You've already forked lazarus-ccr
Extract MathUnit from functionslib for easier testing and more versatile usage. Add t distribution to DistribUnit.
git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7637 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
@ -49,7 +49,7 @@
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<PackageName Value="LCL"/>
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</Item7>
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</RequiredPackages>
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<Units Count="172">
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<Units Count="173">
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<Unit0>
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<Filename Value="LazStats.lpr"/>
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<IsPartOfProject Value="True"/>
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@ -1400,6 +1400,11 @@
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<ResourceBaseClass Value="Form"/>
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<UnitName Value="ChartUnit"/>
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</Unit171>
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<Unit172>
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<Filename Value="units\mathunit.pas"/>
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<IsPartOfProject Value="True"/>
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<UnitName Value="MathUnit"/>
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</Unit172>
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</Units>
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</ProjectOptions>
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<CompilerOptions>
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@ -7,8 +7,8 @@ uses
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cthreads,
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{$ENDIF}{$ENDIF}
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Interfaces, // this includes the LCL widgetset
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Forms, tachartlazaruspkg, tachartprint, lhelpcontrolpkg,
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Globals, LicenseUnit, OptionsUnit, MainDM, MainUnit; //, utils, chartunit;
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Forms, tachartlazaruspkg, tachartprint, lhelpcontrolpkg, Globals, LicenseUnit,
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OptionsUnit, MainDM, MainUnit, MathUnit; //, utils, chartunit;
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{$R LazStats.res}
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@ -51,7 +51,8 @@ var
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implementation
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uses
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Math;
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Math,
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MathUnit;
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{ TSigmaChartFrm }
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@ -252,9 +253,9 @@ begin
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D3Value := D3[grpsize-1];
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D4Value := D4[grpsize-1];
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C4 := sqrt(2.0 / (grpsize - 1));
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gamma := exp(gammln(grpsize / 2.0));
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gamma := exp(GammaLn(grpsize / 2.0));
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C4 := C4 * gamma;
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gamma := exp(gammln((grpsize-1) / 2.0));
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gamma := exp(GammaLn((grpsize-1) / 2.0));
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C4 := C4 / gamma;
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B := GrandSigma * sqrt(1.0 - (C4 * C4)) / C4;
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UCL := GrandSigma + 3.0 * B;
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@ -122,7 +122,7 @@ object DistribFrm: TDistribFrm
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Minors = <>
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Title.LabelFont.Style = [fsBold]
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Title.Visible = True
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Title.Caption = 'Scale'
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Title.Caption = 'Value'
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Title.LabelBrush.Style = bsClear
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Title.TextFormat = tfHTML
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end>
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@ -218,7 +218,7 @@ object DistribFrm: TDistribFrm
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Top = 8
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Width = 144
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Caption = 'Normal Distribution'
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OnClick = NDChkClick
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OnClick = DistributionClick
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TabOrder = 0
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end
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object tChk: TRadioButton
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@ -227,9 +227,8 @@ object DistribFrm: TDistribFrm
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Top = 35
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Width = 144
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Caption = 'Student t Distribution'
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OnClick = tChkClick
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OnClick = DistributionClick
