1: *> \brief \b DSBGVD
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSBGVD + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbgvd.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbgvd.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbgvd.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
22: * Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IWORK( * )
30: * DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
31: * $ WORK( * ), Z( LDZ, * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
41: *> of a real generalized symmetric-definite banded eigenproblem, of the
42: *> form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and
43: *> banded, and B is also positive definite. If eigenvectors are
44: *> desired, it uses a divide and conquer algorithm.
45: *>
46: *> The divide and conquer algorithm makes very mild assumptions about
47: *> floating point arithmetic. It will work on machines with a guard
48: *> digit in add/subtract, or on those binary machines without guard
49: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
50: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
51: *> without guard digits, but we know of none.
52: *> \endverbatim
53: *
54: * Arguments:
55: * ==========
56: *
57: *> \param[in] JOBZ
58: *> \verbatim
59: *> JOBZ is CHARACTER*1
60: *> = 'N': Compute eigenvalues only;
61: *> = 'V': Compute eigenvalues and eigenvectors.
62: *> \endverbatim
63: *>
64: *> \param[in] UPLO
65: *> \verbatim
66: *> UPLO is CHARACTER*1
67: *> = 'U': Upper triangles of A and B are stored;
68: *> = 'L': Lower triangles of A and B are stored.
69: *> \endverbatim
70: *>
71: *> \param[in] N
72: *> \verbatim
73: *> N is INTEGER
74: *> The order of the matrices A and B. N >= 0.
75: *> \endverbatim
76: *>
77: *> \param[in] KA
78: *> \verbatim
79: *> KA is INTEGER
80: *> The number of superdiagonals of the matrix A if UPLO = 'U',
81: *> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
82: *> \endverbatim
83: *>
84: *> \param[in] KB
85: *> \verbatim
86: *> KB is INTEGER
87: *> The number of superdiagonals of the matrix B if UPLO = 'U',
88: *> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
89: *> \endverbatim
90: *>
91: *> \param[in,out] AB
92: *> \verbatim
93: *> AB is DOUBLE PRECISION array, dimension (LDAB, N)
94: *> On entry, the upper or lower triangle of the symmetric band
95: *> matrix A, stored in the first ka+1 rows of the array. The
96: *> j-th column of A is stored in the j-th column of the array AB
97: *> as follows:
98: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
99: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
100: *>
101: *> On exit, the contents of AB are destroyed.
102: *> \endverbatim
103: *>
104: *> \param[in] LDAB
105: *> \verbatim
106: *> LDAB is INTEGER
107: *> The leading dimension of the array AB. LDAB >= KA+1.
108: *> \endverbatim
109: *>
110: *> \param[in,out] BB
111: *> \verbatim
112: *> BB is DOUBLE PRECISION array, dimension (LDBB, N)
113: *> On entry, the upper or lower triangle of the symmetric band
114: *> matrix B, stored in the first kb+1 rows of the array. The
115: *> j-th column of B is stored in the j-th column of the array BB
116: *> as follows:
117: *> if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
118: *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
119: *>
120: *> On exit, the factor S from the split Cholesky factorization
121: *> B = S**T*S, as returned by DPBSTF.
122: *> \endverbatim
123: *>
124: *> \param[in] LDBB
125: *> \verbatim
126: *> LDBB is INTEGER
127: *> The leading dimension of the array BB. LDBB >= KB+1.
128: *> \endverbatim
129: *>
130: *> \param[out] W
131: *> \verbatim
132: *> W is DOUBLE PRECISION array, dimension (N)
133: *> If INFO = 0, the eigenvalues in ascending order.
134: *> \endverbatim
135: *>
136: *> \param[out] Z
137: *> \verbatim
138: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
139: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
140: *> eigenvectors, with the i-th column of Z holding the
141: *> eigenvector associated with W(i). The eigenvectors are
142: *> normalized so Z**T*B*Z = I.
143: *> If JOBZ = 'N', then Z is not referenced.
144: *> \endverbatim
145: *>
146: *> \param[in] LDZ
147: *> \verbatim
148: *> LDZ is INTEGER
149: *> The leading dimension of the array Z. LDZ >= 1, and if
150: *> JOBZ = 'V', LDZ >= max(1,N).
151: *> \endverbatim
152: *>
153: *> \param[out] WORK
154: *> \verbatim
155: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
156: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
157: *> \endverbatim
158: *>
159: *> \param[in] LWORK
160: *> \verbatim
161: *> LWORK is INTEGER
162: *> The dimension of the array WORK.
163: *> If N <= 1, LWORK >= 1.
164: *> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
165: *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
166: *>
167: *> If LWORK = -1, then a workspace query is assumed; the routine
168: *> only calculates the optimal sizes of the WORK and IWORK
169: *> arrays, returns these values as the first entries of the WORK
170: *> and IWORK arrays, and no error message related to LWORK or
171: *> LIWORK is issued by XERBLA.
172: *> \endverbatim
173: *>
174: *> \param[out] IWORK
175: *> \verbatim
176: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
177: *> On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
178: *> \endverbatim
179: *>
180: *> \param[in] LIWORK
181: *> \verbatim
182: *> LIWORK is INTEGER
183: *> The dimension of the array IWORK.
184: *> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
185: *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
186: *>
187: *> If LIWORK = -1, then a workspace query is assumed; the
188: *> routine only calculates the optimal sizes of the WORK and
189: *> IWORK arrays, returns these values as the first entries of
190: *> the WORK and IWORK arrays, and no error message related to
191: *> LWORK or LIWORK is issued by XERBLA.
