1: *> \brief \b DSBGV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSBGV + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbgv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
22: * LDZ, WORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
30: * $ WORK( * ), Z( LDZ, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DSBGV computes all the eigenvalues, and optionally, the eigenvectors
40: *> of a real generalized symmetric-definite banded eigenproblem, of
41: *> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
42: *> and banded, and B is also positive definite.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] JOBZ
49: *> \verbatim
50: *> JOBZ is CHARACTER*1
51: *> = 'N': Compute eigenvalues only;
52: *> = 'V': Compute eigenvalues and eigenvectors.
53: *> \endverbatim
54: *>
55: *> \param[in] UPLO
56: *> \verbatim
57: *> UPLO is CHARACTER*1
58: *> = 'U': Upper triangles of A and B are stored;
59: *> = 'L': Lower triangles of A and B are stored.
60: *> \endverbatim
61: *>
62: *> \param[in] N
63: *> \verbatim
64: *> N is INTEGER
65: *> The order of the matrices A and B. N >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in] KA
69: *> \verbatim
70: *> KA is INTEGER
71: *> The number of superdiagonals of the matrix A if UPLO = 'U',
72: *> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
73: *> \endverbatim
74: *>
75: *> \param[in] KB
76: *> \verbatim
77: *> KB is INTEGER
78: *> The number of superdiagonals of the matrix B if UPLO = 'U',
79: *> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
80: *> \endverbatim
81: *>
82: *> \param[in,out] AB
83: *> \verbatim
84: *> AB is DOUBLE PRECISION array, dimension (LDAB, N)
85: *> On entry, the upper or lower triangle of the symmetric band
86: *> matrix A, stored in the first ka+1 rows of the array. The
87: *> j-th column of A is stored in the j-th column of the array AB
88: *> as follows:
89: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
90: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
91: *>
92: *> On exit, the contents of AB are destroyed.
93: *> \endverbatim
94: *>
95: *> \param[in] LDAB
96: *> \verbatim
97: *> LDAB is INTEGER
98: *> The leading dimension of the array AB. LDAB >= KA+1.
99: *> \endverbatim
100: *>
101: *> \param[in,out] BB
102: *> \verbatim
103: *> BB is DOUBLE PRECISION array, dimension (LDBB, N)
104: *> On entry, the upper or lower triangle of the symmetric band
105: *> matrix B, stored in the first kb+1 rows of the array. The
106: *> j-th column of B is stored in the j-th column of the array BB
107: *> as follows:
108: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
109: *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
110: *>
111: *> On exit, the factor S from the split Cholesky factorization
112: *> B = S**T*S, as returned by DPBSTF.
113: *> \endverbatim
114: *>
115: *> \param[in] LDBB
116: *> \verbatim
117: *> LDBB is INTEGER
118: *> The leading dimension of the array BB. LDBB >= KB+1.
119: *> \endverbatim
120: *>
121: *> \param[out] W
122: *> \verbatim
123: *> W is DOUBLE PRECISION array, dimension (N)
124: *> If INFO = 0, the eigenvalues in ascending order.
125: *> \endverbatim
126: *>
127: *> \param[out] Z
128: *> \verbatim
129: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
130: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
131: *> eigenvectors, with the i-th column of Z holding the
132: *> eigenvector associated with W(i). The eigenvectors are
133: *> normalized so that Z**T*B*Z = I.
134: *> If JOBZ = 'N', then Z is not referenced.
135: *> \endverbatim
136: *>
137: *> \param[in] LDZ
138: *> \verbatim
139: *> LDZ is INTEGER
140: *> The leading dimension of the array Z. LDZ >= 1, and if
141: *> JOBZ = 'V', LDZ >= N.
142: *> \endverbatim
143: *>
144: *> \param[out] WORK
145: *> \verbatim
146: *> WORK is DOUBLE PRECISION array, dimension (3*N)
147: *> \endverbatim
148: *>
149: *> \param[out] INFO
150: *> \verbatim
151: *> INFO is INTEGER
152: *> = 0: successful exit
153: *> < 0: if INFO = -i, the i-th argument had an illegal value
154: *> > 0: if INFO = i, and i is:
155: *> <= N: the algorithm failed to converge:
156: *> i off-diagonal elements of an intermediate
157: *> tridiagonal form did not converge to zero;
158: *> > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
159: *> returned INFO = i: B is not positive definite.
160: *> The factorization of B could not be completed and
161: *> no eigenvalues or eigenvectors were computed.
162: *> \endverbatim
163: *
164: * Authors:
165: * ========
166: *
167: *> \author Univ. of Tennessee
168: *> \author Univ. of California Berkeley
169: *> \author Univ. of Colorado Denver
170: *> \author NAG Ltd.
171: *
172: *> \ingroup doubleOTHEReigen
173: *
174: * =====================================================================
175: SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
176: $ LDZ, WORK, INFO )
177: *
178: * -- LAPACK driver routine --
179: * -- LAPACK is a software package provided by Univ. of Tennessee, --
180: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181: *
182: * .. Scalar Arguments ..
183: CHARACTER JOBZ, UPLO
184: INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
185: * ..
186: * .. Array Arguments ..
187: DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
188: $ WORK( * ), Z( LDZ, * )
189: * ..
190: *
191: * =====================================================================
192: *
193: * .. Local Scalars ..
194: LOGICAL UPPER, WANTZ
195: CHARACTER VECT
196: INTEGER IINFO, INDE, INDWRK
197: * ..
198: * .. External Functions ..
199: LOGICAL LSAME
200: EXTERNAL LSAME
201: * ..
202: * .. External Subroutines ..
203: EXTERNAL DPBSTF, DSBGST, DSBTRD, DSTEQR, DSTERF, XERBLA
204: * ..
205: * .. Executable Statements ..
206: *
207: * Test the input parameters.
208: *
209: WANTZ = LSAME( JOBZ, 'V' )
210: UPPER = LSAME( UPLO, 'U' )
211: *
212: INFO = 0
213: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
214: INFO = -1
215: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
216: INFO = -2
217: ELSE IF( N.LT.0 ) THEN
218: INFO = -3
219: ELSE IF( KA.LT.0 ) THEN
220: INFO = -4
221: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
222: INFO = -5
223: ELSE IF( LDAB.LT.KA+1 ) THEN
224: INFO = -7
225: ELSE IF( LDBB.LT.KB+1 ) THEN
226: INFO = -9
227: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
228: INFO = -12
229: END IF
230: IF( INFO.NE.0 ) THEN
231: CALL XERBLA( 'DSBGV ', -INFO )
232: RETURN
233: END IF
234: *
235: * Quick return if possible
236: *
237: IF( N.EQ.0 )
238: $ RETURN
239: *
240: * Form a split Cholesky factorization of B.
241: *
242: CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
243: IF( INFO.NE.0 ) THEN
244: INFO = N + INFO
245: RETURN
246: END IF
247: *
248: * Transform problem to standard eigenvalue problem.
249: *
250: INDE = 1
251: INDWRK = INDE + N
252: CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
253: $ WORK( INDWRK ), IINFO )
254: *
255: * Reduce to tridiagonal form.
256: *
257: IF( WANTZ ) THEN
258: VECT = 'U'
259: ELSE
260: VECT = 'N'
261: END IF
262: CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
263: $ WORK( INDWRK ), IINFO )
264: *
265: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
266: *
267: IF( .NOT.WANTZ ) THEN
268: CALL DSTERF( N, W, WORK( INDE ), INFO )
269: ELSE
270: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
271: $ INFO )
272: END IF
273: RETURN
274: *
275: * End of DSBGV
276: *
277: END
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