1 SUBROUTINE DSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
2 $ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
3 $ LDZ, WORK, IWORK, IFAIL, INFO )
4 *
5 * -- LAPACK driver routine (version 3.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * November 2006
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, IU, KA, KB, LDAB, LDBB, LDQ, LDZ, M,
13 $ N
14 DOUBLE PRECISION ABSTOL, VL, VU
15 * ..
16 * .. Array Arguments ..
17 INTEGER IFAIL( * ), IWORK( * )
18 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
19 $ W( * ), WORK( * ), Z( LDZ, * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * DSBGVX computes selected eigenvalues, and optionally, eigenvectors
26 * of a real generalized symmetric-definite banded eigenproblem, of
27 * the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
28 * and banded, and B is also positive definite. Eigenvalues and
29 * eigenvectors can be selected by specifying either all eigenvalues,
30 * a range of values or a range of indices for the desired eigenvalues.
31 *
32 * Arguments
33 * =========
34 *
35 * JOBZ (input) CHARACTER*1
36 * = 'N': Compute eigenvalues only;
37 * = 'V': Compute eigenvalues and eigenvectors.
38 *
39 * RANGE (input) CHARACTER*1
40 * = 'A': all eigenvalues will be found.
41 * = 'V': all eigenvalues in the half-open interval (VL,VU]
42 * will be found.
43 * = 'I': the IL-th through IU-th eigenvalues will be found.
44 *
45 * UPLO (input) CHARACTER*1
46 * = 'U': Upper triangles of A and B are stored;
47 * = 'L': Lower triangles of A and B are stored.
48 *
49 * N (input) INTEGER
50 * The order of the matrices A and B. N >= 0.
51 *
52 * KA (input) INTEGER
53 * The number of superdiagonals of the matrix A if UPLO = 'U',
54 * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
55 *
56 * KB (input) INTEGER
57 * The number of superdiagonals of the matrix B if UPLO = 'U',
58 * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
59 *
60 * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
61 * On entry, the upper or lower triangle of the symmetric band
62 * matrix A, stored in the first ka+1 rows of the array. The
63 * j-th column of A is stored in the j-th column of the array AB
64 * as follows:
65 * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
66 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
67 *
68 * On exit, the contents of AB are destroyed.
69 *
70 * LDAB (input) INTEGER
71 * The leading dimension of the array AB. LDAB >= KA+1.
72 *
73 * BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
74 * On entry, the upper or lower triangle of the symmetric band
75 * matrix B, stored in the first kb+1 rows of the array. The
76 * j-th column of B is stored in the j-th column of the array BB
77 * as follows:
78 * if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
79 * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
80 *
81 * On exit, the factor S from the split Cholesky factorization
82 * B = S**T*S, as returned by DPBSTF.
83 *
84 * LDBB (input) INTEGER
85 * The leading dimension of the array BB. LDBB >= KB+1.
86 *
87 * Q (output) DOUBLE PRECISION array, dimension (LDQ, N)
88 * If JOBZ = 'V', the n-by-n matrix used in the reduction of
89 * A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
90 * and consequently C to tridiagonal form.
91 * If JOBZ = 'N', the array Q is not referenced.
92 *
93 * LDQ (input) INTEGER
94 * The leading dimension of the array Q. If JOBZ = 'N',
95 * LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
96 *
97 * VL (input) DOUBLE PRECISION
98 * VU (input) DOUBLE PRECISION
99 * If RANGE='V', the lower and upper bounds of the interval to
100 * be searched for eigenvalues. VL < VU.
101 * Not referenced if RANGE = 'A' or 'I'.
102 *
103 * IL (input) INTEGER
104 * IU (input) INTEGER
105 * If RANGE='I', the indices (in ascending order) of the
106 * smallest and largest eigenvalues to be returned.
107 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
108 * Not referenced if RANGE = 'A' or 'V'.
109 *
110 * ABSTOL (input) DOUBLE PRECISION
111 * The absolute error tolerance for the eigenvalues.
112 * An approximate eigenvalue is accepted as converged
113 * when it is determined to lie in an interval [a,b]
114 * of width less than or equal to
115 *
116 * ABSTOL + EPS * max( |a|,|b| ) ,
117 *
118 * where EPS is the machine precision. If ABSTOL is less than
119 * or equal to zero, then EPS*|T| will be used in its place,
120 * where |T| is the 1-norm of the tridiagonal matrix obtained
121 * by reducing A to tridiagonal form.
