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 * 2005-11-28
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 * 2005-11-28
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 * - Implement eval_euler() and eval_trapezoid().
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 * - Implement eval_euler() and eval_trapezoid().
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 *
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 *
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 * 2005-11-29
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 * 2005-11-29
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 * - Implement eval_romberg() and eval_simpson().
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 * - Implement eval_romberg() and eval_simpson().
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 * - eval_trapezoid() was giving horrible results, fix it.
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 *
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 *
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 */
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 */
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#include <cmath>
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#include <cmath>
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#include <cstdio>
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#include <cstdio>
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/**
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/**
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 * Evaluate the integral of the function given, over the interval given,
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 * Evaluate the integral of the function given, over the interval given,
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 * using the trapezoid method.
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 * using the trapezoid method.
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 *
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 *
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 * This is derived from the book's pseudocode on Pg 207.
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 *
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 * @param a the lower bound of the integral
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 * @param a the lower bound of the integral
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 * @param b the upper bound of the integral
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 * @param b the upper bound of the integral
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 * @param n the number of intervals to use
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 * @param n the number of intervals to use
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 * @param f the function to evaluate
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 * @param f the function to evaluate
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 */
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 */
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float eval_trapezoid (const float a, const float b, const int n, float(*f)(float))
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float eval_trapezoid (const float a, const float b, const int n, float(*f)(float))
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{
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{
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    const float h = (b - a) / n;
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    const float h = (b - a) / n;
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    float answer = 0.0, xi_last = 0.0, xi_now = 0.0;
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    float sum = 0.0;
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    int i = 0;
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    int i = 0;
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    xi_last = a + (i * h); // i = 0 here
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    sum = (1.0/2.0) * (f(a) + f(b));
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    for (i=1; i<=n; i++)
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    for (i=1; i<=n-1; i++)
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    {
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        xi_now = a + (i * h);
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        sum += f(a + (i * h));
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        answer += (f (xi_last) + f (xi_now) * (xi_now - xi_last));
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        xi_last = xi_now; // shift xi's
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    }
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    return answer;
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    return h * sum;
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}
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}
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/**
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/**
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 * Evaluate the integral of the function given, over the interval given,
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 * Evaluate the integral of the function given, over the interval given,
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 * using the Romberg method.
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 * using the Romberg method.