public static void JacobiMethod(decimal[,] A, decimal accuracy)
{
int rows = A.GetLength(0);
int cols = A.GetLength(1);
decimal sigma = 0;
int i_max = 0, j_max = 1;
/*m==n and A symmetric*/
while (sigma > accuracy)
{
/*find max off-diagonal element */
for (int i = 0; i < rows; i++)
{
for (int j = i + 1; j < cols; j++)
{
if (i != j && MathDecimal.Abs(A[i_max, j_max]) < MathDecimal.Abs(A[i, j]))
{
i_max = i;
j_max = j;
}
}
}
}
}
public static decimal[] Gauss(decimal[,] A, decimal[] y)
{
decimal l, sum, temp;
decimal[] res = new decimal[y.Length];
int n = A.GetLength(0);
for (int i = 0; i < n - 1; i++)
{
int maxIndex = i;
//Find the index of the row with maximal element
for (int j = i + 1; j < n; j++)
{
if (MathDecimal.Abs(A[j, i]) > MathDecimal.Abs(A[maxIndex, i]))
{
maxIndex = j;
}
}
//Change the rows with indices i and maxIndex
for (int j = i; j < n; j++)
{
temp = A[i, j];
A[i, j] = A[maxIndex, j];
A[maxIndex, j] = temp;
}
temp = y[i];
y[i] = y[maxIndex];
y[maxIndex] = temp;
//Eliminate the elements under the main diagonal in the i-th column
for (int j = i + 1; j < n; j++)
{
l = A[j, i] / A[i, i];
A[j, i] = 0;
for (int k = i + 1; k < n; k++)
{
A[j, k] -= l * A[i, k];
}
y[j] -= l * y[i];
}
}
//Backward substitution
for (int i = n - 1; i >= 0; i--)
{
sum = 0;
for (int j = i + 1; j < n; j++)
{
sum += A[i, j] * res[j];
}
res[i] = (y[i] - sum) / A[i, i];
}
return(res);
}
public static List <decimal[, ]> LUDecomposition(decimal[,] A)
{
int rows = A.GetLength(0);
int cols = A.GetLength(1);
decimal l, temp;
int maxRowIndex, maxColIndex;
List <decimal[, ]> result = new List <decimal[, ]>();
decimal[,] L = new decimal[rows, cols];
decimal[,] Alocal = new decimal[rows, cols];
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
Alocal[i, j] = A[i, j];
}
}
for (int i = 0; i < cols; i++)
{
L[i, i] = 1;
}
decimal[,] Pi1 = new decimal[rows, rows];
for (int i = 0; i < rows; i++)
{
Pi1[i, i] = 1;
}
decimal[,] Pi2 = new decimal[cols, cols];
for (int i = 0; i < cols; i++)
{
Pi2[i, i] = 1;
}
for (int i = 0; i < cols; i++)
{
//Find the largest element in the i-th column
maxRowIndex = i;
maxColIndex = i;
for (int j = i + 1; j < rows; j++)
{
for (int k = i; k < cols; k++)
{
if (MathDecimal.Abs(Alocal[maxRowIndex, maxColIndex]) < MathDecimal.Abs(Alocal[j, k]))
{
maxRowIndex = j;
maxColIndex = k;
}
}
}
//Exchange rows
for (int j = i; j < cols; j++)
{
temp = Alocal[i, j];
Alocal[i, j] = Alocal[maxRowIndex, j];
Alocal[maxRowIndex, j] = temp;
}
for (int j = 0; j < i; j++)
{
temp = L[i, j];
L[i, j] = L[maxRowIndex, j];
L[maxRowIndex, j] = temp;
}
for (int j = 0; j < rows; j++)
{
temp = Pi1[i, j];
Pi1[i, j] = Pi1[maxRowIndex, j];
Pi1[maxRowIndex, j] = temp;
}
//Exchange columns
for (int j = 0; j < rows; j++)
{
temp = Alocal[j, i];
Alocal[j, i] = Alocal[j, maxColIndex];
Alocal[j, maxColIndex] = temp;
}
for (int j = 0; j < cols; j++)
{
temp = Pi2[j, i];
Pi2[j, i] = Pi2[j, maxColIndex];
Pi2[j, maxColIndex] = temp;
}
//Proceed with elimination
for (int j = i + 1; j < rows; j++)
{
l = Alocal[j, i] / Alocal[i, i];
L[j, i] = l;
Alocal[j, i] = 0;
for (int k = i + 1; k < cols; k++)
{
Alocal[j, k] = Alocal[j, k] - l * Alocal[i, k];
}
}
}
decimal[,] U = new decimal[cols, cols];
for (int i = 0; i < cols; i++)
{
for (int j = 0; j < cols; j++)
{
U[i, j] = Alocal[i, j];
}
}
result.Add(L);
result.Add(U);
result.Add(Pi1);
result.Add(Pi2);
return(result);
}