LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ chpgvx()

subroutine chpgvx ( integer itype,
character jobz,
character range,
character uplo,
integer n,
complex, dimension( * ) ap,
complex, dimension( * ) bp,
real vl,
real vu,
integer il,
integer iu,
real abstol,
integer m,
real, dimension( * ) w,
complex, dimension( ldz, * ) z,
integer ldz,
complex, dimension( * ) work,
real, dimension( * ) rwork,
integer, dimension( * ) iwork,
integer, dimension( * ) ifail,
integer info )

CHPGVX

Download CHPGVX + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> CHPGVX computes selected eigenvalues and, optionally, 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.  Eigenvalues and eigenvectors can be selected by
!> specifying either a range of values or a range of indices for the
!> desired eigenvalues.
!> 
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]RANGE
!>          RANGE is CHARACTER*1
!>          = 'A': all eigenvalues will be found;
!>          = 'V': all eigenvalues in the half-open interval (VL,VU]
!>                 will be found;
!>          = 'I': the IL-th through IU-th eigenvalues will be found.
!> 
[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.
!> 
[in]VL
!>          VL is REAL
!>
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues. VL < VU.
!>          Not referenced if RANGE = 'A' or 'I'.
!> 
[in]VU
!>          VU is REAL
!>
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues. VL < VU.
!>          Not referenced if RANGE = 'A' or 'I'.
!> 
[in]IL
!>          IL is INTEGER
!>
!>          If RANGE='I', the index of the
!>          smallest eigenvalue to be returned.
!>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
!>          Not referenced if RANGE = 'A' or 'V'.
!> 
[in]IU
!>          IU is INTEGER
!>
!>          If RANGE='I', the index of the
!>          largest eigenvalue to be returned.
!>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
!>          Not referenced if RANGE = 'A' or 'V'.
!> 
[in]ABSTOL
!>          ABSTOL is REAL
!>          The absolute error tolerance for the eigenvalues.
!>          An approximate eigenvalue is accepted as converged
!>          when it is determined to lie in an interval [a,b]
!>          of width less than or equal to
!>
!>                  ABSTOL + EPS *   max( |a|,|b| ) ,
!>
!>          where EPS is the machine precision.  If ABSTOL is less than
!>          or equal to zero, then  EPS*|T|  will be used in its place,
!>          where |T| is the 1-norm of the tridiagonal matrix obtained
!>          by reducing AP to tridiagonal form.
!>
!>          Eigenvalues will be computed most accurately when ABSTOL is
!>          set to twice the underflow threshold 2*SLAMCH('S'), not zero.
!>          If this routine returns with INFO>0, indicating that some
!>          eigenvectors did not converge, try setting ABSTOL to
!>          2*SLAMCH('S').
!> 
[out]M
!>          M is INTEGER
!>          The total number of eigenvalues found.  0 <= M <= N.
!>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
!> 
[out]W
!>          W is REAL array, dimension (N)
!>          On normal exit, the first M elements contain the selected
!>          eigenvalues in ascending order.
!> 
[out]Z
!>          Z is COMPLEX array, dimension (LDZ, N)
!>          If JOBZ = 'N', then Z is not referenced.
!>          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
!>          contain the orthonormal eigenvectors of the matrix A
!>          corresponding to the selected eigenvalues, with the i-th
!>          column of Z holding the eigenvector associated with W(i).
!>          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 an eigenvector fails to converge, then that column of Z
!>          contains the latest approximation to the eigenvector, and the
!>          index of the eigenvector is returned in IFAIL.
!>          Note: the user must ensure that at least max(1,M) columns are
!>          supplied in the array Z; if RANGE = 'V', the exact value of M
!>          is not known in advance and an upper bound must be used.
!> 
[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 (2*N)
!> 
[out]RWORK
!>          RWORK is REAL array, dimension (7*N)
!> 
[out]IWORK
!>          IWORK is INTEGER array, dimension (5*N)
!> 
[out]IFAIL
!>          IFAIL is INTEGER array, dimension (N)
!>          If JOBZ = 'V', then if INFO = 0, the first M elements of
!>          IFAIL are zero.  If INFO > 0, then IFAIL contains the
!>          indices of the eigenvectors that failed to converge.
!>          If JOBZ = 'N', then IFAIL is not referenced.
!> 
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  CPPTRF or CHPEVX returned an error code:
!>             <= N:  if INFO = i, CHPEVX failed to converge;
!>                    i eigenvectors failed to converge.  Their indices
!>                    are stored in array IFAIL.
!>             > 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.
!> 
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 272 of file chpgvx.f.

