public TestSimpleIdentification()
{
TestName = "Простая модель с идентификацией";
TestFileName = "TestSimpleIdentification";
Vector <double> mW = Exts.Vector(0, 0); Matrix <double> dW = Exts.Diag(0, 1.0);
Vector <double> mNu = Exts.Vector(0); Matrix <double> dNu = Exts.Diag(1.0);
Vector <double> mEta = Exts.Vector(0, 0.0); Matrix <double> dEta = Exts.Diag(0.27, 0);
Func <int, Vector <double>, Vector <double> > phi1 = (s, x) => Exts.Vector(x[0], x[0] * x[1]);
Func <int, Vector <double>, Matrix <double> > phi2 = (s, x) => Exts.Diag(0.0, 1.0);
Func <int, Vector <double>, Vector <double> > psi1 = (s, x) => Exts.Vector(x[1]);
Func <int, Vector <double>, Matrix <double> > psi2 = (s, x) => Exts.Matrix(0.1);
RandomVector <Normal> NormalW = new RandomVector <Normal>(mW, dW);
RandomVector <Normal> NormalNu = new RandomVector <Normal>(mNu, dNu);
ContinuousUniform UniformW = new ContinuousUniform(-0.9, 0.9);
Phi1 = phi1;
Phi2 = phi2;
Psi1 = psi1;
Psi2 = psi2;
Xi = (s, x) => phi1(s, x) + phi2(s, x) * mW;
Zeta = (s, x, y, k) => y - psi1(s, x) - psi2(s, x) * mNu;
W = (s) => NormalW.Sample();
Nu = (s) => NormalNu.Sample();
DW = dW;
DNu = dNu;
X0 = () => Exts.Vector(UniformW.Sample(), 0.0);
X0Hat = mEta;
DX0Hat = dEta;
}
public TestCubicSensorScalar(double _dw, double _dnu)
{
TestName = "Кубический сенсор";
TestFileName = "CubicSensor";
Vector <double> mW = Exts.Vector(0); Matrix <double> dW = Exts.Diag(_dw);
Vector <double> mNu = Exts.Vector(0); Matrix <double> dNu = Exts.Diag(_dnu);
Vector <double> mEta = Exts.Vector(0.1); Matrix <double> dEta = Exts.Diag(1.16);
Func <int, Vector <double>, Vector <double> > phi = (s, x) => Exts.Vector(x[0] / (1 + x[0] * x[0]));
Func <int, Vector <double>, Vector <double> > psi = (s, x) => Exts.Vector(Math.Pow(x[0], 3) + Math.Pow(x[0], 1));
Func <int, Vector <double>, Matrix <double> > dpsi = (s, x) => Exts.Matrix(3.0 * Math.Pow(x[0], 2) + 1.0);
//Phi1_latex = new string[] { @"\frac{x_t}{1 + x_t^2}"};
//Psi1_latex = new string[] { @"x_t^3+x_t"};
//P_W = @"\mathcal{N}\left(" + mW.ToLatex() + ", " + mW.ToLatex() + @"\right)";
//P_Nu = @"\mathcal{N}\left(" + mNu.ToLatex() + ", " + dNu.ToLatex() + @"\right)";
//P_Eta = @"\mathcal{N}\left(" + mEta.ToLatex() + ", " + dEta.ToLatex() + @"\right)";
Normal[] NormalW = new Normal[1] {
new Normal(mW[0], Math.Sqrt(dW[0, 0]))
};
Normal[] NormalNu = new Normal[1] {
new Normal(mNu[0], Math.Sqrt(dNu[0, 0]))
};
Normal[] NormalEta = new Normal[1] {
new Normal(mEta[0], Math.Sqrt(dEta[0, 0]))
};
//Expression<Func<int, Vector<double>, Vector<double>>> expr = (s, x) => Vector(x[0] / (1 + x[0] * x[0]), x[1] / (1 + x[1] * x[1])); ;
Phi1 = phi;
Psi1 = psi;
dPhi = (s, x) => Exts.Diag(0.9);
dPsi = (s, x) => Exts.Diag(1.0);
Xi = (s, x) => phi(s, x) + mW;
