LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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◆ 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 principal minor of order i of B is not positive. 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)
Definition cblat2.f:3285
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
subroutine zhpgst(itype, uplo, n, ap, bp, info)
ZHPGST
Definition zhpgst.f:113
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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
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