Working with matrices

Write a module with three functions about matrices, and their pytests: sum_of_diagonal, create_matrix and multiply.

1) The first function is (sum_of_diagonal) that, given a \(m\) matrix of integers, calculates the sum of the integers that are on the diagonal. Your function has to check that the matrix is square and does indeed have a diagonal to add. For example:

\({\tt sum of diagonal}( \begin{bmatrix} 1 & 2 & 3 & 4 \\ 2 & 4 & 6 & 1 \\ 0 & 5 & 8 & 2 \\ 2 & 9 & 6 & 3 \\ \end{bmatrix}) = 16\), \(\;\;\) \({\tt sum of diagonal}( \begin{bmatrix} 1 & 5 \\ 3 & 4 \\ \end{bmatrix}) = 5\)

Your function must pass the following tests:

@pytest.mark.parametrize("testcase, input, output",[ (1, [[1,2,3],[4,5,6],[7,8,9]], 15), (2, [[1,0,1],[1,1,0],[1,1,1]], 3), (3, [[2,0],[0,2]], 4), (4, [[2,0],[0,2,3]], "the matrix is not square"), (5, [], 0)]

def test_sum_of_diagonal(testcase, input, output): 
    assert sum_of_diagonal(input) == output, "case 0".format(testcase)

2) Next, we write a function (create_matrix) that, given two numbers \(n\) and \(m\), returns a list that represents a matrix with \(n\) rows and \(m\) columns, all values being 0.

\[{\tt create matrix}(3,4) = \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{bmatrix})\]

Design a set of test cases and automate them with the pytest.

3) The third function is for (multiply). Given two matrices \(m_1\) and \(m_2\), returns \(m_1 \times m_2\). Remember¹ that we can only multiply 2 matrices if the number of columns in the \(m_1\) matrix is equal to the number of rows in the \(m_2\) matrix.

Your function must pass the following tests:

@pytest.mark.parametrize("testcase, input1, input2, output",[(1, [[12,7,3], [4, 5,6], [7, 8,9]], [[5,8,1,2],[6,7,3,0], [4,5,9,1]], [[114, 160, 60, 27], [ 74, 97, 73,14], [119, 157, 112, 23]] ), (2, [[12,7,3, 0], [ 4,5,6,12],[ 6,7,8, 9] ], [[8,5,8,1,2], [6,9,7,3,0], [4,5,9,1,0],[4,5,9,1,0] ], [[150, 138, 172, 36, 24], [134, 155, 229, 37,8], [158, 178, 250, 44, 12] ] ), (3, [], [], [] ),(4,[[]],[[]], "they cannot be multiplied" ), (5,[[]],[[[]]], "they cannot be multiplied" ), (6,[[[]]],[[]], [[]] ) ])

def test_multiply(testcase, input1, input2, output): 
    assert multiply(input1, input2) == output, "case 0".format(testcase)

1. https://es.wikipedia.org/wiki/Multiplicación_de_matrices ↩