Zeta = (s, x, y, k) => y - psi(s, x) - mNu;
//Zeta = (s, x, y, k) => k * dpsi(s,x).Transpose() * (dpsi(s,x) * k * dpsi(s,x).Transpose() + dNu ).PseudoInverse() * (y - psi(s, x) - mNu);
W = (s) => Exts.Vector(NormalW[0].Sample());
Nu = (s) => Exts.Vector(NormalNu[0].Sample());
DW = dW;
DNu = dNu;
X0 = () => Exts.Vector(NormalEta[0].Sample());
X0Hat = mEta;
DX0Hat = dEta;
}
public TestSampledRegression(double _dnu)
{
{
TestName = "Модель семплированной регрессии";
TestFileName = "SampledRegression";
Vector <double> a = Exts.Vector(0.3, 0.4, 0.7);
Vector <double> b = Exts.Vector(1.4, 3.0, 3.0);
Vector <double> c = Exts.Vector(0.9, 1.5, 2.5);
Vector <double> d = Exts.Vector(0.33, 0.37, 0.3);
Vector <double> m = Exts.Vector(b[0] / (1 - a[0]), b[1] / (1 - a[1]), b[2] / (1 - a[2]));
Vector <double> S = Exts.Vector(c[0] / Math.Sqrt(1 - a[0] * a[0]), c[1] / Math.Sqrt(1 - a[1] * a[1]), c[2] / Math.Sqrt(1 - a[2] * a[2]));
Func <double, int> I = x =>
{
if (x < 3)
{
return(0);
}
else if (x < 7)
{
return(1);
}
else
{
return(2);
}
};
Vector <double> mW = Exts.Vector(0); Matrix <double> dW = Exts.Diag(1.0);
Vector <double> mNu = Exts.Vector(0); Matrix <double> dNu = Exts.Diag(_dnu);
Vector <double> mEta = Exts.Vector(0); Matrix <double> dEta = Exts.Diag(1.0);
Func <int, Vector <double>, Vector <double> > phi1 = (s, x) => Exts.Vector(a[I(x[0])] * x[0] + b[I(x[0])]);
Func <int, Vector <double>, Matrix <double> > phi2 = (s, x) => Exts.Matrix(c[I(x[0])]);
Func <int, Vector <double>, Vector <double> > psi = (s, x) => Exts.Vector(x[0]);
//Phi1_latex = new string[] { @"a^T e(x_t) x_t + b^T e(x_t)" };
//Phi2_latex = new string[][] { new string[] { @"c^T e(x_t)" } };
//Psi1_latex = new string[] { @"x_t" };
//P_W = @"\mathcal{N}\left(" + mW.ToLatex() + ", " + dW.ToLatex() + @"\right)";
//P_Nu = @"\mathcal{N}\left(" + mNu.ToLatex() + ", " + dNu.ToLatex() + @"\right)";
//P_Eta = @"\mathcal{N}\left(" + mEta.ToLatex() + ", " + dEta.ToLatex() + @"\right)";
Normal[] NormalW = new Normal[1] {
new Normal(mW[0], Math.Sqrt(dW[0, 0]))
};
Normal[] NormalNu = new Normal[1] {
new Normal(mNu[0], Math.Sqrt(dNu[0, 0]))
};
Normal[] NormalEta = new Normal[1] {
new Normal(mEta[0], Math.Sqrt(dEta[0, 0]))
};
//Expression<Func<int, Vector<double>, Vector<double>>> expr = (s, x) => Vector(x[0] / (1 + x[0] * x[0]), x[1] / (1 + x[1] * x[1])); ;
Phi1 = phi1;
Phi2 = phi2;
Psi1 = psi;
//Xi = (s, x) => phi1(s, x) + phi2(s, x) * mW;
Xi = (s, x) =>
{
double num = 0;
double den = 0;
for (int i = 0; i < a.Count; i++)
{
num += d[i] * Normal.PDF(m[i], S[i], x[0]) * (a[i] * x[0] + b[i]);
den += d[i] * Normal.PDF(m[i], S[i], x[0]);
}
return(Exts.Vector(num / den));
};
Zeta = (s, x, y, k) => y - psi(s, x) - mNu;
W = (s) => Exts.Vector(NormalW[0].Sample());
Nu = (s) => Exts.Vector(NormalNu[0].Sample());
