Polynomial Curve Fitting
Thursday, September 10th, 2009A customer recently asked how to reproduce the results of the MATLAB polyfit function in NMath. This is easily done using NMath in C#.
| MATLAB | NMath | |
|---|---|---|
| Standard package | CenterSpace.NMath.Analysis |
|
polyfit( x, y, degree ) |
PolynomialLeastSquares( degree, x, y ) |
|
| Notes: polynomial coefficients are returned in the reverse order. | ||
|
| ||
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
6th degree polynomial fit using Polynomial Least Squares.
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
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