 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ssygv()

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

SSYGV

Purpose:
``` SSYGV 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 REAL 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 REAL 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 REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] WORK ``` WORK is REAL 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 SSYTRD 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: SPOTRF or SSYEV returned an error code: <= N: if INFO = i, SSYEV 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.```
Date
December 2016

Definition at line 177 of file ssygv.f.

177 *
178 * -- LAPACK driver routine (version 3.7.0) --
179 * -- LAPACK is a software package provided by Univ. of Tennessee, --
180 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181 * December 2016
182 *
183 * .. Scalar Arguments ..
184  CHARACTER jobz, uplo
185  INTEGER info, itype, lda, ldb, lwork, n
186 * ..
187 * .. Array Arguments ..
188  REAL a( lda, * ), b( ldb, * ), w( * ), work( * )
189 * ..
190 *
191 * =====================================================================
192 *
193 * .. Parameters ..
194  REAL one
195  parameter( one = 1.0e+0 )
196 * ..
197 * .. Local Scalars ..
198  LOGICAL lquery, upper, wantz
199  CHARACTER trans
200  INTEGER lwkmin, lwkopt, nb, neig
201 * ..
202 * .. External Functions ..
203  LOGICAL lsame
204  INTEGER ilaenv
205  EXTERNAL ilaenv, lsame
206 * ..
207 * .. External Subroutines ..
208  EXTERNAL spotrf, ssyev, ssygst, strmm, strsm, xerbla
209 * ..
210 * .. Intrinsic Functions ..
211  INTRINSIC max
212 * ..
213 * .. Executable Statements ..
214 *
215 * Test the input parameters.
216 *
217  wantz = lsame( jobz, 'V' )
218  upper = lsame( uplo, 'U' )
219  lquery = ( lwork.EQ.-1 )
220 *
221  info = 0
222  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
223  info = -1
224  ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
225  info = -2
226  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
227  info = -3
228  ELSE IF( n.LT.0 ) THEN
229  info = -4
230  ELSE IF( lda.LT.max( 1, n ) ) THEN
231  info = -6
232  ELSE IF( ldb.LT.max( 1, n ) ) THEN
233  info = -8
234  END IF
235 *
236  IF( info.EQ.0 ) THEN
237  lwkmin = max( 1, 3*n - 1 )
238  nb = ilaenv( 1, 'SSYTRD', uplo, n, -1, -1, -1 )
239  lwkopt = max( lwkmin, ( nb + 2 )*n )
240  work( 1 ) = lwkopt
241 *
242  IF( lwork.LT.lwkmin .AND. .NOT.lquery ) THEN
243  info = -11
244  END IF
245  END IF
246 *
247  IF( info.NE.0 ) THEN
248  CALL xerbla( 'SSYGV ', -info )
249  RETURN
250  ELSE IF( lquery ) THEN
251  RETURN
252  END IF
253 *
254 * Quick return if possible
255 *
256  IF( n.EQ.0 )
257  \$ RETURN
258 *
259 * Form a Cholesky factorization of B.
260 *
261  CALL spotrf( uplo, n, b, ldb, info )
262  IF( info.NE.0 ) THEN
263  info = n + info
264  RETURN
265  END IF
266 *
267 * Transform problem to standard eigenvalue problem and solve.
268 *
269  CALL ssygst( itype, uplo, n, a, lda, b, ldb, info )
270  CALL ssyev( jobz, uplo, n, a, lda, w, work, lwork, info )
271 *
272  IF( wantz ) THEN
273 *
274 * Backtransform eigenvectors to the original problem.
275 *
276  neig = n
277  IF( info.GT.0 )
278  \$ neig = info - 1
279  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
280 *
281 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
282 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
283 *
284  IF( upper ) THEN
285  trans = 'N'
286  ELSE
287  trans = 'T'
288  END IF
289 *
290  CALL strsm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
291  \$ b, ldb, a, lda )
292 *
293  ELSE IF( itype.EQ.3 ) THEN
294 *
295 * For B*A*x=(lambda)*x;
296 * backtransform eigenvectors: x = L*y or U**T*y
297 *
298  IF( upper ) THEN
299  trans = 'T'
300  ELSE
301  trans = 'N'
302  END IF
303 *
304  CALL strmm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
305  \$ b, ldb, a, lda )
306  END IF
307  END IF
308 *
309  work( 1 ) = lwkopt
310  RETURN
311 *
312 * End of SSYGV
313 *
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:183
subroutine spotrf(UPLO, N, A, LDA, INFO)
SPOTRF
Definition: spotrf.f:109
subroutine strmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRMM
Definition: strmm.f:179
subroutine ssygst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
SSYGST
Definition: ssygst.f:129
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
subroutine ssyev(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO)
SSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices ...
Definition: ssyev.f:134
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