TypeError: only size-1 arrays can be converted to Python scalars when trying to plot a function

Question

I've got the current code:

from math import cos, sin, pi
import numpy as np
import matplotlib.pyplot as plt

def f(x):
    
    values = []
    s = 0
    for n in range(1, 6, 1):
        s += -((2/(n*pi))*(((cos((n*pi)/2))-1)*(sin((n/2)*x))))
        values.append(s)
        
    return values

x = np.linspace(-2*pi, 6*pi, 500)
plt.plot(f(x))

I'm supposed to plot f(x), but when I run the code, I get this error:

TypeError: only size-1 arrays can be converted to Python scalars

Any ideas as to what I'm doing wrong?

Answer 1

I think the x value in the formula only applies for one value of x, and since you have multiple x in a form of a list, you have to iterate through each of them (for example, using for xval in x:), perform the calculation and append the calculated value to the values list

from math import cos, sin, pi
import numpy as np
import matplotlib.pyplot as plt

def f(x):
    values = []
    for xval in x:
        s = 0
        for n in range(1, 6, 1):
            s += -((2/(n*pi))*(((cos((n*pi)/2))-1)*(sin((n/2)*xval))))
        values.append(s * -1)
        
    return values

x = np.linspace(-2*pi, 6*pi, 500)
plt.plot(f(x))
plt.show()

Answer 2

If you are new to programming, this may appear a little different from you are doing right now, however I have essentially split the functions up to explain what each component does and, more importantly, used numpy's built-in functions which will prove to be more efficient than nested loops, especially as your data becomes larger.

To understand what's happening with the function f, look-up (list) comprehensions in Python, but it's basically a for loop expressed in a single line.

In [24]: import numpy as np
    ...: import matplotlib.pyplot as plt

In [25]: def summand(n, x):
    ...:     """ Return an array of `x`'s size for a given value of `n`.
    ...:     Each element of the array is a value of the function computed
    ...:     at a value in `x` with the given `n`.
    ...:     """
    ...:     return (2 / (n * np.pi)) * (np.cos(n * np.pi / 2) - 1) * np.sin(n * x / 2)
    ...:

In [26]: def f(x, N=5):
    ...:     """ Return the sum of the summands computed for
    ...:     values of `n` ranging from 1 to N+1 with a given array `x`
    ...:     """
    ...:     return sum(summand(n, x) for n in range(1, N+1))
    ...:

In [27]: x = np.linspace(-2*np.pi, 6*np.pi, 500)

In [28]: plt.plot(x, f(x))
Out[28]: [<matplotlib.lines.Line2D at 0x23e60b52a00>]

In [29]: plt.show()