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: Excedded maximum number of iterations whithout convegence." << 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: Excedded maximum number of iterations whithout convegence." << 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;
}