1 SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
2 $ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
3 $ LIWORK, INFO )
4 *
5 * -- LAPACK driver routine (version 3.3.1) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * -- April 2011 --
9 * @precisions normal z -> c
10 *
11 * .. Scalar Arguments ..
12 CHARACTER JOBZ, UPLO
13 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
14 $ LWORK, N
15 * ..
16 * .. Array Arguments ..
17 INTEGER IWORK( * )
18 DOUBLE PRECISION RWORK( * ), W( * )
19 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
20 $ Z( LDZ, * )
21 * ..
22 *
23 * Purpose
24 * =======
25 *
26 * ZHBGVD 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. If eigenvectors are
30 * desired, it uses a divide and conquer algorithm.
31 *
32 * The divide and conquer algorithm makes very mild assumptions about
33 * floating point arithmetic. It will work on machines with a guard
34 * digit in add/subtract, or on those binary machines without guard
35 * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
36 * Cray-2. It could conceivably fail on hexadecimal or decimal machines
37 * without guard digits, but we know of none.
38 *
39 * Arguments
40 * =========
41 *
42 * JOBZ (input) CHARACTER*1
43 * = 'N': Compute eigenvalues only;
44 * = 'V': Compute eigenvalues and eigenvectors.
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 * W (output) DOUBLE PRECISION array, dimension (N)
89 * If INFO = 0, the eigenvalues in ascending order.
90 *
91 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
92 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
93 * eigenvectors, with the i-th column of Z holding the
94 * eigenvector associated with W(i). The eigenvectors are
95 * normalized so that Z**H*B*Z = I.
96 * If JOBZ = 'N', then Z is not referenced.
97 *
98 * LDZ (input) INTEGER
99 * The leading dimension of the array Z. LDZ >= 1, and if
100 * JOBZ = 'V', LDZ >= N.
101 *
102 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
103 * On exit, if INFO=0, WORK(1) returns the optimal LWORK.
104 *
105 * LWORK (input) INTEGER
106 * The dimension of the array WORK.
107 * If N <= 1, LWORK >= 1.
108 * If JOBZ = 'N' and N > 1, LWORK >= N.
109 * If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
110 *
111 * If LWORK = -1, then a workspace query is assumed; the routine
112 * only calculates the optimal sizes of the WORK, RWORK and
113 * IWORK arrays, returns these values as the first entries of
114 * the WORK, RWORK and IWORK arrays, and no error message
115 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
116 *
117 * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
118 * On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
119 *
120 * LRWORK (input) INTEGER
121 * The dimension of array RWORK.
122 * If N <= 1, LRWORK >= 1.
123 * If JOBZ = 'N' and N > 1, LRWORK >= N.
124 * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
125 *
126 * If LRWORK = -1, then a workspace query is assumed; the
127 * routine only calculates the optimal sizes of the WORK, RWORK
128 * and IWORK arrays, returns these values as the first entries
129 * of the WORK, RWORK and IWORK arrays, and no error message
130 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
131 *
132 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
133 * On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
134 *
135 * LIWORK (input) INTEGER
136 * The dimension of array IWORK.
137 * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
138 * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
139 *
140 * If LIWORK = -1, then a workspace query is assumed; the
141 * routine only calculates the optimal sizes of the WORK, RWORK
142 * and IWORK arrays, returns these values as the first entries
143 * of the WORK, RWORK and IWORK arrays, and no error message
144 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
145 *
146 * INFO (output) INTEGER
147 * = 0: successful exit
148 * < 0: if INFO = -i, the i-th argument had an illegal value
149 * > 0: if INFO = i, and i is:
150 * <= N: the algorithm failed to converge:
151 * i off-diagonal elements of an intermediate
152 * tridiagonal form did not converge to zero;
153 * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
154 * returned INFO = i: B is not positive definite.
155 * The factorization of B could not be completed and
156 * no eigenvalues or eigenvectors were computed.
