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615 lines
22 KiB
ObjectPascal
615 lines
22 KiB
ObjectPascal
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unit SensUnit;
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{$mode objfpc}{$H+}
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interface
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uses
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Classes, SysUtils, FileUtil, LResources, Forms, Controls, Graphics, Dialogs,
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StdCtrls, Buttons, ExtCtrls,
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MainUnit, Globals, FunctionsLib, OutputUnit,
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ContextHelpUnit, MatrixLib, GraphLib;
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type
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{ TSensForm }
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TSensForm = class(TForm)
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AllBtn: TBitBtn;
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AlphaEdit: TEdit;
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Bevel1: TBevel;
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CancelBtn: TButton;
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Memo1: TLabel;
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ResetBtn: TButton;
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ComputeBtn: TButton;
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ReturnBtn: TButton;
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InBtn: TBitBtn;
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Label1: TLabel;
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Label2: TLabel;
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Label3: TLabel;
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SelectedList: TListBox;
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OutBtn: TBitBtn;
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VarList: TListBox;
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PrtRanksChk: TCheckBox;
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PrtSlopesChk: TCheckBox;
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PrtDataChk: TCheckBox;
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GroupBox3: TGroupBox;
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SlopesChk: TCheckBox;
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PlotChk: TCheckBox;
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GroupBox2: TGroupBox;
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StandardizeChk: TCheckBox;
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AvgSlopeChk: TCheckBox;
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GroupBox1: TGroupBox;
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procedure AllBtnClick(Sender: TObject);
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procedure ComputeBtnClick(Sender: TObject);
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procedure FormActivate(Sender: TObject);
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procedure FormCreate(Sender: TObject);
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procedure InBtnClick(Sender: TObject);
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procedure OutBtnClick(Sender: TObject);
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procedure ResetBtnClick(Sender: TObject);
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private
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{ private declarations }
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FAutoSized: Boolean;
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public
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{ public declarations }
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end;
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var
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SensForm: TSensForm;
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implementation
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uses
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Math;
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{ TSensForm }
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procedure TSensForm.ResetBtnClick(Sender: TObject);
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VAR i : integer;
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begin
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AlphaEdit.Text := '0.05';
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StandardizeChk.Checked := false;
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PlotChk.Checked := false;
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SlopesChk.Checked := false;
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InBtn.Enabled := true;
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OutBtn.Enabled := false;
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AvgSlopeChk.Checked := false;
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SelectedList.Clear;
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VarList.Clear;
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for i := 1 to NoVariables do VarList.Items.Add(OS3MainFrm.DataGrid.Cells[i,0]);
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end;
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procedure TSensForm.InBtnClick(Sender: TObject);
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VAR index, i : integer;
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begin
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index := VarList.Items.Count;
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i := 0;
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while i < index do
