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LazStats: Further refactoring of ResistanceLineUnit. Some rearrangement of units to make MathUnit only dependent on Globals (for easier testing).

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git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7756 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
2020-10-10 11:02:59 +00:00
parent ae55a077f0
commit a91ba1bc04
15 changed files with 391 additions and 235 deletions
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2
applications/lazstats/source/forms/analysis/descriptive/multxvsyunit.pas
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@ -67,7 +67,7 @@ implementation
uses
TATypes,
Math, Utils;
Math, Utils, MathUnit;
{ TMultXvsYFrm }

136
applications/lazstats/source/forms/analysis/descriptive/resistancelineunit.pas
View File

@ -1,7 +1,7 @@
// Use file "Sickness.laz" for testing
// to do Not sure about the "red" slope line...
// to do: There are also two positions where a negative intercept is made positive. Why? Correct?
// to do: There are also two code positions where a negative intercept is made positive. Why? Correct?
unit ResistanceLineUnit;
@ -12,9 +12,8 @@ interface
uses
Classes, SysUtils, FileUtil, Forms, Controls, Graphics, Dialogs,
StdCtrls, ExtCtrls, Buttons, Printers, ComCtrls,
MainUnit, Globals, FunctionsLib, OutputUnit, DataProcs, DictionaryUnit,
//BlankFrmUnit,
BasicStatsReportAndChartFormUnit;
MainUnit, Globals, DataProcs, DictionaryUnit,
MathUnit, BasicStatsReportAndChartFormUnit;
type
@ -55,8 +54,8 @@ type
private
procedure PlotMedians(const XMedians, YMedians: DblDyneVec;
ASlope, AIntercept: Double);
procedure PlotXY(const XPoints, YPoints, UpConf, LowConf: DblDyneVec;
XMean, YMean, R, ASlope, AIntercept: Double);
procedure PlotXY(const XPoints, YPoints: DblDyneVec;
ARegressionResults: TBivariateRegressionResults);
procedure ResidualsToGrid(xCol, yCol: Integer;
const AColNoSelected: IntDyneVec; Slope, Intercept: Double);
@ -68,8 +67,7 @@ type
const XMedians, YMedians: DblDyneVec; const GrpSize: IntDyneVec;
Slope1, Slope2, Slope, Intercept: Double);
procedure WriteXYReport(AReport: TStrings; AFileName: String;
xMean, yMean, xVariance, yVariance, xStdDev, yStdDev, R, Slope, Intercept, SEPred: double;
N: Integer);
const ARegressionResults: TBivariateRegressionResults);
protected
procedure AdjustConstraints; override;
@ -91,7 +89,7 @@ implementation
uses
Math, Grids,
TATypes, TAChartUtils, TAChartAxisUtils, TALegend, TASources, TACustomSeries,
ChartFrameUnit, Utils, MathUnit, GridProcs;
ChartFrameUnit, Utils, GridProcs;
{ TResistanceLineForm }
@ -142,15 +140,13 @@ var
xMedians: DblDyneVec = nil;
yMedians: DblDyneVec = nil;
colNoSelected : IntDyneVec = nil;
upConf: DblDyneVec = nil;
lowConf: DblDyneVec = nil;
grpSize: IntDyneVec = nil;
xCol, yCol: Integer;
i, N, DF: integer;
xMean, yMean, xVariance, yVariance, xStdDev, yStdDev, SXX, SXY, SYY, t: Double;
confBand, yPred: double;
R, SEPred, interceptFit, slopeFit, slope1, slope2, slopeRL, seData: double;
c, c1, c2, c3 : double; // constants obtained from control points
regressionRes: TBivariateRegressionResults;
N: Integer;
confBand: Double;
slope1, slope2, slopeRL: Double;
c1, c2, c3, c: Double;
lReport: TStrings;
dataGrid: TStringGrid;
begin
@ -178,9 +174,9 @@ begin
xyPoints[0] := CollectValues(dataGrid, xCol, colNoSelected);
xyPoints[1] := CollectValues(dataGrid, ycol, colNoSelected);
