LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine chpgv ( integer ITYPE, character JOBZ, character UPLO, integer N, complex, dimension( * ) AP, complex, dimension( * ) BP, real, dimension( * ) W, complex, dimension( ldz, * ) Z, integer LDZ, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CHPGV

Purpose:
``` CHPGV computes all the eigenvalues and, optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian, stored in packed format,
and B is also positive definite.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x``` [in] JOBZ ``` JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in,out] AP ``` AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed.``` [in,out] BP ``` BP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H, in the same storage format as B.``` [out] W ``` W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] Z ``` Z is COMPLEX array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = 'N', then Z is not referenced.``` [in] LDZ ``` LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).``` [out] WORK ` WORK is COMPLEX array, dimension (max(1, 2*N-1))` [out] RWORK ` RWORK is REAL array, dimension (max(1, 3*N-2))` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: CPPTRF or CHPEV returned an error code: <= N: if INFO = i, CHPEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not convergeto zero; > N: if INFO = N + i, for 1 <= i <= n, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.```
Date
November 2015

Definition at line 167 of file chpgv.f.

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 *
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 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
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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