利用java求积分（定积分和无穷限积分）

// compute the numeric integration.
public class Integration {

public Integration(){}

// apply simpson rule to approximately compute the integration.
public double simpsonRule(double upper, double lower, int n, Function df) {
double result = 0;

double unit = (upper-lower)/n;
double factor1 = unit / 3;
double[] x = new double[n+1];

for (int i = 0; i < x.length; i++) {
x[i] = lower + unit*i;
}
for (int i = 0; i < x.length; i++) {
if(i==0 || i==x.length-1) {
result += df.fun(x[i]);
}else if(i%2 == 0) { // if i is even num.
result += 2*df.fun(x[i]);
}else { // if i is odd num.
result += 4*df.fun(x[i]);
}
}

result *= factor1;
return result;
}
// compute the standard normal distribution integration
// refer to the integration table in p382 of "probability and statistics" from ZheJiang University.
public double stdGaussValue(double realUpper) {
Integration integration = new Integration();
double upper = 1.0;
double lower = 0.0;
int n = 200; // splited into 200 subintervals.
// double realUpper = 0.03;

if(realUpper >= 5.0) {
return 1.0;
}
double result =
integration.simpsonRule(upper, lower, n, new Function() {
@Override
public double fun(double x) {
if(x==0) {
return 0;
}
double t =  realUpper-(1-x)/x;
return Math.pow(Math.E, -0.5*t*t) / (x*x);
}
});
result /= Math.pow(2*Math.PI, 0.5);
result = new BigDecimal(result).
setScale(6, RoundingMode.HALF_UP).doubleValue(); // save 6 decimal places.
return result;
}
}

public class IntegrationTest { //test case.

public static void main(String[] args) {
Integration integration = new Integration();
double result = integration.stdGaussValue(4.42);

System.out.println(result);
}

public static void main3(String[] args) {
Integration integration = new Integration();
double upper = 1.0;
double lower = 0.0;
int n = 50;
double realUpper = 0.39;

double result =
integration.simpsonRule(upper, lower, n, new Function() {
@Override
public double fun(double x) {
if(x==0) {
return 0;
}
double t =  realUpper-(1-x)/x;
return Math.pow(Math.E, -0.5*t*t) / (x*x);
}
});
result /= Math.pow(2*Math.PI, 0.5);

result = new BigDecimal(result).
setScale(4, RoundingMode.HALF_UP).doubleValue();
System.out.println(result);
}

public static void main2(String[] args) {
Integration integration = new Integration();
double upper = 1.0;
double lower = 0.0;
int n = 10;

double result =
integration.simpsonRule(upper, lower, n, new Function() {
@Override
public double fun(double x) {
return Math.pow(Math.E, -x*x/2);
}
});
result /= Math.pow(2*Math.PI, 0.5);
System.out.println(result);

BigDecimal decimal = new BigDecimal(result).setScale(4, RoundingMode.HALF_UP);
result = Double.valueOf(decimal.toString());
System.out.println(result);
}

public static void main1(String[] args) {
Integration integration = new Integration();
double upper = 1.0;
double lower = 0;
int n = 10;

double result =
integration.simpsonRule(upper, lower, n, new Function() {
@Override
public double fun(double x) {
return 4 / (1+Math.pow(x,2.0));
}
});
System.out.println(result);
}
}