LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dspev.f
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1*> \brief <b> DSPEV 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/dspev.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspev.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspev.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER JOBZ, UPLO
25* INTEGER INFO, LDZ, N
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
38*> real symmetric matrix A in packed storage.
39*> \endverbatim
40*
41* Arguments:
42* ==========
43*
44*> \param[in] JOBZ
45*> \verbatim
46*> JOBZ is CHARACTER*1
47*> = 'N': Compute eigenvalues only;
48*> = 'V': Compute eigenvalues and eigenvectors.
49*> \endverbatim
50*>
51*> \param[in] UPLO
52*> \verbatim
53*> UPLO is CHARACTER*1
54*> = 'U': Upper triangle of A is stored;
55*> = 'L': Lower triangle of A is stored.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*> N is INTEGER
61*> The order of the matrix A. N >= 0.
62*> \endverbatim
63*>
64*> \param[in,out] AP
65*> \verbatim
66*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
67*> On entry, the upper or lower triangle of the symmetric matrix
68*> A, packed columnwise in a linear array. The j-th column of A
69*> is stored in the array AP as follows:
70*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
71*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
72*>
73*> On exit, AP is overwritten by values generated during the
74*> reduction to tridiagonal form. If UPLO = 'U', the diagonal
75*> and first superdiagonal of the tridiagonal matrix T overwrite
76*> the corresponding elements of A, and if UPLO = 'L', the
77*> diagonal and first subdiagonal of T overwrite the
78*> corresponding elements of A.
79*> \endverbatim
80*>
81*> \param[out] W
82*> \verbatim
83*> W is DOUBLE PRECISION array, dimension (N)
84*> If INFO = 0, the eigenvalues in ascending order.
85*> \endverbatim
86*>
87*> \param[out] Z
88*> \verbatim
89*> Z is DOUBLE PRECISION array, dimension (LDZ, N)
90*> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
91*> eigenvectors of the matrix A, with the i-th column of Z
92*> holding the eigenvector associated with W(i).
93*> If JOBZ = 'N', then Z is not referenced.
94*> \endverbatim
95*>
96*> \param[in] LDZ
97*> \verbatim
98*> LDZ is INTEGER
99*> The leading dimension of the array Z. LDZ >= 1, and if
100*> JOBZ = 'V', LDZ >= max(1,N).
101*> \endverbatim
102*>
103*> \param[out] WORK
104*> \verbatim
105*> WORK is DOUBLE PRECISION array, dimension (3*N)
106*> \endverbatim
107*>
108*> \param[out] INFO
109*> \verbatim
110*> INFO is INTEGER
111*> = 0: successful exit.
112*> < 0: if INFO = -i, the i-th argument had an illegal value.
113*> > 0: if INFO = i, the algorithm failed to converge; i
114*> off-diagonal elements of an intermediate tridiagonal
115*> form did not converge to zero.
116*> \endverbatim
117*
118* Authors:
119* ========
120*
121*> \author Univ. of Tennessee
122*> \author Univ. of California Berkeley
123*> \author Univ. of Colorado Denver
124*> \author NAG Ltd.
125*
126*> \ingroup hpev
127*
128* =====================================================================
129 SUBROUTINE dspev( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
130*
131* -- LAPACK driver routine --
132* -- LAPACK is a software package provided by Univ. of Tennessee, --
133* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134*
135* .. Scalar Arguments ..
136 CHARACTER JOBZ, UPLO
137 INTEGER INFO, LDZ, N
138* ..
139* .. Array Arguments ..
140 DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
141* ..
142*
143* =====================================================================
144*
145* .. Parameters ..
146 DOUBLE PRECISION ZERO, ONE
147 parameter( zero = 0.0d0, one = 1.0d0 )
148* ..
149* .. Local Scalars ..
150 LOGICAL WANTZ
151 INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE
152 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
153 \$ SMLNUM
154* ..
155* .. External Functions ..
156 LOGICAL LSAME
157 DOUBLE PRECISION DLAMCH, DLANSP
158 EXTERNAL lsame, dlamch, dlansp
159* ..
160* .. External Subroutines ..
161 EXTERNAL dopgtr, dscal, dsptrd, dsteqr, dsterf, xerbla
162* ..
163* .. Intrinsic Functions ..
164 INTRINSIC sqrt
165* ..
166* .. Executable Statements ..
167*
168* Test the input parameters.
169*
170 wantz = lsame( jobz, 'V' )
171*
172 info = 0
173 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
174 info = -1
175 ELSE IF( .NOT.( lsame( uplo, 'U' ) .OR. lsame( uplo, 'L' ) ) )
176 \$ THEN
177 info = -2
178 ELSE IF( n.LT.0 ) THEN
179 info = -3
180 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
181 info = -7
182 END IF
183*
184 IF( info.NE.0 ) THEN
185 CALL xerbla( 'DSPEV ', -info )
186 RETURN
187 END IF
188*
189* Quick return if possible
190*
191 IF( n.EQ.0 )
192 \$ RETURN
193*
194 IF( n.EQ.1 ) THEN
195 w( 1 ) = ap( 1 )
196 IF( wantz )
197 \$ z( 1, 1 ) = one
198 RETURN
199 END IF
200*
201* Get machine constants.
202*
203 safmin = dlamch( 'Safe minimum' )
204 eps = dlamch( 'Precision' )
205 smlnum = safmin / eps
206 bignum = one / smlnum
207 rmin = sqrt( smlnum )
208 rmax = sqrt( bignum )
209*
210* Scale matrix to allowable range, if necessary.
211*
212 anrm = dlansp( 'M', uplo, n, ap, work )
213 iscale = 0
214 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
215 iscale = 1
216 sigma = rmin / anrm
217 ELSE IF( anrm.GT.rmax ) THEN
218 iscale = 1
219 sigma = rmax / anrm
220 END IF
221 IF( iscale.EQ.1 ) THEN
222 CALL dscal( ( n*( n+1 ) ) / 2, sigma, ap, 1 )
223 END IF
224*
225* Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
226*
227 inde = 1
228 indtau = inde + n
229 CALL dsptrd( uplo, n, ap, w, work( inde ), work( indtau ), iinfo )
230*
231* For eigenvalues only, call DSTERF. For eigenvectors, first call
232* DOPGTR to generate the orthogonal matrix, then call DSTEQR.
233*
234 IF( .NOT.wantz ) THEN
235 CALL dsterf( n, w, work( inde ), info )
236 ELSE
237 indwrk = indtau + n
238 CALL dopgtr( uplo, n, ap, work( indtau ), z, ldz,
239 \$ work( indwrk ), iinfo )
240 CALL dsteqr( jobz, n, w, work( inde ), z, ldz, work( indtau ),
241 \$ info )
242 END IF
243*
244* If matrix was scaled, then rescale eigenvalues appropriately.
245*
246 IF( iscale.EQ.1 ) THEN
247 IF( info.EQ.0 ) THEN
248 imax = n
249 ELSE
250 imax = info - 1
251 END IF
252 CALL dscal( imax, one / sigma, w, 1 )
253 END IF
254*
255 RETURN
256*
257* End of DSPEV
258*
259 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dspev(jobz, uplo, n, ap, w, z, ldz, work, info)
DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Definition dspev.f:130
subroutine dsptrd(uplo, n, ap, d, e, tau, info)
DSPTRD
Definition dsptrd.f:150
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
subroutine dsteqr(compz, n, d, e, z, ldz, work, info)
DSTEQR
Definition dsteqr.f:131
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:86
subroutine dopgtr(uplo, n, ap, tau, q, ldq, work, info)
DOPGTR
Definition dopgtr.f:114