/*------------------------------------------------------------------*\
|* Visualization functions *|
\*------------------------------------------------------------------*/
void plotFunction(FunctionENUM function)
{
switch (function)
{
case FUNCTION1:
for (double i = LEFT; i <= RIGHT; i += 0.001)
{
graphWin.plot(i, f1(i), 1);
}
break;
case FUNCTION2:
for (double i = LEFT; i <= RIGHT; i += 0.0001)
{
graphWin.plot(i, f2(i), 1);
}
break;
case GOLD_FUNCTION:
for (int i = 0; i < 19; i++)
{
graphWin.segment(map(i, 0, 19, 0, RIGHT), map(arrayGold[i], 250, 1700, 0, TOP), map(i + 1, 0, 19, 0, RIGHT), map(arrayGold[i + 1], 250, 1700, 0, TOP));
}
break;
default:
cout << "The given function does not exist";
break;
}
}
void bolzanoBisectionRecursive(double a, double b, double epsilon)
{
if(fabs(b-a) <= epsilon)
{
#ifdef USING_FIRST_FUNCTION
if (f(a) <= epsilon )
#else
if (g(a) <= epsilon )
#endif
cout << endl << ">>> " << b << " <<<<" << endl << endl;
return;
}
double c = (a+b)/2;
graphWin.segment(a,MAXHEIGHT,a,MINHEIGHT);
graphWin.segment(b,MAXHEIGHT,b,MINHEIGHT);
graphWin.segment(c,MAXHEIGHT,c,MINHEIGHT);
cout << "Analysing interval [" << a <<", " << b << "] with middle point at : "<< c <<endl;
if (c == 0)
{
cout << "0 is in " << c << endl;
}
#ifdef USING_FIRST_FUNCTION
if (oppositeSigns(f(a),f(c)))
#else
if (oppositeSigns(g(a),g(c)))
#endif
{
cout << " Narrowing interval to [" << a <<", " << c << "]" << endl;
bolzanoBisectionRecursive(a,c,epsilon);
}
#ifdef USING_FIRST_FUNCTION
if (oppositeSigns(f(c), f(b)))
#else
if (oppositeSigns(g(c), g(b)))
#endif
{
cout << " Narrowing interval to [" << c <<", " << b << "]" << endl;
bolzanoBisectionRecursive(c,b,epsilon);
}
}
void fixedPoint(double epsilon, double lambda, double startingPoint,bool isFirst)
{
double previousPoint = startingPoint;
int loopCounter = 0;
while (fabs(fixedPointAdapterFunction(previousPoint) - previousPoint) > epsilon && loopCounter < LOOP_LIMIT)
{
previousPoint=fixedPointAdapterFunction(previousPoint, lambda);
if(numberLine == 2)
{
plotAdaptedFunction(lambda);//we plot it here to have the proper lamda drawn
graphWin.segment(previousPoint, fixedPointAdapterFunction(previousPoint, lambda), fixedPointAdapterFunction(previousPoint, lambda), fixedPointAdapterFunction(previousPoint, lambda));
graphWin.segment(previousPoint, previousPoint, previousPoint, fixedPointAdapterFunction(previousPoint, lambda));
}
loopCounter++;
}
#ifdef USING_FIRST_FUNCTION
if(f(previousPoint) <= epsilon)
#else
if(g(previousPoint) <= epsilon)
#endif
{
graphWin.plot(previousPoint,fixedPointAdapterFunction(previousPoint, lambda),5);
cout << "x = " << previousPoint << endl;
}
else
{
cout << "x MAUVAIS = " << previousPoint << endl;
}
double tester = 2.0;
if(lambda > tester)
{
numberLine++;
lambda -= tester;
fixedPoint(epsilon, lambda,startingPoint);
}
}
void plotSecondDegreeDerivatedFunction(FunctionENUM function, double h)
{
if (function != GOLD_FUNCTION)
{
for (double i = LEFT; i <= RIGHT; i += 0.001)
{
graphWin.plot(i, calculateSecondDegreeDerivative(function, i, h), 1);
}
}
else
{
for (double i = 0; i < 18; i += 1)
{
double secondDegreeDerivative = calculateSecondDegreeDerivative(function, i, h);
double secondDegreeDerivativePlusOne = calculateSecondDegreeDerivative(function, i + 1, h);
graphWin.segment(map(i, 0, 19, 0, RIGHT), map(secondDegreeDerivative, 250, 1700, 0, TOP), map(i + 1, 0, 19, 0, RIGHT), map(secondDegreeDerivativePlusOne, 250, 1700, 0, TOP));
}
}
}
void plotDerivatedFunction(FunctionENUM function, DerivationMethodENUM derivationMethod, double h)
{
if (function != GOLD_FUNCTION)
{
for (double i = LEFT; i <= RIGHT; i += 0.001)
{
graphWin.plot(i, calculateDerivative(function, i, h, derivationMethod), 1);
}
}
else
{
double leftLimit = derivationMethod == CENTRAL_DIFFERENCE ? 1 : 0;
for (double i = leftLimit; i < 18; i += 1)
{
double derivative = calculateDerivative(function, i, h, derivationMethod);
