For example, here’s some MATLAB code for fitting a polynomial of degree 6 to some data, and then evaluating the fitted polynomial at a point (x = 0.25).

 x = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 
        1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5]

 y = [0 0.112462916018285 0.222702589210478 0.328626759459127 0.428392355046668 0.520499877813047 0.603856090847926 0.677801193837419 0.742100964707661 0.796908212422832 0.842700792949715 0.880205069574082 0.910313978229635 0.934007944940652 0.952285119762649 0.966105146475311 0.976348383344644 0.983790458590775 0.989090501635731 0.992790429235257 0.995322265018953 0.997020533343667 0.998137153702018 0.998856823402643 0.999311486103355 0.999593047982555]

p = polyfit(x,y,6)
p = 0.0084   -0.0983    0.4217   -0.7435    0.1471    1.1064    0.0004
f = polyval(p, 0.25); 
f = 0.2762

Here’s the equivalent C# NMath code:

#using CenterSpace.NMath.Analysis
public void FitData()
{
  DoubleVector x = new DoubleVector("[0 0.1 0.2 0.3 0.4 0.5 
    0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 
    2.2 2.3 2.4 2.5]");

  DoubleVector y = new DoubleVector("[0 0.112462916018285 0.222702589210478 0.328626759459127   0.428392355046668 0.520499877813047 0.603856090847926 0.677801193837419 0.742100964707661 0.796908212422832 0.842700792949715 0.880205069574082 0.910313978229635 0.934007944940652 0.952285119762649 0.966105146475311 0.976348383344644 0.983790458590775 0.989090501635731 0.992790429235257 0.995322265018953 0.997020533343667 0.998137153702018 0.998856823402643 0.999311486103355 0.999593047982555]");

  PolynomialLeastSquares pls = new PolynomialLeastSquares( 6, x, y );
  Console.WriteLine( pls.Coefficients );
  Console.WriteLine();
  Console.WriteLine( pls.FittedPolynomial.Evaluate( 0.25 ) );
}

This creates the output.

[ 0.000441173961987631 1.10644604462547 0.147104056633056 
  -0.743462849129717 0.421736169818002 -0.0982995753367523 
  0.00841937177923124 ]

0.276183548385269

Note that the order of the coefficient vector in NMath is reversed relative that returned from MATLAB’s polyfit() function. In NMath, the constant is at index 0 and the leading coefficient is at index Coefficients.Length - 1. If you wish, you can use the Reverse() method on the coefficient vector to reverse the ordering.

-Ken

Notes
Visualization provided in partnership with Nevron

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