public static void Inv(double[][] A, int n)
{
// Init n*2 matrix to invert.
double[][] Inv = new double[n][];
for (int i = 0; i < n; i++)
{
Inv[i] = new double[n * 2];
for (int j = 0; j < n * 2; j++)
{
Inv[i][j] = 0;
}
}
// LEFT SIDE: Fill up Inv matrix with values from A.
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
Inv[i][j] = A[i][j];
}
}
// RIGHT SIDE: Full up with ones on the main diagonal.
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n * 2; j++)
{
if (j == (i + n))
{
Inv[i][j] = 1;
}
}
}
Console.WriteLine("Inverting, using such matrix:");
MatrixUtils.ShowM(Inv, n, n * 2);
// Pivoting.
for (int i = n - 1; i >= 1; i--)
{
// if (Inv[i - 1][0] < Inv[i][0])
if (Math.Abs(Inv[i - 1][0]) < Math.Abs(Inv[i][0]))
{
for (int j = 0; j < n * 2; j++)
{
double d = Inv[i][j];
Inv[i][j] = Inv[i - 1][j];
Inv[i - 1][j] = d;
}
}
}
Console.WriteLine("Matrix after pivoting:");
MatrixUtils.ShowM(Inv, n, n * 2);
// Reducing.
for (int j = 0; j < n; j++)
{
for (int i = 0; i < n; i++)
{
if (i != j)
{
double d = Inv[i][j];
for (int k = 0; k < 2 * n; k++)
{
Inv[i][k] -= (Inv[j][k] / Inv[j][j]) * d;
}
}
else
{
double d = Inv[i][j];
for (int k = 0; k < 2 * n; k++)
{
Inv[i][k] /= d;
}
}
}
}
Console.WriteLine("Matrix after reducing:");
MatrixUtils.ShowM(Inv, n, n * 2);
Console.WriteLine("The inversed matrix is on the right side.");
}
public static void GaussElimination(double[][] A, double[] X, int n)
{
int swappingFlag = 0;
// Pivoting.
for (int i = 0; i < n; i++)
{
for (int k = i + 1; k < n; k++)
{
if (Math.Abs(A[i][i]) < Math.Abs(A[k][i]))
{
swappingFlag++;
for (int j = 0; j <= n; j++)
{
double temp = A[i][j];
A[i][j] = A[k][j];
A[k][j] = temp;
}
}
}
}
Console.WriteLine("Matrix after pivoting:");
MatrixUtils.ShowM(A, n, n + 1);
// Elimination.
for (int i = 0; i < n - 1; i++)
{
for (int k = i + 1; k < n; k++)
{
double t = A[k][i] / A[i][i];
for (int j = 0; j <= n; j++)
{
//make the elements below the pivot elements equal to zero or elimnate the variables.
A[k][j] = A[k][j] - t * A[i][j];
}
}
}
Console.WriteLine("Matrix after elimination:");
MatrixUtils.ShowM(A, n, n + 1);
// Check if some of the arguments on the main diagonal equals to 0.
for (int i = 0; i < n; i++)
{
if (A[i][i] == 0)
{
Console.WriteLine("Noticed FREE argument with index {0}, starting from 0", i);
}
}
// Check if at least one B[i] after elimination does not equal to 0.
bool matrixHasSolution = false;
for (int i = 0; i < n; i++)
{
if (A[i][n] != 0)
{
matrixHasSolution = true;
}
}
if (!matrixHasSolution)
{
Console.WriteLine("Matrix A does not have solutions.");
Console.WriteLine("Reason: after elimination there are no B[i], which does not equal to 0");
throw new ArgumentException();
}
// Check if there are MORE AMOUNT OF VARIABLES THAN EQUATIONS.
for (int i = 0; i < n; i++)
{ /* TODO */
}
// Back-substitution.
for (int i = n - 1; i >= 0; i--)
{
X[i] = A[i][n];
for (int j = n - 1; j > i; j--)
{
X[i] -= A[i][j] * X[j];
}
X[i] = X[i] / A[i][i];
}
// Determinant of a matrix.
double det = 1;
for (int i = 0; i < n; i++)
{
det *= A[i][i];
}
det = (swappingFlag % 2 == 0) ? det : -det;
Console.WriteLine("Determinant is: {0}\n", det);
}
