/// <summary>
/// Executes LUP decomposition.
/// </summary>
/// <param name="epsilon">Constant used for checking if the pivot element is equal to zero.</param>
/// <param name="b">Vector containing values from the right side of system of linear equations.</param>
/// <returns>Permutated identity matrix P.</returns>
public Matrica LUPDecomposition(double epsilon, Matrica b)
{
if (this.NoOfRows != this.NoOfColumns)
{
throw new ArgumentException("Ne možete izvršiti LU dekompoziciju nad matricom koja nije kvadratna!");
}
Matrica identityMatrixP = GenerateIdentityMatrix(this.NoOfRows);
int pivotElementRow;
for (int i = 0; i < this.NoOfColumns - 1; i++)
{
pivotElementRow = this.ChoosePivotElement(i, i);
if (Math.Abs(this.LoadedMatrix[pivotElementRow][i]) <= epsilon)
{
throw new DivideByZeroException("Stožerni element je manji od ili jednak vrijednosti " + epsilon + ". Nije moguće riješiti ovaj sustav pomoću LUP dekompozicije.");
}
identityMatrixP.SwitchRows(i, pivotElementRow);
this.SwitchRows(i, pivotElementRow);
b.SwitchRows(i, pivotElementRow);
for (int j = i + 1; j < this.NoOfRows; j++)
{
if (Math.Abs(this.LoadedMatrix[i][i]) <= epsilon)
{
throw new DivideByZeroException("Nije moguće dijeliti s nulom!!");
}
this.LoadedMatrix[j][i] /= this.LoadedMatrix[i][i];
for (int k = i + 1; k < this.NoOfColumns; k++)
{
this.LoadedMatrix[j][k] -= this.LoadedMatrix[j][i] * this.LoadedMatrix[i][k];
}
}
}
return(identityMatrixP);
}
/// <summary>
/// Executes LUP decomposition.
/// </summary>
/// <param name="epsilon">Constant used for checking if the pivot element is equal to zero.</param>
/// <param name="b">Vector containing values from the right side of system of linear equations.</param>
/// <returns>Permutated identity matrix P.</returns>
public Matrica LUPDecomposition(double epsilon, Matrica b)
{
if (this.NoOfRows != this.NoOfColumns)
{
throw new ArgumentException("It is not possible to execute LU decomposition over the nonsquare matrix!");
}
Matrica identityMatrixP = GenerateIdentityMatrix(this.NoOfRows);
int pivotElementRow;
for (int i = 0; i < this.NoOfColumns - 1; i++)
{
pivotElementRow = this.ChoosePivotElement(i, i);
if (Math.Abs(this.LoadedMatrix[pivotElementRow][i]) <= epsilon)
{
throw new DivideByZeroException("Pivot element is less than or equal to " + epsilon + ". Solve the linear equation system using the LUP decomposition.");
}
identityMatrixP.SwitchRows(i, pivotElementRow);
this.SwitchRows(i, pivotElementRow);
b.SwitchRows(i, pivotElementRow);
for (int j = i + 1; j < this.NoOfRows; j++)
{
if (Math.Abs(this.LoadedMatrix[i][i]) <= epsilon)
{
throw new DivideByZeroException("It is not possible to divide by zero!!");
}
this.LoadedMatrix[j][i] /= this.LoadedMatrix[i][i];
for (int k = i + 1; k < this.NoOfColumns; k++)
{
this.LoadedMatrix[j][k] -= this.LoadedMatrix[j][i] * this.LoadedMatrix[i][k];
}
}
}
return(identityMatrixP);
}