Pearson correlation among elements of an array

[jvdp1]

Related to the functions cov and var

As usual, everything can/must be discussed.

Other implementations

• Octave corr
• Matlab corr
• R cor
• Julia cor
• Numpy corrcoef

Specs:

corr - Pearson correlation of array elements

Description

Returns the Pearson correlation of the elements of array along dimension dim if the corresponding element in mask is true.

The Pearson correlation between two rows (or columns), say x and y, of array is defined as:

 corr(x, y) = cov(x, y) / sqrt( var(x) * var(y))

Syntax

result = corr(array, dim [, mask])

Arguments

array: Shall be a rank-1 or a rank-2 array of type integer, real, or complex.

dim: Shall be a scalar of type integer with a value in the range from 1 to n, where n is the rank of array.

mask (optional): Shall be of type logical and either a scalar or an array of the same shape as array.

Return value

If array is of rank 1 and of type real or complex, the result is of type real corresponding to the type of array.
If array is of rank 2 and of type real or complex, the result is of the same type as array.
If array is of type integer, the result is of type real(dp).

If array is of rank 1 and of size larger than 1, a scalar equal to 1 is returned. Otherwise, IEEE NaN is returned.
If array is of rank 2, a rank-2 array with the corresponding correlations is returned.

If mask is specified, the result is the Pearson correlation of all elements of array corresponding to true elements of mask. If every element of mask is false, the result is IEEE
NaN.

Example

program demo_corr
    use stdlib_experimental_stats, only: corr
    implicit none
    real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
    real :: y(1:2, 1:3) = reshape([ -1., 40., -3., 4., 10., 6. ], [ 2, 3])
    print *, corr(x, 1)           !returns 1.
    print *, corr(y, 2)           !returns reshape([ 1., -.32480, -.32480, 1. ], [ 2, 3])
end program demo_corr

[certik]

That looks good to me, thanks!

[certik]

Otherwise I think it looks good. Thanks!

[certik]

Thanks for fixing it. I think it looks great now and ready to merge.

[milancurcic]

Thank you!

[jvdp1]

If there are no other objections/comments to this PR, I will then merge this evening.

[jvdp1]

Thank you for your inputs. I'll merge.