public void MatrixSelfMultiplication()
{
RectangularMatrix A = GenerateRandomMatrix(3, 4);
SymmetricMatrix AAT = A.MultiplySelfByTranspose();
Assert.IsTrue(TestUtilities.IsNearlyEqual(AAT, A * A.Transpose()));
SymmetricMatrix ATA = A.MultiplyTransposeBySelf();
Assert.IsTrue(TestUtilities.IsNearlyEqual(ATA, A.Transpose() * A));
}
public void CastRectangularToSquare()
{
RectangularMatrix A = GenerateRandomMatrix(2, 3);
RectangularMatrix AT = A.Transpose();
RectangularMatrix ATA1 = AT * A;
SquareMatrix ATA2 = (SquareMatrix)ATA1;
Assert.IsTrue(ATA2 == ATA1);
SymmetricMatrix ATA3 = A.MultiplyTransposeBySelf();
Assert.IsTrue(ATA2 == ATA3);
RectangularMatrix AAT1 = A * AT;
SquareMatrix AAT2 = (SquareMatrix)AAT1;
Assert.IsTrue(AAT2 == AAT1);
SymmetricMatrix AAT3 = A.MultiplySelfByTranspose();
Assert.IsTrue(AAT2 == AAT3);
}
public void RectangularMatrixArithmetic()
{
RectangularMatrix M = GenerateRandomMatrix(2, 3);
RectangularMatrix MA = M + M;
RectangularMatrix M2 = 2.0 * M;
Assert.IsTrue(MA == M2);
RectangularMatrix MB = MA / 2.0;
Assert.IsTrue(MB == M);
RectangularMatrix MS = M - M;
RectangularMatrix M0 = 0.0 * M;
Assert.IsTrue(MS == M0);
RectangularMatrix MN = -M;
RectangularMatrix MM = -1.0 * M;
Assert.IsTrue(MN == MM);
RectangularMatrix MT = M.Transpose();
Assert.IsTrue(MT.RowCount == M.ColumnCount);
Assert.IsTrue(MT.ColumnCount == M.RowCount);
RectangularMatrix MMT = M * MT;
Assert.IsTrue(MMT.RowCount == M.RowCount);
Assert.IsTrue(MMT.ColumnCount == MT.ColumnCount);
}
static public AnyMatrix <Double> GetBestFitEllipse(List <MyShortPoint> Points)
{
int numPoints = Points.Count;
RectangularMatrix D1 = new RectangularMatrix(numPoints, 3);
RectangularMatrix D2 = new RectangularMatrix(numPoints, 3);
SquareMatrix S1 = new SquareMatrix(3);
SquareMatrix S2 = new SquareMatrix(3);
SquareMatrix S3 = new SquareMatrix(3);
SquareMatrix T = new SquareMatrix(3);
SquareMatrix M = new SquareMatrix(3);
SquareMatrix C1 = new SquareMatrix(3);
RectangularMatrix a1 = new RectangularMatrix(3, 1);
RectangularMatrix a2 = new RectangularMatrix(3, 1);
RectangularMatrix result = new RectangularMatrix(6, 1);
RectangularMatrix temp;
C1[0, 0] = 0;
C1[0, 1] = 0;
C1[0, 2] = 0.5;
C1[1, 0] = 0;
C1[1, 1] = -1;
C1[1, 2] = 0;
C1[2, 0] = 0.5;
C1[2, 1] = 0;
C1[2, 2] = 0;
//2 D1 = [x .? 2, x .* y, y .? 2]; % quadratic part of the design matrix
//3 D2 = [x, y, ones(size(x))]; % linear part of the design matrix
for (int xx = 0; xx < Points.Count; xx++)
{
MyShortPoint p = Points[xx];
D1[xx, 0] = p.x * p.x;
D1[xx, 1] = p.x * p.y;
D1[xx, 2] = p.y * p.y;
D2[xx, 0] = p.x;
D2[xx, 1] = p.y;
D2[xx, 2] = 1;
}
//4 S1 = D1’ * D1; % quadratic part of the scatter matrix
temp = D1.Transpose() * D1;
for (int xx = 0; xx < 3; xx++)
{
for (int yy = 0; yy < 3; yy++)
{
S1[xx, yy] = temp[xx, yy];
}
}
//5 S2 = D1’ * D2; % combined part of the scatter matrix
temp = D1.Transpose() * D2;
for (int xx = 0; xx < 3; xx++)
{
for (int yy = 0; yy < 3; yy++)
{
S2[xx, yy] = temp[xx, yy];
}
}
//6 S3 = D2’ * D2; % linear part of the scatter matrix
temp = D2.Transpose() * D2;
for (int xx = 0; xx < 3; xx++)
{
for (int yy = 0; yy < 3; yy++)
{
S3[xx, yy] = temp[xx, yy];
}
}
//7 T = – inv(S3) * S2’; % for getting a2 from a1
T = -1 * S3.Inverse() * S2.Transpose();
//8 M = S1 + S2 * T; % reduced scatter matrix
M = S1 + S2 * T;
//9 M = [M(3, ./ 2; - M(2, ; M(1, ./ 2]; % premultiply by inv(C1)
M = C1 * M;
//10 [evec, eval] = eig(M); % solve eigensystem
ComplexEigensystem eigenSystem = M.Eigensystem();
//11 cond = 4 * evec(1, .* evec(3, – evec(2, .? 2; % evaluate a’Ca
//12 a1 = evec(:, find(cond > 0)); % eigenvector for min. pos. eigenvalue
for (int xx = 0; xx < eigenSystem.Dimension; xx++)
{
Complex[] vector = eigenSystem.Eigenvector(xx);
Complex condition = 4 * vector[0] * vector[2] - vector[1] * vector[1];
if (condition.Im == 0 && condition.Re > 0)
{
// Solution is found
// Console.WriteLine(“\nSolution Found!”);
//System.Windows.Forms.MessageBox.Show("Ellipse gOT");
for (int yy = 0; yy < vector.Length; yy++)
{
a1[yy, 0] = vector[yy].Re;
}
}
}
//13 a2 = T * a1; % ellipse coefficients
a2 = T * a1;
//14 a = [a1; a2]; % ellipse coefficients
result[0, 0] = a1[0, 0];
result[1, 0] = a1[1, 0];
result[2, 0] = a1[2, 0];
result[3, 0] = a2[0, 0];
result[4, 0] = a2[1, 0];
result[5, 0] = a2[2, 0];
return(result);
}
private static SquareMatrix MultiplyTranspose(RectangularMatrix m1, RectangularMatrix m2)
{
var resultRectangular = m1.Transpose() * m2;
return(ToSquareMatrix(resultRectangular));
}