corr_a

corr_a(fs1, fs2[, area])

Computes the correlation between fs1 and fs2 over a weighted area.

Parameters

• fs1 (Fieldset) – first input fieldset

• fs2 (Fieldset) – second input fieldset

• area (list) – area as [N,W,S,E] to perform the computations

Return type

number or list

If area is not specified the whole field will be used in the calculation. The result is a number for a single field or a list for a multi-field Fieldset.

With n fields in fs by denoting the i-th value in the k-th field by \(x_{i}^{k}\) the output values can be written as:

\[ \begin{align}\begin{aligned}z_{i} = \frac {1}{N} \sum_{k}^{N}x_{i}^{k}y_{i}^{k} - \frac {1}{N} \sum_{k}^{N}x_{i}^{k} \frac {1}{N} \sum_{k}^{N}y_{i}^{k}\\v_{i} = \frac {1}{n} \sum_{k}^{n} (x_{i}^{k})^2 - \frac {1}{n} (\sum_{k}^{n} x_{i}^{k})^2\end{aligned}\end{align} \]

Note

The following lines are equivalent although the first one is more efficient:

z = corr_a (x, y)
z = covar_a (x, y) / (sqrt(var_a(x)) * sqrt(var_a(y)))