1 SUBROUTINE ZHBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
2 $ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
3 $ LDZ, WORK, RWORK, 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 RWORK( * ), W( * )
19 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
20 $ WORK( * ), Z( LDZ, * )
21 * ..
22 *
23 * Purpose
24 * =======
25 *
26 * ZHBGVX computes all the eigenvalues, and optionally, the eigenvectors
27 * of a complex generalized Hermitian-definite banded eigenproblem, of
28 * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
29 * and banded, and B is also positive definite. Eigenvalues and
30 * eigenvectors can be selected by specifying either all eigenvalues,
31 * a range of values or a range of indices for the desired eigenvalues.
32 *
33 * Arguments
34 * =========
35 *
36 * JOBZ (input) CHARACTER*1
37 * = 'N': Compute eigenvalues only;
38 * = 'V': Compute eigenvalues and eigenvectors.
39 *
40 * RANGE (input) CHARACTER*1
41 * = 'A': all eigenvalues will be found;
42 * = 'V': all eigenvalues in the half-open interval (VL,VU]
43 * will be found;
44 * = 'I': the IL-th through IU-th eigenvalues will be found.
45 *
46 * UPLO (input) CHARACTER*1
47 * = 'U': Upper triangles of A and B are stored;
48 * = 'L': Lower triangles of A and B are stored.
49 *
50 * N (input) INTEGER
51 * The order of the matrices A and B. N >= 0.
52 *
53 * KA (input) INTEGER
54 * The number of superdiagonals of the matrix A if UPLO = 'U',
55 * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
56 *
57 * KB (input) INTEGER
58 * The number of superdiagonals of the matrix B if UPLO = 'U',
59 * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
60 *
61 * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
62 * On entry, the upper or lower triangle of the Hermitian band
63 * matrix A, stored in the first ka+1 rows of the array. The
64 * j-th column of A is stored in the j-th column of the array AB
65 * as follows:
66 * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
67 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
68 *
69 * On exit, the contents of AB are destroyed.
70 *
71 * LDAB (input) INTEGER
72 * The leading dimension of the array AB. LDAB >= KA+1.
73 *
74 * BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
75 * On entry, the upper or lower triangle of the Hermitian band
76 * matrix B, stored in the first kb+1 rows of the array. The
77 * j-th column of B is stored in the j-th column of the array BB
78 * as follows:
79 * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
80 * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
81 *
82 * On exit, the factor S from the split Cholesky factorization
83 * B = S**H*S, as returned by ZPBSTF.
84 *
85 * LDBB (input) INTEGER
86 * The leading dimension of the array BB. LDBB >= KB+1.
87 *
88 * Q (output) COMPLEX*16 array, dimension (LDQ, N)
89 * If JOBZ = 'V', the n-by-n matrix used in the reduction of
90 * A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
91 * and consequently C to tridiagonal form.
92 * If JOBZ = 'N', the array Q is not referenced.
93 *
94 * LDQ (input) INTEGER
95 * The leading dimension of the array Q. If JOBZ = 'N',
96 * LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
97 *
98 * VL (input) DOUBLE PRECISION
99 * VU (input) DOUBLE PRECISION
100 * If RANGE='V', the lower and upper bounds of the interval to
101 * be searched for eigenvalues. VL < VU.
102 * Not referenced if RANGE = 'A' or 'I'.
103 *
104 * IL (input) INTEGER
105 * IU (input) INTEGER
106 * If RANGE='I', the indices (in ascending order) of the
107 * smallest and largest eigenvalues to be returned.
108 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
109 * Not referenced if RANGE = 'A' or 'V'.
110 *
111 * ABSTOL (input) DOUBLE PRECISION
112 * The absolute error tolerance for the eigenvalues.
113 * An approximate eigenvalue is accepted as converged
114 * when it is determined to lie in an interval [a,b]
115 * of width less than or equal to
116 *
117 * ABSTOL + EPS * max( |a|,|b| ) ,
118 *
119 * where EPS is the machine precision. If ABSTOL is less than
120 * or equal to zero, then EPS*|T| will be used in its place,
121 * where |T| is the 1-norm of the tridiagonal matrix obtained
122 * by reducing AP to tridiagonal form.
123 *
124 * Eigenvalues will be computed most accurately when ABSTOL is
125 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
126 * If this routine returns with INFO>0, indicating that some
127 * eigenvectors did not converge, try setting ABSTOL to
128 * 2*DLAMCH('S').