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TabOrder = 3
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Visible = False
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end
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object FChk: TRadioButton
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Left = 16
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@ -237,7 +236,7 @@ object DistribFrm: TDistribFrm
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Top = 62
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Width = 144
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Caption = 'Central F Distribution'
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OnClick = FChkClick
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OnClick = DistributionClick
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TabOrder = 2
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end
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object ChiChk: TRadioButton
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@ -246,7 +245,7 @@ object DistribFrm: TDistribFrm
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Top = 89
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Width = 144
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Caption = 'Chi-Square Distribution'
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OnClick = ChiChkClick
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OnClick = DistributionClick
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TabOrder = 1
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end
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end
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@ -51,25 +51,22 @@ type
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DF2Label: TLabel;
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MeanLabel: TLabel;
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GroupBox1: TGroupBox;
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procedure ChiChkClick(Sender: TObject);
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procedure ComputeBtnClick(Sender: TObject);
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procedure FChkClick(Sender: TObject);
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procedure FormActivate(Sender: TObject);
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procedure FormShow(Sender: TObject);
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procedure CalcChiSq(const AX: Double; out AY: Double);
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procedure CalcF(const AX: Double; out AY: Double);
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procedure CalcND(const AX: Double; out AY: Double);
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procedure Calct(const AX: Double; out AY: Double);
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procedure NDChkClick(Sender: TObject);
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procedure DistributionClick(Sender: TObject);
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procedure PrintBtnClick(Sender: TObject);
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procedure ResetBtnClick(Sender: TObject);
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procedure SaveBtnClick(Sender: TObject);
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procedure tChkClick(Sender: TObject);
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private
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{ private declarations }
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DF1: Integer;
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DF2: Integer;
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procedure NDPlot;
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procedure NormalDistPlot;
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procedure ChiPlot;
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procedure FPlot;
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procedure tPlot;
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@ -85,9 +82,8 @@ var
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implementation
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uses
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//spe, // a numlib unit (tDist)
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OSPrinters,
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TAChartUtils, TADrawerSVG, TAPrint;
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TAChartUtils, TADrawerSVG, TAPrint,
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MathUnit;
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{ TDistribFrm }
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@ -131,28 +127,8 @@ begin
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end;
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procedure TDistribFrm.CalcF(const AX: Double; out AY: Double);
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var
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ratio1, ratio2, ratio3, ratio4: double;
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part1, part2, part3, part4, part5, part6, part7, part8, part9: double;
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begin
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// Returns the height of the density curve for the F statistic
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ratio1 := (DF1 + DF2) / 2.0;
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ratio2 := (DF1 - 2.0) / 2.0;
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ratio3 := DF1 / 2.0;
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ratio4 := DF2 / 2.0;
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part1 := exp(lngamma(ratio1));
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part2 := power(DF1, ratio3);