DW = dW;
DNu = dNu;
X0 = () => Exts.Vector(NormalEta[0].Sample());
X0Hat = mEta;
DX0Hat = dEta;
}
}
public HopefullyTheLastTestSwitchingObservationsIdentification(double _dnu)
{
{
TestName = "Надеюсь, последняя модель с переключающимися каналами наблюдений и идентификацией";
TestFileName = "HopefullyTheLastSwitchingObservationsIdentification";
Vector <double> sig = Exts.Vector(1.0, 4.0, 10.0);
double l1 = -0.6745;
double l2 = 0.6745;
Func <double, int> I = x =>
{
if (x < l1)
{
return(0);
}
else if (x < l2)
{
return(1);
}
else
{
return(2);
}
};
Func <double, double> F = x =>
{
return(0.4 - x * Math.Exp(-0.3 * x * x));
};
//Vector<double> f = Exts.Vector(Normal.CDF(m, S, l1), Normal.CDF(m, S, l2) - Normal.CDF(m, S, l1), 1.0 - Normal.CDF(m, S, l2));
Vector <double> f = Exts.Vector(0.25, 0.5, 0.25);
Vector <double> mW = Exts.Vector(0, 0); Matrix <double> dW = Exts.Diag(1e-5, 1.0);
Vector <double> mNu = Exts.Vector(0); Matrix <double> dNu = Exts.Diag(1e-5);
Vector <double> mEta = Exts.Vector(0, 0.0); Matrix <double> dEta = Exts.Diag(0.27, 1e-5);
Func <int, Vector <double>, Vector <double> > phi1 = (s, x) => Exts.Vector(x[0], x[0] * F(x[1]));
Func <int, Vector <double>, Matrix <double> > phi2 = (s, x) => Exts.Diag(1.0, sig[I(x[1])]);
Func <int, Vector <double>, Vector <double> > psi1 = (s, x) => Exts.Vector(x[1]);
Func <int, Vector <double>, Matrix <double> > psi2 = (s, x) => Exts.Matrix(1.0);
Normal[] NormalW = new Normal[2] {
new Normal(mW[0], Math.Sqrt(dW[0, 0])), new Normal(mW[1], Math.Sqrt(dW[1, 1]))
};
Normal[] NormalNu = new Normal[1] {
new Normal(mNu[0], Math.Sqrt(dNu[0, 0]))
};
ContinuousUniform UniformW = new ContinuousUniform(-0.9, 0.9);
Phi1 = phi1;
Phi2 = phi2;
Psi1 = psi1;
Psi2 = psi2;
Xi = (s, x) => phi1(s, x) + phi2(s, x) * mW;
Zeta = (s, x, y, k) => y - psi1(s, x) - psi2(s, x) * mNu;
W = (s) => Exts.Vector(NormalW[0].Sample(), NormalW[1].Sample());
Nu = (s) => Exts.Vector(NormalNu[0].Sample());
DW = dW;
DNu = dNu;
X0 = () => Exts.Vector(UniformW.Sample(), 0.0);
X0Hat = mEta;
DX0Hat = dEta;
}
}
public TestSwitchingObservationsIdentification(double _dnu)
{
{
TestName = "Модель с переключающимися каналами наблюдений и идентификацией";
TestFileName = "SwitchingObservationsIdentification";
double a = 0.8;
double b = 0.2;
double c = 6.0;
//Vector<double> d = Exts.Vector(10.0, 1.0, 1.0);
//Vector<double> sig = Exts.Vector(1.0, 1.0, 10.0);
Vector <double> d = Exts.Vector(4.0, 1.0, 0.5);
Vector <double> sig = Exts.Vector(1.0, 1.0, 3.0);
double m = b / (1 - a);
double S = Math.Sqrt(c * c / (1 - a * a));
double l1 = -0.6745;
double l2 = 0.6745;
Func <double, int> I = x =>
{
if (x < l1)
{
return(0);
}
else if (x < l2)
{
return(1);
}
else
{
return(2);
}
};