129 *
130 * M (output) INTEGER
131 * The total number of eigenvalues found. 0 <= M <= N.
132 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
133 *
134 * W (output) DOUBLE PRECISION array, dimension (N)
135 * If INFO = 0, the eigenvalues in ascending order.
136 *
137 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
138 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
139 * eigenvectors, with the i-th column of Z holding the
140 * eigenvector associated with W(i). The eigenvectors are
141 * normalized so that Z**H*B*Z = I.
142 * If JOBZ = 'N', then Z is not referenced.
143 *
144 * LDZ (input) INTEGER
145 * The leading dimension of the array Z. LDZ >= 1, and if
146 * JOBZ = 'V', LDZ >= N.
147 *
148 * WORK (workspace) COMPLEX*16 array, dimension (N)
149 *
150 * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
151 *
152 * IWORK (workspace) INTEGER array, dimension (5*N)
153 *
154 * IFAIL (output) INTEGER array, dimension (N)
155 * If JOBZ = 'V', then if INFO = 0, the first M elements of
156 * IFAIL are zero. If INFO > 0, then IFAIL contains the
157 * indices of the eigenvectors that failed to converge.
158 * If JOBZ = 'N', then IFAIL is not referenced.
159 *
160 * INFO (output) INTEGER
161 * = 0: successful exit
162 * < 0: if INFO = -i, the i-th argument had an illegal value
163 * > 0: if INFO = i, and i is:
164 * <= N: then i eigenvectors failed to converge. Their
165 * indices are stored in array IFAIL.
166 * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
167 * returned INFO = i: B is not positive definite.
168 * The factorization of B could not be completed and
169 * no eigenvalues or eigenvectors were computed.
170 *
171 * Further Details
172 * ===============
173 *
174 * Based on contributions by
175 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
176 *
177 * =====================================================================
178 *
179 * .. Parameters ..
180 DOUBLE PRECISION ZERO
181 PARAMETER ( ZERO = 0.0D+0 )
182 COMPLEX*16 CZERO, CONE
183 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
184 $ CONE = ( 1.0D+0, 0.0D+0 ) )
185 * ..
186 * .. Local Scalars ..
187 LOGICAL ALLEIG, INDEIG, TEST, UPPER, VALEIG, WANTZ
188 CHARACTER ORDER, VECT
189 INTEGER I, IINFO, INDD, INDE, INDEE, INDIBL, INDISP,
190 $ INDIWK, INDRWK, INDWRK, ITMP1, J, JJ, NSPLIT
191 DOUBLE PRECISION TMP1
192 * ..
193 * .. External Functions ..
194 LOGICAL LSAME
195 EXTERNAL LSAME
196 * ..
197 * .. External Subroutines ..
198 EXTERNAL DCOPY, DSTEBZ, DSTERF, XERBLA, ZCOPY, ZGEMV,
199 $ ZHBGST, ZHBTRD, ZLACPY, ZPBSTF, ZSTEIN, ZSTEQR,
200 $ ZSWAP
201 * ..
202 * .. Intrinsic Functions ..
203 INTRINSIC MIN
204 * ..
205 * .. Executable Statements ..
206 *
207 * Test the input parameters.
208 *
209 WANTZ = LSAME( JOBZ, 'V' )
210 UPPER = LSAME( UPLO, 'U' )
211 ALLEIG = LSAME( RANGE, 'A' )
212 VALEIG = LSAME( RANGE, 'V' )
213 INDEIG = LSAME( RANGE, 'I' )
214 *
215 INFO = 0
216 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
217 INFO = -1
218 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
219 INFO = -2
220 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
221 INFO = -3
222 ELSE IF( N.LT.0 ) THEN
223 INFO = -4
224 ELSE IF( KA.LT.0 ) THEN
225 INFO = -5
226 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
227 INFO = -6
228 ELSE IF( LDAB.LT.KA+1 ) THEN
229 INFO = -8
230 ELSE IF( LDBB.LT.KB+1 ) THEN
231 INFO = -10
232 ELSE IF( LDQ.LT.1 .OR. ( WANTZ .AND. LDQ.LT.N ) ) THEN
233 INFO = -12
234 ELSE
235 IF( VALEIG ) THEN
236 IF( N.GT.0 .AND. VU.LE.VL )
237 $ INFO = -14
238 ELSE IF( INDEIG ) THEN
239 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
240 INFO = -15
241 ELSE IF ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
242 INFO = -16
243 END IF
244 END IF
245 END IF
246 IF( INFO.EQ.0) THEN
247 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
248 INFO = -21
249 END IF
250 END IF
251 *
252 IF( INFO.NE.0 ) THEN
253 CALL XERBLA( 'ZHBGVX', -INFO )
254 RETURN
255 END IF
256 *
257 * Quick return if possible
258 *
259 M = 0
260 IF( N.EQ.0 )
261 $ RETURN
262 *
263 * Form a split Cholesky factorization of B.
