LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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chpgv.f
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1*> \brief \b CHPGV
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CHPGV + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chpgv.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chpgv.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chpgv.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CHPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22* RWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBZ, UPLO
26* INTEGER INFO, ITYPE, LDZ, N
27* ..
28* .. Array Arguments ..
29* REAL RWORK( * ), W( * )
30* COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CHPGV computes all the eigenvalues and, optionally, the eigenvectors
40*> of a complex generalized Hermitian-definite eigenproblem, of the form
41*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
42*> Here A and B are assumed to be Hermitian, stored in packed format,
43*> and B is also positive definite.
44*> \endverbatim
45*
46* Arguments:
47* ==========
48*
49*> \param[in] ITYPE
50*> \verbatim
51*> ITYPE is INTEGER
52*> Specifies the problem type to be solved:
53*> = 1: A*x = (lambda)*B*x
54*> = 2: A*B*x = (lambda)*x
55*> = 3: B*A*x = (lambda)*x
56*> \endverbatim
57*>
58*> \param[in] JOBZ
59*> \verbatim
60*> JOBZ is CHARACTER*1
61*> = 'N': Compute eigenvalues only;
62*> = 'V': Compute eigenvalues and eigenvectors.
63*> \endverbatim
64*>
65*> \param[in] UPLO
66*> \verbatim
67*> UPLO is CHARACTER*1
68*> = 'U': Upper triangles of A and B are stored;
69*> = 'L': Lower triangles of A and B are stored.
70*> \endverbatim
71*>
72*> \param[in] N
73*> \verbatim
74*> N is INTEGER
75*> The order of the matrices A and B. N >= 0.
76*> \endverbatim
77*>
78*> \param[in,out] AP
79*> \verbatim
80*> AP is COMPLEX array, dimension (N*(N+1)/2)
81*> On entry, the upper or lower triangle of the Hermitian matrix
82*> A, packed columnwise in a linear array. The j-th column of A
83*> is stored in the array AP as follows:
84*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
85*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
86*>
87*> On exit, the contents of AP are destroyed.
88*> \endverbatim
89*>
90*> \param[in,out] BP
91*> \verbatim
92*> BP is COMPLEX array, dimension (N*(N+1)/2)
93*> On entry, the upper or lower triangle of the Hermitian matrix
94*> B, packed columnwise in a linear array. The j-th column of B
95*> is stored in the array BP as follows:
96*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
97*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
98*>
99*> On exit, the triangular factor U or L from the Cholesky
100*> factorization B = U**H*U or B = L*L**H, in the same storage
101*> format as B.
102*> \endverbatim
103*>
104*> \param[out] W
105*> \verbatim
106*> W is REAL array, dimension (N)
107*> If INFO = 0, the eigenvalues in ascending order.
108*> \endverbatim
109*>
110*> \param[out] Z
111*> \verbatim
112*> Z is COMPLEX array, dimension (LDZ, N)
113*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
114*> eigenvectors. The eigenvectors are normalized as follows:
115*> if ITYPE = 1 or 2, Z**H*B*Z = I;
116*> if ITYPE = 3, Z**H*inv(B)*Z = I.
117*> If JOBZ = 'N', then Z is not referenced.
118*> \endverbatim
119*>
120*> \param[in] LDZ
121*> \verbatim
122*> LDZ is INTEGER
123*> The leading dimension of the array Z. LDZ >= 1, and if
124*> JOBZ = 'V', LDZ >= max(1,N).
125*> \endverbatim
126*>
127*> \param[out] WORK
128*> \verbatim
129*> WORK is COMPLEX array, dimension (max(1, 2*N-1))
130*> \endverbatim
131*>
132*> \param[out] RWORK
133*> \verbatim
134*> RWORK is REAL array, dimension (max(1, 3*N-2))
135*> \endverbatim
136*>
137*> \param[out] INFO
138*> \verbatim
139*> INFO is INTEGER
140*> = 0: successful exit
141*> < 0: if INFO = -i, the i-th argument had an illegal value
142*> > 0: CPPTRF or CHPEV returned an error code:
143*> <= N: if INFO = i, CHPEV failed to converge;
144*> i off-diagonal elements of an intermediate
145*> tridiagonal form did not convergeto zero;
146*> > N: if INFO = N + i, for 1 <= i <= n, then the leading
147*> minor of order i of B is not positive definite.
