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Squashed commit of the following: commit 9cd7538 Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 22:48:56 2020 +0200 corr_dev: addition of specs commit 4af1d2d Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 22:29:42 2020 +0200 corr_dev: addition of tests for csp and int32 commit aef4416 Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 22:29:08 2020 +0200 corr_dev: addition of tests for csp and int32 commit 0e6ec5d Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 22:19:56 2020 +0200 corr_dev: clarification commit 1fdabd9 Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 22:14:44 2020 +0200 corr_dev: correction of an issue with complex commit 1632355 Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 21:41:12 2020 +0200 corr_dev:completed impl commit 1fe73b1 Merge: 9da1d97 ce987d2 Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 13:13:46 2020 +0200 Merge remote-tracking branch 'upstream/master' into corr_dev commit 9da1d97 Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 12:46:05 2020 +0200 corr_dev: addition of tests for int64 commit d03d828 Author: Vandenplas, Jeremie <[email protected]> Date: Sat May 16 12:22:13 2020 +0200 corr_dev: addition of test for dp complex numbers commit 7901ee2 Author: Vandenplas, Jeremie <[email protected]> Date: Fri May 15 20:18:03 2020 +0200 corr_dev: correction for vector with all elements false commit 2a119c2 Author: Vandenplas, Jeremie <[email protected]> Date: Fri May 15 19:02:12 2020 +0200 corr_dev: done until mask commit 19c1f8e Author: Vandenplas, Jeremie <[email protected]> Date: Fri May 15 16:42:47 2020 +0200 corr_dev: implemented some correlation functions commit ec16e9c Author: Vandenplas, Jeremie <[email protected]> Date: Fri May 15 16:12:13 2020 +0200 corr_dev: init
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‎doc/specs/stdlib_experimental_stats.md

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@@ -6,6 +6,54 @@ title: experimental_stats
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[TOC]
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## `corr` - Pearson correlation of array elements
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### Description
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Returns the Pearson correlation of the elements of `array` along dimension `dim` if the corresponding element in `mask` is `true`.
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The Pearson correlation between two rows (or columns), say `x` and `y`, of `array` is defined as:
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```
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corr(x, y) = cov(x, y) / sqrt( var(x) * var(y))
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```
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### Syntax
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`result = corr(array, dim [, mask])`
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### Arguments
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`array`: Shall be a rank-1 or a rank-2 array of type `integer`, `real`, or `complex`.
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`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`.
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`mask` (optional): Shall be of type `logical` and either a scalar or an array of the same shape as `array`.
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### Return value
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If `array` is of rank 1 and of type `real` or `complex`, the result is of type `real` corresponding to the type of `array`.
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If `array` is of rank 2 and of type `real` or `complex`, the result is of the same type as `array`.
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If `array` is of type `integer`, the result is of type `real(dp)`.
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If `array` is of rank 1 and of size larger than 1, a scalar equal to 1 is returned. Otherwise, IEEE `NaN` is returned.
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If `array` is of rank 2, a rank-2 array with the corresponding correlations is returned.
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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`.
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### Example
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```fortran
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program demo_corr
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use stdlib_experimental_stats, only: corr
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implicit none
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real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
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real :: y(1:2, 1:3) = reshape([ -1., 40., -3., 4., 10., 6. ], [ 2, 3])
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print *, corr(x, 1) !returns 1.
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print *, corr(y, 2) !returns reshape([ 1., -.32480, -.32480, 1. ], [ 2, 3])
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end program demo_corr
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```
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## `cov` - covariance of array elements
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### Description

‎src/CMakeLists.txt

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stdlib_experimental_linalg_diag.fypp
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stdlib_experimental_optval.fypp
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stdlib_experimental_stats.fypp
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stdlib_experimental_stats_corr.fypp
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stdlib_experimental_stats_cov.fypp
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stdlib_experimental_stats_mean.fypp
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stdlib_experimental_stats_moment.fypp

‎src/stdlib_experimental_stats.fypp

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implicit none
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private
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! Public API
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public :: cov, mean, moment, var
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public :: corr, cov, mean, moment, var
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interface corr
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#:for k1, t1 in RC_KINDS_TYPES
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#:set RName = rname("corr",1, t1, k1)
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:)
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integer, intent(in) :: dim
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logical, intent(in), optional :: mask
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real(${k1}$) :: res
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end function ${RName}$
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#:endfor
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#:for k1, t1 in INT_KINDS_TYPES
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#:set RName = rname("corr",1, t1, k1, 'dp')
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:)
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integer, intent(in) :: dim
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logical, intent(in), optional :: mask
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real(dp) :: res
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end function ${RName}$
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#:endfor
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#:for k1, t1 in RC_KINDS_TYPES
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#:set RName = rname("corr_mask",1, t1, k1)
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:)
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integer, intent(in) :: dim
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logical, intent(in) :: mask(:)
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real(${k1}$) :: res
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end function ${RName}$
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#:endfor
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#:for k1, t1 in INT_KINDS_TYPES
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#:set RName = rname("corr_mask",1, t1, k1, 'dp')
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:)
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integer, intent(in) :: dim
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logical, intent(in) :: mask(:)
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real(dp) :: res
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end function ${RName}$
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#:endfor
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#:for k1, t1 in RC_KINDS_TYPES
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#:set RName = rname("corr",2, t1, k1)
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:, :)
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integer, intent(in) :: dim
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logical, intent(in), optional :: mask
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${t1}$ :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
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, merge(size(x, 1), size(x, 2), mask = 1<dim))
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end function ${RName}$
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#:endfor
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#:for k1, t1 in INT_KINDS_TYPES
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#:set RName = rname("corr",2, t1, k1, 'dp')
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:, :)
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integer, intent(in) :: dim
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logical, intent(in), optional :: mask
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real(dp) :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
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, merge(size(x, 1), size(x, 2), mask = 1<dim))
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end function ${RName}$
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#:endfor
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#:for k1, t1 in RC_KINDS_TYPES
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#:set RName = rname("corr_mask",2, t1, k1)
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:, :)
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integer, intent(in) :: dim
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logical, intent(in) :: mask(:,:)
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${t1}$ :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
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, merge(size(x, 1), size(x, 2), mask = 1<dim))
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end function ${RName}$
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#:endfor
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#:for k1, t1 in INT_KINDS_TYPES
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#:set RName = rname("corr_mask",2, t1, k1, 'dp')
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module function ${RName}$(x, dim, mask) result(res)
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${t1}$, intent(in) :: x(:, :)
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integer, intent(in) :: dim
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logical, intent(in) :: mask(:,:)
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real(dp) :: res(merge(size(x, 1), size(x, 2), mask = 1<dim)&
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, merge(size(x, 1), size(x, 2), mask = 1<dim))
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end function ${RName}$
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#:endfor
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end interface corr
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interface cov
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#:for k1, t1 in RC_KINDS_TYPES

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