using System;

namespace Science.Mathematics.VectorCalculus
{
    public class Matrix
    {
        protected double[,] el;
        protected int m, n;
        public int RowDimension
        {
            get { return m; }
        }
        public int ColumnDimension
        {
            get { return n; }
        }
        public Matrix(double[,] x)
        {
            m = x.GetLength(0);
            n = x.GetLength(1);
            el = new double[m, n];
            for (int k = 0; k < m; k++)
                for (int kk = 0; kk < n; kk++)
                    el[k, kk] = x[k, kk];
        }
        public Matrix(int rowDimension, int columnDimension)
        {
            m = rowDimension;
            n = columnDimension;
            el = new double[m, n];
        }
        public double this[int whereRow, int whereColumn]
        {
            get { return el[whereRow, whereColumn]; }
            set { el[whereRow, whereColumn] = value; }
        }
        public Matrix Transpose
        {
            get
            {
                Matrix ma = new Matrix(n,m);
                for (int k = 0; k < m; k++)
                   for (int kk = 0; kk < n; kk++)
                     ma[kk,k] = el[k, kk];
                return ma;
            }
        }        
        public static Matrix operator *(double a, Matrix c)
        {
            Matrix b = new Matrix(c.RowDimension, c.ColumnDimension);
            for (int k = 0; k < c.RowDimension; k++)
                for (int j = 0; j < c.ColumnDimension; j++)
                  b[k,j] = a * c[k, j];
            return b;
        }
        public static Matrix operator *(Matrix c, double a)
        {
            return a * c;
        }
        public static Matrix operator +(Matrix a, Matrix c)
        {
            Matrix b = new Matrix(a.RowDimension, a.ColumnDimension);
            for (int k = 0; k < a.RowDimension; k++)
                for (int j = 0; j < a.ColumnDimension; j++)
                    b[k, j] = a[k, j] + c[k, j];
            return b;
        }
        public static Matrix operator -(Matrix a, Matrix c)
        {
            Matrix b = new Matrix(a.RowDimension, a.ColumnDimension);
            for (int k = 0; k < a.RowDimension; k++)
                for (int j = 0; j < a.ColumnDimension; j++)
                    b[k, j] = a[k, j] - c[k, j];
            return b;
        }
        public static Matrix operator -(Matrix c)
        {
            Matrix b = new Matrix(c.RowDimension, c.ColumnDimension);
            for (int k = 0; k < c.RowDimension; k++)
                for (int j = 0; j < c.ColumnDimension; j++)
                    b[k, j] = - c[k, j];
            return b;
        }

        public static Vector operator *(Matrix a, Vector c)
        {
            Vector b = new Vector(a.RowDimension);
            for (int k = 0; k < b.Dimension; k++)
            {
                double sum = 0.0;
                for (int s = 0; s < c.Dimension; s++)
                    sum += a[k, s] * c[s];
                b[k] = sum;
            }
            return b;
        }
        public static Vector operator *(Vector c, Matrix a)
        {
            Vector b = new Vector(a.ColumnDimension);
            for (int k = 0; k < b.Dimension; k++)
            {
                double sum = 0.0;
                for (int s = 0; s < c.Dimension; s++)
                    sum += c[s] * a[s, k];
                b[k] = sum;
            }
            return b;
        }
        public static Matrix operator *(Matrix a, Matrix c)
        {
            Matrix b = new Matrix(a.RowDimension, c.ColumnDimension);
            for (int k = 0; k < b.RowDimension; k++)
                for (int j = 0; j < b.ColumnDimension; j++)
                {
                    double sum = 0.0;
                    for (int s = 0; s < a.ColumnDimension; s++)
                        sum += a[k, s] * c[s, j];
                    b[k, j] = sum;
                }
            return b;
        }

        public override string ToString()
        {
            string res = "";
            for (int i = 0; i < this.RowDimension; i++)
            {
                for (int j = 0; j < this.ColumnDimension; j++)
                    res += this[i, j].ToString() + "     ";
                res += "\r\n";
            }
            res += "\r\n";
            return res;
        }  
    }
}