Add various power mean functions to Maths category

Added Double, Cardinal & Integer overloads of PowerMean &
WeightedPowerMean functions.

Added source code files for each function.

Added meta data for each function to maths.ini.

Author: delphidabbler

collection/691.dat

@@ -0,0 +1,22 @@
+function PowerMean(const A: array of Double; const Lambda: Double): Double;
+  overload;
+var
+  Sum: Double;
+  X: Double;
+begin
+  if System.Length(A) = 0 then
+    raise SysUtils.EArgumentException.Create('Array is empty');
+  if Math.IsZero(Lambda) then
+    raise SysUtils.EArgumentException.Create('Lambda must not be zero');
+  Sum := 0.0;
+  for X in A do
+  begin
+    if Math.Sign(X) = NegativeValue then
+      raise SysUtils.EArgumentException.Create(
+        'All array elements must be non-negative'
+      );
+    if not Math.IsZero(X) then
+      Sum := Sum + Math.Power(X, Lambda);
+  end;
+  Result := Math.Power(Sum / System.Length(A), 1 / Lambda);
+end;

collection/692.dat

@@ -0,0 +1,11 @@
+function PowerMean(const A: array of Integer; const Lambda: Double): Double;
+  overload;
+var
+  Floats: Types.TDoubleDynArray;
+  Idx: Integer;
+begin
+  System.SetLength(Floats, System.Length(A));
+  for Idx := 0 to Pred(System.Length(A)) do
+    Floats[Idx] := A[Idx];
+  Result := PowerMean(Floats, Lambda);
+end;

collection/693.dat

@@ -0,0 +1,11 @@
+function PowerMean(const A: array of Cardinal; const Lambda: Double): Double;
+  overload;
+var
+  Floats: Types.TDoubleDynArray;
+  Idx: Integer;
+begin
+  System.SetLength(Floats, System.Length(A));
+  for Idx := 0 to Pred(System.Length(A)) do
+    Floats[Idx] := A[Idx];
+  Result := PowerMean(Floats, Lambda);
+end;

collection/694.dat

@@ -0,0 +1,35 @@
+function WeightedPowerMean(const Values, Weights: array of Double;
+  const Lambda: Double): Double; overload;
+var
+  NormalisedWeights: Types.TDoubleDynArray;
+  PowerSum: Double;
+  Idx: Integer;
+  Value: Double;
+  Weight: Double;
+begin
+  if System.Length(Values) = 0 then
+    raise SysUtils.EArgumentException.Create('Array of values is empty');
+  if System.Length(Values) <> System.Length(Weights) then
+    raise SysUtils.EArgumentException.Create(
+      'Number of values and number of weights must be the same'
+    );
+  if Math.IsZero(Lambda) then
+    raise SysUtils.EArgumentException.Create('Lambda must not be zero');
+  NormalisedWeights := NormaliseByWeight(Weights);
+  PowerSum := 0.0;
+  for Idx := 0 to Pred(System.Length(Values)) do
+  begin
+    Value := Values[Idx];
+    Weight := NormalisedWeights[Idx];
+    if Math.Sign(Value) = Math.NegativeValue then
+      raise SysUtils.EArgumentException.Create(
+        'All values must be non-negative'
+      );
+    if not Math.IsZero(Value) and not Math.IsZero(Weight) then
+      PowerSum := PowerSum + Weight * Math.Power(Value, Lambda);
+  end;
+  if not Math.IsZero(PowerSum) then
+    Result := Math.Power(PowerSum, 1 / Lambda)
+  else
+    Result := 0.0;
+end;

collection/695.dat

@@ -0,0 +1,11 @@
+function WeightedPowerMean(const Values: array of Integer;
+  const Weights: array of Double; const Lambda: Double): Double; overload;
+var
+  FloatValues: Types.TDoubleDynArray;
+  Idx: Integer;
+begin
+  System.SetLength(FloatValues, System.Length(Values));
+  for Idx := 0 to Pred(System.Length(Values)) do
+    FloatValues[Idx] := Values[Idx];
+  Result := WeightedPowerMean(FloatValues, Weights, Lambda);
+end;

collection/696.dat

@@ -0,0 +1,11 @@
+function WeightedPowerMean(const Values: array of Cardinal;
+  const Weights: array of Double; const Lambda: Double): Double; overload;
+var
+  FloatValues: Types.TDoubleDynArray;
+  Idx: Integer;
+begin
+  System.SetLength(FloatValues, System.Length(Values));
+  for Idx := 0 to Pred(System.Length(Values)) do
+    FloatValues[Idx] := Values[Idx];
+  Result := WeightedPowerMean(FloatValues, Weights, Lambda);
+end;

