Addition of a subroutine to compute the median of array elements

doc/specs/stdlib_stats.md

@@ -26,6 +26,10 @@ The Pearson correlation between two rows (or columns), say `x` and `y`, of `arra
 
 `result = [[stdlib_stats(module):corr(interface)]](array, dim [, mask])`
 
+### Class
+
+Generic subroutine
+
 ### Arguments
 
 `array`: Shall be a rank-1 or a rank-2 array of type `integer`, `real`, or `complex`.
@@ -83,6 +87,10 @@ The scaling can be changed with the logical argument `corrected`. If `corrected`
 
 `result = [[stdlib_stats(module):cov(interface)]](array, dim [, mask [, corrected]])`
 
+### Class
+
+Generic subroutine
+
 ### Arguments
 
 `array`: Shall be a rank-1 or a rank-2 array of type `integer`, `real`, or `complex`.
@@ -134,6 +142,10 @@ Returns the mean of all the elements of `array`, or of the elements of `array` a
 
 `result = [[stdlib_stats(module):mean(interface)]](array, dim [, mask])`
 
+### Class
+
+Generic subroutine
+
 ### Arguments
 
 `array`: Shall be an array of type `integer`, `real`, or `complex`.
@@ -166,6 +178,75 @@ program demo_mean
 end program demo_mean
 ```
 
+## `median` - median of array elements
+
+### Status
+
+Experimental
+
+### Description
+
+Returns the median 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 median of the elements of `array` is defined as the "middle"
+element, after that the elements are sorted in an increasing order, e.g. `array_sorted =
+sort(array)`. If `n = size(array)` is an even number, the median is:
+
+```
+median(array) = array_sorted( floor( (n + 1) / 2.))
+```
+
+and if `n` is an odd number, the median is:
+
+```
+median(array) = mean( array_sorted( floor( (n + 1) / 2.):floor( (n + 1) / 2.) + 1 ) )
+```
+
+The array is sorted using the subroutine `[[stdlib_sorting(module):ord_sort(interface)]]`
+provided by the `[[stdlib_sorting(module)]]` module.
+
+### Syntax
+
+`result = [[stdlib_stats(module):median(interface)]](array [, mask])`
+
+`result = [[stdlib_stats(module):median(interface)]](array, dim [, mask])`
+
+### Class
+
+Generic subroutine
+
+### Arguments
+
+`array`: Shall be an array of type `integer` or `real`.
+
+`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`, the result is of type `real` with the same kind as `array`.
+If `array` is of type `integer`, the result is of type `real(dp)`.
+
+If `dim` is absent, a scalar with the median 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 median 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_median
+    use stdlib_stats, only: median
+    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 *, median(x)                                  !returns 3.5
+    print *, median(y)                                  !returns 3.5
+    print *, median(y, 1)                               !returns [ 1.5, 3.5, 5.5 ]
+    print *, median(y, 1,y > 3.)                        !returns [ NaN, 4.0, 5.5 ]
+end program demo_median
+```
+
 ## `moment` - central moments of array elements
 
 ### Status
@@ -199,6 +280,10 @@ The _k_-th order moment about `center` is defined as :
 
 `result = [[stdlib_stats(module):moment(interface)]](array, order, dim [, center [, mask]])`
 
+### Class
+
+Generic subroutine
+
 ### Arguments
 
 `array`: Shall be an array of type `integer`, `real`, or `complex`.
@@ -264,6 +349,10 @@ The use of the term `n-1` for scaling is called Bessel 's correction. The scalin
 
 `result = [[stdlib_stats(module):var(interface)]](array, dim [, mask [, corrected]])`
 
+### Class
+
+Generic subroutine
+
 ### Arguments
 
 `array`: Shall be an array of type `integer`, `real`, or `complex`.

