public class GrayModel
    {
        private double a0, a1, a2;
        private int size;
        private double error;

        public GrayModel()
        {
        }

        public void build(double[] x0)
        {
            size = x0.Length;
            double[] x1 = new double[size];
            x1[0] = x0[0];
            for (int i = 1; i < size; i++)
            {
                x1[i] = x0[i] + x1[i - 1];
            }
            double[,] b = new double[size - 1, 2];
            double[,] bt = new double[2, size - 1];
            double[,] y = new double[size - 1, 1];
            for (int i = 0; i < b.GetLength(0); i++)
            {
                b[i, 0] = -(x1[i] + x1[i + 1]) / 2;
                b[i, 1] = 1;
                bt[0, i] = b[i, 0];
                bt[1, i] = 1;
                y[i, 0] = x0[i + 1];
            }
            double[,] t = new double[2, 2];
            multiply(bt, b, t);
            t = inverse(t);
            double[,] t1 = new double[2, size - 1];
            multiply(t, bt, t1);
            double[,] t2 = new double[2, 1];
            multiply(t1, y, t2);
            a0 = t2[0, 0];
            double u = t2[1, 0];
            a2 = u / a0;
            a1 = x0[0] - a2;
            a0 = -a0;

            error = 0;
            for (int i = 0; i < x0.Length; i++)
            {
                double d = (x0[i] - getX0(i));
                error += d * d;
            }
            error /= x0.Length;
        }

        /// <summary>
        /// 误差
        /// </summary>
        /// <returns></returns>
        public double getError()
        {
            return error;
        }

        double getX1(int k)
        {
            return a1 * Math.Exp(a0 * k) + a2;
        }

        double getX0(int k)
        {
            // return a0 * a1 * Math.exp(a0 * k);  
            if (k == 0)
                return a1 * Math.Exp(a0 * k) + a2;
            else
                return a1 * (Math.Exp(a0 * k) - Math.Exp(a0 * (k - 1)));
        }

       /// <summary>
       /// 预测后续的值
       /// </summary>
       /// <param name="index"></param>
       /// <returns></returns>
        public double nextValue(int index)
        {
            if (index < 0)
                throw new Exception("超出索引范围");
            return getX0(size + index);
        }

       /// <summary>
       /// 预测下一个值
       /// </summary>
       /// <returns></returns>
        public double nextValue()
        {
            return nextValue(0);
        }

        static double[,] inverse(double[,] t)
        {
            double[,] a = new double[2, 2];
            double det = t[0, 0] * t[1, 1] - t[0, 1] * t[1, 0];
            a[0, 0] = t[1, 1] / det;
            a[0, 1] = -t[1, 0] / det;
            a[1, 0] = -t[0, 1] / det;
            a[1, 1] = t[0, 0] / det;
            return a;
        }

        static void multiply(double[,] left, double[,] right, double[,] dest)
        {
            int n1 = left.GetLength(0);
            int m1 = left.GetLength(1);
            int m2 = right.GetLength(1);
            for (int k = 0; k < n1; k++)
            {
                for (int s = 0; s < m2; s++)
                {
                    dest[k, s] = 0;
                    for (int i = 0; i < m1; i++)
                    {
                        dest[k, s] += left[k, i] * right[i, s];
                    }
                }
            }
        }
    }

 static void Main(string[] args)

        {

           double[] a=new double[]{2.874,3.278,3.337,3.390,3.679};

           GrayModel gm = new GrayModel();

           gm.build(a);

            Console.WriteLine(gm.nextValue());

            Console.Read();

        }