i need to make fast numpy array that generates random integers in each row with a different range.
Code that works by my but is slow when i increase vectors number to 300000:
import numpy as np
import random
population_size = 4
vectors_number = population_size * 3
add_matrix = []
for i in range(0, int(vectors_number/population_size)):
candidates = list(range(population_size*i, population_size*(i+1)))
random_index = random.sample(candidates, 4)
add_matrix.append(random_index)
winning_matrix = np.row_stack(add_matrix)
print(winning_matrix)
Each row is choose 4 random numbers from variable range.
Output:
[[ 3 0 1 2]
[ 4 6 7 5]
[11 9 8 10]]
Best would by create that matrix using only numpy without loops
Here's a vectorized approach following this trick to extract unique random samples -
ncols = 4
N = int(vectors_number/population_size)
offset = np.arange(N)[:,None]*population_size
winning_matrix = np.random.rand(N,population_size).argsort(1)[:,:ncols] + offset
We can also leverage np.argpartition to replace the last step -
r = np.random.rand(N,population_size)
out = r.argpartition(ncols,axis=1)[:,:ncols] + offset
Timings -
In [63]: import numpy as np
...: import random
...:
...: population_size = 64
...: vectors_number = population_size * 300000
In [64]: %%timeit
...: add_matrix = []
...: for i in range(0, int(vectors_number/population_size)):
...: candidates = list(range(population_size*i, population_size*(i+1)))
...: random_index = random.sample(candidates, 4)
...: add_matrix.append(random_index)
...:
...: winning_matrix = np.row_stack(add_matrix)
1 loop, best of 3: 1.82 s per loop
In [65]: %%timeit
...: ncols = 4
...: N = int(vectors_number/population_size)
...: offset = np.arange(N)[:,None]*population_size
...: out = np.random.rand(N,population_size).argsort(1)[:,:ncols] + offset
1 loop, best of 3: 718 ms per loop
In [66]: %%timeit
...: ncols = 4
...: N = int(vectors_number/population_size)
...: offset = np.arange(N)[:,None]*population_size
...: r = np.random.rand(N,population_size)
...: out = r.argpartition(ncols,axis=1)[:,:ncols] + offset
1 loop, best of 3: 428 ms per loop
In your case the loops can be compressed using map and list comprehensions.
winning_matrix = np.vstack ([random.sample (candidate, d2) for candidate in map (lambda i: list(range(population_size*i, population_size*(i+1))), range(0, int(vectors_number/population_size)))])
Output:
array([[ 0, 1, 3, 2],
[ 5, 6, 4, 7],
[11, 10, 9, 8]])
This can be broken down as
# This is your loop generating the arrays from where you are sampling
range_list = map (lambda i: list(range(population_size*i, population_size*(i+1))), range(0, int(vectors_number/population_size)))
# This does the generation of the matrix, using exactly following your method
winning_matrix = np.vstack ([random.sample (candidate, d2) for candidate in range_list])
In case of generation of random integers with different ranges (and not from a sample), you can follow the below method.
How about something like this
# Generating upper and lower bounds for each row.
pair_ranges = product (list (range (1, 5)), list (range (5, 9)))
d2 = 4
np.vstack ([np.random.random_integers (x, y, [1, d2]) for x, y in pair_ranges])
Output:
array([[2, 5, 2, 5],
[5, 6, 2, 4],
[1, 3, 2, 3],
[4, 2, 4, 4],
[2, 6, 4, 6],
[7, 2, 6, 3],
[4, 5, 3, 5],
[4, 6, 3, 6],
[3, 6, 3, 6]])
The rows will have random integers between range
array([[1, 5],
[1, 6],
[1, 7],
[2, 5],
[2, 6],
[2, 7],
[3, 5],
[3, 6],
[3, 7]])
Since we are only choosing 4 out of 64 collisions will be rare, we can therefore draw with replacement and correct afterwards.
import numpy as np
def multiperm(y, x, factor=16, remap=False):
draw = np.random.randint(0, factor*x, (y, x))
idx = np.full((y, factor*x), -1, dtype=np.int8 if factor*x < 128 else int)
yi, xi = np.ogrid[:y, :x]
idx[yi, draw] = xi
yd, xd = np.where(idx[yi, draw] != xi)
while yd.size > 0:
ndraw = np.random.randint(0, factor*x, yd.shape)
draw[yd, xd] = ndraw
good = idx[yd, ndraw] == -1
idx[yd[good], ndraw[good]] = xd[good]
good[good] = idx[yd[good], ndraw[good]] == xd[good]
yd, xd = yd[~good], xd[~good]
if remap:
idx = np.zeros((y, factor*x), dtype=np.int8)
idx[yi, draw] = 1
idx[0, 0] -= 1
return idx.ravel().cumsum().reshape(idx.shape)[yi, draw]
else:
return draw + factor*x*yi
from timeit import timeit
print(timeit("multiperm(300_000, 4)", globals=globals(), number=100)*10, 'ms')
# sanity checks
check = multiperm(300_000, 4)
print(np.all(np.arange(300_000) * 64 <= check.T) and np.all(np.arange(1, 300_001) * 64 > check.T))
print(len(set(check.ravel().tolist())) == check.size)
Sample run:
44.83660604993929 ms
True
True
Revisiting the question with better understanding, realizing only the first random 4 of a 64 population are needed for the result, I came to this answer. There is still a loop but it is a loop over small number of required columns, it basically swaps the only the first 4 (FINALIST) columns with a a random other column:
import numpy as np
PLAYERS = 64 # per game
GAMES = 300000
FINALISTS = 4 # we only want to know the first four
# every player in every game has a unique id
matrix = np.arange(PLAYERS * GAMES).reshape((GAMES, PLAYERS))
games = np.arange(GAMES)
swaps = np.random.randint(0, PLAYERS, size=(FINALISTS, GAMES))
for i in range(FINALISTS):
# some trickey stuff to create tuples for indexing
dst = tuple(np.vstack([ games, i * np.ones(GAMES, dtype=np.int) ]))
src = tuple(np.vstack([ games, swaps[i] ]))
# do the a swap for location i
matrix[dst], matrix[src] = matrix[src], matrix[dst]
winning_matrix = matrix[:,:FINALISTS]
print(winning_matrix)