N := Length(xyPoints[0]);
if N = 0 then
if N < 3 then
begin
ErrorMsg('No data points.');
ErrorMsg('At least three data points required.');
exit;
end;
if N <> Length(xyPoints[1]) then
@ -192,36 +188,9 @@ begin
// Sort on the x values
SortOnX(xyPoints[0], xyPoints[1]);
// Calculate means, variances, stddevs
Calc_MeanVarStdDevSS(xyPoints[0], xMean, xVariance, xStdDev, SXX);
Calc_MeanVarStdDevSS(xyPoints[1], yMean, yVariance, yStdDev, SYY);
// Calculate linear fit of x vs y
SXY := 0;
for i := 0 to N-1 do
SXY := SXY + xyPoints[0, i] * xyPoints[1, i];
R := (SXY - xMean * yMean * N) / ((N - 1) * xStdDev * yStdDev);
sePred := sqrt(1.0 - sqr(R)) * yStdDev * sqrt((N - 1) / (N - 2));
slopeFit := R * yStdDev / xStdDev;
interceptFit := yMean - slopeFit * xMean;
// Get upper and lower confidence limits for each x value
if ConfChk.Checked then
begin
SetLength(upConf, N);
SetLength(lowConf, N);
confBand := StrToFloat(ConfEdit.Text) / 100.0;
DF := N - 2;
t := InverseT(ConfBand, DF);
for i := 0 to N-1 do
begin
yPred := interceptFit + slopeFit * xyPoints[0, i];
seData := sePred * sqrt(1.0 + 1/N + sqr(xyPoints[0, i] - xMean)/SXX);
upConf[i] := yPred + t * seData;
lowConf[i] := yPred - t * seData;
end;
end;
// Calculate bivariate regression
confBand := StrToFloat(ConfEdit.Text) / 100;
Calc_BivariateRegression(xyPoints[0], xyPoints[1], confBand, regressionRes);
// Do the resistant line analysis
ResistantLineAnalysis(xyPoints, xMedians, yMedians, grpSize);
@ -240,6 +209,7 @@ begin
if GridChk.Checked then
ResidualsToGrid(xCol, yCol, colNoSelected, slopeRL, c);
// Write results to report in ReportFrame
lReport := TStringList.Create;
try
WriteMedianReport(lReport,
@ -250,9 +220,7 @@ begin
if DescChk.Checked then
WriteXYReport(lReport,
OS3MainFrm.FileNameEdit.Text,
xMean, yMean, xVariance, yVariance, xStdDev, yStdDev,
R, slopeFit, interceptFit, sePred,
N
regressionRes
);
FReportFrame.DisplayReport(lReport);
@ -260,8 +228,9 @@ begin
lReport.Free;
end;
// Plot results in ChartFrame
if PlotPointsChk.Checked then
PlotXY(xyPoints[0], xyPoints[1], upConf, lowConf, xMean, yMean, R, slopeFit, interceptFit);
PlotXY(xyPoints[0], xyPoints[1], regressionRes);
if PlotMediansChk.Checked then
PlotMedians(XMedians, YMedians, slopeRL, c);
@ -312,14 +281,16 @@ begin
end;
procedure TResistanceLineForm.PlotXY(const XPoints, YPoints, UpConf, LowConf: DblDyneVec;
XMean, YMean, R, ASlope, AIntercept: Double);
procedure TResistanceLineForm.PlotXY(const XPoints, YPoints: DblDyneVec;
ARegressionResults: TBivariateRegressionResults);
var
ser: TChartSeries;
xPts: DblDyneVec = nil;
yPts: DblDyneVec = nil;
conf: DblDyneVec = nil;
rightLabels: TListChartSource;
topLabels: TListChartSource;
i: Integer;
begin
rightLabels := FChartFrame.Chart.AxisList[2].Marks.Source as TListChartSource;
rightLabels.Clear;
@ -331,19 +302,21 @@ begin
FChartFrame.Chart.Margins.Right := 4;
FChartFrame.SetTitle('X vs Y plot using file '+ OS3MainFrm.FileNameEdit.Text);
FChartFrame.SetFooter(Format('R(X,Y) = %.3f, Slope = %.2f, Intercept = %.2f', [R, ASlope, AIntercept]));
with ARegressionResults do
FChartFrame.SetFooter(Format('R(X,Y) = %.3f, Slope = %.2f, Intercept = %.2f', [R, Slope, Intercept]));
FChartFrame.SetXTitle(XEdit.Text);
FChartFrame.SetYTitle(YEdit.Text);
// Draw means
if MeansChk.Checked then
begin
FChartFrame.VertLine(XMean, clGreen, psDashDot, 'Mean ' + XEdit.Text);
topLabels.Add(XMean, XMean, 'Mean ' + XEdit.Text);
