Fastest way to convert a list of indices to 2D numpy array of ones

Question

I have a list of indices

a = [
  [1,2,4],
  [0,2,3],
  [1,3,4],
  [0,2]]

What's the fastest way to convert this to a numpy array of ones, where each index shows the position where 1 would occur?

Ie what I want is:

output = array([
  [0,1,1,0,1],
  [1,0,1,1,0],
  [0,1,0,1,1],
  [1,0,1,0,0]])

I know the max size of the array beforehand. I know I could loop through each list and insert a 1 into at each index position, but is there a faster/vectorized way to do this?

My use case could have thousands of rows/cols and I need to do this thousands of times, so the faster the better.

Answer 1

How about this:

ncol = 5
nrow = len(a)
out = np.zeros((nrow, ncol), int)
out[np.arange(nrow).repeat([*map(len,a)]), np.concatenate(a)] = 1
out
# array([[0, 1, 1, 0, 1],
#        [1, 0, 1, 1, 0],
#        [0, 1, 0, 1, 1],
#        [1, 0, 1, 0, 0]])

Here are timings for a 1000x1000 binary array, note that I use an optimized version of the above, see function pp below:

pp 21.717635259992676 ms
ts 37.10938713003998 ms
u9 37.32933565042913 ms

Code to produce timings:

import itertools as it
import numpy as np

def make_data(n,m):
    I,J = np.where(np.random.random((n,m))<np.random.random((n,1)))
    return [*map(np.ndarray.tolist, np.split(J, I.searchsorted(np.arange(1,n))))]

def pp():
    sz = np.fromiter(map(len,a),int,nrow)
    out = np.zeros((nrow,ncol),int)
    out[np.arange(nrow).repeat(sz),np.fromiter(it.chain.from_iterable(a),int,sz.sum())] = 1
    return out

def ts():
    out = np.zeros((nrow,ncol),int)
    for i, ix in enumerate(a):
        out[i][ix] = 1
    return out

def u9():
    out = np.zeros((nrow,ncol),int)
    for i, (x, y) in enumerate(zip(a, out)):
        y[x] = 1
        out[i] = y
    return out

nrow,ncol = 1000,1000
a = make_data(nrow,ncol)

from timeit import timeit
assert (pp()==ts()).all()
assert (pp()==u9()).all()

print("pp", timeit(pp,number=100)*10, "ms")
print("ts", timeit(ts,number=100)*10, "ms")
print("u9", timeit(u9,number=100)*10, "ms")

Answer 2

This might not be the fastest way. You will need to compare execution times of these answers using large arrays in order to find out the fastest way. Here's my solution

output = np.zeros((4,5))
for i, ix in enumerate(a):
    output[i][ix] = 1

# output -> 
#   array([[0, 1, 1, 0, 1],
#   [1, 0, 1, 1, 0],
#   [0, 1, 0, 1, 1],
#   [1, 0, 1, 0, 0]])

Answer 3

May not be the best way but the only way I can think of:

output = np.zeros((4,5))
for i, (x, y) in enumerate(zip(a, output)):
    y[x] = 1
    output[i] = y
print(output)

Which outputs:

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

Answer 4

In case you can and want to use Cython you can create a readable (at least if you don't mind the typing) and fast solution.

Here I'm using the IPython bindings of Cython to compile it in a Jupyter notebook:

%load_ext cython

%%cython

cimport cython
cimport numpy as cnp
import numpy as np

@cython.boundscheck(False)  # remove this if you cannot guarantee that nrow/ncol are correct
@cython.wraparound(False)
cpdef cnp.int_t[:, :] mseifert(list a, int nrow, int ncol):
    cdef cnp.int_t[:, :] out = np.zeros([nrow, ncol], dtype=int)
    cdef list subl
    cdef int row_idx
    cdef int col_idx
    for row_idx, subl in enumerate(a):
        for col_idx in subl:
            out[row_idx, col_idx] = 1
    return out

To compare the performance of the solutions presented here I use my library simple_benchmark :

Note that this uses logarithmic axis to simultaneously show the differences for small and large arrays. According to my benchmark my function is actually the fastest of the solutions, however it's also worth pointing out that all of the solutions aren't too far off.

Here is the complete code I used for the benchmark:

import numpy as np
from simple_benchmark import BenchmarkBuilder, MultiArgument
import itertools

b = BenchmarkBuilder()

@b.add_function()
def pp(a, nrow, ncol):
    sz = np.fromiter(map(len, a), int, nrow)
    out = np.zeros((nrow, ncol), int)
    out[np.arange(nrow).repeat(sz), np.fromiter(itertools.chain.from_iterable(a), int, sz.sum())] = 1
    return out

@b.add_function()
def ts(a, nrow, ncol):
    out = np.zeros((nrow, ncol), int)
    for i, ix in enumerate(a):
        out[i][ix] = 1
    return out

@b.add_function()
def u9(a, nrow, ncol):
    out = np.zeros((nrow, ncol), int)
    for i, (x, y) in enumerate(zip(a, out)):
        y[x] = 1
        out[i] = y
    return out

b.add_functions([mseifert])

@b.add_arguments("number of rows/columns")
def argument_provider():
    for n in range(2, 13):
        ncols = 2**n
        a = [
            sorted(set(np.random.randint(0, ncols, size=np.random.randint(0, ncols)))) 
            for _ in range(ncols)
        ]
        yield ncols, MultiArgument([a, ncols, ncols])

r = b.run()
r.plot()

Answer 5

Depending on your use case, you might look into using sparse matrices. The input matrix looks suspiciously like a Compressed Sparse Row (CSR) matrix. Perhaps something like

import numpy as np
from scipy.sparse import csr_matrix
from itertools import accumulate


def ragged2csr(inds):
    offset = len(inds[0])
    lens = [len(x) for x in inds]
    indptr = list(accumulate(lens))
    indptr = np.array([x - offset for x in indptr])
    indices = np.array([val for sublist in inds for val in sublist])
    n = indices.size
    data = np.ones(n)
    return csr_matrix((data, indices, indptr))

Again, if it fits in your use case, a sparse matrix would allow elementwise/masking operations to scale with the number of nonzeros, rather than the number of elements (rows*columns), which could bring significant speedup (for a sparse enough matrix).

Another good introduction to CSR matrices is section 3.4 of Iterative Methods . In this case, data is aa , indices is ja and indptr is ia . This format also has the benefit of being very popular among different packages/libraries.

Answer 6

How about using array indexing? If you knew more about your input, you could get rid of the penalty for having to convert to a linear array first.

import numpy as np


def main():
    row_count = 4
    col_count = 5
    a = [[1,2,4],[0,2,3],[1,3,4],[0,2]]

    # iterate through each row, concatenate all indices and convert them to linear

    # numpy append performs copy even if you don't want it, list append is faster
    b = []
    for row_idx, row in enumerate(a):
        b.append(np.array(row, dtype=np.int64) + (row_idx * col_count))

    linear_idxs = np.hstack(b)
    #could skip previous steps if given index inputs well before hand, or in linear index order. 
    c = np.zeros(row_count * col_count)
    c[linear_idxs] = 1
    c = c.reshape(row_count, col_count)
    print(c)


if __name__ == "__main__":
    main()

#output
# [[0. 1. 1. 0. 1.]
#  [1. 0. 1. 1. 0.]
#  [0. 1. 0. 1. 1.]
#  [1. 0. 1. 0. 0.]]