122 *
123 * Eigenvalues will be computed most accurately when ABSTOL is
124 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
125 * If this routine returns with INFO>0, indicating that some
126 * eigenvectors did not converge, try setting ABSTOL to
127 * 2*DLAMCH('S').
128 *
129 * M (output) INTEGER
130 * The total number of eigenvalues found. 0 <= M <= N.
131 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
132 *
133 * W (output) DOUBLE PRECISION array, dimension (N)
134 * If INFO = 0, the eigenvalues in ascending order.
135 *
136 * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
137 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
138 * eigenvectors, with the i-th column of Z holding the
139 * eigenvector associated with W(i). The eigenvectors are
140 * normalized so Z**T*B*Z = I.
141 * If JOBZ = 'N', then Z is not referenced.
142 *
143 * LDZ (input) INTEGER
144 * The leading dimension of the array Z. LDZ >= 1, and if
145 * JOBZ = 'V', LDZ >= max(1,N).
146 *
147 * WORK (workspace/output) DOUBLE PRECISION array, dimension (7*N)
148 *
149 * IWORK (workspace/output) INTEGER array, dimension (5*N)
150 *
151 * IFAIL (output) INTEGER array, dimension (M)
152 * If JOBZ = 'V', then if INFO = 0, the first M elements of
153 * IFAIL are zero. If INFO > 0, then IFAIL contains the
154 * indices of the eigenvalues that failed to converge.
155 * If JOBZ = 'N', then IFAIL is not referenced.
156 *
157 * INFO (output) INTEGER
158 * = 0 : successful exit
159 * < 0 : if INFO = -i, the i-th argument had an illegal value
160 * <= N: if INFO = i, then i eigenvectors failed to converge.
161 * Their indices are stored in IFAIL.
162 * > N : DPBSTF returned an error code; i.e.,
163 * if INFO = N + i, for 1 <= i <= N, then the leading
164 * minor of order i of B is not positive definite.
165 * The factorization of B could not be completed and
166 * no eigenvalues or eigenvectors were computed.
167 *
168 * Further Details
169 * ===============
170 *
171 * Based on contributions by
172 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
173 *
174 * =====================================================================
175 *
176 * .. Parameters ..
177 DOUBLE PRECISION ZERO, ONE
178 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
179 * ..
180 * .. Local Scalars ..
181 LOGICAL ALLEIG, INDEIG, TEST, UPPER, VALEIG, WANTZ
182 CHARACTER ORDER, VECT
183 INTEGER I, IINFO, INDD, INDE, INDEE, INDIBL, INDISP,
184 $ INDIWO, INDWRK, ITMP1, J, JJ, NSPLIT
185 DOUBLE PRECISION TMP1
186 * ..
187 * .. External Functions ..
188 LOGICAL LSAME
189 EXTERNAL LSAME
190 * ..
191 * .. External Subroutines ..
192 EXTERNAL DCOPY, DGEMV, DLACPY, DPBSTF, DSBGST, DSBTRD,
193 $ DSTEBZ, DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA
194 * ..
195 * .. Intrinsic Functions ..
196 INTRINSIC MIN
197 * ..
198 * .. Executable Statements ..
199 *
200 * Test the input parameters.
201 *
202 WANTZ = LSAME( JOBZ, 'V' )
203 UPPER = LSAME( UPLO, 'U' )
204 ALLEIG = LSAME( RANGE, 'A' )
205 VALEIG = LSAME( RANGE, 'V' )
206 INDEIG = LSAME( RANGE, 'I' )
207 *
208 INFO = 0
209 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
210 INFO = -1
211 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
212 INFO = -2
213 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
214 INFO = -3
215 ELSE IF( N.LT.0 ) THEN
216 INFO = -4
217 ELSE IF( KA.LT.0 ) THEN
218 INFO = -5
219 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
220 INFO = -6
221 ELSE IF( LDAB.LT.KA+1 ) THEN
222 INFO = -8
223 ELSE IF( LDBB.LT.KB+1 ) THEN
224 INFO = -10
225 ELSE IF( LDQ.LT.1 .OR. ( WANTZ .AND. LDQ.LT.N ) ) THEN
226 INFO = -12
227 ELSE
228 IF( VALEIG ) THEN
229 IF( N.GT.0 .AND. VU.LE.VL )
230 $ INFO = -14
231 ELSE IF( INDEIG ) THEN
232 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
233 INFO = -15
234 ELSE IF ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
235 INFO = -16
236 END IF
237 END IF
238 END IF
239 IF( INFO.EQ.0) THEN
240 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
241 INFO = -21
242 END IF
243 END IF
244 *
245 IF( INFO.NE.0 ) THEN
246 CALL XERBLA( 'DSBGVX', -INFO )
247 RETURN
248 END IF
249 *
250 * Quick return if possible
251 *
252 M = 0
253 IF( N.EQ.0 )
254 $ RETURN
255 *
256 * Form a split Cholesky factorization of B.