157 *
158 * Further Details
159 * ===============
160 *
161 * Based on contributions by
162 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167 COMPLEX*16 CONE, CZERO
168 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
169 $ CZERO = ( 0.0D+0, 0.0D+0 ) )
170 * ..
171 * .. Local Scalars ..
172 LOGICAL LQUERY, UPPER, WANTZ
173 CHARACTER VECT
174 INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK,
175 $ LLWK2, LRWMIN, LWMIN
176 * ..
177 * .. External Functions ..
178 LOGICAL LSAME
179 EXTERNAL LSAME
180 * ..
181 * .. External Subroutines ..
182 EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY,
183 $ ZPBSTF, ZSTEDC
184 * ..
185 * .. Executable Statements ..
186 *
187 * Test the input parameters.
188 *
189 WANTZ = LSAME( JOBZ, 'V' )
190 UPPER = LSAME( UPLO, 'U' )
191 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
192 *
193 INFO = 0
194 IF( N.LE.1 ) THEN
195 LWMIN = 1+N
196 LRWMIN = 1+N
197 LIWMIN = 1
198 ELSE IF( WANTZ ) THEN
199 LWMIN = 2*N**2
200 LRWMIN = 1 + 5*N + 2*N**2
201 LIWMIN = 3 + 5*N
202 ELSE
203 LWMIN = N
204 LRWMIN = N
205 LIWMIN = 1
206 END IF
207 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
208 INFO = -1
209 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
210 INFO = -2
211 ELSE IF( N.LT.0 ) THEN
212 INFO = -3
213 ELSE IF( KA.LT.0 ) THEN
214 INFO = -4
215 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
216 INFO = -5
217 ELSE IF( LDAB.LT.KA+1 ) THEN
218 INFO = -7
219 ELSE IF( LDBB.LT.KB+1 ) THEN
220 INFO = -9
221 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
222 INFO = -12
223 END IF
224 *
225 IF( INFO.EQ.0 ) THEN
226 WORK( 1 ) = LWMIN
227 RWORK( 1 ) = LRWMIN
228 IWORK( 1 ) = LIWMIN
229 *
230 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
231 INFO = -14
232 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
233 INFO = -16
234 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
235 INFO = -18
236 END IF
237 END IF
238 *
239 IF( INFO.NE.0 ) THEN
240 CALL XERBLA( 'ZHBGVD', -INFO )
241 RETURN
242 ELSE IF( LQUERY ) THEN
243 RETURN
244 END IF
245 *
246 * Quick return if possible
247 *
248 IF( N.EQ.0 )
249 $ RETURN
250 *
251 * Form a split Cholesky factorization of B.
252 *
253 CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
254 IF( INFO.NE.0 ) THEN
255 INFO = N + INFO
256 RETURN
257 END IF
258 *
259 * Transform problem to standard eigenvalue problem.
260 *
261 INDE = 1
262 INDWRK = INDE + N
263 INDWK2 = 1 + N*N
264 LLWK2 = LWORK - INDWK2 + 2
265 LLRWK = LRWORK - INDWRK + 2
266 CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
267 $ WORK, RWORK( INDWRK ), IINFO )
268 *
269 * Reduce Hermitian band matrix to tridiagonal form.
270 *
271 IF( WANTZ ) THEN
272 VECT = 'U'
273 ELSE
274 VECT = 'N'
275 END IF
276 CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
277 $ LDZ, WORK, IINFO )
278 *
279 * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC.
280 *
281 IF( .NOT.WANTZ ) THEN
282 CALL DSTERF( N, W, RWORK( INDE ), INFO )
283 ELSE
284 CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
285 $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
286 $ INFO )
287 CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
288 $ WORK( INDWK2 ), N )
289 CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
290 END IF
291 *
292 WORK( 1 ) = LWMIN
293 RWORK( 1 ) = LRWMIN
294 IWORK( 1 ) = LIWMIN
295 RETURN
296 *
297 * End of ZHBGVD
298 *
299 END
2 $ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
3 $ LIWORK, INFO )
4 *
5 * -- LAPACK driver routine (version 3.3.1) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * -- April 2011 --
9 * @precisions normal z -> c
10 *
11 * .. Scalar Arguments ..
