LAPACK 3.11.0
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*> The divide and conquer algorithm makes very mild assumptions about
48*> floating point arithmetic. It will work on machines with a guard
49*> digit in add/subtract, or on those binary machines without guard
50*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
51*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
52*> without guard digits, but we know of none.
53*> \endverbatim
54*
55* Arguments:
56* ==========
57*
58*> \param[in] ITYPE
59*> \verbatim
60*> ITYPE is INTEGER
61*> Specifies the problem type to be solved:
62*> = 1: A*x = (lambda)*B*x
63*> = 2: A*B*x = (lambda)*x
64*> = 3: B*A*x = (lambda)*x
65*> \endverbatim
66*>
67*> \param[in] JOBZ
68*> \verbatim
69*> JOBZ is CHARACTER*1
70*> = 'N': Compute eigenvalues only;
71*> = 'V': Compute eigenvalues and eigenvectors.
72*> \endverbatim
73*>
74*> \param[in] UPLO
75*> \verbatim
76*> UPLO is CHARACTER*1
77*> = 'U': Upper triangles of A and B are stored;
78*> = 'L': Lower triangles of A and B are stored.
79*> \endverbatim
80*>
81*> \param[in] N
82*> \verbatim
83*> N is INTEGER
84*> The order of the matrices A and B. N >= 0.
85*> \endverbatim
86*>
87*> \param[in,out] AP
88*> \verbatim
89*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
90*> On entry, the upper or lower triangle of the symmetric matrix
91*> A, packed columnwise in a linear array. The j-th column of A
92*> is stored in the array AP as follows:
93*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
94*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
95*>
96*> On exit, the contents of AP are destroyed.
97*> \endverbatim
98*>
99*> \param[in,out] BP
100*> \verbatim
101*> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
102*> On entry, the upper or lower triangle of the symmetric matrix
103*> B, packed columnwise in a linear array. The j-th column of B
104*> is stored in the array BP as follows:
105*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
106*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
107*>
108*> On exit, the triangular factor U or L from the Cholesky
109*> factorization B = U**T*U or B = L*L**T, in the same storage
110*> format as B.
111*> \endverbatim
112*>
113*> \param[out] W
114*> \verbatim
115*> W is DOUBLE PRECISION array, dimension (N)
116*> If INFO = 0, the eigenvalues in ascending order.
117*> \endverbatim
118*>
119*> \param[out] Z
120*> \verbatim
121*> Z is DOUBLE PRECISION array, dimension (LDZ, N)
122*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
123*> eigenvectors. The eigenvectors are normalized as follows:
124*> if ITYPE = 1 or 2, Z**T*B*Z = I;
125*> if ITYPE = 3, Z**T*inv(B)*Z = I.
126*> If JOBZ = 'N', then Z is not referenced.
127*> \endverbatim
128*>
129*> \param[in] LDZ
130*> \verbatim
131*> LDZ is INTEGER
132*> The leading dimension of the array Z. LDZ >= 1, and if
133*> JOBZ = 'V', LDZ >= max(1,N).
134*> \endverbatim
135*>
136*> \param[out] WORK
137*> \verbatim
138*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
139*> On exit, if INFO = 0, WORK(1) returns the required LWORK.
140*> \endverbatim
141*>
142*> \param[in] LWORK
143*> \verbatim
144*> LWORK is INTEGER
145*> The dimension of the array WORK.
146*> If N <= 1, LWORK >= 1.
147*> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
148*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
149*>
150*> If LWORK = -1, then a workspace query is assumed; the routine
151*> only calculates the required sizes of the WORK and IWORK
152*> arrays, returns these values as the first entries of the WORK
153*> and IWORK arrays, and no error message related to LWORK or
154*> LIWORK is issued by XERBLA.
155*> \endverbatim
156*>
157*> \param[out] IWORK
158*> \verbatim
159*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
160*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
161*> \endverbatim
162*>
163*> \param[in] LIWORK
164*> \verbatim
165*> LIWORK is INTEGER
166*> The dimension of the array IWORK.
167*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
168*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
169*>
170*> If LIWORK = -1, then a workspace query is assumed; the
171*> routine only calculates the required sizes of the WORK and
172*> IWORK arrays, returns these values as the first entries of
173*> the WORK and IWORK arrays, and no error message related to
174*> LWORK or LIWORK is issued by XERBLA.
175*> \endverbatim
176*>
177*> \param[out] INFO
178*> \verbatim
179*> INFO is INTEGER
180*> = 0: successful exit
181*> < 0: if INFO = -i, the i-th argument had an illegal value
182*> > 0: DPPTRF or DSPEVD returned an error code:
183*> <= N: if INFO = i, DSPEVD failed to converge;
184*> i off-diagonal elements of an intermediate
185*> tridiagonal form did not converge to zero;
186*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
187*> minor of order i of B is not positive definite.
188*> The factorization of B could not be completed and
189*> no eigenvalues or eigenvectors were computed.
