Ecriture des methodes

integration.py

@@ -0,0 +1,55 @@
+# -*- coding: utf-8 -*-
+
+import numpy as np
+import matplotlib.pyplot as mp
+import numpy.random as npr
+
+#----------------------------------#
+#         INTEGRAL METHODS         #
+#----------------------------------#
+
+def rect_meth(x, y, n, f):
+    a = (y-x)/n
+    s = 0.0
+    t = np.arange(0, n)
+    for i in t:
+        s += f(x + i*a)
+    return a*s
+
+def simpson_meth(x, y, n, f):
+    a = (y-x)/n
+    s1 = 0.0
+    s2 = 0.0
+    t = np.arange(1, n/2)
+    u = np.arange(1, (n/2)+1)
+    for i in t:
+        s1 += f(x + 2*i*a)
+    s1 = 2*s1
+    for i in u:
+        s2 += f(x + (2*i-1)*a)
+    s2 = 4*s2
+    return (a/3)*(f(x) + s1 + s2 + f(y))
+
+def monte_carlo_meth(x, y, n, f):
+    max = 0.0
+    s = 0.0
+    for i in range(n+1):
+        a = f(x + y*float(i+1)/n)
+        if (max < a):
+            max = a
+    alpha = (b-a)*max
+    for i in range(n):
+        x_random = (b-a)*npr.rand() + x
+        y_random = max*npr.rand()
+        if (y_random <= max):
+            s += (alpha/n) * f(x_random)
+    return s
+
+
+#--------------------#
+#       LENGTH       #
+#--------------------#
+
+def length(I, n, df, x, y):
+    length = lambda x: np.sqrt(1 + (df(x)*df(x)))
+    return I(x, y, n, length)