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R1106/solutions/chapter-05/ch-05-ex-04-solution.cpp
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ch-05-ex-04-solution.cpp
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/*
* chapter-05-exercise-04.cpp
*
* Standard deviation of array
* Input the array as extra command line arguments:
* ./ch-05-ex-04-solution 5.0 4.8 5.3 2.9
*
* Created on: Oct 8, 2012
* Author: Radu Popescu <radu.popescu@epfl.ch>
*/
#include <cstdlib>
#include <cmath>
#include <iostream>
void mean_and_std(const double* const v, const double size,
double& mean, double& stdev)
{
mean = 0.0;
for (int i = 0; i < size; ++i) {
mean += v[i];
}
mean /= size;
double s1 = 0.0;
for (int i = 0; i < size; ++i) {
s1 += std::pow(v[i] - mean, 2);
}
stdev = std::sqrt(s1 / (size - 1));
}
/*
* This function computes the mean and standard deviation of a series
* of floating point numbers using a recurrence relation.
* This is useful for continuous processes and is resistant to round-off
* error.
*
* Attributed to B.P. Welford, Technometrics, 4,(1962), 419-420.
*/
void mean_and_std_rec(const double* const v, const double size,
double& mean, double& stdev)
{
double mean_prev = v[0];
double stdev_accum = 0.0;
double mean_next = 0.0;
for (int i = 1; i < size; ++i) {
mean_next = mean_prev + (v[i] - mean_prev) / (i + 1);
stdev_accum += (v[i] - mean_prev) * (v[i] - mean_next);
mean_prev = mean_next;
}
mean = mean_next;
stdev = std::sqrt(stdev_accum / (size - 1));
}
int main(int argc, char* argv[])
{
if (argc == 1) {
std::cout << "Please input a series of floating point numbers:\n"
<< " ./ch-05-ex-04-solution 5.0 4.8 5.3 2.9"
<< std::endl;
return -1;
}
const int n = argc - 1;
double* const v = new double[n];
for (int i = 0; i < n; ++i) {
v[i] = std::atof(argv[i + 1]);
}
double mean;
double std_deviation;
mean_and_std(v, n, mean, std_deviation);
std::cout << "The mean and standard deviation are: "
<< mean << " and " << std_deviation << std::endl;
mean_and_std_rec(v, n, mean, std_deviation);
std::cout << "The mean and standard deviation are: "
<< mean << " and " << std_deviation << std::endl;
delete[] v;
return 0;
}
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