// Транспонирование
public TMatrix T()
{
TMatrix Result;
double[,] m = new double[this.matrix.GetLength(0), this.matrix.GetLength(1)];
for (int i = 0; i < this.matrix.GetLength(0); i++)
{
for (int j = 0; j < this.matrix.GetLength(1); j++)
{
m[i, j] = this.matrix[i, j];
}
}
Result = new TMatrix(m);
if (Result.matrix.GetLength(0) == Result.matrix.GetLength(1))
{
double Container;
for (int i = 0; i < Result.matrix.GetLength(0) - 1; i++)
{
for (int j = Result.matrix.GetLength(1) - 1; j > i; j--)
{
Container = Result.matrix[i, j];
Result.matrix[i, j] = Result.matrix[j, i];
Result.matrix[j, i] = Container;
}
}
}
return(Result);
}
// Меняет строки
private void ChangeRow(TMatrix E)
{
for (int k = 0; k < matrix.GetLength(1); k++)
{
if (matrix[k, k] == 0)
{
double[] Container = new double[matrix.GetLength(1)];
double[] ContainerE = new double[matrix.GetLength(1)];
for (int i = 0; i < matrix.GetLength(0); i++)
{
if (matrix[i, k] != 0 & i > k)
{
for (int j = 0; j < matrix.GetLength(1); j++)
{
Container[j] = matrix[k, j];
ContainerE[j] = E.matrix[k, j];
matrix[k, j] = matrix[i, j];
E.matrix[k, j] = E.matrix[i, j];
E.matrix[i, j] = ContainerE[j];
matrix[i, j] = Container[j];
}
break;
}
}
}
}
}
// Какой-то Холецкий от Дена
public TMatrix Chol()
{
double value = 0;
double[,] l = this.Razloz().matrix;
double[,] x = new double[matrix.GetLength(0), matrix.GetLength(1)];
for (int i = this.matrix.GetLength(0) - 1; i >= 0; i--)
{
for (int j = this.matrix.GetLength(0) - 1; j >= 0; j--)
{
if (i == j)
{
value = 0;
for (int k = i + 1; k < matrix.GetLength(0); k++)
{
value = value + l[k, i] * x[k, i];
}
x[i, i] = 1 / l[i, i] * (1 / l[i, i] - value);
}
else if (j < i)
{
value = 0;
for (int k = j + 1; k < matrix.GetLength(0); k++)
{
if (x[k, i] != 0)
{
value = value + l[k, j] * x[k, i];
}
else
{
value = value + l[k, j] * x[i, k];
}
}
x[i, j] = (-1 / l[j, j] * value);
}
}
}
for (int i = this.matrix.GetLength(0) - 1; i >= 0; i--)
{
for (int j = this.matrix.GetLength(0) - 1; j >= 0; j--)
{
if (i < j)
{
x[i, j] = x[j, i];
}
}
}
TMatrix res = new TMatrix(x);
return(res);
}
// Умножение на число
public TMatrix Mult(double a)
{
double[,] result = new double[matrix.GetLength(0), matrix.GetLength(1)];
for (int i = 0; i < matrix.GetLength(0); i++)
{
for (int j = 0; j < matrix.GetLength(1); j++)
{
result[i, j] = matrix[i, j] * a;
}
}
TMatrix ResultMatrix = new TMatrix(result);
return(ResultMatrix);
}
// Создание единичной матрицы размера оригинала
private TMatrix CreateE()
{
double[,] result = new double[matrix.GetLength(0), matrix.GetLength(1)];
for (int i = 0; i < matrix.GetLength(0); i++)
{
for (int j = 0; j < matrix.GetLength(1); j++)
{
result[i, j] = 0;
result[i, i] = 1;
}
}
TMatrix ResultMatrix = new TMatrix(result);
return(ResultMatrix);
}
// Сумма матриц
public TMatrix Sum(TMatrix B)
{
TMatrix ResultMatrix;
double[,] result = new double[matrix.GetLength(0), matrix.GetLength(1)];
if (matrix.GetLength(0) == B.matrix.GetLength(0) & matrix.GetLength(1) == B.matrix.GetLength(1))
{
for (int i = 0; i < matrix.GetLength(0); i++)
{
for (int j = 0; j < matrix.GetLength(1); j++)
