LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ chpev()

 subroutine chpev ( character JOBZ, character UPLO, integer N, complex, dimension( * ) AP, real, dimension( * ) W, complex, dimension( ldz, * ) Z, integer LDZ, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

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

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Purpose:
CHPEV computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage.
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, 2*N-1)) [out] RWORK RWORK is REAL 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: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

Definition at line 136 of file chpev.f.

138 *
139 * -- LAPACK driver routine --
140 * -- LAPACK is a software package provided by Univ. of Tennessee, --
141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142 *
143 * .. Scalar Arguments ..
144  CHARACTER JOBZ, UPLO
145  INTEGER INFO, LDZ, N
146 * ..
147 * .. Array Arguments ..
148  REAL RWORK( * ), W( * )
149  COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  REAL ZERO, ONE
156  parameter( zero = 0.0e0, one = 1.0e0 )
157 * ..
158 * .. Local Scalars ..
159  LOGICAL WANTZ
160  INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
161  \$ ISCALE
162  REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
163  \$ SMLNUM
164 * ..
165 * .. External Functions ..
166  LOGICAL LSAME
167  REAL CLANHP, SLAMCH
168  EXTERNAL lsame, clanhp, slamch
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL chptrd, csscal, csteqr, cupgtr, sscal, ssterf,
172  \$ xerbla
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC sqrt
176 * ..
177 * .. Executable Statements ..
178 *
179 * Test the input parameters.
180 *
181  wantz = lsame( jobz, 'V' )
182 *
183  info = 0
184  IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
185  info = -1
186  ELSE IF( .NOT.( lsame( uplo, 'L' ) .OR. lsame( uplo, 'U' ) ) )
187  \$ THEN
188  info = -2
189  ELSE IF( n.LT.0 ) THEN
190  info = -3
191  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
192  info = -7
193  END IF
194 *
195  IF( info.NE.0 ) THEN
196  CALL xerbla( 'CHPEV ', -info )
197  RETURN
198  END IF
199 *
200 * Quick return if possible
201 *
202  IF( n.EQ.0 )
203  \$ RETURN
204 *
205  IF( n.EQ.1 ) THEN
206  w( 1 ) = real( ap( 1 ) )
207  rwork( 1 ) = 1
208  IF( wantz )
209  \$ z( 1, 1 ) = one
210  RETURN
211  END IF
212 *
213 * Get machine constants.
214 *
215  safmin = slamch( 'Safe minimum' )
216  eps = slamch( 'Precision' )
217  smlnum = safmin / eps
218  bignum = one / smlnum
219  rmin = sqrt( smlnum )
220  rmax = sqrt( bignum )
221 *
222 * Scale matrix to allowable range, if necessary.
223 *
224  anrm = clanhp( 'M', uplo, n, ap, rwork )
225  iscale = 0
226  IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
227  iscale = 1
228  sigma = rmin / anrm
229  ELSE IF( anrm.GT.rmax ) THEN
230  iscale = 1
231  sigma = rmax / anrm
232  END IF
233  IF( iscale.EQ.1 ) THEN
234  CALL csscal( ( n*( n+1 ) ) / 2, sigma, ap, 1 )
235  END IF
236 *
237 * Call CHPTRD to reduce Hermitian packed matrix to tridiagonal form.
238 *
239  inde = 1
240  indtau = 1
241  CALL chptrd( uplo, n, ap, w, rwork( inde ), work( indtau ),
242  \$ iinfo )
243 *
244 * For eigenvalues only, call SSTERF. For eigenvectors, first call
245 * CUPGTR to generate the orthogonal matrix, then call CSTEQR.
246 *
247  IF( .NOT.wantz ) THEN
248  CALL ssterf( n, w, rwork( inde ), info )
249  ELSE
250  indwrk = indtau + n
251  CALL cupgtr( uplo, n, ap, work( indtau ), z, ldz,
252  \$ work( indwrk ), iinfo )
253  indrwk = inde + n
254  CALL csteqr( jobz, n, w, rwork( inde ), z, ldz,
255  \$ rwork( indrwk ), info )
256  END IF
257 *
258 * If matrix was scaled, then rescale eigenvalues appropriately.
259 *
260  IF( iscale.EQ.1 ) THEN
261  IF( info.EQ.0 ) THEN
262  imax = n
263  ELSE
264  imax = info - 1
265  END IF
266  CALL sscal( imax, one / sigma, w, 1 )
267  END IF
268 *
269  RETURN
270 *
271 * End of CHPEV
272 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
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:117
subroutine cupgtr(UPLO, N, AP, TAU, Q, LDQ, WORK, INFO)
CUPGTR
Definition: cupgtr.f:114
subroutine chptrd(UPLO, N, AP, D, E, TAU, INFO)
CHPTRD
Definition: chptrd.f:151
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:132
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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