G4Solver.icc

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template <class Function>
G4bool G4Solver<Function>::Bisection(Function & theFunction)
{
    // Check the interval before start
    if (a > b || std::abs(a-b) <= tolerance) 
    {
    G4cerr << "G4Solver::Bisection: The interval must be properly set." << G4endl;
    return false;
    }
    G4double fa = theFunction(a);
    G4double fb = theFunction(b);
    if (fa*fb > 0.0) 
    {
    G4cerr << "G4Solver::Bisection: The interval must include a root." << G4endl;
    return false;
    }
    
    G4double eps=tolerance*(b-a);
    
    
    // Finding the root
    for (G4int i = 0; i < MaxIter; i++) 
    {
    G4double c = (a+b)/2.0;
    if ((b-a) < eps) 
    {
        root = c;
        return true;
    }
    G4double fc = theFunction(c);
    if (fc == 0.0) 
    {
        root = c;
        return true;
    }
    if (fa*fc < 0.0) 
    {
        a=c;
        fa=fc;
    } 
    else 
    {
        b=c;
        fb=fc;
    }
    }
    G4cerr << "G4Solver::Bisection: Exceeded maximum number of iterations without convergence." << G4endl;
    return false;
}
 
 
template <class Function>
G4bool G4Solver<Function>::RegulaFalsi(Function & theFunction)
{
    // Check the interval before start
    if (a > b || std::abs(a-b) <= tolerance) 
    {
    G4cerr << "G4Solver::RegulaFalsi: The interval must be properly set." << G4endl;
    return false;
    }
    G4double fa = theFunction(a);
    G4double fb = theFunction(b);
    if (fa*fb > 0.0) 
    {
    G4cerr << "G4Solver::RegulaFalsi: The interval must include a root." << G4endl;
    return false;
    }
    
    G4double eps=tolerance*(b-a);
    
    
    // Finding the root
    for (G4int i = 0; i < MaxIter; i++) 
    {
    G4double c = (a*fb-b*fa)/(fb-fa);
    G4double delta = std::min(std::abs(c-a),std::abs(b-c));
    if (delta < eps) 
    {
        root = c;
        return true;
    }
    G4double fc = theFunction(c);
    if (fc == 0.0) 
    {
        root = c;
        return true;
    }
    if (fa*fc < 0.0) 
    {
        b=c;
        fb=fc;
    } 
    else 
    {
        a=c;
        fa=fc;
    }
    }
    G4cerr << "G4Solver::Bisection: Exceeded maximum number of iterations without convergence." << G4endl;
    return false;
 
}   
 
template <class Function>
G4bool G4Solver<Function>::Brent(Function & theFunction)
{
    
    const G4double precision = 3.0e-8;
    
    // Check the interval before start
    if (a > b || std::abs(a-b) <= tolerance) 
    {
    G4cerr << "G4Solver::Brent: The interval must be properly set." << G4endl;
    return false;
    }
    G4double fa = theFunction(a);
    G4double fb = theFunction(b);
    if (fa*fb > 0.0) 
    {
    G4cerr << "G4Solver::Brent: The interval must include a root." << G4endl;
    return false;
    }
    
    G4double c = b;
    G4double fc = fb;
    G4double d = 0.0;
    G4double e = 0.0;
    