257 *
258 CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
259 IF( INFO.NE.0 ) THEN
260 INFO = N + INFO
261 RETURN
262 END IF
263 *
264 * Transform problem to standard eigenvalue problem.
265 *
266 CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ,
267 $ WORK, IINFO )
268 *
269 * Reduce symmetric band matrix to tridiagonal form.
270 *
271 INDD = 1
272 INDE = INDD + N
273 INDWRK = INDE + N
274 IF( WANTZ ) THEN
275 VECT = 'U'
276 ELSE
277 VECT = 'N'
278 END IF
279 CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, WORK( INDD ),
280 $ WORK( INDE ), Q, LDQ, WORK( INDWRK ), IINFO )
281 *
282 * If all eigenvalues are desired and ABSTOL is less than or equal
283 * to zero, then call DSTERF or SSTEQR. If this fails for some
284 * eigenvalue, then try DSTEBZ.
285 *
286 TEST = .FALSE.
287 IF( INDEIG ) THEN
288 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
289 TEST = .TRUE.
290 END IF
291 END IF
292 IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
293 CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
294 INDEE = INDWRK + 2*N
295 CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
296 IF( .NOT.WANTZ ) THEN
297 CALL DSTERF( N, W, WORK( INDEE ), INFO )
298 ELSE
299 CALL DLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
300 CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
301 $ WORK( INDWRK ), INFO )
302 IF( INFO.EQ.0 ) THEN
303 DO 10 I = 1, N
304 IFAIL( I ) = 0
305 10 CONTINUE
306 END IF
307 END IF
308 IF( INFO.EQ.0 ) THEN
309 M = N
310 GO TO 30
311 END IF
312 INFO = 0
313 END IF
314 *
315 * Otherwise, call DSTEBZ and, if eigenvectors are desired,
316 * call DSTEIN.
317 *
318 IF( WANTZ ) THEN
319 ORDER = 'B'
320 ELSE
321 ORDER = 'E'
322 END IF
323 INDIBL = 1
324 INDISP = INDIBL + N
325 INDIWO = INDISP + N
326 CALL DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL,
327 $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
328 $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
329 $ IWORK( INDIWO ), INFO )
330 *
331 IF( WANTZ ) THEN
332 CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
333 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
334 $ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO )
335 *
336 * Apply transformation matrix used in reduction to tridiagonal
337 * form to eigenvectors returned by DSTEIN.
338 *
339 DO 20 J = 1, M
340 CALL DCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
341 CALL DGEMV( 'N', N, N, ONE, Q, LDQ, WORK, 1, ZERO,
342 $ Z( 1, J ), 1 )
343 20 CONTINUE
344 END IF
345 *
346 30 CONTINUE
347 *
348 * If eigenvalues are not in order, then sort them, along with
349 * eigenvectors.
350 *
351 IF( WANTZ ) THEN
352 DO 50 J = 1, M - 1
353 I = 0
354 TMP1 = W( J )
355 DO 40 JJ = J + 1, M
356 IF( W( JJ ).LT.TMP1 ) THEN
357 I = JJ
358 TMP1 = W( JJ )
359 END IF
360 40 CONTINUE
361 *
362 IF( I.NE.0 ) THEN
363 ITMP1 = IWORK( INDIBL+I-1 )
364 W( I ) = W( J )
365 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
366 W( J ) = TMP1
367 IWORK( INDIBL+J-1 ) = ITMP1
368 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
369 IF( INFO.NE.0 ) THEN
370 ITMP1 = IFAIL( I )
371 IFAIL( I ) = IFAIL( J )
372 IFAIL( J ) = ITMP1
373 END IF
374 END IF
375 50 CONTINUE
376 END IF
377 *
378 RETURN
379 *
380 * End of DSBGVX
381 *
382 END
2 $ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
3 $ LDZ, WORK, IWORK, IFAIL, INFO )
4 *
5 * -- LAPACK driver routine (version 3.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * November 2006
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, IU, KA, KB, LDAB, LDBB, LDQ, LDZ, M,
13 $ N
14 DOUBLE PRECISION ABSTOL, VL, VU
15 * ..
