1 SUBROUTINE ZHEGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
2 $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
3 $ LWORK, RWORK, IWORK, IFAIL, 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 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N
13 DOUBLE PRECISION ABSTOL, VL, VU
14 * ..
15 * .. Array Arguments ..
16 INTEGER IFAIL( * ), IWORK( * )
17 DOUBLE PRECISION RWORK( * ), W( * )
18 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
19 $ Z( LDZ, * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * ZHEGVX computes selected eigenvalues, and optionally, eigenvectors
26 * of a complex generalized Hermitian-definite eigenproblem, of the form
27 * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
28 * B are assumed to be Hermitian and B is also positive definite.
29 * Eigenvalues and eigenvectors can be selected by specifying either a
30 * range of values or a range of indices for the desired eigenvalues.
31 *
32 * Arguments
33 * =========
34 *
35 * ITYPE (input) INTEGER
36 * Specifies the problem type to be solved:
37 * = 1: A*x = (lambda)*B*x
38 * = 2: A*B*x = (lambda)*x
39 * = 3: B*A*x = (lambda)*x
40 *
41 * JOBZ (input) CHARACTER*1
42 * = 'N': Compute eigenvalues only;
43 * = 'V': Compute eigenvalues and eigenvectors.
44 *
45 * RANGE (input) CHARACTER*1
46 * = 'A': all eigenvalues will be found.
47 * = 'V': all eigenvalues in the half-open interval (VL,VU]
48 * will be found.
49 * = 'I': the IL-th through IU-th eigenvalues will be found.
50 **
51 * UPLO (input) CHARACTER*1
52 * = 'U': Upper triangles of A and B are stored;
53 * = 'L': Lower triangles of A and B are stored.
54 *
55 * N (input) INTEGER
56 * The order of the matrices A and B. N >= 0.
57 *
58 * A (input/output) COMPLEX*16 array, dimension (LDA, N)
59 * On entry, the Hermitian matrix A. If UPLO = 'U', the
60 * leading N-by-N upper triangular part of A contains the
61 * upper triangular part of the matrix A. If UPLO = 'L',
62 * the leading N-by-N lower triangular part of A contains
63 * the lower triangular part of the matrix A.
64 *
65 * On exit, the lower triangle (if UPLO='L') or the upper
66 * triangle (if UPLO='U') of A, including the diagonal, is
67 * destroyed.
68 *
69 * LDA (input) INTEGER
70 * The leading dimension of the array A. LDA >= max(1,N).
71 *
72 * B (input/output) COMPLEX*16 array, dimension (LDB, N)
73 * On entry, the Hermitian matrix B. If UPLO = 'U', the
74 * leading N-by-N upper triangular part of B contains the
75 * upper triangular part of the matrix B. If UPLO = 'L',
76 * the leading N-by-N lower triangular part of B contains
77 * the lower triangular part of the matrix B.
78 *
79 * On exit, if INFO <= N, the part of B containing the matrix is
80 * overwritten by the triangular factor U or L from the Cholesky
81 * factorization B = U**H*U or B = L*L**H.
82 *
83 * LDB (input) INTEGER
84 * The leading dimension of the array B. LDB >= max(1,N).
85 *
86 * VL (input) DOUBLE PRECISION
87 * VU (input) DOUBLE PRECISION
88 * If RANGE='V', the lower and upper bounds of the interval to
89 * be searched for eigenvalues. VL < VU.
90 * Not referenced if RANGE = 'A' or 'I'.
91 *
92 * IL (input) INTEGER
93 * IU (input) INTEGER
94 * If RANGE='I', the indices (in ascending order) of the
95 * smallest and largest eigenvalues to be returned.
96 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
97 * Not referenced if RANGE = 'A' or 'V'.
98 *
99 * ABSTOL (input) DOUBLE PRECISION
100 * The absolute error tolerance for the eigenvalues.
101 * An approximate eigenvalue is accepted as converged
102 * when it is determined to lie in an interval [a,b]
103 * of width less than or equal to
104 *
105 * ABSTOL + EPS * max( |a|,|b| ) ,
106 *
107 * where EPS is the machine precision. If ABSTOL is less than
108 * or equal to zero, then EPS*|T| will be used in its place,
109 * where |T| is the 1-norm of the tridiagonal matrix obtained
110 * by reducing A to tridiagonal form.
111 *
112 * Eigenvalues will be computed most accurately when ABSTOL is
113 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
114 * If this routine returns with INFO>0, indicating that some
115 * eigenvectors did not converge, try setting ABSTOL to
116 * 2*DLAMCH('S').
