Curve fitting to a 3D polynomial with variable powers

Question

I have 3 data sets. 2 for polynomial itself (let's call them x and y) and 1 for the function value (it's gonna be z).

Polynomial looks something like this (assuming the power of both dimensions is 3):

z = a00 + a01*x + a02*x^2 + a03*x^3 + a10*y + a11*y*x + a12*y*x^2 ... etc

I need to be able to set the power of each dimension when preparing for approximation of values of "a".

I don't really get how CurveFitting functions work with Math.NET Numerics, but i've tried Fit.LinearMultiDim and MultipleRegression.QR. I'm having trouble with initializing the Func delegate


    var zs = new double[]
    {
        //values here

    };

    var x = new double[]
    {
        //values here
    };

    var y = new double[]
    {
        //values here. But the amounts are equal
    };

    var design = Matrix<double>.Build.DenseOfRowArrays(Generate.Map2(x, y,(t, w) =>
    {
        var list = new List<double>();      //Can i get this working?
        for (int i = 0; i <= 3; i++)
        {
            for (int j = 0; j <= 3; j++)
            {
                list.Add(Math.Pow(t, j)*Math.Pow(w, i));
            }
        }
        return list.ToArray();
    }));

    double[] p = MultipleRegression.QR(design, Vector<double>.Build.Dense(zs)).ToArray();

So ideally i need to be able to compose the function with some sort of loop that accounts for the max power of both variables.

UPD: The function is always above zero on any axis

@DaveInCaz yes. Thanks for the correction. English is not my native language — TabakaevGA, May 21 '19 at 12:43
If you only need a good approximating fit to the data, a spline can be a good choice. — James Phillips, May 22 '19 at 11:54

TabakaevGA · Accepted Answer · 2019-05-28T16:17:02.347

I think i got it working.

Here's the code:

    List<Func<double[], double>> ps = new List<Func<double[],double>>();

                for (int i = 0; i <= polynomialOrderFirstVal; i++)
                {
                    for (int j = 0; j <= polynomialOrderSecVal; j++)
                    {
                        var orderFirst = j;
                        var orderSecond = i;
                        ps.Add(d => Math.Pow(d[0], orderFirst) * Math.Pow(d[1],orderSecond));
                    }
                }
                var psArr = ps.ToArray();
                double[] coefs = Fit.LinearMultiDim(x, y, psArr);

Curve fitting to a 3D polynomial with variable powers

1 Answers1