How to reverse engineer original array from boolean indexed array?

Question

Ok so I wrote some code for vectorizing a symmetric matrix, it just takes the unique elements and turns them into a 1d vector, while also multiplying the off diagonal elements by root2:

def vectorize_mat(mat):
    assert mat.shape[0] == mat.shape[1], 'Matrix is not square'

    n = int(mat.shape[0])
    vec_len = 0.5*n*(n+1)
    weight_mat = (np.tri(n,k=-1)*np.sqrt(2))+np.identity(n)
    mask_mat = np.tri(n).astype(bool)
    vec_mat = (mat*weight_mat)[mask_mat]

    return vec_mat

and this works really well, now I'm trying to figure out how to reconstruct the original array from the vector. I've gotten the original matrix dimensions like so:

v = len(vec_mat)
n = isqrt(2*v)

where isqrt() is an integer square root from:Integer square root in python

but I'm struggling with what to do next. I can now reconstruct the weight and mask matrices. So obviously I could vectorize the weight matrix and divide the vector by it, or divide the reconstructed matrix by the weight matrix to undo that step, but it's the reshaping and stuff (from the boolean indexing) that I don't know how to do. Maybe there's some super simple answer out there,but I can't seem to see it.

score 1 · Accepted Answer · answered Nov 15 '18 at 12:20

To answer your headline question. Indexing - including boolean indexing - can be used for assignment.

Here is an example. Let us first extract the lower triangle using a mask.

>>> a = np.arange(25).reshape(5, 5)
>>> y, x = np.ogrid[:5, :5]
>>> lower = y>=x
>>> b = a[lower]

Now b contains the lower triangle. We can use the same mask to reconstruct the lower triangle and fill the upper triangle symmetrically:

>>> recon = np.empty_like(a)
>>> recon[lower] = b
>>> recon.T[lower] = b
>>> recon
array([[ 0,  5, 10, 15, 20],
       [ 5,  6, 11, 16, 21],
       [10, 11, 12, 17, 22],
       [15, 16, 17, 18, 23],
       [20, 21, 22, 23, 24]])

How to reverse engineer original array from boolean indexed array?

1 Answers1