LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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ssygvd.f
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1*> \brief \b SSYGVD
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download SSYGVD + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssygvd.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssygvd.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssygvd.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
22* LWORK, IWORK, LIWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBZ, UPLO
26* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N
27* ..
28* .. Array Arguments ..
29* INTEGER IWORK( * )
30* REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> SSYGVD computes all the eigenvalues, and optionally, the eigenvectors
40*> of a real generalized symmetric-definite eigenproblem, of the form
41*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
42*> B are assumed to be symmetric and B is also positive definite.
43*> If eigenvectors are desired, it uses a divide and conquer algorithm.
44*>
45*> The divide and conquer algorithm makes very mild assumptions about
46*> floating point arithmetic. It will work on machines with a guard
47*> digit in add/subtract, or on those binary machines without guard
48*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
49*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
50*> without guard digits, but we know of none.
51*> \endverbatim
52*
53* Arguments:
54* ==========
55*
56*> \param[in] ITYPE
57*> \verbatim
58*> ITYPE is INTEGER
59*> Specifies the problem type to be solved:
60*> = 1: A*x = (lambda)*B*x
61*> = 2: A*B*x = (lambda)*x
62*> = 3: B*A*x = (lambda)*x
63*> \endverbatim
64*>
65*> \param[in] JOBZ
66*> \verbatim
67*> JOBZ is CHARACTER*1
68*> = 'N': Compute eigenvalues only;
69*> = 'V': Compute eigenvalues and eigenvectors.
70*> \endverbatim
71*>
72*> \param[in] UPLO
73*> \verbatim
74*> UPLO is CHARACTER*1
75*> = 'U': Upper triangles of A and B are stored;
76*> = 'L': Lower triangles of A and B are stored.
77*> \endverbatim
78*>
79*> \param[in] N
80*> \verbatim
81*> N is INTEGER
82*> The order of the matrices A and B. N >= 0.
83*> \endverbatim
84*>
85*> \param[in,out] A
86*> \verbatim
87*> A is REAL array, dimension (LDA, N)
88*> On entry, the symmetric matrix A. If UPLO = 'U', the
89*> leading N-by-N upper triangular part of A contains the
90*> upper triangular part of the matrix A. If UPLO = 'L',
91*> the leading N-by-N lower triangular part of A contains
92*> the lower triangular part of the matrix A.
93*>
94*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
95*> matrix Z of eigenvectors. The eigenvectors are normalized
96*> as follows:
97*> if ITYPE = 1 or 2, Z**T*B*Z = I;
98*> if ITYPE = 3, Z**T*inv(B)*Z = I.
99*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
100*> or the lower triangle (if UPLO='L') of A, including the
101*> diagonal, is destroyed.
102*> \endverbatim
103*>
104*> \param[in] LDA
105*> \verbatim
106*> LDA is INTEGER
107*> The leading dimension of the array A. LDA >= max(1,N).
108*> \endverbatim
109*>
110*> \param[in,out] B
111*> \verbatim
112*> B is REAL array, dimension (LDB, N)
113*> On entry, the symmetric matrix B. If UPLO = 'U', the
114*> leading N-by-N upper triangular part of B contains the
115*> upper triangular part of the matrix B. If UPLO = 'L',
116*> the leading N-by-N lower triangular part of B contains
117*> the lower triangular part of the matrix B.
118*>
119*> On exit, if INFO <= N, the part of B containing the matrix is
120*> overwritten by the triangular factor U or L from the Cholesky
121*> factorization B = U**T*U or B = L*L**T.
122*> \endverbatim
123*>
124*> \param[in] LDB
125*> \verbatim
126*> LDB is INTEGER
127*> The leading dimension of the array B. LDB >= max(1,N).
128*> \endverbatim
129*>
130*> \param[out] W
131*> \verbatim
132*> W is REAL array, dimension (N)
133*> If INFO = 0, the eigenvalues in ascending order.
134*> \endverbatim
135*>
136*> \param[out] WORK
137*> \verbatim
138*> WORK is REAL array, dimension (MAX(1,LWORK))
139*> On exit, if INFO = 0, WORK(1) returns the optimal 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+1.
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 optimal 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 optimal LIWORK.
161*> \endverbatim
162*>
163*> \param[in] LIWORK
164*> \verbatim
165*> LIWORK is INTEGER
166*> The dimension of the array IWORK.
167*> If N <= 1, LIWORK >= 1.
168*> If JOBZ = 'N' and N > 1, LIWORK >= 1.
169*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
170*>
171*> If LIWORK = -1, then a workspace query is assumed; the
172*> routine only calculates the optimal sizes of the WORK and
173*> IWORK arrays, returns these values as the first entries of
174*> the WORK and IWORK arrays, and no error message related to
175*> LWORK or LIWORK is issued by XERBLA.
176*> \endverbatim
177*>
178*> \param[out] INFO
179*> \verbatim
180*> INFO is INTEGER
181*> = 0: successful exit
182*> < 0: if INFO = -i, the i-th argument had an illegal value
183*> > 0: SPOTRF or SSYEVD returned an error code:
184*> <= N: if INFO = i and JOBZ = 'N', then the algorithm
185*> failed to converge; i off-diagonal elements of an
186*> intermediate tridiagonal form did not converge to
187*> zero;
188*> if INFO = i and JOBZ = 'V', then the algorithm
189*> failed to compute an eigenvalue while working on
190*> the submatrix lying in rows and columns INFO/(N+1)
191*> through mod(INFO,N+1);
192*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
193*> minor of order i of B is not positive definite.
194*> The factorization of B could not be completed and
195*> no eigenvalues or eigenvectors were computed.
196*> \endverbatim
197*
198* Authors:
199* ========
200*
201*> \author Univ. of Tennessee
202*> \author Univ. of California Berkeley
203*> \author Univ. of Colorado Denver
204*> \author NAG Ltd.
205*
206*> \ingroup realSYeigen
207*
208*> \par Further Details:
209* =====================
210*>
211*> \verbatim
212*>
213*> Modified so that no backsubstitution is performed if SSYEVD fails to
214*> converge (NEIG in old code could be greater than N causing out of
215*> bounds reference to A - reported by Ralf Meyer). Also corrected the
216*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
217*> \endverbatim
218*
219*> \par Contributors:
220* ==================
221*>
222*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
223*>
224* =====================================================================
225 SUBROUTINE ssygvd( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
226 $ LWORK, IWORK, LIWORK, INFO )
227*
228* -- LAPACK driver routine --
229* -- LAPACK is a software package provided by Univ. of Tennessee, --
230* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
231*
232* .. Scalar Arguments ..
233 CHARACTER JOBZ, UPLO
234 INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LWORK, N
235* ..
236* .. Array Arguments ..
237 INTEGER IWORK( * )
238 REAL A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
239* ..
240*
241* =====================================================================
242*
243* .. Parameters ..
244 REAL ONE
245 parameter( one = 1.0e+0 )
246* ..
247* .. Local Scalars ..
248 LOGICAL LQUERY, UPPER, WANTZ
249 CHARACTER TRANS
250 INTEGER LIOPT, LIWMIN, LOPT, LWMIN
251* ..
252* .. External Functions ..
253 LOGICAL LSAME
254 EXTERNAL lsame
255* ..
256* .. External Subroutines ..
257 EXTERNAL spotrf, ssyevd, ssygst, strmm, strsm, xerbla
258* ..
259* .. Intrinsic Functions ..
260 INTRINSIC max, real
261* ..
262* .. Executable Statements ..
263*
264* Test the input parameters.
265*
266 wantz = lsame( jobz, 'V' )
267 upper = lsame( uplo, 'U' )
268 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
269*
270 info = 0
271 IF( n.LE.1 ) THEN
272 liwmin = 1
273 lwmin = 1
274 ELSE IF( wantz ) THEN
275 liwmin = 3 + 5*n
276 lwmin = 1 + 6*n + 2*n**2
277 ELSE
278 liwmin = 1
279 lwmin = 2*n + 1
280 END IF
281 lopt = lwmin
282 liopt = liwmin
283 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
284 info = -1
285 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
286 info = -2
287 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
288 info = -3
289 ELSE IF( n.LT.0 ) THEN
290 info = -4
291 ELSE IF( lda.LT.max( 1, n ) ) THEN
292 info = -6
293 ELSE IF( ldb.LT.max( 1, n ) ) THEN
294 info = -8
295 END IF
296*
297 IF( info.EQ.0 ) THEN
298 work( 1 ) = lopt
299 iwork( 1 ) = liopt
300*
301 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
302 info = -11
303 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
304 info = -13
305 END IF
306 END IF
307*
308 IF( info.NE.0 ) THEN
309 CALL xerbla( 'SSYGVD', -info )
310 RETURN
311 ELSE IF( lquery ) THEN
312 RETURN
313 END IF
314*
315* Quick return if possible
316*
317 IF( n.EQ.0 )
318 $ RETURN
319*
320* Form a Cholesky factorization of B.
321*
322 CALL spotrf( uplo, n, b, ldb, info )
323 IF( info.NE.0 ) THEN
324 info = n + info
325 RETURN
326 END IF
327*
328* Transform problem to standard eigenvalue problem and solve.
329*
330 CALL ssygst( itype, uplo, n, a, lda, b, ldb, info )
331 CALL ssyevd( jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork,
332 $ info )
333 lopt = int( max( real( lopt ), real( work( 1 ) ) ) )
334 liopt = int( max( real( liopt ), real( iwork( 1 ) ) ) )
335*
336 IF( wantz .AND. info.EQ.0 ) THEN
337*
338* Backtransform eigenvectors to the original problem.
339*
340 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
341*
342* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
343* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
344*
345 IF( upper ) THEN
346 trans = 'N'
347 ELSE
348 trans = 'T'
349 END IF
350*
351 CALL strsm( 'Left', uplo, trans, 'Non-unit', n, n, one,
352 $ b, ldb, a, lda )
353*
354 ELSE IF( itype.EQ.3 ) THEN
355*
356* For B*A*x=(lambda)*x;
357* backtransform eigenvectors: x = L*y or U**T*y
358*
359 IF( upper ) THEN
360 trans = 'T'
361 ELSE
362 trans = 'N'
363 END IF
364*
365 CALL strmm( 'Left', uplo, trans, 'Non-unit', n, n, one,
366 $ b, ldb, a, lda )
367 END IF
368 END IF
369*
370 work( 1 ) = lopt
371 iwork( 1 ) = liopt
372*
373 RETURN
374*
375* End of SSYGVD
376*
377 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine spotrf(UPLO, N, A, LDA, INFO)
SPOTRF
Definition: spotrf.f:107
subroutine ssygst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
SSYGST
Definition: ssygst.f:127
subroutine ssyevd(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, INFO)
SSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices
Definition: ssyevd.f:183
subroutine ssygvd(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, IWORK, LIWORK, INFO)
SSYGVD
Definition: ssygvd.f:227
subroutine strmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRMM
Definition: strmm.f:177
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181