static void Main(string[] args)
{
Matrix <int> m = new Matrix <int>(2, 2);
m[0, 0] = 2;
m[1, 1] = 2;
m[0, 1] = 12;
Console.WriteLine(m[0, 0]);
Console.ReadKey();
Matrix <int> m2 = new Matrix <int>(2, 2);
m2[0, 0] = 1;
m2[1, 1] = 2;
var m3 = m * m2;
Console.WriteLine("a = \r\n" + m);
Console.WriteLine("b = \r\n" + m2);
Console.WriteLine("a * b = \r\n" + m3);
Console.WriteLine();
Console.WriteLine(Matrix <int> .Adjoint(m).ToString());
Console.ReadKey();
var v1 = new Vector <double>(new List <double> {
1, 1, 1
});
var v2 = new Vector <double>(new List <double> {
1, 2, 1
});
var v3 = new Vector <double>(new List <double> {
-4, 3, 1
});
Console.WriteLine("v1: " + v1.ToString());
Console.WriteLine("v2: " + v2.ToString());
Console.WriteLine("v3: " + v3.ToString());
var vects = new List <Vector <double> > {
v1, v2, v3
};
var orthoVects = GramSchmidt <double> .Orthogonalize(vects);
var orthoNormVects = GramSchmidt <double> .Normalize(orthoVects);
foreach (var v in orthoNormVects)
{
Console.WriteLine(v);
}
Console.ReadKey();
}
public void When_Transpose_Q(int size)
{
// Arrange
Random device = new Random();
Matrix A = new Matrix(size, size);
Matrix I = new Matrix(size, size);
for (int i = 0; i < size; i++)
{
I.Elem[i][i] = 1;
for (int j = 0; j < size; j++)
{
A.Elem[i][j] = device.NextDouble();
}
}
Matrix Q1 = new Matrix(A.Row, A.Column);
Matrix R1 = new Matrix(A.Row, A.Column);
Matrix Q2 = new Matrix(A.Row, A.Column);
Matrix R2 = new Matrix(A.Row, A.Column);
Matrix Q3 = new Matrix(A.Row, A.Column);
Matrix R3 = new Matrix(A.Row, A.Column);
for (int i = 0; i < A.Row; i++)
{
Q3.Elem[i][i] = 1.0;
}
Matrix Q4 = new Matrix(A.Row, A.Column);
Matrix R4 = new Matrix(A.Row, A.Column);
for (int i = 0; i < A.Row; i++)
{
Q4.Elem[i][i] = 1.0;
}
GramSchmidt.Classic(A, Q1, R1);
GramSchmidt.Modified(A, Q2, R2);
Givens.Orthogon(A, Q3, R3);
Householder.Orthogon(A, Q4, R4);
// Act
Matrix QT1 = Q1.Transpose();
Matrix QT2 = Q2.Transpose();
Matrix QT3 = Q3.Transpose();
Matrix QT4 = Q4.Transpose();
// Assert
Assert.That(QT1 * Q1 == I);
Assert.That(QT2 * Q2 == I);
Assert.That(QT3 * Q3 == I);
Assert.That(QT4 * Q4 == I);
}
public void When_Solve_ORT()
{
// Arrange
Matrix A = new Matrix(3, 3);
A.Elem[0][0] = 2;
A.Elem[0][1] = 3;
A.Elem[0][2] = -1;
A.Elem[1][0] = 1;
A.Elem[1][1] = -2;
A.Elem[1][2] = 1;
A.Elem[2][0] = 1;
A.Elem[2][1] = 0;
A.Elem[2][2] = 2;
Vector F = new Vector(3);
F.Elem[0] = 9;
F.Elem[1] = 3;
F.Elem[2] = 2;
// Act
Vector gramSchmidtC = GramSchmidt.StartModifiedSolverQR(A, F);
Vector gramSchmidtM = GramSchmidt.StartModifiedSolverQR(A, F);
Vector givens = Givens.StartSolverQR(A, F);
Vector householder = Householder.StartSolverQR(A, F);
// Assert
Assert.That(A * gramSchmidtC == F);
Assert.That(A * gramSchmidtM == F);
Assert.That(A * givens == F);
Assert.That(A * householder == F);
}
/// <summary>
/// Computes the QR decomposition for a matrix using Modified Gram-Schmidt Orthogonalization.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <returns>The QR decomposition object.</returns>
public static GramSchmidt GramSchmidt(this Matrix <double> matrix)
{
return((GramSchmidt)GramSchmidt <double> .Create(matrix));
}
/// <summary>
/// Computes the QR decomposition for a matrix using Modified Gram-Schmidt Orthogonalization.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <returns>The QR decomposition object.</returns>
public static GramSchmidt GramSchmidt(this Matrix <Complex> matrix)
{
return((GramSchmidt)GramSchmidt <Complex> .Create(matrix));
}
/// <summary>
/// Computes the QR decomposition for a matrix using Modified Gram-Schmidt Orthogonalization.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <returns>The QR decomposition object.</returns>
public static GramSchmidt GramSchmidt(this Matrix <float> matrix)
{
return((GramSchmidt)GramSchmidt <float> .Create(matrix));
}
