Add 6 new routines to Maths category

Added Integer, Cardinal and Double overloads of each of the new
ArithMean and WeightedArithMean routines.

Author: delphidabbler

Diff for: collection/650.dat

@@ -0,0 +1,12 @@
+function ArithMean(const A: array of Double): Double; overload;
+var
+  X: Double;
+begin
+  if Length(A) = 0 then
+    raise SysUtils.EArgumentException.Create(
+      'ArithMean: array is empty'
+    );
+  Result := 0.0;
+  for X in A do
+    Result := Result + X / Length(A);
+end;

Diff for: collection/651.dat

@@ -0,0 +1,12 @@
+function ArithMean(const A: array of Integer): Double; overload;
+var
+  X: Integer;
+begin
+  if Length(A) = 0 then
+    raise SysUtils.EArgumentException.Create(
+      'ArithMean: array is empty'
+    );
+  Result := 0.0;
+  for X in A do
+    Result := Result + X / Length(A);
+end;

Diff for: collection/652.dat

@@ -0,0 +1,12 @@
+function ArithMean(const A: array of Cardinal): Double; overload;
+var
+  X: Cardinal;
+begin
+  if Length(A) = 0 then
+    raise SysUtils.EArgumentException.Create(
+      'ArithMean: array is empty'
+    );
+  Result := 0.0;
+  for X in A do
+    Result := Result + X / Length(A);
+end;

Diff for: collection/653.dat

@@ -0,0 +1,26 @@
+function WeightedArithMean(const Values: array of Double;
+  const Weights: array of Double): Double; overload;
+var
+  WeightSum: Double;
+  Weight: Double;
+  Idx: Integer;
+begin
+  if Length(Values) = 0 then
+    raise SysUtils.EArgumentException.Create('Array of values is empty');
+  if Length(Values) <> Length(Weights) then
+    raise SysUtils.EArgumentException.Create(
+      'Number of values and number of weights must be the same'
+    );
+  WeightSum := 0.0;
+  for Weight in Weights do
+  begin
+    if Math.Sign(Weight) = Math.NegativeValue then
+      raise SysUtils.EArgumentException.Create('Weights must all be >= 0');
+    WeightSum := WeightSum + Weight;
+  end;
+  if Math.IsZero(WeightSum) then
+    raise SysUtils.EArgumentException.Create('All weights are 0');
+  Result := 0.0;
+  for Idx := Low(Values) to High(Values) do
+    Result := Result + Weights[Idx] * Values[Idx] / WeightSum;
+end;

Diff for: collection/654.dat

@@ -0,0 +1,11 @@
+function WeightedArithMean(const Values: array of Integer;
+  const Weights: array of Double): Double; overload;
+var
+  Idx: Integer;
+  DblVals: array of Double;
+begin
+  SetLength(DblVals, Length(Values));
+  for Idx := Low(Values) to High(Values) do
+    DblVals[Idx] := Values[Idx];
+  Result := WeightedArithMean(DblVals, Weights);
+end;

Diff for: collection/655.dat

@@ -0,0 +1,11 @@
+function WeightedArithMean(const Values: array of Cardinal;
+  const Weights: array of Double): Double; overload;
+var
+  Idx: Integer;
+  DblVals: array of Double;
+begin
+  SetLength(DblVals, Length(Values));
+  for Idx := Low(Values) to High(Values) do
+    DblVals[Idx] := Values[Idx];
+  Result := WeightedArithMean(DblVals, Weights);
+end;

Diff for: collection/maths.ini

@@ -1681,3 +1681,77 @@ DelphiXE3=Y
 DelphiXE4=Y
 Delphi10S=Y
 FPC=Y
+
+[ArithMean_Double]
+DisplayName="ArithMean (Double overload)"
+DescEx="<p>Returns the arithmetic mean of an array of <var>Double</var> values.</p><p><var>EArgumentException</var> is raised if the array is empty.</p>"
+Units=SysUtils
+SeeAlso=ArithMean_Integer,ArithMean_Cardinal
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=650.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[ArithMean_Integer]
+DisplayName="ArithMean (Integer overload)"
+DescEx="<p>Returns the arithmetic mean of an array of <var>Integer</var> values.</p><p><var>EArgumentException</var> is raised if the array is empty.</p>"
+Units=SysUtils
+SeeAlso=ArithMean_Double,ArithMean_Cardinal
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=651.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[ArithMean_Cardinal]
+DisplayName="ArithMean (Cardinal overload)"
+DescEx="<p>Returns the arithmetic mean of an array of <var>Cardinal</var> values.</p><p><var>EArgumentException</var> is raised if the array is empty.</p>"
+Units=SysUtils
+SeeAlso=ArithMean_Double,ArithMean_Integer
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=652.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[WeightedArithMean_Double]
+DisplayName="WeightedArithMean (Double overload)"
+DescEx="<p>Calculates and returns the weighted average of the <var>Double</var> elements of array <var>Values</var> where each element is weighted by the corresponding element in the array <var>Weights</var>.</p><p>An <var>EArgumentException</var> exception is raised if any of the following pre-conditions are not met: <var>Values</var> must be non-empty; <var>Values</var> &amp; <var>Weights</var> must have the same number of elements; all elements of <var>Weights</var> must be non-negative, with at least one element being non-zero.</p>"
+Units=SysUtils,Math
+SeeAlso=ArithMean_Double,WeightedArithMean_Integer,WeightedArithMean_Cardinal
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=653.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[WeightedArithMean_Integer]
+DisplayName="WeightedArithMean (Integer overload)"
+DescEx="<p>Calculates and returns the weighted average of the <var>Integer</var> elements of array <var>Values</var> where each element is weighted by the corresponding element in the array <var>Weights</var>.</p><p>An <var>EArgumentException</var> exception is raised if any of the following pre-conditions are not met: <var>Values</var> must be non-empty; <var>Values</var> &amp; <var>Weights</var> must have the same number of elements; all elements of <var>Weights</var> must be non-negative, with at least one element being non-zero.</p>"
+Units=
+Depends=WeightedArithMean_Double
+SeeAlso=ArithMean_Integer,WeightedArithMean_Double,WeightedArithMean_Cardinal
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=654.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[WeightedArithMean_Cardinal]
+DisplayName="WeightedArithMean (Cardinal overload)"
+DescEx="<p>Calculates and returns the weighted average of the <var>Cardinal</var> elements of array <var>Values</var> where each element is weighted by the corresponding element in the array <var>Weights</var>.</p><p>An <var>EArgumentException</var> exception is raised if any of the following pre-conditions are not met: <var>Values</var> must be non-empty; <var>Values</var> &amp; <var>Weights</var> must have the same number of elements; all elements of <var>Weights</var> must be non-negative, with at least one element being non-zero.</p>"
+Units=
+Depends=WeightedArithMean_Double
+SeeAlso=ArithMean_Cardinal,WeightedArithMean_Double,WeightedArithMean_Integer
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=655.dat
+DelphiXE=Y
+Delphi12A=Y