    for (G4int i=0; i < MaxIter; i++) 
    {
    // Rename a,b,c and adjust bounding interval d
    if (fb*fc > 0.0) 
    {
        c = a;
        fc = fa;
        d = b - a;
        e = d;
    }
    if (std::abs(fc) < std::abs(fb)) 
    {
        a = b;
        b = c;
        c = a;
        fa = fb;
        fb = fc;
        fc = fa;
    }
    G4double Tol1 = 2.0*precision*std::abs(b) + 0.5*tolerance;
    G4double xm = 0.5*(c-b);
    if (std::abs(xm) <= Tol1 || fb == 0.0) 
    {
        root = b;
        return true;
    }
    // Inverse quadratic interpolation
    if (std::abs(e) >= Tol1 && std::abs(fa) > std::abs(fb)) 
    {
        G4double ss = fb/fa;
        G4double p = 0.0;
        G4double q = 0.0;
        if (a == c) 
        {
        p = 2.0*xm*ss;
        q = 1.0 - ss;
        } 
        else 
        {
        q = fa/fc;
        G4double r = fb/fc;
        p = ss*(2.0*xm*q*(q-r)-(b-a)*(r-1.0));
        q = (q-1.0)*(r-1.0)*(ss-1.0);
        }
        // Check bounds
        if (p > 0.0) q = -q;
        p = std::abs(p);
        G4double min1 = 3.0*xm*q-std::abs(Tol1*q);
        G4double min2 = std::abs(e*q);
        if (2.0*p < std::min(min1,min2)) 
        {
        // Interpolation
        e = d;
        d = p/q;
        } 
        else 
        {
        // Bisection
        d = xm;
        e = d;
        }
    } 
    else 
    {
        // Bounds decreasing too slowly, use bisection
        d = xm;
        e = d;
    }
    // Move last guess to a 
    a = b;
    fa = fb;
    if (std::abs(d) > Tol1) b += d;
    else 
    {
        if (xm >= 0.0) b += std::abs(Tol1);
        else b -= std::abs(Tol1);
    }
    fb = theFunction(b);
    }
    G4cerr << "G4Solver::Brent: Number of iterations exceeded." << G4endl;
    return false;
}
 
 
 
template <class Function>
G4bool G4Solver<Function>::Crenshaw(Function & theFunction)
{
    // Check the interval before start
    if (a > b || std::abs(a-b) <= tolerance) 
    {
    G4cerr << "G4Solver::Crenshaw: The interval must be properly set." << G4endl;
    return false;
    }
 
    G4double fa = theFunction(a);
    if (fa == 0.0) 
    {
    root = a;
    return true;
    }
 
    G4double Mlast = a;
 
    G4double fb = theFunction(b);
    if (fb == 0.0)
    {
    root = b;
    return true;
    }
 
    if (fa*fb > 0.0) 
    {
    G4cerr << "G4Solver::Crenshaw: The interval must include a root." << G4endl;
    return false;
    }
 
    
    for (G4int i=0; i < MaxIter; i++) 
      {
    G4double c = 0.5 * (b + a);
    G4double fc = theFunction(c);
    if (fc == 0.0 || std::abs(c - a) < tolerance) 
      {
        root = c;
        return true;
      }
 
    if (fc * fa  > 0.0)
      {
        G4double tmp = a;
        a = b;
        b = tmp;
        tmp = fa;
        fa = fb;
        fb = tmp;
      }
    
    G4double fc0 = fc - fa;
    G4double fb1 = fb - fc;
    G4double fb0 = fb - fa;
    if (fb * fb0 < 2.0 * fc * fc0)
      {
        b = c;
        fb = fc;
      }
    else 
      {
        G4double B = (c - a) / fc0;
        G4double C = (fc0 - fb1) / (fb1 * fb0);
        G4double M = a - B * fa * (1.0 - C * fc);
        G4double fM = theFunction(M);
        if (fM == 0.0 || std::abs(M - Mlast) < tolerance)
          {
        root = M;
        return true;
          }
        Mlast = M;
        if (fM * fa < 0.0)
          {
        b = M;
        fb = fM;
          }
        else 
        {
        a = M;
        fa = fM;
        b = c;
        fb = fc;
        }
    }
    }
    return false;
}
 
 
 
 
template <class Function>   
void G4Solver<Function>::SetIntervalLimits(const G4double Limit1, const G4double Limit2)
{
    if (std::abs(Limit1-Limit2) <= tolerance) 
    {
    G4cerr << "G4Solver::SetIntervalLimits: Interval must be wider than tolerance." << G4endl;
    return;
    }
    if (Limit1 < Limit2) 
    {
    a = Limit1;
    b = Limit2;
    } 
    else 
    {
    a = Limit2;
    b = Limit1;
    }
    return;
}