Python-List索引中的Weierstrass函数超出范围错误

Question

I am trying to code and plot the Weierstrass function in Python.

http://mathworld.wolfram.com/WeierstrassFunction.html

f(x)=∑sin(πk^(a)x)/(πk^(a)) from k=1 to ∞

I'm a little stuck because I keep running into a "list index out of range error" at the line yval = wer(a, (xl[i]), e)

I'm not sure where I'm going wrong, or if my thought process is incorrect. Any help is greatly appreciated! Thanks!

Here is the code:

import math,pylab

x0 = float(input('Enter beginning of interval: ')) #start of interval
xf = float(input('Enter endpoint of interval: ')) #end of interval
a = float(input('Enter a value for a: '))
#x = float(input('Enter a value for x: ')) 
e = float(input('Enter desired error tolerance: '))
n = int(input('Enter number of iterations: '))

def wer(a, x, e): # a is givin number, e is error tolerance

    Sum1 = 0
    Sum2 = 0
    k = 1

    while(True):
        #sine of pi times k to the a times x over pi times k to the a
        Sum1 = math.sin((math.pi)*pow(k,a)*(x))/((math.pi)*(pow(k,a)))
        Sum2 = Sum1 + math.sin((math.pi)*pow((k+1),a)*(x))/((math.pi)*pow((k+1),a))

        if (abs(Sum2-Sum1) < e):
            break
        else:
            k+=1
    return Sum1

def append(x0, xf, n):

    xl = [] #list containing x values
    yl = [] #corresponding y values
    dx = (xf-x0)/n #length of each subinterval

    for i in range (0, (n+1)):
        xval = x0 + (i * dx)
        yval = wer(a, (xl[i]), e) #ERROR HERE

        xl.append(xval)
        yl.append(yval)
        #print i,':',xl
    return xl, yl


append(x0, xf, n)   
pylab.plot(xl,yl)

Answer 1

The first time through the loop at the end xl[0] will be passed to the wer function but xl is an empty array. I am not sure what you are trying to do but should it be xval that you pass to the function rather than xl[0]?

Answer 2

At the start of each iteration xl doesn't have the i -th element yet, since you add it at the end of the loop; you should either perform the xl.append immediately after calculating xval , or just use xval instead of xl[i] in the yval formula.