Correlation coefficient for two T-dimensional vectors

correlation.cpp

#include <stdlib.h>
#include <iostream>
#include <fstream>
#include <sstream>
#include <cmath>
#include <string>
using namespace std;

/// The sums() function computes several sums from vectors x and y,
/// and stores the values in a, b, c, d, and e
void sums(double* x, double* y, int T,
          double* a, double* b, double* c, double* d, double* e);

int main(void) {

    // FIXME
    double* x = new double[T];
    double* y = new double[T];

    // Read data from a CSV file
    // (via http://j.mp/1lu215m)
    ifstream file( "data.csv" );
    string line; 
    int line_counter = 0;
    while( getline( file, line ) ) {
        istringstream iss( line );
        string result;
        
        getline( iss, result, ',' );
        x[line_counter] = atoi( result.c_str() );

        getline( iss, result, ',' );
        y[line_counter] = atoi( result.c_str() );
    }

    // Allocate space for sums
    double a, b, c, d, e;
    a = 0.0; b = 0.0; c = 0.0; d = 0.0; e = 0.0;
    sums(x,y,T,&a,&b,&c,&d,&e);

    // Plug the sums into the correlation coefficient formula 
    double r = (T*c - a*b)/sqrt((T*d - a*a)*(T*e - b*b));

    delete[] x;
    delete[] y;

    cout << " r = " << r << "\n";

    return 0;
}

void sums(  double* x,
            double* y,
            int T,
            double* a, 
            double* b,
            double* c,
            double* d, 
            double* e) 
{
    double sum_x = 0.0;
    double sum_y = 0.0;
    double sum_xy = 0.0;
    double sum_x2 = 0.0;
    double sum_y2 = 0.0;

    for( unsigned long t=0; t < T; ++t ) {
        sum_x += x[t];
        sum_y += y[t];
        sum_xy += x[t] * y[t];
        sum_x2 += x[t]*x[t];
        sum_y2 += y[t]*y[t];
    }

    *a = sum_x;
    *b = sum_y;
    *c = sum_xy;
    *d = sum_x2; 
    *e = sum_y2;
}