collection/maths.ini

@@ -2225,3 +2225,92 @@ AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tes
 Snip=690.dat
 DelphiXE=Y
 Delphi12A=Y
+
+[PowerMean_Double]
+DisplayName="PowerMean (Double overload)"
+DescEx="<p>Returns the power mean of the elements of <var>Double</var> array <var>Values</var>, with exponent <var>Lambda</var>.</p><p>An <var>EArgumentException</var> is raised if the array is empty, if any array element is negative or if <var>Lambda</var> is zero.</p>"
+Extra="<p>The <em>power mean</em> is also known as the <em>generalised mean</em> and the <em>Holder mean</em>.</p><p>See <a href="https://en.m.wikipedia.org/wiki/Generalized_mean">Wikipedia</a> for further information.</p>"
+Kind=routine
+Units=SysUtils,Math
+SeeAlso=ArithmeticMean_Double,GeometricMean_Double,HarmonicMean_Double,PowerMean_Cardinal,PowerMean_Integer,LogarithmicMean,WeightedPowerMean_Double
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=691.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[PowerMean_Integer]
+DisplayName="PowerMean (Integer overload)"
+DescEx="<p>Returns the power mean of the elements of <var>Integer</var> array <var>Values</var>, with exponent <var>Lambda</var>.</p><p>An <var>EArgumentException</var> is raised if the array is empty, if any array element is negative or if <var>Lambda</var> is zero.</p>"
+Extra="<p>The <em>power mean</em> is also known as the <em>generalised mean</em> and the <em>Holder mean</em>.</p><p>See <a href="https://en.m.wikipedia.org/wiki/Generalized_mean">Wikipedia</a> for further information.</p>"
+Kind=routine
+Units=Types
+Depends=PowerMean_Double
+SeeAlso=ArithmeticMean_Integer,GeometricMean_Integer,HarmonicMean_Integer,PowerMean_Double,PowerMean_Cardinal,LogarithmicMean,WeightedPowerMean_Integer
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=692.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[PowerMean_Cardinal]
+DisplayName="PowerMean (Cardinal overload)"
+DescEx="<p>Returns the power mean of the elements of <var>Cardinal</var> array <var>Values</var>, with exponent <var>Lambda</var>.</p><p>An <var>EArgumentException</var> is raised if the array is empty or if <var>Lambda</var> is zero.</p>"
+Extra="<p>The <em>power mean</em> is also known as the <em>generalised mean</em> and the <em>Holder mean</em>.</p><p>See <a href="https://en.m.wikipedia.org/wiki/Generalized_mean">Wikipedia</a> for further information.</p>"
+Kind=routine
+Units=Types
+Depends=PowerMean_Double
+SeeAlso=ArithmeticMean_Cardinal,GeometricMean_Cardinal,HarmonicMean_Cardinal,PowerMean_Double,PowerMean_Integer,LogarithmicMean,WeightedPowerMean_Cardinal
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=693.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[WeightedPowerMean_Double]
+DisplayName="WeightedPowerMean (Double overload)"
+DescEx="<p>Returns the weighted power mean of the elements of <var>Double</var> array <var>Values</var>, with exponent <var>Lambda</var>. Each term 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; no element of <var>Values</var> may be negative; <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; <var>Lambda</var> must not be zero.</p>"
+Extra="<p>The <em>power mean</em> is also known as the <em>generalised mean</em> and the <em>Holder mean</em>.</p><p>See <a href="https://www.statisticshowto.com/power-mean-generalized-mean/">Statistics How To</a> for further information.</p>"
+Kind=routine
+Units=SysUtils,Types,Math
+Depends=NormaliseByWeight_Double
+SeeAlso=WeightedArithmeticMean_Double,WeightedGeometricMean_Double,WeightedHarmonicMean_Double,PowerMean_Double,WeightedPowerMean_Cardinal,WeightedPowerMean_Integer
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=694.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[WeightedPowerMean_Integer]
+DisplayName="WeightedPowerMean (Integer overload)"
+DescEx="<p>Returns the weighted power mean of the elements of <var>Integer</var> array <var>Values</var>, with exponent <var>Lambda</var>. Each term 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; no element of <var>Values</var> may be negative; <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; <var>Lambda</var> must not be zero.</p>"
+Extra="<p>The <em>power mean</em> is also known as the <em>generalised mean</em> and the <em>Holder mean</em>.</p><p>See <a href="https://www.statisticshowto.com/power-mean-generalized-mean/">Statistics How To</a> for further information.</p>"
+Kind=routine
+Units=Types
+Depends=WeightedPowerMean_Double
+SeeAlso=WeightedArithmeticMean_Integer,WeightedGeometricMean_Integer,WeightedHarmonicMean_Integer,PowerMean_Integer,WeightedPowerMean_Cardinal,WeightedPowerMean_Double
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=695.dat
+DelphiXE=Y
+Delphi12A=Y
+
+[WeightedPowerMean_Cardinal]
+DisplayName="WeightedPowerMean (Cardinal overload)"
+DescEx="<p>Returns the weighted power mean of the elements of <var>Cardinal</var> array <var>Values</var>, with exponent <var>Lambda</var>. Each term 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; <var>Lambda</var> must not be zero.</p>"
+Extra="<p>The <em>power mean</em> is also known as the <em>generalised mean</em> and the <em>Holder mean</em>.</p><p>See <a href="https://www.statisticshowto.com/power-mean-generalized-mean/">Statistics How To</a> for further information.</p>"
+Kind=routine
+Units=Types
+Depends=WeightedPowerMean_Double
+SeeAlso=WeightedArithmeticMean_Cardinal,WeightedGeometricMean_Cardinal,WeightedHarmonicMean_Cardinal,PowerMean_Cardinal,WeightedPowerMean_Double,WeightedPowerMean_Integer
+TestInfo=advanced
+AdvancedTest.Level=unit-tests
+AdvancedTest.URL="https://github.com/delphidabbler/code-snippets/tree/master/tests/Cat-Maths"
+Snip=696.dat
+DelphiXE=Y
+Delphi12A=Y