LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dsyev.f
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1*> \brief <b> DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY 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/dsyev.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyev.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyev.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER JOBZ, UPLO
25* INTEGER INFO, LDA, LWORK, N
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DSYEV computes all eigenvalues and, optionally, eigenvectors of a
38*> real symmetric matrix A.
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] A
65*> \verbatim
66*> A is DOUBLE PRECISION array, dimension (LDA, N)
67*> On entry, the symmetric matrix A. If UPLO = 'U', the
68*> leading N-by-N upper triangular part of A contains the
69*> upper triangular part of the matrix A. If UPLO = 'L',
70*> the leading N-by-N lower triangular part of A contains
71*> the lower triangular part of the matrix A.
72*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
73*> orthonormal eigenvectors of the matrix A.
74*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
75*> or the upper triangle (if UPLO='U') of A, including the
76*> diagonal, is destroyed.
77*> \endverbatim
78*>
79*> \param[in] LDA
80*> \verbatim
81*> LDA is INTEGER
82*> The leading dimension of the array A. LDA >= max(1,N).
83*> \endverbatim
84*>
85*> \param[out] W
86*> \verbatim
87*> W is DOUBLE PRECISION array, dimension (N)
88*> If INFO = 0, the eigenvalues in ascending order.
89*> \endverbatim
90*>
91*> \param[out] WORK
92*> \verbatim
93*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
94*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
95*> \endverbatim
96*>
97*> \param[in] LWORK
98*> \verbatim
99*> LWORK is INTEGER
100*> The length of the array WORK. LWORK >= max(1,3*N-1).
101*> For optimal efficiency, LWORK >= (NB+2)*N,
102*> where NB is the blocksize for DSYTRD returned by ILAENV.
103*>
104*> If LWORK = -1, then a workspace query is assumed; the routine
105*> only calculates the optimal size of the WORK array, returns
106*> this value as the first entry of the WORK array, and no error
107*> message related to LWORK is issued by XERBLA.
108*> \endverbatim
109*>
110*> \param[out] INFO
111*> \verbatim
112*> INFO is INTEGER
113*> = 0: successful exit
114*> < 0: if INFO = -i, the i-th argument had an illegal value
115*> > 0: if INFO = i, the algorithm failed to converge; i
116*> off-diagonal elements of an intermediate tridiagonal
117*> form did not converge to zero.
118*> \endverbatim
119*
120* Authors:
121* ========
122*
123*> \author Univ. of Tennessee
124*> \author Univ. of California Berkeley
125*> \author Univ. of Colorado Denver
126*> \author NAG Ltd.
127*
128*> \ingroup doubleSYeigen
129*
130* =====================================================================
131 SUBROUTINE dsyev( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
132*
133* -- LAPACK driver routine --
134* -- LAPACK is a software package provided by Univ. of Tennessee, --
135* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136*
137* .. Scalar Arguments ..
138 CHARACTER JOBZ, UPLO
139 INTEGER INFO, LDA, LWORK, N
140* ..
141* .. Array Arguments ..
142 DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
143* ..
144*
145* =====================================================================
146*
147* .. Parameters ..
148 DOUBLE PRECISION ZERO, ONE
149 parameter( zero = 0.0d0, one = 1.0d0 )
150* ..
151* .. Local Scalars ..
152 LOGICAL LOWER, LQUERY, WANTZ
153 INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
154 \$ LLWORK, LWKOPT, NB
155 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
156 \$ SMLNUM
157* ..
158* .. External Functions ..
159 LOGICAL LSAME
160 INTEGER ILAENV
161 DOUBLE PRECISION DLAMCH, DLANSY
162 EXTERNAL lsame, ilaenv, dlamch, dlansy
163* ..
164* .. External Subroutines ..
165 EXTERNAL dlascl, dorgtr, dscal, dsteqr, dsterf, dsytrd,
166 \$ xerbla
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC max, sqrt
170* ..
171* .. Executable Statements ..
172*
173* Test the input parameters.
