public void InverseInterface()
{
// [ 1, -1, 3 ] -1
// [ 2, 1, 2 ]
// [ -2, -2, 1 ]
//
// =
//
// [ 1, -1, -1 ]
// [ -(6/5), 7/5, 4/5 ]
// [ -(2/5), 4/5, 3/5 ]
IMathematicalMatrix matrix = new Matrix(3, 3);
matrix[0, 0] = 1;
matrix[0, 1] = -1;
matrix[0, 2] = 3;
matrix[1, 0] = 2;
matrix[1, 1] = 1;
matrix[1, 2] = 2;
matrix[2, 0] = -2;
matrix[2, 1] = -2;
matrix[2, 2] = 1;
var a = matrix.Inverse();
Assert.AreEqual(a[0, 0], 1, 0.000000001);
Assert.AreEqual(a[0, 1], -1, 0.000000001);
Assert.AreEqual(a[0, 2], -1, 0.000000001);
Assert.AreEqual(a[1, 0], (6F / 5F) * -1F, 0.00001);
Assert.AreEqual(a[1, 1], 7F / 5F, 0.00001);
Assert.AreEqual(a[1, 2], 4F / 5F, 0.00001);
Assert.AreEqual(a[2, 0], (2F / 5F) * -1F, 0.00001);
Assert.AreEqual(a[2, 1], 4F / 5F, 0.00001);
Assert.AreEqual(a[2, 2], 3F / 5F, 0.00001);
}
/// <summary>
/// Samples a matrix normal distributed random variable.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="m">The mean of the matrix normal.</param>
/// <param name="v">The covariance matrix for the rows.</param>
/// <param name="k">The covariance matrix for the columns.</param>
/// <exception cref="ArgumentOutOfRangeException">If the dimensions of the mean and two covariance matrices don't match.</exception>
/// <returns>a sequence of samples from the distribution.</returns>
public static Matrix<double> Sample(Random rnd, Matrix<double> m, Matrix<double> v, Matrix<double> k)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(m, v, k))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
var n = m.RowCount;
var p = m.ColumnCount;
// Compute the Kronecker product of V and K, this is the covariance matrix for the stacked matrix.
var vki = v.KroneckerProduct(k.Inverse());
// Sample a vector valued random variable with VKi as the covariance.
var vector = SampleVectorNormal(rnd, new DenseVector(n * p, 0.0), vki);
// Unstack the vector v and add the mean.
var r = m.Clone();
for (var i = 0; i < n; i++)
{
for (var j = 0; j < p; j++)
{
r[i, j] += vector[(j * n) + i];
}
}
return r;
}
/// <summary>
/// Samples an inverse Wishart distributed random variable by sampling
/// a Wishart random variable and inverting the matrix.
/// </summary>
/// <param name="rnd">The random number generator to use.</param>
/// <param name="nu">The degrees of freedom.</param>
/// <param name="s">The scale matrix.</param>
/// <returns>a sample from the distribution.</returns>
public static Matrix<double> Sample(Random rnd, double nu, Matrix<double> s)
{
if (Control.CheckDistributionParameters && !IsValidParameterSet(nu, s))
{
throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
}
var r = Wishart.Sample(rnd, nu, s.Inverse());
return r.Inverse();
}
public void Convertor()
{
var eigen1 = new Eigen(matrix1);
var p1 = new Matrix();
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
p1[i, j] = eigen1.Eigenvectors[i, j].Real;
}
}
var y1 = Matrix.Multiply(Matrix.Multiply(p1.Inverse(), matrix1), p1);
var diagonalizing = new Matrix();
for (int i = 0; i < 3; i++)
{
