public static Matrix SolveLUP(Matrix a, Matrix b)
{
ConsoleEx.WriteLineGreen();
ConsoleEx.WriteLineGreen("Solving a system of linear equations Ax=b where:");
ConsoleEx.WriteLine("A:");
ConsoleEx.WriteLine(a.ToString());
ConsoleEx.WriteLine("b:");
ConsoleEx.WriteLine(b.ToString());
var aCopy = a.Copy();
var decomposition = new LUPDecomposition();
if (decomposition.Decompose(aCopy))
{
var result = Solve(decomposition.L, decomposition.U, decomposition.P * b);
if (result != null)
{
Console.WriteLine();
ConsoleEx.WriteLineGreen("The given system has the following solution:");
ConsoleEx.WriteLine("x:");
ConsoleEx.WriteLine(result.ToString());
}
else
{
ConsoleEx.WriteLineRed("The given system has no solutions.");
}
return(result);
}
ConsoleEx.WriteLineRed("The given system has no solutions.");
return(null);
}
public Matrix ToInverseMatrix()
{
if (!IsSquareMatrix())
{
throw new ArgumentException("Square matrix required.");
}
try
{
// Create identity matrix
Matrix e = Matrix.Identity(_rows);
// LUP decomposition of A
var lupDecomposition = new LUPDecomposition();
lupDecomposition.PrintOutput = false;
lupDecomposition.Decompose(this.Copy());
Matrix l = lupDecomposition.L;
Matrix u = lupDecomposition.U;
Matrix p = lupDecomposition.P;
Matrix result = new Matrix(_rows, _cols);
for (int c = 0; c < result._cols; c++)
{
Matrix y = LinearEquationSolver.SubstituteForward(l, p * e.GetColumn(c));
Matrix x = LinearEquationSolver.SubstituteBackward(u, y);
result.SetColumn(c, x);
}
return(result);
}
catch (Exception)
{
throw new ArgumentException("Matrix is singular.");
}
}