174*
175 wantz = lsame( jobz, 'V' )
176 lower = lsame( uplo, 'L' )
177 lquery = ( lwork.EQ.-1 )
178*
179 info = 0
180 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
181 info = -1
182 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
183 info = -2
184 ELSE IF( n.LT.0 ) THEN
185 info = -3
186 ELSE IF( lda.LT.max( 1, n ) ) THEN
187 info = -5
188 END IF
189*
190 IF( info.EQ.0 ) THEN
191 nb = ilaenv( 1, 'DSYTRD', uplo, n, -1, -1, -1 )
192 lwkopt = max( 1, ( nb+2 )*n )
193 work( 1 ) = lwkopt
194*
195 IF( lwork.LT.max( 1, 3*n-1 ) .AND. .NOT.lquery )
196 \$ info = -8
197 END IF
198*
199 IF( info.NE.0 ) THEN
200 CALL xerbla( 'DSYEV ', -info )
201 RETURN
202 ELSE IF( lquery ) THEN
203 RETURN
204 END IF
205*
206* Quick return if possible
207*
208 IF( n.EQ.0 ) THEN
209 RETURN
210 END IF
211*
212 IF( n.EQ.1 ) THEN
213 w( 1 ) = a( 1, 1 )
214 work( 1 ) = 2
215 IF( wantz )
216 \$ a( 1, 1 ) = one
217 RETURN
218 END IF
219*
220* Get machine constants.
221*
222 safmin = dlamch( 'Safe minimum' )
223 eps = dlamch( 'Precision' )
224 smlnum = safmin / eps
225 bignum = one / smlnum
226 rmin = sqrt( smlnum )
227 rmax = sqrt( bignum )
228*
229* Scale matrix to allowable range, if necessary.
230*
231 anrm = dlansy( 'M', uplo, n, a, lda, work )
232 iscale = 0
233 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
234 iscale = 1
235 sigma = rmin / anrm
236 ELSE IF( anrm.GT.rmax ) THEN
237 iscale = 1
238 sigma = rmax / anrm
239 END IF
240 IF( iscale.EQ.1 )
241 \$ CALL dlascl( uplo, 0, 0, one, sigma, n, n, a, lda, info )
242*
243* Call DSYTRD to reduce symmetric matrix to tridiagonal form.
244*
245 inde = 1
246 indtau = inde + n
247 indwrk = indtau + n
248 llwork = lwork - indwrk + 1
249 CALL dsytrd( uplo, n, a, lda, w, work( inde ), work( indtau ),
250 \$ work( indwrk ), llwork, iinfo )
251*
252* For eigenvalues only, call DSTERF. For eigenvectors, first call
253* DORGTR to generate the orthogonal matrix, then call DSTEQR.
254*
255 IF( .NOT.wantz ) THEN
256 CALL dsterf( n, w, work( inde ), info )
257 ELSE
258 CALL dorgtr( uplo, n, a, lda, work( indtau ), work( indwrk ),
259 \$ llwork, iinfo )
260 CALL dsteqr( jobz, n, w, work( inde ), a, lda, work( indtau ),
261 \$ info )
262 END IF
263*
264* If matrix was scaled, then rescale eigenvalues appropriately.
265*
266 IF( iscale.EQ.1 ) THEN
267 IF( info.EQ.0 ) THEN
268 imax = n
269 ELSE
270 imax = info - 1
271 END IF
272 CALL dscal( imax, one / sigma, w, 1 )
273 END IF
274*
275* Set WORK(1) to optimal workspace size.
276*
277 work( 1 ) = lwkopt
278*
279 RETURN
280*
281* End of DSYEV
282*
283 END
subroutine dlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: dlascl.f:143
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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 dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dorgtr(UPLO, N, A, LDA, TAU, WORK, LWORK, INFO)
DORGTR
Definition: dorgtr.f:123
subroutine dsytrd(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
DSYTRD
Definition: dsytrd.f:192
subroutine dsyev(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO)
DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
Definition: dsyev.f:132