forum.alglib.net

[data]
x: 0 0.475 2.01 5.96 15.0 32.9
y:0.75 3.2 13.8 53.7 170.4 387.8

[curve]
f(x) = (a*x + b*x^(2/3) + c*x^(1/3) + d)^3

How to fit the curve? Parameter a=?, b=?, c=? and d=?

Thanks!

Look at http://www.alglib.net/translator/man/ma ... sfit_d_nlf - it demonstrates fitting using function value only (no analytic derivatives). You can add differentiation later, if you want.

My source code below:


public static void function_cx_1_func(double[] c, double[] x, ref double func, object obj)
{
// this callback calculates f(c,x)= (c0*x + c1*x^(2/3) + c2*x^(1/3) + c3)^3
// where x is a position on X-axis and c is adjustable parameter
func = System.Math.Pow((c[0] * x[0] + c[1] * Math.Pow(x[0], 2 / 3) + c[2] * Math.Pow(x[0], 1 / 3) + c[3]), 3);
}
static void Main(string[] args)
{
//
// In this example we demonstrate exponential fitting
// by f(x) = (c0*x + c1*x^(2/3) + c2*x^(1/3) + c3)^3
// using function value only.
//
// Gradient is estimated using combination of numerical differences
// and secant updates. diffstep variable stores differentiation step
// (we have to tell algorithm what step to use).
//
double[,] x = new double[,] { { 0 }, { 0.47 }, { 2.01 }, { 5.96 }, { 15 }, { 32.9 }};
double[] y = new double[] { 0.75, 3.2, 13.8, 53.7, 170.4, 387.8 };
double[] c = new double[] { 0.1, 0.1, 0.1, 0.1 };
double epsf = 0;
double epsx = 0.0000001;
int maxits = 0;
int info;
alglib.lsfitstate state;
alglib.lsfitreport rep;
double diffstep = 0.00001;

//
// Fitting without weights
//
alglib.lsfitcreatef(x, y, c, diffstep, out state);
alglib.lsfitsetcond(state, epsf, epsx, maxits);
alglib.lsfitfit(state, function_cx_1_func, null, null);
alglib.lsfitresults(state, out info, out c, out rep);
System.Console.WriteLine("{0}", info); // EXPECTED: 2
System.Console.WriteLine("{0}", alglib.ap.format(c, 5)); // EXPECTED: [-0.22, 1.4, -0.23, 0.909]

//
// Fitting with weights
// (you can change weights and see how it changes result)
//
double[] w = new double[] { 1, 1, 1, 1, 1, 1};
alglib.lsfitcreatewf(x, y, w, c, diffstep, out state);
alglib.lsfitsetcond(state, epsf, epsx, maxits);
alglib.lsfitfit(state, function_cx_1_func, null, null);
alglib.lsfitresults(state, out info, out c, out rep);
System.Console.WriteLine("{0}", info); // EXPECTED: 2
System.Console.WriteLine("{0}", alglib.ap.format(c, 5)); // EXPECTED: [-0.22, 1.4, -0.23, 0.909]
System.Console.ReadLine();
}

I hope the result is: EXPECTED: [-0.22, 1.4, -0.23, 0.909],

But the actual output is as follows:
2
{0.13321,0.98960,0.98985,0.99026}
2
{0.13321,0.98960,0.98985,0.99026}

Check into the formula found to be wrong.

How can i do?

Thanks!

That is easy :) you have to write 2.0/3.0 and 1.0/3.0 instead of 2/3 and 1/3. Former is 0.666 and 0.333, while latter is 0 and 0 again (integer division instead of real one).

o, Year!

Thanks!