LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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dspgvd.f
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1*> \brief \b DSPGVD
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DSPGVD + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgvd.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgvd.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgvd.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22* LWORK, IWORK, LIWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBZ, UPLO
26* INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
27* ..
28* .. Array Arguments ..
29* INTEGER IWORK( * )
30* DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
31* $ Z( LDZ, * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
41*> of a real generalized symmetric-definite eigenproblem, of the form
42*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
43*> B are assumed to be symmetric, stored in packed format, and B is also
44*> positive definite.
45*> If eigenvectors are desired, it uses a divide and conquer algorithm.
46*>
47*> \endverbatim
48*
49* Arguments:
50* ==========
51*
52*> \param[in] ITYPE
53*> \verbatim
54*> ITYPE is INTEGER
55*> Specifies the problem type to be solved:
56*> = 1: A*x = (lambda)*B*x
57*> = 2: A*B*x = (lambda)*x
58*> = 3: B*A*x = (lambda)*x
59*> \endverbatim
60*>
61*> \param[in] JOBZ
62*> \verbatim
63*> JOBZ is CHARACTER*1
64*> = 'N': Compute eigenvalues only;
65*> = 'V': Compute eigenvalues and eigenvectors.
66*> \endverbatim
67*>
68*> \param[in] UPLO
69*> \verbatim
70*> UPLO is CHARACTER*1
71*> = 'U': Upper triangles of A and B are stored;
72*> = 'L': Lower triangles of A and B are stored.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The order of the matrices A and B. N >= 0.
79*> \endverbatim
80*>
81*> \param[in,out] AP
82*> \verbatim
83*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
84*> On entry, the upper or lower triangle of the symmetric matrix
85*> A, packed columnwise in a linear array. The j-th column of A
86*> is stored in the array AP as follows:
87*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
88*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
89*>
90*> On exit, the contents of AP are destroyed.
91*> \endverbatim
92*>
93*> \param[in,out] BP
94*> \verbatim
95*> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
96*> On entry, the upper or lower triangle of the symmetric matrix
97*> B, packed columnwise in a linear array. The j-th column of B
98*> is stored in the array BP as follows:
99*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
100*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
101*>
102*> On exit, the triangular factor U or L from the Cholesky
103*> factorization B = U**T*U or B = L*L**T, in the same storage
104*> format as B.
105*> \endverbatim
106*>
107*> \param[out] W
108*> \verbatim
109*> W is DOUBLE PRECISION array, dimension (N)
110*> If INFO = 0, the eigenvalues in ascending order.
111*> \endverbatim
112*>
113*> \param[out] Z
114*> \verbatim
115*> Z is DOUBLE PRECISION array, dimension (LDZ, N)
116*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
117*> eigenvectors. The eigenvectors are normalized as follows:
118*> if ITYPE = 1 or 2, Z**T*B*Z = I;
119*> if ITYPE = 3, Z**T*inv(B)*Z = I.
120*> If JOBZ = 'N', then Z is not referenced.
121*> \endverbatim
122*>
123*> \param[in] LDZ
124*> \verbatim
125*> LDZ is INTEGER
126*> The leading dimension of the array Z. LDZ >= 1, and if
127*> JOBZ = 'V', LDZ >= max(1,N).
128*> \endverbatim
129*>
130*> \param[out] WORK
131*> \verbatim
132*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
133*> On exit, if INFO = 0, WORK(1) returns the required LWORK.
134*> \endverbatim
135*>
136*> \param[in] LWORK
137*> \verbatim
138*> LWORK is INTEGER
139*> The dimension of the array WORK.
140*> If N <= 1, LWORK >= 1.
141*> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
142*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
143*>
144*> If LWORK = -1, then a workspace query is assumed; the routine
145*> only calculates the required sizes of the WORK and IWORK
146*> arrays, returns these values as the first entries of the WORK
147*> and IWORK arrays, and no error message related to LWORK or
148*> LIWORK is issued by XERBLA.
149*> \endverbatim
150*>
151*> \param[out] IWORK
152*> \verbatim
153*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
154*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
155*> \endverbatim
156*>
157*> \param[in] LIWORK
158*> \verbatim
159*> LIWORK is INTEGER
160*> The dimension of the array IWORK.
161*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
162*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
163*>
164*> If LIWORK = -1, then a workspace query is assumed; the
165*> routine only calculates the required sizes of the WORK and
166*> IWORK arrays, returns these values as the first entries of
167*> the WORK and IWORK arrays, and no error message related to
168*> LWORK or LIWORK is issued by XERBLA.
169*> \endverbatim
170*>
171*> \param[out] INFO
172*> \verbatim
173*> INFO is INTEGER
174*> = 0: successful exit
175*> < 0: if INFO = -i, the i-th argument had an illegal value
176*> > 0: DPPTRF or DSPEVD returned an error code:
177*> <= N: if INFO = i, DSPEVD failed to converge;
178*> i off-diagonal elements of an intermediate
179*> tridiagonal form did not converge to zero;
180*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
181*> principal minor of order i of B is not positive.
182*> The factorization of B could not be completed and
183*> no eigenvalues or eigenvectors were computed.
