Gabriele Cosmo
350 lines
7.3 KiB
Plaintext
350 lines
7.3 KiB
Plaintext
//
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// ********************************************************************
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// * DISCLAIMER *
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// * *
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// * The following disclaimer summarizes all the specific disclaimers *
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// * of contributors to this software. The specific disclaimers,which *
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// * govern, are listed with their locations in: *
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// * http://cern.ch/geant4/license *
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// * *
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// * Neither the authors of this software system, nor their employing *
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// * institutes,nor the agencies providing financial support for this *
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// * work make any representation or warranty, express or implied, *
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// * regarding this software system or assume any liability for its *
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// * use. *
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// * *
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// * This code implementation is the intellectual property of the *
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// * GEANT4 collaboration. *
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// * By copying, distributing or modifying the Program (or any work *
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// * based on the Program) you indicate your acceptance of this *
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// * statement, and all its terms. *
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// ********************************************************************
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//
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template <class Function>
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G4bool G4Solver<Function>::Bisection(Function & theFunction)
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{
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// Check the interval before start
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if (a > b || abs(a-b) <= tolerance)
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{
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G4cerr << "G4Solver::Bisection: The interval must be properly set." << G4endl;
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return false;
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}
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G4double fa = theFunction(a);
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G4double fb = theFunction(b);
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if (fa*fb > 0.0)
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{
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G4cerr << "G4Solver::Bisection: The interval must include a root." << G4endl;
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return false;
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}
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G4double eps=tolerance*(b-a);
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// Finding the root
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for (G4int i = 0; i < MaxIter; i++)
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{
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G4double c = (a+b)/2.0;
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if ((b-a) < eps)
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{
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root = c;
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return true;
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}
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G4double fc = theFunction(c);
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if (fc == 0.0)
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{
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root = c;
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return true;
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}
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if (fa*fc < 0.0)
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{
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a=c;
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fa=fc;
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}
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else
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{
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b=c;
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fb=fc;
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}
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}
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G4cerr << "G4Solver::Bisection: Excedded maximum number of iterations whithout convegence." << G4endl;
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return false;
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}
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template <class Function>
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G4bool G4Solver<Function>::RegulaFalsi(Function & theFunction)
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{
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// Check the interval before start
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if (a > b || abs(a-b) <= tolerance)
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{
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G4cerr << "G4Solver::RegulaFalsi: The interval must be properly set." << G4endl;
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return false;
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}
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G4double fa = theFunction(a);
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G4double fb = theFunction(b);
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if (fa*fb > 0.0)
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{
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G4cerr << "G4Solver::RegulaFalsi: The interval must include a root." << G4endl;
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return false;
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}
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G4double eps=tolerance*(b-a);
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// Finding the root
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for (G4int i = 0; i < MaxIter; i++)
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{
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G4double c = (a*fb-b*fa)/(fb-fa);
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G4double delta = std::min(abs(c-a),abs(b-c));
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if (delta < eps)
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{
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root = c;
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return true;
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}
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G4double fc = theFunction(c);
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if (fc == 0.0)
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{
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root = c;
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return true;
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}
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if (fa*fc < 0.0)
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{
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b=c;
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fb=fc;
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}
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else
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{
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a=c;
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fa=fc;
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}
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}
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G4cerr << "G4Solver::Bisection: Excedded maximum number of iterations whithout convegence." << G4endl;
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return false;
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}
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template <class Function>
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G4bool G4Solver<Function>::Brent(Function & theFunction)
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{
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const G4double precision = 3.0e-8;
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// Check the interval before start
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if (a > b || abs(a-b) <= tolerance)
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{
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G4cerr << "G4Solver::Brent: The interval must be properly set." << G4endl;
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return false;
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}
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G4double fa = theFunction(a);
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G4double fb = theFunction(b);
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if (fa*fb > 0.0)
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{
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G4cerr << "G4Solver::Brent: The interval must include a root." << G4endl;
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return false;
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}
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G4double c = b;
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G4double fc = fb;
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G4double d = 0.0;
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G4double e = 0.0;
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for (G4int i=0; i < MaxIter; i++)
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{
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// Rename a,b,c and adjust bounding interval d
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if (fb*fc > 0.0)
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{
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c = a;
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fc = fa;
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d = b - a;
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e = d;
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}
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if (abs(fc) < abs(fb))
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{
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a = b;
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b = c;
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c = a;
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fa = fb;