{
result[i, j] = matrix[i, j] + B.matrix[i, j];
}
}
}
ResultMatrix = new TMatrix(result);
return(ResultMatrix);
}
// Обратная матрица методом Гаусса
public TMatrix Gauss()
{
double[,] Container = new double[matrix.GetLength(0), matrix.GetLength(1)];
TMatrix result = CreateE();
int i = 0;
int j = 0;
for (i = 0; i < matrix.GetLength(0); i++)
{
for (j = 0; j < matrix.GetLength(1); j++)
{
Container[i, j] = matrix[i, j];
}
}
double value;
for (i = 0; i < matrix.GetLength(0); i++)
{
ChangeRow(result);
value = matrix[i, i];
for (j = 0; j < matrix.GetLength(1); j++)
{
result.matrix[i, j] = result.matrix[i, j] / value;
matrix[i, j] = matrix[i, j] / value;
}
for (int k = 0; k < matrix.GetLength(0); k++)
{
value = matrix[k, i];
for (j = 0; j < matrix.GetLength(1); j++)
{
if (k != i)
{
result.matrix[k, j] = result.matrix[k, j] - value * result.matrix[i, j];
matrix[k, j] = matrix[k, j] - value * matrix[i, j];
}
}
}
}
matrix = Container;
return(result);
}
// Произведение матриц
public TMatrix Mult(TMatrix B)
{
TMatrix ResultMatrix;
double[,] result = new double[B.matrix.GetLength(0), B.matrix.GetLength(1)];
if (matrix.GetLength(0) == B.matrix.GetLength(1))
{
for (int i = 0; i < matrix.GetLength(0); i++)
{
for (int j = 0; j < matrix.GetLength(1); j++)
{
for (int k = 0; k < matrix.GetLength(0); k++)
{
result[i, j] = result[i, j] + matrix[i, k] * B.matrix[k, j];
}
}
}
}
ResultMatrix = new TMatrix(result);
return(ResultMatrix);
}
// Какое то разложение от Дена
public TMatrix Razloz()
{
double value = 0;
double[,] result = new double[matrix.GetLength(0), matrix.GetLength(1)];
for (int i = 0; i < matrix.GetLength(0); i++)
{
for (int j = 0; j < matrix.GetLength(0); j++)
{
if (i == j)
{
value = 0;
for (int k = 0; k < i; k++)
{
value = value + result[i, k] * result[i, k];
}
result[i, i] = Math.Sqrt(matrix[i, i] - value);
}
else
if (i > j)
{
value = 0;
for (int k = 0; k < j; k++)
{
value = value + result[i, k] * result[j, k];
}
result[i, j] = (matrix[i, j] - value) / result[j, j];
}
else
if (i < j)
{
result[i, j] = 0;
}
}
}
TMatrix res = new TMatrix(result);
return(res);
}
// Определитель
public double det()
{
double Result = 0;
if (matrix.GetLength(0) >= 3)
{
for (int k = 0; k < matrix.GetLength(0); k++)
{
double[,] mas = new double[matrix.GetLength(0) - 1, matrix.GetLength(1) - 1];
for (int i = 0; i < mas.GetLength(0); i++)
{
for (int j = 0; j < mas.GetLength(1); j++)
{
if (j == k)
{
mas[i, j] = matrix[i + 1, j + 1];
}
if (j < k)
{
mas[i, j] = matrix[i + 1, j];
}
if (j > k)
{
mas[i, j] = matrix[i + 1, j + 1];
}
}
}
TMatrix mat = new TMatrix(mas);
Result = Result + Math.Pow(-1, k) * matrix[0, k] * mat.det();
}
return(Result);
}
else if (matrix.GetLength(0) == 2)
{
Result = matrix[0, 0] * matrix[1, 1] - matrix[1, 0] * matrix[0, 1];
}
return(Result);
}
public static TMatrix operator +(TMatrix a, TMatrix b)
{
TMatrix Result = a.Sum(b);
return(Result);
}
public static TMatrix operator *(double b, TMatrix a)
{
TMatrix Result = a.Mult(b);
return(Result);
}
public static TMatrix operator *(TMatrix a, TMatrix b)
{
TMatrix Result = a.Mult(b);
return(Result);
}