LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ chegv()

 subroutine chegv ( integer itype, character jobz, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) w, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info )

CHEGV

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Purpose:
CHEGV computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-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 Hermitian 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 COMPLEX array, dimension (LDA, N) On entry, the Hermitian 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**H*B*Z = I; if ITYPE = 3, Z**H*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 COMPLEX array, dimension (LDB, N) On entry, the Hermitian 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**H*U or B = L*L**H. [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 COMPLEX 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(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for CHETRD 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] RWORK RWORK is REAL array, dimension (max(1, 3*N-2)) [out] INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: CPOTRF or CHEEV returned an error code: <= N: if INFO = i, CHEEV 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 principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

Definition at line 179 of file chegv.f.

181*
182* -- LAPACK driver routine --
183* -- LAPACK is a software package provided by Univ. of Tennessee, --
184* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
185*
186* .. Scalar Arguments ..
187 CHARACTER JOBZ, UPLO
188 INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
189* ..
190* .. Array Arguments ..
191 REAL RWORK( * ), W( * )
192 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
193* ..
194*
195* =====================================================================
196*
197* .. Parameters ..
198 COMPLEX ONE
199 parameter( one = ( 1.0e+0, 0.0e+0 ) )
200* ..
201* .. Local Scalars ..
202 LOGICAL LQUERY, UPPER, WANTZ
203 CHARACTER TRANS
204 INTEGER LWKOPT, NB, NEIG
205* ..
206* .. External Functions ..
207 LOGICAL LSAME
208 INTEGER ILAENV
209 REAL SROUNDUP_LWORK
210 EXTERNAL ilaenv, lsame, sroundup_lwork
211* ..
212* .. External Subroutines ..
213 EXTERNAL cheev, chegst, cpotrf, ctrmm, ctrsm, xerbla
214* ..
215* .. Intrinsic Functions ..
216 INTRINSIC max
217* ..
218* .. Executable Statements ..
219*
220* Test the input parameters.
221*
222 wantz = lsame( jobz, 'V' )
223 upper = lsame( uplo, 'U' )
224 lquery = ( lwork.EQ. -1 )
225*
226 info = 0
227 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
228 info = -1
229 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
230 info = -2
231 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
232 info = -3
233 ELSE IF( n.LT.0 ) THEN
234 info = -4
235 ELSE IF( lda.LT.max( 1, n ) ) THEN
236 info = -6
237 ELSE IF( ldb.LT.max( 1, n ) ) THEN
238 info = -8
239 END IF
240*
241 IF( info.EQ.0 ) THEN
242 nb = ilaenv( 1, 'CHETRD', uplo, n, -1, -1, -1 )
243 lwkopt = max( 1, ( nb + 1 )*n )
244 work( 1 ) = sroundup_lwork(lwkopt)
245*
246 IF( lwork.LT.max( 1, 2*n-1 ) .AND. .NOT.lquery ) THEN
247 info = -11
248 END IF
249 END IF
250*
251 IF( info.NE.0 ) THEN
252 CALL xerbla( 'CHEGV ', -info )
253 RETURN
254 ELSE IF( lquery ) THEN
255 RETURN
256 END IF
257*
258* Quick return if possible
259*
260 IF( n.EQ.0 )
261 \$ RETURN
262*
263* Form a Cholesky factorization of B.
264*
265 CALL cpotrf( uplo, n, b, ldb, info )
266 IF( info.NE.0 ) THEN
267 info = n + info
268 RETURN
269 END IF
270*
271* Transform problem to standard eigenvalue problem and solve.
272*
273 CALL chegst( itype, uplo, n, a, lda, b, ldb, info )
274 CALL cheev( jobz, uplo, n, a, lda, w, work, lwork, rwork, info )
275*
276 IF( wantz ) THEN
277*
278* Backtransform eigenvectors to the original problem.
279*
280 neig = n
281 IF( info.GT.0 )
282 \$ neig = info - 1
283 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
284*
285* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
286* backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
287*
288 IF( upper ) THEN
289 trans = 'N'
290 ELSE
291 trans = 'C'
292 END IF
293*
294 CALL ctrsm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
295 \$ b, ldb, a, lda )
296*
297 ELSE IF( itype.EQ.3 ) THEN
298*
299* For B*A*x=(lambda)*x;
300* backtransform eigenvectors: x = L*y or U**H*y
301*
302 IF( upper ) THEN
303 trans = 'C'
304 ELSE
305 trans = 'N'
306 END IF
307*
308 CALL ctrmm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
309 \$ b, ldb, a, lda )
310 END IF
311 END IF
312*
313 work( 1 ) = sroundup_lwork(lwkopt)
314*
315 RETURN
316*
317* End of CHEGV
318*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine cheev(jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
CHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition cheev.f:140
subroutine chegst(itype, uplo, n, a, lda, b, ldb, info)
CHEGST
Definition chegst.f:128
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine cpotrf(uplo, n, a, lda, info)
CPOTRF
Definition cpotrf.f:107
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
subroutine ctrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRMM
Definition ctrmm.f:177
subroutine ctrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRSM
Definition ctrsm.f:180
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