trapezoidal and simpsons

Author: izaakrogan

README.md

@@ -0,0 +1 @@
+Some numerical methods in Python

curves.py

@@ -0,0 +1,22 @@
+# trapezoidal
+def trapezoidal(f,a,b,n):
+    fs = list(map(lambda x: f(x), np.linspace(a,b,n+1)));
+    return ( sum(fs)-(fs[0]+fs[-1])*0.5)*(b-a)/n
+
+# simpson
+def simpson(f,a,b,n):
+    r = np.linspace(a,b,n+1)
+    total = 0
+    for i in range(len(r)-1):
+        total += (((b-a)/n)/6)*(f(r[i])+4*f((r[i]+r[i+1])/2)+f(r[i+1]))
+    return total
+
+def f(x):
+    return 2/(x**2+1)
+
+print(trapezoidal(f,-1.0,1.0,10.0))
+print(simpson(f,-1.0,1.0,10.0))
+
+p = 4 # run through powers and check numbers are the same
+for i in range(1,20): # checking it experimentally
+    print((simpson(np.cos,0.0,1.0,i)-np.sin(1.0))*(i**p))

precise.py

@@ -0,0 +1,9 @@
+# multiple precision
+
+from mpmath import *
+mp.dps  = 500
+newton(f,df,mpf(1))
+
+random.uniform(-1,1)
+
+from numpy import *