diagonalizing[i, i] = 1 / Math.Sqrt(y1[i, i]);
}
var y2 = Matrix.Multiply(p1.Transpose(),Matrix.Multiply(matrix2,p1));
var z2 = Matrix.Multiply(Matrix.Multiply(diagonalizing.Transpose(), y2),diagonalizing);
var eigen2 = new Eigen(z2);
var eigen_vectors2 = new Matrix();
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
eigen_vectors2[i, j] = eigen2.Eigenvectors[i, j].Real;
}
}
var v2 = Matrix.Multiply(Matrix.Multiply(eigen_vectors2.Transpose(),z2), eigen_vectors2);
var new_means1 = Matrix.Multiply(eigen_vectors2,Matrix.Multiply(diagonalizing, Matrix.Multiply(p1.Transpose(), means1)));
var new_means2 = Matrix.Multiply(eigen_vectors2,Matrix.Multiply(Matrix.Multiply(diagonalizing, p1.Transpose()), means2));
PrintMatrix(y1, "y1");
PrintMatrix(y2, "y2");
PrintMatrix(z2, "z2");
PrintMatrix(v2, "v2");
eigen2 = new Eigen(matrix2);
var p2 = new Matrix();
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
p2[i, j] = eigen2.Eigenvectors[i, j].Real;
}
}
var y = Matrix.Multiply(Matrix.Multiply(p2.Inverse(), matrix2), p2);
var diagonalizing2 = new Matrix();
for (int i = 0; i < 3; i++)
{
diagonalizing2[i, i] = Math.Sqrt(y[i, i]);
}
var diagonalizing3 = new Matrix();
for (int i = 0; i < 3; i++)
{
diagonalizing3[i, i] = Math.Sqrt(y1[i, i]);
}
for (int i = 0; i < 200; i++)
{
var penBlue = new Pen(Color.Blue);
var penRed = new Pen(Color.Red);
var vector1 = GenerateGaussianVector(means1);
vector1 = Matrix.Multiply(p1, Matrix.Multiply(diagonalizing3, vector1));
var vector2 = GenerateGaussianVector(means2);
vector2 = Matrix.Multiply(p2, Matrix.Multiply(diagonalizing2, vector2));
// x1-x2 before
var g = pn_12before.CreateGraphics();
var point = new Point((int)(vector1[0] * 6 + 150), (int)(vector1[1] * 6 + 130));
var s = new System.Drawing.Size(2,2);
var circle = new Rectangle(point,s);
g.DrawRectangle(penBlue, circle);
point = new Point((int)(vector2[0] * 6 + 150), (int)(vector2[1] * 6 + 130));
circle = new Rectangle(point, s);
g.DrawRectangle(penRed, circle);
// x1-x3 before
g = pn_13before.CreateGraphics();
point = new Point((int)(vector1[0] * 6 + 150), (int)(vector1[2] * 6 + 130));
circle = new Rectangle(point, s);
g.DrawRectangle(penBlue, circle);
point = new Point((int)(vector2[0] * 6 + 150), (int)(vector2[2] * 6 + 130));
circle = new Rectangle(point, s);
g.DrawRectangle(penRed, circle);
// after
vector1 = GenerateGaussianVector(new_means1);
vector2 = GenerateGaussianVector(new_means2);
var eigen = new Eigen(v2);
var m = new Matrix();
for (int k = 0; k < 3; k++)
{
for (int j = 0; j < 3; j++)
{
m[k, j] = eigen.Eigenvectors[k, j].Real;
}
}
var result1 = Matrix.Multiply(Matrix.Multiply(m.Inverse(), v2), m);
var diagonal = new Matrix();
for (int k = 0; k < 3; k++)
diagonal[k, k] = 1 / Math.Sqrt(result1[k, k]);
vector2 = Matrix.Multiply(m, Matrix.Multiply(diagonal, vector2));
// x1-x2 after
g = pn_12after.CreateGraphics();
int scalar = 10;
point = new Point((int)(vector1[0] * scalar + 110), (int)(vector1[1] * scalar + 130));
circle = new Rectangle(point, s);
g.DrawRectangle(penBlue, circle);
