalues appropriately.
221: *
222: IF( ISCALE.EQ.1 ) THEN
223: IF( INFO.EQ.0 ) THEN
224: IMAX = N
225: ELSE
226: IMAX = INFO - 1
227: END IF
228: CALL DSCAL( IMAX, ONE / SIGMA, D, 1 )
229: END IF
230: *
231: RETURN
232: *
233: * End of DSTEV
234: *
235: END
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