 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ zhpgv()

 subroutine zhpgv ( integer ITYPE, character JOBZ, character UPLO, integer N, complex*16, dimension( * ) AP, complex*16, dimension( * ) BP, double precision, dimension( * ) W, complex*16, dimension( ldz, * ) Z, integer LDZ, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO )

ZHPGV

Purpose:
ZHPGV 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*16 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*16 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 DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. [out] Z Z is COMPLEX*16 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*16 array, dimension (max(1, 2*N-1)) [out] RWORK RWORK is DOUBLE PRECISION 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: ZPPTRF or ZHPEV returned an error code: <= N: if INFO = i, ZHPEV 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.

Definition at line 163 of file zhpgv.f.

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  DOUBLE PRECISION RWORK( * ), W( * )
176  COMPLEX*16 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 xerbla, zhpev, zhpgst, zpptrf, ztpmv, ztpsv
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( 'ZHPGV ', -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 zpptrf( 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 zhpgst( itype, uplo, n, ap, bp, info )
233  CALL zhpev( 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 ztpsv( 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 ztpmv( 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 ZHPGV
278 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPSV
Definition: ztpsv.f:144
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:142
subroutine zhpgst(ITYPE, UPLO, N, AP, BP, INFO)
ZHPGST
Definition: zhpgst.f:113
subroutine zpptrf(UPLO, N, AP, INFO)
ZPPTRF
Definition: zpptrf.f:119
subroutine zhpev(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO)
ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Definition: zhpev.f:138
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