我需要计算矩阵： ( X^(T) * X ) ^(-1)。代码和注释的图例：
x is double[,] array;
xT - transposed matrix
^(-1) - inverted matrix
每次我生成新的随机矩阵来使用它时，我发现该程序非常不稳定，因为它不能与任何输入数据一起正常工作。我对此很确定，因为如果一切正常，我最终需要得到单位矩阵，但有时我会得到一个非常糟糕的反转矩阵，所以我没有得到单位矩阵。我很失望，因为我总是使用相同类型的数据并且不转换任何东西。编译器是MVS 2010。希望你能帮助我。
这是我的Program.cs：
static void Main(string[] args)
{
Matrix x = new Matrix(5, 4);
//Matrix temp = new Matrix(x.Row, x.Col);
//double[] y = new double[x.Row];
//double[] b = new double[x.Row];
//this data isn't calculated correctly. used for debugging
x.MatrixX[0, 0] = 7; x.MatrixX[0, 1] = 6; x.MatrixX[0, 2] = 5; x.MatrixX[0, 3] = 8;
x.MatrixX[1, 0] = 7; x.MatrixX[1, 1] = 5; x.MatrixX[1, 2] = 8; x.MatrixX[1, 3] = 5;
x.MatrixX[2, 0] = 6; x.MatrixX[2, 1] = 8; x.MatrixX[2, 2] = 6; x.MatrixX[2, 3] = 8;
x.MatrixX[3, 0] = 8; x.MatrixX[3, 1] = 5; x.MatrixX[3, 2] = 8; x.MatrixX[3, 3] = 7;
x.MatrixX[4, 0] = 8; x.MatrixX[4, 1] = 5; x.MatrixX[4, 2] = 6; x.MatrixX[4, 3] = 7;
/*
7,00000 6,00000 5,00000 8,00000
7,00000 5,00000 8,00000 5,00000
6,00000 8,00000 6,00000 8,00000
8,00000 5,00000 8,00000 7,00000
8,00000 5,00000 6,00000 7,00000
*/
//random matrix generation
/*
Random rnd = new Random();
for (int i = 0; i < x.Row; i++)
for (int j = 0; j < x.Col; j++)
x.MatrixX[i, j] = rnd.Next(5, 10);
*/
/*i'm going to calculate: ( X^(T) * X )^(-1)
* 1. transpose X
* 2. multiply X and (1)
* 3. invert matrix (2)
* +4. i wanna check the results: Multilate of (2) and (3) = Identity_matrix.
* */
Matrix.Display(x);
//1
Matrix xt = Matrix.Transpose(x);
Matrix.Display(xt);
//2
Matrix xxt = Matrix.Multiply(x, xt);
Matrix.Display(xxt);
//3
Matrix xxtinv = Matrix.Invert(Matrix.Multiply(x, xt));
Matrix.Display(xxtinv);
//4
Console.WriteLine("Invert(xxt) * xxt. IdentityMatrix:");
Matrix IdentityMatrix = Matrix.Multiply(xxtinv, xxt);
Matrix.Display(IdentityMatrix);
Console.ReadKey();
}
这是具有所有功能的Matrix.cs ：
public class Matrix
{
private double[,] matrix;
private int row;
private int col;
#region constructors
public Matrix(int Row, int Col)
{
this.row = Row;
this.col = Col;
matrix = new double[Row, Col];
}
public Matrix()
{
Random rnd = new Random();
Row = rnd.Next(3, 7);
Col = rnd.Next(3, 7);
matrix = new double[Row, Col];
for (int i = 0; i < Row; i++)
for (int j = 0; j < Col; j++)
matrix[i, j] = rnd.Next(5, 10);
}
public Matrix(Matrix a)
{
this.Col = a.Col;
this.Row = a.Row;
this.matrix = a.matrix;
}
#endregion
#region properties
public int Col
{
get { return col; }
set { col = value; }
}
public int Row
{
get { return row; }
set { row = value; }
}
public double[,] MatrixX
{
get { return matrix; }
set { matrix = value; }
}
#endregion
static public Matrix Transpose(Matrix array)
{
Matrix temp = new Matrix(array.Col, array.Row);
for (int i = 0; i < array.Row; i++)
for (int j = 0; j < array.Col; j++)
temp.matrix[j, i] = array.matrix[i, j];
return temp;
}
static public void Display(Matrix array)
{
for (int i = 0; i < array.Row; i++)
{
for (int j = 0; j < array.Col; j++)
Console.Write("{0,5:f2}\t", array.matrix[i, j]);
Console.WriteLine();
}
Console.WriteLine();
}
static public Matrix Multiply(Matrix a, Matrix b)
{
if (a.Col != b.Row) throw new Exception("multiplication is impossible: a.Col != b.Row");
Matrix r = new Matrix(a.Row, b.Col);
for (int i = 0; i < a.Row; i++)
{
for (int j = 0; j < b.Col; j++)
{
double sum = 0;
for (int k = 0; k < b.Row; k++)
sum += a.matrix[i, k] * b.matrix[k, j];
r.matrix[i, j] = sum;
}
}
return r;
}
static public Matrix Invert(Matrix a)
{
Matrix E = new Matrix(a.Row, a.Col);
double temp = 0;
int n = a.Row;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
{
E.matrix[i, j] = 0.0;
if (i == j)
E.matrix[i, j] = 1.0;
}
for (int k = 0; k < n; k++)
{
temp = a.matrix[k, k];
for (int j = 0; j < n; j++)
{
a.matrix[k, j] /= temp;
E.matrix[k, j] /= temp;
}
for (int i = k + 1; i < n; i++)
{
temp = a.matrix[i, k];
for (int j = 0; j < n; j++)
{
a.matrix[i, j] -= a.matrix[k, j] * temp;
E.matrix[i, j] -= E.matrix[k, j] * temp;
}
}
}
for (int k = n - 1; k > 0; k--)
{
for (int i = k - 1; i >= 0; i--)
{
temp = a.matrix[i, k];
for (int j = 0; j < n; j++)
{
a.matrix[i, j] -= a.matrix[k, j] * temp;
E.matrix[i, j] -= E.matrix[k, j] * temp;
}
}
}
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
{
a.matrix[i, j] = E.matrix[i, j];
}
return a;
}
}