124 lines
3.3 KiB
Java
124 lines
3.3 KiB
Java
class NumericalIntegration
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{
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interface FPFunction
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{
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double eval(double n);
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}
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public static double rectangularLeft(double a, double b, int n, FPFunction f)
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{
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return rectangular(a, b, n, f, 0);
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}
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public static double rectangularMidpoint(double a, double b, int n, FPFunction f)
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{
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return rectangular(a, b, n, f, 1);
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}
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public static double rectangularRight(double a, double b, int n, FPFunction f)
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{
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return rectangular(a, b, n, f, 2);
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}
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public static double trapezium(double a, double b, int n, FPFunction f)
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{
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double range = checkParamsGetRange(a, b, n);
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double nFloat = (double)n;
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double sum = 0.0;
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for (int i = 1; i < n; i++)
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{
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double x = a + range * (double)i / nFloat;
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sum += f.eval(x);
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}
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sum += (f.eval(a) + f.eval(b)) / 2.0;
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return sum * range / nFloat;
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}
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public static double simpsons(double a, double b, int n, FPFunction f)
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{
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double range = checkParamsGetRange(a, b, n);
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double nFloat = (double)n;
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double sum1 = f.eval(a + range / (nFloat * 2.0));
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double sum2 = 0.0;
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for (int i = 1; i < n; i++)
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{
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double x1 = a + range * ((double)i + 0.5) / nFloat;
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sum1 += f.eval(x1);
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double x2 = a + range * (double)i / nFloat;
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sum2 += f.eval(x2);
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}
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return (f.eval(a) + f.eval(b) + sum1 * 4.0 + sum2 * 2.0) * range / (nFloat * 6.0);
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}
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private static double rectangular(double a, double b, int n, FPFunction f, int mode)
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{
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double range = checkParamsGetRange(a, b, n);
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double modeOffset = (double)mode / 2.0;
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double nFloat = (double)n;
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double sum = 0.0;
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for (int i = 0; i < n; i++)
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{
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double x = a + range * ((double)i + modeOffset) / nFloat;
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sum += f.eval(x);
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}
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return sum * range / nFloat;
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}
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private static double checkParamsGetRange(double a, double b, int n)
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{
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if (n <= 0)
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throw new IllegalArgumentException("Invalid value of n");
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double range = b - a;
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if (range <= 0)
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throw new IllegalArgumentException("Invalid range");
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return range;
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}
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private static void testFunction(String fname, double a, double b, int n, FPFunction f)
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{
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System.out.println("Testing function \"" + fname + "\", a=" + a + ", b=" + b + ", n=" + n);
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System.out.println("rectangularLeft: " + rectangularLeft(a, b, n, f));
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System.out.println("rectangularMidpoint: " + rectangularMidpoint(a, b, n, f));
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System.out.println("rectangularRight: " + rectangularRight(a, b, n, f));
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System.out.println("trapezium: " + trapezium(a, b, n, f));
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System.out.println("simpsons: " + simpsons(a, b, n, f));
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System.out.println();
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return;
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}
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public static void main(String[] args)
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{
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testFunction("x^3", 0.0, 1.0, 100, new FPFunction() {
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public double eval(double n) {
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return n * n * n;
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}
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}
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);
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testFunction("1/x", 1.0, 100.0, 1000, new FPFunction() {
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public double eval(double n) {
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return 1.0 / n;
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}
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}
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);
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testFunction("x", 0.0, 5000.0, 5000000, new FPFunction() {
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public double eval(double n) {
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return n;
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}
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}
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);
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testFunction("x", 0.0, 6000.0, 6000000, new FPFunction() {
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public double eval(double n) {
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return n;
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}
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}
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);
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return;
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}
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}
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