1: *> \brief \b DSPGVX
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSPGVX + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgvx.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgvx.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgvx.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
22: * IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
23: * IFAIL, INFO )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER JOBZ, RANGE, UPLO
27: * INTEGER IL, INFO, ITYPE, IU, LDZ, M, N
28: * DOUBLE PRECISION ABSTOL, VL, VU
29: * ..
30: * .. Array Arguments ..
31: * INTEGER IFAIL( * ), IWORK( * )
32: * DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
33: * $ Z( LDZ, * )
34: * ..
35: *
36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> DSPGVX computes selected eigenvalues, and optionally, eigenvectors
43: *> of a real generalized symmetric-definite eigenproblem, of the form
44: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
45: *> and B are assumed to be symmetric, stored in packed storage, and B
46: *> is also positive definite. Eigenvalues and eigenvectors can be
47: *> selected by specifying either a range of values or a range of indices
48: *> for the desired eigenvalues.
49: *> \endverbatim
50: *
51: * Arguments:
52: * ==========
53: *
54: *> \param[in] ITYPE
55: *> \verbatim
56: *> ITYPE is INTEGER
57: *> Specifies the problem type to be solved:
58: *> = 1: A*x = (lambda)*B*x
59: *> = 2: A*B*x = (lambda)*x
60: *> = 3: B*A*x = (lambda)*x
61: *> \endverbatim
62: *>
63: *> \param[in] JOBZ
64: *> \verbatim
65: *> JOBZ is CHARACTER*1
66: *> = 'N': Compute eigenvalues only;
67: *> = 'V': Compute eigenvalues and eigenvectors.
68: *> \endverbatim
69: *>
70: *> \param[in] RANGE
71: *> \verbatim
72: *> RANGE is CHARACTER*1
73: *> = 'A': all eigenvalues will be found.
74: *> = 'V': all eigenvalues in the half-open interval (VL,VU]
75: *> will be found.
76: *> = 'I': the IL-th through IU-th eigenvalues will be found.
77: *> \endverbatim
78: *>
79: *> \param[in] UPLO
80: *> \verbatim
81: *> UPLO is CHARACTER*1
82: *> = 'U': Upper triangle of A and B are stored;
83: *> = 'L': Lower triangle of A and B are stored.
84: *> \endverbatim
85: *>
86: *> \param[in] N
87: *> \verbatim
88: *> N is INTEGER
89: *> The order of the matrix pencil (A,B). N >= 0.
90: *> \endverbatim
91: *>
92: *> \param[in,out] AP
93: *> \verbatim
94: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
95: *> On entry, the upper or lower triangle of the symmetric matrix
96: *> A, packed columnwise in a linear array. The j-th column of A
97: *> is stored in the array AP as follows:
98: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
99: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
100: *>
101: *> On exit, the contents of AP are destroyed.
102: *> \endverbatim
103: *>
104: *> \param[in,out] BP
105: *> \verbatim
106: *> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
107: *> On entry, the upper or lower triangle of the symmetric matrix
108: *> B, packed columnwise in a linear array. The j-th column of B
109: *> is stored in the array BP as follows:
110: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
111: *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
112: *>
113: *> On exit, the triangular factor U or L from the Cholesky
114: *> factorization B = U**T*U or B = L*L**T, in the same storage
115: *> format as B.
116: *> \endverbatim
117: *>
118: *> \param[in] VL
119: *> \verbatim
120: *> VL is DOUBLE PRECISION
121: *>
122: *> If RANGE='V', the lower bound of the interval to
123: *> be searched for eigenvalues. VL < VU.
124: *> Not referenced if RANGE = 'A' or 'I'.
125: *> \endverbatim
126: *>
127: *> \param[in] VU
128: *> \verbatim
129: *> VU is DOUBLE PRECISION
130: *>
131: *> If RANGE='V', the upper bound of the interval to
132: *> be searched for eigenvalues. VL < VU.
133: *> Not referenced if RANGE = 'A' or 'I'.
134: *> \endverbatim
135: *>
136: *> \param[in] IL
137: *> \verbatim
138: *> IL is INTEGER
139: *>
140: *> If RANGE='I', the index of the
141: *> smallest eigenvalue to be returned.
142: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
143: *> Not referenced if RANGE = 'A' or 'V'.
