chegv-f(3)

chegv.f –

Synopsis

Functions/Subroutines

subroutine chegv (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, INFO)
CHEGST

Function/Subroutine Documentation

subroutine chegv (integerITYPE, characterJOBZ, characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, real, dimension( * )W, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerINFO)

CHEGST

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:

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

JOBZ

 JOBZ is CHARACTER*1
 = 'N': Compute eigenvalues only;
 = 'V': Compute eigenvalues and eigenvectors.

UPLO

 UPLO is CHARACTER*1
 = 'U': Upper triangles of A and B are stored;
 = 'L': Lower triangles of A and B are stored.

 N is INTEGER
 The order of the matrices A and B. N >= 0.

 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.

LDA

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(1,N).

 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.

LDB

 LDB is INTEGER
 The leading dimension of the array B. LDB >= max(1,N).

 W is REAL array, dimension (N)
 If INFO = 0, the eigenvalues in ascending order.

WORK

 WORK is COMPLEX array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

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.

RWORK

 RWORK is REAL array, dimension (max(1, 3*N-2))

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
 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 181 of file chegv.f.

Author

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