Fill in the entry matrix from arrays of column / row indexes

Question

I am looking for an effective way to create an entry matrix from two arrays containing indexes, one represents the row indices in this matrix, the other represents the columns.

eg. I have:

#matrix will be size 4x3 in this example
#array of rows idxs, with values from 0 to 3
[0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3]
#array of columns idxs, with values from 0 to 2
[0, 1, 1, 1, 2, 2, 0, 1, 2, 0, 2, 2, 2, 2]

And you need to create an entry matrix, for example:

[[1  0  0]
 [0  2  0]
 [0  1  2]
 [2  1  5]]

I can create an array from one hot vector in simple form, but I can not get it to work when there is more than one case:

n_rows    = 4
n_columns = 3
#data
rows    = np.array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3])
columns = np.array([0, 1, 1, 1, 2, 2, 0, 1, 2, 0, 2, 2, 2, 2])
#empty matrix
new_matrix = np.zeros([n_rows, n_columns])
#adding 1 for each [row, column] occurrence:
new_matrix[rows, columns] += 1
print(new_matrix)

What returns:

[[ 1.  0.  0.]
 [ 0.  1.  0.]
 [ 0.  1.  1.]
 [ 1.  1.  1.]]

It seems that indexing and adding such a value does not work when there is more than one occurrence / index, moreover, printing seems very good:

print(new_matrix[rows, :])

:

[[ 1.  0.  0.]
 [ 0.  1.  0.]
 [ 0.  1.  0.]
 [ 0.  1.  1.]
 [ 0.  1.  1.]
 [ 0.  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.  1.]]

So maybe I missed something? Or is it impossible to do, and I need to look for another way to do this?

Answer 1

np.add.at, :

>>> np.add.at(new_matrix, (rows, columns), 1)
>>> new_matrix
array([[ 1.,  0.,  0.],
       [ 0.,  2.,  0.],
       [ 0.,  1.,  2.],
       [ 2.,  1.,  5.]])

np.add.at in-place, 1 , (row, columns) tuple.

Answer 2

№ 1

, np.bincount -

def bincount_app(rows, columns, n_rows, n_columns):
    # Get linear index equivalent
    lidx = (columns.max()+1)*rows + columns

    # Use binned count on the linear indices
    return np.bincount(lidx, minlength=n_rows*n_columns).reshape(n_rows,n_columns)

-

In [242]: n_rows    = 4
     ...: n_columns = 3
     ...: 
     ...: rows    = np.array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3])
     ...: columns = np.array([0, 1, 1, 1, 2, 2, 0, 1, 2, 0, 2, 2, 2, 2])

In [243]: bincount_app(rows, columns, n_rows, n_columns)
Out[243]: 
array([[1, 0, 0],
       [0, 2, 0],
       [0, 1, 2],
       [2, 1, 5]])

# 2

slicing, , :

def mask_diff_app(rows, columns, n_rows, n_columns):
    lidx = (columns.max()+1)*rows + columns
    lidx.sort()
    mask = np.concatenate(([True],lidx[1:] != lidx[:-1],[True]))
    count = np.diff(np.flatnonzero(mask))
    new_matrix = np.zeros([n_rows, n_columns],dtype=int)
    new_matrix.flat[lidx[mask[:-1]]] = count
    return new_matrix

№ 3

csr_matrix, , , , , , .

:

from scipy.sparse import csr_matrix

def sparse_matrix_app(rows, columns, n_rows, n_columns):
    out_shp = (n_rows, n_columns)
    data = np.ones(len(rows),dtype=int)
    return csr_matrix((data, (rows, columns)), shape=out_shp)

/ , -

sparse_matrix_app(rows, columns, n_rows, n_columns).toarray()

-

In [319]: sparse_matrix_app(rows, columns, n_rows, n_columns).toarray()
Out[319]: 
array([[1, 0, 0],
       [0, 2, 0],
       [0, 1, 2],
       [2, 1, 5]])

---

-

# @cᴏʟᴅsᴘᴇᴇᴅ soln
def add_at_app(rows, columns, n_rows, n_columns):
    new_matrix = np.zeros([n_rows, n_columns],dtype=int)
    np.add.at(new_matrix, (rows, columns), 1)

№1: (1000, 1000) no. = 10k

In [307]: # Setup
     ...: n_rows = 1000
     ...: n_columns = 1000
     ...: rows = np.random.randint(0,1000,(10000))
     ...: columns = np.random.randint(0,1000,(10000))

In [308]: %timeit add_at_app(rows, columns, n_rows, n_columns)
     ...: %timeit bincount_app(rows, columns, n_rows, n_columns)
     ...: %timeit mask_diff_app(rows, columns, n_rows, n_columns)
     ...: %timeit sparse_matrix_app(rows, columns, n_rows, n_columns)
1000 loops, best of 3: 1.05 ms per loop
1000 loops, best of 3: 424 µs per loop
1000 loops, best of 3: 1.05 ms per loop
1000 loops, best of 3: 1.41 ms per loop

№2: (1000, 1000) no. = 100k

In [309]: # Setup
     ...: n_rows = 1000
     ...: n_columns = 1000
     ...: rows = np.random.randint(0,1000,(100000))
     ...: columns = np.random.randint(0,1000,(100000))

In [310]: %timeit add_at_app(rows, columns, n_rows, n_columns)
     ...: %timeit bincount_app(rows, columns, n_rows, n_columns)
     ...: %timeit mask_diff_app(rows, columns, n_rows, n_columns)
     ...: %timeit sparse_matrix_app(rows, columns, n_rows, n_columns)
100 loops, best of 3: 11.4 ms per loop
1000 loops, best of 3: 1.27 ms per loop
100 loops, best of 3: 7.44 ms per loop
10 loops, best of 3: 20.4 ms per loop

№ 3:

, , , . :

In [314]: # Setup
     ...: n_rows = 5000
     ...: n_columns = 5000
     ...: rows = np.random.randint(0,5000,(1000))
     ...: columns = np.random.randint(0,5000,(1000))

In [315]: %timeit add_at_app(rows, columns, n_rows, n_columns)
     ...: %timeit bincount_app(rows, columns, n_rows, n_columns)
     ...: %timeit mask_diff_app(rows, columns, n_rows, n_columns)
     ...: %timeit sparse_matrix_app(rows, columns, n_rows, n_columns)
100 loops, best of 3: 11.7 ms per loop
100 loops, best of 3: 11.1 ms per loop
100 loops, best of 3: 11.1 ms per loop
1000 loops, best of 3: 269 µs per loop

, , , , -

In [317]: %timeit sparse_matrix_app(rows, columns, n_rows, n_columns).toarray()
100 loops, best of 3: 11.7 ms per loop