point = new Point((int)(vector2[0] * scalar + 110), (int)(vector2[1] * scalar + 130));
circle = new Rectangle(point, s);
g.DrawRectangle(penRed, circle);
// x1-x3 after
g = pn_13after.CreateGraphics();
point = new Point((int)(vector1[0] * scalar + 110), (int)(vector1[2] * scalar + 130));
circle = new Rectangle(point, s);
g.DrawRectangle(penBlue, circle);
point = new Point((int)(vector2[0] * scalar + 110), (int)(vector2[2] * scalar + 130));
circle = new Rectangle(point, s);
g.DrawRectangle(penRed, circle);
}
}
/// <summary>
/// Compute finite difference coefficients according to the method provided here:
///
/// http://en.wikipedia.org/wiki/Finite_difference_coefficients
///
/// </summary>
/// <returns>An array of the coefficients for FD.</returns>
public double[] CreateCoefficients()
{
var result = new double[_pointCount];
var delts = new Matrix(_pointCount, _pointCount);
double[][] t = delts.Data;
for (int j = 0; j < _pointCount; j++)
{
double delt = (j - _center);
double x = 1.0;
for (int k = 0; k < _pointCount; k++)
{
t[j][k] = x/EncogMath.Factorial(k);
x *= delt;
}
}
Matrix invMatrix = delts.Inverse();
double f = EncogMath.Factorial(_pointCount);
for (int k = 0; k < _pointCount; k++)
{
result[k] = (Math.Round(invMatrix.Data[1][k]*f))/f;
}
return result;
}
public void InvertPivotTest()
{
var matrix = new Matrix<double>(new double[,] { { 5, 2, 1 }, { 1, 4, 3 }, { 1, 10, 2 } });
var res = matrix.Inverse();
double delta = 0.0001;
Assert.AreEqual(0.2157, res[1, 1], delta);
Assert.AreEqual(-0.0588, res[1, 2], delta);
Assert.AreEqual(-0.0196, res[1, 3], delta);
Assert.AreEqual(-0.0098, res[2, 1], delta);
Assert.AreEqual(-0.0882, res[2, 2], delta);
Assert.AreEqual(0.1373, res[2, 3], delta);
Assert.AreEqual(-0.0588, res[3, 1], delta);
Assert.AreEqual(0.4706, res[3, 2], delta);
Assert.AreEqual(-0.1765, res[3, 3], delta);
MatrixHelpers.NotNaNOrInfinity(res);
}
public void InverseTest()
{
var target = new Matrix<double>(new double[,] { { 57, -76, -32 }, { 27, -72, -74 }, { -93, -2, -4 } });
var expected = new Matrix<double>(new double[,] { { -0.0004556401744, 0.0007810974419, -0.01080518128 }, { -0.02274946300, 0.01042765085, -0.01091583675 }, { 0.02196836555, -0.02337434095, 0.006678383128 } });
var actual = target.Inverse();
double delta = 0.00000000001;
MatrixHelpers.Compare(expected, actual, delta);
}
//DLT算法
public void Adjustment()
{
int count=data.oCount;
Matrix B=new Matrix(count * 2, 11);
Matrix l=new Matrix(count * 2, 1);
//求L系数初值
for (int j = 0; j < data.Count;j++)
{
for (int i = 0; i < data.oCount;i++)
{
double x = data.oIPoints[j][i].X,
y = data.oIPoints[j][i].Y,
X = data.oPoints[i].X,
Y = data.oPoints[i].Y,
Z = data.oPoints[i].Z;
B[2 * i,0] = X;
B[2 * i,1] = Y;
B[2 * i,2] = Z;
B[2 * i,3] = 1;
B[2 * i,8] = -x*X;
B[2 * i,9] = -x*Y;
B[2 * i,10] = -x*Z;
B[2 * i + 1,4] = X;
B[2 * i + 1,5] = Y;
B[2 * i + 1,6] = Z;
B[2 * i + 1,7] = 1;
B[2 * i + 1,8] = -y*X;
B[2 * i + 1,9] = -y*Y;
B[2 * i + 1,10] = -y*Z;
l[2 * i,0] = x;
l[2 * i + 1,0] = y;
}
int xCount = 12;//未知数个数