double derivativePlusOne = calculateDerivative(function, i + 1, h, derivationMethod);
graphWin.segment(map(i, 0, 19, 0, RIGHT), map(derivative, 250, 1700, 0, TOP), map(i + 1, 0, 19, 0, RIGHT), map(derivativePlusOne, 250, 1700, 0, TOP));
}
}
}
void plotDerivationMethod(FunctionENUM function, double x, double h, DerivationMethodENUM derivativeMethod)
{
switch (function)
{
case FUNCTION1:
switch (derivativeMethod)
{
case PROGRESSIVE_DIFFERENCE:
for (double delta = 0; delta <= h; delta += h)
{
graphWin.plot(x + delta, f1(x + delta), 4);
graphWin.segment(x + delta, 0, x + delta, f1(x + delta));
graphWin.segment(0, f1(x + delta), x + delta, f1(x + delta));
}
//Segment between two points
graphWin.segment(x, f1(x), x + h, f1(x + h));
break;
case CENTRAL_DIFFERENCE:
for (double delta = -h; delta <= h; delta += h)
{
//Points
graphWin.plot(x + delta, f1(x + delta), 4);
//Lines from X axe
graphWin.segment(x + delta, 0, x + delta, f1(x + delta));
//Lines from Y axe
graphWin.segment(0, f1(x + delta), x + delta, f1(x + delta));
}
//Segment between two points
graphWin.segment(x - h, f1(x - h), x + h, f1(x + h));
break;
case FOURTH_DEGREE_POLYNOM:
for (double delta = -h; delta <= h; delta += h / 2)
{
graphWin.segment(x + delta, 0, x + delta, f1(x + delta));
graphWin.plot(x + delta, f1(x + delta), 4);
}
break;
default:
break;
}
break;
case FUNCTION2:
switch (derivativeMethod)
{
case PROGRESSIVE_DIFFERENCE:
for (double delta = 0; delta <= h; delta += h)
{
graphWin.plot(x + delta, f2(x + delta), 4);
graphWin.segment(x + delta, 0, x + delta, f2(x + delta));
graphWin.segment(0, f2(x + delta), x + delta, f2(x + delta));
}
//Segment between two points
graphWin.segment(x, f2(x), x + h, f2(x + h));
break;
case CENTRAL_DIFFERENCE:
for (double delta = -h; delta <= h; delta += h)
{
//Points
graphWin.plot(x + delta, f2(x + delta), 4);
//Lines from X axe
graphWin.segment(x + delta, 0, x + delta, f2(x + delta));
//Lines from Y axe
graphWin.segment(0, f2(x + delta), x + delta, f2(x + delta));
}
//Segment between two points
graphWin.segment(x - h, f2(x - h), x + h, f2(x + h));
break;
case FOURTH_DEGREE_POLYNOM:
for (double delta = -h; delta <= h; delta += h / 2)
{
graphWin.segment(x + delta, 0, x + delta, f2(x + delta));
graphWin.plot(x + delta, f2(x + delta), 4);
}
break;
default:
break;
}
break;
default:
break;
}
}
std::vector<long double> findRoot()
{
const long double epsilon = std::numeric_limits<double>::epsilon();
const long double STEP = 2*epsilon;
std::vector<long double> solutions;
//FindRoot
//Recherche les racines du côté x >= 0
long double oldStep = 2*epsilon;
for(long double x=oldStep; x<graphWin.xMax(); x+=fabsl(g(x)-x))
{
//Dessin des barres comme dans le cours
graphWin.segment(x-oldStep,x-oldStep,x-oldStep,g(x-oldStep));
if(x > g(x))
{
if(f == f1)
graphWin.segment(x-oldStep,g(x-oldStep),x,g(x-oldStep));
else
graphWin.segment(x-oldStep,x-oldStep,x,x-oldStep);
}
else
graphWin.segment(x-oldStep,x,x,x);
if(fabsl(g(x)-x) <= epsilon)
{
solutions.push_back(x);
x+=STEP;//On ajoute suffisement de STEP pour que la fonction puisse repartir et chercher d'autres solutions
}
oldStep = fabsl(g(x)-x);
}
oldStep = 2*epsilon;
//Recherche les racines du côté x < 0
for(long double x=-epsilon; x > graphWin.xMin(); x-=fabsl(g(x)-x))
{
//Dessin des barres comme dans le cours
graphWin.segment(x+oldStep,x+oldStep,x+oldStep,g(x+oldStep));
if(x < g(x))
{
if(f == f1)
graphWin.segment(x+oldStep,g(x+oldStep),x,g(x+oldStep));
else
graphWin.segment(x+oldStep,x+oldStep,x,x+oldStep);
}
else
graphWin.segment(x+oldStep,x,x,x);
if(fabsl(g(x)-x) <= epsilon)
{
solutions.push_back(x);
x-=STEP;//On ajoute le STEP initiale pour que la fonction puisse repartir et chercher d'autres solutions
}
oldStep = fabsl(g(x)-x);
}
sort(solutions.begin(),solutions.end());
return solutions;
}
void plotLinearFunction()
{
graphWin.segment(LEFTLIMIT, LEFTLIMIT, RIGHTLIMIT, RIGHTLIMIT);
}