117 *
118 * M (output) INTEGER
119 * The total number of eigenvalues found. 0 <= M <= N.
120 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
121 *
122 * W (output) DOUBLE PRECISION array, dimension (N)
123 * The first M elements contain the selected
124 * eigenvalues in ascending order.
125 *
126 * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
127 * If JOBZ = 'N', then Z is not referenced.
128 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
129 * contain the orthonormal eigenvectors of the matrix A
130 * corresponding to the selected eigenvalues, with the i-th
131 * column of Z holding the eigenvector associated with W(i).
132 * The eigenvectors are normalized as follows:
133 * if ITYPE = 1 or 2, Z**T*B*Z = I;
134 * if ITYPE = 3, Z**T*inv(B)*Z = I.
135 *
136 * If an eigenvector fails to converge, then that column of Z
137 * contains the latest approximation to the eigenvector, and the
138 * index of the eigenvector is returned in IFAIL.
139 * Note: the user must ensure that at least max(1,M) columns are
140 * supplied in the array Z; if RANGE = 'V', the exact value of M
141 * is not known in advance and an upper bound must be used.
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) COMPLEX*16 array, dimension (MAX(1,LWORK))
148 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
149 *
150 * LWORK (input) INTEGER
151 * The length of the array WORK. LWORK >= max(1,2*N).
152 * For optimal efficiency, LWORK >= (NB+1)*N,
153 * where NB is the blocksize for ZHETRD returned by ILAENV.
154 *
155 * If LWORK = -1, then a workspace query is assumed; the routine
156 * only calculates the optimal size of the WORK array, returns
157 * this value as the first entry of the WORK array, and no error
158 * message related to LWORK is issued by XERBLA.
159 *
160 * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
161 *
162 * IWORK (workspace) INTEGER array, dimension (5*N)
163 *
164 * IFAIL (output) INTEGER array, dimension (N)
165 * If JOBZ = 'V', then if INFO = 0, the first M elements of
166 * IFAIL are zero. If INFO > 0, then IFAIL contains the
167 * indices of the eigenvectors that failed to converge.
168 * If JOBZ = 'N', then IFAIL is not referenced.
169 *
170 * INFO (output) INTEGER
171 * = 0: successful exit
172 * < 0: if INFO = -i, the i-th argument had an illegal value
173 * > 0: ZPOTRF or ZHEEVX returned an error code:
174 * <= N: if INFO = i, ZHEEVX failed to converge;
175 * i eigenvectors failed to converge. Their indices
176 * are stored in array IFAIL.
177 * > N: if INFO = N + i, for 1 <= i <= N, then the leading
178 * minor of order i of B is not positive definite.
179 * The factorization of B could not be completed and
180 * no eigenvalues or eigenvectors were computed.
181 *
182 * Further Details
183 * ===============
184 *
185 * Based on contributions by
186 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
187 *
188 * =====================================================================
189 *
190 * .. Parameters ..
191 COMPLEX*16 CONE
192 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
193 * ..
194 * .. Local Scalars ..
195 LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ
196 CHARACTER TRANS
197 INTEGER LWKOPT, NB
198 * ..
199 * .. External Functions ..
200 LOGICAL LSAME
201 INTEGER ILAENV
202 EXTERNAL LSAME, ILAENV
203 * ..
204 * .. External Subroutines ..
205 EXTERNAL XERBLA, ZHEEVX, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
206 * ..
207 * .. Intrinsic Functions ..
208 INTRINSIC MAX, MIN
209 * ..
210 * .. Executable Statements ..
211 *
212 * Test the input parameters.
213 *
214 WANTZ = LSAME( JOBZ, 'V' )
215 UPPER = LSAME( UPLO, 'U' )
216 ALLEIG = LSAME( RANGE, 'A' )
217 VALEIG = LSAME( RANGE, 'V' )
218 INDEIG = LSAME( RANGE, 'I' )
219 LQUERY = ( LWORK.EQ.-1 )
220 *
221 INFO = 0
222 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
223 INFO = -1
224 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
225 INFO = -2
226 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
227 INFO = -3
228 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
229 INFO = -4
230 ELSE IF( N.LT.0 ) THEN
231 INFO = -5
232 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
233 INFO = -7
234 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
235 INFO = -9
236 ELSE
237 IF( VALEIG ) THEN
238 IF( N.GT.0 .AND. VU.LE.VL )
239 $ INFO = -11
240 ELSE IF( INDEIG ) THEN
241 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
242 INFO = -12
243 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
244 INFO = -13
245 END IF
246 END IF
247 END IF
248 IF (INFO.EQ.0) THEN
249 IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN
250 INFO = -18
251 END IF
252 END IF
253 *
254 IF( INFO.EQ.0 ) THEN
255 NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
256 LWKOPT = MAX( 1, ( NB + 1 )*N )
257 WORK( 1 ) = LWKOPT
258 *
259 IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
260 INFO = -20
261 END IF
262 END IF
263 *
264 IF( INFO.NE.0 ) THEN
265 CALL XERBLA( 'ZHEGVX', -INFO )
266 RETURN
267 ELSE IF( LQUERY ) THEN
268 RETURN
269 END IF
270 *
271 * Quick return if possible
272 *
273 M = 0
274 IF( N.EQ.0 ) THEN
275 RETURN
276 END IF
277 *
278 * Form a Cholesky factorization of B.
279 *
280 CALL ZPOTRF( UPLO, N, B, LDB, INFO )
281 IF( INFO.NE.0 ) THEN
282 INFO = N + INFO
283 RETURN
284 END IF
285 *
286 * Transform problem to standard eigenvalue problem and solve.
287 *
288 CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
289 CALL ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,
290 $ M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL,
291 $ INFO )
292 *
293 IF( WANTZ ) THEN
294 *
295 * Backtransform eigenvectors to the original problem.
296 *
297 IF( INFO.GT.0 )
298 $ M = INFO - 1
299 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
300 *
301 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
302 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
303 *
304 IF( UPPER ) THEN
305 TRANS = 'N'
306 ELSE
307 TRANS = 'C'
308 END IF
309 *
310 CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B,
311 $ LDB, Z, LDZ )
312 *
313 ELSE IF( ITYPE.EQ.3 ) THEN
314 *
315 * For B*A*x=(lambda)*x;
316 * backtransform eigenvectors: x = L*y or U**H *y
317 *
318 IF( UPPER ) THEN
319 TRANS = 'C'
320 ELSE
321 TRANS = 'N'
322 END IF
323 *
324 CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B,
325 $ LDB, Z, LDZ )
326 END IF
327 END IF
328 *
329 * Set WORK(1) to optimal complex workspace size.
330 *
331 WORK( 1 ) = LWKOPT
332 *
333 RETURN
334 *
335 * End of ZHEGVX
336 *
337 END
2 $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
3 $ LWORK, RWORK, IWORK, IFAIL, 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 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N
13 DOUBLE PRECISION ABSTOL, VL, VU
14 * ..
15 * .. Array Arguments ..
16 INTEGER IFAIL( * ), IWORK( * )
17 DOUBLE PRECISION RWORK( * ), W( * )
18 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
19 $ Z( LDZ, * )
20 * ..
21 *
22 * Purpose
23 * =======
24 *
25 * ZHEGVX computes selected eigenvalues, and optionally, eigenvectors
26 * of a complex generalized Hermitian-definite eigenproblem, of the form
27 * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
28 * B are assumed to be Hermitian and B is also positive definite.
29 * Eigenvalues and eigenvectors can be selected by specifying either a
30 * range of values or a range of indices for the desired eigenvalues.
31 *
32 * Arguments
33 * =========
34 *
35 * ITYPE (input) INTEGER
36 * Specifies the problem type to be solved:
37 * = 1: A*x = (lambda)*B*x
38 * = 2: A*B*x = (lambda)*x
39 * = 3: B*A*x = (lambda)*x
40 *
41 * JOBZ (input) CHARACTER*1
42 * = 'N': Compute eigenvalues only;
43 * = 'V': Compute eigenvalues and eigenvectors.
44 *
45 * RANGE (input) CHARACTER*1
46 * = 'A': all eigenvalues will be found.
47 * = 'V': all eigenvalues in the half-open interval (VL,VU]
48 * will be found.
49 * = 'I': the IL-th through IU-th eigenvalues will be found.
50 **
51 * UPLO (input) CHARACTER*1
52 * = 'U': Upper triangles of A and B are stored;
53 * = 'L': Lower triangles of A and B are stored.
54 *
55 * N (input) INTEGER
56 * The order of the matrices A and B. N >= 0.
57 *
58 * A (input/output) COMPLEX*16 array, dimension (LDA, N)
59 * On entry, the Hermitian matrix A. If UPLO = 'U', the
60 * leading N-by-N upper triangular part of A contains the
61 * upper triangular part of the matrix A. If UPLO = 'L',
62 * the leading N-by-N lower triangular part of A contains
63 * the lower triangular part of the matrix A.
64 *
65 * On exit, the lower triangle (if UPLO='L') or the upper
66 * triangle (if UPLO='U') of A, including the diagonal, is
67 * destroyed.
68 *
69 * LDA (input) INTEGER
70 * The leading dimension of the array A. LDA >= max(1,N).
71 *
72 * B (input/output) COMPLEX*16 array, dimension (LDB, N)
73 * On entry, the Hermitian matrix B. If UPLO = 'U', the
74 * leading N-by-N upper triangular part of B contains the
75 * upper triangular part of the matrix B. If UPLO = 'L',
76 * the leading N-by-N lower triangular part of B contains
77 * the lower triangular part of the matrix B.
78 *
79 * On exit, if INFO <= N, the part of B containing the matrix is
80 * overwritten by the triangular factor U or L from the Cholesky
81 * factorization B = U**H*U or B = L*L**H.
82 *
83 * LDB (input) INTEGER
84 * The leading dimension of the array B. LDB >= max(1,N).
85 *
86 * VL (input) DOUBLE PRECISION
87 * VU (input) DOUBLE PRECISION
88 * If RANGE='V', the lower and upper bounds of the interval to
89 * be searched for eigenvalues. VL < VU.
90 * Not referenced if RANGE = 'A' or 'I'.
91 *
92 * IL (input) INTEGER
93 * IU (input) INTEGER
94 * If RANGE='I', the indices (in ascending order) of the
95 * smallest and largest eigenvalues to be returned.
96 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
97 * Not referenced if RANGE = 'A' or 'V'.
98 *
99 * ABSTOL (input) DOUBLE PRECISION
100 * The absolute error tolerance for the eigenvalues.
101 * An approximate eigenvalue is accepted as converged
102 * when it is determined to lie in an interval [a,b]
103 * of width less than or equal to
104 *
105 * ABSTOL + EPS * max( |a|,|b| ) ,
106 *
107 * where EPS is the machine precision. If ABSTOL is less than
108 * or equal to zero, then EPS*|T| will be used in its place,
109 * where |T| is the 1-norm of the tridiagonal matrix obtained
110 * by reducing A to tridiagonal form.
111 *
112 * Eigenvalues will be computed most accurately when ABSTOL is
113 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
114 * If this routine returns with INFO>0, indicating that some
115 * eigenvectors did not converge, try setting ABSTOL to
116 * 2*DLAMCH('S').
117 *
118 * M (output) INTEGER
119 * The total number of eigenvalues found. 0 <= M <= N.
120 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
121 *
122 * W (output) DOUBLE PRECISION array, dimension (N)
123 * The first M elements contain the selected
124 * eigenvalues in ascending order.
125 *
126 * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
127 * If JOBZ = 'N', then Z is not referenced.
128 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
129 * contain the orthonormal eigenvectors of the matrix A
130 * corresponding to the selected eigenvalues, with the i-th
131 * column of Z holding the eigenvector associated with W(i).
132 * The eigenvectors are normalized as follows:
133 * if ITYPE = 1 or 2, Z**T*B*Z = I;
134 * if ITYPE = 3, Z**T*inv(B)*Z = I.
135 *
136 * If an eigenvector fails to converge, then that column of Z
137 * contains the latest approximation to the eigenvector, and the
138 * index of the eigenvector is returned in IFAIL.
139 * Note: the user must ensure that at least max(1,M) columns are
140 * supplied in the array Z; if RANGE = 'V', the exact value of M
141 * is not known in advance and an upper bound must be used.
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) COMPLEX*16 array, dimension (MAX(1,LWORK))
148 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
149 *
150 * LWORK (input) INTEGER
151 * The length of the array WORK. LWORK >= max(1,2*N).
152 * For optimal efficiency, LWORK >= (NB+1)*N,
153 * where NB is the blocksize for ZHETRD returned by ILAENV.
154 *
155 * If LWORK = -1, then a workspace query is assumed; the routine
156 * only calculates the optimal size of the WORK array, returns
157 * this value as the first entry of the WORK array, and no error
158 * message related to LWORK is issued by XERBLA.
159 *
160 * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
161 *
162 * IWORK (workspace) INTEGER array, dimension (5*N)
163 *
164 * IFAIL (output) INTEGER array, dimension (N)
165 * If JOBZ = 'V', then if INFO = 0, the first M elements of
166 * IFAIL are zero. If INFO > 0, then IFAIL contains the
167 * indices of the eigenvectors that failed to converge.
168 * If JOBZ = 'N', then IFAIL is not referenced.
169 *
170 * INFO (output) INTEGER
171 * = 0: successful exit
172 * < 0: if INFO = -i, the i-th argument had an illegal value
173 * > 0: ZPOTRF or ZHEEVX returned an error code:
174 * <= N: if INFO = i, ZHEEVX failed to converge;
175 * i eigenvectors failed to converge. Their indices
176 * are stored in array IFAIL.
