How to replace a small matrix in a larger matrix with different rows and columns

user_14922017 0
Viewed 128

Suppose we have a large A(n*n) and a small B(m*m) matrices (m<n). Also, there is a set J with the size of m which are values from {1,2,3,...,n}. I want to replace the matrix B in rows and columns of matrix A such that the first row (column) of matrix B is replaced in the first element of set J. For example,

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

and

J = [1, 3, 5]
B =[[2 3 4],
    [5 6 7],
    [8 9 10]]

Then, the result will be:

   [[2 1 3 1 4],
    [1 1 1 1 1],
A = [5 1 6 1 7],
    [1 1 1 1 1],
    [8 1 9 1 10]]
numpy arrays python
3 Answers

Try this:

tmp = A[J-1]
tmp[:, J-1] = B
A[J-1] = tmp

>>> A
array([[ 2,  1,  3,  1,  4],
       [ 1,  1,  1,  1,  1],
       [ 5,  1,  6,  1,  7],
       [ 1,  1,  1,  1,  1],
       [ 8,  1,  9,  1, 10]])

Why the roundtrip using a tmp variable, where the more intuitive way would be A[J-1][:, J-1] = B? That is because A[J-1][:, J-1] cannot be a view of A (there is no simple striding of A that will give you that sub-array), and thus it is instead a view of a copy of A[J-1] (which you can use as lvalue but will be lost). So, instead, we explicitly "put back into A" the value of tmp.

user_7581740

will the obvious way of doing things cut it?

A = [[1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1]]
J = [1, 3, 5]
B = [[2, 3, 4],
     [5, 6, 7],
     [8, 9, 10]]

print(A)
for rB,rA in enumerate(J):
    for cB,cA in enumerate(J):
        A[rA-1][cA-1] = B[rB][cB]   #list indices are 0-based
print(A)
exit(-1)


#ok, let`s do it functional way
J = list(map(lambda x:x-1, J))  # convert inex array 0-based indices
lira = lambda l,i,r,a: r if type(l) is not list else lira(l[:i[0]] + [lira(l[i[0]], a, r[0], a)] + l[i[0] + 1:], i[1:], r[1:], a) if i else l
A = lira(A,J,B,J)
print(A)
user_150733910

You can use built-in np.ix_ for this purpose:

A[np.ix_(J-1,J-1)] = B

output:

array([[ 2.,  1.,  3.,  1.,  4.],
       [ 1.,  1.,  1.,  1.,  1.],
       [ 5.,  1.,  6.,  1.,  7.],
       [ 1.,  1.,  1.,  1.,  1.],
       [ 8.,  1.,  9.,  1., 10.]])
user_49759810
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