3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
9 *> Download ZHPGVD + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgvd.f">
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgvd.f">
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgvd.f">
21 * SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22 * LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
24 * .. Scalar Arguments ..
25 * CHARACTER JOBZ, UPLO
26 * INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
28 * .. Array Arguments ..
30 * DOUBLE PRECISION RWORK( * ), W( * )
31 * COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
40 *> ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
41 *> of a complex generalized Hermitian-definite eigenproblem, of the form
42 *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
43 *> B are assumed to be Hermitian, stored in packed format, and B is also
45 *> If eigenvectors are desired, it uses a divide and conquer algorithm.
47 *> The divide and conquer algorithm makes very mild assumptions about
48 *> floating point arithmetic. It will work on machines with a guard
49 *> digit in add/subtract, or on those binary machines without guard
50 *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
51 *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
52 *> without guard digits, but we know of none.
61 *> Specifies the problem type to be solved:
62 *> = 1: A*x = (lambda)*B*x
63 *> = 2: A*B*x = (lambda)*x
64 *> = 3: B*A*x = (lambda)*x
69 *> JOBZ is CHARACTER*1
70 *> = 'N': Compute eigenvalues only;
71 *> = 'V': Compute eigenvalues and eigenvectors.
76 *> UPLO is CHARACTER*1
77 *> = 'U': Upper triangles of A and B are stored;
78 *> = 'L': Lower triangles of A and B are stored.
84 *> The order of the matrices A and B. N >= 0.
89 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
90 *> On entry, the upper or lower triangle of the Hermitian matrix
91 *> A, packed columnwise in a linear array. The j-th column of A
92 *> is stored in the array AP as follows:
93 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
94 *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
96 *> On exit, the contents of AP are destroyed.
101 *> BP is COMPLEX*16 array, dimension (N*(N+1)/2)
102 *> On entry, the upper or lower triangle of the Hermitian matrix
103 *> B, packed columnwise in a linear array. The j-th column of B
104 *> is stored in the array BP as follows:
105 *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
106 *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
108 *> On exit, the triangular factor U or L from the Cholesky
109 *> factorization B = U**H*U or B = L*L**H, in the same storage
115 *> W is DOUBLE PRECISION array, dimension (N)
116 *> If INFO = 0, the eigenvalues in ascending order.
121 *> Z is COMPLEX*16 array, dimension (LDZ, N)
122 *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
123 *> eigenvectors. The eigenvectors are normalized as follows:
124 *> if ITYPE = 1 or 2, Z**H*B*Z = I;
125 *> if ITYPE = 3, Z**H*inv(B)*Z = I.
126 *> If JOBZ = 'N', then Z is not referenced.
132 *> The leading dimension of the array Z. LDZ >= 1, and if
133 *> JOBZ = 'V', LDZ >= max(1,N).
138 *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
139 *> On exit, if INFO = 0, WORK(1) returns the required LWORK.
145 *> The dimension of the array WORK.
146 *> If N <= 1, LWORK >= 1.
147 *> If JOBZ = 'N' and N > 1, LWORK >= N.
148 *> If JOBZ = 'V' and N > 1, LWORK >= 2*N.
150 *> If LWORK = -1, then a workspace query is assumed; the routine
151 *> only calculates the required sizes of the WORK, RWORK and
152 *> IWORK arrays, returns these values as the first entries of
153 *> the WORK, RWORK and IWORK arrays, and no error message
154 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
159 *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
160 *> On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
166 *> The dimension of array RWORK.
167 *> If N <= 1, LRWORK >= 1.
168 *> If JOBZ = 'N' and N > 1, LRWORK >= N.
169 *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
171 *> If LRWORK = -1, then a workspace query is assumed; the
172 *> routine only calculates the required sizes of the WORK, RWORK
173 *> and IWORK arrays, returns these values as the first entries
174 *> of the WORK, RWORK and IWORK arrays, and no error message
175 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
180 *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
181 *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
187 *> The dimension of array IWORK.
188 *> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
189 *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
191 *> If LIWORK = -1, then a workspace query is assumed; the
192 *> routine only calculates the required sizes of the WORK, RWORK
193 *> and IWORK arrays, returns these values as the first entries
194 *> of the WORK, RWORK and IWORK arrays, and no error message
195 *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
201 *> = 0: successful exit
202 *> < 0: if INFO = -i, the i-th argument had an illegal value
203 *> > 0: ZPPTRF or ZHPEVD returned an error code:
204 *> <= N: if INFO = i, ZHPEVD failed to converge;
205 *> i off-diagonal elements of an intermediate
206 *> tridiagonal form did not convergeto zero;
207 *> > N: if INFO = N + i, for 1 <= i <= n, then the leading
208 *> minor of order i of B is not positive definite.
209 *> The factorization of B could not be completed and
210 *> no eigenvalues or eigenvectors were computed.
216 *> \author Univ. of Tennessee
217 *> \author Univ. of California Berkeley
218 *> \author Univ. of Colorado Denver
221 *> \date December 2016
223 *> \ingroup complex16OTHEReigen
225 *> \par Contributors:
228 *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
230 * =====================================================================
231 SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
232 $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
234 * -- LAPACK driver routine (version 3.7.0) --
235 * -- LAPACK is a software package provided by Univ. of Tennessee, --
236 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
239 * .. Scalar Arguments ..
241 INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
243 * .. Array Arguments ..
245 DOUBLE PRECISION RWORK( * ), W( * )
246 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
249 * =====================================================================
251 * .. Local Scalars ..
252 LOGICAL LQUERY, UPPER, WANTZ
254 INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG
256 * .. External Functions ..
260 * .. External Subroutines ..
261 EXTERNAL XERBLA, ZHPEVD, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
263 * .. Intrinsic Functions ..
266 * .. Executable Statements ..
268 * Test the input parameters.
270 WANTZ = LSAME( JOBZ, 'V' )
271 UPPER = LSAME( UPLO, 'U' )
272 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
275 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
277 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
279 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
281 ELSE IF( N.LT.0 ) THEN
283 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
295 LRWMIN = 1 + 5*N + 2*N**2
307 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
309 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
311 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
317 CALL XERBLA( 'ZHPGVD', -INFO )
319 ELSE IF( LQUERY ) THEN
323 * Quick return if possible
328 * Form a Cholesky factorization of B.
330 CALL ZPPTRF( UPLO, N, BP, INFO )
336 * Transform problem to standard eigenvalue problem and solve.
338 CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
339 CALL ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
340 $ LRWORK, IWORK, LIWORK, INFO )
341 LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
342 LRWMIN = MAX( DBLE( LRWMIN ), DBLE( RWORK( 1 ) ) )
343 LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
347 * Backtransform eigenvectors to the original problem.
352 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
354 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
355 * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
364 CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
368 ELSE IF( ITYPE.EQ.3 ) THEN
370 * For B*A*x=(lambda)*x;
371 * backtransform eigenvectors: x = L*y or U**H *y
380 CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),