144: *> \endverbatim
145: *>
146: *> \param[in] IU
147: *> \verbatim
148: *> IU is INTEGER
149: *>
150: *> If RANGE='I', the index of the
151: *> largest eigenvalue to be returned.
152: *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
153: *> Not referenced if RANGE = 'A' or 'V'.
154: *> \endverbatim
155: *>
156: *> \param[in] ABSTOL
157: *> \verbatim
158: *> ABSTOL is DOUBLE PRECISION
159: *> The absolute error tolerance for the eigenvalues.
160: *> An approximate eigenvalue is accepted as converged
161: *> when it is determined to lie in an interval [a,b]
162: *> of width less than or equal to
163: *>
164: *> ABSTOL + EPS * max( |a|,|b| ) ,
165: *>
166: *> where EPS is the machine precision. If ABSTOL is less than
167: *> or equal to zero, then EPS*|T| will be used in its place,
168: *> where |T| is the 1-norm of the tridiagonal matrix obtained
169: *> by reducing A to tridiagonal form.
170: *>
171: *> Eigenvalues will be computed most accurately when ABSTOL is
172: *> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
173: *> If this routine returns with INFO>0, indicating that some
174: *> eigenvectors did not converge, try setting ABSTOL to
175: *> 2*DLAMCH('S').
176: *> \endverbatim
177: *>
178: *> \param[out] M
179: *> \verbatim
180: *> M is INTEGER
181: *> The total number of eigenvalues found. 0 <= M <= N.
182: *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
183: *> \endverbatim
184: *>
185: *> \param[out] W
186: *> \verbatim
187: *> W is DOUBLE PRECISION array, dimension (N)
188: *> On normal exit, the first M elements contain the selected
189: *> eigenvalues in ascending order.
190: *> \endverbatim
191: *>
192: *> \param[out] Z
193: *> \verbatim
194: *> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
195: *> If JOBZ = 'N', then Z is not referenced.
196: *> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
197: *> contain the orthonormal eigenvectors of the matrix A
198: *> corresponding to the selected eigenvalues, with the i-th
199: *> column of Z holding the eigenvector associated with W(i).
200: *> The eigenvectors are normalized as follows:
201: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
202: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
203: *>
204: *> If an eigenvector fails to converge, then that column of Z
205: *> contains the latest approximation to the eigenvector, and the
206: *> index of the eigenvector is returned in IFAIL.
207: *> Note: the user must ensure that at least max(1,M) columns are
208: *> supplied in the array Z; if RANGE = 'V', the exact value of M
209: *> is not known in advance and an upper bound must be used.
210: *> \endverbatim
211: *>
212: *> \param[in] LDZ
213: *> \verbatim
214: *> LDZ is INTEGER
215: *> The leading dimension of the array Z. LDZ >= 1, and if
216: *> JOBZ = 'V', LDZ >= max(1,N).
217: *> \endverbatim
218: *>
219: *> \param[out] WORK
220: *> \verbatim
221: *> WORK is DOUBLE PRECISION array, dimension (8*N)
222: *> \endverbatim
223: *>
224: *> \param[out] IWORK
225: *> \verbatim
226: *> IWORK is INTEGER array, dimension (5*N)
227: *> \endverbatim
228: *>
229: *> \param[out] IFAIL
230: *> \verbatim
231: *> IFAIL is INTEGER array, dimension (N)
232: *> If JOBZ = 'V', then if INFO = 0, the first M elements of
233: *> IFAIL are zero. If INFO > 0, then IFAIL contains the
234: *> indices of the eigenvectors that failed to converge.
235: *> If JOBZ = 'N', then IFAIL is not referenced.
236: *> \endverbatim
237: *>
238: *> \param[out] INFO
239: *> \verbatim
240: *> INFO is INTEGER
241: *> = 0: successful exit
242: *> < 0: if INFO = -i, the i-th argument had an illegal value
243: *> > 0: DPPTRF or DSPEVX returned an error code:
244: *> <= N: if INFO = i, DSPEVX failed to converge;
245: *> i eigenvectors failed to converge. Their indices
246: *> are stored in array IFAIL.
247: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
248: *> minor of order i of B is not positive definite.
249: *> The factorization of B could not be completed and
250: *> no eigenvalues or eigenvectors were computed.
251: *> \endverbatim
252: *
253: * Authors:
254: * ========
255: *
256: *> \author Univ. of Tennessee
257: *> \author Univ. of California Berkeley
258: *> \author Univ. of Colorado Denver
259: *> \author NAG Ltd.