12 CHARACTER JOBZ, UPLO
13 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
14 $ LWORK, N
15 * ..
16 * .. Array Arguments ..
17 INTEGER IWORK( * )
18 DOUBLE PRECISION RWORK( * ), W( * )
19 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
20 $ Z( LDZ, * )
21 * ..
22 *
23 * Purpose
24 * =======
25 *
26 * ZHBGVD 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. If eigenvectors are
30 * desired, it uses a divide and conquer algorithm.
31 *
32 * The divide and conquer algorithm makes very mild assumptions about
33 * floating point arithmetic. It will work on machines with a guard
34 * digit in add/subtract, or on those binary machines without guard
35 * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
36 * Cray-2. It could conceivably fail on hexadecimal or decimal machines
37 * without guard digits, but we know of none.
38 *
39 * Arguments
40 * =========
41 *
42 * JOBZ (input) CHARACTER*1
43 * = 'N': Compute eigenvalues only;
44 * = 'V': Compute eigenvalues and eigenvectors.
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 * W (output) DOUBLE PRECISION array, dimension (N)
89 * If INFO = 0, the eigenvalues in ascending order.
90 *
91 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
92 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
93 * eigenvectors, with the i-th column of Z holding the
94 * eigenvector associated with W(i). The eigenvectors are
95 * normalized so that Z**H*B*Z = I.
96 * If JOBZ = 'N', then Z is not referenced.
97 *
98 * LDZ (input) INTEGER
99 * The leading dimension of the array Z. LDZ >= 1, and if
100 * JOBZ = 'V', LDZ >= N.
101 *
102 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
103 * On exit, if INFO=0, WORK(1) returns the optimal LWORK.
104 *
105 * LWORK (input) INTEGER
106 * The dimension of the array WORK.
107 * If N <= 1, LWORK >= 1.
108 * If JOBZ = 'N' and N > 1, LWORK >= N.
109 * If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
110 *
111 * If LWORK = -1, then a workspace query is assumed; the routine
112 * only calculates the optimal sizes of the WORK, RWORK and
113 * IWORK arrays, returns these values as the first entries of
114 * the WORK, RWORK and IWORK arrays, and no error message
115 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
116 *
117 * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
118 * On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
119 *
120 * LRWORK (input) INTEGER
121 * The dimension of array RWORK.
122 * If N <= 1, LRWORK >= 1.
123 * If JOBZ = 'N' and N > 1, LRWORK >= N.
124 * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
125 *
126 * If LRWORK = -1, then a workspace query is assumed; the
127 * routine only calculates the optimal sizes of the WORK, RWORK
128 * and IWORK arrays, returns these values as the first entries
129 * of the WORK, RWORK and IWORK arrays, and no error message
130 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
131 *
132 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
133 * On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
134 *
135 * LIWORK (input) INTEGER
136 * The dimension of array IWORK.
137 * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
138 * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
139 *
140 * If LIWORK = -1, then a workspace query is assumed; the
141 * routine only calculates the optimal sizes of the WORK, RWORK
142 * and IWORK arrays, returns these values as the first entries
143 * of the WORK, RWORK and IWORK arrays, and no error message
144 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
145 *
146 * INFO (output) INTEGER
147 * = 0: successful exit
148 * < 0: if INFO = -i, the i-th argument had an illegal value
149 * > 0: if INFO = i, and i is:
150 * <= N: the algorithm failed to converge:
151 * i off-diagonal elements of an intermediate
152 * tridiagonal form did not converge to zero;
153 * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
154 * returned INFO = i: B is not positive definite.
155 * The factorization of B could not be completed and
156 * no eigenvalues or eigenvectors were computed.
157 *
158 * Further Details
159 * ===============
160 *
161 * Based on contributions by
162 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
163 *
164 * =====================================================================
165 *
166 * .. Parameters ..