148*> The factorization of B could not be completed and
149*> no eigenvalues or eigenvectors were computed.
150*> \endverbatim
151*
152* Authors:
153* ========
154*
155*> \author Univ. of Tennessee
156*> \author Univ. of California Berkeley
157*> \author Univ. of Colorado Denver
158*> \author NAG Ltd.
159*
160*> \ingroup complexOTHEReigen
161*
162* =====================================================================
163 SUBROUTINE chpgv( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
164 $ RWORK, INFO )
165*
166* -- LAPACK driver routine --
167* -- LAPACK is a software package provided by Univ. of Tennessee, --
168* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
169*
170* .. Scalar Arguments ..
171 CHARACTER JOBZ, UPLO
172 INTEGER INFO, ITYPE, LDZ, N
173* ..
174* .. Array Arguments ..
175 REAL RWORK( * ), W( * )
176 COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
177* ..
178*
179* =====================================================================
180*
181* .. Local Scalars ..
182 LOGICAL UPPER, WANTZ
183 CHARACTER TRANS
184 INTEGER J, NEIG
185* ..
186* .. External Functions ..
187 LOGICAL LSAME
188 EXTERNAL lsame
189* ..
190* .. External Subroutines ..
191 EXTERNAL chpev, chpgst, cpptrf, ctpmv, ctpsv, xerbla
192* ..
193* .. Executable Statements ..
194*
195* Test the input parameters.
196*
197 wantz = lsame( jobz, 'V' )
198 upper = lsame( uplo, 'U' )
199*
200 info = 0
201 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
202 info = -1
203 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
204 info = -2
205 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
206 info = -3
207 ELSE IF( n.LT.0 ) THEN
208 info = -4
209 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
210 info = -9
211 END IF
212 IF( info.NE.0 ) THEN
213 CALL xerbla( 'CHPGV ', -info )
214 RETURN
215 END IF
216*
217* Quick return if possible
218*
219 IF( n.EQ.0 )
220 $ RETURN
221*
222* Form a Cholesky factorization of B.
223*
224 CALL cpptrf( uplo, n, bp, info )
225 IF( info.NE.0 ) THEN
226 info = n + info
227 RETURN
228 END IF
229*
230* Transform problem to standard eigenvalue problem and solve.
231*
232 CALL chpgst( itype, uplo, n, ap, bp, info )
233 CALL chpev( jobz, uplo, n, ap, w, z, ldz, work, rwork, info )
234*
235 IF( wantz ) THEN
236*
237* Backtransform eigenvectors to the original problem.
238*
239 neig = n
240 IF( info.GT.0 )
241 $ neig = info - 1
242 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
243*
244* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
245* backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
246*
247 IF( upper ) THEN
248 trans = 'N'
249 ELSE
250 trans = 'C'
251 END IF
252*
253 DO 10 j = 1, neig
254 CALL ctpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
255 $ 1 )
256 10 CONTINUE
257*
258 ELSE IF( itype.EQ.3 ) THEN
259*
260* For B*A*x=(lambda)*x;
261* backtransform eigenvectors: x = L*y or U**H*y
262*
263 IF( upper ) THEN
264 trans = 'C'
265 ELSE
266 trans = 'N'
267 END IF
268*
269 DO 20 j = 1, neig
270 CALL ctpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
271 $ 1 )
272 20 CONTINUE
273 END IF
274 END IF
275 RETURN
276*
277* End of CHPGV
278*
279 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPSV
Definition: ctpsv.f:144
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
subroutine cpptrf(UPLO, N, AP, INFO)
CPPTRF
Definition: cpptrf.f:119
subroutine chpgst(ITYPE, UPLO, N, AP, BP, INFO)
CHPGST
Definition: chpgst.f:113
subroutine chpev(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO)
CHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Definition: chpev.f:138
subroutine chpgv(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK, INFO)
CHPGV
Definition: chpgv.f:165