LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ chpevd()

subroutine chpevd ( character jobz,
character uplo,
integer n,
complex, dimension( * ) ap,
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 )

CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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

Purpose:
!>
!> CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
!> a complex Hermitian matrix A in packed storage.  If eigenvectors are
!> desired, it uses a divide and conquer algorithm.
!>
!>
Parameters
[in]JOBZ
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors.
!>
[in]UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A.  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, AP is overwritten by values generated during the
!>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
!>          and first superdiagonal of the tridiagonal matrix T overwrite
!>          the corresponding elements of A, and if UPLO = 'L', the
!>          diagonal and first subdiagonal of T overwrite the
!>          corresponding elements of A.
!>
[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 orthonormal
!>          eigenvectors of the matrix A, with the i-th column of Z
!>          holding the eigenvector associated with W(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 must be at least 1.
!>          If JOBZ = 'N' and N > 1, LWORK must be at least N.
!>          If JOBZ = 'V' and N > 1, LWORK must be at least 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 must be at least 1.
!>          If JOBZ = 'N' and N > 1, LRWORK must be at least N.
!>          If JOBZ = 'V' and N > 1, LRWORK must be at least
!>                    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 must be at least 1.
!>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 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:  if INFO = i, the algorithm failed to converge; i
!>                off-diagonal elements of an intermediate tridiagonal
!>                form did not converge to zero.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 190 of file chpevd.f.

