TMtx.EigSymGen Method (TMtx, TVec, double, double, TMtx, TIntegerArray, double, TEigGenType)

Computes generalized eigenvalues with reduction of the symmetric-definite generalized eigenvalues/eigenvectors problem to the normal eigenvalue case.

Pascal

procedure EigSymGen(const B: TMtx; const D: TVec; Minimum: double; Maximum: double; V: TMtx; var VInfo: TIntegerArray; Tolerance: double = 0; const EigGenType: TEigGenType = etAzBz); overload;

Description

The routine computes selected eigenvalues and optionally also eigenvectors. The problem is of type:

A*x = lambda*B*x, A*B*x = lambda*x, or B*A*x = lambda*x

A and B are symmetric (Hermitian) and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying a range of values. Eigenvectors are not computed, if V is passed as nil. (NULL).

Tolerance parameter specifies 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

Tolerance + EPS / max( |a|,|b| ) ,

where EPS is the machine precision. If Tolerance 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 A to tridiagonal form.

Eigenvalues will be computed most accurately when Tolerance is set to twice the underflow threshold, not zero. If this routine returns fails , indicating that some eigenvectors did not converge, try setting Tolerance to 2*UnderflowThreshold.

If V is assinged, VInfo contains values equal to 0 at indices for which eigenvector calculation converged. Eigenvector are stored within V in columns. The returned column count may vary between calls depending on the number of eigenvectors that converged. The eigenvectors are normalized as follows:

etAzBz, etBAz, Z**T*B*Z := I; etABz , Z**T*inv(B)*Z := I.

Group

EigSymGen Method

Links

TMtx Class, TMtx Members, MtxVec Namespace, EigSymGen Method

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