Example: Covariances

This example illustrates the use of Covariances class for the first 50 observations in the Fisher iris data (Fisher 1936). Note that the first variable is constant over the first 50 observations.

import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.PrintMatrix;
import com.imsl.math.PrintMatrixFormat;

public class CovariancesEx1 {
    public static void main(String args[]) throws Exception {
        double[][] x = {
            {1.0, 5.1, 3.5, 1.4, .2}, {1.0, 4.9, 3.0, 1.4, .2},
            {1.0, 4.7, 3.2, 1.3, .2}, {1.0, 4.6, 3.1, 1.5, .2},
            {1.0, 5.0, 3.6, 1.4, .2}, {1.0, 5.4, 3.9, 1.7, .4},
            {1.0, 4.6, 3.4, 1.4, .3}, {1.0, 5.0, 3.4, 1.5, .2},
            {1.0, 4.4, 2.9, 1.4, .2}, {1.0, 4.9, 3.1, 1.5, .1},
            {1.0, 5.4, 3.7, 1.5, .2}, {1.0, 4.8, 3.4, 1.6, .2},
            {1.0, 4.8, 3.0, 1.4, .1}, {1.0, 4.3, 3.0, 1.1, .1},
            {1.0, 5.8, 4.0, 1.2, .2}, {1.0, 5.7, 4.4, 1.5, .4},
            {1.0, 5.4, 3.9, 1.3, .4}, {1.0, 5.1, 3.5, 1.4, .3},
            {1.0, 5.7, 3.8, 1.7, .3}, {1.0, 5.1, 3.8, 1.5, .3},
            {1.0, 5.4, 3.4, 1.7, .2}, {1.0, 5.1, 3.7, 1.5, .4},
            {1.0, 4.6, 3.6, 1.0, .2}, {1.0, 5.1, 3.3, 1.7, .5},
            {1.0, 4.8, 3.4, 1.9, .2}, {1.0, 5.0, 3.0, 1.6, .2},
            {1.0, 5.0, 3.4, 1.6, .4}, {1.0, 5.2, 3.5, 1.5, .2},
            {1.0, 5.2, 3.4, 1.4, .2}, {1.0, 4.7, 3.2, 1.6, .2},
            {1.0, 4.8, 3.1, 1.6, .2}, {1.0, 5.4, 3.4, 1.5, .4},
            {1.0, 5.2, 4.1, 1.5, .1}, {1.0, 5.5, 4.2, 1.4, .2},
            {1.0, 4.9, 3.1, 1.5, .2}, {1.0, 5.0, 3.2, 1.2, .2},
            {1.0, 5.5, 3.5, 1.3, .2}, {1.0, 4.9, 3.6, 1.4, .1},
            {1.0, 4.4, 3.0, 1.3, .2}, {1.0, 5.1, 3.4, 1.5, .2},
            {1.0, 5.0, 3.5, 1.3, .3}, {1.0, 4.5, 2.3, 1.3, .3},
            {1.0, 4.4, 3.2, 1.3, .2}, {1.0, 5.0, 3.5, 1.6, .6},
            {1.0, 5.1, 3.8, 1.9, .4}, {1.0, 4.8, 3.0, 1.4, .3},
            {1.0, 5.1, 3.8, 1.6, .2}, {1.0, 4.6, 3.2, 1.4, .2},
            {1.0, 5.3, 3.7, 1.5, .2}, {1.0, 5.0, 3.3, 1.4, .2}
        };
        Covariances co = new Covariances(x);
        
        PrintMatrix pm = 
        new PrintMatrix("Sample Variances-covariances Matrix");
        
        NumberFormat nf = NumberFormat.getInstance();
        nf.setMinimumFractionDigits(4);
        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.setNumberFormat(nf);
        pm.setMatrixType(PrintMatrix.UPPER_TRIANGULAR);
        
        pm.print(pmf, co.compute(Covariances.VARIANCE_COVARIANCE_MATRIX));
    }
}

Output

    Sample Variances-covariances Matrix
     0       1       2       3       4     
0  0.0000  0.0000  0.0000  0.0000  0.0000  
1          0.1242  0.0992  0.0164  0.0103  
2                  0.1437  0.0117  0.0093  
3                          0.0302  0.0061  
4                                  0.0111