264 *
265 CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
266 IF( INFO.NE.0 ) THEN
267 INFO = N + INFO
268 RETURN
269 END IF
270 *
271 * Transform problem to standard eigenvalue problem.
272 *
273 CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ,
274 $ WORK, RWORK, IINFO )
275 *
276 * Solve the standard eigenvalue problem.
277 * Reduce Hermitian band matrix to tridiagonal form.
278 *
279 INDD = 1
280 INDE = INDD + N
281 INDRWK = INDE + N
282 INDWRK = 1
283 IF( WANTZ ) THEN
284 VECT = 'U'
285 ELSE
286 VECT = 'N'
287 END IF
288 CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, RWORK( INDD ),
289 $ RWORK( INDE ), Q, LDQ, WORK( INDWRK ), IINFO )
290 *
291 * If all eigenvalues are desired and ABSTOL is less than or equal
292 * to zero, then call DSTERF or ZSTEQR. If this fails for some
293 * eigenvalue, then try DSTEBZ.
294 *
295 TEST = .FALSE.
296 IF( INDEIG ) THEN
297 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
298 TEST = .TRUE.
299 END IF
300 END IF
301 IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
302 CALL DCOPY( N, RWORK( INDD ), 1, W, 1 )
303 INDEE = INDRWK + 2*N
304 CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
305 IF( .NOT.WANTZ ) THEN
306 CALL DSTERF( N, W, RWORK( INDEE ), INFO )
307 ELSE
308 CALL ZLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
309 CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
310 $ RWORK( INDRWK ), INFO )
311 IF( INFO.EQ.0 ) THEN
312 DO 10 I = 1, N
313 IFAIL( I ) = 0
314 10 CONTINUE
315 END IF
316 END IF
317 IF( INFO.EQ.0 ) THEN
318 M = N
319 GO TO 30
320 END IF
321 INFO = 0
322 END IF
323 *
324 * Otherwise, call DSTEBZ and, if eigenvectors are desired,
325 * call ZSTEIN.
326 *
327 IF( WANTZ ) THEN
328 ORDER = 'B'
329 ELSE
330 ORDER = 'E'
331 END IF
332 INDIBL = 1
333 INDISP = INDIBL + N
334 INDIWK = INDISP + N
335 CALL DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL,
336 $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
337 $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
338 $ IWORK( INDIWK ), INFO )
339 *
340 IF( WANTZ ) THEN
341 CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
342 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
343 $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
344 *
345 * Apply unitary matrix used in reduction to tridiagonal
346 * form to eigenvectors returned by ZSTEIN.
347 *
348 DO 20 J = 1, M
349 CALL ZCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
350 CALL ZGEMV( 'N', N, N, CONE, Q, LDQ, WORK, 1, CZERO,
351 $ Z( 1, J ), 1 )
352 20 CONTINUE
353 END IF
354 *
355 30 CONTINUE
356 *
357 * If eigenvalues are not in order, then sort them, along with
358 * eigenvectors.
359 *
360 IF( WANTZ ) THEN
361 DO 50 J = 1, M - 1
362 I = 0
363 TMP1 = W( J )
364 DO 40 JJ = J + 1, M
365 IF( W( JJ ).LT.TMP1 ) THEN
366 I = JJ
367 TMP1 = W( JJ )
368 END IF
369 40 CONTINUE
370 *
371 IF( I.NE.0 ) THEN
372 ITMP1 = IWORK( INDIBL+I-1 )
373 W( I ) = W( J )
374 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
375 W( J ) = TMP1
376 IWORK( INDIBL+J-1 ) = ITMP1
377 CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
378 IF( INFO.NE.0 ) THEN
379 ITMP1 = IFAIL( I )
380 IFAIL( I ) = IFAIL( J )
381 IFAIL( J ) = ITMP1
382 END IF
383 END IF
384 50 CONTINUE
385 END IF
386 *
387 RETURN
388 *
389 * End of ZHBGVX
390 *
391 END
2 $ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
3 $ LDZ, WORK, RWORK, 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 RWORK( * ), W( * )
19 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
20 $ WORK( * ), Z( LDZ, * )
21 * ..
