/// <summary>
/// Solves system of linear equations using LU/LUP decomposition, forward and backward substitution.
/// </summary>
/// <param name="A">Values on the left side of system of linear equations which are multiplied by unknown vector x.</param>
/// <param name="b">Vector containing values from the right side of system of linear equations.</param>
/// <param name="epsilon">Constant used for checking if we are dividing value by zero.</param>
/// <returns>Vector x (result of solving system of linear equations).</returns>
public static Matrica SolveSystemOfLinearEquations(Matrica A, Matrica b, double epsilon)
{
Console.WriteLine("Matrica A:");
Console.WriteLine("============");
A.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Vektor b:");
Console.WriteLine("===========");
b.WriteMatrixInConsole();
Console.WriteLine();
Matrica copyOfA = new Matrica();
copyOfA.Equals(A);
Matrica copyOfb = new Matrica();
copyOfb.Equals(b);
try
{
A.LUDecomposition(epsilon);
Console.WriteLine("Matrica L:");
Console.WriteLine("============");
Matrica L = A.GetLMatrixFromLU();
L.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Matrica U:");
Console.WriteLine("============");
Matrica U = A.GetUMatrixFromLU();
U.WriteMatrixInConsole();
Console.WriteLine();
Matrica y = ForwardSubstitution(A, b);
Console.WriteLine("Vektor y:");
Console.WriteLine("===========");
y.WriteMatrixInConsole();
Console.WriteLine();
Matrica x = BackwardSubstitution(A, y, epsilon);
Console.WriteLine("Vektor x:");
Console.WriteLine("===========");
x.WriteMatrixInConsole();
Console.WriteLine();
return(x);
}
catch (DivideByZeroException)
{
Console.WriteLine("Nije moguće riješiti ovaj sustav LU dekompozicijom. Izvođenje LUP dekompozicije...");
A = copyOfA;
b = copyOfb;
Matrica P = A.LUPDecomposition(epsilon, b);
Console.WriteLine("Matrica P:");
Console.WriteLine("============");
P.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Matrica L:");
Console.WriteLine("============");
Matrica L = A.GetLMatrixFromLU();
L.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Matrica U:");
Console.WriteLine("============");
Matrica U = A.GetUMatrixFromLU();
U.WriteMatrixInConsole();
Console.WriteLine();
Matrica y = ForwardSubstitution(A, b);
Console.WriteLine("Vektor y:");
Console.WriteLine("===========");
y.WriteMatrixInConsole();
Console.WriteLine();
Matrica x = BackwardSubstitution(A, y, epsilon);
Console.WriteLine("Vektor x:");
Console.WriteLine("===========");
x.WriteMatrixInConsole();
Console.WriteLine();
return(x);
}
}
/// <summary>
/// Solves system of linear equations using LU/LUP decomposition, forward and backward substitution.
/// </summary>
/// <param name="A">Values on the left side of system of linear equations which are multiplied by unknown vector x.</param>
/// <param name="b">Vector containing values from the right side of system of linear equations.</param>
/// <param name="epsilon">Constant used for checking if we are dividing value by zero.</param>
/// <returns>Vector x (result of solving system of linear equations).</returns>
public static Matrica SolveSystemOfLinearEquations(Matrica A, Matrica b, double epsilon)
{
Console.WriteLine("Matrix A:");
Console.WriteLine("============");
A.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Vector b:");
Console.WriteLine("===========");
b.WriteMatrixInConsole();
Console.WriteLine();
Matrica copyOfA = new Matrica();
copyOfA.Equals(A);
Matrica copyOfb = new Matrica();
copyOfb.Equals(b);
try
{
A.LUDecomposition(epsilon);
Console.WriteLine("Matrix L:");
Console.WriteLine("============");
Matrica L = A.GetLMatrixFromLU();
L.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Matrix U:");
Console.WriteLine("============");
Matrica U = A.GetUMatrixFromLU();
U.WriteMatrixInConsole();
Console.WriteLine();
Matrica y = ForwardSubstitution(A, b);
Console.WriteLine("Vector y:");
Console.WriteLine("===========");
y.WriteMatrixInConsole();
Console.WriteLine();
Matrica x = BackwardSubstitution(A, y, epsilon);
Console.WriteLine("Vector x:");
Console.WriteLine("===========");
x.WriteMatrixInConsole();
Console.WriteLine();
return(x);
}
catch (DivideByZeroException)
{
Console.WriteLine("It is not possible to solve this system using LU decomposition. Executing LUP decomposition...");
A = copyOfA;
b = copyOfb;
Matrica P = A.LUPDecomposition(epsilon, b);
Console.WriteLine("Matrix P:");
Console.WriteLine("============");
P.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Matrix L:");
Console.WriteLine("============");
Matrica L = A.GetLMatrixFromLU();
L.WriteMatrixInConsole();
Console.WriteLine();
Console.WriteLine("Matrix U:");
Console.WriteLine("============");
Matrica U = A.GetUMatrixFromLU();
U.WriteMatrixInConsole();
Console.WriteLine();
Matrica y = ForwardSubstitution(A, b);
Console.WriteLine("Vector y:");
Console.WriteLine("===========");
y.WriteMatrixInConsole();
Console.WriteLine();
Matrica x = BackwardSubstitution(A, y, epsilon);
Console.WriteLine("Vector x:");
Console.WriteLine("===========");
x.WriteMatrixInConsole();
Console.WriteLine();
return(x);
}
}