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part3 := power(DF2, ratio4);
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part4 := exp(lngamma(ratio3));
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part5 := exp(lngamma(ratio4));
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part6 := power(AX, ratio2);
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part7 := power((AX*DF1 + DF2), ratio1);
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part8 := (part1 * part2 * part3) / (part4 * part5);
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if (part7 = 0.0) then
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part9 := 0.0
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else
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part9 := part6 / part7;
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AY := part8 * part9;
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AY := FDensity(AX, DF1, DF2);
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end;
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procedure TDistribFrm.CalcND(const AX: Double; out AY: Double);
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@ -162,17 +138,35 @@ end;
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procedure TDistribFrm.CalcChiSq(const AX: Double; out AY: Double);
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begin
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AY := 1.0 / (power(2.0, DF1*0.5) * exp(lngamma(DF1*0.5))) * power(AX, (DF1-2.0)*0.5) * (1.0 / exp(AX*0.5));
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AY := Chi2Density(AX, DF1);
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end;
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procedure TDistribFrm.Calct(const AX: Double; out AY: Double);
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begin
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AY := Student(AX, DF1, 1.0);
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//AY := tDist(AX, DF1, 1);
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AY := tDensity(AX, DF1);
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end;
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procedure TDistribFrm.NDChkClick(Sender: TObject);
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procedure TDistribFrm.DistributionClick(Sender: TObject);
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var
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rb: TRadiobutton;
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begin
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rb := Sender as TRadioButton;
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GroupBox2.Enabled := rb.Checked;
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AlphaLabel.Enabled := rb.Checked;
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AlphaEdit.Enabled := rb.Checked;
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DF1Edit.Enabled := (rb <> NDChk) and rb.Checked;
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DF1Label.Enabled := DF1Edit.Enabled;
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DF2Edit.Enabled := (rb = FChk) and rb.Checked;
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DF2Label.Enabled := DF2Edit.Enabled;
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MeanEdit.Enabled := false;
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MeanLabel.Enabled := false;
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{
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if NDChk.Checked then
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begin
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GroupBox2.Enabled := true;
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@ -187,6 +181,7 @@ begin
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end
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else
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GroupBox2.Enabled := false;
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}
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end;
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procedure TDistribFrm.PrintBtnClick(Sender: TObject);
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@ -233,7 +228,7 @@ begin
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ok := false;
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if NDChk.Checked then
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begin
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NDPlot();
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NormalDistPlot();
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ok := true;
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end;
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@ -259,60 +254,7 @@ begin
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MessageDlg('Please select a distribution.', mtError, [mbOK], 0);
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end;
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procedure TDistribFrm.FChkClick(Sender: TObject);
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begin
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if FChk.Checked then
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begin
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GroupBox2.Enabled := true;
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DF2Label.Enabled := true;
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AlphaLabel.Enabled := true;
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AlphaEdit.Enabled := true;
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DF1Edit.Enabled := true;
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DF2Edit.Enabled := true;
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DF1Label.Enabled := true;
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MeanLabel.Enabled := false;
