stats

Descriptive statistics

corr - Pearson correlation of array elements

Status

Experimental

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 and has the same kind as array. If array is of rank 2 and of type real or complex, the result is of the same type and kind 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_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

cov - covariance of array elements

Status

Experimental

Description

Returns the covariance of the elements of array along dimension dim if the corresponding element 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]])

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.

corrected (optional): Shall be a scalar of type logical. If corrected is .true. (default value), the sum is scaled with n-1. If corrected is .false., then the sum is scaled with n.

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, a scalar with the covariance (that is the variance) of all elements in array is returned. If array is of rank 2, a rank-2 array is returned.

If mask is specified, the result is the covariance 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_cov
    use stdlib_stats, only: cov
    implicit none
    real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
    real :: y(1:2, 1:3) = reshape([ 1., 2., 3., 4., 5., 6. ], [ 2, 3])
    print *, cov(x, 1)                          !returns 3.5
    print *, cov(x, 1, corrected = .false.)     !returns 2.9167
    print *, cov(y, 1)                          !returns a square matrix of size 3 with all elements equal to 0.5
end program demo_cov

mean - mean of array elements

Status

Experimental

Description

Returns the mean of all the elements of array, or of the elements of array along dimension dim if provided, and if the corresponding element in mask is true.

Syntax

result = mean(array [, mask])

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

Arguments

array: Shall be an 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 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 dim is absent, a scalar with the mean of all elements in array is returned. Otherwise, an array of rank n-1, where n equals the rank of array, and a shape similar to that of array with dimension dim dropped is returned.

If mask is specified, the result is the mean 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_mean
    use stdlib_stats, only: mean
    implicit none
    real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
    real :: y(1:2, 1:3) = reshape([ 1., 2., 3., 4., 5., 6. ], [ 2, 3])
    print *, mean(x)                                  !returns 3.5
    print *, mean(y)                                  !returns 3.5
    print *, mean(y, 1)                               !returns [ 1.5, 3.5, 5.5 ]
    print *, mean(y, 1,y > 3.)                        !returns [ NaN, 4.0, 5.5 ]
end program demo_mean

moment - central moments of array elements

Status

Experimental

Description

Returns the k-th order central moment of all the elements of array, or of the elements of array along dimension dim if provided, and if the corresponding element in mask is true.

If a scalar or an array center is provided, the function returns the k-th order moment about 'center', of all the elements of array, or of the elements of array along dimension dim if provided, and if the corresponding element in mask is true.

The k-th order central moment is defined as :

 moment(array) = 1/n sum_i (array(i) - mean(array))^k

where n is the number of elements.

The k-th order moment about center is defined as :

 moment(array) = 1/n sum_i (array(i) - center)^k

Syntax

result = moment(array, order [, center [, mask]])

result = moment(array, order, dim [, center [, mask]])

Arguments

array: Shall be an array of type integer, real, or complex.

order: Shall be an scalar of type integer.

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.

center (optional): Shall be a scalar of the same type of result if dim is not provided. If dim is provided, center shall be a scalar or an array (with a shape similar to that of array with dimension dim dropped) of the same type of result.

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 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 dim is absent, a scalar with the k-th (central) moment of all elements in array is returned. Otherwise, an array of rank n-1, where n equals the rank of array, and a shape similar to that of array with dimension dim dropped is returned.

If mask is specified, the result is the k-th (central) moment 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_moment
    use stdlib_stats, only: moment
    implicit none
    real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
    real :: y(1:2, 1:3) = reshape([ 1., 2., 3., 4., 5., 6. ], [ 2, 3])
    print *, moment(x, 2)                            !returns 2.9167
    print *, moment(y, 2)                            !returns 2.9167
    print *, moment(y, 2, 1)                         !returns [0.25, 0.25, 0.25]
    print *, moment(y, 2, 1, mask = (y > 3.))        !returns [NaN, 0., 0.25]
    print *, moment(x, 2, center = 0.)               !returns 15.1667
    print *, moment(y, 1, 1, center = 0.)            !returns [1.5, 3.5, 5.5]
end program demo_moment

var - variance of array elements

Status

Experimental

Description

Returns the variance of all the elements of array, or of the elements of array along dimension dim if provided, and if the corresponding element in mask is true.

Per default, the variance is defined as the best unbiased estimator and is computed as:

 var(array) = 1/(n-1) sum_i (array(i) - mean(array))^2

where n is the number of elements.

The use of the term n-1 for scaling is called Bessel 's correction. 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 = var(array [, mask [, corrected]])

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

Arguments

array: Shall be an 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.

corrected (optional): Shall be a scalar of type logical. If corrected is .true. (default value), the sum is scaled with n-1. If corrected is .false., then the sum is scaled with n.

Return value

If array is of type real or complex, the result is of type real corresponding to the type of array. If array is of type integer, the result is of type real(dp).

If dim is absent, a scalar with the variance of all elements in array is returned. Otherwise, an array of rank n-1, where n equals the rank of array, and a shape similar to that of array with dimension dim dropped is returned.

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

If the variance is computed with only one single element, then the result is IEEE NaN if corrected is .true. and is 0. if corrected is .false..

Example

program demo_var
    use stdlib_stats, only: var
    implicit none
    real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
    real :: y(1:2, 1:3) = reshape([ 1., 2., 3., 4., 5., 6. ], [ 2, 3])
    print *, var(x)                                  !returns 3.5
    print *, var(x, corrected = .false.)             !returns 2.9167
    print *, var(y)                                  !returns 3.5
    print *, var(y, 1)                               !returns [0.5, 0.5, 0.5]
    print *, var(y, 1, y > 3.)                       !returns [NaN, NaN, 0.5]
    print *, var(y, 1, y > 3., corrected=.false.)    !returns [NaN, 0., 0.25]
end program demo_var