16 * .. Array Arguments ..
17 INTEGER IFAIL( * ), IWORK( * )
18 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
19 $ W( * ), WORK( * ), Z( LDZ, * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * DSBGVX computes selected eigenvalues, and optionally, eigenvectors
26 * of a real generalized symmetric-definite banded eigenproblem, of
27 * the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
28 * and banded, and B is also positive definite. Eigenvalues and
29 * eigenvectors can be selected by specifying either all eigenvalues,
30 * a range of values or a range of indices for the desired eigenvalues.
31 *
32 * Arguments
33 * =========
34 *
35 * JOBZ (input) CHARACTER*1
36 * = 'N': Compute eigenvalues only;
37 * = 'V': Compute eigenvalues and eigenvectors.
38 *
39 * RANGE (input) CHARACTER*1
40 * = 'A': all eigenvalues will be found.
41 * = 'V': all eigenvalues in the half-open interval (VL,VU]
42 * will be found.
43 * = 'I': the IL-th through IU-th eigenvalues will be found.
44 *
45 * UPLO (input) CHARACTER*1
46 * = 'U': Upper triangles of A and B are stored;
47 * = 'L': Lower triangles of A and B are stored.
48 *
49 * N (input) INTEGER
50 * The order of the matrices A and B. N >= 0.
51 *
52 * KA (input) INTEGER
53 * The number of superdiagonals of the matrix A if UPLO = 'U',
54 * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
55 *
56 * KB (input) INTEGER
57 * The number of superdiagonals of the matrix B if UPLO = 'U',
58 * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
59 *
60 * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
61 * On entry, the upper or lower triangle of the symmetric band
62 * matrix A, stored in the first ka+1 rows of the array. The
63 * j-th column of A is stored in the j-th column of the array AB
64 * as follows:
65 * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
66 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
67 *
68 * On exit, the contents of AB are destroyed.
69 *
70 * LDAB (input) INTEGER
71 * The leading dimension of the array AB. LDAB >= KA+1.
72 *
73 * BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
74 * On entry, the upper or lower triangle of the symmetric band
75 * matrix B, stored in the first kb+1 rows of the array. The
76 * j-th column of B is stored in the j-th column of the array BB
77 * as follows:
78 * if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
79 * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
80 *
81 * On exit, the factor S from the split Cholesky factorization
82 * B = S**T*S, as returned by DPBSTF.
83 *
84 * LDBB (input) INTEGER
85 * The leading dimension of the array BB. LDBB >= KB+1.
86 *
87 * Q (output) DOUBLE PRECISION array, dimension (LDQ, N)
88 * If JOBZ = 'V', the n-by-n matrix used in the reduction of
89 * A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
90 * and consequently C to tridiagonal form.
91 * If JOBZ = 'N', the array Q is not referenced.
92 *
93 * LDQ (input) INTEGER
94 * The leading dimension of the array Q. If JOBZ = 'N',
95 * LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
96 *
97 * VL (input) DOUBLE PRECISION
98 * VU (input) DOUBLE PRECISION
99 * If RANGE='V', the lower and upper bounds of the interval to
100 * be searched for eigenvalues. VL < VU.
101 * Not referenced if RANGE = 'A' or 'I'.
102 *
103 * IL (input) INTEGER
104 * IU (input) INTEGER
105 * If RANGE='I', the indices (in ascending order) of the
106 * smallest and largest eigenvalues to be returned.
107 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
108 * Not referenced if RANGE = 'A' or 'V'.
109 *
110 * ABSTOL (input) DOUBLE PRECISION
111 * The absolute error tolerance for the eigenvalues.
112 * An approximate eigenvalue is accepted as converged
113 * when it is determined to lie in an interval [a,b]
114 * of width less than or equal to
115 *
116 * ABSTOL + EPS * max( |a|,|b| ) ,
117 *
118 * where EPS is the machine precision. If ABSTOL is less than
119 * or equal to zero, then EPS*|T| will be used in its place,
120 * where |T| is the 1-norm of the tridiagonal matrix obtained
121 * by reducing A to tridiagonal form.