260: *
261: *> \ingroup doubleOTHEReigen
262: *
263: *> \par Contributors:
264: * ==================
265: *>
266: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
267: *
268: * =====================================================================
269: SUBROUTINE DSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU,
270: $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
271: $ IFAIL, INFO )
272: *
273: * -- LAPACK driver routine --
274: * -- LAPACK is a software package provided by Univ. of Tennessee, --
275: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
276: *
277: * .. Scalar Arguments ..
278: CHARACTER JOBZ, RANGE, UPLO
279: INTEGER IL, INFO, ITYPE, IU, LDZ, M, N
280: DOUBLE PRECISION ABSTOL, VL, VU
281: * ..
282: * .. Array Arguments ..
283: INTEGER IFAIL( * ), IWORK( * )
284: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
285: $ Z( LDZ, * )
286: * ..
287: *
288: * =====================================================================
289: *
290: * .. Local Scalars ..
291: LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ
292: CHARACTER TRANS
293: INTEGER J
294: * ..
295: * .. External Functions ..
296: LOGICAL LSAME
297: EXTERNAL LSAME
298: * ..
299: * .. External Subroutines ..
300: EXTERNAL DPPTRF, DSPEVX, DSPGST, DTPMV, DTPSV, XERBLA
301: * ..
302: * .. Intrinsic Functions ..
303: INTRINSIC MIN
304: * ..
305: * .. Executable Statements ..
306: *
307: * Test the input parameters.
308: *
309: UPPER = LSAME( UPLO, 'U' )
310: WANTZ = LSAME( JOBZ, 'V' )
311: ALLEIG = LSAME( RANGE, 'A' )
312: VALEIG = LSAME( RANGE, 'V' )
313: INDEIG = LSAME( RANGE, 'I' )
314: *
315: INFO = 0
316: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
317: INFO = -1
318: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
319: INFO = -2
320: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
321: INFO = -3
322: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
323: INFO = -4
324: ELSE IF( N.LT.0 ) THEN
325: INFO = -5
326: ELSE
327: IF( VALEIG ) THEN
328: IF( N.GT.0 .AND. VU.LE.VL ) THEN
329: INFO = -9
330: END IF
331: ELSE IF( INDEIG ) THEN
332: IF( IL.LT.1 ) THEN
333: INFO = -10
334: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
335: INFO = -11
336: END IF
337: END IF
338: END IF
339: IF( INFO.EQ.0 ) THEN
340: IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
341: INFO = -16
342: END IF
343: END IF
344: *
345: IF( INFO.NE.0 ) THEN
346: CALL XERBLA( 'DSPGVX', -INFO )
347: RETURN
348: END IF
349: *
350: * Quick return if possible
351: *
352: M = 0
353: IF( N.EQ.0 )
354: $ RETURN
355: *
356: * Form a Cholesky factorization of B.
357: *
358: CALL DPPTRF( UPLO, N, BP, INFO )
359: IF( INFO.NE.0 ) THEN
360: INFO = N + INFO
361: RETURN
362: END IF
363: *
364: * Transform problem to standard eigenvalue problem and solve.
365: *
366: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
367: CALL DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M,
368: $ W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
369: *
370: IF( WANTZ ) THEN
371: *
372: * Backtransform eigenvectors to the original problem.
373: *
374: IF( INFO.GT.0 )
375: $ M = INFO - 1
376: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
377: *
378: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
379: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
380: *
381: IF( UPPER ) THEN
382: TRANS = 'N'
383: ELSE
384: TRANS = 'T'
385: END IF
386: *
387: DO 10 J = 1, M
388: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
389: $ 1 )
390: 10 CONTINUE
391: *
392: ELSE IF( ITYPE.EQ.3 ) THEN
393: *
394: * For B*A*x=(lambda)*x;
395: * backtransform eigenvectors: x = L*y or U**T*y
396: *
397: IF( UPPER ) THEN
398: TRANS = 'T'
399: ELSE
400: TRANS = 'N'
401: END IF
402: *
403: DO 20 J = 1, M
404: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
405: $ 1 )
406: 20 CONTINUE
407: END IF
408: END IF
409: *
410: RETURN
411: *
412: * End of DSPGVX
413: *
414: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dspgvx.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack