1 SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
2 $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
3 *
4 * -- LAPACK driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER JOBZ, UPLO
11 INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
12 * ..
13 * .. Array Arguments ..
14 INTEGER IWORK( * )
15 DOUBLE PRECISION RWORK( * ), W( * )
16 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
23 * of a complex generalized Hermitian-definite eigenproblem, of the form
24 * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
25 * B are assumed to be Hermitian, stored in packed format, and B is also
26 * positive definite.
27 * If eigenvectors are desired, it uses a divide and conquer algorithm.
28 *
29 * The divide and conquer algorithm makes very mild assumptions about
30 * floating point arithmetic. It will work on machines with a guard
31 * digit in add/subtract, or on those binary machines without guard
32 * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
33 * Cray-2. It could conceivably fail on hexadecimal or decimal machines
34 * without guard digits, but we know of none.
35 *
36 * Arguments
37 * =========
38 *
39 * ITYPE (input) INTEGER
40 * Specifies the problem type to be solved:
41 * = 1: A*x = (lambda)*B*x
42 * = 2: A*B*x = (lambda)*x
43 * = 3: B*A*x = (lambda)*x
44 *
45 * JOBZ (input) CHARACTER*1
46 * = 'N': Compute eigenvalues only;
47 * = 'V': Compute eigenvalues and eigenvectors.
48 *
49 * UPLO (input) CHARACTER*1
50 * = 'U': Upper triangles of A and B are stored;
51 * = 'L': Lower triangles of A and B are stored.
52 *
53 * N (input) INTEGER
54 * The order of the matrices A and B. N >= 0.
55 *
56 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
57 * On entry, the upper or lower triangle of the Hermitian matrix
58 * A, packed columnwise in a linear array. The j-th column of A
59 * is stored in the array AP as follows:
60 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
61 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
62 *
63 * On exit, the contents of AP are destroyed.
64 *
65 * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
66 * On entry, the upper or lower triangle of the Hermitian matrix
67 * B, packed columnwise in a linear array. The j-th column of B
68 * is stored in the array BP as follows:
69 * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
70 * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
71 *
72 * On exit, the triangular factor U or L from the Cholesky
73 * factorization B = U**H*U or B = L*L**H, in the same storage
74 * format as B.
75 *
76 * W (output) DOUBLE PRECISION array, dimension (N)
77 * If INFO = 0, the eigenvalues in ascending order.
78 *
79 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
80 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
81 * eigenvectors. The eigenvectors are normalized as follows:
82 * if ITYPE = 1 or 2, Z**H*B*Z = I;
83 * if ITYPE = 3, Z**H*inv(B)*Z = I.
84 * If JOBZ = 'N', then Z is not referenced.
85 *
86 * LDZ (input) INTEGER
87 * The leading dimension of the array Z. LDZ >= 1, and if
88 * JOBZ = 'V', LDZ >= max(1,N).
89 *
90 * WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
91 * On exit, if INFO = 0, WORK(1) returns the required LWORK.
92 *
93 * LWORK (input) INTEGER
94 * The dimension of the array WORK.
95 * If N <= 1, LWORK >= 1.
96 * If JOBZ = 'N' and N > 1, LWORK >= N.
97 * If JOBZ = 'V' and N > 1, LWORK >= 2*N.
98 *
99 * If LWORK = -1, then a workspace query is assumed; the routine
100 * only calculates the required sizes of the WORK, RWORK and
101 * IWORK arrays, returns these values as the first entries of
102 * the WORK, RWORK and IWORK arrays, and no error message
103 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
104 *
105 * RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
106 * On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
107 *
108 * LRWORK (input) INTEGER
109 * The dimension of array RWORK.
110 * If N <= 1, LRWORK >= 1.
111 * If JOBZ = 'N' and N > 1, LRWORK >= N.
112 * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
113 *
114 * If LRWORK = -1, then a workspace query is assumed; the
115 * routine only calculates the required sizes of the WORK, RWORK
116 * and IWORK arrays, returns these values as the first entries
117 * of the WORK, RWORK and IWORK arrays, and no error message
118 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
119 *
120 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
121 * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
122 *
123 * LIWORK (input) INTEGER
124 * The dimension of array IWORK.
125 * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
126 * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
127 *
128 * If LIWORK = -1, then a workspace query is assumed; the
129 * routine only calculates the required sizes of the WORK, RWORK
130 * and IWORK arrays, returns these values as the first entries
131 * of the WORK, RWORK and IWORK arrays, and no error message
132 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
133 *
134 * INFO (output) INTEGER
135 * = 0: successful exit
136 * < 0: if INFO = -i, the i-th argument had an illegal value
137 * > 0: ZPPTRF or ZHPEVD returned an error code:
138 * <= N: if INFO = i, ZHPEVD failed to converge;
139 * i off-diagonal elements of an intermediate
140 * tridiagonal form did not convergeto zero;
141 * > N: if INFO = N + i, for 1 <= i <= n, then the leading
142 * minor of order i of B is not positive definite.
143 * The factorization of B could not be completed and
144 * no eigenvalues or eigenvectors were computed.
145 *
146 * Further Details
147 * ===============
148 *
149 * Based on contributions by
150 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
151 *
152 * =====================================================================
153 *
154 * .. Local Scalars ..
155 LOGICAL LQUERY, UPPER, WANTZ
156 CHARACTER TRANS
157 INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG
158 * ..
159 * .. External Functions ..
160 LOGICAL LSAME
161 EXTERNAL LSAME
162 * ..
163 * .. External Subroutines ..
164 EXTERNAL XERBLA, ZHPEVD, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
165 * ..
166 * .. Intrinsic Functions ..
167 INTRINSIC DBLE, MAX
168 * ..
169 * .. Executable Statements ..
170 *
171 * Test the input parameters.
172 *
173 WANTZ = LSAME( JOBZ, 'V' )
174 UPPER = LSAME( UPLO, 'U' )
175 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
176 *
177 INFO = 0
178 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
179 INFO = -1
180 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
181 INFO = -2
182 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
183 INFO = -3
184 ELSE IF( N.LT.0 ) THEN
185 INFO = -4
186 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
187 INFO = -9
188 END IF
189 *
190 IF( INFO.EQ.0 ) THEN
191 IF( N.LE.1 ) THEN
192 LWMIN = 1
193 LIWMIN = 1
194 LRWMIN = 1
195 ELSE
196 IF( WANTZ ) THEN
197 LWMIN = 2*N
198 LRWMIN = 1 + 5*N + 2*N**2
199 LIWMIN = 3 + 5*N
200 ELSE
201 LWMIN = N
202 LRWMIN = N
203 LIWMIN = 1
204 END IF
205 END IF
206 *
207 WORK( 1 ) = LWMIN
208 RWORK( 1 ) = LRWMIN
209 IWORK( 1 ) = LIWMIN
210 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
211 INFO = -11
212 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
213 INFO = -13
214 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
215 INFO = -15
216 END IF
217 END IF
218 *
219 IF( INFO.NE.0 ) THEN
220 CALL XERBLA( 'ZHPGVD', -INFO )
221 RETURN
222 ELSE IF( LQUERY ) THEN
223 RETURN
224 END IF
225 *
226 * Quick return if possible
227 *
228 IF( N.EQ.0 )
229 $ RETURN
230 *
231 * Form a Cholesky factorization of B.
232 *
233 CALL ZPPTRF( UPLO, N, BP, INFO )
234 IF( INFO.NE.0 ) THEN
235 INFO = N + INFO
236 RETURN
237 END IF
238 *
239 * Transform problem to standard eigenvalue problem and solve.
240 *
241 CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
242 CALL ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
243 $ LRWORK, IWORK, LIWORK, INFO )
244 LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
245 LRWMIN = MAX( DBLE( LRWMIN ), DBLE( RWORK( 1 ) ) )
246 LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
247 *
248 IF( WANTZ ) THEN
249 *
250 * Backtransform eigenvectors to the original problem.
251 *
252 NEIG = N
253 IF( INFO.GT.0 )
254 $ NEIG = INFO - 1
255 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
256 *
257 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
258 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
259 *
260 IF( UPPER ) THEN
261 TRANS = 'N'
262 ELSE
263 TRANS = 'C'
264 END IF
265 *
266 DO 10 J = 1, NEIG
267 CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
268 $ 1 )
269 10 CONTINUE
270 *
271 ELSE IF( ITYPE.EQ.3 ) THEN
272 *
273 * For B*A*x=(lambda)*x;
274 * backtransform eigenvectors: x = L*y or U**H *y
275 *
276 IF( UPPER ) THEN
277 TRANS = 'C'
278 ELSE
279 TRANS = 'N'
280 END IF
281 *
282 DO 20 J = 1, NEIG
283 CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
284 $ 1 )
285 20 CONTINUE
286 END IF
287 END IF
288 *
289 WORK( 1 ) = LWMIN
290 RWORK( 1 ) = LRWMIN
291 IWORK( 1 ) = LIWMIN
292 RETURN
293 *
294 * End of ZHPGVD
295 *
296 END
2 $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
3 *
4 * -- LAPACK driver routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER JOBZ, UPLO
11 INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
12 * ..
13 * .. Array Arguments ..
14 INTEGER IWORK( * )
15 DOUBLE PRECISION RWORK( * ), W( * )
16 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
23 * of a complex generalized Hermitian-definite eigenproblem, of the form
24 * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
25 * B are assumed to be Hermitian, stored in packed format, and B is also
26 * positive definite.
27 * If eigenvectors are desired, it uses a divide and conquer algorithm.
28 *
29 * The divide and conquer algorithm makes very mild assumptions about
30 * floating point arithmetic. It will work on machines with a guard
31 * digit in add/subtract, or on those binary machines without guard
32 * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
33 * Cray-2. It could conceivably fail on hexadecimal or decimal machines
34 * without guard digits, but we know of none.
35 *
36 * Arguments
37 * =========
38 *
39 * ITYPE (input) INTEGER
40 * Specifies the problem type to be solved:
41 * = 1: A*x = (lambda)*B*x
42 * = 2: A*B*x = (lambda)*x
43 * = 3: B*A*x = (lambda)*x
44 *
45 * JOBZ (input) CHARACTER*1
46 * = 'N': Compute eigenvalues only;
47 * = 'V': Compute eigenvalues and eigenvectors.
48 *
49 * UPLO (input) CHARACTER*1
50 * = 'U': Upper triangles of A and B are stored;
51 * = 'L': Lower triangles of A and B are stored.
52 *
53 * N (input) INTEGER
54 * The order of the matrices A and B. N >= 0.
55 *
56 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
57 * On entry, the upper or lower triangle of the Hermitian matrix
58 * A, packed columnwise in a linear array. The j-th column of A
59 * is stored in the array AP as follows:
60 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
61 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
62 *
63 * On exit, the contents of AP are destroyed.
64 *
65 * BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
66 * On entry, the upper or lower triangle of the Hermitian matrix
67 * B, packed columnwise in a linear array. The j-th column of B
68 * is stored in the array BP as follows:
69 * if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
70 * if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
71 *
72 * On exit, the triangular factor U or L from the Cholesky
73 * factorization B = U**H*U or B = L*L**H, in the same storage
74 * format as B.
75 *
76 * W (output) DOUBLE PRECISION array, dimension (N)
77 * If INFO = 0, the eigenvalues in ascending order.
78 *
79 * Z (output) COMPLEX*16 array, dimension (LDZ, N)
80 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
81 * eigenvectors. The eigenvectors are normalized as follows:
82 * if ITYPE = 1 or 2, Z**H*B*Z = I;
83 * if ITYPE = 3, Z**H*inv(B)*Z = I.
84 * If JOBZ = 'N', then Z is not referenced.
85 *
86 * LDZ (input) INTEGER
87 * The leading dimension of the array Z. LDZ >= 1, and if
88 * JOBZ = 'V', LDZ >= max(1,N).
89 *
90 * WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
91 * On exit, if INFO = 0, WORK(1) returns the required LWORK.
92 *
93 * LWORK (input) INTEGER
94 * The dimension of the array WORK.
95 * If N <= 1, LWORK >= 1.
96 * If JOBZ = 'N' and N > 1, LWORK >= N.
97 * If JOBZ = 'V' and N > 1, LWORK >= 2*N.
98 *
99 * If LWORK = -1, then a workspace query is assumed; the routine
100 * only calculates the required sizes of the WORK, RWORK and
101 * IWORK arrays, returns these values as the first entries of
102 * the WORK, RWORK and IWORK arrays, and no error message
103 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
104 *
105 * RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
106 * On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
107 *
108 * LRWORK (input) INTEGER
109 * The dimension of array RWORK.
110 * If N <= 1, LRWORK >= 1.
111 * If JOBZ = 'N' and N > 1, LRWORK >= N.
112 * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
113 *
114 * If LRWORK = -1, then a workspace query is assumed; the
115 * routine only calculates the required sizes of the WORK, RWORK
116 * and IWORK arrays, returns these values as the first entries
117 * of the WORK, RWORK and IWORK arrays, and no error message
118 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
119 *
120 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
121 * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
122 *
123 * LIWORK (input) INTEGER
124 * The dimension of array IWORK.
125 * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
126 * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
127 *
128 * If LIWORK = -1, then a workspace query is assumed; the
129 * routine only calculates the required sizes of the WORK, RWORK
130 * and IWORK arrays, returns these values as the first entries
131 * of the WORK, RWORK and IWORK arrays, and no error message
132 * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
133 *
134 * INFO (output) INTEGER
135 * = 0: successful exit
136 * < 0: if INFO = -i, the i-th argument had an illegal value
137 * > 0: ZPPTRF or ZHPEVD returned an error code:
138 * <= N: if INFO = i, ZHPEVD failed to converge;
139 * i off-diagonal elements of an intermediate
140 * tridiagonal form did not convergeto zero;
141 * > N: if INFO = N + i, for 1 <= i <= n, then the leading
142 * minor of order i of B is not positive definite.
143 * The factorization of B could not be completed and
144 * no eigenvalues or eigenvectors were computed.
145 *
146 * Further Details
147 * ===============
148 *
149 * Based on contributions by
150 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
151 *
152 * =====================================================================
153 *
154 * .. Local Scalars ..
155 LOGICAL LQUERY, UPPER, WANTZ
156 CHARACTER TRANS
157 INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG
158 * ..
159 * .. External Functions ..
160 LOGICAL LSAME
161 EXTERNAL LSAME
162 * ..
163 * .. External Subroutines ..
164 EXTERNAL XERBLA, ZHPEVD, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
165 * ..
166 * .. Intrinsic Functions ..
167 INTRINSIC DBLE, MAX
168 * ..
169 * .. Executable Statements ..
170 *
171 * Test the input parameters.
172 *
173 WANTZ = LSAME( JOBZ, 'V' )
174 UPPER = LSAME( UPLO, 'U' )
175 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
176 *
177 INFO = 0
178 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
179 INFO = -1
180 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
181 INFO = -2
182 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
183 INFO = -3
184 ELSE IF( N.LT.0 ) THEN
185 INFO = -4
186 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
187 INFO = -9
188 END IF
189 *
190 IF( INFO.EQ.0 ) THEN
191 IF( N.LE.1 ) THEN
192 LWMIN = 1
193 LIWMIN = 1
194 LRWMIN = 1
195 ELSE
196 IF( WANTZ ) THEN
197 LWMIN = 2*N
198 LRWMIN = 1 + 5*N + 2*N**2
199 LIWMIN = 3 + 5*N
200 ELSE
201 LWMIN = N
202 LRWMIN = N
203 LIWMIN = 1
204 END IF
205 END IF
206 *
207 WORK( 1 ) = LWMIN
208 RWORK( 1 ) = LRWMIN
209 IWORK( 1 ) = LIWMIN
210 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
211 INFO = -11
212 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
213 INFO = -13
214 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
215 INFO = -15
216 END IF
217 END IF
218 *
219 IF( INFO.NE.0 ) THEN
220 CALL XERBLA( 'ZHPGVD', -INFO )
221 RETURN
222 ELSE IF( LQUERY ) THEN
223 RETURN
224 END IF
225 *
226 * Quick return if possible
227 *
228 IF( N.EQ.0 )
229 $ RETURN
230 *
231 * Form a Cholesky factorization of B.
232 *
233 CALL ZPPTRF( UPLO, N, BP, INFO )
234 IF( INFO.NE.0 ) THEN
235 INFO = N + INFO
236 RETURN
237 END IF
238 *
239 * Transform problem to standard eigenvalue problem and solve.
240 *
241 CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
242 CALL ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
243 $ LRWORK, IWORK, LIWORK, INFO )
244 LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
245 LRWMIN = MAX( DBLE( LRWMIN ), DBLE( RWORK( 1 ) ) )
246 LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
247 *
248 IF( WANTZ ) THEN
249 *
250 * Backtransform eigenvectors to the original problem.
251 *
252 NEIG = N
253 IF( INFO.GT.0 )
254 $ NEIG = INFO - 1
255 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
256 *
257 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
258 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
259 *
260 IF( UPPER ) THEN
261 TRANS = 'N'
262 ELSE
263 TRANS = 'C'
264 END IF
265 *
266 DO 10 J = 1, NEIG
267 CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
268 $ 1 )
269 10 CONTINUE
270 *
271 ELSE IF( ITYPE.EQ.3 ) THEN
272 *
273 * For B*A*x=(lambda)*x;
274 * backtransform eigenvectors: x = L*y or U**H *y
275 *
276 IF( UPPER ) THEN
277 TRANS = 'C'
278 ELSE
279 TRANS = 'N'
280 END IF
281 *
282 DO 20 J = 1, NEIG
283 CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
284 $ 1 )
285 20 CONTINUE
286 END IF
287 END IF
288 *
289 WORK( 1 ) = LWMIN
290 RWORK( 1 ) = LRWMIN
291 IWORK( 1 ) = LIWMIN
292 RETURN
293 *
294 * End of ZHPGVD
295 *
296 END