Program to find determinant of a n x n matrix not working-CodePudding

when i give a 3X3 matrix as input,it returns index error at line: m[0][0]*m[1][1]-m[0][1]*m[1][0]

import copy

def matrixdeterminant(m):
    if len(m)==1:
        return m[0]
    elif len(m)==2:
        return m[0][0]*m[1][1]-m[0][1]*m[1][0]
    else:
        matrixdeterminantlist=copy.deepcopy(m)
        determinantlist=[]
        m.pop(0)

        for i in range(len(matrixdeterminantlist[0])):
            for j in range(len(m)):
                m[j].pop(i)
            determinantlist.append(matrixdeterminantlist[0][i]*matrixdeterminant(m)*(-1)**(i 2))

            m=copy.deepcopy(matrixdeterminantlist)
   
    return sum(determinantlist)

CodePudding user response：

First issue I can spot: you wrote return m[0] rather than return m[0][0] for the case where len(m) == 1.

If m is a 1x1 matrix, then it looks something like [[x]], and you want to return x, not [x], so you have to return m[0][0], not m[0].

Another important issue in your code is the way you pop elements from m and then try to restore m from its copies. This is overly complicated and you restore m wrongly inside the loop, so at some points the dimensions of m are all screwed-up. I recommend to avoid using .pop at all, and instead, build the submatrices using list comprehensions.

Here is a simplified version:

def matrixdeterminant(m):
    if len(m)==1:
        return m[0][0]
    elif len(m)==2:
        return m[0][0]*m[1][1]-m[0][1]*m[1][0]
    else:
        determinantlist=[]
        sign = 1
        for i in range(len(m)):
            submatrix = [row[1:] for j,row in enumerate(m) if j != i]
            minor = matrixdeterminant(submatrix)
            determinantlist.append(sign * m[i][0] * minor)
            sign *= -1
        return sum(determinantlist)

And here is yet another version:

from itertools import cycle

def matdet(m):
    if len(m) == 1:
        return m[0][0]
    else:
        return sum(
            s * mj[0] * matdet([row[1:] for i,row in enumerate(m) if i != j])
            for s,(j,mj) in zip(cycle([1,-1]), enumerate(m))
        )

Once it's producing numerical values instead of error messages, I strongly encourage you to test your determinant function by comparing its output on big random matrices, against the output of a matrix determinant function from a standard python module such as numpy or sympy or scipy: