using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CaeGlobals
{
    // https://docs.microsoft.com/en-us/archive/msdn-magazine/2016/july/test-run-matrix-inversion-using-csharp#the-demo-program


    // Scale nodes
    //if (_currentView == ViewGeometryModelResults.Results && _results.Mesh != null)
    //{
    //    float[] values;
    //    double[][] deformedCoor;
    //    float scale = GetScale();
    //    //
    //    _results.GetNodesAndValues(_currentFieldData, cellFaceNodeIds, out deformedCoor, out values);
    //    // A - first cell point
    //    // B - second cell point
    //    // C - third cell point
    //    // P - point
    //    // A * u + B * v + C * w = P
    //    double[][] linSys = new double[3][];
    //    linSys[0] = new double[] { deformedCoor[0][0], deformedCoor[1][0], deformedCoor[2][0] };
    //    linSys[1] = new double[] { deformedCoor[0][1], deformedCoor[1][1], deformedCoor[2][1] };
    //    linSys[2] = new double[] { deformedCoor[0][2], deformedCoor[1][2], deformedCoor[2][2] };
    //    double[][] invLinSys = Matrix.MatrixInverse(linSys);
    //    //
    //    double[][] p = new double[][] { new double[] { point[0] }, new double[] { point[1] }, new double[] { point[2] } };
    //    //
    //    double[][] uvw = Matrix.MatrixProduct(invLinSys, p);
    //    //
    //    double[][] coor;
    //    _results.GetNodesAndValues(_currentFieldData, cellFaceNodeIds, out coor, out values);
    //    //
    //    linSys[0] = new double[] { coor[0][0], coor[1][0], coor[2][0] };
    //    linSys[1] = new double[] { coor[0][1], coor[1][1], coor[2][1] };
    //    linSys[2] = new double[] { coor[0][2], coor[1][2], coor[2][2] };
    //    //
    //    p = Matrix.MatrixProduct(linSys, uvw);
    //    //
    //    point[0] = p[0][0];
    //    point[1] = p[1][0];
    //    point[2] = p[2][0];
    //}


    public class Matrix
    {
        public static double[][] MatrixInverse(double[][] matrix)
        {
            // assumes determinant is not 0
            // that is, the matrix does have an inverse
            int n = matrix.Length;
            double[][] result = MatrixCreate(n, n); // make a copy of matrix
            for (int i = 0; i < n; ++i)
                for (int j = 0; j < n; ++j)
                    result[i][j] = matrix[i][j];

            double[][] lum; // combined lower & upper
            int[] perm;
            int toggle;
            toggle = MatrixDecompose(matrix, out lum, out perm);

            double[] b = new double[n];
            for (int i = 0; i < n; ++i)
            {
                for (int j = 0; j < n; ++j)
                    if (i == perm[j])
                        b[j] = 1.0;
                    else
                        b[j] = 0.0;

                double[] x = Helper(lum, b); // 
                for (int j = 0; j < n; ++j)
                    result[j][i] = x[j];
            }
            return result;
        } // MatrixInverse

        static int MatrixDecompose(double[][] m, out double[][] lum, out int[] perm)
        {
            // Crout's LU decomposition for matrix determinant and inverse
            // stores combined lower & upper in lum[][]
            // stores row permuations into perm[]
            // returns +1 or -1 according to even or odd number of row permutations
            // lower gets dummy 1.0s on diagonal (0.0s above)
            // upper gets lum values on diagonal (0.0s below)

            int toggle = +1; // even (+1) or odd (-1) row permutatuions
            int n = m.Length;

            // make a copy of m[][] into result lu[][]
            lum = MatrixCreate(n, n);
            for (int i = 0; i < n; ++i)
                for (int j = 0; j < n; ++j)
                    lum[i][j] = m[i][j];


