// Calculates the correlation coefficient for two lists of numbers in an array
// in O(5n)
double correlation_coefficient(double a[], double b[], int n) {
double arithmetic_meanA = arithmetic_mean(a, n); // O(n)
double arithmetic_meanB = arithmetic_mean(b, n); // O(n)
double stddevA = standard_deviation(a, n); // O(2n)
double stddevB = standard_deviation(b, n); // O(2n)
double total = 0;
for (int i = 0; i < n; ++i) { // O(n)
total += ((a[i] - arithmetic_meanA) / stddevA) * ((b[i] - arithmetic_meanB) / stddevB);
}
return total / (double) (n - 1);
}
Value_type<I> correlation_coefficient(I firstA, I lastA,
I firstB, I lastB, T id) {
typedef Value_type<I> R;
R arithmetic_meanA = arithmetic_mean(firstA, lastA, id);
R arithmetic_meanB = arithmetic_mean(firstB, lastB, id);
R stddevA = standard_deviation(firstA, lastA, id);
R stddevB = standard_deviation(firstB, lastB, id);
R count = R(id);
R total = R(id);
while (firstA != lastA) {
total += ((*firstA - arithmetic_meanA) / stddevA) * ((*firstB - arithmetic_meanB) / stddevB);
++firstA;
++firstB;
++count;
}
return total / (count - R(1));
}
// Calculates the variance in a list of numbers in an array in O(2n)
double variance(double a[], int n) {
double m = arithmetic_mean(a, n); // O(n)
double sumSquares = 0;
for (int i = 0; i < n; ++i) { // O(n)
double diff = a[i] - m;
sumSquares += (diff * diff);
}
return sumSquares / (double) (n - 1);
}
Value_type<I> variance(I first, I last, T id) {
typedef Value_type<I> R;
R count = R(id);
R var = R(id);
R m = arithmetic_mean(first, last, id);
while (first != last) {
R diff = (*first) - m;
var += (diff * diff);
++count;
++first;
}
return var / (count - R(1));
}
inline S
generalized_mean(I first, I last, T p) {
// Check for well known cases.
if (p == -1)
return harmonic_mean(first, last);
if (p == 0)
return geometric_mean(first, last);
if (p == 1)
return arithmetic_mean(first, last);
if (p == 2)
return quadratic_mean(first, last);
if (p == 3)
return cubic_mean(first, last);
// Either handle the infinity case or compute the generalized
// value.
if (is_infinity(p))
return generalized_mean_inf(first, last, p);
else
return generalized_mean_non_inf(first, last, p);
}