[Python]Trapezium rule

[The_ouroboros]

A parte l'orrida forma(che poi si puo sistemare).
Sto cercando di creare una funzione per la regola del trapezio di integrazione numerica.
con k=1,..,n

Codice PHP:

#!/usr/bin/env python 

def trapezium_rule(f, a, b):
  "Approximate the definite integral of f from a to b by Trapezium rule." 
  return (b - a) * ((f(a) + f(b))/2)
  
"Approximate the definite integral of f from a to b(subdivided) by Trapezium rule. n is the numbers of partitions "  
def trapezium_plus(f,a,b,n):    
  z = (b-a)/2*n 
  res = z 
  x = {0:0}
  
  for i in range(1, n):
      tmp = a + i*((b-a)/n)
      x[i]= tmp
      
  x[1] = f(x[1])
  x[n] = f(x[n])
  
  for j in range(2, n-1):
      x[j] = 2 * f(x[j])    
      
  out = 0
  
  for k in range(1, n):
       out += x[k]
       
  res = z*out    
  return res
    
from math import sin
from math import pi
print 'BEGIN'
print 'integral of sin(x) from 0 to 2*pi:\n'
print '\n'
print trapezium_plus(sin, 0, 2*pi, 30)
print 'END' 


Il risultato che mi esce è però

BEGIN
integral of sin(x) from 0 to 2*pi:



Traceback (most recent call last):
  File "trapezium.py", line 37, in <module>
    print trapezium_plus(sin, 0, 2*pi, 30)
  File "trapezium.py", line 19, in trapezium_plus
    x[n] = f(x[n])
KeyError: 30

Dove sbaglio??

Grazie

[The_ouroboros]

in metacodice sarebbe:

FUNCTION trapez(f,a,b,n)
  z = (b-a)/2*n
  FOR i=1:n
    x(i)=a+i*((b-a)/n)
  END
  res = f(x(1))+f(x(n))
  FOR i=2:n-1
    res = res + f(x(i))
  END
  res = res*z
RETURN res

[cdimauro]

Prova così:

def trapez(f, a, b, n):
  z = (b - a) / 2 * n
  for i in xrange(1, n + 1):
    x[i] = a + i * ((b - a) / n)
  res = f(x[1]) + f(x[n])
  for i in xrange(2, n):
    res += f(x[i])
  return res * z

[The_ouroboros]

grazie... mi ero un po impantanato in una cavolata

[The_ouroboros]

#!/usr/bin/env python 

def trapezium_rule(f, a, b):
  "Approximate the definite integral of f from a to b by Trapezium rule." 
  return (b - a) * ((f(a) + f(b))/2)
  
"Approximate the definite integral of f from a to b(subdivided) by Trapezium rule. n is the numbers of partitions "  
def trapezium_plus(f,a,b,n):	
  z = (b-a)/2*n 
  res = z 
  x = {0:0}
  
  for i in range(1, n+1):
  	x[i]= a + i*((b-a)/n)
  	
  res = f(x[1]) + f(x[n])
  
  for j in range(2, n):
  	x[j] = 2 * f(x[j])	
  
  for k in range(1, n):
  	 res += x[k]	
  	 
  return res * z
  
"by cdimauro"    
def trapez(f, a, b, n):
  x = {0:0}
  z = (b - a) / 2 * n
  for i in xrange(1, n + 1):
    x[i] = a + i * ((b - a) / n)
  res = f(x[1]) + f(x[n])
  for i in xrange(2, n):
    res += f(x[i])
  return res * z
	
from math import sin
from math import pi

n = input ('Number of iteration?')
print 'BEGIN'
print '\nWith', n, ' iteration'
print '\nIntegral of sin(x) from 0 to 2*pi(ref from Simpson):\t 2.5648942583e-16'
print '\nIntegral of sin(x) from 0 to 2*pi(trapezium_plus):\t' , trapezium_plus(sin, 0, 2*pi, n)
print '\nIntegral of sin(x) from 0 to 2*pi(trapez):\t' , trapez(sin, 0, 2*pi, n)
print '\nEND'