LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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zhpgvd.f
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1*> \brief \b ZHPGVD
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZHPGVD + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgvd.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgvd.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgvd.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBZ, UPLO
26* INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
27* ..
28* .. Array Arguments ..
29* INTEGER IWORK( * )
30* DOUBLE PRECISION RWORK( * ), W( * )
31* COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
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
44*> positive definite.
45*> If eigenvectors are desired, it uses a divide and conquer algorithm.
46*>
47*> \endverbatim
48*
49* Arguments:
50* ==========
51*
52*> \param[in] ITYPE
53*> \verbatim
54*> ITYPE is INTEGER
55*> Specifies the problem type to be solved:
56*> = 1: A*x = (lambda)*B*x
57*> = 2: A*B*x = (lambda)*x
58*> = 3: B*A*x = (lambda)*x
59*> \endverbatim
60*>
61*> \param[in] JOBZ
62*> \verbatim
63*> JOBZ is CHARACTER*1
64*> = 'N': Compute eigenvalues only;
65*> = 'V': Compute eigenvalues and eigenvectors.
66*> \endverbatim
67*>
68*> \param[in] UPLO
69*> \verbatim
70*> UPLO is CHARACTER*1
71*> = 'U': Upper triangles of A and B are stored;
72*> = 'L': Lower triangles of A and B are stored.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The order of the matrices A and B. N >= 0.
79*> \endverbatim
80*>
81*> \param[in,out] AP
82*> \verbatim
83*> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
84*> On entry, the upper or lower triangle of the Hermitian matrix
85*> A, packed columnwise in a linear array. The j-th column of A
86*> is stored in the array AP as follows:
87*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
88*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
89*>
90*> On exit, the contents of AP are destroyed.
91*> \endverbatim
92*>
93*> \param[in,out] BP
94*> \verbatim
95*> BP is COMPLEX*16 array, dimension (N*(N+1)/2)
96*> On entry, the upper or lower triangle of the Hermitian matrix
97*> B, packed columnwise in a linear array. The j-th column of B
98*> is stored in the array BP as follows:
99*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
100*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
101*>
102*> On exit, the triangular factor U or L from the Cholesky
103*> factorization B = U**H*U or B = L*L**H, in the same storage
104*> format as B.
105*> \endverbatim
106*>
107*> \param[out] W
108*> \verbatim
109*> W is DOUBLE PRECISION array, dimension (N)
110*> If INFO = 0, the eigenvalues in ascending order.
111*> \endverbatim
112*>
113*> \param[out] Z
114*> \verbatim
115*> Z is COMPLEX*16 array, dimension (LDZ, N)
116*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
117*> eigenvectors. The eigenvectors are normalized as follows:
118*> if ITYPE = 1 or 2, Z**H*B*Z = I;
119*> if ITYPE = 3, Z**H*inv(B)*Z = I.
120*> If JOBZ = 'N', then Z is not referenced.
121*> \endverbatim
122*>
123*> \param[in] LDZ
124*> \verbatim
125*> LDZ is INTEGER
126*> The leading dimension of the array Z. LDZ >= 1, and if
127*> JOBZ = 'V', LDZ >= max(1,N).
128*> \endverbatim
129*>
130*> \param[out] WORK
131*> \verbatim
132*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
133*> On exit, if INFO = 0, WORK(1) returns the required LWORK.
134*> \endverbatim
135*>
136*> \param[in] LWORK
137*> \verbatim
138*> LWORK is INTEGER
139*> The dimension of the array WORK.
140*> If N <= 1, LWORK >= 1.
141*> If JOBZ = 'N' and N > 1, LWORK >= N.
142*> If JOBZ = 'V' and N > 1, LWORK >= 2*N.
143*>
144*> If LWORK = -1, then a workspace query is assumed; the routine
145*> only calculates the required sizes of the WORK, RWORK and
146*> IWORK arrays, returns these values as the first entries of
147*> the WORK, RWORK and IWORK arrays, and no error message
148*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
149*> \endverbatim
150*>
151*> \param[out] RWORK
152*> \verbatim
153*> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
154*> On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
155*> \endverbatim
156*>
157*> \param[in] LRWORK
158*> \verbatim
159*> LRWORK is INTEGER
160*> The dimension of array RWORK.
161*> If N <= 1, LRWORK >= 1.
162*> If JOBZ = 'N' and N > 1, LRWORK >= N.
163*> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
164*>
165*> If LRWORK = -1, then a workspace query is assumed; the
166*> routine only calculates the required sizes of the WORK, RWORK
167*> and IWORK arrays, returns these values as the first entries
168*> of the WORK, RWORK and IWORK arrays, and no error message
169*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
170*> \endverbatim
171*>
172*> \param[out] IWORK
173*> \verbatim
174*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
175*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
176*> \endverbatim
177*>
178*> \param[in] LIWORK
179*> \verbatim
180*> LIWORK is INTEGER
181*> The dimension of array IWORK.
182*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
183*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
184*>
185*> If LIWORK = -1, then a workspace query is assumed; the
186*> routine only calculates the required sizes of the WORK, RWORK
187*> and IWORK arrays, returns these values as the first entries
188*> of the WORK, RWORK and IWORK arrays, and no error message
189*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
190*> \endverbatim
191*>
192*> \param[out] INFO
193*> \verbatim
194*> INFO is INTEGER
195*> = 0: successful exit
196*> < 0: if INFO = -i, the i-th argument had an illegal value
197*> > 0: ZPPTRF or ZHPEVD returned an error code:
198*> <= N: if INFO = i, ZHPEVD failed to converge;
199*> i off-diagonal elements of an intermediate
200*> tridiagonal form did not convergeto zero;
201*> > N: if INFO = N + i, for 1 <= i <= n, then the leading
202*> principal minor of order i of B is not positive.
