LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ chpgvd()

subroutine chpgvd ( 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,
integer lwork,
real, dimension( * ) rwork,
integer lrwork,
integer, dimension( * ) iwork,
integer liwork,
integer info )

CHPGVD

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

Purpose:
!>
!> CHPGVD 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.
!> If eigenvectors are desired, it uses a divide and conquer algorithm.
!>
!> 
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,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the required LWORK.
!> 
[in]LWORK
!>          LWORK is INTEGER
!>          The dimension of array WORK.
!>          If N <= 1,               LWORK >= 1.
!>          If JOBZ = 'N' and N > 1, LWORK >= N.
!>          If JOBZ = 'V' and N > 1, LWORK >= 2*N.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the required sizes of the WORK, RWORK and
!>          IWORK arrays, returns these values as the first entries of
!>          the WORK, RWORK and IWORK arrays, and no error message
!>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
!> 
[out]RWORK
!>          RWORK is REAL array, dimension (MAX(1,LRWORK))
!>          On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
!> 
[in]LRWORK
!>          LRWORK is INTEGER
!>          The dimension of array RWORK.
!>          If N <= 1,               LRWORK >= 1.
!>          If JOBZ = 'N' and N > 1, LRWORK >= N.
!>          If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
!>
!>          If LRWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the required sizes of the WORK, RWORK
!>          and IWORK arrays, returns these values as the first entries
!>          of the WORK, RWORK and IWORK arrays, and no error message
!>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
!> 
[out]IWORK
!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
!> 
[in]LIWORK
!>          LIWORK is INTEGER
!>          The dimension of array IWORK.
!>          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
!>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
!>
!>          If LIWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the required sizes of the WORK, RWORK
!>          and IWORK arrays, returns these values as the first entries
!>          of the WORK, RWORK and IWORK arrays, and no error message
!>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
!> 
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  CPPTRF or CHPEVD returned an error code:
!>             <= N:  if INFO = i, CHPEVD 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.
!> 
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 221 of file chpgvd.f.

224*
225* -- LAPACK driver routine --
226* -- LAPACK is a software package provided by Univ. of Tennessee, --
227* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
228*
229* .. Scalar Arguments ..
230 CHARACTER JOBZ, UPLO
231 INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
232* ..
233* .. Array Arguments ..
234 INTEGER IWORK( * )
235 REAL RWORK( * ), W( * )
236 COMPLEX AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
237* ..
238*
239* =====================================================================
240*
241* .. Local Scalars ..
242 LOGICAL LQUERY, UPPER, WANTZ
243 CHARACTER TRANS
244 INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG
245* ..
246* .. External Functions ..
247 LOGICAL LSAME
248 REAL SROUNDUP_LWORK
249 EXTERNAL lsame, sroundup_lwork
250* ..
251* .. External Subroutines ..
252 EXTERNAL chpevd, chpgst, cpptrf, ctpmv, ctpsv,
253 $ xerbla
254* ..
255* .. Intrinsic Functions ..
256 INTRINSIC max, real
257* ..
258* .. Executable Statements ..
259*
260* Test the input parameters.
261*
262 wantz = lsame( jobz, 'V' )
263 upper = lsame( uplo, 'U' )
264 lquery = ( lwork.EQ.-1 .OR. lrwork.EQ.-1 .OR. liwork.EQ.-1 )
265*
266 info = 0
267 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
268 info = -1
269 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
270 info = -2
271 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
272 info = -3
273 ELSE IF( n.LT.0 ) THEN
274 info = -4
275 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
276 info = -9
277 END IF
278*
279 IF( info.EQ.0 ) THEN
280 IF( n.LE.1 ) THEN
281 lwmin = 1
282 liwmin = 1
283 lrwmin = 1
284 ELSE
285 IF( wantz ) THEN
286 lwmin = 2*n
287 lrwmin = 1 + 5*n + 2*n**2
288 liwmin = 3 + 5*n
289 ELSE
290 lwmin = n
291 lrwmin = n
292 liwmin = 1
293 END IF
294 END IF
295*
296 work( 1 ) = sroundup_lwork(lwmin)
297 rwork( 1 ) = real( lrwmin )
298 iwork( 1 ) = liwmin
299 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
300 info = -11
301 ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
302 info = -13
303 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
304 info = -15
305 END IF
306 END IF
307*
308 IF( info.NE.0 ) THEN
309 CALL xerbla( 'CHPGVD', -info )
310 RETURN
311 ELSE IF( lquery ) THEN
312 RETURN
313 END IF
314*
315* Quick return if possible
316*
317 IF( n.EQ.0 )
318 $ RETURN
319*
320* Form a Cholesky factorization of B.
321*
322 CALL cpptrf( uplo, n, bp, info )
323 IF( info.NE.0 ) THEN
324 info = n + info
325 RETURN
326 END IF
327*
328* Transform problem to standard eigenvalue problem and solve.
329*
330 CALL chpgst( itype, uplo, n, ap, bp, info )
331 CALL chpevd( jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork,
332 $ lrwork, iwork, liwork, info )
333 lwmin = int( max( real( lwmin ), real( work( 1 ) ) ) )
334 lrwmin = int( max( real( lrwmin ), real( rwork( 1 ) ) ) )
335 liwmin = int( max( real( liwmin ), real( iwork( 1 ) ) ) )
336*
337 IF( wantz ) THEN
338*
339* Backtransform eigenvectors to the original problem.
340*
341 neig = n
342 IF( info.GT.0 )
343 $ neig = info - 1
344 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
345*
346* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
347* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
348*
349 IF( upper ) THEN
350 trans = 'N'
351 ELSE
352 trans = 'C'
353 END IF
354*
355 DO 10 j = 1, neig
356 CALL ctpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
357 $ 1 )
358 10 CONTINUE
359*
360 ELSE IF( itype.EQ.3 ) THEN
361*
362* For B*A*x=(lambda)*x;
363* backtransform eigenvectors: x = L*y or U**H *y
364*
365 IF( upper ) THEN
366 trans = 'C'
367 ELSE
368 trans = 'N'
369 END IF
370*
371 DO 20 j = 1, neig
372 CALL ctpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
373 $ 1 )
374 20 CONTINUE
375 END IF
376 END IF
377*
378 work( 1 ) = sroundup_lwork(lwmin)
379 rwork( 1 ) = real( lrwmin )
380 iwork( 1 ) = liwmin
381 RETURN
382*
383* End of CHPGVD
384*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chpevd(jobz, uplo, n, ap, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition chpevd.f:192
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
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
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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