Annotation of rpl/lapack/lapack/dstevd.f, revision 1.9
1.8 bertrand 1: *> \brief <b> DSTEVD 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 DSTEVD + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstevd.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstevd.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstevd.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
22: * LIWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ
26: * INTEGER INFO, LDZ, LIWORK, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IWORK( * )
30: * DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
40: *> real symmetric tridiagonal matrix. If eigenvectors are desired, it
41: *> uses a divide and conquer algorithm.
42: *>
43: *> The divide and conquer algorithm makes very mild assumptions about
44: *> floating point arithmetic. It will work on machines with a guard
45: *> digit in add/subtract, or on those binary machines without guard
46: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
47: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
48: *> without guard digits, but we know of none.
49: *> \endverbatim
50: *
51: * Arguments:
52: * ==========
53: *
54: *> \param[in] JOBZ
55: *> \verbatim
56: *> JOBZ is CHARACTER*1
57: *> = 'N': Compute eigenvalues only;
58: *> = 'V': Compute eigenvalues and eigenvectors.
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> The order of the matrix. N >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] D
68: *> \verbatim
69: *> D is DOUBLE PRECISION array, dimension (N)
70: *> On entry, the n diagonal elements of the tridiagonal matrix
71: *> A.
72: *> On exit, if INFO = 0, the eigenvalues in ascending order.
73: *> \endverbatim
74: *>
75: *> \param[in,out] E
76: *> \verbatim
77: *> E is DOUBLE PRECISION array, dimension (N-1)
78: *> On entry, the (n-1) subdiagonal elements of the tridiagonal
79: *> matrix A, stored in elements 1 to N-1 of E.
80: *> On exit, the contents of E are destroyed.
81: *> \endverbatim
82: *>
83: *> \param[out] Z
84: *> \verbatim
85: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
86: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
87: *> eigenvectors of the matrix A, with the i-th column of Z
88: *> holding the eigenvector associated with D(i).
89: *> If JOBZ = 'N', then Z is not referenced.
90: *> \endverbatim
91: *>
92: *> \param[in] LDZ
93: *> \verbatim
94: *> LDZ is INTEGER
95: *> The leading dimension of the array Z. LDZ >= 1, and if
96: *> JOBZ = 'V', LDZ >= max(1,N).
97: *> \endverbatim
98: *>
99: *> \param[out] WORK
100: *> \verbatim
101: *> WORK is DOUBLE PRECISION array,
102: *> dimension (LWORK)
103: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
104: *> \endverbatim
105: *>
106: *> \param[in] LWORK
107: *> \verbatim
108: *> LWORK is INTEGER
109: *> The dimension of the array WORK.
110: *> If JOBZ = 'N' or N <= 1 then LWORK must be at least 1.
111: *> If JOBZ = 'V' and N > 1 then LWORK must be at least
112: *> ( 1 + 4*N + N**2 ).
113: *>
114: *> If LWORK = -1, then a workspace query is assumed; the routine
115: *> only calculates the optimal sizes of the WORK and IWORK
116: *> arrays, returns these values as the first entries of the WORK
117: *> and IWORK arrays, and no error message related to LWORK or
118: *> LIWORK is issued by XERBLA.
119: *> \endverbatim
120: *>
121: *> \param[out] IWORK
122: *> \verbatim
123: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
124: *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
125: *> \endverbatim
126: *>
127: *> \param[in] LIWORK
128: *> \verbatim
129: *> LIWORK is INTEGER
130: *> The dimension of the array IWORK.
131: *> If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1.
132: *> If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N.
133: *>
134: *> If LIWORK = -1, then a workspace query is assumed; the
135: *> routine only calculates the optimal sizes of the WORK and
136: *> IWORK arrays, returns these values as the first entries of
137: *> the WORK and IWORK arrays, and no error message related to
138: *> LWORK or LIWORK is issued by XERBLA.
139: *> \endverbatim
140: *>
141: *> \param[out] INFO
142: *> \verbatim
143: *> INFO is INTEGER
144: *> = 0: successful exit
145: *> < 0: if INFO = -i, the i-th argument had an illegal value
146: *> > 0: if INFO = i, the algorithm failed to converge; i
147: *> off-diagonal elements of E did not converge to zero.
148: *> \endverbatim
149: *
150: * Authors:
151: * ========
152: *
153: *> \author Univ. of Tennessee
154: *> \author Univ. of California Berkeley
155: *> \author Univ. of Colorado Denver
156: *> \author NAG Ltd.
