Indexerror: index 3 is out of Bounds for Axis 0 with size 3

Question

I have this code in Python, but the following error appears:

Indexerror: index 3 is out of Bounds for Axis 0 with size 3

Code:

import numpy as np
import math

A=11
T=(math.pi)/60
tf=15000
u=[]
x=[]
x=2*(np.ones((3,1)))

for i in range(1,tf):
    u = np.append(u,A*math.cos(i*T))
for k in range(3,tf):
    x = np.append(x,(2.1579*x[k]-1.3203*x[k-1]+0.16239*x[k-2]+0.0003416*u[k]+0.0019463*u[k-1])
print(x)

Answer 1

The range used in your loop for k in range( 3, tf ) is extrapolating the limit of your Numpy Array x already in the first iteration.

Your Numpy Array was initialized with only 3 elements:

x = 2 *(np.ones((3,1)))

The first iteration of your for the index k is 3 making your equation try to access a fourth element outside the boundaries of your array:

x[k]   # Mesmo que x[3]

The solution is to make your interval start from index 2:

for k in range( 2, tf )

Follows solution with Numpy Arrays:

import numpy as np
import math

A = 11
T = (math.pi) / 60
tf = 15000

u = (np.zeros((tf,1)))
x = 2.0 * (np.ones((3,1)))

for i in range( 1, tf ):
    u[i] = A * math.cos(i * T)

for k in range( 2, tf ):
    x = np.append( x, 2.1579 * x[k] - 1.3203 * x[k-1] + 0.16239 * x[k-2] + 0.0003416 * u[k] + 0.0019463 * u[k-1] )

print(x)

List solution built-in:

import math

A = 11
T = (math.pi) / 60
tf = 15000

x = [ 2.0 for i in range( 3 ) ]
u = [ A * math.cos(i * T) for i in range( 1, tf ) ]

for k in range( 2, tf ):
    x.append( 2.1579 * x[k] - 1.3203 * x[k-1] + 0.16239 * x[k-2] + 0.0003416 * u[k] + 0.0019463 * u[k-1] )

print(x)

EDIT:

To save the list x in a file called saida.txt just do something like:

with open( 'saida.txt', 'w' ) as arq:
    for n in x:
        arq.write( str(n) + '\n' )