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MeanEdit.Enabled := false;
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end
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else
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GroupBox2.Enabled := false;
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end;
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procedure TDistribFrm.ChiChkClick(Sender: TObject);
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begin
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if ChiChk.Checked then
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begin
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GroupBox2.Enabled := true;
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DF1Label.Enabled := true;
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DF1Edit.Enabled := true;
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DF2Label.Enabled := false;
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MeanLabel.Enabled := false;
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AlphaLabel.Enabled := true;
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AlphaEdit.Enabled := true;
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DF2Edit.Enabled := false;
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MeanEdit.Enabled := false;
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end else
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GroupBox2.Enabled := false;
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end;
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procedure TDistribFrm.tChkClick(Sender: TObject);
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begin
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if tChk.Checked then
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begin
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GroupBox2.Enabled := true;
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DF1Label.Enabled := true;
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DF1Edit.Enabled := true;
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DF2Label.Enabled := false;
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MeanLabel.Enabled := false;
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AlphaLabel.Enabled := true;
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AlphaEdit.Enabled := true;
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DF2Edit.Enabled := false;
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MeanEdit.Enabled := false;
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end else
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GroupBox2.Enabled := false;
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end;
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procedure TDistribFrm.NDPlot;
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procedure TDistribFrm.NormalDistPlot;
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var
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alpha: Double;
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zMax, zCrit, pCrit: Double;
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@ -416,7 +358,7 @@ begin
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Chart.Title.Text.Add(Format('Critical value = %.3f', [tCrit]));
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Chart.Title.Visible := true;
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Chart.BottomAxis.Title.Caption := 't';
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FuncSeries.Extent.XMin := -tMax;
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FuncSeries.Extent.XMin := -tmax;
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FuncSeries.Extent.XMax := tMax;
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FuncSeries.Extent.UseXMin := true;
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FuncSeries.Extent.UseXMax := true;
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@ -10,7 +10,6 @@ uses
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MainUnit, dataprocs;
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function chisquaredprob(X : double; k : integer) : double;
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function gammln(xx : double) : double;
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PROCEDURE matinv(VAR a, vtimesw, v, w: DblDyneMat; n: integer);
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FUNCTION sign(a,b: double): double;
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FUNCTION isign(a,b : integer): integer;
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@ -66,6 +65,9 @@ procedure poisson_pdf ( x : integer; VAR a : double; VAR pdf : double );
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implementation
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uses
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MathUnit;
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function chisquaredprob(X : double; k : integer) : double;
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var
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factor : double; // factor which multiplies sum of series
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@ -86,7 +88,7 @@ begin
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begin
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x1 := 0.5 * X;
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k1 := 0.5 * k;
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g := gammln(k1 + 1);
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g := GammaLn(k1 + 1);
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factor := exp(k1 * ln(x1) - g - x1);
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sum := 0.0;
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if factor > 0 then
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@ -104,34 +106,7 @@ begin