Matrix L0 = ((B.T()*B).Inverse()*(B.T()*l));
Matrix L=new Matrix(xCount, 1);
for (int i = 0; i < xCount-1; i++)
L[i,0] = L0[i,0];
Matrix M=new Matrix(count * 2, xCount);
Matrix W=new Matrix(count * 2, 1);
double f = 9999;
//迭代求解L系数
while (abs(f - inE[j].fx) >= 0.01)
{
f = inE[j].fx;
double x0 = (L[0,0] * L[8,0] + L[1,0] * L[9,0] + L[2,0] * L[10,0]) /
(pow2(L[8,0]) + pow2(L[9,0]) + pow2(L[10,0])),
y0 = (L[4,0] * L[8,0] + L[5,0] * L[9,0] + L[6,0] * L[10,0]) /
(pow2(L[8,0]) + pow2(L[9,0]) + pow2(L[10,0]));
for (int i = 0; i < data.oCount; i++)
{
double x = data.oIPoints[j][i].X,
y = data.oIPoints[j][i].Y,
X = data.oPoints[i].X,
Y = data.oPoints[i].Y,
Z = data.oPoints[i].Z;
double A = X*L[8,0] +Y*L[9,0] +Z*L[10,0] + 1;
double r_2 = (x - x0)*(x - x0) + (y - y0)*(y - y0);
M[2 * i,0] = X / A;
M[2 * i,1] = Y / A;
M[2 * i,2] = Z / A;
M[2 * i,3] = 1 / A;
M[2 * i,8] = -X*x / A;
M[2 * i,9] = -Y*x / A;
M[2 * i,10] = -Z*x / A;
M[2 * i,11] = -(x - x0)*r_2;
M[2 * i + 1,4] = X / A;
M[2 * i + 1,5] = Y / A;
M[2 * i + 1,6] = Z / A;
M[2 * i + 1,7] = 1 / A;
M[2 * i + 1,8] = -X*y / A;
M[2 * i + 1,9] = -Y*y / A;
M[2 * i + 1,10] = -Z*y / A;
M[2 * i + 1,11] = -(y - y0)*r_2;
W[2 * i,0] = x / A;
W[2 * i + 1,0] = y / A;
}
Matrix nL = (M.T()*M).Inverse()*M.T()*W;
double dbeta, ds, fx, fy,Xs,Ys,Zs,a3,b3,c3,b1,b2;
double gama3 = 1 / sqrt(pow2(nL[8,0]) + pow2(nL[9,0]) + pow2(nL[10,0]));
x0 = (nL[0,0] * nL[8,0] + nL[1,0] * nL[9,0] + nL[2,0] * nL[10,0]) /
(pow2(nL[8,0]) + pow2(nL[9,0]) + pow2(nL[10,0]));
y0 = (nL[4,0] * nL[8,0] + nL[5,0] * nL[9,0] + nL[6,0] * nL[10,0]) /
(pow2(nL[8,0]) + pow2(nL[9,0]) + pow2(nL[10,0]));
double At = gama3*gama3*(pow2(nL[0,0]) + pow2(nL[1,0]) + pow2(nL[2,0])) - x0*x0,
Bt = gama3*gama3*(pow2(nL[4,0]) + pow2(nL[5,0]) + pow2(nL[6,0])) - y0*y0,
Ct = gama3*gama3*(nL[0,0] * nL[4,0] + nL[1,0] * nL[5,0] + nL[2,0] * nL[6,0]) - x0*y0;
if (Ct >= 0)
{
dbeta = -asin(sqrt(Ct*Ct / At / Bt));
}
else
{
dbeta = asin(sqrt(Ct*Ct / At / Bt));
}
ds = sqrt(At / Bt) - 1;
fx = sqrt((At*Bt - Ct*Ct) / Bt);
fy = sqrt((At*Bt - Ct*Ct) / At);
Matrix t=new Matrix(3, 3),b=new Matrix(3,1);
t[0,0] = L[0,0];
t[0,1] = L[1,0];
t[0,2] = L[2,0];
t[1,0] = L[4,0];
t[1,1] = L[5,0];
t[1,2] = L[6,0];
t[2,0] = L[8,0];
t[2,1] = L[9,0];
t[2,2] = L[10,0];
b[0,0] = L[3,0];
b[1,0] = L[7,0];
b[2,0] = -1;
Matrix xyz = t.Inverse()*b;
Xs = xyz[0,0];
Ys = xyz[1,0];
Zs = xyz[2,0];
a3 = gama3*L[8,0];
b3 = gama3*L[9,0];
c3 = gama3*L[10,0];
b2 = (-gama3*L[5,0] + b3*y0)*(1 + ds)*cos(dbeta) / fx;
b1 = (-gama3*L[1,0] + b2*fx*tan(dbeta) + b3*x0) / fx;
outE[j].ps.X=Xs;
outE[j].ps.Y=Ys;
outE[j].ps.Z=Zs;
outE[j].phi = atan(-a3 / c3);
outE[j].omege = asin(-b3);
outE[j].kappa = atan(b1 / b2);
inE[j].p0.X=x0;
inE[j].p0.Y=y0;
inE[j].fx = fx;
inE[j].fy = fy;
other[j].dbeta = dbeta;
other[j].ds = ds;
other[j].k1 = nL[xCount - 1,0];
L = nL;
}
Ls.Add(L);
}
//像点改正
for (int i = 0; i < data.Count;i++)
{
for (int j = 0; j < data.pCount;j++)
{
double x = data.iPoints[i][j].X,
y = data.iPoints[i][j].Y,
x0 = inE[i].p0.X,
y0 = inE[i].p0.Y,
k1 = other[i].k1,