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begin
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if (VarList.Selected[i]) then
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begin
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SelectedList.Items.Add(VarList.Items.Strings[i]);
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VarList.Items.Delete(i);
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index := index - 1;
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i := 0;
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end
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else i := i + 1;
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end;
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OutBtn.Enabled := true;
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end;
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procedure TSensForm.AllBtnClick(Sender: TObject);
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VAR count, i : integer;
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begin
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count := VarList.Items.Count;
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if count <= 0 then exit;
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for i := 0 to VarList.Items.Count-1 do
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SelectedList.Items.Add(VarList.Items.Strings[i]);
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VarList.Clear;
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OutBtn.Enabled := true;
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InBtn.Enabled := false;
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end;
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procedure TSensForm.ComputeBtnClick(Sender: TObject);
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VAR
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NoVars, noselected, count, half, q, tp, low, hi, col : integer;
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Values, Slopes, AvgSlopes : DblDyneMat;
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RankedQ, Sorted : DblDyneVec;
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RowLabels, ColLabels, RankLabels : StrDyneVec;
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selected : IntDyneVec;
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temp, MedianSlope, MannKendall, Z, C, M1, M2, Alpha, mean, stddev : double;
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cellstring, outline : string;
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i, j, k, no2do : integer;
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Standardize, Plot, SlopePlot, AvgSlope : boolean;
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begin
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Standardize := false;
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Plot := false;
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SlopePlot := false;
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AvgSlope := false;
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if StandardizeChk.Checked then Standardize := true;
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if PlotChk.Checked then Plot := true;
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if SlopesChk.Checked then SlopePlot := true;
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if AvgSlopeChk.Checked then AvgSlope := true;
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Alpha := 1.0 - StrToFloat(AlphaEdit.Text);
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noselected := SelectedList.Items.Count;
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if noselected = 0 then
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begin
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ShowMessage('ERROR! First select variables to analyze.');
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exit;
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end;
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SetLength(RowLabels,NoCases);
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SetLength(ColLabels,NoCases);
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SetLength(selected,noselected);
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SetLength(Values,NoCases,noselected+1);
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SetLength(Slopes,NoCases,NoCases);
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SetLength(RankedQ,NoVars);
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SetLength(Sorted,NoCases);
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SetLength(AvgSlopes,NoCases,NoCases);
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for i := 0 to NoCases-1 do
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begin
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RowLabels[i] := OS3MainFrm.DataGrid.Cells[0,i+1];
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ColLabels[i] := RowLabels[i];
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for j := 0 to NoCases-1 do Slopes[i,j] := 0.0;
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end;
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// get selected variables
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for i := 1 to noselected do
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begin
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cellstring := SelectedList.Items.Strings[i-1];
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for j := 1 to NoVariables do
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if cellstring = OS3MainFrm.DataGrid.Cells[j,0] then
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selected[i-1] := j;
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end;