275*
276* -- LAPACK driver routine --
277* -- LAPACK is a software package provided by Univ. of Tennessee, --
278* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
279*
280* .. Scalar Arguments ..
281 CHARACTER JOBZ, RANGE, UPLO
282 INTEGER IL, INFO, ITYPE, IU, LDZ, M, N
283 REAL ABSTOL, VL, VU
284* ..
285* .. Array Arguments ..
286 INTEGER IFAIL( * ), IWORK( * )
287 REAL RWORK( * ), W( * )
288 COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
289* ..
290*
291* =====================================================================
292*
293* .. Local Scalars ..
294 LOGICAL ALLEIG, INDEIG, UPPER, VALEIG, WANTZ
295 CHARACTER TRANS
296 INTEGER J
297* ..
298* .. External Functions ..
299 LOGICAL LSAME
300 EXTERNAL lsame
301* ..
302* .. External Subroutines ..
303 EXTERNAL chpevx, chpgst, cpptrf, ctpmv, ctpsv,
304 $ xerbla
305* ..
306* .. Intrinsic Functions ..
307 INTRINSIC min
308* ..
309* .. Executable Statements ..
310*
311* Test the input parameters.
312*
313 wantz = lsame( jobz, 'V' )
314 upper = lsame( uplo, 'U' )
315 alleig = lsame( range, 'A' )
316 valeig = lsame( range, 'V' )
317 indeig = lsame( range, 'I' )
318*
319 info = 0
320 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
321 info = -1
322 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
323 info = -2
324 ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
325 info = -3
326 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
327 info = -4
328 ELSE IF( n.LT.0 ) THEN
329 info = -5
330 ELSE
331 IF( valeig ) THEN
332 IF( n.GT.0 .AND. vu.LE.vl ) THEN
333 info = -9
334 END IF
335 ELSE IF( indeig ) THEN
336 IF( il.LT.1 ) THEN
337 info = -10
338 ELSE IF( iu.LT.min( n, il ) .OR. iu.GT.n ) THEN
339 info = -11
340 END IF
341 END IF
342 END IF
343 IF( info.EQ.0 ) THEN
344 IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
345 info = -16
346 END IF
347 END IF
348*
349 IF( info.NE.0 ) THEN
350 CALL xerbla( 'CHPGVX', -info )
351 RETURN
352 END IF
353*
354* Quick return if possible
355*
356 IF( n.EQ.0 )
357 $ RETURN
358*
359* Form a Cholesky factorization of B.
360*
361 CALL cpptrf( uplo, n, bp, info )
362 IF( info.NE.0 ) THEN
363 info = n + info
364 RETURN
365 END IF
366*
367* Transform problem to standard eigenvalue problem and solve.
368*
369 CALL chpgst( itype, uplo, n, ap, bp, info )
370 CALL chpevx( jobz, range, uplo, n, ap, vl, vu, il, iu, abstol,
371 $ m,
372 $ w, z, ldz, work, rwork, iwork, ifail, info )
373*
374 IF( wantz ) THEN
375*
376* Backtransform eigenvectors to the original problem.
377*
378 IF( info.GT.0 )
379 $ m = info - 1
380 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
381*
382* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
383* backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
384*
385 IF( upper ) THEN
386 trans = 'N'
387 ELSE
388 trans = 'C'
389 END IF
390*
391 DO 10 j = 1, m
392 CALL ctpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
393 $ 1 )
394 10 CONTINUE
395*
396 ELSE IF( itype.EQ.3 ) THEN
397*
398* For B*A*x=(lambda)*x;
399* backtransform eigenvectors: x = L*y or U**H*y
400*
401 IF( upper ) THEN
402 trans = 'C'
403 ELSE
404 trans = 'N'
405 END IF
406*
407 DO 20 j = 1, m
408 CALL ctpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
409 $ 1 )
410 20 CONTINUE
411 END IF
412 END IF
413*
414 RETURN
415*
416* End of CHPGVX
417*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chpevx(jobz, range, uplo, n, ap, vl, vu, il, iu, abstol, m, w, z, ldz, work, rwork, iwork, ifail, info)
CHPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition chpevx.f:238
subroutine chpgst(itype, uplo, n, ap, bp, info)
CHPGST
Definition chpgst.f:111
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine cpptrf(uplo, n, ap, info)
CPPTRF
Definition cpptrf.f:117
subroutine ctpmv(uplo, trans, diag, n, ap, x, incx)
CTPMV
Definition ctpmv.f:142
subroutine ctpsv(uplo, trans, diag, n, ap, x, incx)
CTPSV
Definition ctpsv.f:144
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