//Vector<double> f = Exts.Vector(Normal.CDF(m, S, l1), Normal.CDF(m, S, l2) - Normal.CDF(m, S, l1), 1.0 - Normal.CDF(m, S, l2));
Vector <double> f = Exts.Vector(0.25, 0.5, 0.25);
Vector <double> mW = Exts.Vector(0, 0, a); Matrix <double> dW = Exts.Diag(1.0, 1.0, 0.04 / 3.0);
Vector <double> mNu = Exts.Vector(0); Matrix <double> dNu = Exts.Diag(_dnu);
Vector <double> mEta = Exts.Vector(0, 0.0, a); Matrix <double> dEta = Exts.Diag(1.0, 1.0, 0.04 / 3.0);
Func <int, Vector <double>, Vector <double> > phi1 = (s, x) => Exts.Vector(x[2] * x[0] + b, 0, 0);
Func <int, Vector <double>, Matrix <double> > phi2 = (s, x) => Exts.Diag(c, 1.0, 1.0);
Func <int, Vector <double>, Vector <double> > psi1 = (s, x) => Exts.Vector(d[I(x[1])] * x[0]);
Func <int, Vector <double>, Matrix <double> > psi2 = (s, x) => Exts.Matrix(sig[I(x[1])]);
Normal[] NormalW = new Normal[2] {
new Normal(mW[0], Math.Sqrt(dW[0, 0])), new Normal(mW[1], Math.Sqrt(dW[1, 1]))
};
Normal[] NormalNu = new Normal[1] {
new Normal(mNu[0], Math.Sqrt(dNu[0, 0]))
};
Normal[] NormalEta = new Normal[2] {
new Normal(mEta[0], Math.Sqrt(dEta[0, 0])), new Normal(mEta[1], Math.Sqrt(dEta[1, 1]))
};
ContinuousUniform UniformW = new ContinuousUniform(a - 0.2, a + 0.2);
//Expression<Func<int, Vector<double>, Vector<double>>> expr = (s, x) => Vector(x[0] / (1 + x[0] * x[0]), x[1] / (1 + x[1] * x[1])); ;
Phi1 = phi1;
Phi2 = phi2;
Psi1 = psi1;
Psi2 = psi2;
Xi = (s, x) => phi1(s, x) + phi2(s, x) * mW;
//Zeta = (s, x, y, k) => y - psi1(s, x) - psi2(s, x) * mNu;
Zeta = (s, x, y, k) =>
{
double num = 0;
double den = 0;
for (int i = 0; i < d.Count; i++)
{
double xi = k[0, 0] * d[i] / (d[i] * d[i] * k[0, 0] + sig[i] * sig[i]) * (y[0] - d[i] * x[0]);
num += f[i] * Normal.PDF(d[i] * x[0], Math.Sqrt(d[i] * d[i] * k[0, 0] + sig[i] * sig[i]), y[0]) * xi;
den += f[i] * Normal.PDF(d[i] * x[0], Math.Sqrt(d[i] * d[i] * k[0, 0] + sig[i] * sig[i]), y[0]);
}
return(Exts.Vector(num / den));
};
W = (s) => Exts.Vector(NormalW[0].Sample(), NormalW[1].Sample(), UniformW.Sample());
Nu = (s) => Exts.Vector(NormalNu[0].Sample());
DW = dW;
DNu = dNu;
X0 = () => Exts.Vector(NormalEta[0].Sample(), NormalEta[1].Sample(), UniformW.Sample());
X0Hat = mEta;
DX0Hat = dEta;
}
}
public TestSwitchingObservations(double _dnu)
{
{
TestName = "Модель с переключающимися каналами наблюдений";
TestFileName = "SwitchingObservations";
double a = 0.8;
double b = 0.2;
double c = 6.0;
//Vector<double> d = Exts.Vector(10.0, 1.0, 1.0);
//Vector<double> sig = Exts.Vector(1.0, 1.0, 10.0);
Vector <double> d = Exts.Vector(4.0, 1.0, 0.5);
Vector <double> sig = Exts.Vector(1.0, 1.0, 3.0);
double m = b / (1 - a);
double S = Math.Sqrt(c * c / (1 - a * a));
double l1 = -0.6745;
double l2 = 0.6745;
Func <double, int> I = x =>
{
if (x < l1)
{
return(0);
}
else if (x < l2)