22 *
23 * Purpose
24 * =======
25 *
26 * ZHBGVX computes all the eigenvalues, and optionally, the eigenvectors
27 * of a complex generalized Hermitian-definite banded eigenproblem, of
28 * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
29 * and banded, and B is also positive definite. Eigenvalues and
30 * eigenvectors can be selected by specifying either all eigenvalues,
31 * a range of values or a range of indices for the desired eigenvalues.
32 *
33 * Arguments
34 * =========
35 *
36 * JOBZ (input) CHARACTER*1
37 * = 'N': Compute eigenvalues only;
38 * = 'V': Compute eigenvalues and eigenvectors.
39 *
40 * RANGE (input) CHARACTER*1
41 * = 'A': all eigenvalues will be found;
42 * = 'V': all eigenvalues in the half-open interval (VL,VU]
43 * will be found;
44 * = 'I': the IL-th through IU-th eigenvalues will be found.
45 *
46 * UPLO (input) CHARACTER*1
47 * = 'U': Upper triangles of A and B are stored;
48 * = 'L': Lower triangles of A and B are stored.
49 *
50 * N (input) INTEGER
51 * The order of the matrices A and B. N >= 0.
52 *
53 * KA (input) INTEGER
54 * The number of superdiagonals of the matrix A if UPLO = 'U',
55 * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
56 *
57 * KB (input) INTEGER
58 * The number of superdiagonals of the matrix B if UPLO = 'U',
59 * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
60 *
61 * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
62 * On entry, the upper or lower triangle of the Hermitian band
63 * matrix A, stored in the first ka+1 rows of the array. The
64 * j-th column of A is stored in the j-th column of the array AB
65 * as follows:
66 * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
67 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
68 *
69 * On exit, the contents of AB are destroyed.
70 *
71 * LDAB (input) INTEGER
72 * The leading dimension of the array AB. LDAB >= KA+1.
73 *
74 * BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
75 * On entry, the upper or lower triangle of the Hermitian band
76 * matrix B, stored in the first kb+1 rows of the array. The
77 * j-th column of B is stored in the j-th column of the array BB
78 * as follows:
79 * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
80 * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
81 *
82 * On exit, the factor S from the split Cholesky factorization
83 * B = S**H*S, as returned by ZPBSTF.
84 *
85 * LDBB (input) INTEGER
86 * The leading dimension of the array BB. LDBB >= KB+1.
87 *
88 * Q (output) COMPLEX*16 array, dimension (LDQ, N)
89 * If JOBZ = 'V', the n-by-n matrix used in the reduction of
90 * A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
91 * and consequently C to tridiagonal form.
92 * If JOBZ = 'N', the array Q is not referenced.
93 *
94 * LDQ (input) INTEGER
95 * The leading dimension of the array Q. If JOBZ = 'N',
96 * LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
97 *
98 * VL (input) DOUBLE PRECISION
99 * VU (input) DOUBLE PRECISION
100 * If RANGE='V', the lower and upper bounds of the interval to
101 * be searched for eigenvalues. VL < VU.
102 * Not referenced if RANGE = 'A' or 'I'.
103 *
104 * IL (input) INTEGER
105 * IU (input) INTEGER
106 * If RANGE='I', the indices (in ascending order) of the
107 * smallest and largest eigenvalues to be returned.
108 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
109 * Not referenced if RANGE = 'A' or 'V'.
110 *
111 * ABSTOL (input) DOUBLE PRECISION
112 * The absolute error tolerance for the eigenvalues.
113 * An approximate eigenvalue is accepted as converged
114 * when it is determined to lie in an interval [a,b]
115 * of width less than or equal to
116 *
117 * ABSTOL + EPS * max( |a|,|b| ) ,
118 *
119 * where EPS is the machine precision. If ABSTOL is less than
120 * or equal to zero, then EPS*|T| will be used in its place,
121 * where |T| is the 1-norm of the tridiagonal matrix obtained
122 * by reducing AP to tridiagonal form.
123 *
124 * Eigenvalues will be computed most accurately when ABSTOL is
125 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
126 * If this routine returns with INFO>0, indicating that some
127 * eigenvectors did not converge, try setting ABSTOL to
128 * 2*DLAMCH('S').
