以下是Riemann Integrator的代码:
public class RiemannIntegrator {
public static void main (String [] args)
{
double lower = Double.parseDouble(args[args.length -2]);
double higher = Double.parseDouble(args[args.length -1]);
double[] coefficients = new double[args.length - 3];
if (args[0].equals("poly"))
{
for (int i = 1; i < args.length - 2; i++)
{
coefficients[i-1] = Double.parseDouble(args[i]);
}
System.out.println(integral("poly", coefficients, lower, higher));
}
}
private static double integral(String s, double[] function, double lowBound, double highBound)
{
double area = 0; // Area of the rectangle
double sumOfArea = 0; // Sum of the area of the rectangles
double width = highBound - lowBound;
if (s.equals("poly"))
{
for (int i = 1; i <= ((highBound - lowBound) / width); i++) // Represents # of rectangles
{
System.out.println("Rectangles:" + i);
for (int j = 0; j < function.length; j++) // Goes through all the coefficients
{
area = width * function[j] * Math.pow ( (double)( (i * width + lowBound + (i -1.0) * width + highBound) / 2.0 ),function.length- 1- j);
/*Above code computes area of each rectangle */
sumOfArea += area;
}
}
}
width = width / 2.0;
System.out.println("polynomial, function (of any length), lower boundary, higher boundary.");
function.toString();
System.out.println("Lower Bound:" + lowBound + ", Higher Bound: " + highBound + ".");
System.out.println("The integral is:");
return sumOfArea;
}
}
它在很大程度上起作用,然而,数学错误往往是错误的,我不知道我哪里出错了。例如,如果我想找到x ^ 3 + 2x ^ 2 + 3x函数的总和,我的计算器和Wolfram Alpha上的得到2.416667。但是,在我的程序中,它告诉我,我得到6.我认为它可能与矩形的数量有关,因为它总是告诉我,我得到一个矩形。有人可以帮忙吗?
答案 0 :(得分:0)
你需要另一个循环,类似于
double width = highBound - lowBound;
double epsilon = .001; // This determines how accurate you want the solution to be, closer to zero = more accurate
double prevValue = -1.0;
double curValue = -1.0; // initialize curValue to a negative value with greater magnitude than epsilon - this ensures that the while loop evaluates to true on the first pass
do {
... // this is where your for loop goes
prevValue = curValue;
curValue = sumOfArea;
width /= 2.0;
} while(Math.abs(prevValue - curValue) > epsilon);
这个想法是你不断减少矩形的宽度,直到宽度= w的sumOfArea与宽度= 2w的sumOfArea大致相同(即在epsilon内)。
有更快+更准确的集成算法,例如Newton-Cotes,但我假设你在此事上没有选择。