with ARegressionResults do
begin
FChartFrame.VertLine(XMean, clGreen, psDashDot, 'Mean ' + XEdit.Text);
topLabels.Add(XMean, XMean, 'Mean ' + XEdit.Text);
FChartFrame.HorLine(YMean, clGreen, psDash, 'Mean ' + YEdit.Text);
rightLabels.Add(YMean, YMean, 'Mean ' + YEdit.Text);
end;
FChartFrame.HorLine(YMean, clGreen, psDash, 'Mean ' + YEdit.Text);
rightLabels.Add(YMean, YMean, 'Mean ' + YEdit.Text);
end;
// Draw slope line
if LineChk.Checked then
@ -351,24 +324,29 @@ begin
SetLength(xPts, 2);
SetLength(yPts, 2);
xPts[0] := XPoints[0];
yPts[0] := AIntercept + XPoints[0] * ASlope;
xPts[1] := XPoints[High(XPoints)];
yPts[1] := AIntercept + XPoints[High(XPoints)] * ASlope;
with ARegressionResults do
begin
yPts[0] := Intercept + XPoints[0] * Slope;
yPts[1] := Intercept + XPoints[High(XPoints)] * Slope;
end;
ser := FChartFrame.PlotXY(ptLines, xpts, ypts, nil, nil, 'Regression', clBlack);
rightLabels.Add(ser.XValue[ser.Count-1], ser.YValue[ser.Count-1], 'Regression');
end;
// Draw upper confidence band
if ConfChk.Checked then
begin
ser := FChartFrame.PlotXY(ptLines, XPoints, UpConf, nil, nil, 'Upper confidence band', clRed);
// Draw upper confidence band
SetLength(conf, ARegressionResults.Count);
for i := 0 to ARegressionResults.Count-1 do
conf[i] := ARegressionResults.ConfidenceLimits(XPoints[i], true);
ser := FChartFrame.PlotXY(ptLines, XPoints, conf, nil, nil, 'Upper confidence band', clRed);
rightLabels.Add(ser.yValue[ser.Count-1], ser.YValue[ser.Count-1], 'UCL');
end;
// Draw lower confidence band
if ConfChk.Checked then
begin
ser := FChartFrame.PlotXY(ptLines, XPoints, LowConf, nil, nil, 'Lower confidence band', clRed);
// Draw lower confidence band
for i := 0 to ARegressionResults.Count-1 do
conf[i] := ARegressionResults.ConfidenceLimits(XPoints[i], false);
ser := FChartFrame.PlotXY(ptLines, XPoints, conf, nil, nil, 'Lower confidence band', clRed);
rightLabels.Add(ser.yValue[ser.Count-1], ser.YValue[ser.Count-1], 'LCL');
end;
@ -587,8 +565,11 @@ end;
procedure TResistanceLineForm.WriteXYReport(AReport: TStrings; AFileName: String;
const ARegressionResults: TBivariateRegressionResults);
{
xMean, yMean, xVariance, yVariance, xStdDev, yStdDev, R, slope, intercept, SEPred: double;
N: Integer);
}
begin
AReport.Add('');
AReport.Add(DIVIDER);
@ -599,10 +580,22 @@ begin
AReport.Add('Variables:');
AReport.Add(' X: ' + XEdit.Text);
AReport.Add(' Y: ' + YEdit.Text);
// AReport.Add('X = %s, Y = %s from file: %s', [XEdit.Text, YEdit.Text, AFileName]);
AReport.Add('');
AReport.Add('Variable Mean Variance Std.Dev.');
AReport.Add('---------- -------- -------- --------');
with ARegressionResults do
begin
AReport.Add('%-10s %8.2f %8.2f %8.2f', [XEdit.Text, XMean, XVariance, XStdDev]);
AReport.Add('%-10s %8.2f %8.2f %8.2f', [YEdit.Text, YMean, YVariance, YStdDev]);
AReport.Add('');
AReport.Add('Correlation: %8.4f', [R]);
AReport.Add('Slope: %8.3f', [Slope]);
AReport.Add('Intercept: %8.3f', [Intercept]);
AReport.Add('Standard Error of Estimate: %8.3f', [StdErrorPredicted]);
AReport.Add('Number of good cases: %8d', [Count]);
end;
{
AReport.Add('%-10s %8.2f %8.2f %8.2f', [XEdit.Text, xMean, xVariance, xStdDev]);
AReport.Add('%-10s %8.2f %8.2f %8.2f', [YEdit.Text, yMean, yVariance, yStdDev]);
AReport.Add('');
@ -611,6 +604,7 @@ begin
AReport.Add('Intercept: %8.3f', [Intercept]);
AReport.Add('Standard Error of Estimate: %8.3f', [SEPred]);
AReport.Add('Number of good cases: %8d', [N]);
}
end;