192*
193* -- LAPACK driver routine --
194* -- LAPACK is a software package provided by Univ. of Tennessee, --
195* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
196*
197* .. Scalar Arguments ..
198 CHARACTER JOBZ, UPLO
199 INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
200* ..
201* .. Array Arguments ..
202 INTEGER IWORK( * )
203 REAL RWORK( * ), W( * )
204 COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
205* ..
206*
207* =====================================================================
208*
209* .. Parameters ..
210 REAL ZERO, ONE
211 parameter( zero = 0.0e+0, one = 1.0e+0 )
212 COMPLEX CONE
213 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
214* ..
215* .. Local Scalars ..
216 LOGICAL LQUERY, WANTZ
217 INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
218 $ ISCALE, LIWMIN, LLRWK, LLWRK, LRWMIN, LWMIN
219 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
220 $ SMLNUM
221* ..
222* .. External Functions ..
223 LOGICAL LSAME
224 REAL CLANHP, SLAMCH, SROUNDUP_LWORK
225 EXTERNAL lsame, clanhp, slamch,
226 $ sroundup_lwork
227* ..
228* .. External Subroutines ..
229 EXTERNAL chptrd, csscal, cstedc, cupmtr, sscal,
230 $ ssterf,
231 $ xerbla
232* ..
233* .. Intrinsic Functions ..
234 INTRINSIC sqrt
235* ..
236* .. Executable Statements ..
237*
238* Test the input parameters.
239*
240 wantz = lsame( jobz, 'V' )
241 lquery = ( lwork.EQ.-1 .OR. lrwork.EQ.-1 .OR. liwork.EQ.-1 )
242*
243 info = 0
244 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
245 info = -1
246 ELSE IF( .NOT.( lsame( uplo, 'L' ) .OR.
247 $ lsame( uplo, 'U' ) ) )
248 $ THEN
249 info = -2
250 ELSE IF( n.LT.0 ) THEN
251 info = -3
252 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
253 info = -7
254 END IF
255*
256 IF( info.EQ.0 ) THEN
257 IF( n.LE.1 ) THEN
258 lwmin = 1
259 liwmin = 1
260 lrwmin = 1
261 ELSE
262 IF( wantz ) THEN
263 lwmin = 2*n
264 lrwmin = 1 + 5*n + 2*n**2
265 liwmin = 3 + 5*n
266 ELSE
267 lwmin = n
268 lrwmin = n
269 liwmin = 1
270 END IF
271 END IF
272 work( 1 ) = sroundup_lwork(lwmin)
273 rwork( 1 ) = real( lrwmin )
274 iwork( 1 ) = liwmin
275*
276 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
277 info = -9
278 ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
279 info = -11
280 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
281 info = -13
282 END IF
283 END IF
284*
285 IF( info.NE.0 ) THEN
286 CALL xerbla( 'CHPEVD', -info )
287 RETURN
288 ELSE IF( lquery ) THEN
289 RETURN
290 END IF
291*
292* Quick return if possible
293*
294 IF( n.EQ.0 )
295 $ RETURN
296*
297 IF( n.EQ.1 ) THEN
298 w( 1 ) = real( ap( 1 ) )
299 IF( wantz )
300 $ z( 1, 1 ) = cone
301 RETURN
302 END IF
303*
304* Get machine constants.
305*
306 safmin = slamch( 'Safe minimum' )
307 eps = slamch( 'Precision' )
308 smlnum = safmin / eps
309 bignum = one / smlnum
310 rmin = sqrt( smlnum )
311 rmax = sqrt( bignum )
312*
313* Scale matrix to allowable range, if necessary.
314*
315 anrm = clanhp( 'M', uplo, n, ap, rwork )
316 iscale = 0
317 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
318 iscale = 1
319 sigma = rmin / anrm
320 ELSE IF( anrm.GT.rmax ) THEN
321 iscale = 1
322 sigma = rmax / anrm
323 END IF
324 IF( iscale.EQ.1 ) THEN
325 CALL csscal( ( n*( n+1 ) ) / 2, sigma, ap, 1 )
326 END IF
327*
328* Call CHPTRD to reduce Hermitian packed matrix to tridiagonal form.
329*
330 inde = 1
331 indtau = 1
332 indrwk = inde + n
333 indwrk = indtau + n
334 llwrk = lwork - indwrk + 1
335 llrwk = lrwork - indrwk + 1
336 CALL chptrd( uplo, n, ap, w, rwork( inde ), work( indtau ),
337 $ iinfo )
338*
339* For eigenvalues only, call SSTERF. For eigenvectors, first call
340* CUPGTR to generate the orthogonal matrix, then call CSTEDC.
341*
342 IF( .NOT.wantz ) THEN
343 CALL ssterf( n, w, rwork( inde ), info )
344 ELSE
345 CALL cstedc( 'I', n, w, rwork( inde ), z, ldz,
346 $ work( indwrk ),
347 $ llwrk, rwork( indrwk ), llrwk, iwork, liwork,
348 $ info )
349 CALL cupmtr( 'L', uplo, 'N', n, n, ap, work( indtau ), z,
350 $ ldz,
351 $ work( indwrk ), iinfo )
352 END IF
353*
354* If matrix was scaled, then rescale eigenvalues appropriately.
355*
356 IF( iscale.EQ.1 ) THEN
357 IF( info.EQ.0 ) THEN
358 imax = n
359 ELSE
360 imax = info - 1
361 END IF
362 CALL sscal( imax, one / sigma, w, 1 )
363 END IF
364*
365 work( 1 ) = sroundup_lwork(lwmin)
366 rwork( 1 ) = real( lrwmin )
367 iwork( 1 ) = liwmin
368 RETURN
369*
370* End of CHPEVD
371*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
chptrd
subroutine chptrd(uplo, n, ap, d, e, tau, info)
CHPTRD
Definition chptrd.f:149
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
clanhp
real function clanhp(norm, uplo, n, ap, work)
CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clanhp.f:115
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
sroundup_lwork
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
Definition sroundup_lwork.f:59
csscal
subroutine csscal(n, sa, cx, incx)
CSSCAL
Definition csscal.f:78
sscal
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
cstedc
subroutine cstedc(compz, n, d, e, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
CSTEDC
Definition cstedc.f:204
ssterf
subroutine ssterf(n, d, e, info)
SSTERF
Definition ssterf.f:84
cupmtr
subroutine cupmtr(side, uplo, trans, m, n, ap, tau, c, ldc, work, info)
CUPMTR
Definition cupmtr.f:149
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