Why is my trapezoid rule implementation not producing expected results?-CodePudding

I have implemented a function to find the trapezoid rule of a given function, the function produces poor results for

$\log _{2}(x)$ .

When I try to calculate the trapezoid rule with n < 8 it produces a value much larger than the actual area, which is unexpected, I have graphed f(x) and drawn how I believe the first few numbers of trapezoids would look, and they all should be producing less than the target area.

However, as n increases, the error becomes lower and lower and at n = 10000000 it is within a 0.001 of the solution.

  private interface MathFunc {
    double apply(double value);
  }
  private static final double A = 1;
  private static final double B = 9;
  public static void main(String args[]) {
    MathFunc func = (x) -> Math.log(x) / Math.log(2);
    double realValue = 16.98776493946568;
    for(int i = 1; i <= 8; i*=2) {
      double value = trapezoidRule(A, B, func, i);
      System.out.println(i   " Trapezoid Summation for f(x): "   value);
      double absError = Math.abs(value - realValue);
      System.out.println("Abs Error: "   absError);
      System.out.println("% Error: "   (absError/realValue)*100);
      System.out.println();
    }
  }
  static double trapezoidRule(double a, double b, MathFunc f, double n) {
    double deltaX = (b-a)/n;
    double i = 0;
    double sum = 0.0;
    while( i   <= n ) {
      if(i == 0 || i == n) {
        sum  = f.apply(a   (i*deltaX));
      } else {
        sum  = 2 * f.apply(a   (i*deltaX));
      }
    }
    return (deltaX * sum) / 2.0;
  }

CodePudding user response：

while( i   <= n )

Was causing an issue, as it was doing an extra iteration.

while( i   < n )

Produces the correct values.

CodePudding user response：

If you step through trapezoidRule for n = 1 in a debugger, you'll see that the loop is executed for i=1 and i=2. Since i=2 is treated as a midpoint, it is counted twice.

Why is the loop executed for wrong values of i? The expression i uses the post-increment operator, which increments the variable after returning its value. You should be using a pre-increment operator i, or a for loop like any sane person:

for (double i = 0; i <= n; i  ) {