6.4 Computing Selected Eigenvalues

Often you require only some of the eigenvalues: either all the eigenvalues in a range of real numbers (a,b), or the i^th through j^th eigenvalues. You can solve these problems using the server objects DoubleSymRangeEigServer and DoubleSymSomeEigServer. In addition to showing how to solve this specific problem, this section demonstrates how to use a server object to adjust an algorithm's parameters.

This program computes the eigenvalues of the matrix A in the range (a,b). Eigenvectors are not computed.

#include <iostream.h>
#include <dsymmat.h>
#include <rw/dseigsrv.h>

main()
{
    DoubleSymMat A;                           // 1
    double a,b;
    cin >> A >> a >> b;
    DoubleSymRangeEigServer server;           // 2
    server.computeEigenVectors(FALSE);        // 3
    server.setRange(a,b);                     // 4
    DoubleSymEigDecomp decomp = server(A);    // 5
    cout << decomp.eigenValues() << endl;
}

//1	First, the matrix and the range are read in from standard input.
//2	When the eigenvalue server is constructed, the algorithm parameters are all set to default values.
//3	Here we change the setting of a parameter so that only eigenvalues, and not eigenvectors, are computed.
//4	Here we set the range in which we are interested and ...
//5	We compute the decomposition.

If instead of needing all the eigenvalues in a certain range, you need the i^th through j^th eigenvalues, you use a DoubleSymSomeEigServer object like this:

#include <iostream.h>
#include <rw/dsymmat.h>
#include <rw/dseigsrv.h>

main()
{
    DoubleSymMat A; 
    int i,j;
    cin >> A >> i >> j;
    DoubleSymSomeEigServer server; 
    server.computeEigenVectors(FALSE); 
    server.setRange(RWRange(i,j));                   // 1
    DoubleSymEigDecomp decomp = server(A); 
    cout << decomp.eigenValues() << endl;
}

The program is the same as the previous program except for //1, where we set the range of interest. The range is set using one of the subscripting objects RWSlice, RWRange, or RWToEnd. See the Math.h++ User's Guide and Reference Manual for more information on the subscripting objects.