129 *
130 * M (output) INTEGER
131 * The total number of eigenvalues found. 0 <= M <= N.
132 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
133 *
134 * W (output) DOUBLE PRECISION array, dimension (N)
135 * If INFO = 0, the eigenvalues in ascending order.
136 *
137 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
138 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
139 * eigenvectors, with the i-th column of Z holding the
140 * eigenvector associated with W(i). The eigenvectors are
141 * normalized so that Z**H*B*Z = I.
142 * If JOBZ = 'N', then Z is not referenced.
143 *
144 * LDZ (input) INTEGER
145 * The leading dimension of the array Z. LDZ >= 1, and if
146 * JOBZ = 'V', LDZ >= N.
147 *
148 * WORK (workspace) COMPLEX*16 array, dimension (N)
149 *
150 * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
151 *
152 * IWORK (workspace) INTEGER array, dimension (5*N)
153 *
154 * IFAIL (output) INTEGER array, dimension (N)
155 * If JOBZ = 'V', then if INFO = 0, the first M elements of
156 * IFAIL are zero. If INFO > 0, then IFAIL contains the
157 * indices of the eigenvectors that failed to converge.
158 * If JOBZ = 'N', then IFAIL is not referenced.
159 *
160 * INFO (output) INTEGER
161 * = 0: successful exit
162 * < 0: if INFO = -i, the i-th argument had an illegal value
163 * > 0: if INFO = i, and i is:
164 * <= N: then i eigenvectors failed to converge. Their
165 * indices are stored in array IFAIL.
166 * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
167 * returned INFO = i: B is not positive definite.
168 * The factorization of B could not be completed and
169 * no eigenvalues or eigenvectors were computed.
170 *
171 * Further Details
172 * ===============
173 *
174 * Based on contributions by
175 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
176 *
177 * =====================================================================
178 *
179 * .. Parameters ..
180 DOUBLE PRECISION ZERO
181 PARAMETER ( ZERO = 0.0D+0 )
182 COMPLEX*16 CZERO, CONE
183 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
184 $ CONE = ( 1.0D+0, 0.0D+0 ) )
185 * ..
186 * .. Local Scalars ..
187 LOGICAL ALLEIG, INDEIG, TEST, UPPER, VALEIG, WANTZ
188 CHARACTER ORDER, VECT
189 INTEGER I, IINFO, INDD, INDE, INDEE, INDIBL, INDISP,
190 $ INDIWK, INDRWK, INDWRK, ITMP1, J, JJ, NSPLIT
191 DOUBLE PRECISION TMP1
192 * ..
193 * .. External Functions ..
194 LOGICAL LSAME
195 EXTERNAL LSAME
196 * ..
197 * .. External Subroutines ..
198 EXTERNAL DCOPY, DSTEBZ, DSTERF, XERBLA, ZCOPY, ZGEMV,
199 $ ZHBGST, ZHBTRD, ZLACPY, ZPBSTF, ZSTEIN, ZSTEQR,
200 $ ZSWAP
201 * ..
202 * .. Intrinsic Functions ..
203 INTRINSIC MIN
204 * ..
205 * .. Executable Statements ..
206 *
207 * Test the input parameters.
208 *
209 WANTZ = LSAME( JOBZ, 'V' )
210 UPPER = LSAME( UPLO, 'U' )
211 ALLEIG = LSAME( RANGE, 'A' )
212 VALEIG = LSAME( RANGE, 'V' )
213 INDEIG = LSAME( RANGE, 'I' )
214 *
215 INFO = 0
216 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
217 INFO = -1
218 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
219 INFO = -2
220 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
221 INFO = -3
222 ELSE IF( N.LT.0 ) THEN
223 INFO = -4
224 ELSE IF( KA.LT.0 ) THEN
225 INFO = -5
226 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
227 INFO = -6
228 ELSE IF( LDAB.LT.KA+1 ) THEN
229 INFO = -8
230 ELSE IF( LDBB.LT.KB+1 ) THEN
231 INFO = -10
232 ELSE IF( LDQ.LT.1 .OR. ( WANTZ .AND. LDQ.LT.N ) ) THEN
233 INFO = -12
234 ELSE
235 IF( VALEIG ) THEN
236 IF( N.GT.0 .AND. VU.LE.VL )
237 $ INFO = -14
238 ELSE IF( INDEIG ) THEN
239 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
240 INFO = -15
241 ELSE IF ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
242 INFO = -16
243 END IF
244 END IF
245 END IF
246 IF( INFO.EQ.0) THEN
247 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
248 INFO = -21
249 END IF
250 END IF
251 *
252 IF( INFO.NE.0 ) THEN
253 CALL XERBLA( 'ZHBGVX', -INFO )
254 RETURN
255 END IF
256 *
257 * Quick return if possible
258 *
259 M = 0
260 IF( N.EQ.0 )
261 $ RETURN
262 *
263 * Form a split Cholesky factorization of B.