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fb = fc;
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fc = fa;
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}
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G4double Tol1 = 2.0*precision*abs(b) + 0.5*tolerance;
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G4double xm = 0.5*(c-b);
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if (abs(xm) <= Tol1 || fb == 0.0)
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{
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root = b;
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return true;
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}
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// Inverse quadratic interpolation
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if (abs(e) >= Tol1 && abs(fa) > abs(fb))
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{
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G4double s = fb/fa;
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G4double p = 0.0;
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G4double q = 0.0;
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if (a == c)
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{
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p = 2.0*xm*s;
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q = 1.0 - s;
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}
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else
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{
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q = fa/fc;
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G4double r = fb/fc;
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p = s*(2.0*xm*q*(q-r)-(b-a)*(r-1.0));
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q = (q-1.0)*(r-1.0)*(s-1.0);
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}
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// Check bounds
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if (p > 0.0) q = -q;
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p = abs(p);
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G4double min1 = 3.0*xm*q-abs(Tol1*q);
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G4double min2 = abs(e*q);
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if (2.0*p < std::min(min1,min2))
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{
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// Interpolation
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e = d;
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d = p/q;
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}
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else
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{
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// Bisection
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d = xm;
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e = d;
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}
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}
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else
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{
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// Bounds decreasing too slowly, use bisection
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d = xm;
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e = d;
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}
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// Move last guess to a
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a = b;
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fa = fb;
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if (abs(d) > Tol1) b += d;
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else
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{
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if (xm >= 0.0) b += abs(Tol1);
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else b -= abs(Tol1);
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}
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fb = theFunction(b);
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}
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G4cerr << "G4Solver::Brent: Number of iterations exceeded." << G4endl;
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return false;
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}
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template <class Function>
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G4bool G4Solver<Function>::Crenshaw(Function & theFunction)
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{
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// Check the interval before start
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if (a > b || abs(a-b) <= tolerance)
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{
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G4cerr << "G4Solver::Crenshaw: The interval must be properly set." << G4endl;
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return false;
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}
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G4double fa = theFunction(a);
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if (fa == 0.0)
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{
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root = a;
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return true;
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}
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G4double Mlast = a;
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G4double fb = theFunction(b);
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if (fb == 0.0)
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{
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root = b;
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return true;
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}
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if (fa*fb > 0.0)
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{
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G4cerr << "G4Solver::Crenshaw: The interval must include a root." << G4endl;
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return false;
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}
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for (G4int i=0; i < MaxIter; i++)
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{
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G4double c = 0.5 * (b + a);
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G4double fc = theFunction(c);
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if (fc == 0.0 || abs(c - a) < tolerance)
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{
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root = c;
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return true;
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}
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if (fc * fa > 0.0)
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{
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G4double tmp = a;
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a = b;
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b = tmp;
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tmp = fa;
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fa = fb;
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fb = tmp;
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}
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G4double fc0 = fc - fa;
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G4double fb1 = fb - fc;
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G4double fb0 = fb - fa;
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if (fb * fb0 < 2.0 * fc * fc0)
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{
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b = c;
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fb = fc;
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}
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else
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{
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G4double B = (c - a) / fc0;
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G4double C = (fc0 - fb1) / (fb1 * fb0);
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G4double M = a - B * fa * (1.0 - C * fc);
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G4double fM = theFunction(M);
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if (fM == 0.0 || abs(M - Mlast) < tolerance)
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{
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root = M;
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return true;
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}
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Mlast = M;
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if (fM * fa < 0.0)
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{
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b = M;
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fb = fM;
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}
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else
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{
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a = M;
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fa = fM;
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b = c;
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fb = fc;
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}
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}
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}
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return false;
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}
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template <class Function>
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void G4Solver<Function>::SetIntervalLimits(const G4double Limit1, const G4double Limit2)
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{
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if (abs(Limit1-Limit2) <= tolerance)
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{
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G4cerr << "G4Solver::SetIntervalLimits: Interval must be wider than tolerance." << G4endl;
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return;
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}
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if (Limit1 < Limit2)
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{
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a = Limit1;
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b = Limit2;
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}
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else
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{
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a = Limit2;
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b = Limit1;
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}
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return;
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}
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