问题
I am trying to integrate a very simple function. integral(x.dx). Instead of getting an answer of 1, I am getting an answer as 0, or 0.5 when I include limits from 0 to 1. Is there something I misunderstand about the implementation of the integration in apache commons library?
import org.apache.commons.math3.analysis.integration.*;
import org.apache.commons.math3.analysis.polynomials.*;
public static void main(String args[])
{
SimpsonIntegrator simpson = new SimpsonIntegrator();
TrapezoidIntegrator trapezoid = new TrapezoidIntegrator();
double[] vector = new double[2];
vector[0] = 0;
vector[1] = 1;
PolynomialFunction f = new PolynomialFunction(vector);
UnivariateFunction uf = (UnivariateFunction)new PolynomialFunction(vector);
System.out.println("To String " + uf.toString());
System.out.println("Degree: " + f.degree());
double i = simpson.integrate(10, uf, -Float.MAX_VALUE, Float.MAX_VALUE);
double j = trapezoid.integrate(10, uf, 0, 1);
System.out.println("Simpson integral : " + i);
System.out.println("Trapezoid integral : " + j);
}
/*** OUTPUT
To String x
Degree: 1
Simpson integral : 0.0
Trapezoid integral : 0.5
***/
回答1:
I think this is functioning as expected. The function you are integrating is the straight line of slope 1.
Between 0 and 1 you get an area of 0.5. Over all of the space the integrals above and below cancel out to give 0.
来源:https://stackoverflow.com/questions/16896961/how-to-compute-integration-of-a-function-in-apache-commons-math3-library