122 *
123 * Eigenvalues will be computed most accurately when ABSTOL is
124 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
125 * If this routine returns with INFO>0, indicating that some
126 * eigenvectors did not converge, try setting ABSTOL to
127 * 2*DLAMCH('S').
128 *
129 * M (output) INTEGER
130 * The total number of eigenvalues found. 0 <= M <= N.
131 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
132 *
133 * W (output) DOUBLE PRECISION array, dimension (N)
134 * If INFO = 0, the eigenvalues in ascending order.
135 *
136 * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
137 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
138 * eigenvectors, with the i-th column of Z holding the
139 * eigenvector associated with W(i). The eigenvectors are
140 * normalized so Z**T*B*Z = I.
141 * If JOBZ = 'N', then Z is not referenced.
142 *
143 * LDZ (input) INTEGER
144 * The leading dimension of the array Z. LDZ >= 1, and if
145 * JOBZ = 'V', LDZ >= max(1,N).
146 *
147 * WORK (workspace/output) DOUBLE PRECISION array, dimension (7*N)
148 *
149 * IWORK (workspace/output) INTEGER array, dimension (5*N)
150 *
151 * IFAIL (output) INTEGER array, dimension (M)
152 * If JOBZ = 'V', then if INFO = 0, the first M elements of
153 * IFAIL are zero. If INFO > 0, then IFAIL contains the
154 * indices of the eigenvalues that failed to converge.
155 * If JOBZ = 'N', then IFAIL is not referenced.
156 *
157 * INFO (output) INTEGER
158 * = 0 : successful exit
159 * < 0 : if INFO = -i, the i-th argument had an illegal value
160 * <= N: if INFO = i, then i eigenvectors failed to converge.
161 * Their indices are stored in IFAIL.
162 * > N : DPBSTF returned an error code; i.e.,
163 * if INFO = N + i, for 1 <= i <= N, then the leading
164 * minor of order i of B is not positive definite.
165 * The factorization of B could not be completed and
166 * no eigenvalues or eigenvectors were computed.
167 *
168 * Further Details
169 * ===============
170 *
171 * Based on contributions by
172 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
173 *
174 * =====================================================================
175 *
176 * .. Parameters ..
177 DOUBLE PRECISION ZERO, ONE
178 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
179 * ..
180 * .. Local Scalars ..
181 LOGICAL ALLEIG, INDEIG, TEST, UPPER, VALEIG, WANTZ
182 CHARACTER ORDER, VECT
183 INTEGER I, IINFO, INDD, INDE, INDEE, INDIBL, INDISP,
184 $ INDIWO, INDWRK, ITMP1, J, JJ, NSPLIT
185 DOUBLE PRECISION TMP1
186 * ..
187 * .. External Functions ..
188 LOGICAL LSAME
189 EXTERNAL LSAME
190 * ..
191 * .. External Subroutines ..
192 EXTERNAL DCOPY, DGEMV, DLACPY, DPBSTF, DSBGST, DSBTRD,
193 $ DSTEBZ, DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA
194 * ..
195 * .. Intrinsic Functions ..
196 INTRINSIC MIN
197 * ..
198 * .. Executable Statements ..
199 *
200 * Test the input parameters.
201 *
202 WANTZ = LSAME( JOBZ, 'V' )
203 UPPER = LSAME( UPLO, 'U' )
204 ALLEIG = LSAME( RANGE, 'A' )
205 VALEIG = LSAME( RANGE, 'V' )
206 INDEIG = LSAME( RANGE, 'I' )
207 *
208 INFO = 0
209 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
210 INFO = -1
211 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
212 INFO = -2
213 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
214 INFO = -3
215 ELSE IF( N.LT.0 ) THEN
216 INFO = -4
217 ELSE IF( KA.LT.0 ) THEN
218 INFO = -5
219 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
220 INFO = -6
221 ELSE IF( LDAB.LT.KA+1 ) THEN
222 INFO = -8
223 ELSE IF( LDBB.LT.KB+1 ) THEN
224 INFO = -10
225 ELSE IF( LDQ.LT.1 .OR. ( WANTZ .AND. LDQ.LT.N ) ) THEN
226 INFO = -12
227 ELSE
228 IF( VALEIG ) THEN
229 IF( N.GT.0 .AND. VU.LE.VL )
230 $ INFO = -14
231 ELSE IF( INDEIG ) THEN
232 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
233 INFO = -15
234 ELSE IF ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
235 INFO = -16
236 END IF
237 END IF
238 END IF
239 IF( INFO.EQ.0) THEN
240 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
241 INFO = -21
242 END IF
243 END IF
244 *
245 IF( INFO.NE.0 ) THEN
246 CALL XERBLA( 'DSBGVX', -INFO )
247 RETURN
248 END IF
249 *
250 * Quick return if possible
251 *
252 M = 0
253 IF( N.EQ.0 )
254 $ RETURN
255 *
256 * Form a split Cholesky factorization of B.