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OutputFrm.RichEdit.Clear;
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OutputFrm.RichEdit.Lines.Add('Sens Detection and Estimation of Trends');
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outline := format('Number of data points = %d, Confidence Interval = %4.2f',
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[NoCases,Alpha]);
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OutputFrm.RichEdit.Lines.Add(outline);
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OutputFrm.RichEdit.Lines.Add('');
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//Get the data
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if AvgSlope then for i := 0 to NoCases-1 do Values[i,noselected] := 0.0;
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for j := 0 to noselected-1 do
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begin
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col := selected[j];
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for i := 1 to NoCases do
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begin
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Values[i-1,j] := round(StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[col,i])));
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if AvgSlope then Values[i-1,noselected] := Values[i-1,noselected] +
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Values[i-1,j];
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end;
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end;
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if PrtDataChk.Checked then
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begin
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outline:= 'CASE';
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MAT_PRINT(Values,NoCases,noselected,outline,RowLabels,ColLabels,NoCases);
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OutputFrm.ShowModal;
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end;
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// standardize if more than one variable and standardization elected
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if (noselected > 1) and (standardize = true) then
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begin
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for j := 0 to noselected-1 do
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begin
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mean := 0.0;
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stddev := 0.0;
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for i := 0 to NoCases-1 do
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begin
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mean := mean + Values[i,j];
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stddev := stddev + (Values[i,j] * Values[i,j]);
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end;
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stddev := stddev - (mean * mean) / NoCases;
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stddev := stddev / (NoCases - 1);
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stddev := sqrt(stddev);
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mean := mean / NoCases;
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for i := 0 to NoCases-1 do
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Values[i,j] := (Values[i,j] - mean)/ stddev;
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col := selected[j];
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outline := format('Variable = %s, mean = %8.3f, standard deviation = %8.3f',
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[OS3MainFrm.DataGrid.Cells[col,0],mean,stddev]);
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OutputFrm.RichEdit.Lines.Add(outline);
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end;
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end;
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// average the values if elected
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if AvgSlope then for i := 0 to NoCases - 1 do Values[i,noselected] :=
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Values[i,noselected] / noselected;
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// get interval slopes
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no2do := noselected;
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if AvgSlope then no2do := no2do + 1;
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for j := 0 to no2do - 1 do
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begin
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if j < noselected then
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begin
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col := selected[j];
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cellstring := OS3MainFrm.DataGrid.Cells[col,0];
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end
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else
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begin
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col := 0;
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cellstring := 'Combined Scores';
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end;
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for i := 0 to NoCases-2 do
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begin
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for k := i + 1 to NoCases-1 do
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Slopes[i,k] := (Values[k,j] - Values[i,j]) / (k-i);
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end;