            // make perm[]
            perm = new int[n];
            for (int i = 0; i < n; ++i)
                perm[i] = i;

            for (int j = 0; j < n - 1; ++j) // process by column. note n-1 
            {
                double max = Math.Abs(lum[j][j]);
                int piv = j;

                for (int i = j + 1; i < n; ++i) // find pivot index
                {
                    double xij = Math.Abs(lum[i][j]);
                    if (xij > max)
                    {
                        max = xij;
                        piv = i;
                    }
                } // i

                if (piv != j)
                {
                    double[] tmp = lum[piv]; // swap rows j, piv
                    lum[piv] = lum[j];
                    lum[j] = tmp;

                    int t = perm[piv]; // swap perm elements
                    perm[piv] = perm[j];
                    perm[j] = t;

                    toggle = -toggle;
                }

                double xjj = lum[j][j];
                if (xjj != 0.0)
                {
                    for (int i = j + 1; i < n; ++i)
                    {
                        double xij = lum[i][j] / xjj;
                        lum[i][j] = xij;
                        for (int k = j + 1; k < n; ++k)
                            lum[i][k] -= xij * lum[j][k];
                    }
                }

            } // j

            return toggle;
        } // MatrixDecompose

        static double[] Helper(double[][] luMatrix, double[] b) // helper
        {
            int n = luMatrix.Length;
            double[] x = new double[n];
            b.CopyTo(x, 0);

            for (int i = 1; i < n; ++i)
            {
                double sum = x[i];
                for (int j = 0; j < i; ++j)
                    sum -= luMatrix[i][j] * x[j];
                x[i] = sum;
            }

            x[n - 1] /= luMatrix[n - 1][n - 1];
            for (int i = n - 2; i >= 0; --i)
            {
                double sum = x[i];
                for (int j = i + 1; j < n; ++j)
                    sum -= luMatrix[i][j] * x[j];
                x[i] = sum / luMatrix[i][i];
            }

            return x;
        } // Helper

        static double MatrixDeterminant(double[][] matrix)
        {
            double[][] lum;
            int[] perm;
            int toggle = MatrixDecompose(matrix, out lum, out perm);
            double result = toggle;
            for (int i = 0; i < lum.Length; ++i)
                result *= lum[i][i];
            return result;
        }

        // ----------------------------------------------------------------

        public static double[][] MatrixCreate(int rows, int cols)
        {
            double[][] result = new double[rows][];
            for (int i = 0; i < rows; ++i)
                result[i] = new double[cols];
            return result;
        }

        public static double[][] MatrixProduct(double[][] matrixA,
          double[][] matrixB)
        {
            int aRows = matrixA.Length;
            int aCols = matrixA[0].Length;
            int bRows = matrixB.Length;
            int bCols = matrixB[0].Length;
            if (aCols != bRows)
                throw new Exception("Non-conformable matrices");

            double[][] result = MatrixCreate(aRows, bCols);

            for (int i = 0; i < aRows; ++i) // each row of A
                for (int j = 0; j < bCols; ++j) // each col of B
                    for (int k = 0; k < aCols; ++k) // could use k < bRows
                        result[i][j] += matrixA[i][k] * matrixB[k][j];

            return result;
        }

        public static double[][] MatrixTranspose(double[][] matrix)
        {
            int aRows = matrix.Length;
            int aCols = matrix[0].Length;

            double[][] result = MatrixCreate(aCols, aRows);

            for (int i = 0; i < aRows; ++i) // each row of A
                for (int j = 0; j < aCols; ++j) // each col of B
                    result[j][i] = matrix[i][j];

            return result;
        }

        static string MatrixAsString(double[][] matrix)
        {
            string s = "";
            for (int i = 0; i < matrix.Length; ++i)
            {
                for (int j = 0; j < matrix[i].Length; ++j)
                    s += matrix[i][j].ToString("F3").PadLeft(8) + " ";
                s += Environment.NewLine;
            }
            return s;
        }

        static double[][] ExtractLower(double[][] lum)
        {
            // lower part of an LU Doolittle decomposition (dummy 1.0s on diagonal, 0.0s above)
            int n = lum.Length;
            double[][] result = MatrixCreate(n, n);
            for (int i = 0; i < n; ++i)
            {
                for (int j = 0; j < n; ++j)
                {
                    if (i == j)
                        result[i][j] = 1.0;
                    else if (i > j)
                        result[i][j] = lum[i][j];
                }
            }
            return result;
        }

        static double[][] ExtractUpper(double[][] lum)
        {
            // upper part of an LU (lu values on diagional and above, 0.0s below)
            int n = lum.Length;
            double[][] result = MatrixCreate(n, n);
            for (int i = 0; i < n; ++i)
            {
                for (int j = 0; j < n; ++j)
                {
                    if (i <= j)
                        result[i][j] = lum[i][j];
                }
            }
            return result;
        }
    }
}