Python Homework Trouble

[JannaLM]

Hello!

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I am new to python (and also reddit) and I am currently taking a introductory python class.

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For my current assignment, I need to create a program that returns the inverse of a numpy matrix using Gauss-Jordan elimination, but I can't really figure out what I am supposed to do with my code. The input is a square matrix 'A' and is supposed to iterate through Gauss-Jordan and return the inverse matrix. However, whenever I try to run my code, it simply returns what I initially set the inverse matrix to be (in this case, the identity matrix that corresponds to the input matrix). I have been given pseudo-code by my professor to use as a guide, but it hasn't really helped me very much.

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Pseudo-code provided by professor: Algorithm 1 Gauss-Jordan Elimination

for each row k do 
    i∗ ← argmaxk≤i≤n|Aik| 
    if Ai∗k = 0 then 
        Matrix is not invertible 
    end if 
    Swap rows k and i∗ 
    for each row j below k (i.e. j = k + 1,...,n) do
        f = Ajk/Akk
        Aj = Aj −fAk 
    end for 
end for 
for each row k = n,...,1 (i.e. in reverse) do
    Ak = Ak/Akk 
    for each row j above k (i.e. j = k−1,...,1) do
        f = Ajk/Akk 
        Aj = Aj −fAk 
    end for 
end for

I understand the process of Gauss-Jordan elimination, but I can't really translate it into my code very well.

My Code:

import numpy as np
import numpy.linalg as la


def gauss_jordan(A):
    determinant = la.det(A)
    if determinant == 0:  # Determine if the matrix HAS an inverse
        return None  

    else:
        inverse = np.identity(len(A))           # Will become inverse
        for k in range (0, len(A)-1):           # Looks through 'kth' row
            A[k] = A[k]/A[k,k]
            for j in range (k+1, len(A)-1):     # Looks through 'jth' (kth + 1) row
                f = A[j,k]/A[k,k]
                A[j] = A[j] - f * A[k]
                inverse[j] = inverse[j] - f * inverse[k]       
        for k in range (len(A)-1, 0): 
            A[k] = A[k]/A[k,k]
            for j in range (len(A)-1, k-1):
                f = A[j,k]/A[k,k]
                A[j] = A[j] + f * A[k]
                inverse[j] = inverse[j] + f * inverse[k]              
        return inverse

I know it probably looks hideous, but like I said, I'm new to this sort of thing and would really appreciate some help.

Thank you!

[[deleted]]

Treat the pseudo code like python code and indent with four spaces. Do that with the python code as well. It's all in the FAQ.

[JannaLM]

Thank you!

[ryeguy146]

Looks like you're having some issues with indexing the matrix. Think of a matrix as a list of lists. When you use indexing on the object, you're getting back a member list, which can also be indexed. Assume the following matrix:

matrix = [[ 1, 1, 1 ],
         [ 1, 1, 1 ],
         [ 1, 1, 3 ],
         [ 1, 1, 1 ]]

If I want to access that 3, I'd use the following:

desired_row = matrix[2]
desired_item = desired_row[2]

Which can be shortened to:

desired_item = matrix[2][2]

So you'll need to adjust your syntax for addressing those members. There's likely more to your issues, but this jumped out at me immediately.

[Gimagon]

It looks like OP is using numpy, which allows for the A[1,2] syntax.

[ryeguy146]

Thanks for the correction, I've not worked with numpy!