mean- mean of array elementsmoment- central moment of array elementsvar- variance of array elements
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.
result = mean(array [, mask])
result = mean(array, dim [, mask])
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 by a scalar or an array of the same shape as array.
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.
program demo_mean
use stdlib_experimental_stats, only: mean
implicit none
real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
print *, mean(x) !returns 3.5
print *, mean( reshape(x, [ 2, 3 ] )) !returns 3.5
print *, mean( reshape(x, [ 2, 3 ] ), 1) !returns [ 1.5, 3.5, 5.5 ]
print *, mean( reshape(x, [ 2, 3 ] ), 1,&
reshape(x, [ 2, 3 ] ) > 3.) !returns [ NaN, 4.0, 5.5 ]
end program demo_meanReturns 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.
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.
result = moment(array, order [, mask])
result = moment(array, order, dim [, mask])
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.
mask (optional): Shall be of type logical and either by a scalar or an array of the same shape as array.
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.
program demo_moment
use stdlib_experimental_stats, only: moment
implicit none
real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
print *, moment(x, 2) !returns 2.9167
print *, moment( reshape(x, [ 2, 3 ] ), 2) !returns 2.9167
print *, moment( reshape(x, [ 2, 3 ] ), 2, 1) !returns [0.25, 0.25, 0.25]
print *, moment( reshape(x, [ 2, 3 ] ), 2, 1,&
reshape(x, [ 2, 3 ] ) > 3.) !returns [NaN, 0., 0.25]
end program demo_momentReturns 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.
result = var(array [, mask [, corrected]])
result = var(array, dim [, mask [, corrected]])
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 by 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.
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..
program demo_var
use stdlib_experimental_stats, only: var
implicit none
real :: x(1:6) = [ 1., 2., 3., 4., 5., 6. ]
print *, var(x) !returns 3.5
print *, var(x, corrected = .false.) !returns 2.9167
print *, var( reshape(x, [ 2, 3 ] )) !returns 3.5
print *, var( reshape(x, [ 2, 3 ] ), 1) !returns [0.5, 0.5, 0.5]
print *, var( reshape(x, [ 2, 3 ] ), 1,&
reshape(x, [ 2, 3 ] ) > 3.) !returns [NaN, NaN, 0.5]
print *, var( reshape(x, [ 2, 3 ] ), 1,&
reshape(x, [ 2, 3 ] ) > 3.,&
corrected=.false.) !returns [NaN, 0., 0.25]
end program demo_var