LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zhbev.f
Go to the documentation of this file.
1 *> \brief <b> ZHBEV 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 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbev.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbev.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbev.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
22 * RWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER JOBZ, UPLO
26 * INTEGER INFO, KD, LDAB, LDZ, N
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION RWORK( * ), W( * )
30 * COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
40 *> a complex Hermitian band matrix A.
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] KD
67 *> \verbatim
68 *> KD is INTEGER
69 *> The number of superdiagonals of the matrix A if UPLO = 'U',
70 *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
71 *> \endverbatim
72 *>
73 *> \param[in,out] AB
74 *> \verbatim
75 *> AB is COMPLEX*16 array, dimension (LDAB, N)
76 *> On entry, the upper or lower triangle of the Hermitian band
77 *> matrix A, stored in the first KD+1 rows of the array. The
78 *> j-th column of A is stored in the j-th column of the array AB
79 *> as follows:
80 *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
81 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
82 *>
83 *> On exit, AB is overwritten by values generated during the
84 *> reduction to tridiagonal form. If UPLO = 'U', the first
85 *> superdiagonal and the diagonal of the tridiagonal matrix T
86 *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
87 *> the diagonal and first subdiagonal of T are returned in the
88 *> first two rows of AB.
89 *> \endverbatim
90 *>
91 *> \param[in] LDAB
92 *> \verbatim
93 *> LDAB is INTEGER
94 *> The leading dimension of the array AB. LDAB >= KD + 1.
95 *> \endverbatim
96 *>
97 *> \param[out] W
98 *> \verbatim
99 *> W is DOUBLE PRECISION array, dimension (N)
100 *> If INFO = 0, the eigenvalues in ascending order.
101 *> \endverbatim
102 *>
103 *> \param[out] Z
104 *> \verbatim
105 *> Z is COMPLEX*16 array, dimension (LDZ, N)
106 *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
107 *> eigenvectors of the matrix A, with the i-th column of Z
108 *> holding the eigenvector associated with W(i).
109 *> If JOBZ = 'N', then Z is not referenced.
110 *> \endverbatim
111 *>
112 *> \param[in] LDZ
113 *> \verbatim
114 *> LDZ is INTEGER
115 *> The leading dimension of the array Z. LDZ >= 1, and if
116 *> JOBZ = 'V', LDZ >= max(1,N).
117 *> \endverbatim
118 *>
119 *> \param[out] WORK
120 *> \verbatim
121 *> WORK is COMPLEX*16 array, dimension (N)
122 *> \endverbatim
123 *>
124 *> \param[out] RWORK
125 *> \verbatim
126 *> RWORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))
127 *> \endverbatim
128 *>
129 *> \param[out] INFO
130 *> \verbatim
131 *> INFO is INTEGER
132 *> = 0: successful exit.
133 *> < 0: if INFO = -i, the i-th argument had an illegal value.
134 *> > 0: if INFO = i, the algorithm failed to converge; i
135 *> off-diagonal elements of an intermediate tridiagonal
136 *> form did not converge to zero.
137 *> \endverbatim
138 *
139 * Authors:
140 * ========
141 *
142 *> \author Univ. of Tennessee
143 *> \author Univ. of California Berkeley
144 *> \author Univ. of Colorado Denver
145 *> \author NAG Ltd.
146 *
147 *> \date November 2011
148 *
149 *> \ingroup complex16OTHEReigen
150 *
151 * =====================================================================
152  SUBROUTINE zhbev( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
153  \$ rwork, info )
154 *
155 * -- LAPACK driver routine (version 3.4.0) --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 * November 2011
159 *
160 * .. Scalar Arguments ..
161  CHARACTER JOBZ, UPLO
162  INTEGER INFO, KD, LDAB, LDZ, N
163 * ..
164 * .. Array Arguments ..