264 *
265 CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
266 IF( INFO.NE.0 ) THEN
267 INFO = N + INFO
268 RETURN
269 END IF
270 *
271 * Transform problem to standard eigenvalue problem.
272 *
273 CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ,
274 $ WORK, RWORK, IINFO )
275 *
276 * Solve the standard eigenvalue problem.
277 * Reduce Hermitian band matrix to tridiagonal form.
278 *
279 INDD = 1
280 INDE = INDD + N
281 INDRWK = INDE + N
282 INDWRK = 1
283 IF( WANTZ ) THEN
284 VECT = 'U'
285 ELSE
286 VECT = 'N'
287 END IF
288 CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, RWORK( INDD ),
289 $ RWORK( INDE ), Q, LDQ, WORK( INDWRK ), IINFO )
290 *
291 * If all eigenvalues are desired and ABSTOL is less than or equal
292 * to zero, then call DSTERF or ZSTEQR. If this fails for some
293 * eigenvalue, then try DSTEBZ.
294 *
295 TEST = .FALSE.
296 IF( INDEIG ) THEN
297 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
298 TEST = .TRUE.
299 END IF
300 END IF
301 IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
302 CALL DCOPY( N, RWORK( INDD ), 1, W, 1 )
303 INDEE = INDRWK + 2*N
304 CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
305 IF( .NOT.WANTZ ) THEN
306 CALL DSTERF( N, W, RWORK( INDEE ), INFO )
307 ELSE
308 CALL ZLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
309 CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
310 $ RWORK( INDRWK ), INFO )
311 IF( INFO.EQ.0 ) THEN
312 DO 10 I = 1, N
313 IFAIL( I ) = 0
314 10 CONTINUE
315 END IF
316 END IF
317 IF( INFO.EQ.0 ) THEN
318 M = N
319 GO TO 30
320 END IF
321 INFO = 0
322 END IF
323 *
324 * Otherwise, call DSTEBZ and, if eigenvectors are desired,
325 * call ZSTEIN.
326 *
327 IF( WANTZ ) THEN
328 ORDER = 'B'
329 ELSE
330 ORDER = 'E'
331 END IF
332 INDIBL = 1
333 INDISP = INDIBL + N
334 INDIWK = INDISP + N
335 CALL DSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL,
336 $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
337 $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
338 $ IWORK( INDIWK ), INFO )
339 *
340 IF( WANTZ ) THEN
341 CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
342 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
343 $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
344 *
345 * Apply unitary matrix used in reduction to tridiagonal
346 * form to eigenvectors returned by ZSTEIN.
347 *
348 DO 20 J = 1, M
349 CALL ZCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
350 CALL ZGEMV( 'N', N, N, CONE, Q, LDQ, WORK, 1, CZERO,
351 $ Z( 1, J ), 1 )
352 20 CONTINUE
353 END IF
354 *
355 30 CONTINUE
356 *
357 * If eigenvalues are not in order, then sort them, along with
358 * eigenvectors.
359 *
360 IF( WANTZ ) THEN
361 DO 50 J = 1, M - 1
362 I = 0
363 TMP1 = W( J )
364 DO 40 JJ = J + 1, M
365 IF( W( JJ ).LT.TMP1 ) THEN
366 I = JJ
367 TMP1 = W( JJ )
368 END IF
369 40 CONTINUE
370 *
371 IF( I.NE.0 ) THEN
372 ITMP1 = IWORK( INDIBL+I-1 )
373 W( I ) = W( J )
374 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
375 W( J ) = TMP1
376 IWORK( INDIBL+J-1 ) = ITMP1
377 CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
378 IF( INFO.NE.0 ) THEN
379 ITMP1 = IFAIL( I )
380 IFAIL( I ) = IFAIL( J )
381 IFAIL( J ) = ITMP1
382 END IF
383 END IF
384 50 CONTINUE
385 END IF
386 *
387 RETURN
388 *
389 * End of ZHBGVX
390 *
391 END