如何计算矩阵行列式？ n * n或仅5 * 5

大家。 我需要找到矩阵n*n （或5*5 ）行列式。 我有一个从Pascal翻译过的函数，但是有一个INDEX OUT OF RANGE EXCEPTION 。 有人能帮助我吗？

这是我的代码：

 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; } 

Thanx任何帮助。

Answer 1

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

最后的J值将大于数组大小。 因此，您必须重新检查数组大小以及所有索引是如何从pascal转换的。

Answer 2

计算n * n行列式的工作解决方案如下：

 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; } } 

Answer 3

当您可以下载工作C＃代码时，为什么还要花费翻译

• http://www.codeproject.com/KB/cs/CSML.aspx
• http://www.codeproject.com/KB/recipes/AdvancedMatrixLibrary.aspx
• http://www.codeproject.com/KB/recipes/psdotnetmatrix.aspx

Answer 4

对于更大的矩阵，您可能希望运行Bareiss算法来计算行列式：

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

Answer 5

我认为这个算法并不好，至少对于5×5矩阵的计算。 即使我们纠正了这一点

for（j = i + 1; j

就像这样

for（j = i + 1; j

然后编写完整的代码，例如：

 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); } } 

结果是：行列式是：-8行列式是：-142行列式是：-NaN

因为除零而发生NaN（我调试了它）对于某些非常特定的输入，这可能是正常的，但在一般情况下，这不是一个好的算法。

因此，它适用于3x3和4x4但不适用于5x5

我把这个写给任何可能遇到这个问题的人，以避免在尝试实施或修复一些错误算法的东西时丢失几个小时。