chegvx-f(3)

chegvx.f –

Synopsis

Functions/Subroutines

subroutine chegvx (ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO)
CHEGST

Function/Subroutine Documentation

subroutine chegvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

CHEGST

Purpose:

 CHEGVX computes selected eigenvalues, and optionally, 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.
 Eigenvalues and eigenvectors can be selected by specifying either a
 range of values or a range of indices for the desired eigenvalues.

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.

RANGE

 RANGE is CHARACTER*1
 = 'A': all eigenvalues will be found.
 = 'V': all eigenvalues in the half-open interval (VL,VU]
 will be found.
 = 'I': the IL-th through IU-th eigenvalues will be found.

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, the lower triangle (if UPLO='L') or the upper
 triangle (if UPLO='U') 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 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).

 VL is REAL

 VU is REAL
 If RANGE='V', the lower and upper bounds of the interval to
 be searched for eigenvalues. VL < VU.
 Not referenced if RANGE = 'A' or 'I'.

 IL is INTEGER

 IU is INTEGER
 If RANGE='I', the indices (in ascending order) of the
 smallest and largest eigenvalues to be returned.
 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
 Not referenced if RANGE = 'A' or 'V'.

ABSTOL

 ABSTOL is REAL
 The absolute error tolerance for the eigenvalues.
 An approximate eigenvalue is accepted as converged
 when it is determined to lie in an interval [a,b]
 of width less than or equal to
 ABSTOL + EPS * max( |a|,|b| ) ,
 where EPS is the machine precision. If ABSTOL is less than
 or equal to zero, then EPS*|T| will be used in its place,
 where |T| is the 1-norm of the tridiagonal matrix obtained
 by reducing C to tridiagonal form, where C is the symmetric
 matrix of the standard symmetric problem to which the
 generalized problem is transformed.
 Eigenvalues will be computed most accurately when ABSTOL is
 set to twice the underflow threshold 2*SLAMCH('S'), not zero.
 If this routine returns with INFO>0, indicating that some
 eigenvectors did not converge, try setting ABSTOL to
 2*SLAMCH('S').

 M is INTEGER
 The total number of eigenvalues found. 0 <= M <= N.
 If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

 W is REAL array, dimension (N)
 The first M elements contain the selected
 eigenvalues in ascending order.

 Z is COMPLEX array, dimension (LDZ, max(1,M))
 If JOBZ = 'N', then Z is not referenced.
 If JOBZ = 'V', then if INFO = 0, the first M columns of Z
 contain the orthonormal eigenvectors of the matrix A
 corresponding to the selected eigenvalues, with the i-th
 column of Z holding the eigenvector associated with W(i).
 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 an eigenvector fails to converge, then that column of Z
 contains the latest approximation to the eigenvector, and the
 index of the eigenvector is returned in IFAIL.
 Note: the user must ensure that at least max(1,M) columns are
 supplied in the array Z; if RANGE = 'V', the exact value of M
 is not known in advance and an upper bound must be used.

LDZ

 LDZ is INTEGER
 The leading dimension of the array Z. LDZ >= 1, and if
 JOBZ = 'V', LDZ >= max(1,N).

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).
 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 (7*N)

IWORK

 IWORK is INTEGER array, dimension (5*N)

IFAIL

 IFAIL is INTEGER array, dimension (N)
 If JOBZ = 'V', then if INFO = 0, the first M elements of
 IFAIL are zero. If INFO > 0, then IFAIL contains the
 indices of the eigenvectors that failed to converge.
 If JOBZ = 'N', then IFAIL is not referenced.

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value
 > 0: CPOTRF or CHEEVX returned an error code:
 <= N: if INFO = i, CHEEVX failed to converge;
 i eigenvectors failed to converge. Their indices
 are stored in array IFAIL.
 > 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

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 297 of file chegvx.f.

Author

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