/// <summary>
/// Main form constructor.
/// </summary>
public MainForm()
{
InitializeComponent();
Matrix T = new Matrix(4), resM = new Matrix(2);
Vector F = new Vector(4), resV = new Vector(2);
T[0, 0] = 1; T[0, 1] = 2; T[0, 2] = 3; T[0, 3] = 4;
T[1, 0] = 2; T[1, 1] = 3; T[1, 2] = 4; T[1, 3] = 1;
T[2, 0] = 3; T[2, 1] = 4; T[2, 2] = 1; T[2, 3] = 2;
T[3, 0] = 4; T[3, 1] = 1; T[3, 2] = 2; T[3, 3] = 3;
F[0] = 1; F[1] = 2; F[2] = 3; F[3] = 4;
T.Condensate(F, out resM, out resV);
Console.WriteLine("Original matrix\n{0}", T);
Console.WriteLine("Original vector\n{0}", F);
Console.WriteLine("Condensated matrix\n{0}", resM);
Console.WriteLine("Condensated vector\n{0}", resV);
Console.WriteLine("Inverted Original matrix\n{0}", T.GetInverse());
Console.WriteLine("Inverted Condensated matrix\n{0}", resM.GetInverse());
}
/// <summary>
/// Gets sub-Vector of specified size, starting at specified position from this Vector.
/// </summary>
/// <param name="startPosition">Zero-based index of starting position.</param>
/// <param name="size">Size of sub-Vector.</param>
/// <returns>Returns Vector.</returns>
public Vector GetSubVector(int startPosition, int size)
{
Vector result = new Vector(size);
for (int i = 0; i < size; i++)
{
result[i] = this[i + startPosition];
}
return result;
}
/// <summary>
/// Creates and returns new instance of this Vector (deep-copy).
/// </summary>
/// <returns>
/// Returns Vector.</returns>
public Vector Copy()
{
Vector result = new Vector(this.Size);
for (int i = 0; i < this.Size; i++)
{
result[i] = this[i];
}
return result;
}
/// <summary>
/// Adds two Vectors and returns resulting Vector.
/// </summary>
/// <param name="V1">First Vector.</param>
/// <param name="V2">Second Vector.</param>
/// <returns>Returns Vector.</returns>
public static Vector operator +(Vector V1, Vector V2)
{
if (V1.Size != V2.Size)
{
throw new ArgumentException("Vector addition error. Inappropriate sizes. [" + V1.Size + "]+[" + V2.Size + "]");
}
else
{
Vector result = new Vector(V1.Size);
for (int i = 0; i < V1.Size; i++)
{
result[i] = V1[i] + V2[i];
}
return result;
}
}
/// <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;
}
}
/// <summary>
/// Multiplies given Matrix on given Vector and returns resulting Vector.
/// </summary>
/// <param name="M">Matrix to be multiplied.</param>
/// <param name="V">Vector to be multiplied.</param>
/// <returns>Returns Vector.</returns>
public static Vector operator *(Matrix M, Vector V)
{
if (M.Columns != V.Size)
{
throw new ArgumentException("Inappropriate size of Matrix and Vector.");
}
else
{
Vector result = new Vector(M.Rows);
for (int i = 0; i < M.Rows; i++)
{
for (int j = 0; j < V.Size; j++)
{
result[i] += M[i, j] * V[j];
}
}
return result;
}
}
