chegvd-f(3)

chegvd.f –

Synopsis

Functions/Subroutines

subroutine chegvd (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHEGST

Function/Subroutine Documentation

subroutine chegvd (integerITYPE, characterJOBZ, characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, real, dimension( * )W, complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)

CHEGST

Purpose:

 CHEGVD 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.
 If eigenvectors are desired, it uses a divide and conquer algorithm.
 The divide and conquer algorithm makes very mild assumptions about
 floating point arithmetic. It will work on machines with a guard
 digit in add/subtract, or on those binary machines without guard
 digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
 Cray-2. It could conceivably fail on hexadecimal or decimal machines
 without guard digits, but we know of none.

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 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.
 If N <= 1, LWORK >= 1.
 If JOBZ = 'N' and N > 1, LWORK >= N + 1.
 If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.
 If LWORK = -1, then a workspace query is assumed; the routine
 only calculates the optimal sizes of the WORK, RWORK and
 IWORK arrays, returns these values as the first entries of
 the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

 RWORK is REAL array, dimension (MAX(1,LRWORK))
 On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

 LRWORK is INTEGER
 The dimension of the array RWORK.
 If N <= 1, LRWORK >= 1.
 If JOBZ = 'N' and N > 1, LRWORK >= N.
 If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
 If LRWORK = -1, then a workspace query is assumed; the
 routine only calculates the optimal sizes of the WORK, RWORK
 and IWORK arrays, returns these values as the first entries
 of the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

 IWORK is INTEGER array, dimension (MAX(1,LIWORK))
 On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

 LIWORK is INTEGER
 The dimension of the array IWORK.
 If N <= 1, LIWORK >= 1.
 If JOBZ = 'N' and N > 1, LIWORK >= 1.
 If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
 If LIWORK = -1, then a workspace query is assumed; the
 routine only calculates the optimal sizes of the WORK, RWORK
 and IWORK arrays, returns these values as the first entries
 of the WORK, RWORK and IWORK arrays, and no error message
 related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value
 > 0: CPOTRF or CHEEVD returned an error code:
 <= N: if INFO = i and JOBZ = 'N', then the algorithm
 failed to converge; i off-diagonal elements of an
 intermediate tridiagonal form did not converge to
 zero;
 if INFO = i and JOBZ = 'V', then the algorithm
 failed to compute an eigenvalue while working on
 the submatrix lying in rows and columns INFO/(N+1)
 through mod(INFO,N+1);
 > 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

Further Details:

 Modified so that no backsubstitution is performed if CHEEVD fails to
 converge (NEIG in old code could be greater than N causing out of
 bounds reference to A - reported by Ralf Meyer). Also corrected the
 description of INFO and the test on ITYPE. Sven, 16 Feb 05.

Contributors:

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

Definition at line 249 of file chegvd.f.

Author

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