 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dsygv()

 subroutine dsygv ( integer ITYPE, character JOBZ, character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) W, double precision, dimension( * ) WORK, integer LWORK, integer INFO )

DSYGV

Purpose:
``` DSYGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric and B is also
positive definite.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x``` [in] JOBZ ``` JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in,out] A ``` A is DOUBLE PRECISION array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in,out] B ``` B is DOUBLE PRECISION array, dimension (LDB, N) On entry, the symmetric positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] W ``` W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] WORK ``` WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.``` [in] LWORK ``` LWORK is INTEGER The length of the array WORK. LWORK >= max(1,3*N-1). For optimal efficiency, LWORK >= (NB+2)*N, where NB is the blocksize for DSYTRD returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: DPOTRF or DSYEV returned an error code: <= N: if INFO = i, DSYEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.```

Definition at line 173 of file dsygv.f.

175 *
176 * -- LAPACK driver routine --
177 * -- LAPACK is a software package provided by Univ. of Tennessee, --
178 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
179 *
180 * .. Scalar Arguments ..
181  CHARACTER JOBZ, UPLO
182  INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
183 * ..
184 * .. Array Arguments ..
185  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
186 * ..
187 *
188 * =====================================================================
189 *
190 * .. Parameters ..
191  DOUBLE PRECISION ONE
192  parameter( one = 1.0d+0 )
193 * ..
194 * .. Local Scalars ..
195  LOGICAL LQUERY, UPPER, WANTZ
196  CHARACTER TRANS
197  INTEGER LWKMIN, LWKOPT, NB, NEIG
198 * ..
199 * .. External Functions ..
200  LOGICAL LSAME
201  INTEGER ILAENV
202  EXTERNAL lsame, ilaenv
203 * ..
204 * .. External Subroutines ..
205  EXTERNAL dpotrf, dsyev, dsygst, dtrmm, dtrsm, xerbla
206 * ..
207 * .. Intrinsic Functions ..
208  INTRINSIC max
209 * ..
210 * .. Executable Statements ..
211 *
212 * Test the input parameters.
213 *
214  wantz = lsame( jobz, 'V' )
215  upper = lsame( uplo, 'U' )
216  lquery = ( lwork.EQ.-1 )
217 *
218  info = 0
219  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
220  info = -1
221  ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
222  info = -2
223  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
224  info = -3
225  ELSE IF( n.LT.0 ) THEN
226  info = -4
227  ELSE IF( lda.LT.max( 1, n ) ) THEN
228  info = -6
229  ELSE IF( ldb.LT.max( 1, n ) ) THEN
230  info = -8
231  END IF
232 *
233  IF( info.EQ.0 ) THEN
234  lwkmin = max( 1, 3*n - 1 )
235  nb = ilaenv( 1, 'DSYTRD', uplo, n, -1, -1, -1 )
236  lwkopt = max( lwkmin, ( nb + 2 )*n )
237  work( 1 ) = lwkopt
238 *
239  IF( lwork.LT.lwkmin .AND. .NOT.lquery ) THEN
240  info = -11
241  END IF
242  END IF
243 *
244  IF( info.NE.0 ) THEN
245  CALL xerbla( 'DSYGV ', -info )
246  RETURN
247  ELSE IF( lquery ) THEN
248  RETURN
249  END IF
250 *
251 * Quick return if possible
252 *
253  IF( n.EQ.0 )
254  \$ RETURN
255 *
256 * Form a Cholesky factorization of B.
257 *
258  CALL dpotrf( uplo, n, b, ldb, info )
259  IF( info.NE.0 ) THEN
260  info = n + info
261  RETURN
262  END IF
263 *
264 * Transform problem to standard eigenvalue problem and solve.
265 *
266  CALL dsygst( itype, uplo, n, a, lda, b, ldb, info )
267  CALL dsyev( jobz, uplo, n, a, lda, w, work, lwork, info )
268 *
269  IF( wantz ) THEN
270 *
271 * Backtransform eigenvectors to the original problem.
272 *
273  neig = n
274  IF( info.GT.0 )
275  \$ neig = info - 1
276  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
277 *
278 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
279 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
280 *
281  IF( upper ) THEN
282  trans = 'N'
283  ELSE
284  trans = 'T'
285  END IF
286 *
287  CALL dtrsm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
288  \$ b, ldb, a, lda )
289 *
290  ELSE IF( itype.EQ.3 ) THEN
291 *
292 * For B*A*x=(lambda)*x;
293 * backtransform eigenvectors: x = L*y or U**T*y
294 *
295  IF( upper ) THEN
296  trans = 'T'
297  ELSE
298  trans = 'N'
299  END IF
300 *
301  CALL dtrmm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
302  \$ b, ldb, a, lda )
303  END IF
304  END IF
305 *
306  work( 1 ) = lwkopt
307  RETURN
308 *
309 * End of DSYGV
310 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:177
subroutine dpotrf(UPLO, N, A, LDA, INFO)
DPOTRF
Definition: dpotrf.f:107
subroutine dsygst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
DSYGST
Definition: dsygst.f:127
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
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