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if PrtSlopesChk.Checked then
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begin
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outline := 'CASE';
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MAT_PRINT(Slopes,NoCases,NoCases,outline,RowLabels,ColLabels,NoCases);
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end;
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// get ranked slopes and median estimator
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count := 0;
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for i := 0 to NoCases-2 do
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begin
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for k := i+1 to NoCases-1 do
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begin
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RankedQ[count] := Slopes[i,k];
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count := count + 1;
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end;
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end;
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//sort into ascending order
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for i := 0 to count - 2 do
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begin
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for k := i + 1 to count-1 do
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begin
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if RankedQ[i] > RankedQ[k] then
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begin
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temp := RankedQ[i];
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RankedQ[i] := RankedQ[k];
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RankedQ[k] := temp;
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end;
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end;
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end;
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if PrtRanksChk.Checked then
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begin
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SetLength(RankLabels,count);
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for k := 0 to count-1 do RankLabels[k] := IntToStr(k+1);
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OutputFrm.RichEdit.Lines.Add('Ranked Slopes');
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for i := 0 to count-1 do
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begin
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outline := format('Label = %s, Ranked Q = %8.3f',
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[RankLabels[i],RankedQ[i]]);
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OutputFrm.RichEdit.Lines.Add(outline);
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end;
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OutputFrm.ShowModal;
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RankLabels := nil;
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end;
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// get median slope
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half := count div 2;
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if (2 * half) < count then MedianSlope := RankedQ[half]
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else MedianSlope := (RankedQ[half-1] + RankedQ[half]) / 2.0;
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// get Mann-Kendall statistic based on tied values
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for i := 0 to NoCases-1 do Sorted[i] := Values[i,j];
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for i := 0 to NoCases-2 do
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begin
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for k := i+1 to NoCases-1 do
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begin
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if Sorted[i] > Sorted[k] then
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begin
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temp := Sorted[i];
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Sorted[i] := Sorted[k];
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Sorted[k] := temp;
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end;
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end;
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end;
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MannKendall := 0.0;
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q := 0;
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i := -1;
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while (i < NoCases-2) do
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begin
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i := i + 1;
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tp := 1; // no. of ties for pth (i) value
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for k := i + 1 to NoCases-1 do
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begin
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if Sorted[k] <> Sorted[i] then
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begin
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i := k-1;
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break;
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end
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else tp := tp + 1;
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end; // next k
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if tp > 1 then
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begin
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q := q + 1;
