75 lines
2.1 KiB
Java
75 lines
2.1 KiB
Java
import static java.lang.Math.*;
|
|
import java.util.function.Function;
|
|
|
|
public class Test {
|
|
final static int N = 5;
|
|
|
|
static double[] lroots = new double[N];
|
|
static double[] weight = new double[N];
|
|
static double[][] lcoef = new double[N + 1][N + 1];
|
|
|
|
static void legeCoef() {
|
|
lcoef[0][0] = lcoef[1][1] = 1;
|
|
|
|
for (int n = 2; n <= N; n++) {
|
|
|
|
lcoef[n][0] = -(n - 1) * lcoef[n - 2][0] / n;
|
|
|
|
for (int i = 1; i <= n; i++) {
|
|
lcoef[n][i] = ((2 * n - 1) * lcoef[n - 1][i - 1]
|
|
- (n - 1) * lcoef[n - 2][i]) / n;
|
|
}
|
|
}
|
|
}
|
|
|
|
static double legeEval(int n, double x) {
|
|
double s = lcoef[n][n];
|
|
for (int i = n; i > 0; i--)
|
|
s = s * x + lcoef[n][i - 1];
|
|
return s;
|
|
}
|
|
|
|
static double legeDiff(int n, double x) {
|
|
return n * (x * legeEval(n, x) - legeEval(n - 1, x)) / (x * x - 1);
|
|
}
|
|
|
|
static void legeRoots() {
|
|
double x, x1;
|
|
for (int i = 1; i <= N; i++) {
|
|
x = cos(PI * (i - 0.25) / (N + 0.5));
|
|
do {
|
|
x1 = x;
|
|
x -= legeEval(N, x) / legeDiff(N, x);
|
|
} while (x != x1);
|
|
|
|
lroots[i - 1] = x;
|
|
|
|
x1 = legeDiff(N, x);
|
|
weight[i - 1] = 2 / ((1 - x * x) * x1 * x1);
|
|
}
|
|
}
|
|
|
|
static double legeInte(Function<Double, Double> f, double a, double b) {
|
|
double c1 = (b - a) / 2, c2 = (b + a) / 2, sum = 0;
|
|
for (int i = 0; i < N; i++)
|
|
sum += weight[i] * f.apply(c1 * lroots[i] + c2);
|
|
return c1 * sum;
|
|
}
|
|
|
|
public static void main(String[] args) {
|
|
legeCoef();
|
|
legeRoots();
|
|
|
|
System.out.print("Roots: ");
|
|
for (int i = 0; i < N; i++)
|
|
System.out.printf(" %f", lroots[i]);
|
|
|
|
System.out.print("\nWeight:");
|
|
for (int i = 0; i < N; i++)
|
|
System.out.printf(" %f", weight[i]);
|
|
|
|
System.out.printf("%nintegrating Exp(x) over [-3, 3]:%n\t%10.8f,%n"
|
|
+ "compared to actual%n\t%10.8f%n",
|
|
legeInte(x -> exp(x), -3, 3), exp(3) - exp(-3));
|
|
}
|
|
}
|