using System;

namespace Science.Mathematics.VectorCalculus
{
    public class ImplicitFunctionTheorem
    {
        private double[] f;
        private double[] t;
        private Function.ToLastType<double[], double[], double[]> Fm;
        public ImplicitFunctionTheorem(Function.ToLastType<double[], double[], double[]> function,
            double[] x0, double[] z0)
        {
            f = x0;
            t = z0;
            Fm = function;
        }

        private int i = 0;
        public void FindDeterminant()
        {
            Function.ToLastType<double[], double> fff;
            Gradient obj;
            MatrixSquare ma = new MatrixSquare(t.Length);
            for(int j = 0; j < t.Length; j++)
            {
                i = j;
                fff = new Function.ToLastType<double[], double>(ff);
                obj = new Gradient(fff, t);
                obj.Compute();
                for (int k = 0; k < t.Length; k++)
                {
                    ma[j, k] = obj.Result[k];
                }
            }
            d = ma.Determinant;
        }
        private double ff(double[] xx)
        {
            return Fm(f, xx)[i];
        }

        private double d;
        public double Determinant
        {
            get { return d; }
        }
    }
}