184*> \endverbatim
185*
186* Authors:
187* ========
188*
189*> \author Univ. of Tennessee
190*> \author Univ. of California Berkeley
191*> \author Univ. of Colorado Denver
192*> \author NAG Ltd.
193*
194*> \ingroup hpgvd
195*
196*> \par Contributors:
197* ==================
198*>
199*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
200*
201* =====================================================================
202 SUBROUTINE dspgvd( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
203 $ LWORK, IWORK, LIWORK, INFO )
204*
205* -- LAPACK driver routine --
206* -- LAPACK is a software package provided by Univ. of Tennessee, --
207* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
208*
209* .. Scalar Arguments ..
210 CHARACTER JOBZ, UPLO
211 INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
212* ..
213* .. Array Arguments ..
214 INTEGER IWORK( * )
215 DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
216 $ z( ldz, * )
217* ..
218*
219* =====================================================================
220*
221* .. Local Scalars ..
222 LOGICAL LQUERY, UPPER, WANTZ
223 CHARACTER TRANS
224 INTEGER J, LIWMIN, LWMIN, NEIG
225* ..
226* .. External Functions ..
227 LOGICAL LSAME
228 EXTERNAL lsame
229* ..
230* .. External Subroutines ..
231 EXTERNAL dpptrf, dspevd, dspgst, dtpmv, dtpsv, xerbla
232* ..
233* .. Intrinsic Functions ..
234 INTRINSIC dble, max
235* ..
236* .. Executable Statements ..
237*
238* Test the input parameters.
239*
240 wantz = lsame( jobz, 'V' )
241 upper = lsame( uplo, 'U' )
242 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
243*
244 info = 0
245 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
246 info = -1
247 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
248 info = -2
249 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
250 info = -3
251 ELSE IF( n.LT.0 ) THEN
252 info = -4
253 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
254 info = -9
255 END IF
256*
257 IF( info.EQ.0 ) THEN
258 IF( n.LE.1 ) THEN
259 liwmin = 1
260 lwmin = 1
261 ELSE
262 IF( wantz ) THEN
263 liwmin = 3 + 5*n
264 lwmin = 1 + 6*n + 2*n**2
265 ELSE
266 liwmin = 1
267 lwmin = 2*n
268 END IF
269 END IF
270 work( 1 ) = lwmin
271 iwork( 1 ) = liwmin
272 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
273 info = -11
274 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
275 info = -13
276 END IF
277 END IF
278*
279 IF( info.NE.0 ) THEN
280 CALL xerbla( 'DSPGVD', -info )
281 RETURN
282 ELSE IF( lquery ) THEN
283 RETURN
284 END IF
285*
286* Quick return if possible
287*
288 IF( n.EQ.0 )
289 $ RETURN
290*
291* Form a Cholesky factorization of BP.
292*
293 CALL dpptrf( uplo, n, bp, info )
294 IF( info.NE.0 ) THEN
295 info = n + info
296 RETURN
297 END IF
298*
299* Transform problem to standard eigenvalue problem and solve.
300*
301 CALL dspgst( itype, uplo, n, ap, bp, info )
302 CALL dspevd( jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork,
303 $ liwork, info )
304 lwmin = int( max( dble( lwmin ), dble( work( 1 ) ) ) )
305 liwmin = int( max( dble( liwmin ), dble( iwork( 1 ) ) ) )
306*
307 IF( wantz ) THEN
308*
309* Backtransform eigenvectors to the original problem.
310*
311 neig = n
312 IF( info.GT.0 )
313 $ neig = info - 1
314 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
315*
316* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
317* backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
318*
319 IF( upper ) THEN
320 trans = 'N'
321 ELSE
322 trans = 'T'
323 END IF
324*
325 DO 10 j = 1, neig
326 CALL dtpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
327 $ 1 )
328 10 CONTINUE
329*
330 ELSE IF( itype.EQ.3 ) THEN
331*
332* For B*A*x=(lambda)*x;
333* backtransform eigenvectors: x = L*y or U**T *y
334*
335 IF( upper ) THEN
336 trans = 'T'
337 ELSE
338 trans = 'N'
339 END IF
340*
341 DO 20 j = 1, neig
342 CALL dtpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
343 $ 1 )
344 20 CONTINUE
345 END IF
346 END IF
347*
348 work( 1 ) = lwmin
349 iwork( 1 ) = liwmin
350*
351 RETURN
352*
353* End of DSPGVD
354*
355 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dspevd(jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork, liwork, info)
DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition dspevd.f:172
subroutine dspgst(itype, uplo, n, ap, bp, info)
DSPGST
Definition dspgst.f:113
subroutine dspgvd(itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, iwork, liwork, info)
DSPGVD
Definition dspgvd.f:204
subroutine dpptrf(uplo, n, ap, info)
DPPTRF
Definition dpptrf.f:119
subroutine dtpmv(uplo, trans, diag, n, ap, x, incx)
DTPMV
Definition dtpmv.f:142
subroutine dtpsv(uplo, trans, diag, n, ap, x, incx)
DTPSV
Definition dtpsv.f:144