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end; //end if .. else
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Result := chi2prob;
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end;
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//---------------------------------------------------------------------
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function gammln(xx : double) : double;
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var
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X, tmp, ser : double;
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cof : array[0..5] of double;
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j : integer;
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begin
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cof[0] := 76.18009173;
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cof[1] := -86.50532033;
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cof[2] := 24.01409822;
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cof[3] := -1.231739516;
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cof[4] := 0.00120858003;
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cof[5] := -0.00000536382;
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X := xx - 1.0;
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tmp := X + 5.5;
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tmp := tmp - ((X + 0.5) * ln(tmp));
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ser := 1.0;
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for j := 0 to 5 do
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begin
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X := X + 1.0;
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ser := ser + cof[j] / X;
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end;
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Result := ( -tmp + ln(2.50662827465 * ser) );
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end;
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//-------------------------------------------------------------------
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PROCEDURE matinv(VAR a, vtimesw, v, w: DblDyneMat; n: integer);
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(* adapted from the singular value decomposition of a matrix *)
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@ -568,74 +543,6 @@ BEGIN
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END;
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//-----------------------------------------------------------------
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function betacf(a,b,x: double): extended;
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CONST
|
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itmax=100;
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eps=3.0e-7;
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VAR
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tem,qap,qam,qab,em,d: extended;
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bz,bpp,bp,bm,az,app: extended;
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am,aold,ap: extended;
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m: integer;
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BEGIN
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am := 1.0;
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bm := 1.0;
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az := 1.0;
|
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qab := a+b;
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qap := a+1.0;
|
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qam := a-1.0;
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bz := 1.0 - qab * x / qap;
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FOR m := 1 to itmax DO BEGIN
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em := m;
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tem := em+em;
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d := em * (b - m) * x / ((qam + tem) * (a + tem));
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ap := az + d * am;
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bp := bz + d * bm;
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term1 := -(a + em);
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term2 := qab + em;
|
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term3 := term1 * term2 * x;
|
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term4 := a + tem;
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term5 := qap + tem;
|
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term6 := term4 * term5;
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d := term3 / term6;
|
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app := ap + d * az;
|
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bpp := bp + d * bz;
|
||||
aold := az;
|
||||
am := ap/bpp;
|
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bm := bp/bpp;
|
||||
az := app/bpp;
|
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bz := 1.0;
|
||||
IF ((abs(az-aold)) < (eps*abs(az))) THEN
|
||||
Break;
|
||||
END;
|
||||
{ ShowMessage('WARNING! a or b too big, or itmax too small in betacf');}
|
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Result := az
|
||||
END;
|
||||
|
||||
FUNCTION betai(a,b,x: extended): extended;
|
||||
VAR
|
||||
bt: extended;
|
||||
BEGIN
|
||||
IF ((x <= 0.0) OR (x >= 1.0)) THEN BEGIN
|
||||
{ ShowMessage('ERROR! Problem in routine BETAI');}
|
||||
betai := 0.5;
|
||||
exit;
|
||||
END;
|
||||
IF ((x <= 0.0) OR (x >= 1.0)) THEN bt := 0.0
|
||||
ELSE
|
||||
begin
|
||||
term1 := gammln(a + b) -
|
||||
gammln(a) - gammln(b);
|
||||
term2 := a * ln(x);
|
||||
term3 := b * ln(1.0 - x);
|
||||
term4 := term1 + term2 + term3;
|
||||
bt := exp(term4);
|
||||
term5 := (a + 1.0) / (a + b + 2.0);
