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I often face the "UnicodeDecodeError" when I'm writing some calculating programs. It says for example :

UnicodeDecodeError: 'utf-8' codec can't decode byte 0xe9 in position 57: invalid continuation byte

My question is : how can I locate which word in my code causes the error ? I have no idea how to know were this 'position 57' is situated. And by the way, what means 'invalid continuation byte' ?

Thanks for the answers.

PS : this error comes from this code where I try to apply the 4th order Runge-Kutta method to the Lorenz equations :

# Auteur : Bastien Massion 

# NOMA : 13701700

# Date création fichier : 23 novembre 2018 18h24

# Date dernière modification : 23 novembre 2018 19h05



# Je jure que ceci est le fruit de mon travail personnel



from numpy import *



def lorfunction(t, u): # u = [u_0, u_1, u_2] = [x, y, z]

    fx = 10*u[1] - 10*u[0]

    fy = 28*u[0] - u[0]*u[2] - u[1]

    fz = u[0]*u[1] - 8/3*u[2]

    return [fx, fy, fz]



def lorenz(Tstart, Tend, Ustart, n):

    T, h = linspace(Tstart,Tend, n+1, retstep = True)

    U = zeros((n+1, 3))

    U[0,:] = Ustart



    for i in range(0, n):

        Ka = lorfunction(T[i], U[i])

        Kb = lorfunction(T[i] + h/2, U[i] + h/2*Ka)

        Kc = lorfunction(T[i] + h/2, U[i] + h/2*Kb)

        Kd = lorfunction(T[i] + h, U[i] + h*Kc)

        U[i+1] = U[i] + h/6*(Ka + 2*Kb + 2*Kc + Kd)



    return T,U



print (lorenz(0.0, 100.0, [0,1,0,], 10000))

UnicodeDecodeError: 'utf-8' codec can't decode byte 0xe9 in position 57: invalid continuation byte

The 57 is the byte position of complaint in your Python source file.
In your case it seems to be the position of the é in # Date création fichier.

0xe9 is the byte at that position. I recognize it as the ISO-8859-1
(a.k.a. ISO-Latin-1) representation of the character é.

So it seems your Python source file is actually encoded in ISO-8859-1,
but the Python interpreter for some reason assumes it to be encoded in UTF-8.

By the way:

In UTF-8 characters above 128 are encoded by 2 or more bytes,
the first being called the start byte, the others called continuation bytes.
For more explanation see the UTF-8 examples.

To understand the error I need to elaborate more.
Consider the bytes 0xe9 0x61 0x74, as occuring in your Python file:

Decoding the 3 bytes as ISO-8859-1 (being a single-byte encoding) would result in 3 characters: éat.

Decoding the same bytes as UTF-8 is more complicated.
The byte 0xe9 (because beginning with the bits 1110) is a starting byte
to be followed by 2 continuation bytes.
Each continuation byte needs to begin with the bits 10,
But the next 2 bytes (0x61 0x74) violate this condition.
Thus, a UnicodeError saying invalid continuation byte is thrown.

To avoid this kind of problem you have some alternative options:

• 
  

  Keep your Python source encoded in ISO-8859-1
  and add the line

  
  
  

   # -*- coding:iso-8859-1 -*-
  
  

  
  
  

  at the beginning of the file
  as described in PEP 263 -- Defining Python Source Code Encodings.

  
  


• Save your Python source in UTF-8.
  and rely on UTF-8 being the default source-encoding of your Python-interpreter.


• 
  

  Save your Python source in UTF-8.
  and add the line

  
  
  

   # -*- coding:utf-8 -*-
  
  

  
  

I would prefer the first or third option.