r_2=(x-x0)*(x-x0)+(y-y0)*(y-y0);
data.iPoints[i][j].X=(x+k1*(x-x0)*r_2);
data.iPoints[i][j].Y=(y + k1*(y - y0)*r_2);
}
}
//前方交会
for (int i = 0; i < data.pCount;i++)
{
Matrix Bc=new Matrix(2 * data.Count, 3);
Matrix lc=new Matrix(2 * data.Count, 1);
for (int j = 0; j < data.Count;j++)
{
double x = data.iPoints[j][i].X,
y = data.iPoints[j][i].Y;
Bc[2 * j,0] = Ls[j][0,0] - x*Ls[j][8,0];
Bc[2 * j,1] = Ls[j][1,0] - x*Ls[j][9,0];
Bc[2 * j,2] = Ls[j][2,0] - x*Ls[j][10,0];
Bc[2 * j + 1,0] = Ls[j][4,0] - y*Ls[j][8,0];
Bc[2 * j + 1,1] = Ls[j][5,0] - y*Ls[j][9,0];
Bc[2 * j + 1,2] = Ls[j][6,0] - y*Ls[j][10,0];
lc[2 * j,0] = Ls[j][3,0] - x;
lc[2 * j + 1,0] = Ls[j][7,0] - y;
}
Matrix t = -(Bc.T()*Bc).Inverse()*Bc.T()*lc;
data.allPoints.Add(new _3D_Point(t[0,0], t[1,0], t[2,0]));
}
}
public void Simple2()
{
// [ 19.6, 24.974999999999998, 36.999999999999993 ] -1
// [ 24.974999999999998, 52.125000000000014, 67.5 ]
// [ 36.999999999999993, 67.5, 100.0 ]
//
// =
//
// [ 1, -1, -1 ]
// [ -(6/5), 7/5, 4/5 ]
// [ -(2/5), 4/5, 3/5 ]
var matrix = new Matrix(3, 3);
matrix[0, 0] = 19.6;
matrix[0, 1] = 24.974999999999998;
matrix[0, 2] = 36.999999999999993;
matrix[1, 0] = 24.974999999999998;
matrix[1, 1] = 52.125000000000014;
matrix[1, 2] = 67.5;
matrix[2, 0] = 36.999999999999993;
matrix[2, 1] = 67.5;
matrix[2, 2] = 100.0;
var inv = matrix.Inverse();
Assert.AreEqual(inv[0, 0], 0.169204737732656, 0.000000001);
Assert.AreEqual(inv[0, 1], -1.44028932924345E-16, 0.000000001);
Assert.AreEqual(inv[0, 2], -0.0626057529610827, 0.000000001);
Assert.AreEqual(inv[1, 0], -7.20806576118106E-17, 0.00001);
Assert.AreEqual(inv[1, 1], 0.152380952380952, 0.00001);
Assert.AreEqual(inv[1, 2], -0.102857142857143, 0.00001);
Assert.AreEqual(inv[2, 0], -0.0626057529610828, 0.00001);
Assert.AreEqual(inv[2, 1], -0.102857142857142, 0.00001);
Assert.AreEqual(inv[2, 2], 0.102592700024172, 0.00001);
}
public void Convertor()
{
#region Calculate v2 new means
var eigen1 = new Eigen(matrix1);
var p1 = new Matrix();
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
p1[i, j] = eigen1.Eigenvectors[i, j].Real;
}
}
var y1 = Matrix.Multiply(Matrix.Multiply(p1.Inverse(), matrix1), p1);
var diagonalizing = new Matrix();
for (int i = 0; i < 3; i++)
{
diagonalizing[i, i] = 1 / Math.Sqrt(y1[i, i]);
}
var y2 = Matrix.Multiply(p1.Transpose(), Matrix.Multiply(matrix2, p1));
var z2 = Matrix.Multiply(Matrix.Multiply(diagonalizing.Transpose(), y2), diagonalizing);
var eigen2 = new Eigen(z2);
var eigen_vectors2 = new Matrix();
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
eigen_vectors2[i, j] = eigen2.Eigenvectors[i, j].Real;
}
}
var v2 = Matrix.Multiply(Matrix.Multiply(eigen_vectors2.Transpose(), z2), eigen_vectors2);
new_means1 = Matrix.Multiply(eigen_vectors2, Matrix.Multiply(diagonalizing, Matrix.Multiply(p1.Transpose(), means1)));
new_means2 = Matrix.Multiply(eigen_vectors2, Matrix.Multiply(Matrix.Multiply(diagonalizing, p1.Transpose()), means2));
#endregion
#region generate 200 points
for (int i = 0; i < 200; i++)
{
