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[cours-mesi.git] / tps / chap3 / methodes.py

diff --git a/tps/chap3/methodes.py b/tps/chap3/methodes.py
index 8ae3b711091bd03d226b2fea6df00ce5e62ea04f..9c9424e6110fff1b72177deac4a9b90f5f6cffce 100644 (file)
--- a/tps/chap3/methodes.py
+++ b/tps/chap3/methodes.py
@@ -16,79 +16,61 @@ def fp(x):
 
 
 def  iteration_dichotomie(a,b,m,epsilon,f):
-    def maj_test(xn,xnm1):
-        return f(xn) != 0 and abs(xnm1-xn) > epsilon  
-    xnm1 = a 
-    xn= a
+    def maj_test(xn,xnm1,n,m):
+        return f(xn) == 0 or abs(xnm1-xn) <= epsilon or n >= m    
+    xn= float(a)
+    xnm1 =float(b) 
     X=[]
-    n = 1
-    an= a
-    bn=b
-    test = True
-    while n <= m and test:
+    n = 0
+    an= float(a)
+    bn=float(b)
+    test = maj_test(xn,xnm1,n,m)
+    while not test:
         xnm1 = xn
         xn=float(an+bn)/2
-        test = maj_test(xn,xnm1)
         X +=[xn]
         if f(an)*f(xn)<=0 : 
             bn=xn
         else :
             an=xn
         n +=1
+        test = maj_test(xn,xnm1,n,m)
     return (n,X)
 
 def  iteration_newton(x0,m,epsilon,f,fp):
-    def maj_test(xn,xnm1):
-        return f(xn) != 0 and abs(xnm1-xn) > epsilon  
-    n=0;
-    test= f(x0) != 0
-    xn=x0
-    X=[x0]
-    while n < m and test:
+    def maj_test(xn,xnm1,epsilon,n,m,f):
+        return f(xn) == 0 or abs(xnm1-xn) <= epsilon or n >= m
+    n = 0
+    xn = float(x0)
+    X = [x0]
+    test = maj_test(xn,xn+2*epsilon,epsilon,n,m,f)
+    while not test:
         qn=fp(xn)
         xnm1=xn
         xn= xn-f(xn)/qn
         X += [xn]
         n=n+1
-        test= maj_test(xn,xnm1)
-
-#f(x) !=0 and n<m  and abs(x-xm1)>epsilon
+        test= maj_test(xn,xnm1,epsilon,n,m,f)
     return (n,X)
 
 
 def  iteration_corde(a,b,x0,m,epsilon,f):
-    def maj_test(xn,xnm1):
-        return f(xn) != 0 and abs(xnm1-xn) > epsilon  
-    n=0;
+    def maj_test(xn,xnm1,n,m,f):
+        return f(xn)== 0 or abs(xnm1-xn) <= epsilon or n >= m
+    n=0
     q=float(f(b)-f(a))/(b-a)
-    test= f(x0) != 0
-    xn=x0
-    X=[x0]
-    while n < m and test:
+    xnm1 = float(b)
+    xn=float(x0)
+    test= maj_test(xn,xnm1,n,m,f)
+    X=[float(x0)]
+    while not test:
         xnm1=xn
-        xn= xn-f(xn)/q
+        xn= xn-float(f(xn))/q
         X += [xn]
         n=n+1
-        test= maj_test(xn,xnm1)
-
-#f(x) !=0 and n<m  and abs(x-xm1)>epsilon
+        test= maj_test(xn,xnm1,n,m,f)
     return (n,X)
 
-"""def  iteration_newton(x0,m,epsilon,f,fp):
-    n=0;
-    delta=float(1)/fp(x0)
-    test= f(x0) != 0
-    x=x0
-    X=[x0]
-    while(test):
-        xm1=x
-        x= x-delta*f(x)
-        delta=float(1)/fp(x)
-        X += [x]
-        n=n+1
-        test= not (f(x)==0 or n>=m  or abs(x-xm1)<=epsilon)
-    return (n,X)
-"""
 
 def  iteration_lagrange(x0,x1,m,epsilon,f):
     n=0;
@@ -138,24 +120,24 @@ def  iteration_muller(x0,x1,x2,m,epsilon,f):
 
 def main():
     print "TP 3.1 ............ dichotomie"
-    print iteration_dichotomie(0,pi/2,200,0.00000001,f)
+    print iteration_dichotomie(0,pi/2,45,1E-9,f)
 
-    
     print "TP 3.1 ............ corde"
-    print iteration_corde(0,pi/2,0,200,0.00000001,f)
-
+    print iteration_corde(0,pi/2,0,200,1E-9,f)
 
     print "TP 3.1 ............ newton"
-    print iteration_newton(0,200,0.00000001,f,fp)
+    print iteration_newton(0,200,1E-9,f,fp)
 
 
+
+"""
     print "TP 3.1 ............ lagrange"
     print iteration_lagrange(0,pi/2,200,0.00000001,f)
 
     print "TP 3.1 ............ muller"
     print iteration_muller(0,pi/4,pi/2,200,0.00000001,f)
     
-
+"""
 if __name__ == '__main__':
     main()