257 *
258 CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
259 IF( INFO.NE.0 ) THEN
260 INFO = N + INFO
261 RETURN
262 END IF
263 *
264 * Transform problem to standard eigenvalue problem.
265 *
266 CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ,
267 $ WORK, IINFO )
268 *
269 * Reduce symmetric band matrix to tridiagonal form.
270 *
271 INDD = 1
272 INDE = INDD + N
273 INDWRK = INDE + N
274 IF( WANTZ ) THEN
275 VECT = 'U'
276 ELSE
277 VECT = 'N'
278 END IF
279 CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, WORK( INDD ),
280 $ WORK( INDE ), Q, LDQ, WORK( INDWRK ), IINFO )
281 *
282 * If all eigenvalues are desired and ABSTOL is less than or equal
283 * to zero, then call DSTERF or SSTEQR. If this fails for some
284 * eigenvalue, then try DSTEBZ.
285 *
286 TEST = .FALSE.
287 IF( INDEIG ) THEN
288 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
289 TEST = .TRUE.
290 END IF
291 END IF
292 IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
293 CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
294 INDEE = INDWRK + 2*N
295 CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
296 IF( .NOT.WANTZ ) THEN
297 CALL DSTERF( N, W, WORK( INDEE ), INFO )
298 ELSE
299 CALL DLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
300 CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
301 $ WORK( INDWRK ), INFO )
302 IF( INFO.EQ.0 ) THEN
303 DO 10 I = 1, N
304 IFAIL( I ) = 0
305 10 CONTINUE
306 END IF
307 END IF
308 IF( INFO.EQ.0 ) THEN
309 M = N
310 GO TO 30
311 END IF
312 INFO = 0
313 END IF
314 *
315 * Otherwise, call DSTEBZ and, if eigenvectors are desired,
316 * call DSTEIN.
317 *
318 IF( WANTZ ) THEN
319 ORDER = 'B'
320 ELSE
321 ORDER = 'E'
322 END IF
323 INDIBL = 1
324 INDISP = INDIBL + N
325 INDIWO = INDISP + N
326 CALL DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL,
327 $ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
328 $ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
329 $ IWORK( INDIWO ), INFO )
330 *
331 IF( WANTZ ) THEN
332 CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
333 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
334 $ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO )
335 *
336 * Apply transformation matrix used in reduction to tridiagonal
337 * form to eigenvectors returned by DSTEIN.
338 *
339 DO 20 J = 1, M
340 CALL DCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
341 CALL DGEMV( 'N', N, N, ONE, Q, LDQ, WORK, 1, ZERO,
342 $ Z( 1, J ), 1 )
343 20 CONTINUE
344 END IF
345 *
346 30 CONTINUE
347 *
348 * If eigenvalues are not in order, then sort them, along with
349 * eigenvectors.
350 *
351 IF( WANTZ ) THEN
352 DO 50 J = 1, M - 1
353 I = 0
354 TMP1 = W( J )
355 DO 40 JJ = J + 1, M
356 IF( W( JJ ).LT.TMP1 ) THEN
357 I = JJ
358 TMP1 = W( JJ )
359 END IF
360 40 CONTINUE
361 *
362 IF( I.NE.0 ) THEN
363 ITMP1 = IWORK( INDIBL+I-1 )
364 W( I ) = W( J )
365 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
366 W( J ) = TMP1
367 IWORK( INDIBL+J-1 ) = ITMP1
368 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
369 IF( INFO.NE.0 ) THEN
370 ITMP1 = IFAIL( I )
371 IFAIL( I ) = IFAIL( J )
372 IFAIL( J ) = ITMP1
373 END IF
374 END IF
375 50 CONTINUE
376 END IF
377 *
378 RETURN
379 *
380 * End of DSBGVX
381 *
382 END