Trait ndarray_stats::CorrelationExt

source · 
pub trait CorrelationExt<A, S>where
    S: Data<Elem = A>,{
    fn cov(&self, ddof: A) -> Array2<A>
    where
        A: Float + FromPrimitive;
    fn pearson_correlation(&self) -> Array2<A>
    where
        A: Float + FromPrimitive;
}
Expand description

Extension trait for ArrayBase providing functions to compute different correlation measures.

Required Methods

Return the covariance matrix C for a 2-dimensional array of observations M.

Let (r, o) be the shape of M:

  • r is the number of random variables;
  • o is the number of observations we have collected for each random variable.

Every column in M is an experiment: a single observation for each random variable. Each row in M contains all the observations for a certain random variable.

The parameter ddof specifies the “delta degrees of freedom”. For example, to calculate the population covariance, use ddof = 0, or to calculate the sample covariance (unbiased estimate), use ddof = 1.

The covariance of two random variables is defined as:

               1       n
cov(X, Y) = ――――――――   ∑ (xᵢ - x̅)(yᵢ - y̅)
            n - ddof  i=1

where

    1   n
x̅ = ―   ∑ xᵢ
    n  i=1

and similarly for ̅y.

Panics if ddof is greater than or equal to the number of observations, if the number of observations is zero and division by zero panics for type A, or if the type cast of n_observations from usize to A fails.

Example
extern crate ndarray;
extern crate ndarray_stats;
use ndarray::{aview2, arr2};
use ndarray_stats::CorrelationExt;

let a = arr2(&[[1., 3., 5.],
               [2., 4., 6.]]);
let covariance = a.cov(1.);
assert_eq!(
   covariance,
   aview2(&[[4., 4.], [4., 4.]])
);

Return the Pearson correlation coefficients for a 2-dimensional array of observations M.

Let (r, o) be the shape of M:

  • r is the number of random variables;
  • o is the number of observations we have collected for each random variable.

Every column in M is an experiment: a single observation for each random variable. Each row in M contains all the observations for a certain random variable.

The Pearson correlation coefficient of two random variables is defined as:

             cov(X, Y)
rho(X, Y) = ――――――――――――
            std(X)std(Y)

Let R be the matrix returned by this function. Then

R_ij = rho(X_i, X_j)

Panics if M is empty, if the type cast of n_observations from usize to A fails or if the standard deviation of one of the random

Example

variables is zero and division by zero panics for type A.

extern crate ndarray;
extern crate ndarray_stats;
use ndarray::arr2;
use ndarray_stats::CorrelationExt;

let a = arr2(&[[1., 3., 5.],
               [2., 4., 6.]]);
let corr = a.pearson_correlation();
assert!(
    corr.all_close(
        &arr2(&[
            [1., 1.],
            [1., 1.],
        ]),
        1e-7
    )
);

Implementations on Foreign Types

Implementors