203*> The factorization of B could not be completed and
204*> no eigenvalues or eigenvectors were computed.
205*> \endverbatim
206*
207* Authors:
208* ========
209*
210*> \author Univ. of Tennessee
211*> \author Univ. of California Berkeley
212*> \author Univ. of Colorado Denver
213*> \author NAG Ltd.
214*
215*> \ingroup hpgvd
216*
217*> \par Contributors:
218* ==================
219*>
220*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
221*
222* =====================================================================
223 SUBROUTINE zhpgvd( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
224 $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
225*
226* -- LAPACK driver routine --
227* -- LAPACK is a software package provided by Univ. of Tennessee, --
228* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
229*
230* .. Scalar Arguments ..
231 CHARACTER JOBZ, UPLO
232 INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
233* ..
234* .. Array Arguments ..
235 INTEGER IWORK( * )
236 DOUBLE PRECISION RWORK( * ), W( * )
237 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
238* ..
239*
240* =====================================================================
241*
242* .. Local Scalars ..
243 LOGICAL LQUERY, UPPER, WANTZ
244 CHARACTER TRANS
245 INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG
246* ..
247* .. External Functions ..
248 LOGICAL LSAME
249 EXTERNAL lsame
250* ..
251* .. External Subroutines ..
252 EXTERNAL xerbla, zhpevd, zhpgst, zpptrf, ztpmv, ztpsv
253* ..
254* .. Intrinsic Functions ..
255 INTRINSIC dble, max
256* ..
257* .. Executable Statements ..
258*
259* Test the input parameters.
260*
261 wantz = lsame( jobz, 'V' )
262 upper = lsame( uplo, 'U' )
263 lquery = ( lwork.EQ.-1 .OR. lrwork.EQ.-1 .OR. liwork.EQ.-1 )
264*
265 info = 0
266 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
267 info = -1
268 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
269 info = -2
270 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
271 info = -3
272 ELSE IF( n.LT.0 ) THEN
273 info = -4
274 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
275 info = -9
276 END IF
277*
278 IF( info.EQ.0 ) THEN
279 IF( n.LE.1 ) THEN
280 lwmin = 1
281 liwmin = 1
282 lrwmin = 1
283 ELSE
284 IF( wantz ) THEN
285 lwmin = 2*n
286 lrwmin = 1 + 5*n + 2*n**2
287 liwmin = 3 + 5*n
288 ELSE
289 lwmin = n
290 lrwmin = n
291 liwmin = 1
292 END IF
293 END IF
294*
295 work( 1 ) = lwmin
296 rwork( 1 ) = lrwmin
297 iwork( 1 ) = liwmin
298 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
299 info = -11
300 ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
301 info = -13
302 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
303 info = -15
304 END IF
305 END IF
306*
307 IF( info.NE.0 ) THEN
308 CALL xerbla( 'ZHPGVD', -info )
309 RETURN
310 ELSE IF( lquery ) THEN
311 RETURN
312 END IF
313*
314* Quick return if possible
315*
316 IF( n.EQ.0 )
317 $ RETURN
318*
319* Form a Cholesky factorization of B.
320*
321 CALL zpptrf( uplo, n, bp, info )
322 IF( info.NE.0 ) THEN
323 info = n + info
324 RETURN
325 END IF
326*
327* Transform problem to standard eigenvalue problem and solve.
328*
329 CALL zhpgst( itype, uplo, n, ap, bp, info )
330 CALL zhpevd( jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork,
331 $ lrwork, iwork, liwork, info )
332 lwmin = int( max( dble( lwmin ), dble( work( 1 ) ) ) )
333 lrwmin = int( max( dble( lrwmin ), dble( rwork( 1 ) ) ) )
334 liwmin = int( max( dble( liwmin ), dble( iwork( 1 ) ) ) )
335*
336 IF( wantz ) THEN
337*
338* Backtransform eigenvectors to the original problem.
339*
340 neig = n
341 IF( info.GT.0 )
342 $ neig = info - 1
343 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
344*
345* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
346* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
347*
348 IF( upper ) THEN
349 trans = 'N'
350 ELSE
351 trans = 'C'
352 END IF
353*
354 DO 10 j = 1, neig
355 CALL ztpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
356 $ 1 )
357 10 CONTINUE
358*
359 ELSE IF( itype.EQ.3 ) THEN
360*
361* For B*A*x=(lambda)*x;
362* backtransform eigenvectors: x = L*y or U**H *y
363*
364 IF( upper ) THEN
365 trans = 'C'
366 ELSE
367 trans = 'N'
368 END IF
369*
370 DO 20 j = 1, neig
371 CALL ztpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
372 $ 1 )
373 20 CONTINUE
374 END IF
375 END IF
376*
377 work( 1 ) = lwmin
378 rwork( 1 ) = lrwmin
379 iwork( 1 ) = liwmin
380 RETURN
381*
382* End of ZHPGVD
383*
384 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zhpevd(jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition zhpevd.f:194
subroutine zhpgst(itype, uplo, n, ap, bp, info)
ZHPGST
Definition zhpgst.f:113
subroutine zhpgvd(itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHPGVD
Definition zhpgvd.f:225
subroutine zpptrf(uplo, n, ap, info)
ZPPTRF
Definition zpptrf.f:119
subroutine ztpmv(uplo, trans, diag, n, ap, x, incx)
ZTPMV
Definition ztpmv.f:142
subroutine ztpsv(uplo, trans, diag, n, ap, x, incx)
ZTPSV
Definition ztpsv.f:144