177 * > N: if INFO = N + i, for 1 <= i <= N, then the leading
178 * minor of order i of B is not positive definite.
179 * The factorization of B could not be completed and
180 * no eigenvalues or eigenvectors were computed.
181 *
182 * Further Details
183 * ===============
184 *
185 * Based on contributions by
186 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
187 *
188 * =====================================================================
189 *
190 * .. Parameters ..
191 COMPLEX*16 CONE
192 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
193 * ..
194 * .. Local Scalars ..
195 LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ
196 CHARACTER TRANS
197 INTEGER LWKOPT, NB
198 * ..
199 * .. External Functions ..
200 LOGICAL LSAME
201 INTEGER ILAENV
202 EXTERNAL LSAME, ILAENV
203 * ..
204 * .. External Subroutines ..
205 EXTERNAL XERBLA, ZHEEVX, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
206 * ..
207 * .. Intrinsic Functions ..
208 INTRINSIC MAX, MIN
209 * ..
210 * .. Executable Statements ..
211 *
212 * Test the input parameters.
213 *
214 WANTZ = LSAME( JOBZ, 'V' )
215 UPPER = LSAME( UPLO, 'U' )
216 ALLEIG = LSAME( RANGE, 'A' )
217 VALEIG = LSAME( RANGE, 'V' )
218 INDEIG = LSAME( RANGE, 'I' )
219 LQUERY = ( LWORK.EQ.-1 )
220 *
221 INFO = 0
222 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
223 INFO = -1
224 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
225 INFO = -2
226 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
227 INFO = -3
228 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
229 INFO = -4
230 ELSE IF( N.LT.0 ) THEN
231 INFO = -5
232 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
233 INFO = -7
234 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
235 INFO = -9
236 ELSE
237 IF( VALEIG ) THEN
238 IF( N.GT.0 .AND. VU.LE.VL )
239 $ INFO = -11
240 ELSE IF( INDEIG ) THEN
241 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
242 INFO = -12
243 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
244 INFO = -13
245 END IF
246 END IF
247 END IF
248 IF (INFO.EQ.0) THEN
249 IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN
250 INFO = -18
251 END IF
252 END IF
253 *
254 IF( INFO.EQ.0 ) THEN
255 NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
256 LWKOPT = MAX( 1, ( NB + 1 )*N )
257 WORK( 1 ) = LWKOPT
258 *
259 IF( LWORK.LT.MAX( 1, 2*N ) .AND. .NOT.LQUERY ) THEN
260 INFO = -20
261 END IF
262 END IF
263 *
264 IF( INFO.NE.0 ) THEN
265 CALL XERBLA( 'ZHEGVX', -INFO )
266 RETURN
267 ELSE IF( LQUERY ) THEN
268 RETURN
269 END IF
270 *
271 * Quick return if possible
272 *
273 M = 0
274 IF( N.EQ.0 ) THEN
275 RETURN
276 END IF
277 *
278 * Form a Cholesky factorization of B.
279 *
280 CALL ZPOTRF( UPLO, N, B, LDB, INFO )
281 IF( INFO.NE.0 ) THEN
282 INFO = N + INFO
283 RETURN
284 END IF
285 *
286 * Transform problem to standard eigenvalue problem and solve.
287 *
288 CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
289 CALL ZHEEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,
290 $ M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL,
291 $ INFO )
292 *
293 IF( WANTZ ) THEN
294 *
295 * Backtransform eigenvectors to the original problem.
296 *
297 IF( INFO.GT.0 )
298 $ M = INFO - 1
299 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
300 *
301 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
302 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
303 *
304 IF( UPPER ) THEN
305 TRANS = 'N'
306 ELSE
307 TRANS = 'C'
308 END IF
309 *
310 CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B,
311 $ LDB, Z, LDZ )
312 *
313 ELSE IF( ITYPE.EQ.3 ) THEN
314 *
315 * For B*A*x=(lambda)*x;
316 * backtransform eigenvectors: x = L*y or U**H *y
317 *
318 IF( UPPER ) THEN
319 TRANS = 'C'
320 ELSE
321 TRANS = 'N'
322 END IF
323 *
324 CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, CONE, B,
325 $ LDB, Z, LDZ )
326 END IF
327 END IF
328 *
329 * Set WORK(1) to optimal complex workspace size.
330 *
331 WORK( 1 ) = LWKOPT
332 *
333 RETURN
334 *
335 * End of ZHEGVX
336 *
337 END