192: *> \endverbatim
193: *>
194: *> \param[out] INFO
195: *> \verbatim
196: *> INFO is INTEGER
197: *> = 0: successful exit
198: *> < 0: if INFO = -i, the i-th argument had an illegal value
199: *> > 0: if INFO = i, and i is:
200: *> <= N: the algorithm failed to converge:
201: *> i off-diagonal elements of an intermediate
202: *> tridiagonal form did not converge to zero;
203: *> > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
204: *> returned INFO = i: B is not positive definite.
205: *> The factorization of B could not be completed and
206: *> no eigenvalues or eigenvectors were computed.
207: *> \endverbatim
208: *
209: * Authors:
210: * ========
211: *
212: *> \author Univ. of Tennessee
213: *> \author Univ. of California Berkeley
214: *> \author Univ. of Colorado Denver
215: *> \author NAG Ltd.
216: *
217: *> \ingroup doubleOTHEReigen
218: *
219: *> \par Contributors:
220: * ==================
221: *>
222: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
223: *
224: * =====================================================================
225: SUBROUTINE DSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
226: $ Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO )
227: *
228: * -- LAPACK driver routine --
229: * -- LAPACK is a software package provided by Univ. of Tennessee, --
230: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
231: *
232: * .. Scalar Arguments ..
233: CHARACTER JOBZ, UPLO
234: INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N
235: * ..
236: * .. Array Arguments ..
237: INTEGER IWORK( * )
238: DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
239: $ WORK( * ), Z( LDZ, * )
240: * ..
241: *
242: * =====================================================================
243: *
244: * .. Parameters ..
245: DOUBLE PRECISION ONE, ZERO
246: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
247: * ..
248: * .. Local Scalars ..
249: LOGICAL LQUERY, UPPER, WANTZ
250: CHARACTER VECT
251: INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLWRK2,
252: $ LWMIN
253: * ..
254: * .. External Functions ..
255: LOGICAL LSAME
256: EXTERNAL LSAME
257: * ..
258: * .. External Subroutines ..
259: EXTERNAL DGEMM, DLACPY, DPBSTF, DSBGST, DSBTRD, DSTEDC,
260: $ DSTERF, XERBLA
261: * ..
262: * .. Executable Statements ..
263: *
264: * Test the input parameters.
265: *
266: WANTZ = LSAME( JOBZ, 'V' )
267: UPPER = LSAME( UPLO, 'U' )
268: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
269: *
270: INFO = 0
271: IF( N.LE.1 ) THEN
272: LIWMIN = 1
273: LWMIN = 1
274: ELSE IF( WANTZ ) THEN
275: LIWMIN = 3 + 5*N
276: LWMIN = 1 + 5*N + 2*N**2
277: ELSE
278: LIWMIN = 1
279: LWMIN = 2*N
280: END IF
281: *
282: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
283: INFO = -1
284: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
285: INFO = -2
286: ELSE IF( N.LT.0 ) THEN
287: INFO = -3
288: ELSE IF( KA.LT.0 ) THEN
289: INFO = -4
290: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
291: INFO = -5
292: ELSE IF( LDAB.LT.KA+1 ) THEN
293: INFO = -7
294: ELSE IF( LDBB.LT.KB+1 ) THEN
295: INFO = -9
296: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
297: INFO = -12
298: END IF
299: *
300: IF( INFO.EQ.0 ) THEN
301: WORK( 1 ) = LWMIN
302: IWORK( 1 ) = LIWMIN
303: *
304: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
305: INFO = -14
306: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
307: INFO = -16
308: END IF
309: END IF
310: *
311: IF( INFO.NE.0 ) THEN
312: CALL XERBLA( 'DSBGVD', -INFO )
313: RETURN
314: ELSE IF( LQUERY ) THEN
315: RETURN
316: END IF
317: *
318: * Quick return if possible
319: *
320: IF( N.EQ.0 )
321: $ RETURN
322: *
323: * Form a split Cholesky factorization of B.
324: *
325: CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
326: IF( INFO.NE.0 ) THEN
327: INFO = N + INFO
328: RETURN
329: END IF
330: *
331: * Transform problem to standard eigenvalue problem.
332: *
333: INDE = 1
334: INDWRK = INDE + N
335: INDWK2 = INDWRK + N*N
336: LLWRK2 = LWORK - INDWK2 + 1
337: CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
338: $ WORK, IINFO )
339: *
340: * Reduce to tridiagonal form.
341: *
342: IF( WANTZ ) THEN
343: VECT = 'U'
344: ELSE
345: VECT = 'N'
346: END IF
347: CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
348: $ WORK( INDWRK ), IINFO )
349: *
350: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
351: *
352: IF( .NOT.WANTZ ) THEN
353: CALL DSTERF( N, W, WORK( INDE ), INFO )
354: ELSE
355: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
356: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
357: CALL DGEMM( 'N', 'N', N, N, N, ONE, Z, LDZ, WORK( INDWRK ), N,
358: $ ZERO, WORK( INDWK2 ), N )
359: CALL DLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
360: END IF
361: *
362: WORK( 1 ) = LWMIN
363: IWORK( 1 ) = LIWMIN
364: *
365: RETURN
366: *
367: * End of DSBGVD
368: *
369: END
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