165  DOUBLE PRECISION RWORK( * ), W( * )
166  COMPLEX*16 AB( ldab, * ), WORK( * ), Z( ldz, * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  DOUBLE PRECISION ZERO, ONE
173  parameter ( zero = 0.0d0, one = 1.0d0 )
174 * ..
175 * .. Local Scalars ..
176  LOGICAL LOWER, WANTZ
177  INTEGER IINFO, IMAX, INDE, INDRWK, ISCALE
178  DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
179  \$ smlnum
180 * ..
181 * .. External Functions ..
182  LOGICAL LSAME
183  DOUBLE PRECISION DLAMCH, ZLANHB
184  EXTERNAL lsame, dlamch, zlanhb
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL dscal, dsterf, xerbla, zhbtrd, zlascl, zsteqr
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC sqrt
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196  wantz = lsame( jobz, 'V' )
197  lower = lsame( uplo, 'L' )
198 *
199  info = 0
200  IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
201  info = -1
202  ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
203  info = -2
204  ELSE IF( n.LT.0 ) THEN
205  info = -3
206  ELSE IF( kd.LT.0 ) THEN
207  info = -4
208  ELSE IF( ldab.LT.kd+1 ) THEN
209  info = -6
210  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
211  info = -9
212  END IF
213 *
214  IF( info.NE.0 ) THEN
215  CALL xerbla( 'ZHBEV ', -info )
216  RETURN
217  END IF
218 *
219 * Quick return if possible
220 *
221  IF( n.EQ.0 )
222  \$ RETURN
223 *
224  IF( n.EQ.1 ) THEN
225  IF( lower ) THEN
226  w( 1 ) = ab( 1, 1 )
227  ELSE
228  w( 1 ) = ab( kd+1, 1 )
229  END IF
230  IF( wantz )
231  \$ z( 1, 1 ) = one
232  RETURN
233  END IF
234 *
235 * Get machine constants.
236 *
237  safmin = dlamch( 'Safe minimum' )
238  eps = dlamch( 'Precision' )
239  smlnum = safmin / eps
240  bignum = one / smlnum
241  rmin = sqrt( smlnum )
242  rmax = sqrt( bignum )
243 *
244 * Scale matrix to allowable range, if necessary.
245 *
246  anrm = zlanhb( 'M', uplo, n, kd, ab, ldab, rwork )
247  iscale = 0
248  IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
249  iscale = 1
250  sigma = rmin / anrm
251  ELSE IF( anrm.GT.rmax ) THEN
252  iscale = 1
253  sigma = rmax / anrm
254  END IF
255  IF( iscale.EQ.1 ) THEN
256  IF( lower ) THEN
257  CALL zlascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
258  ELSE
259  CALL zlascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
260  END IF
261  END IF
262 *
263 * Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
264 *
265  inde = 1
266  CALL zhbtrd( jobz, uplo, n, kd, ab, ldab, w, rwork( inde ), z,
267  \$ ldz, work, iinfo )
268 *
269 * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
270 *
271  IF( .NOT.wantz ) THEN
272  CALL dsterf( n, w, rwork( inde ), info )
273  ELSE
274  indrwk = inde + n
275  CALL zsteqr( jobz, n, w, rwork( inde ), z, ldz,
276  \$ rwork( indrwk ), info )
277  END IF
278 *
279 * If matrix was scaled, then rescale eigenvalues appropriately.
280 *
281  IF( iscale.EQ.1 ) THEN
282  IF( info.EQ.0 ) THEN
283  imax = n
284  ELSE
285  imax = info - 1
286  END IF
287  CALL dscal( imax, one / sigma, w, 1 )
288  END IF
289 *
290  RETURN
291 *
292 * End of ZHBEV
293 *
294  END
subroutine dsterf(N, D, E, INFO)
DSTERF
Definition: dsterf.f:88
subroutine zhbev(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, RWORK, INFO)
ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: zhbev.f:154
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
ZSTEQR
Definition: zsteqr.f:134
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:55
subroutine zlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: zlascl.f:145
subroutine zhbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
ZHBTRD
Definition: zhbtrd.f:165