c# - 行列式の計算方法は? nn または単に 55

Question

みんな。n*n行列(または5*5)行列式を見つける必要があります。Pascal から翻訳された関数がありますが、 INDEX OUT OF RANGE EXCEPTION. 誰か助けてくれませんか？

これが私のコードです：

public static double DET(double[,] a, int n)
    {
        int i, j, k;
        double det = 0;
        for (i = 0; i < n - 1; i++)
        {   
            for (j = i + 1; j < n + 1; j++)
            {
                det = a[j, i] / a[i, i];
                for (k = i; k < n; k++)
                    a[j, k] = a[j, k] - det * a[i, k]; // Here's exception
            }
        }
        det = 1;
        for (i = 0; i < n; i++)
            det = det * a[i, i];
            return det;
    }

助けてくれてありがとう。

score 4 · Accepted Answer

n * n 行列式を計算するための作業ソリューションは次のようになります。

using System;

internal class MatrixDecompositionProgram
{
    private static void Main(string[] args)
    {
        float[,] m = MatrixCreate(4, 4);
        m[0, 0] = 3.0f; m[0, 1] = 7.0f; m[0, 2] = 2.0f; m[0, 3] = 5.0f;
        m[1, 0] = 1.0f; m[1, 1] = 8.0f; m[1, 2] = 4.0f; m[1, 3] = 2.0f;
        m[2, 0] = 2.0f; m[2, 1] = 1.0f; m[2, 2] = 9.0f; m[2, 3] = 3.0f;
        m[3, 0] = 5.0f; m[3, 1] = 4.0f; m[3, 2] = 7.0f; m[3, 3] = 1.0f;

        int[] perm;
        int toggle;

        float[,] luMatrix = MatrixDecompose(m, out perm, out toggle);

        float[,] lower = ExtractLower(luMatrix);
        float[,] upper = ExtractUpper(luMatrix);

        float det = MatrixDeterminant(m);

        Console.WriteLine("Determinant of m computed via decomposition = " + det.ToString("F1"));
    }

    // --------------------------------------------------------------------------------------------------------------
    private static float[,] MatrixCreate(int rows, int cols)
    {
        // allocates/creates a matrix initialized to all 0.0. assume rows and cols > 0
        // do error checking here
        float[,] result = new float[rows, cols];
        return result;
    }

    // --------------------------------------------------------------------------------------------------------------
    private static float[,] MatrixDecompose(float[,] 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.GetLength(0);
        int cols = matrix.GetLength(1);

        //Check if matrix is square
        if (rows != cols)
            throw new Exception("Attempt to MatrixDecompose a non-square mattrix");

        float[,] result = MatrixDuplicate(matrix); // make a copy of the input matrix

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

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

        for (int j = 0; j < rows - 1; ++j) // each column, j is counter for coulmns
        {
            float colMax = Math.Abs(result[j, j]); // find largest value in col j
            int pRow = j;
            for (int i = j + 1; i < rows; ++i)
            {
                if (result[i, j] > colMax)
                {
                    colMax = result[i, j];
                    pRow = i;
                }
            }

            if (pRow != j) // if largest value not on pivot, swap rows
            {
                float[] rowPtr = new float[result.GetLength(1)];

                //in order to preserve value of j new variable k for counter is declared
                //rowPtr[] is a 1D array that contains all the elements on a single row of the matrix
                //there has to be a loop over the columns to transfer the values
                //from the 2D array to the 1D rowPtr array.
                //----tranfer 2D array to 1D array BEGIN

                for (int k = 0; k < result.GetLength(1); k++)
                {
                    rowPtr[k] = result[pRow, k];
                }

                for (int k = 0; k < result.GetLength(1); k++)
                {
                    result[pRow, k] = result[j, k];
                }

                for (int k = 0; k < result.GetLength(1); k++)
                {
                    result[j, k] = rowPtr[k];
                }

                //----tranfer 2D array to 1D array END

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

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

            if (Math.Abs(result[j, j]) < 1.0E-20) // if diagonal after swap is zero . . .
                return null; // consider a throw

            for (int i = j + 1; i < rows; ++i)
            {
                result[i, j] /= result[j, j];
                for (int k = j + 1; k < rows; ++k)
                {
                    result[i, k] -= result[i, j] * result[j, k];
                }
            }
        } // main j column loop

        return result;
    } // MatrixDecompose

    // --------------------------------------------------------------------------------------------------------------
    private static float MatrixDeterminant(float[,] matrix)
    {
        int[] perm;
        int toggle;
        float[,] lum = MatrixDecompose(matrix, out perm, out toggle);
        if (lum == null)
            throw new Exception("Unable to compute MatrixDeterminant");
        float result = toggle;
        for (int i = 0; i < lum.GetLength(0); ++i)
            result *= lum[i, i];

        return result;
    }

    // --------------------------------------------------------------------------------------------------------------
    private static float[,] MatrixDuplicate(float[,] matrix)
    {
        // allocates/creates a duplicate of a matrix. assumes matrix is not null.
        float[,] result = MatrixCreate(matrix.GetLength(0), matrix.GetLength(1));
        for (int i = 0; i < matrix.GetLength(0); ++i) // copy the values
            for (int j = 0; j < matrix.GetLength(1); ++j)
                result[i, j] = matrix[i, j];
        return result;
    }

