我正在努力实现代码＆amp;算法在这里找到：
deteminant of matrix 和这里： How to calculate matrix determinant? n*n or just 5*5
但我坚持不懈。
我的第一个问题是这个算法实际使用的规则（因为在数学中显然有一些规则可以用来计算行列式） - 所以我想先检查算法是否为算法正确应用。
我的第二个问题是我做错了（我的意思是实现）或算法本身有什么问题，因为它看起来像3x3和4x4它工作正常，但对于5x5它给出了NaN的。用几个在线矩阵行列式计算器检查结果，除5x5外，它们都很好。
这是我的代码：
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));
//Console.WriteLine("readElement(j, i): " + this.readElement(j, i));
//Console.WriteLine("readElement(i, i): " + this.readElement(i, i));
//Console.WriteLine("det is" + det);
for (k = i; k < n; k++)
{
value = this.readElement(j, k) - det * this.readElement(i, k);
//Console.WriteLine("Set value is:" + value);
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);
}
}
答案 0 :(得分：2)
为什么重新发明轮子？用于获得用于反转矩阵的确定的 AND 的公知方法是进行LU分解。事实上，MSDN杂志最近发布了一篇关于如何使用C# http://msdn.microsoft.com/en-us/magazine/jj863137.aspx进行此操作的帖子。
示例代码是
矩阵决定因素
使用矩阵分解方法，可以很容易地编码方法来计算矩阵的行列式：
static double MatrixDeterminant(double[][] matrix)
{
int[] perm;
int toggle;
double[][] lum = MatrixDecompose(matrix, out perm, out toggle);
if (lum == null)
throw new Exception("Unable to compute MatrixDeterminant");
double result = toggle;
for (int i = 0; i < lum.Length; ++i)
result *= lum[i][i];
return result;
}
通过符号检查从分解矩阵上的对角线的乘积评估行列式。阅读文章了解更多详情。
请注意，他们使用锯齿状数组作为矩阵，但您可以用自己的矩阵存储替换lum[i][j]到lum[i,j]。
答案 1 :(得分：1)
@ ja72 非常感谢您的指示。计算任何n * n行列式的最终解决方案如下：
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;
}
}