/// <summary>
/// Gets local variables computed from given global variables, and local system of linear equations.
/// </summary>
/// <param name="F">Right part Vector of local system of linear equations.</param>
/// <param name="G">Vector of global variables.</param>
/// <returns>Vector.</returns>
public Vector GetLocalVariables(Vector F, Vector G)
{
Vector result = new Vector(F.Size - G.Size), Fl = F.GetSubVector(2, result.Size);
Matrix C, D;
C = this.GetSubMatrix(2, 0, this.Rows - 2, 2);
D = this.GetSubMatrix(2, 2, this.Rows - 2, this.Columns - 2);
result = D.GetInverse() * (Fl - C * G);
return result;
}
/// <summary>
/// Runs condensation on this Matrix.
/// </summary>
/// <param name="F">Right part Vector of local system of linear equations.</param>
/// <param name="resM">Resulting Matrix.</param>
/// <param name="resV">Resulting Vector.</param>
public void Condensate(Vector F, out Matrix resM, out Vector resV)
{
if (this.Columns != this.Rows || this.Columns < 2 || this.Rows < 2)
{
throw new ArgumentException("Condensate method called from not square Matrix or one of it's dimensions is less then 2.");
}
else
{
resM = new Matrix(2);
resV = new Vector(2);
if (this.Columns == 2)
{
resM = this.Copy();
resV = F.Copy();
return;
}
Matrix A, B, C, D;
Vector Fg, Fl;
A = this.GetSubMatrix(0, 0, 2, 2);
B = this.GetSubMatrix(0, 2, 2, this.Columns - 2);
C = this.GetSubMatrix(2, 0, this.Rows - 2, 2);
D = this.GetSubMatrix(2, 2, this.Rows - 2, this.Columns - 2);
Fg = F.GetSubVector(0, 2);
Fl = F.GetSubVector(2, F.Size - 2);
resM = A - B * D.GetInverse() * C;
resV = Fg - B * D.GetInverse() * Fl;
}
}