190*> \endverbatim
191*
192* Authors:
193* ========
194*
195*> \author Univ. of Tennessee
196*> \author Univ. of California Berkeley
197*> \author Univ. of Colorado Denver
198*> \author NAG Ltd.
199*
200*> \ingroup doubleOTHEReigen
201*
202*> \par Contributors:
203* ==================
204*>
205*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
206*
207* =====================================================================
208 SUBROUTINE dspgvd( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
209 $ LWORK, IWORK, LIWORK, INFO )
210*
211* -- LAPACK driver routine --
212* -- LAPACK is a software package provided by Univ. of Tennessee, --
213* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
214*
215* .. Scalar Arguments ..
216 CHARACTER JOBZ, UPLO
217 INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
218* ..
219* .. Array Arguments ..
220 INTEGER IWORK( * )
221 DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
222 $ z( ldz, * )
223* ..
224*
225* =====================================================================
226*
227* .. Local Scalars ..
228 LOGICAL LQUERY, UPPER, WANTZ
229 CHARACTER TRANS
230 INTEGER J, LIWMIN, LWMIN, NEIG
231* ..
232* .. External Functions ..
233 LOGICAL LSAME
234 EXTERNAL lsame
235* ..
236* .. External Subroutines ..
237 EXTERNAL dpptrf, dspevd, dspgst, dtpmv, dtpsv, xerbla
238* ..
239* .. Intrinsic Functions ..
240 INTRINSIC dble, max
241* ..
242* .. Executable Statements ..
243*
244* Test the input parameters.
245*
246 wantz = lsame( jobz, 'V' )
247 upper = lsame( uplo, 'U' )
248 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
249*
250 info = 0
251 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
252 info = -1
253 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
254 info = -2
255 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
256 info = -3
257 ELSE IF( n.LT.0 ) THEN
258 info = -4
259 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
260 info = -9
261 END IF
262*
263 IF( info.EQ.0 ) THEN
264 IF( n.LE.1 ) THEN
265 liwmin = 1
266 lwmin = 1
267 ELSE
268 IF( wantz ) THEN
269 liwmin = 3 + 5*n
270 lwmin = 1 + 6*n + 2*n**2
271 ELSE
272 liwmin = 1
273 lwmin = 2*n
274 END IF
275 END IF
276 work( 1 ) = lwmin
277 iwork( 1 ) = liwmin
278 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
279 info = -11
280 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
281 info = -13
282 END IF
283 END IF
284*
285 IF( info.NE.0 ) THEN
286 CALL xerbla( 'DSPGVD', -info )
287 RETURN
288 ELSE IF( lquery ) THEN
289 RETURN
290 END IF
291*
292* Quick return if possible
293*
294 IF( n.EQ.0 )
295 $ RETURN
296*
297* Form a Cholesky factorization of BP.
298*
299 CALL dpptrf( uplo, n, bp, info )
300 IF( info.NE.0 ) THEN
301 info = n + info
302 RETURN
303 END IF
304*
305* Transform problem to standard eigenvalue problem and solve.
306*
307 CALL dspgst( itype, uplo, n, ap, bp, info )
308 CALL dspevd( jobz, uplo, n, ap, w, z, ldz, work, lwork, iwork,
309 $ liwork, info )
310 lwmin = int( max( dble( lwmin ), dble( work( 1 ) ) ) )
311 liwmin = int( max( dble( liwmin ), dble( iwork( 1 ) ) ) )
312*
313 IF( wantz ) THEN
314*
315* Backtransform eigenvectors to the original problem.
316*
317 neig = n
318 IF( info.GT.0 )
319 $ neig = info - 1
320 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
321*
322* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
323* backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
324*
325 IF( upper ) THEN
326 trans = 'N'
327 ELSE
328 trans = 'T'
329 END IF
330*
331 DO 10 j = 1, neig
332 CALL dtpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
333 $ 1 )
334 10 CONTINUE
335*
336 ELSE IF( itype.EQ.3 ) THEN
337*
338* For B*A*x=(lambda)*x;
339* backtransform eigenvectors: x = L*y or U**T *y
340*
341 IF( upper ) THEN
342 trans = 'T'
343 ELSE
344 trans = 'N'
345 END IF
346*
347 DO 20 j = 1, neig
348 CALL dtpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
349 $ 1 )
350 20 CONTINUE
351 END IF
352 END IF
353*
354 work( 1 ) = lwmin
355 iwork( 1 ) = liwmin
356*
357 RETURN
358*
359* End of DSPGVD
360*
361 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dtpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPSV
Definition: dtpsv.f:144
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:142
subroutine dpptrf(UPLO, N, AP, INFO)
DPPTRF
Definition: dpptrf.f:119
subroutine dspgst(ITYPE, UPLO, N, AP, BP, INFO)
DSPGST
Definition: dspgst.f:113
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:178
subroutine dspgvd(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
DSPGVD
Definition: dspgvd.f:210