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

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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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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