2
applications/lazstats/source/forms/analysis/measurement_programs/gradebookunit.pas
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@ -105,7 +105,7 @@ implementation
uses
Math,
Utils;
Utils, MathUnit;
{ TGradebookFrm }

2
applications/lazstats/source/forms/analysis/measurement_programs/gradingunit.pas
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@ -72,7 +72,7 @@ implementation
uses
Math,
Utils, GradebookUnit;
Utils, MathUnit, GradebookUnit;
{ TGradingFrm }

3
applications/lazstats/source/forms/analysis/multivariate/kmeansunit.pas
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@ -85,7 +85,8 @@ var
implementation
uses
Math, Utils;
Math,
Utils, MathUnit;
{ TKMeansFrm }

3
applications/lazstats/source/forms/analysis/multivariate/medianpolishunit.pas
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@ -83,7 +83,8 @@ var
implementation
uses
Math, Utils;
Math,
Utils, MathUnit;
{ TMedianPolishForm }

3
applications/lazstats/source/forms/analysis/multivariate/pathunit.pas
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@ -84,7 +84,8 @@ var
implementation
uses
Math, Utils;
Math,
Utils, MathUnit;
{ TPathFrm }

3
applications/lazstats/source/forms/analysis/multivariate/singlelinkunit.pas
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@ -61,7 +61,8 @@ var
implementation
uses
Math, Utils;
Math,
Utils, MathUnit;
{ TSingleLinkFrm }

3
applications/lazstats/source/forms/analysis/nonparametric/sensunit.pas
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@ -65,7 +65,8 @@ var
implementation
uses
Math, Utils;
Math,
Utils, MathUnit;
{ TSensForm }

9
applications/lazstats/source/forms/misc/graphlib.pas
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@ -9,6 +9,15 @@ uses
ExtCtrls, StdCtrls, Printers, Math,
Globals;
const
DATA_COLORS: array[0..10] of TColor = (
$A1A45D, $3153C4, $0996E7, $4AE8F6, $A7A2B1,
$84A7C9, $51798C, $87CDD8, $536508, $7BD8F3,
$846402
);
// NOTE: This is a duplication of the declaration in ChartUnitFrame and will
// become obsolete when the GraphLib unit will be finally replaced by TAChart.
type

12
applications/lazstats/source/frames/chartframeunit.pas
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@ -10,6 +10,18 @@ uses
TATools,
Globals, MainDM;
const
DATA_COLORS: array[0..10] of TColor = (
$A1A45D, $3153C4, $0996E7, $4AE8F6, $A7A2B1,
$84A7C9, $51798C, $87CDD8, $536508, $7BD8F3,
$846402
);
DATA_SYMBOLS: array[0..5] of TSeriesPointerStyle = (
psRectangle, psCircle, psDiamond,
psDownTriangle, psHexagon, psFullStar
);
type
TPlotType = (ptLines, ptSymbols, ptLinesAndSymbols, ptBars,
ptArea);

