Covariance of array elements

[jvdp1]

Draft proposal for covariance of array elements opened for discussion

Related to #113

To be discussed:

• Name: the currently proposed name is cov. But what about covariance,....?
• API: similar to the API of variance
• Implementation: only for arrays of rank 1 and rank 2.
• Implementation: the API accepts only 1 array.
  An implementation to compute the covariance among 2 arrays still needs to be done.

Others:
Octave cov
Matlab cov
Julia cov
R cov
Numpy cov

cov - covariance of array elements

Description

Returns the covariance of the elements of array along dimension dim if the corresponding e
lement in mask is true.

Per default, the covariance is defined as:

 cov(array) = 1/(n-1) sum_i (array(i) - mean(array) * (array(i) - mean(array))) 

where n is the number of elements.

The scaling can be changed with the logical argument corrected. If corrected is .false.,
then the sum is scaled with n, otherwise with n-1.

Syntax

result = cov(array, dim [, mask [, corrected]])

[ivan-pi]

I am fine with both cov or covariance. In case we decide to go for the long version, I would suggest renaming var to variance. They can always be renamed at import if desired, using use stdlib_stats, only: cov => covariance.

Overall a nice proposal, so I am fine with merging.

[milancurcic]

Great!

I vote for cov (is there chance of it being confused with something else? I don't think so).

[certik]

Looks good. Yes cov seems fine, consistent with other languages.

[jvdp1]

It seems that all of you agreed with cov as name for this function.
If there are no other comments about the implementation and API, it could be merged.

Note: An implementation to compute the covariance between 2 arrays still needs to be done, but it will be for another PR.

[jvdp1]

I will merge this PR. Thank you for your reviews and approvals.