src/CMakeLists.txt

@@ -18,6 +18,7 @@ set(fppFiles
     stdlib_stats_corr.fypp
     stdlib_stats_cov.fypp
     stdlib_stats_mean.fypp
+    stdlib_stats_median.fypp
     stdlib_stats_moment.fypp
     stdlib_stats_moment_all.fypp
     stdlib_stats_moment_mask.fypp

src/Makefile.manual

@@ -18,6 +18,7 @@ SRCFYPP =\
         stdlib_stats_corr.fypp \
         stdlib_stats_cov.fypp \
         stdlib_stats_mean.fypp \
+        stdlib_stats_median.fypp \
         stdlib_stats_moment.fypp \
         stdlib_stats_moment_all.fypp \
         stdlib_stats_moment_mask.fypp \
@@ -108,6 +109,11 @@ stdlib_stats_mean.o: \
 	stdlib_optval.o \
 	stdlib_kinds.o \
 	stdlib_stats.o
+stdlib_stats_median.o: \
+	stdlib_optval.o \
+	stdlib_kinds.o \
+	stdlib_sorting.o \
+	stdlib_stats.o
 stdlib_stats_moment.o: \
 	stdlib_optval.o \
 	stdlib_kinds.o \

src/common.fypp

@@ -156,4 +156,61 @@ ${prefix + joinstr.join([line.strip() for line in txt.split("\n")]) + suffix}$
   #:endcall
 #:enddef
 
+#!
+#! Generates an array rank suffix for subarrays along a dimension
+#!
+#! Args:
+#!   varname (str): Name of the variable to be used as origin
+#!   rank (int): Rank of the original variable
+#!   dim (int): Dimension of the variable
+#!
+#! Returns:
+#!   Array rank suffix string enclosed in braces
+#!
+#! E.g.,
+#!  select_subvector('j', 5, 2)
+#!   -> (j_, :, j___, j____, j_____)
+#!
+#:def select_subvector(varname, rank, idim)
+  #:assert rank > 0
+  #:call join_lines(joinstr=", ", prefix="(", suffix=")")
+    #:for i in range(1, idim)
+      ${varname}$${ "_" * (i) }$
+    #:endfor
+    :
+    #:for i in range(idim + 1, rank + 1)
+      ${varname}$${ "_" * (i) }$
+    #:endfor
+  #:endcall
+#:enddef
+
+#!
+#! Generates an array rank suffix for arrays
+#!
+#! Args:
+#!   varname (str): Name of the variable to be used as origin
+#!   rank (int): Rank of the original variable
+#!   idim (int): Dimension of the variable
+#!
+#! Returns:
+#!   Array rank suffix string enclosed in braces
+#!
+#! E.g.,
+#!  reduce_subvector('j', 5, 2)
+#!   -> (j_, j___, j____, j_____)
+#!
+#:def reduce_subvector(varname, rank, idim)
+  #:assert rank > 0
+  #:if rank > 1
+    #:call join_lines(joinstr=", ", prefix="(", suffix=")")
+      #:for i in range(1, idim)
+        ${varname}$${ "_" * (i) }$
+      #:endfor
+      #:for i in range(idim + 1, rank + 1)
+        ${varname}$${ "_" * (i) }$
+      #:endfor
+    #:endcall
+  #:endif
+#:enddef
+
 #:endmute

src/stdlib_stats.fypp

@@ -2,6 +2,7 @@
 #:set RANKS = range(1, MAXRANK + 1)
 #:set REDRANKS = range(2, MAXRANK + 1)
 #:set RC_KINDS_TYPES = REAL_KINDS_TYPES + CMPLX_KINDS_TYPES
+#:set IR_KINDS_TYPES_OUTPUT = list(zip(REAL_KINDS, REAL_TYPES, REAL_KINDS)) + list(zip(INT_KINDS,INT_TYPES, ['dp']*len(INT_KINDS)))
 module stdlib_stats
   !! Provides support for various statistical methods. This includes currently
   !! descriptive statistics
@@ -11,14 +12,14 @@ module stdlib_stats
   implicit none
   private
   ! Public API
-  public :: corr, cov, mean, moment, var
+  public :: corr, cov, mean, median, moment, var
 
 
   interface corr
     !! version: experimental
     !!
     !! Pearson correlation of array elements
-    !! ([Specification](../page/specs/stdlib_stats.html#description))
+    !! ([Specification](../page/specs/stdlib_stats.html#corr-pearson-correlation-of-array-elements))
     #:for k1, t1 in RC_KINDS_TYPES
       #:set RName = rname("corr",1, t1, k1)
       module function ${RName}$(x, dim, mask) result(res)
@@ -110,7 +111,7 @@ module stdlib_stats