    // --------------------------------------------------------------------------------------------------------------
    private static float[,] ExtractLower(float[,] matrix)
    {
        // lower part of a Doolittle decomposition (1.0s on diagonal, 0.0s in upper)
        int rows = matrix.GetLength(0); int cols = matrix.GetLength(1);
        float[,] result = MatrixCreate(rows, cols);
        for (int i = 0; i < rows; ++i)
        {
            for (int j = 0; j < cols; ++j)
            {
                if (i == j)
                    result[i, j] = 1.0f;
                else if (i > j)
                    result[i, j] = matrix[i, j];
            }
        }
        return result;
    }

    // --------------------------------------------------------------------------------------------------------------
    private static float[,] ExtractUpper(float[,] matrix)
    {
        // upper part of a Doolittle decomposition (0.0s in the strictly lower part)
        int rows = matrix.GetLength(0); int cols = matrix.GetLength(1);
        float[,] result = MatrixCreate(rows, cols);
        for (int i = 0; i < rows; ++i)
        {
            for (int j = 0; j < cols; ++j)
            {
                if (i <= j)
                    result[i, j] = matrix[i, j];
            }
        }
        return result;
    }
}

score 3 · Accepted Answer

for (j = i + 1; j < n + 1; j++)

最後の J 値は配列サイズよりも大きくなります。したがって、配列のサイズと、すべてのインデックスがパスカルからどのように変換されたかを再確認する必要があります。

score 2 · Accepted Answer

動作する C# コードをダウンロードできるのに、わざわざ翻訳する必要はありません

score 1 · Accepted Answer

より大きな行列の場合、行列式を計算するためにBareissアルゴリズムを実行することをお勧めします。

http://en.wikipedia.org/wiki/Bareiss_algorithm

score 0 · Accepted Answer

このアルゴリズムは、少なくとも5x5行列の計算には適していないと思います。これを直しても

for（j = i + 1; j <n + 1; j ++）

このように

for（j = i + 1; j <n; j ++）

次に、次のような完全なコードを記述します。

using System;

public class Matrix
{
    private int row_matrix; //number of rows for matrix
    private int column_matrix; //number of colums for matrix
    private double[,] matrix; //holds values of matrix itself

    //create r*c matrix and fill it with data passed to this constructor
    public Matrix(double[,] double_array)
    {
        matrix = double_array;
        row_matrix = matrix.GetLength(0);
        column_matrix = matrix.GetLength(1);
        Console.WriteLine("Contructor which sets matrix size {0}*{1} and fill it with initial data executed.", row_matrix, column_matrix);
    }

    //returns total number of rows
    public int countRows()
    {
        return row_matrix;
    }

    //returns total number of columns
    public int countColumns()
    {
        return column_matrix;
    }

    //returns value of an element for a given row and column of matrix
    public double readElement(int row, int column)
    {
        return matrix[row, column];
    }

    //sets value of an element for a given row and column of matrix
    public void setElement(double value, int row, int column)
    {
        matrix[row, column] = value;
    }

    public double deterMatrix()
    {
        double det = 0;
        double value = 0;
        int i, j, k;

        i = row_matrix;
        j = column_matrix;
        int n = i;

        if (i != j)
        {
            Console.WriteLine("determinant can be calculated only for sqaure matrix!");
            return det;
        }

        for (i = 0; i < n - 1; i++)
        {
            for (j = i + 1; j < n; j++)
            {
                det = (this.readElement(j, i) / this.readElement(i, i));

                for (k = i; k < n; k++)
                {
                    value = this.readElement(j, k) - det * this.readElement(i, k);

                    this.setElement(value, j, k);
                }
            }
        }
        det = 1;
        for (i = 0; i < n; i++)
            det = det * this.readElement(i, i);

        return det;
    }
}

internal class Program
{
    private static void Main(string[] args)
    {
        Matrix mat03 = new Matrix(new[,]
        {
            {1.0, 2.0, -1.0},
            {-2.0, -5.0, -1.0},
            {1.0, -1.0, -2.0},
        });

        Matrix mat04 = new Matrix(new[,]
        {
            {1.0, 2.0, 1.0, 3.0},
            {-2.0, -5.0, -2.0, 1.0},
            {1.0, -1.0, -3.0, 2.0},
            {4.0, -1.0, -3.0, 1.0},
        });

        Matrix mat05 = new Matrix(new[,]
        {
            {1.0, 2.0, 1.0, 2.0, 3.0},
            {2.0, 1.0, 2.0, 2.0, 1.0},
            {3.0, 1.0, 3.0, 1.0, 2.0},
            {1.0, 2.0, 4.0, 3.0, 2.0},
            {2.0, 2.0, 1.0, 2.0, 1.0},
        });

        double determinant = mat03.deterMatrix();
        Console.WriteLine("determinant is: {0}", determinant);

        determinant = mat04.deterMatrix();
        Console.WriteLine("determinant is: {0}", determinant);

        determinant = mat05.deterMatrix();
        Console.WriteLine("determinant is: {0}", determinant);
    }
}

結果は次のとおりです。行列式は次のとおりです。-8行列式は次のとおりです。-142行列式は次のとおりです。-NaN

NaNは、ゼロによる除算が原因で発生します（デバッグしました）。非常に特殊な入力の場合、これは正常に機能する可能性がありますが、一般的な場合、これは適切なアルゴリズムではありません。

したがって、3x3と4x4で機能しますが、5x5では機能しません。

そもそもアルゴリズムが間違っているものを実装または修正しようとして数時間を失うことを避けるために、この質問に出くわす可能性のある人にこれを書きました。

c# - 行列式の計算方法は? n*n または単に 5*5

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c# - 行列式の計算方法は? nn または単に 55