计算对称矩阵

Question

I have a list of 0,1 3x3 matrices. I want to count how many of them are symmetrical. How can I implement that? I was trying this:

def transpose(mat, tr, N): 
    for i in range(N): 
        for j in range(N): 
            tr[i][j] = mat[j][i] 


l=0
def count(list):
        for y in list:
            tr = [ [0 for j in range(3) ] for i in range(3) ] 
            transpose(y, tr, 3)
            if int(y[i][j]) == int(tr[i][j]):
               l+= 1

But the answer is wrong.

Answer 1

I would just define:

def is_symmetric(matrix, n):
   return all(matrix[i][j] == matrix[j][i] for i in range(n) for j in range(n))

The bug in your code is that you're comparing one value of y against one value of tr. You're not comparing all of them.

As an optimization, you could actually do:

def is_symmetric(matrix, n):
    return all(matrix[i][j] == matrix[j][i] 
               for i, j in itertools.combinations(range(n), 2))

This eliminates looking at the diagonal and looking at each pair of elements twice.

Answer 2

First, please take a look at numpy which can solve such a problem trivially:

is_symmetric = lambda m: m.shape == m.T.shape and np.all(np.isclose(m, m.T))

But in pure Python, with a nested list of integers (for floats do not use == to check for equality, check abs(xy) < eps ), the following should work:

def is_symmetric(m):
    square = len(m) == len(m[0])
    return square and all(m[i][j] == m[j][i]
                          for i in range(len(m))
                          for j in range(i+1, len(m)))

def count_symmetric(li):
    return sum(is_symmetric(m) for m in li)

Answer 3

Your transpose function is not returning a value. Python is not call by reference so you must return the transposed matrix. Like so:

def transpose(mat, N): 
    tr = [[0 for _ in range(N)] for _ in range(N)]
    for i in range(N): 
        for j in range(N): 
            tr[i][j] = mat[j][i]
    return tr

Next we need to compare the matrices, we can do that simply using the == operator.

>>> mat1 = [[1,0], [0,1]]
>>> mat2 = [[1,2], [3,4]]

>>> print(mat1 == transpose(mat1, 2))
True
>>> print(mat2 == transpose(mat2, 2))
False

We can then form a count function

def count_symetric(l):
    count = 0
    for mat in l:
        if mat == transpose(mat, 3):
            count += 1