更高效的集成回路 [英] More efficient Integration Loop

问题描述

public double Integral(double[] x, double intPointOne, double intPointTwo)
{
    double integral = 0;
    double i = intPointOne;
    do
    {
        integral += Function(x[i])*.001;
        i = i + .001;
    }
    while (i <= intPointTwo);
    return integral;
}

下面是简单地用一个函数我一定要整合来自X1-X2功能零件的总和。我怎么可以让这个循环更高效（使用更少的循环），但更准确呢？

Here's a function I have to integrate a function from x1-x2 simply using a summation of parts. How can I make this loop more efficient (using less loops), but more accurate?

的其中，功能变化，每一次迭代中，但它应该是无关紧要的，因为它的幅度（或边界秩序）应该保持相对同... 的

Where Function changes every iteration, but it should be irrelevant as it's order of magnitude (or boundary) should stay relatively the same...

推荐答案

1）考虑部分的http://apps.nrbook.com/c/index.html 以不同的算法。

1) look into section 4.3 of http://apps.nrbook.com/c/index.html for a different algorithm.

2）要控制你可能需要指定范围的准确度/速度系数 x_low 和 x_high 以及你想在积分多少片。所以，你的函数看起来像这样

2) To control the accuracy/speed factor you may need to specify the bounds x_low and x_high as well as how many slices you want in the integral. So your function would look like this

// Integrate function f(x) using the trapezoidal rule between x=x_low..x_high
double Integrate(Func<double,double> f, double x_low, double x_high, int N_steps)
{
    double h = (x_high-x_low)/N_steps;
    double res = (f(x_low)+f(x_high))/2;
    for(int i=1; i < N; i++)
    {
        res += f(x_low+i*h);
    }
    return h*res;
}

一旦你明白了这个基本的整合，你可以移动到更周密的计划提到在数值Recipies和其他来源。

Once you understand this basic integration, you can move on to more elaborate schemes mentioned in Numerical Recipies and other sources.

要使用此代码的问题，比如命令A =整合（Math.Sin，0，Math.PI， 1440）;

To use this code issue a command like A = Integrate( Math.Sin, 0, Math.PI, 1440 );

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