167 COMPLEX*16 CONE, CZERO
168 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
169 $ CZERO = ( 0.0D+0, 0.0D+0 ) )
170 * ..
171 * .. Local Scalars ..
172 LOGICAL LQUERY, UPPER, WANTZ
173 CHARACTER VECT
174 INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK,
175 $ LLWK2, LRWMIN, LWMIN
176 * ..
177 * .. External Functions ..
178 LOGICAL LSAME
179 EXTERNAL LSAME
180 * ..
181 * .. External Subroutines ..
182 EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY,
183 $ ZPBSTF, ZSTEDC
184 * ..
185 * .. Executable Statements ..
186 *
187 * Test the input parameters.
188 *
189 WANTZ = LSAME( JOBZ, 'V' )
190 UPPER = LSAME( UPLO, 'U' )
191 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
192 *
193 INFO = 0
194 IF( N.LE.1 ) THEN
195 LWMIN = 1+N
196 LRWMIN = 1+N
197 LIWMIN = 1
198 ELSE IF( WANTZ ) THEN
199 LWMIN = 2*N**2
200 LRWMIN = 1 + 5*N + 2*N**2
201 LIWMIN = 3 + 5*N
202 ELSE
203 LWMIN = N
204 LRWMIN = N
205 LIWMIN = 1
206 END IF
207 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
208 INFO = -1
209 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
210 INFO = -2
211 ELSE IF( N.LT.0 ) THEN
212 INFO = -3
213 ELSE IF( KA.LT.0 ) THEN
214 INFO = -4
215 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
216 INFO = -5
217 ELSE IF( LDAB.LT.KA+1 ) THEN
218 INFO = -7
219 ELSE IF( LDBB.LT.KB+1 ) THEN
220 INFO = -9
221 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
222 INFO = -12
223 END IF
224 *
225 IF( INFO.EQ.0 ) THEN
226 WORK( 1 ) = LWMIN
227 RWORK( 1 ) = LRWMIN
228 IWORK( 1 ) = LIWMIN
229 *
230 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
231 INFO = -14
232 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
233 INFO = -16
234 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
235 INFO = -18
236 END IF
237 END IF
238 *
239 IF( INFO.NE.0 ) THEN
240 CALL XERBLA( 'ZHBGVD', -INFO )
241 RETURN
242 ELSE IF( LQUERY ) THEN
243 RETURN
244 END IF
245 *
246 * Quick return if possible
247 *
248 IF( N.EQ.0 )
249 $ RETURN
250 *
251 * Form a split Cholesky factorization of B.
252 *
253 CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
254 IF( INFO.NE.0 ) THEN
255 INFO = N + INFO
256 RETURN
257 END IF
258 *
259 * Transform problem to standard eigenvalue problem.
260 *
261 INDE = 1
262 INDWRK = INDE + N
263 INDWK2 = 1 + N*N
264 LLWK2 = LWORK - INDWK2 + 2
265 LLRWK = LRWORK - INDWRK + 2
266 CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
267 $ WORK, RWORK( INDWRK ), IINFO )
268 *
269 * Reduce Hermitian band matrix to tridiagonal form.
270 *
271 IF( WANTZ ) THEN
272 VECT = 'U'
273 ELSE
274 VECT = 'N'
275 END IF
276 CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
277 $ LDZ, WORK, IINFO )
278 *
279 * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC.
280 *
281 IF( .NOT.WANTZ ) THEN
282 CALL DSTERF( N, W, RWORK( INDE ), INFO )
283 ELSE
284 CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
285 $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
286 $ INFO )
287 CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
288 $ WORK( INDWK2 ), N )
289 CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
290 END IF
291 *
292 WORK( 1 ) = LWMIN
293 RWORK( 1 ) = LRWMIN
294 IWORK( 1 ) = LIWMIN
295 RETURN
296 *
297 * End of ZHBGVD
298 *
299 END