     !! version: experimental
     !!
     !! Covariance of array elements
-    !! ([Specification](../page/specs/stdlib_stats.html#description_1))
+    !! ([Specification](../page/specs/stdlib_stats.html#cov-covariance-of-array-elements))
     #:for k1, t1 in RC_KINDS_TYPES
       #:set RName = rname("cov",1, t1, k1)
       module function ${RName}$(x, dim, mask, corrected) result(res)
@@ -209,7 +210,7 @@ module stdlib_stats
     !! version: experimental
     !!
     !! Mean of array elements
-    !! ([Specification](../page/specs/stdlib_stats.html#description_2))
+    !! ([Specification](../page/specs/stdlib_stats.html#mean-mean-of-array-elements))
     #:for k1, t1 in RC_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("mean_all",rank, t1, k1)
@@ -305,11 +306,65 @@ module stdlib_stats
   end interface mean
 
 
+  interface median
+    !! version: experimental
+    !!
+    !! Median of array elements
+    !! ([Specification](../page/specs/stdlib_stats.html#median-median-of-array-elements))
+    #:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
+      #:for rank in RANKS
+        #:set RName = rname("median_all",rank, t1, k1, o1)
+        module function ${RName}$ (x, mask) result(res)
+          ${t1}$, intent(in) :: x${ranksuffix(rank)}$
+          logical, intent(in), optional :: mask
+          real(${o1}$) :: res
+        end function ${RName}$
+      #:endfor
+    #:endfor
+
+    #:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
+      #:for rank in RANKS
+        #:set RName = rname("median",rank, t1, k1, o1)
+        module function ${RName}$(x, dim, mask) result(res)
+          ${t1}$, intent(in) :: x${ranksuffix(rank)}$
+          integer, intent(in) :: dim
+          logical, intent(in), optional :: mask
+          real(${o1}$) :: res${reduced_shape('x', rank, 'dim')}$
+        end function ${RName}$
+      #:endfor
+    #:endfor
+
+    #:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
+      #:for rank in RANKS
+        #:set RName = rname('median_mask_all',rank, t1, k1, o1)
+        module function ${RName}$(x, mask) result(res)
+          ${t1}$, intent(in) :: x${ranksuffix(rank)}$
+          logical, intent(in) :: mask${ranksuffix(rank)}$
+          real(${o1}$) :: res
+        end function ${RName}$
+      #:endfor
+    #:endfor
+
+    #:for k1, t1, o1 in IR_KINDS_TYPES_OUTPUT
+      #:for rank in RANKS
+        #:set RName = rname('median_mask',rank, t1, k1, o1)
+        module function  ${RName}$(x, dim, mask) result(res)
+          ${t1}$, intent(in) :: x${ranksuffix(rank)}$
+          integer, intent(in) :: dim
+          logical, intent(in) :: mask${ranksuffix(rank)}$
+          real(${o1}$) :: res${reduced_shape('x', rank, 'dim')}$
+        end function ${RName}$
+      #:endfor
+    #:endfor
+
+  end interface
+
+
   interface var
     !! version: experimental
     !!
     !! Variance of array elements
-    !! ([Specification](../page/specs/stdlib_stats.html#description_4))
+    !! ([Specification](../page/specs/stdlib_stats.html#var-variance-of-array-elements))
 
     #:for k1, t1 in RC_KINDS_TYPES
       #:for rank in RANKS
@@ -418,7 +473,7 @@ module stdlib_stats
     !! version: experimental
     !!
     !! Central moment of array elements
-    !! ([Specification](../page/specs/stdlib_stats.html#description_3))
+    !! ([Specification](../page/specs/stdlib_stats.html#moment-central-moments-of-array-elements))
     #:for k1, t1 in RC_KINDS_TYPES
       #:for rank in RANKS
         #:set RName = rname("moment_all",rank, t1, k1)