|
||||
end;
|
||||
IF x < term5 then betai := bt * betacf(a,b,x) / a
|
||||
ELSE betai := 1.0 - bt * betacf(b,a,1.0-x) / b
|
||||
END;
|
||||
|
||||
begin { fprob function }
|
||||
if f <= 0.0 then probf := 1.0 else
|
||||
probf := (betai(0.5*df2,0.5*df1,df2/(df2+df1*f)) +
|
||||
|
||||
188
applications/lazstats/source/units/mathunit.pas
Normal file
188
applications/lazstats/source/units/mathunit.pas
Normal file
@ -0,0 +1,188 @@
|
||||
unit MathUnit;
|
||||
|
||||
{ extract some math functions from functionslib for easier testing }
|
||||
|
||||
{$mode objfpc}{$H+}
|
||||
|
||||
interface
|
||||
|
||||
uses
|
||||
Classes, SysUtils;
|
||||
|
||||
function Beta(a, b: Double): Extended;
|
||||
function BetaI(a,b,x: Double): Extended;
|
||||
|
||||
function GammaLn(x: double): Extended;
|
||||
|
||||
function tDist(x: Double; N: Integer; OneSided: Boolean): Double;
|
||||
function tDensity(x: Double; N: Integer): Double;
|
||||
|
||||
function FDensity(x: Double; DF1, DF2: Integer): Double;
|
||||
|
||||
function Chi2Density(x: Double; N: Integer): Double;
|
||||
|
||||
implementation
|
||||
|
||||
uses
|
||||
Math;
|
||||
|
||||
function Beta(a, b: Double): Extended;
|
||||
begin
|
||||
if (a > 0) and (b > 0) then
|
||||
Result := exp(GammaLn(a) + GammaLn(b) - GammaLn(a+b))
|
||||
else
|
||||
raise Exception.Create('Invalid argument for beta function.');
|
||||
end;
|
||||
|
||||
function BetaCF(a, b, x: double): Extended;
|
||||
const
|
||||
itmax = 100;
|
||||
eps = 3.0e-7;
|
||||
var
|
||||
tem,qap,qam,qab,em,d: extended;
|
||||
bz,bpp,bp,bm,az,app: extended;
|
||||
am,aold,ap: extended;
|
||||
term1, term2, term3, term4, term5, term6: extended;
|
||||
m: integer;
|
||||
BEGIN
|
||||
am := 1.0;
|
||||
bm := 1.0;
|
||||
az := 1.0;
|
||||
qab := a+b;
|
||||
qap := a+1.0;
|
||||
qam := a-1.0;
|
||||
bz := 1.0 - qab * x / qap;
|
||||
for m := 1 to itmax do begin
|
||||
em := m;
|
||||
tem := em+em;
|
||||
d := em * (b - m) * x / ((qam + tem) * (a + tem));
|
||||
ap := az + d * am;
|
||||
bp := bz + d * bm;
|
||||
term1 := -(a + em);
|
||||
term2 := qab + em;
|
||||
term3 := term1 * term2 * x;
|
||||
term4 := a + tem;
|
||||
term5 := qap + tem;
|
||||
term6 := term4 * term5;
|
||||
d := term3 / term6;
|
||||
app := ap + d * az;
|
||||
bpp := bp + d * bz;
|
||||
aold := az;
|
||||
am := ap/bpp;
|
||||
bm := bp/bpp;
|
||||
az := app/bpp;
|
||||
bz := 1.0;
|
||||
if ((abs(az-aold)) < (eps*abs(az))) then
|
||||
Break;
|
||||
end;
|
||||
|
||||
{ ShowMessage('WARNING! a or b too big, or itmax too small in betacf');}
|
||||
Result := az
|
||||
end;
|
||||
|
||||
function BetaI(a,b,x: Double): extended;
|
||||
var
|
||||
bt: extended;
|
||||
term1, term2, term3, term4, term5: extended;
|
||||
begin
|
||||
if ((x < 0.0) or (x > 1.0)) then begin
|
||||
{ ShowMessage('ERROR! Problem in routine BETAI');}
|
||||
Result := 0.5;
|
||||
exit;
|
||||
end;
|
||||
|
||||
if ((x <= 0.0) or (x >= 1.0)) then
|
||||
bt := 0.0
|
||||
else
|
||||
begin
|
||||
term1 := GammaLn(a + b) - GammaLn(a) - GammaLn(b);
|
||||
term2 := a * ln(x);
|
||||
term3 := b * ln(1.0 - x);
|
||||
term4 := term1 + term2 + term3;
|
||||
bt := exp(term4);
|
||||
end;
|
||||
term5 := (a + 1.0) / (a + b + 2.0);
|
||||
if x < term5 then
|
||||
Result := bt * betacf(a,b,x) / a
|
||||
else
|
||||
Result := 1.0 - bt * betacf(b,a,1.0-x) / b
|
||||
end;
|
||||
|
||||
function GammaLn(x: double): Extended;
|
||||
var
|
||||
tmp, ser: double;
|
||||
cof: array[0..5] of double;
|
||||
j: integer;
|
||||
begin
|
||||
cof[0] := 76.18009173;
|
||||
cof[1] := -86.50532033;
|
||||
cof[2] := 24.01409822;
|
||||
cof[3] := -1.231739516;
|
||||
cof[4] := 0.00120858003;
|
||||
cof[5] := -0.00000536382;
|
||||
|
||||
x := x - 1.0;
|
||||
tmp := x + 5.5;
|
||||
tmp := tmp - (x + 0.5) * ln(tmp);
|
||||
ser := 1.0;
|
||||
for j := 0 to 5 do
|
||||
begin
|
||||
x := x + 1.0;
|
||||
ser := ser + cof[j] / x;
|
||||
end;
|
||||
Result := -tmp + ln(2.50662827465 * ser);
|
||||
end;
|
||||
|
||||
// Calculates the (cumulative) t distribution function for N degrees of freedom
|
||||
function tDist(x: Double; N: Integer; OneSided: Boolean): Double;
|
||||
begin
|
||||
Result := betai(0.5*N, 0.5, N/(N + sqr(x)));
|
||||
if OneSided then Result := Result * 0.5;
|
||||
end;
|
||||
|
||||
// Returns the density curve for the t statistic with N degrees of freedom
|
||||
function tDensity(x: Double; N: Integer): Double;
|
||||
var
|
||||
factor: Double;
|
||||
begin
|
||||
factor := exp(gammaLn((N+1)/2) - gammaLn(N/2)) / sqrt(N * pi);
|
||||
Result := factor * Power(1 + sqr(x)/N, (1-n)/2);
|
||||
end;
|
||||
|
||||
// Returns the density curve for the F statistic for DF1 and DF2 degrees of freedom.
|
||||
function FDensity(x: Double; DF1, DF2: Integer): Double;
|
||||
var
|
||||
ratio1, ratio2, ratio3, ratio4: double;
|
||||
part1, part2, part3, part4, part5, part6, part7, part8, part9: double;
|
||||
begin
|
||||
ratio1 := (DF1 + DF2) / 2.0;
|
||||
ratio2 := (DF1 - 2.0) / 2.0;
|
||||
ratio3 := DF1 / 2.0;
|
||||
ratio4 := DF2 / 2.0;
|
||||
part1 := exp(gammaln(ratio1));
|
||||
part2 := power(DF1, ratio3);
|
||||
part3 := power(DF2, ratio4);
|
||||
part4 := exp(gammaln(ratio3));
|
||||
part5 := exp(gammaln(ratio4));
|
||||
part6 := power(x, ratio2);
|
||||
part7 := power((x*DF1 + DF2), ratio1);
|
||||
part8 := (part1 * part2 * part3) / (part4 * part5);
|
||||
if (part7 = 0.0) then
|
||||
part9 := 0.0
|
||||
else
|
||||
part9 := part6 / part7;
|
||||
Result := part8 * part9;
|
||||
end;
|
||||
|
||||
|
||||
// Returns the density curve of the chi2 statistic for N degrees of freedom
|
||||
function Chi2Density(x: Double; N: Integer): Double;
|
||||
var
|
||||
factor: Double;
|
||||
begin
|
||||
factor := Power(2.0, N * 0.5) * exp(gammaLN(N * 0.5));
|
||||
Result := power(x, (N-2.0) * 0.5) / (factor * exp(x * 0.5));
|
||||
end;
|
||||
|
||||
end.
|
||||
|
||||
Reference in New Issue
Block a user