Jakarta Commons Cookbook

8.7. Solving a System of Linear Equations

Problem

You need to find the values of x, y, and z that satisfy the system of linear equations shown in Figure 8-2.

Figure 8-2. A system of linear equations

Solution

Use the RealMatrix and RealMatrixImpl from Commons Math. Represent this system of linear equations as matrices in the Ax=B form, as shown in Figure 8-3. Place the coefficients of A in a RealMatrix, and put B in a double[]. Call the solve( ) method on RealMatrix to retrieve a double[] of values for x, y, and z that satisfy this system of equations.

Figure 8-3. System of linear equations in Ax=B form

The following example takes the coefficients and constants from Figure 8-3 and uses a RealMatrix to solve this system:

import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.linear.RealMatrixImpl;
import org.apache.commons.lang.ArrayUtils;

double[][] coefficients = { { 3.0, 20.0, 89.0 },
                            { 4.0, 40.0, 298.0 },
                            { 7.0, 21.0, 0.42 } };
double[] values = { 1324, 2999, 2039 };

RealMatrix matrix = new RealMatrixImpl( );
matrix.setData( coefficients );
        
double[] answers = matrix.solve( values );

System.out.println( "Answers: " + ArrayUtils.toString( answers ) );

This example solves this system of equations and prints out the values of x, y, and z using Commons Lang