var orig_vector1 = GenerateGaussianVector(means1);
var orig_vector2 = GenerateGaussianVector(means2);
var vector1 = AddCovariance(matrix1, orig_vector1);
var vector2 = AddCovariance(matrix2, orig_vector2);
//for (int j = 0; i < 3;j++ )
//{
// orig_vectors1[i, j] = orig_vector1[j];
// orig_vectors2[i, j] = orig_vector2[j];
//}
try
{
Draw(pn_12before, Color.Blue, vector1[0], vector1[1]);
Draw(pn_13before, Color.Blue, vector1[0], vector1[2]);
Draw(pn_12before, Color.Red, vector2[0], vector2[1]);
Draw(pn_13before, Color.Red, vector2[0], vector2[2]);
// after
//vector1 = ModifyVector(vector1, means1);
//vector2 = ModifyVector(vector2, means2);
vector1 = GenerateGaussianVector(new_means1);
vector2 = GenerateGaussianVector(new_means2);
vector2 = AddCovariance(z2, vector2);
Draw(pn_12after, Color.Blue, vector1[0], vector1[1]);
Draw(pn_13after, Color.Blue, vector1[0], vector1[2]);
Draw(pn_12after, Color.Red, vector2[0], vector2[1]);
Draw(pn_13after, Color.Red, vector2[0], vector2[2]);
}
catch(Exception)
{ }
}
#endregion
#region Calculate discreminant function
var E = new double[,]{{1,0,0},{0,1,0},{0,0,1}};
var identity = new Matrix(E);
DrawDiscreminant(pn_12before, matrix1, matrix2, means1, means2, 0, 1);
DrawDiscreminant(pn_13before, matrix1, matrix2, means1, means2, 0, 2);
DrawDiscreminant(pn_12after, identity, z2, new_means1, new_means2, 0, 1);
DrawDiscreminant(pn_13after, identity, z2, new_means1, new_means2, 0, 2);
#endregion
#region Test
var correct = 0;
var wrong = 0;
// Before
for(int i=0;i<200;i++)
{
var vector1 = GenerateGaussianVector(means1);
var vector2 = GenerateGaussianVector(means2);
vector1 = AddCovariance(matrix1, vector1);
vector2 = AddCovariance(matrix2, vector2);
if (1 == Test(matrix1, matrix2, means1, means2, vector1))
{
correct++;
}
else
{
wrong++;
}
if (2 == Test(matrix1, matrix2, means1, means2, vector2))
{
correct++;
}
else
{
wrong++;
}
}
txb_result.Text += "Before:\r\ncorrect: " + correct.ToString() + "\r\nwrong: " + wrong.ToString();
txb_result.Text += "\r\nAccuracy: " + (double)correct / (correct + wrong);
// After
correct = 0;
wrong = 0;
for(int i=0;i<200;i++)
{
var vector1 = GenerateGaussianVector(new_means1);
var vector2 = GenerateGaussianVector(new_means2);
vector2 = AddCovariance(v2, vector2);
if (1 == Test(identity, v2, new_means1, new_means2, vector1))
{
correct++;
}
else
{
wrong++;
}
if (2 == Test(identity, v2, new_means1, new_means2, vector2))
{
correct++;
}
else
{
wrong++;
}
}
txb_result.Text += "\r\nAfter:\r\ncorrect: " + correct.ToString() + "\r\nwrong: " + wrong.ToString();
txb_result.Text += "\r\nAccuracy: " + (double)correct / (correct + wrong);
#endregion
}
public int Test(Matrix matrix1, Matrix matrix2, double[] means1, double[] means2, double[] vector)
{
var m1 = new Matrix(matrix1);
var m2 = new Matrix(matrix2);
var matrix_means1 = new Vector(means1);
var matrix_means2 = new Vector(means2);
var matrix_vector = new Vector(vector);
// Calculate A B C
var A = m2.Inverse() - m1.Inverse();
