TMtx.Balance Property

Summary

Defines matrix balancing method.

Class
TMtx

Declaration

Property Balance: TBalanceType read FBalance write SetBalance default btFull;

Description

Defines which balance method will be used to balance the calling matrix. Balancing the calling matrix can be very useful when calculating the eigenvalues and eigenvector. Balancing operation can perform one or both of the following similarity transformations:

1.Permute the calling matrix (A) to block of upper triangular form:

where P is a permutation matrix, and A'11 and A' 33 are upper triangular. The diagonal elements of A'11 and A' 33 are eigenvalues of the calling matrix (A).

2.Apply a diagonal similarity transformation to A', to make the rows and columns of A'22 as close in norm as possible:

This scaling can reduce the norm of the matrix (that is, ||A''22|| < ||A'22||), and hence reduce the effect of rounding errors on the accuracy of computed eigenvalues and eigenvectors.

See Also
Eig
EigGen

Example 1

      var A: TMtx;
        d: TVec;
      begin
        CreateIt(A);
        // ...
        A.Balance := btFull; // applies both methods
        A.Eig(d);
        // ...
        FreeIt(A);
      end;