{
return(1);
}
else
{
return(2);
}
};
//Vector<double> f = Exts.Vector(Normal.CDF(m, S, l1), Normal.CDF(m, S, l2) - Normal.CDF(m, S, l1), 1.0 - Normal.CDF(m, S, l2));
Vector <double> f = Exts.Vector(0.25, 0.5, 0.25);
Vector <double> mW = Exts.Vector(0, 0.0); Matrix <double> dW = Exts.Diag(1.0, 1.0);
Vector <double> mNu = Exts.Vector(0); Matrix <double> dNu = Exts.Diag(_dnu);
Vector <double> mEta = Exts.Vector(0, 0.0); Matrix <double> dEta = Exts.Diag(1.0, 1.0); // FOR AIT
//Vector<double> mEta = Exts.Vector(1.0, 0.0); Matrix<double> dEta = Exts.Diag(100.0, 1.0); // FOR IEOPR (no transit)
Func <int, Vector <double>, Vector <double> > phi1 = (s, x) => Exts.Vector(a * x[0] + b, 0);
Func <int, Vector <double>, Matrix <double> > phi2 = (s, x) => Exts.Diag(c, 1.0);
Func <int, Vector <double>, Vector <double> > psi1 = (s, x) => Exts.Vector(d[I(x[1])] * x[0]);
Func <int, Vector <double>, Matrix <double> > psi2 = (s, x) => Exts.Matrix(sig[I(x[1])]);
//Phi1_latex = new string[] { @"a x_t + b", "0" };
//Phi2_latex = new string[][] { new string[] { @"c", "0" }, new string[] { @"0", "1" }};
//Psi1_latex = new string[] { @"d^T * e(x^1_t) * x_t" };
//Psi2_latex = new string[][] { new string[] { @"\sigma^T * e(x^1_t)" } };
//P_W = @"\mathcal{N}\left(" + mW.ToLatex() + ", " + dW.ToLatex() + @"\right)";
//P_Nu = @"\mathcal{N}\left(" + mNu.ToLatex() + ", " + dNu.ToLatex() + @"\right)";
//P_Eta = @"\mathcal{N}\left(" + mEta.ToLatex() + ", " + dEta.ToLatex() + @"\right)";
Normal[] NormalW = new Normal[2] {
new Normal(mW[0], Math.Sqrt(dW[0, 0])), new Normal(mW[1], Math.Sqrt(dW[1, 1]))
};
Normal[] NormalNu = new Normal[1] {
new Normal(mNu[0], Math.Sqrt(dNu[0, 0]))
};
Normal[] NormalEta = new Normal[2] {
new Normal(mEta[0], Math.Sqrt(dEta[0, 0])), new Normal(mEta[1], Math.Sqrt(dEta[1, 1]))
};
//Expression<Func<int, Vector<double>, Vector<double>>> expr = (s, x) => Vector(x[0] / (1 + x[0] * x[0]), x[1] / (1 + x[1] * x[1])); ;
Phi1 = phi1;
Phi2 = phi2;
Psi1 = psi1;
Psi2 = psi2;
Xi = (s, x) => phi1(s, x) + phi2(s, x) * mW;
//Zeta = (s, x, y, k) => y - psi1(s, x) - psi2(s, x) * mNu;
Zeta = (s, x, y, k) =>
{
double num = 0;
double den = 0;
for (int i = 0; i < d.Count; i++)
{
double xi = k[0, 0] * d[i] / (d[i] * d[i] * k[0, 0] + sig[i] * sig[i]) * (y[0] - d[i] * x[0]);
num += f[i] * Normal.PDF(d[i] * x[0], Math.Sqrt(d[i] * d[i] * k[0, 0] + sig[i] * sig[i]), y[0]) * xi;
den += f[i] * Normal.PDF(d[i] * x[0], Math.Sqrt(d[i] * d[i] * k[0, 0] + sig[i] * sig[i]), y[0]);
}
return(Exts.Vector(num / den));
};
W = (s) => Exts.Vector(NormalW[0].Sample(), NormalW[1].Sample());
Nu = (s) => Exts.Vector(NormalNu[0].Sample());
DW = dW;
DNu = dNu;
X0 = () => Exts.Vector(NormalEta[0].Sample(), NormalEta[1].Sample());
X0Hat = mEta;
DX0Hat = dEta;
}
}