LAPACK 3.12.1
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*> Download DSPGVD + dependencies
9*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgvd.f">
10*> [TGZ]</a>
11*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgvd.f">
12*> [ZIP]</a>
13*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgvd.f">
14*> [TXT]</a>
15*
16* Definition:
17* ===========
18*
19* SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
20* LWORK, IWORK, LIWORK, INFO )
21*
22* .. Scalar Arguments ..
23* CHARACTER JOBZ, UPLO
24* INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
25* ..
26* .. Array Arguments ..
27* INTEGER IWORK( * )
28* DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
29* $ Z( LDZ, * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
39*> of a real generalized symmetric-definite eigenproblem, of the form
40*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
41*> B are assumed to be symmetric, stored in packed format, and B is also
42*> positive definite.
43*> If eigenvectors are desired, it uses a divide and conquer algorithm.
44*>
45*> \endverbatim
46*
47* Arguments:
48* ==========
49*
50*> \param[in] ITYPE
51*> \verbatim
52*> ITYPE is INTEGER
53*> Specifies the problem type to be solved:
54*> = 1: A*x = (lambda)*B*x
55*> = 2: A*B*x = (lambda)*x
56*> = 3: B*A*x = (lambda)*x
57*> \endverbatim
58*>
59*> \param[in] JOBZ
60*> \verbatim
61*> JOBZ is CHARACTER*1
62*> = 'N': Compute eigenvalues only;
63*> = 'V': Compute eigenvalues and eigenvectors.
64*> \endverbatim
65*>
66*> \param[in] UPLO
67*> \verbatim
68*> UPLO is CHARACTER*1
69*> = 'U': Upper triangles of A and B are stored;
70*> = 'L': Lower triangles of A and B are stored.
71*> \endverbatim
72*>
73*> \param[in] N
74*> \verbatim
75*> N is INTEGER
76*> The order of the matrices A and B. N >= 0.
77*> \endverbatim
78*>
79*> \param[in,out] AP
80*> \verbatim
81*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
82*> On entry, the upper or lower triangle of the symmetric matrix
83*> A, packed columnwise in a linear array. The j-th column of A
84*> is stored in the array AP as follows:
85*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
86*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
87*>
88*> On exit, the contents of AP are destroyed.
89*> \endverbatim
90*>
91*> \param[in,out] BP
92*> \verbatim
93*> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
94*> On entry, the upper or lower triangle of the symmetric matrix
95*> B, packed columnwise in a linear array. The j-th column of B
96*> is stored in the array BP as follows:
97*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
98*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
99*>
100*> On exit, the triangular factor U or L from the Cholesky
101*> factorization B = U**T*U or B = L*L**T, in the same storage
102*> format as B.
103*> \endverbatim
104*>
105*> \param[out] W
106*> \verbatim
107*> W is DOUBLE PRECISION array, dimension (N)
108*> If INFO = 0, the eigenvalues in ascending order.
109*> \endverbatim
110*>
111*> \param[out] Z
112*> \verbatim
113*> Z is DOUBLE PRECISION array, dimension (LDZ, N)
114*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
115*> eigenvectors. The eigenvectors are normalized as follows:
116*> if ITYPE = 1 or 2, Z**T*B*Z = I;
117*> if ITYPE = 3, Z**T*inv(B)*Z = I.
118*> If JOBZ = 'N', then Z is not referenced.
119*> \endverbatim
120*>
121*> \param[in] LDZ
122*> \verbatim
123*> LDZ is INTEGER
124*> The leading dimension of the array Z. LDZ >= 1, and if
125*> JOBZ = 'V', LDZ >= max(1,N).
126*> \endverbatim
127*>
128*> \param[out] WORK
129*> \verbatim
130*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
131*> On exit, if INFO = 0, WORK(1) returns the required LWORK.
132*> \endverbatim
133*>
134*> \param[in] LWORK
135*> \verbatim
136*> LWORK is INTEGER
137*> The dimension of the array WORK.
138*> If N <= 1, LWORK >= 1.
139*> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
140*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
141*>
142*> If LWORK = -1, then a workspace query is assumed; the routine
143*> only calculates the required sizes of the WORK and IWORK
144*> arrays, returns these values as the first entries of the WORK
145*> and IWORK arrays, and no error message related to LWORK or
146*> LIWORK is issued by XERBLA.
147*> \endverbatim
148*>
149*> \param[out] IWORK
150*> \verbatim
151*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
152*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
153*> \endverbatim
154*>
155*> \param[in] LIWORK
156*> \verbatim
157*> LIWORK is INTEGER
158*> The dimension of the array IWORK.
159*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
160*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
161*>
162*> If LIWORK = -1, then a workspace query is assumed; the
163*> routine only calculates the required sizes of the WORK and
164*> IWORK arrays, returns these values as the first entries of
165*> the WORK and IWORK arrays, and no error message related to
166*> LWORK or LIWORK is issued by XERBLA.
167*> \endverbatim
168*>
169*> \param[out] INFO
170*> \verbatim
171*> INFO is INTEGER
172*> = 0: successful exit
173*> < 0: if INFO = -i, the i-th argument had an illegal value
174*> > 0: DPPTRF or DSPEVD returned an error code:
175*> <= N: if INFO = i, DSPEVD failed to converge;
176*> i off-diagonal elements of an intermediate
177*> tridiagonal form did not converge to zero;
178*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
179*> principal minor of order i of B is not positive.
180*> The factorization of B could not be completed and
181*> no eigenvalues or eigenvectors were computed.
182*> \endverbatim
183*
184* Authors:
185* ========
186*
187*> \author Univ. of Tennessee
188*> \author Univ. of California Berkeley
189*> \author Univ. of Colorado Denver
190*> \author NAG Ltd.
191*
192*> \ingroup hpgvd
193*
194*> \par Contributors:
195* ==================
196*>
197*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
198*
199* =====================================================================
200 SUBROUTINE dspgvd( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ,
201 $ WORK,
202 $ LWORK, IWORK, LIWORK, INFO )
203*
204* -- LAPACK driver routine --
205* -- LAPACK is a software package provided by Univ. of Tennessee, --
206* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
207*
208* .. Scalar Arguments ..
209 CHARACTER JOBZ, UPLO
210 INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
211* ..
212* .. Array Arguments ..
213 INTEGER IWORK( * )
214 DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
215 $ z( ldz, * )
216* ..
217*
218* =====================================================================
219*
220* .. Local Scalars ..
221 LOGICAL LQUERY, UPPER, WANTZ
222 CHARACTER TRANS
223 INTEGER J, LIWMIN, LWMIN, NEIG
224* ..
225* .. External Functions ..
226 LOGICAL LSAME
227 EXTERNAL LSAME
228* ..
229* .. External Subroutines ..
230 EXTERNAL dpptrf, dspevd, dspgst, dtpmv, dtpsv,
231 $ 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:170
subroutine dspgst(itype, uplo, n, ap, bp, info)
DSPGST
Definition dspgst.f:111
subroutine dspgvd(itype, jobz, uplo, n, ap, bp, w, z, ldz, work, lwork, iwork, liwork, info)
DSPGVD
Definition dspgvd.f:203
subroutine dpptrf(uplo, n, ap, info)
DPPTRF
Definition dpptrf.f:117
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