2
applications/lazstats/source/units/dataprocs.pas
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@ -61,7 +61,7 @@ function StringsToInt(StrCol: integer; var NewCol: integer; Prompt: boolean): bo
implementation
uses
Utils, MainUnit;
Utils, MathUnit, MainUnit;
// NOTE: Do not call GridProcs.GoodRecord here because this old function may

21
applications/lazstats/source/units/globals.pas
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@ -5,7 +5,7 @@ unit Globals;
interface
uses
Classes, SysUtils, Graphics, TATypes;
Classes, SysUtils;
type
IntDyneVec = array of integer;
@ -75,27 +75,14 @@ const
DEFAULT_ALPHA_LEVEL = 0.05;
DEFAULT_BETA_LEVEL = 0.20;
{
DATA_COLORS: array[0..11] of TColor = (
clMaroon, clRed, clBlue, clGreen, clNavy, clTeal,
clAqua, clLime, clFuchsia, clGray, clSilver, clOlive
);
}
DATA_COLORS: array[0..10] of TColor = (
$A1A45D, $3153C4, $0996E7, $4AE8F6, $A7A2B1, $84A7C9, $51798C, $87CDD8, $536508, $7BD8F3, $846402
);
DATA_SYMBOLS: array[0..5] of TSeriesPointerStyle = (psRectangle, psCircle, psDiamond,
psDownTriangle, psHexagon, psFullStar);
DIVIDER = '===========================================================================';
DIVIDER_SMALL = '---------------------------------------------------------------------------';
DIVIDER_AUTO = '@=';
DIVIDER_SMALL_AUTO = '@-';
GRAPH_BACK_COLOR = clCream;
GRAPH_WALL_COLOR = clGray;
GRAPH_FLOOR_COLOR = clLtGray;
GRAPH_BACK_COLOR = $F0FBFF; // clCream
GRAPH_WALL_COLOR = $808080; // clGray
GRAPH_FLOOR_COLOR = $C0C0C0; // clLtGray
TAB_FILE_FILTER = 'Tab field files (*.tab)|*.tab;*.TAB|Text files (*.txt)|*.txt;*.TXT|All files (*.*)|*.*';
CSV_FILE_FILTER = 'Comma field files (*.csv)|*.csv;*.CSV|Text files (*.txt)|*.txt;*.TXT|All files (*.*)|*.*';

