Search code examples
pythonrowsubmatrix

splitting matrix in multiple blocks

I have a matrix like that below:

A= [[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]]

and I want to extract submatrices containing equal rows. I don't know a priori how many blocks I'll get and the position of equal rows, since it is an example for a much bigger matrix.

The result I should obtain is in the form

B=[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]
 [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]]

C= [[0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]]

I tried with


for i in range(len(A)):  
    for j in range(i + 1, len(A)): 
        if np.array_equal(A[i], A[j]):
           cluster = np.vstack((A[i], A[j]))
           print(cluster)

but of course I only get separate couples of equal rows and not a single block.

Solution

  • The output of the following program will be a dict in which the keys being the name of the sub-matrices viz., B, C.. etc. And the values will be sub matrices with similar rows

    A= [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
 [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]]

# initiate variables i and dct, L being length of the matrix A
i, L, dct = 0, len(A), {}

# a list 'ref' to find out whether a row is already listed into sub-matrix
ref = []

while i < L:
    sub = []

    #Execute only if a row is not present in ref
    if A[i] not in ref:
    
        #Another list to iterate over which doesn't contain A[i]
        B = A[:i] + A[i+1:]
        
        for j, y in enumerate(B):
            if A[i] == y: sub.append(y)
            
            # if j is the last index in B, append A[i] to both sub and ref
            if j == len(B)-1:
                sub.append(A[i])
                ref.append(A[i])
        
        # Key of the dct being capital alphabets from 'B' and value being submatrix
        dct[chr(65 + len(ref))] = sub
    i += 1
print(dct) 

#Output: {'B': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], 'C': [[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]]}