LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
chpgv.f
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1 *> \brief \b CHPGV
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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 *> \date November 2015
161 *
162 *> \ingroup complexOTHEReigen
163 *
164 * =====================================================================
165  SUBROUTINE chpgv( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
166  \$ rwork, info )
167 *
168 * -- LAPACK driver routine (version 3.6.0) --
169 * -- LAPACK is a software package provided by Univ. of Tennessee, --
170 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171 * November 2015
172 *
173 * .. Scalar Arguments ..
174  CHARACTER JOBZ, UPLO
175  INTEGER INFO, ITYPE, LDZ, N
176 * ..
177 * .. Array Arguments ..
178  REAL RWORK( * ), W( * )
179  COMPLEX AP( * ), BP( * ), WORK( * ), Z( ldz, * )
180 * ..
181 *
182 * =====================================================================
183 *
184 * .. Local Scalars ..
185  LOGICAL UPPER, WANTZ
186  CHARACTER TRANS
187  INTEGER J, NEIG
188 * ..
189 * .. External Functions ..
190  LOGICAL LSAME
191  EXTERNAL lsame
192 * ..
193 * .. External Subroutines ..
194  EXTERNAL chpev, chpgst, cpptrf, ctpmv, ctpsv, xerbla
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input parameters.
199 *
200  wantz = lsame( jobz, 'V' )
201  upper = lsame( uplo, 'U' )
202 *
203  info = 0
204  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
205  info = -1
206  ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
207  info = -2
208  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
209  info = -3
210  ELSE IF( n.LT.0 ) THEN
211  info = -4
212  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
213  info = -9
214  END IF
215  IF( info.NE.0 ) THEN
216  CALL xerbla( 'CHPGV ', -info )
217  RETURN
218  END IF
219 *
220 * Quick return if possible
221 *
222  IF( n.EQ.0 )
223  \$ RETURN
224 *
225 * Form a Cholesky factorization of B.
226 *
227  CALL cpptrf( uplo, n, bp, info )
228  IF( info.NE.0 ) THEN
229  info = n + info
230  RETURN
231  END IF
232 *
233 * Transform problem to standard eigenvalue problem and solve.
234 *
235  CALL chpgst( itype, uplo, n, ap, bp, info )
236  CALL chpev( jobz, uplo, n, ap, w, z, ldz, work, rwork, info )
237 *
238  IF( wantz ) THEN
239 *
240 * Backtransform eigenvectors to the original problem.
241 *
242  neig = n
243  IF( info.GT.0 )
244  \$ neig = info - 1
245  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
246 *
247 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
248 * backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
249 *
250  IF( upper ) THEN
251  trans = 'N'
252  ELSE
253  trans = 'C'
254  END IF
255 *
256  DO 10 j = 1, neig
257  CALL ctpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
258  \$ 1 )
259  10 CONTINUE
260 *
261  ELSE IF( itype.EQ.3 ) THEN
262 *
263 * For B*A*x=(lambda)*x;
264 * backtransform eigenvectors: x = L*y or U**H*y
265 *
266  IF( upper ) THEN
267  trans = 'C'
268  ELSE
269  trans = 'N'
270  END IF
271 *
272  DO 20 j = 1, neig
273  CALL ctpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
274  \$ 1 )
275  20 CONTINUE
276  END IF
277  END IF
278  RETURN
279 *
280 * End of CHPGV
281 *
282  END
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:144
subroutine chpgst(ITYPE, UPLO, N, AP, BP, INFO)
CHPGST
Definition: chpgst.f:115
subroutine cpptrf(UPLO, N, AP, INFO)
CPPTRF
Definition: cpptrf.f:121
subroutine chpgv(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, RWORK, INFO)
CHPGV
Definition: chpgv.f:167
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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 matrice...
Definition: chpev.f:140
subroutine ctpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPSV
Definition: ctpsv.f:146