// Solve
vector<double> Solve(GiNaC::ex Ex, GiNaC::symbol Sym) {
vector<double> Roots;
unsigned Degree = Ex.degree(Sym);
auto Coeffs = GetCoeffs(Ex, Sym);
// Bhaskara.
if (Degree == 2) {
GiNaC::ex A = Coeffs[2];
GiNaC::ex B = Coeffs[1];
GiNaC::ex C = Coeffs[0];
GiNaC::ex Delta = B*B - 4 * A * C;
// Guaranteed real roots.
if (GiNaC::is_a<GiNaC::numeric>(Delta) &&
!GiNaC::ex_to<GiNaC::numeric>(Delta).is_negative()) {
GiNaC::ex Delta = GiNaC::sqrt(B*B - 4 * A * C).evalf();
GiNaC::ex One = ((-B) + Delta)/(2*A);
GiNaC::ex Two = ((-B) - Delta)/(2*A);
if (GiNaC::is_a<GiNaC::numeric>(One))
Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(One.evalf()).to_double());
if (GiNaC::is_a<GiNaC::numeric>(Two))
Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(Two.evalf()).to_double());
}
}
// Cardano.
else if (Degree == 3) {
GiNaC::ex A = Coeffs[3];
GiNaC::ex B = Coeffs[2];
GiNaC::ex C = Coeffs[1];
GiNaC::ex D = Coeffs[1];
GiNaC::ex Delta0 = B*B - 3 * A * C;
GiNaC::ex Delta1 = 2 * B*B*B - 9 * A * B * C + 27 * A * A * D;
GiNaC::ex CD = Delta1 + GiNaC::sqrt(Delta1 * Delta1 - 4 * GiNaC::pow(Delta0, 3));
CD = CD/2;
CD = GiNaC::pow(CD, GiNaC::numeric(1)/3);
GiNaC::symbol U("u");
GiNaC::ex Var = GiNaC::numeric(-1)/(3 * A) * (B + U * CD + Delta0/(U * CD));
GiNaC::ex One = Var.subs(U == 1);
GiNaC::ex Two = Var.subs(U == ((-1 + GiNaC::sqrt(GiNaC::numeric(-3)))/2));
GiNaC::ex Three = Var.subs(U == ((-1 - GiNaC::sqrt(GiNaC::numeric(-3)))/2));
if (GiNaC::is_a<GiNaC::numeric>(One))
Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(One.evalf()).to_double());
if (GiNaC::is_a<GiNaC::numeric>(Two))
Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(Two.evalf()).to_double());
if (GiNaC::is_a<GiNaC::numeric>(Three))
Roots.push_back(GiNaC::ex_to<GiNaC::numeric>(Three.evalf()).to_double());
}
return Roots;
}
MatrixWrapper::ColumnVector
NonLinearAnalyticConditionalGaussian_Ginac::ExpectedValueGet() const
{
MatrixWrapper::ColumnVector u_num (u_size);
MatrixWrapper::ColumnVector x_num (x_size);
MatrixWrapper::ColumnVector func_num(func_size);
GiNaC::ex substitute (func_size);
MatrixWrapper::ColumnVector expected(func_size);
u_num = ConditionalArgumentGet(1);
x_num = ConditionalArgumentGet(0);
// use Mu of additive noise
if (cond_size!=0)
for (unsigned int i=0; i<u_size; i++)
for (unsigned int j=0; j<cond_size; j++)
if (u_sym[i] == cond_sym[j])
u_num(i+1) += (this->AdditiveNoiseMuGet())(j+1);
// evaluate func
for (unsigned int i=0; i<func_size; i++)
{
// temp variable to substitute in
substitute = func_sym(i,0);
// substitute all u_sym with u_num
for (unsigned int j=0; j<u_size; j++)
substitute = substitute.subs( u_sym[j]==u_num(j+1) );
// substitute all x_sym with x_num
for (unsigned int j=0; j<x_size; j++)
substitute = substitute.subs( x_sym[j]==x_num(j+1) );
// build matrix func_num
func_num(i+1) = GiNaC::ex_to<GiNaC::numeric>( substitute.evalf() ).to_double();
}
expected = func_num;
if (cond_size==0)
expected += AdditiveNoiseMuGet();
return expected;
}