# Trait ndarray_stats::CorrelationExt

``````pub trait CorrelationExt<A, S> where    S: Data<Elem = A>, {
fn cov(&self, ddof: A) -> Result<Array2<A>, EmptyInput>    where        A: Float + FromPrimitive;
fn pearson_correlation(&self) -> Result<Array2<A>, EmptyInput>    where        A: Float + FromPrimitive;
fn __private__(&self, _: PrivateMarker);
}``````
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.

If `M` is empty (either zero observations or zero random variables), it returns `Err(EmptyInput)`.

Panics if `ddof` is negative or greater than or equal to the number of observations, or if the type cast of `n_observations` from `usize` to `A` fails.

##### Example
``````use ndarray::{aview2, arr2};
use ndarray_stats::CorrelationExt;

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

If `M` is empty (either zero observations or zero random variables), it returns `Err(EmptyInput)`.

Panics if the type cast of `n_observations` from `usize` to `A` fails or if the standard deviation of one of the random variables is zero and division by zero panics for type A.

##### Example
``````use approx;
use ndarray::arr2;
use ndarray_stats::CorrelationExt;
use approx::AbsDiffEq;

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

This method makes this trait impossible to implement outside of `ndarray-stats` so that we can freely add new methods, etc., to this trait without breaking changes.

We don’t anticipate any other crates needing to implement this trait, but if you do have such a use-case, please let us know.

Warning This method is not considered part of the public API, and client code should not rely on it being present. It may be removed in a non-breaking release.