LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
chpev.f
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1 *> \brief <b> CHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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13 *> [ZIP]</a>
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER JOBZ, UPLO
26 * INTEGER INFO, LDZ, N
27 * ..
28 * .. Array Arguments ..
29 * REAL RWORK( * ), W( * )
30 * COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CHPEV computes all the eigenvalues and, optionally, eigenvectors of a
40 *> complex Hermitian matrix in packed storage.
41 *> \endverbatim
42 *
43 * Arguments:
44 * ==========
45 *
46 *> \param[in] JOBZ
47 *> \verbatim
48 *> JOBZ is CHARACTER*1
49 *> = 'N': Compute eigenvalues only;
50 *> = 'V': Compute eigenvalues and eigenvectors.
51 *> \endverbatim
52 *>
53 *> \param[in] UPLO
54 *> \verbatim
55 *> UPLO is CHARACTER*1
56 *> = 'U': Upper triangle of A is stored;
57 *> = 'L': Lower triangle of A is stored.
58 *> \endverbatim
59 *>
60 *> \param[in] N
61 *> \verbatim
62 *> N is INTEGER
63 *> The order of the matrix A. N >= 0.
64 *> \endverbatim
65 *>
66 *> \param[in,out] AP
67 *> \verbatim
68 *> AP is COMPLEX array, dimension (N*(N+1)/2)
69 *> On entry, the upper or lower triangle of the Hermitian matrix
70 *> A, packed columnwise in a linear array. The j-th column of A
71 *> is stored in the array AP as follows:
72 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
73 *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
74 *>
75 *> On exit, AP is overwritten by values generated during the
76 *> reduction to tridiagonal form. If UPLO = 'U', the diagonal
77 *> and first superdiagonal of the tridiagonal matrix T overwrite
78 *> the corresponding elements of A, and if UPLO = 'L', the
79 *> diagonal and first subdiagonal of T overwrite the
80 *> corresponding elements of A.
81 *> \endverbatim
82 *>
83 *> \param[out] W
84 *> \verbatim
85 *> W is REAL array, dimension (N)
86 *> If INFO = 0, the eigenvalues in ascending order.
87 *> \endverbatim
88 *>
89 *> \param[out] Z
90 *> \verbatim
91 *> Z is COMPLEX array, dimension (LDZ, N)
92 *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
93 *> eigenvectors of the matrix A, with the i-th column of Z
94 *> holding the eigenvector associated with W(i).
95 *> If JOBZ = 'N', then Z is not referenced.
96 *> \endverbatim
97 *>
98 *> \param[in] LDZ
99 *> \verbatim
100 *> LDZ is INTEGER
101 *> The leading dimension of the array Z. LDZ >= 1, and if
102 *> JOBZ = 'V', LDZ >= max(1,N).
103 *> \endverbatim
104 *>
105 *> \param[out] WORK
106 *> \verbatim
107 *> WORK is COMPLEX array, dimension (max(1, 2*N-1))
108 *> \endverbatim
109 *>
110 *> \param[out] RWORK
111 *> \verbatim
112 *> RWORK is REAL array, dimension (max(1, 3*N-2))
113 *> \endverbatim
114 *>
115 *> \param[out] INFO
116 *> \verbatim
117 *> INFO is INTEGER
118 *> = 0: successful exit.
119 *> < 0: if INFO = -i, the i-th argument had an illegal value.
120 *> > 0: if INFO = i, the algorithm failed to converge; i
121 *> off-diagonal elements of an intermediate tridiagonal
122 *> form did not converge to zero.
123 *> \endverbatim
124 *
125 * Authors:
126 * ========
127 *
128 *> \author Univ. of Tennessee
129 *> \author Univ. of California Berkeley
130 *> \author Univ. of Colorado Denver
131 *> \author NAG Ltd.
132 *
133 *> \ingroup complexOTHEReigen
134 *
135 * =====================================================================
136  SUBROUTINE chpev( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
137  $ INFO )
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 *
273  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
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 chpev(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO)
CHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Definition: chpev.f:138
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79