157: *
158: *> \date November 2011
159: *
160: *> \ingroup doubleOTHEReigen
161: *
162: * =====================================================================
1.1 bertrand 163: SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
164: $ LIWORK, INFO )
165: *
1.8 bertrand 166: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 167: * -- LAPACK is a software package provided by Univ. of Tennessee, --
168: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 bertrand 169: * November 2011
1.1 bertrand 170: *
171: * .. Scalar Arguments ..
172: CHARACTER JOBZ
173: INTEGER INFO, LDZ, LIWORK, LWORK, N
174: * ..
175: * .. Array Arguments ..
176: INTEGER IWORK( * )
177: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
178: * ..
179: *
180: * =====================================================================
181: *
182: * .. Parameters ..
183: DOUBLE PRECISION ZERO, ONE
184: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
185: * ..
186: * .. Local Scalars ..
187: LOGICAL LQUERY, WANTZ
188: INTEGER ISCALE, LIWMIN, LWMIN
189: DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
190: $ TNRM
191: * ..
192: * .. External Functions ..
193: LOGICAL LSAME
194: DOUBLE PRECISION DLAMCH, DLANST
195: EXTERNAL LSAME, DLAMCH, DLANST
196: * ..
197: * .. External Subroutines ..
198: EXTERNAL DSCAL, DSTEDC, DSTERF, XERBLA
199: * ..
200: * .. Intrinsic Functions ..
201: INTRINSIC SQRT
202: * ..
203: * .. Executable Statements ..
204: *
205: * Test the input parameters.
206: *
207: WANTZ = LSAME( JOBZ, 'V' )
208: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
209: *
210: INFO = 0
211: LIWMIN = 1
212: LWMIN = 1
213: IF( N.GT.1 .AND. WANTZ ) THEN
214: LWMIN = 1 + 4*N + N**2
215: LIWMIN = 3 + 5*N
216: END IF
217: *
218: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
219: INFO = -1
220: ELSE IF( N.LT.0 ) THEN
221: INFO = -2
222: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
223: INFO = -6
224: END IF
225: *
226: IF( INFO.EQ.0 ) THEN
227: WORK( 1 ) = LWMIN
228: IWORK( 1 ) = LIWMIN
229: *
230: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
231: INFO = -8
232: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
233: INFO = -10
234: END IF
235: END IF
236: *
237: IF( INFO.NE.0 ) THEN
238: CALL XERBLA( 'DSTEVD', -INFO )
239: RETURN
240: ELSE IF( LQUERY ) THEN
241: RETURN
242: END IF
243: *
244: * Quick return if possible
245: *
246: IF( N.EQ.0 )
247: $ RETURN
248: *
249: IF( N.EQ.1 ) THEN
250: IF( WANTZ )
251: $ Z( 1, 1 ) = ONE
252: RETURN
253: END IF
254: *
255: * Get machine constants.
256: *
257: SAFMIN = DLAMCH( 'Safe minimum' )
258: EPS = DLAMCH( 'Precision' )
259: SMLNUM = SAFMIN / EPS
260: BIGNUM = ONE / SMLNUM
261: RMIN = SQRT( SMLNUM )
262: RMAX = SQRT( BIGNUM )
263: *
264: * Scale matrix to allowable range, if necessary.
265: *
266: ISCALE = 0
267: TNRM = DLANST( 'M', N, D, E )
268: IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
269: ISCALE = 1
270: SIGMA = RMIN / TNRM
271: ELSE IF( TNRM.GT.RMAX ) THEN
272: ISCALE = 1
273: SIGMA = RMAX / TNRM
274: END IF
275: IF( ISCALE.EQ.1 ) THEN
276: CALL DSCAL( N, SIGMA, D, 1 )
277: CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
278: END IF
279: *
280: * For eigenvalues only, call DSTERF. For eigenvalues and
281: * eigenvectors, call DSTEDC.
282: *
283: IF( .NOT.WANTZ ) THEN
284: CALL DSTERF( N, D, E, INFO )
285: ELSE
286: CALL DSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
287: $ INFO )
288: END IF
289: *
290: * If matrix was scaled, then rescale eigenvalues appropriately.
291: *
292: IF( ISCALE.EQ.1 )
293: $ CALL DSCAL( N, ONE / SIGMA, D, 1 )
294: *
295: WORK( 1 ) = LWMIN
296: IWORK( 1 ) = LIWMIN
297: *
298: RETURN
299: *
300: * End of DSTEVD
301: *
302: END
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