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MannKendall := MannKendall + (tp * (tp-1) * (2 * tp + 5));
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end;
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end; // end next i
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MannKendall := (NoCases * (NoCases-1) * (2 * NoCases + 5) -
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MannKendall) / 18.0;
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Z := inversez(Alpha);
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if MannKendall > 0 then
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begin
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C := Z * sqrt(MannKendall);
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M1 := (count - C) / 2.0;
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M2 := (count + C) / 2.0;
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end
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else begin
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outline := format('Error: z = %8.3f, Mann-Kendall = %8.3f',
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[Z,MannKendall]);
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OutputFrm.RichEdit.Lines.Add(outline);
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end;
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// show results
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if j < noselected then
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begin
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outline := format('Results for %s',[cellstring]);
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OutputFrm.RichEdit.Lines.Add(outline);
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end
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else
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OutputFrm.RichEdit.Lines.Add('Results for Averaged Values');
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if (noselected > 1) and (Standardize = true) then
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begin
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mean := 0.0;
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stddev := 0.0;
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for i := 0 to NoCases-1 do
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begin
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mean := mean + Values[i,j];
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stddev := stddev + (Values[i,j] * Values[i,j]);
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end;
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stddev := stddev - (mean * mean) / NoCases;
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stddev := stddev / (NoCases - 1);
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stddev := sqrt(stddev);
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mean := mean / NoCases;
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outline := format('Mean = %8.3f, Standard Deviation = %8.3f',
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[mean,stddev]);
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OutputFrm.RichEdit.Lines.Add(outline);
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end;
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outline := format('Median Slope for %d values = %8.3f',
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[count,MedianSlope]);
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OutputFrm.RichEdit.Lines.Add(outline);
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outline := format('Mann-Kendall Variance statistic = %8.3f (%d ties)',
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|
[MannKendall,q]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
outline := format('Ranks of the lower and upper confidence = %8.3f, %8.3f',
|
||
|
|
[M1, M2+1]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
low := round(M1 - 1.0);
|
||
|
|
if ((M1-1) - low) > 0.5 then low := round(M1-1);
|
||
|
|
hi := round(M2);
|
||
|
|
if (M2 - hi) > 0.5 then hi := round(M2);
|
||
|
|
if (low > 0) or (hi <= count) then
|
||
|
|
begin
|
||
|
|
outline := format('Corresponding lower and upper slopes = %8.3f, %8.3f',
|
||
|
|
[RankedQ[low],RankedQ[hi]]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
end
|
||
|
|
else begin
|
||
|
|
outline := format('ERROR! low rank = %d, hi rank = %d',
|
||
|
|
[low, hi]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
end;
|
||
|
|
OutputFrm.RichEdit.Lines.Add('');
|
||
|
|
|
||
|
|
// plot slopes if elected
|
||
|
|
if Plot then
|
||
|
|
begin
|
||
|
|
SetLength(GraphFrm.Xpoints,1,NoCases+1);
|
||
|
|
SetLength(GraphFrm.Ypoints,1,NoCases+1);
|
||
|
|
GraphFrm.GraphType := 2;
|
||
|
|
GraphFrm.nosets := 1;
|
||
|
|
GraphFrm.nbars := NoCases;
|
||
|
|
GraphFrm.BackColor := clYellow;
|
||
|
|
GraphFrm.WallColor := clBlue;
|
||
|
|
GraphFrm.FloorColor := clGray;
|
||
|
|
if j < noselected then GraphFrm.Heading := OS3MainFrm.DataGrid.Cells[col,0]
|
||
|
|
else GraphFrm.Heading := 'Average Values';
|
||
|
|
GraphFrm.barwideprop := 1.0;
|
||
|
|
GraphFrm.AutoScaled := true;
|
||
|
|
GraphFrm.ShowLeftWall := true;
|
||
|
|
GraphFrm.ShowRightWall := true;
|
||
|
|
GraphFrm.ShowBottomWall := true;
|
||
|
|
GraphFrm.YTitle := 'Measure';
|
||
|
|
GraphFrm.XTitle := 'Time';
|
||
|
|
for k := 0 to NoCases - 1 do
|
||
|
|
begin
|
||
|
|
GraphFrm.Ypoints[0,k] := Values[k,j];
|
||
|
|
GraphFrm.Xpoints[0,k] := k+1;
|
||
|
|
end;
|
||
|
|
GraphFrm.ShowModal;
|
||
|
|
GraphFrm.Ypoints := nil;
|
||
|
|
GraphFrm.Xpoints := nil;
|
||
|
|
end;
|
||
|
|
|
||
|
|
// plot ranked slopes if elected
|
||
|
|
if SlopePlot then
|
||
|
|
begin
|
||
|
|
SetLength(GraphFrm.Xpoints,1,count+1);
|
||
|
|
SetLength(GraphFrm.Ypoints,1,count+1);
|
||
|
|
GraphFrm.GraphType := 2;
