mc_integration.c

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

double myFunction(double x);
double monteCarloEstimate(double lowBound, double upBound, int iterations);

int main() {

  double lowerBound, upperBound;
  int iterations;

  lowerBound = 1;
  upperBound = 5;
  iterations = 200;

  double estimate = monteCarloEstimate(lowerBound, upperBound, iterations);

  printf("Estimate for %.1f -> %.1f is %.2f, (%i iterations)\n", lowerBound,
         upperBound, estimate, iterations);

  return 0;
}

double myFunction(double x)
// Function to integrate
{
  return pow(x, 4) * exp(-x);
}

double monteCarloEstimate(double lowBound, double upBound, int iterations)
// Function to execute Monte Carlo integration on predefined function
{

  double totalSum = 0;
  double randNum, functionVal;

  int iter = 0;

  while (iter < iterations - 1) {

    // Select a random number within the limits of integration
    randNum = lowBound + (float)rand() / RAND_MAX * (upBound - lowBound);

    // Sample the function's values
    functionVal = myFunction(randNum);

    // Add the f(x) value to the running sum
    totalSum += functionVal;

    iter++;
  }

  double estimate = (upBound - lowBound) * totalSum / iterations;

  return estimate;
}