Double [,], inversion C#

Question

나는 선형 회귀를 계산해야하는 프로그램을 만들지 만, 행렬의 반전에 갇혀있다.

은 내가 다음 번호로 채워졌다

Double[,] location = new double[3,3] 

을 가지고,하지만 난 선형 대수에서처럼의 역행렬을 계산하는 방법을 모르겠어요. 인터넷에서 솔루션을 검색했지만 Double [,]로 변환하는 방법을 모르는 Matrix 클래스가있었습니다.

선형 대수학에서 행렬의 역행렬처럼 [,] 역행렬을 사용하는 우아한 방법을 알고 있습니까?

Answer 1

예제 코드를 콘솔 프로젝트에 복사하고 실행하면됩니다.

using System; 
using System.Collections.Generic; 
using System.Linq; 




namespace matrixExample 
{ 

    class Program 
    { 

     static void Main(string[] args) 
     { 

      double[][] m = new double[][] { new double[] { 7, 2, 1 }, new double[] { 0, 3, -1 }, new double[] { -3, 4, 2 } }; 
      double[][] inv = MatrixInverse(m); 


      //printing the inverse 
      for (int i = 0; i < 3; i++) 
      { 
       for (int j = 0; j < 3; j++) 
        Console.Write(Math.Round(inv[i][j], 1).ToString().PadLeft(5, ' ') + "|"); 
       Console.WriteLine(); 
      } 

     } 

     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; 
     } 

     static double[][] MatrixIdentity(int n) 
     { 
      // return an n x n Identity matrix 
      double[][] result = MatrixCreate(n, n); 
      for (int i = 0; i < n; ++i) 
      result[i][i] = 1.0; 

      return result; 
     } 

     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 in MatrixProduct"); 

      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 less-than bRows 
         result[i][j] += matrixA[i][k] * matrixB[k][j]; 

      return result; 
     } 

     static double[][] MatrixInverse(double[][] matrix) 
     { 
      int n = matrix.Length; 
      double[][] result = MatrixDuplicate(matrix); 

      int[] perm; 
      int toggle; 
      double[][] lum = MatrixDecompose(matrix, out perm, 
       out toggle); 
      if (lum == null) 
       throw new Exception("Unable to compute inverse"); 

      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 = HelperSolve(lum, b); 

       for (int j = 0; j < n; ++j) 
      result[j][i] = x[j]; 
      } 
      return result; 
     } 

     static double[][] MatrixDuplicate(double[][] matrix) 
     { 
      // allocates/creates a duplicate of a matrix. 
      double[][] result = MatrixCreate(matrix.Length, matrix[0].Length); 
      for (int i = 0; i < matrix.Length; ++i) // copy the values 
       for (int j = 0; j < matrix[i].Length; ++j) 
        result[i][j] = matrix[i][j]; 
      return result; 
     } 

     static double[] HelperSolve(double[][] luMatrix, double[] b) 
     { 
      // before calling this helper, permute b using the perm array 
      // from MatrixDecompose that generated luMatrix 
      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; 
     } 

     static double[][] MatrixDecompose(double[][] matrix, out int[] perm, out int toggle) 
     { 
      // Doolittle LUP decomposition with partial pivoting. 
      // rerturns: result is L (with 1s on diagonal) and U; 
      // perm holds row permutations; toggle is +1 or -1 (even or odd) 
      int rows = matrix.Length; 
      int cols = matrix[0].Length; // assume square 
      if (rows != cols) 
       throw new Exception("Attempt to decompose a non-square m"); 

      int n = rows; // convenience 

      double[][] result = MatrixDuplicate(matrix); 

      perm = new int[n]; // set up row permutation result 
      for (int i = 0; i < n; ++i) { perm[i] = i; } 

      toggle = 1; // toggle tracks row swaps. 
         // +1 -greater-than even, -1 -greater-than odd. used by MatrixDeterminant 

      for (int j = 0; j < n - 1; ++j) // each column 
      { 
       double colMax = Math.Abs(result[j][j]); // find largest val in col 
       int pRow = j; 
       //for (int i = j + 1; i less-than n; ++i) 
       //{ 
       // if (result[i][j] greater-than colMax) 
       // { 
       // colMax = result[i][j]; 
       // pRow = i; 
       // } 
       //} 

       // reader Matt V needed this: 
       for (int i = j + 1; i < n; ++i) 
       { 
        if (Math.Abs(result[i][j]) > colMax) 
        { 
         colMax = Math.Abs(result[i][j]); 
         pRow = i; 
        } 
       } 
       // Not sure if this approach is needed always, or not. 

       if (pRow != j) // if largest value not on pivot, swap rows 
       { 
        double[] rowPtr = result[pRow]; 
        result[pRow] = result[j]; 
        result[j] = rowPtr; 

        int tmp = perm[pRow]; // and swap perm info 
        perm[pRow] = perm[j]; 
        perm[j] = tmp; 

        toggle = -toggle; // adjust the row-swap toggle 
       } 

       // -------------------------------------------------- 
       // This part added later (not in original) 
       // and replaces the 'return null' below. 
       // if there is a 0 on the diagonal, find a good row 
       // from i = j+1 down that doesn't have 
       // a 0 in column j, and swap that good row with row j 
       // -------------------------------------------------- 

       if (result[j][j] == 0.0) 
       { 
        // find a good row to swap 
        int goodRow = -1; 
        for (int row = j + 1; row < n; ++row) 
        { 
         if (result[row][j] != 0.0) 
          goodRow = row; 
        } 

        if (goodRow == -1) 
         throw new Exception("Cannot use Doolittle's method"); 

        // swap rows so 0.0 no longer on diagonal 
        double[] rowPtr = result[goodRow]; 
        result[goodRow] = result[j]; 
        result[j] = rowPtr; 

        int tmp = perm[goodRow]; // and swap perm info 
        perm[goodRow] = perm[j]; 
        perm[j] = tmp; 

        toggle = -toggle; // adjust the row-swap toggle 
       } 
       // -------------------------------------------------- 
       // if diagonal after swap is zero . . 
       //if (Math.Abs(result[j][j]) less-than 1.0E-20) 
       // return null; // consider a throw 

       for (int i = j + 1; i < n; ++i) 
       { 
        result[i][j] /= result[j][j]; 
        for (int k = j + 1; k < n; ++k) 
        { 
         result[i][k] -= result[i][j] * result[j][k]; 
        } 
       } 


      } // main j column loop 

      return result; 
     } 




    } 
} 

Answer 2

나는이 당신을 위해 무엇을 찾고있는 것 같아요 :

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; 
} 

는 참조 용 Test Run - Matrix Inversion Using C#를 참조하십시오.