297
applications/lazstats/source/units/mathunit.pas
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@ -3,6 +3,7 @@ unit MathUnit;
{ extract some math functions from functionslib for easier testing }
{$mode objfpc}{$H+}
{$modeswitch advancedrecords}
interface
@ -20,15 +21,17 @@ function erfc(x: Double) : Double;
function NormalDist(x: Double): Double;
function NormalDistDensity(x, AMean, AStdDev: Double): Double;
function InverseNormalDist(Probability: Double): Double;
function Beta(a, b: Double): Extended;
function BetaI(a,b,x: Double): Extended;
function GammaLn(x: double): Extended;
function tDist(x: Double; DF: Integer; OneSided: Boolean): Double;
function tDensity(x: Double; DF: Integer): Double;
function ProbT(t, DF1: double): double;
function tDist(x, DF: Double; OneSided: Boolean): Double;
function tDensity(x, DF: Double): Double;
function ProbT(t, DF: double): double;
function InverseT(Probability, DF: Double): Double;
function FDensity(x: Double; DF1, DF2: Integer): Double;
function ProbF(F, DF1, DF2: Double): Double;
@ -44,7 +47,6 @@ function FactorialLn(n: Integer): Double;
function PoissonPDF(n: integer; a: double): Double;
function PoissonCDF(n: Integer; a: double): Double;
procedure Calc_MaxMin(const AData: DblDyneVec; out AMax, AMin: Double);
procedure Calc_MeanStdDev(const AData: DblDyneVec; out AMean, AStdDev: Double);
procedure Calc_MeanVarStdDev(const AData: DblDyneVec; out AMean, AVariance, AStdDev: Double);
@ -53,12 +55,38 @@ procedure Calc_SumSS(const AData: DblDyneVec; out Sum, SS: Double);
function Calc_Median(const AData: DblDyneVec): Double;
type
TBivariateRegressionResults = record
Slope, Intercept: Double;
XMean, YMean: Double;
XVariance, YVariance: Double;
XStdDev, YStdDev: Double;
StdErrorPredicted: Double;
R: Double;
t: Double;
SXX, SXY, SYY: Double;
Count, DF: Integer;
function ConfidenceLimits(x: Double; Upper: Boolean): Double;
end;
procedure Calc_BivariateRegression(const xData, yData: DblDyneVec; AConfLevel: Double;
out AResults: TBivariateRegressionResults);
procedure Exchange(var a, b: Double); overload;
procedure Exchange(var a, b: Integer); overload;
procedure Exchange(var a, b: String); overload;
procedure SortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
procedure SortOnX(X: DblDyneVec; Y: DblDyneMat);
procedure QuickSortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil); // not 100% tested...
implementation
uses
Math,
Utils;
Math;
// Utils;
// Calculates the error function
// /x
@ -160,6 +188,80 @@ begin
end;
{ Obtains the inverse of the normal distribution (z), that is the argument for
the NormalDist() function to result in the given probability.
Probability = 0 ... 1 --> Result = -INF ... +INF
Algorithm by Peter John Acklam.
http://home.online.no/~pjacklam/notes/invnorm/index.html }
function InverseNormalDist(Probability: Double): Double;
const
A: array[1..6] of Double = (
-3.969683028665376e+01,
+2.209460984245205e+02,
-2.759285104469687e+02,
+1.383577518672690e+02,
-3.066479806614716e+01,
+2.506628277459239e+00
);
B: array[1..5] of Double = (
-5.447609879822406e+01,
+1.615858368580409e+02,
-1.556989798598866e+02,
+6.680131188771972e+01,
-1.328068155288572e+01
);
C: array[1..6] of Double = (
-7.784894002430293e-03,
-3.223964580411365e-01,
-2.400758277161838e+00,
-2.549732539343734e+00,
+4.374664141464968e+00,
+2.938163982698783e+00
);
D: array[1..4] of Double = (
+7.784695709041462e-03,
+3.224671290700398e-01,
+2.445134137142996e+00,
+3.754408661907416e+00
);
// Switching points between regions.
P_LOW = 0.02425;
P_HIGH = 1 - P_LOW;
var
q, r: Extended;
begin
if Probability <= 0 then
Result := NegInfinity
else
if Probability < P_LOW then
begin
// rational approximation for lower region.
q := Sqrt(-2 * ln(Probability));
Result :=
(((((C[1] * q + C[2]) * q + C[3]) * q + C[4]) * q + C[5]) * q + C[6]) /
((((D[1] * q + D[2]) * q + D[3]) * q + D[4]) * q + 1);
end else
if Probability <= P_HIGH then begin
// rational approximation for central region.
q := Probability - 0.5 ;
r := q * q ;
Result :=
(((((A[1] * r + A[2]) * r + A[3]) * r + A[4]) * r + A[5]) * r + A[6]) * q /
(((((B[1] * r + B[2]) * r + B[3]) * r + B[4]) * r + B[5]) * r + 1);
end else
if Probability < 1 then begin
// rational approximation for upper region.
q := Sqrt(-2 * ln(1 - Probability));
Result :=
-(((((C[1] * q + C[2]) * q + C[3]) * q + C[4]) * q + C[5]) * q + C[6]) /
