Linear Curve Fit Function

[Narcís]

Hi Hans,

According to what Marjan described here you could calculate y in PlotSmoothFit like this:

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      y := coeffs[1] * x - coeffs[1] * MinXValue + coeffs[0] + MinYValue;

which would be the equivalent to Poly funciton call you make:

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      y := Poly( x-MinXValue, coeffs ) + MinYValue;

However, to get same y values as source series you should not add coeffs[0]:

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      y := coeffs[1] * x - coeffs[1] * MinXValue + MinYValue;

Which would be the equivalent to populating coeffs array like this:

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    for i := 2 to imax do
      coeffs[ i-1 ] := AnswerVector[ i ];

So the full method would be like this:

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procedure PlotSmoothFit( var serFit, serSmoothFit : tFastLineSeries;
                         FitFctn : TCurveFittingFunction;
                         smoothness : integer );
var interval, x, y : double;
    i, imax : integer;
    coeffs : array of double;
begin
  with FitFctn do
  begin
    imax := PolyDegree;
    SetLength( coeffs, imax );
    for i := 2 to imax do
      coeffs[ i-1 ] := AnswerVector[ i ];
  end;

  serSmoothFit.DataSource:=nil;

  with serFit do
  begin
    interval := ( MaxXValue - MinXValue )/ smoothness;

    for i := 1 to smoothness do
    begin
      x := MinXValue + (i-1) * interval;
      y := Poly( x-MinXValue, coeffs ) + MinYValue;
      //y := coeffs[1] * x - coeffs[1] * MinXValue + coeffs[0] + MinYValue;
      serSmoothFit.AddXY( x, y );
    end;
  end
end;

Hope this helps!

[Hans Wolfgang]

Yes thanks Narcis this was a great help. The linear fit works fine.

However (see attached) with the cubic fit (polydegree = 4), there is again a bias in fitted results without AnswerVector[1]. If I include it, the match is better. So, if you agree, I will alter the code to test for polydegree and act accordingly.

"Better" in that, for the cubic example in the attachment, the fitted polynomial appears to be evaluated only at the input data points, and it looks like straight lines are drawn between them. That was the original motivation for the "smooth fit", which, as you will see in the attached code, gives the true fitted curve through the entire range of the input data.

[Narcís]

Hi Hans,

Yes thanks Narcis this was a great help. The linear fit works fine.

You're welcome, I'm glad to hear that!

However (see attached) with the cubic fit (polydegree = 4), there is again a bias in fitted results without AnswerVector[1]. If I include it, the match is better. So, if you agree, I will alter the code to test for polydegree and act accordingly.

Yes, sure.

"Better" in that, for the cubic example in the attachment, the fitted polynomial appears to be evaluated only at the input data points, and it looks like straight lines are drawn between them. That was the original motivation for the "smooth fit", which, as you will see in the attached code, gives the true fitted curve through the entire range of the input data.

Ok, or in that case you can just "play" with function's Factor property, for example:

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  TTeeFunction1.Factor:=4;

Doing so you wouldn't have the need to perform the "smooth fit":

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procedure TResTime.FormCreate(Sender: TObject);
begin
  with RtLabData do begin
    AddXY( 5.005E+02, 5.86E+03 );
    AddXY( 6.665E+02, 4.00E+03 );
    AddXY( 8.366E+02, 2.98E+03 );
    AddXY( 9.530E+02, 2.62E+03 );
    AddXY( 1.325E+03, 1.79E+03 );
  end;
  tTeeFunction1.PolyDegree := 4;
  TTeeFunction1.Factor:=4;
  tTeeFunction1.AddPoints( RtLabData );
  //PlotSmoothFit( serFit, serSmoothFit, tTeeFunction1, 500 );
end;

Also, with the code above you could calculate smoothing like in the code below to obtain identical series.

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procedure PlotSmoothFit( var serFit, serSmoothFit : tFastLineSeries;
                         FitFctn : TCurveFittingFunction;
                         smoothness : integer );

var x, y : double; i, imax : integer; coeffs : array of double;

begin
  with FitFctn do begin
    imax := polydegree;
    SetLength( coeffs, imax );
    for i := 1 to imax do
      coeffs[ i-1 ] := AnswerVector[ i ];
    { end }
  end;

  with serFit do begin
    for i := 0 to Count-1 do begin
      x := XValue[i];
      y := poly( x-minXvalue, coeffs ) + minYvalue;
      serSmoothFit.AddXY( x, y )
    end;
  end
end;

Hope this helps!

[Hans Wolfgang]

What is the Factor property? How does it work? My D6 TC5 environment does not know anything about a "Factor". I can go on with smooth fit anyway.

[Narcís]

Hi Hans,

Below there's Factor description at TeeChart Pro v8 documentation.

Default : 4

Gets or sets the number of times the resulting smooth points are in quantity compared to source points.

For example, a value of 4 means the smooth points will be 4 times the number of source points.

The bigger the factor property is, the smoothest resulting curves will be.

[Hans Wolfgang]

Thanks. I'm upgrading right away.

In the attached project I cannot access values of two series.The x and y values show up as xxxE-38. To replicate, please put a breakpoint In uTest2.pas line 120 (for first series) and 122 (for second series), and look at rmax and rmin. Yet the interface shows that the series were plotted correctly.

I then want to reuse one or the other series but cannot access their values.

Would you please show me what is going wrong here.

[Narcís]

Hi Hans,

Thanks. I'm upgrading right away.

Excellent

In the attached project I cannot access values of two series.The x and y values show up as xxxE-38. To replicate, please put a breakpoint In uTest2.pas line 120 (for first series) and 122 (for second series), and look at rmax and rmin. Yet the interface shows that the series were plotted correctly.

I then want to reuse one or the other series but cannot access their values.

I'm not sure about what's going on but I guess it must be a Delphi debugger issue. If you use rmin and rmax as in code below and add a breakpoint at Chart.Title.Text.Add lines you'll see variables value being correct. It's as if debugger doesn't update variables value until they are used.

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  rmax := serFit.maxYvalue;
  rmin := serFit.minYvalue;
  Chart1.Title.Text.Add(FloatToStr(rmax) + ' - ' + FloatToStr(rmin));

  rmax := serSmoothFit.maxYvalue;
  rmin := serSmoothFit.minYvalue;
  Chart1.Title.Text.Add(FloatToStr(rmax) + ' - ' + FloatToStr(rmin));

Does this work fine for you? Can you use series' values successfully at a later time?

Thanks in advance.