|
||
|
|
GraphFrm.nosets := 1;
|
||
|
|
GraphFrm.nbars := count;
|
||
|
|
GraphFrm.BackColor := clYellow;
|
||
|
|
GraphFrm.WallColor := clBlue;
|
||
|
|
GraphFrm.FloorColor := clGray;
|
||
|
|
GraphFrm.Heading := 'Ranked Slopes';
|
||
|
|
GraphFrm.barwideprop := 1.0;
|
||
|
|
GraphFrm.AutoScaled := true;
|
||
|
|
GraphFrm.ShowLeftWall := true;
|
||
|
|
GraphFrm.ShowRightWall := true;
|
||
|
|
GraphFrm.ShowBottomWall := true;
|
||
|
|
GraphFrm.YTitle := 'Slope';
|
||
|
|
GraphFrm.XTitle := 'Rank';
|
||
|
|
for k := 0 to count - 1 do
|
||
|
|
begin
|
||
|
|
GraphFrm.Ypoints[0,k] := RankedQ[k];
|
||
|
|
GraphFrm.Xpoints[0,k] := k+1;
|
||
|
|
end;
|
||
|
|
GraphFrm.ShowModal;
|
||
|
|
GraphFrm.Ypoints := nil;
|
||
|
|
GraphFrm.Xpoints := nil;
|
||
|
|
end;
|
||
|
|
OutputFrm.ShowModal;
|
||
|
|
OutputFrm.RichEdit.Clear;
|
||
|
|
end; // next variable j
|
||
|
|
|
||
|
|
if AvgSlope then
|
||
|
|
begin
|
||
|
|
for i := 0 to NoCases-2 do
|
||
|
|
begin
|
||
|
|
for k := i + 1 to NoCases-1 do
|
||
|
|
begin
|
||
|
|
AvgSlopes[i,k] := AvgSlopes[i,k] + Slopes[i,k];
|
||
|
|
end;
|
||
|
|
end;
|
||
|
|
end;
|
||
|
|
|
||
|
|
// Average multiple measures
|
||
|
|
if AvgSlope then
|
||
|
|
begin
|
||
|
|
OutputFrm.RichEdit.Lines.Add('Results for Averaged Slopes');
|
||
|
|
for i := 0 to NoCases-2 do
|
||
|
|
begin
|
||
|
|
for k := i + 1 to NoCases-1 do
|
||
|
|
AvgSlopes[i,k] := AvgSlopes[i,k] / noselected;
|
||
|
|
end;
|
||
|
|
|
||
|
|
// get ranked slopes and median estimator
|
||
|
|
count := 0;
|
||
|
|
for i := 0 to NoCases-2 do
|
||
|
|
begin
|
||
|
|
for j := i + 1 to NoCases-1 do
|
||
|
|
begin
|
||
|
|
RankedQ[count] := AvgSlopes[i,j];
|
||
|
|
count := count + 1;
|
||
|
|
end;
|
||
|
|
end;
|
||
|
|
for i := 0 to Count-2 do
|
||
|
|
begin
|
||
|
|
for j := i + 1 to count - 1 do
|
||
|
|
begin
|
||
|
|
if RankedQ[i] > RankedQ[j] then
|
||
|
|
begin
|
||
|
|
temp := RankedQ[i];
|
||
|
|
RankedQ[i] := RankedQ[j];
|
||
|
|
RankedQ[j] := temp;
|
||
|
|
end;
|
||
|
|
end;
|
||
|
|
end;
|
||
|
|
// get median slope
|
||
|
|
half := count div 2;
|
||
|
|
if (2 * half) < count then MedianSlope := RankedQ[half + 1]
|
||
|
|
else MedianSlope := (RankedQ[half] + RankedQ[half+1]) / 2.0;
|
||
|
|
// get Mann-Kendall statistic based on tied values
|
||
|
|
MannKendall := 0.0;
|
||
|
|
q := 0;
|
||
|
|
i := -1;
|
||
|
|
while (i < count-1) do
|
||
|
|
begin
|
||
|
|
i := i + 1;
|
||
|
|
tp := 1; // no. of ties for pth (i) value
|
||
|
|
for j := i + 1 to count-1 do
|
||
|
|
begin
|
||
|
|
if RankedQ[j] <> RankedQ[i] then
|
||
|
|
begin
|
||
|
|
i := j - 1;
|
||
|
|
break;
|
||
|
|
end
|
||
|
|
else tp := tp + 1;
|
||
|
|
end;
|
||
|
|
if tp > 1 then
|
||
|
|
begin
|
||
|
|
q := q + 1;
|
||
|
|
MannKendall := MannKendall + (tp * (tp-1) * (2 * tp + 5));
|
||
|
|
end;
|
||
|
|
end; // end do while
|
||
|
|
MannKendall := (NoCases * (NoCases-1) * (2 * NoCases + 5) - MannKendall) / 18.0;
|
||
|
|
Z := inversez(Alpha);
|
||
|
|
if MannKendall < 0.0 then
|
||
|
|
begin
|
||
|
|
outline := format('Error in calculating Mann-Kendall = %8.3f',
|
||
|
|
[MannKendall]);
|
||
|
|
ShowMessage(outline);
|
||
|
|
end;
|
||
|
|
if MannKendall > 0.0 then C := Z * sqrt(MannKendall)
|
||
|
|
else C := Z;
|
||
|
|
M1 := (count - C) / 2.0;
|
||
|
|
M2 := (count + C) / 2.0;
|
||
|
|
// Show results
|
||
|
|
outline := format('Median Slope for %d values = %8.3f for averaged measures',
|
||
|
|
[count,MedianSlope]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
outline := format('Mann-Kendall Variance statistic = %8.3f (%d ties observed)',
|
||
|
|
[MannKendall,q]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
outline := format('Ranks of the lower and upper confidence = (%8.3f, %8.3f)',
|
||
|
|
[M1, M2]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
low := round(M1) - 1;
|
||
|
|
if ((M1-1) - low) > 0.5 then low := round(M1 - 1);
|
||
|
|
hi := round(M2);
|
||
|
|
if (M2 - hi) > 0.5 then hi := round(M2);
|
||
|
|
outline := format('Corresponding lower and upper slopes = (%8.3f, %8.3f)',
|
||
|
|
[RankedQ[low],RankedQ[hi]]);
|
||
|
|
OutputFrm.RichEdit.Lines.Add(outline);
|
||
|
|
end; // end if average slope
|
||
|
|
OutputFrm.ShowModal;
|
||
|
|
|
||
|
|
// cleanup
|
||
|
|
AvgSlopes := nil;
|
||
|
|
Sorted := nil;
|
||
|
|
RankedQ := nil;
|
||
|
|
Slopes := nil;
|
||
|
|
Values := nil;
|
||
|
|
selected := nil;
|
||
|
|
ColLabels := nil;
|
||
|
|
RowLabels := nil;
|
||
|
|
end;
|
||
|
|
|
||
|
|
procedure TSensForm.FormActivate(Sender: TObject);
|
||
|
|
var
|
||
|
|
w: Integer;
|
||
|
|
begin
|
||
|
|
if FAutoSized then
|
||
|
|
exit;
|
||
|
|
|
||
|
|
w := MaxValue([ResetBtn.Width, CancelBtn.Width, ComputeBtn.Width, ReturnBtn.Width]);
|
||
|
|
ResetBtn.Constraints.MinWidth := w;
|
||
|
|
CancelBtn.Constraints.MinWidth := w;
|
||
|
|
ComputeBtn.Constraints.MinWidth := w;
|
||
|
|
ReturnBtn.Constraints.MinWidth := w;
|
||
|
|
|
||
|
|
Constraints.MinWidth := Width;
|
||
|
|
Constraints.MinHeight := Height;
|
||
|
|
|
||
|
|
FAutoSized := true;
|
||
|
|
end;
|
||
|
|
|
||
|
|
procedure TSensForm.FormCreate(Sender: TObject);
|
||
|
|
begin
|
||
|
|
Assert(OS3MainFrm <> nil);
|
||
|
|
if OutputFrm = nil then
|
||
|
|
Application.CreateForm(TOutputFrm, OutputFrm);
|
||
|
|
if GraphFrm = nil then
|
||
|
|
Application.CreateForm(TGraphFrm, GraphFrm);
|
||
|
|
end;
|
||
|
|
|
||
|
|
procedure TSensForm.OutBtnClick(Sender: TObject);
|
||
|
|
VAR index : integer;
|
||
|
|
begin
|
||
|
|
index := SelectedList.ItemIndex;
|
||
|
|
VarList.Items.Add(SelectedList.Items.Strings[index]);
|
||
|
|
SelectedList.Items.Delete(index);
|
||
|
|
InBtn.Enabled := true;
|
||
|
|
if SelectedList.Items.Count = 0 then OutBtn.Enabled := false;
|
||
|
|
end;
|
||
|
|
|
||
|
|
initialization
|
||
|
|
{$I sensunit.lrs}
|
||
|
|
|
||
|
|
end.
|
||
|
|
|