Addition of optional center in API of moment()

src/stdlib_experimental_stats.fypp

@@ -213,9 +213,10 @@ module stdlib_experimental_stats
     #:for k1, t1 in RC_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment_all",rank, t1, k1)
-        module function ${RName}$(x, order, mask) result(res)
+        module function ${RName}$(x, order, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
+          ${t1}$, intent(in), optional :: center
           logical, intent(in), optional :: mask
           ${t1}$ :: res
         end function ${RName}$
@@ -225,9 +226,10 @@ module stdlib_experimental_stats
     #:for k1, t1 in INT_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment_all",rank, t1, k1, 'dp')
-        module function ${RName}$(x, order, mask) result(res)
+        module function ${RName}$(x, order, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
+          real(dp), intent(in), optional :: center
           logical, intent(in), optional :: mask
           real(dp) :: res
         end function ${RName}$
@@ -237,10 +239,11 @@ module stdlib_experimental_stats
     #:for k1, t1 in RC_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment",rank, t1, k1)
-        module function ${RName}$(x, order, dim, mask) result(res)
+        module function ${RName}$(x, order, dim, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
           integer, intent(in) :: dim
+          ${t1}$, intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
           logical, intent(in), optional :: mask
           ${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
         end function ${RName}$
@@ -250,10 +253,11 @@ module stdlib_experimental_stats
     #:for k1, t1 in INT_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment",rank, t1, k1, 'dp')
-        module function ${RName}$(x, order, dim, mask) result(res)
+        module function ${RName}$(x, order, dim, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
           integer, intent(in) :: dim
+          real(dp),intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
           logical, intent(in), optional :: mask
           real(dp) :: res${reduced_shape('x', rank, 'dim')}$
         end function ${RName}$
@@ -263,9 +267,10 @@ module stdlib_experimental_stats
     #:for k1, t1 in RC_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment_mask_all",rank, t1, k1)
-        module function ${RName}$(x, order, mask) result(res)
+        module function ${RName}$(x, order, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
+          ${t1}$, intent(in), optional :: center
           logical, intent(in) :: mask${ranksuffix(rank)}$
           ${t1}$ :: res
         end function ${RName}$
@@ -275,9 +280,10 @@ module stdlib_experimental_stats
     #:for k1, t1 in INT_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment_mask_all",rank, t1, k1, 'dp')
-        module function ${RName}$(x, order, mask) result(res)
+        module function ${RName}$(x, order, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
+          real(dp),intent(in), optional :: center
           logical, intent(in) :: mask${ranksuffix(rank)}$
           real(dp) :: res
         end function ${RName}$
@@ -287,10 +293,11 @@ module stdlib_experimental_stats
     #:for k1, t1 in RC_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment_mask",rank, t1, k1)
-        module function ${RName}$(x, order, dim, mask) result(res)
+        module function ${RName}$(x, order, dim, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
           integer, intent(in) :: dim
+          ${t1}$, intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
           logical, intent(in) :: mask${ranksuffix(rank)}$
           ${t1}$ :: res${reduced_shape('x', rank, 'dim')}$
         end function ${RName}$
@@ -300,10 +307,11 @@ module stdlib_experimental_stats
     #:for k1, t1 in INT_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment_mask",rank, t1, k1, 'dp')
-        module function ${RName}$(x, order, dim, mask) result(res)
+        module function ${RName}$(x, order, dim, center, mask) result(res)
           ${t1}$, intent(in) :: x${ranksuffix(rank)}$
           integer, intent(in) :: order
           integer, intent(in) :: dim
+          real(dp), intent(in), optional :: center${reduced_shape('x', rank, 'dim')}$
           logical, intent(in) :: mask${ranksuffix(rank)}$
           real(dp) :: res${reduced_shape('x', rank, 'dim')}$
         end function ${RName}$

src/stdlib_experimental_stats.md

@@ -1,7 +1,7 @@
 # Descriptive statistics
 
 * [`mean` - mean of array elements](#mean---mean-of-array-elements)
-* [`moment` - central moment of array elements](#moment---central-moment-of-array-elements)
+* [`moment` - raw and central moments of array elements](#moment---raw-and-central-moments-of-array-elements)
 * [`var` - variance of array elements](#var---variance-of-array-elements)
 
 ## `mean` - mean of array elements
@@ -48,25 +48,34 @@ program demo_mean
 end program demo_mean
 ```
 
-## `moment` - central moment of array elements
+## `moment` - raw and central moments of array elements
 
 ### 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`.
+Returns the _k_-th order raw 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 :
+If an array `center` is provided, the function 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`.
+
+
+The _k_-th order raw moment is defined as :
 
 ```
- moment(array) = 1/n sum_i (array(i) - mean(array))^k
+ moment(array) = 1/n sum_i (array(i))^k
 ```
 
 where n is the number of elements.
 
+The _k_-th order central moment is defined as :
+
+```
+ moment(array) = 1/n sum_i (array(i) - center)^k
+```
+
 ### Syntax
 
-`result = moment(array, order [, mask])`
+`result = moment(array, order [, center [, mask]])`
 
-`result = moment(array, order, dim [, mask])`
+`result = moment(array, order, dim [, center [, mask]])`
 
 ### Arguments
 
@@ -76,29 +85,35 @@ where n is the number of elements.
 
 `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 `array` if `array` is `real` or `complex`, or of type `real(dp)` if `array` is of type `integer`. If `dim` is provided, `center` shall be an array (with a shape similar to that of `array` with dimension `dim` dropped) of the same type of `array` if `array` is `real` or `complex`, or of type `real(dp)` if `array` is of type `integer`.
+
 `mask` (optional): Shall be of type `logical` and either by 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 `dim` is absent, a scalar with the _k_-th raw (or central if `center` is provided) 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`.
+If `mask` is specified, the result is the _k_-th raw (or central if `center` is provided) 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
 
 ```fortran
 program demo_moment
-    use stdlib_experimental_stats, only: moment
+    use stdlib_experimental_stats, only: mean, 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]
+    real :: y(1:2, 1:3) = reshape([ 1., 2., 3., 4., 5., 6. ], [ 2, 3])
+    print *, moment(x, 2, center = mean(x))                 !returns 2.9167
+    print *, moment( y, 2,&
+                     center = mean(y))                      !returns 2.9167
+    print *, moment( y, 2, 1,&
+                     center = mean(y, 1))                   !returns [0.25, 0.25, 0.25]
+    print *, moment( y, 2, 1,&
+                     center = mean(y, 1, y > 3.),&
+                     mask = (y > 3.))                       !returns [NaN, 0., 0.25]
 end program demo_moment
 ```