Initial data commit

Task/Numerical-integration/Java/numerical-integration.java

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