((((D[1] * q + D[2]) * q + D[3]) * q + D[4]) * q + 1);
end else
Result := Infinity;
end;
function Beta(a, b: Double): Extended;
begin
if (a > 0) and (b > 0) then
@ -268,14 +370,14 @@ begin
end;
// Calculates the (cumulative) t distribution function for DF degrees of freedom
function tDist(x: Double; DF: Integer; OneSided: Boolean): Double;
function tDist(x, DF: Double; OneSided: Boolean): Double;
begin
Result := betai(0.5*DF, 0.5, DF/(DF + sqr(x)));
if OneSided then Result := Result * 0.5;
end;
// Returns the density curve for the t statistic with DF degrees of freedom
function tDensity(x: Double; DF: Integer): Double;
function tDensity(x, DF: Double): Double;
var
factor: Double;
begin
@ -285,12 +387,23 @@ end;
{ Returns the cumulative probability corresponding to a two-tailed t test with
DF degrees of freedom. }
function ProbT(t, DF1: double): double;
function ProbT(t, DF: double): double;
var
F: double;
begin
F := t * t;
Result := ProbF(F, 1.0, DF1);
Result := ProbF(F, 1.0, DF);
end;
{ Returns the t value corresponding to a two-tailed t test probability. }
function InverseT(Probability, DF: Double): double;
var
z, w: double;
begin
z := InverseNormalDist(Probability);
w := z * ((8.0 * DF + 3.0) / (1.0 + 8.0 * DF));
Result := sqrt(DF * (exp(w * w / DF) - 1.0));
end;
@ -590,6 +703,170 @@ begin
end;
// It is assumed that xData and yData contain at least 3 elements and
// have the same count of elements.
procedure Calc_BivariateRegression(const xData, yData: DblDyneVec; AConfLevel: Double;
out AResults: TBivariateRegressionResults);
var
i: Integer;
begin
with AResults do
begin
Count := Length(xData);
// Calculate means, variances, stddevs
Calc_MeanVarStdDevSS(xData, XMean, XVariance, XStdDev, SXX);
Calc_MeanVarStdDevSS(yData, YMean, YVariance, YStdDev, SYY);
SXY := 0;
for i := 0 to Count-1 do
SXY := SXY + xData[i] * yData[i];
R := (SXY - XMean * YMean * Count) / ((Count - 1) * XStdDev * YStdDev);
StdErrorPredicted := sqrt(1.0 - sqr(R)) * YStdDev * sqrt((Count - 1) / (Count - 2));
Slope := R * YStdDev / XStdDev;
Intercept := YMean - Slope * XMean;
DF := Count - 2;
t := InverseT(AConfLevel, DF);
end;
end;
function TBivariateRegressionResults.ConfidenceLimits(x: Double; Upper: Boolean): Double;
var
yPred, seData: Double;
begin
yPred := Intercept + Slope * x;
seData := StdErrorPredicted * sqrt(1.0 + 1/Count + sqr(x - XMean)/SXX);
if Upper then
Result := yPred + t*seData
else
Result := yPred - t*seData;
end;
procedure Exchange(var a, b: Double);
var
tmp: Double;
begin
tmp := a;
a := b;
b := tmp;
end;
procedure Exchange(var a, b: Integer);
var
tmp: Integer;
begin
tmp := a;
a := b;
b := tmp;
end;
procedure Exchange(var a, b: String);
var
tmp: String;
begin
tmp := a;
a := b;
b := tmp;
end;
procedure SortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
var
i, j, N: Integer;
begin
N := Length(X);
if (Y <> nil) and (N <> Length(Y)) then
raise Exception.Create('[SortOnX] Arrays must have the same length.');
if (Z <> nil) and (N <> Length(Z)) then
raise Exception.Create('[SortOnX] Arrays must have the same length.');
for i := 0 to N - 2 do
begin
for j := i + 1 to N - 1 do
begin
if X[i] > X[j] then //swap
begin
Exchange(X[i], X[j]);
if Y <> nil then
Exchange(Y[i], Y[j]);
if Z <> nil then
Exchange(Z[i], Z[j]);
end;
end;
end;
end;
// NOTE: The matrix Y is transposed relative to the typical usage in LazStats
procedure SortOnX(X: DblDyneVec; Y: DblDyneMat);
var
i, j, k, N, Ny: Integer;
begin
N := Length(X);
if N <> Length(Y[0]) then
raise Exception.Create('[SortOnX] Arrays X and Y (2nd index) must have the same length');
Ny := Length(Y);
for i := 0 to N-2 do
begin
for j := i+1 to N-1 do
if X[i] > X[j] then
begin
Exchange(X[i], X[j]);
for k := 0 to Ny-1 do
Exchange(Y[k, i], Y[k, j]);
end;
end;
end;
procedure QuickSortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
procedure DoQuickSort(L, R: Integer);
var
I,J: Integer;
P: Integer;
begin
repeat
I := L;
J := R;
P := (L+R) div 2;
repeat
while CompareValue(X[P], X[I]) > 0 do inc(I);
while CompareValue(X[P], X[J]) < 0 do dec(J);
if I <= J then begin
if I <> J then begin
Exchange(X[I], X[J]);
if Y <> nil then
Exchange(Y[I], Y[J]);
if Z <> nil then
Exchange(Z[I], Z[J]);
end;
if P = I then
P := J
else if P = J then
P := I;
inc(I);
dec(J);
end;
until I > J;
if L < J then
DoQuickSort(L, J);
L := I;
until I >= R;
end;
begin
DoQuickSort(0, High(X));
end;
initialization
InitFactLn();

