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 Post subject: lsfitcreatef function with vector function
PostPosted: Sun Oct 28, 2018 1:29 pm 
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Joined: Tue May 08, 2018 3:15 pm
Posts: 3
Good day all!


I use C# version of ALGLIB 3.14.0.

I had quite good results in working with lsfitcreatef and lsfitcreatefg. I worked with analytic functions before.
Now I have to work with vectos and have to find results for such task:
-------------------------------------------------------------------------------------------
v1, v2, v are vectors length N and
v = a1 * v1 + a2 * 2
a1 and a2 - are unknown parameters. Need to find tallies for a1 and a2.

In more general case
v1,v2,..,vk (they are not orthogonal)
v = a1 * v1 + a2 * 2 + .... + ak * vk. Need to find tallies for a1, a2, ..., ak.

In most general case
v1,v2,..,vk (they are not orthogonal)
v = a1 * F(v1,ak+1,...,an) + a2 * F(v2,ak+1,...,an) + ... + ak * F(vk,ak+1,...,an), where F(vi,ak+1,...,an) = vi* - transformed vector vi.
ak+1,...,an - parameters of transformation. The form of transformation is the same for all vectors. For example: vi -> vi^(ak+1)
Need to find tallies for a1, a2, ..., ak, ak+1,...,an.
--------------------------------------------------------------------------------------------------------------------------------------------------------

I have tried this code:
Code:
  class Program
    {
        static void Main(string[] args)
        {
            double[] y = new double[] { 2, 2, 3, 3};
         
            double[,] x = new double[y.Length, 1];
           
            for (int i = 0; i < y.Length; i++)
            {
                x[i, 0] = (double)(i);
            }

            double[] s = new double[] {1, 1};       // scale
            double[] c = new double[] {2.2, 1};    // start values
            double[] bndl = new double[] {0.0, 0.0};     // lower bound                                                                                                                                                     
            double[] bndu = new double[] {4.0, 4.0};     // upper bound                                                                                                                                                             
            double epsx = 0.0001;
            int maxits = 0;
            int info;
            alglib.lsfitstate state;
            alglib.lsfitreport rep;
            double diffstep = 0.01;

            alglib.lsfitcreatef(x, y, c, diffstep, out state);         
            alglib.lsfitsetbc(state, bndl, bndu);
            alglib.lsfitsetcond(state, epsx, maxits);
            alglib.lsfitsetscale(state, s);
            alglib.lsfitfit(state, function_cx_2_func, null, null);
            alglib.lsfitresults(state, out info, out c, out rep);
           
            int iterationscount = rep.iterationscount;

            System.Console.WriteLine("{0}", info);
       System.Console.WriteLine("iterationscount = " + iterationscount.ToString());
            System.Console.WriteLine("{0}", alglib.ap.format(c, 7));
            System.Console.ReadKey();
        }

        public static void function_cx_2_func(double[] c, double[] x, ref double func, object obj)
        {
            // vectors a and b
           
            [b]double[] a = new double[] { 1, 1, 0, 0};
            double[] b = new double[] { 0, 0, 1, 1};[/b]
           
            func = func + c[0] * a[(int)x[0]] + c[1] * b[(int)x[0]];
        }
    }

Output:
2
iterationscount = 0
{2.1995969,0.9996091}

While correct result {2.0, 3.0}.

Most likely I was wrong somewhere in the code or in logic of lsfit subpackage.


I solved this task through minlm subpackage:
Code:
class Program
    {
        static void Main(string[] args)
        {
            //
            // This example demonstrates minimization of F(x0,x1) = f0^2+f1^2 + ....  fn^2       
            //
            // using "V" mode of the Levenberg-Marquardt optimizer.
            //
            // Optimization algorithm uses:
            // * function vector f[] = {f1,f2,...,fn^2}
            //
            // No other information (Jacobian, gradient, etc.) is needed.
            //

            double[] x = new double[] { 0, 0 };
            double epsx = 0.0000000001;
            int maxits = 100;                     
            alglib.minlmstate state;
            alglib.minlmreport rep;
            double[] bndl = new double[] { 0, 0 };               
            double[] bndu = new double[] { +4, +4 };   

            alglib.minlmcreatev(4, x, 0.0001, out state);
            alglib.minlmsetbc(state, bndl, bndu);           
            alglib.minlmsetcond(state, epsx, maxits);             
            alglib.minlmoptimize(state, function2_fvec, null, null);
            alglib.minlmresults(state, out x, out rep);

            System.Console.WriteLine("{0}", alglib.ap.format(x, 7));
            System.Console.WriteLine("{0}", alglib.ap.format(rep.iterationscount, 7));
            System.Console.ReadLine();
           
        }
       
        public static void function2_fvec(double[] x, double[] fi, object obj)
        {
            double[] array1 = new double[] { 1, 1, 0, 0 };
            double[] array2 = new double[] { 0, 0, 1, 1};
            double[] array3 = new double[] { 2, 2, 3, 3};       

            for (int i = 0; i < array1.Length; i++)
            {
                fi[i] = System.Math.Pow(array3[i] - x[0] * array1[i] - x[1] * array2[i], 2);
            }
        }
    }

Output
{2.0000000,3.0000000}
44.0000000+0.0000000i
OK

Sergey, could you spare a little time for my problem, please?
I hoped use lsfit subpackage due to more compact form for function2_fvec as well as for uniformity of code in other similar tasks.

And second question: what is the differece between lsfit subpackage and minlm subpackage?
Is it possible to say that some package is better for NLS-fiting?

With the best regards

Dmitri


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 Post subject: Re: lsfitcreatef function with vector function
PostPosted: Wed Oct 31, 2018 1:22 pm 
Offline
Site Admin

Joined: Fri May 07, 2010 7:06 am
Posts: 849
Hi!

lsfit subpackage is intended for "simple" situations like when you have scalar target function which is same for all dataset points, minlm is intended for general situation - i.e. for anything else. Given that, it does not makes much sense in extending lsfit with more complex cases (like yours) - you already have minlm for such tasks :)


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