Problem reproducing MATLAB code in Python involving a for loop

Question

I have constructed the following code using MATLAB:

numero=60;
a=zeros(numero,1)
b=zeros(numero+1,1)   
for i=1:numero+1
    a(i)=-cos(pi*(i-1)/numero)
end
figure
plot(a,b, '*')

It serves to calculate the nodes of a Chebyshev polynomial of order numero and store it in a vector called a. I need to reproduce this in Python. My attempt at a solution is

from mpmath import chebyt, chop, taylor
import numpy as np
import sympy as sp


numero=60
nodes = []
for i in range(numero+2):
     auxiliary=-np.cos(np.pi*(i-1)/numero)
     nodes.append(auxiliary)

[float(i) for i in nodes]
nodes.sort()
print(nodes)

However, there are is an issue in python's output. The first is the fact that the second number of the list, -0.9986295347545738 appears twice, it is also the third element of nodes. I don't know why this happens and I would like to know if someone can tell me how to avoid this error.

please, post your expected output

bcosta12
– bcosta12

2019-12-02 14:39:59 +00:00
Commented Dec 2, 2019 at 14:39 — bcosta12
– bcosta12, Commented Dec 2, 2019 at 14:39

CDJB · Accepted Answer · 2019-12-02 14:50:28Z

3

The issue comes about in this line:

for i in range(numero+2)

compared to:

for i=1:numero+1

The variable i is starting at 0, and really we want it to start at 1. We can see that this causes the error from the following:

>>> -np.cos(np.pi*(0-1)/numero)
-0.9986295347545738
>>> -np.cos(np.pi*(1-1)/numero)
1.0
>>> -np.cos(np.pi*(2-1)/numero)
-0.9986295347545738

etc. So the fix is to switch to:

for i in range(1, numero+2)

You can also omit these lines:

[float(i) for i in nodes]
nodes.sort()

This gives output:

[-1.0, -0.9986295347545738, -0.9945218953682733, -0.9876883405951378, ..., 0.9876883405951377, 0.9945218953682734, 0.9986295347545738, 1.0]

as expected.

edited Dec 2, 2019 at 14:50

answered Dec 2, 2019 at 14:41

CDJB

14.6k6 gold badges36 silver badges58 bronze badges

Sign up to request clarification or add additional context in comments.

Collectives™ on Stack Overflow

Problem reproducing MATLAB code in Python involving a for loop

1 Answer 1

Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

Comments

Your Answer

Sign up or log in

Post as a guest

Related