128
applications/lazstats/source/units/utils.pas
View File

@ -21,15 +21,6 @@ function AnySelected(AListbox: TListBox): Boolean;
procedure ErrorMsg(const AMsg: String);
procedure ErrorMsg(const AMsg: String; const AParams: array of const);
procedure Exchange(var a, b: Double); overload;
procedure Exchange(var a, b: Integer); overload;
procedure Exchange(var a, b: String); overload;
procedure SortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
procedure SortOnX(X: DblDyneVec; Y: DblDyneMat);
procedure QuickSortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil); // not 100% tested...
function CenterString(S: String; Width: Integer): String;
function IndexOfString(L: StrDyneVec; s: String): Integer;
@ -107,125 +98,6 @@ begin
ErrorMsg(Format(AMsg, AParams));
end;
procedure Exchange(var a, b: Double);
var
tmp: Double;
begin
tmp := a;
a := b;
b := tmp;
end;
procedure Exchange(var a, b: Integer);
var
tmp: Integer;
begin
tmp := a;
a := b;
b := tmp;
end;
procedure Exchange(var a, b: String);
var
tmp: String;
begin
tmp := a;
a := b;
b := tmp;
end;
procedure SortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
var
i, j, N: Integer;
begin
N := Length(X);
if (Y <> nil) and (N <> Length(Y)) then
raise Exception.Create('[SortOnX] Arrays must have the same length.');
if (Z <> nil) and (N <> Length(Z)) then
raise Exception.Create('[SortOnX] Arrays must have the same length.');
for i := 0 to N - 2 do
begin
for j := i + 1 to N - 1 do
begin
if X[i] > X[j] then //swap
begin
Exchange(X[i], X[j]);
if Y <> nil then
Exchange(Y[i], Y[j]);
if Z <> nil then
Exchange(Z[i], Z[j]);
end;
end;
end;
end;
// NOTE: The matrix Y is transposed relative to the typical usage in LazStats
procedure SortOnX(X: DblDyneVec; Y: DblDyneMat);
var
i, j, k, N, Ny: Integer;
begin
N := Length(X);
if N <> Length(Y[0]) then
raise Exception.Create('[SortOnX] Arrays X and Y (2nd index) must have the same length');
Ny := Length(Y);
for i := 0 to N-2 do
begin
for j := i+1 to N-1 do
if X[i] > X[j] then
begin
Exchange(X[i], X[j]);
for k := 0 to Ny-1 do
Exchange(Y[k, i], Y[k, j]);
end;
end;
end;
procedure QuickSortOnX(X: DblDyneVec; Y: DblDyneVec = nil; Z: DblDyneVec = nil);
procedure DoQuickSort(L, R: Integer);
var
I,J: Integer;
P: Integer;
begin
repeat
I := L;
J := R;
P := (L+R) div 2;
repeat
while CompareValue(X[P], X[I]) > 0 do inc(I);
while CompareValue(X[P], X[J]) < 0 do dec(J);
if I <= J then begin
if I <> J then begin
Exchange(X[I], X[J]);
if Y <> nil then
Exchange(Y[I], Y[J]);
if Z <> nil then
Exchange(Z[I], Z[J]);
end;
if P = I then
P := J
else if P = J then
P := I;
inc(I);
dec(J);
end;
until I > J;
if L < J then
DoQuickSort(L, J);
L := I;
until I >= R;
end;
begin
DoQuickSort(0, High(X));
end;
function CenterString(S: String; Width: Integer): String;
var