// activité 3

function y=f(x) 
y=x.*x-2
endfunction

function y=df(x)
y=2*x 
endfunction

function [x,n]=newton(f,df,x0,eps)
  x = x0;
   n=0
  while (abs(f(x))>eps) & n< 50  
    x = x - f(x)/df(x);
    n=n+1
   end
endfunction

function [x,n]=secante(f,x0,eps)
df=(f(x0+0.001)-f(x0))/0.001
x=x0-f(x0)/df 
n=0
  while (abs(f(x))>eps) & n< 50  
    df=(f(x)-f(x0))/(x-x0)
    x0=x
    x = x - f(x)/df;
    n=n+1
   end
endfunction


function graphe2(f,df,a,b)
// Methode de Newton
x=linspace(a,b,50)
y=feval(x,f)
clf()
plot2d(x,y)
plot2d(x,0*x,1)
n=0
i=1
while n==0
i=i+1
c=a-f(a)/df(a)
plot2d([a c],[f(a) 0],i)
plot2d([c c],[0 f(c)],i)
a=c
n=input("Pour continuer tapez 0 sinon 1")
end
endfunction

function graphe3(f,a,b)
// Methode de la secante
x=linspace(a,b,50)
y=feval(x,f)
clf()
plot2d(x,y)
plot2d(x,0*x,1)
n=0
i=2

df=(f(a+0.001)-f(a))/0.001
c=a-f(a)/df 
plot2d([a c],[f(a) 0],i)
plot2d([c c],[0 f(c)],i)

while n==0
i=i+1
df=(f(c)-f(a))/(c-a)
x=a-f(a)/df
a=c
c=x
plot2d([a c],[f(a) 0],i)
plot2d([c c],[0 f(c)],i)
n=input("Pour continuer tapez 0 sinon 1")
end
endfunction



function y=g(x)
y=0.5*(x+2/x)
endfunction

function colimacon(g,a,b)
clf
x=linspace(a,b,100)
y=feval(x,g)
ymin=min(0,a,min(y))
ymax=max(0,b,max(y))
plot2d(x,feval(x,g),1,rect=[a ymin b ymax])
plot2d(x,x,2)
u0=input('entrer u0')
plot2d([u0 u0],[0 g(u0)],3)
n=1
i=3
while n==1
plot2d([u0 g(u0)],[g(u0) g(u0)],i)
u0=g(u0)
plot2d([u0 u0],[u0 g(u0)],i)
i=i+1
n=input("pour continuer taper 1")
end
endfunction