var B = 2 * (Matrix.Multiply(matrix_means1.ToMatrix().Transpose(), m1.Inverse()) - Matrix.Multiply(matrix_means2.ToMatrix().Transpose(), m2.Inverse()));
var C = (Matrix.Multiply(Matrix.Multiply(matrix_means2.ToMatrix().Transpose(), m2.Inverse()), matrix_means2.ToMatrix())).Determinant() - (Matrix.Multiply(Matrix.Multiply(matrix_means1.ToMatrix().Transpose(), m1.Inverse()), matrix_means1.ToMatrix()).Determinant() - 2 * (Math.Log10(m1.Determinant() / m2.Determinant())));
var result = Matrix.Multiply(Matrix.Multiply(matrix_vector.ToMatrix().Transpose(), A), matrix_vector.ToMatrix()).Determinant() + B[0, 0] * matrix_vector[0] + B[0, 2] * matrix_vector[2] + B[0, 2] * matrix_vector[2] + C;
if (result > 0)
{
return 1;
}
return 2;
}
public void DrawDiscreminant(Panel p, Matrix matrix1, Matrix matrix2, double[] means1, double[] means2, int x, int y)
{
var m1 = new Matrix(matrix1);
var m2 = new Matrix(matrix2);
var matrix_means1 = new Vector(means1);
var matrix_means2 = new Vector(means2);
// Calculate A B C
var A = m2.Inverse() - m1.Inverse();
var B = 2 * (Matrix.Multiply(matrix_means1.ToMatrix().Transpose(), m1.Inverse()) - Matrix.Multiply(matrix_means2.ToMatrix().Transpose(), m2.Inverse()));
var C = (Matrix.Multiply(Matrix.Multiply(matrix_means2.ToMatrix().Transpose(), m2.Inverse()), matrix_means2.ToMatrix())).Determinant() - (Matrix.Multiply(Matrix.Multiply(matrix_means1.ToMatrix().Transpose(), m1.Inverse()), matrix_means1.ToMatrix()).Determinant() - 2 * (Math.Log10(m1.Determinant() / m2.Determinant())));
var a11 = A[x, x];
var a12 = A[x, y];
var a21 = A[y, x];
var a22 = A[y, y];
var b1 = B[0, x];
var b2 = B[0, y];
for (double i = -20; i < 20; i = i + 0.1)
{
var quad = a22;
var line = a12 * i + a21 * i + b2;
var cons = C + b1 * i + a11 * i * i;
if ((line * line - 4 * quad * cons) >= 0)
{
try
{
if (quad != 0)
{
var j = (-line + Math.Sqrt(line * line - 4 * quad * cons)) / (2 * quad);
Draw(p, Color.Black, i, j);
j = (-line - Math.Sqrt(line * line - 4 * quad * cons)) / (2 * quad);
Draw(p, Color.Black, i, j);
}
else if (line != 0)
{
var j = -cons / line;
Draw(p, Color.Black, i, j);
}
}
catch(Exception)
{ }
}
}
}
public void TestInverse()
{
double[] data = new double[] { 1, 3, 2, 5};
Matrix m = new Matrix(data,2,2);
Assert.AreEqual(m[0, 0], 1);
Matrix inv = m.Inverse();
Assert.AreEqual(inv[0, 0], -5);
}
public void ExceptionZeroDeterminant()
{
var matrix = new Matrix(3, 3);
// [ 4, 4, 4 ]
// [ 4, 4, 4 ]
// [ 4, 4, 4 ]
// Determinant = 0
matrix[0, 0] = 4;
matrix[0, 1] = 4;
matrix[0, 2] = 4;
matrix[1, 0] = 4;
matrix[1, 1] = 4;
matrix[1, 2] = 4;
matrix.Inverse();
}
public double[] AddCovariance(double[,] matrix, double[] vector)
{
var eigen = new Eigen(matrix);
var p = new Matrix();
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
p[i, j] = eigen.Eigenvectors[i, j].Real;
}
}
var y = Matrix.Multiply(Matrix.Multiply(p.Inverse(), matrix), p);
var diagonalizing = new Matrix();
for (int i = 0; i < 3; i++)
{
diagonalizing[i, i] = Math.Sqrt(y[i, i]);
}
return Matrix.Multiply(Matrix.Multiply(p, diagonalizing), vector);
}
