Binary-search without an explicit array - numpy

Question

I want to perform a binary-search using e.g. np.searchsorted, however, I do not want to create an explicit array containing values. Instead, I want to define a function giving the value to be expected at the desired position of the array, e.g. p(i) = i, where i denotes the position within the array.
Generating an array of values regarding the function would, in my case, be neither efficient nor elegant. Is there any way to achieve this?

Answer 1

What about something like:
import collections
class GeneratorSequence(collections.Sequence):
def __init__(self, func, size):
self._func = func
self._len = size
def __len__(self):
return self._len
def __getitem__(self, i):
if 0 <= i < self._len:
return self._func(i)
else:
raise IndexError
def __iter__(self):
for i in range(self._len):
yield self[i]
This would work with np.searchsorted(), e.g.:
import numpy as np
gen_seq = GeneratorSequence(lambda x: x ** 2, 100)
np.searchsorted(gen_seq, 9)
# 3
You could also write your own binary search function, you do not really need NumPy in this case, and it can actually be beneficial:
def bin_search(seq, item):
first = 0
last = len(seq) - 1
found = False
while first <= last and not found:
midpoint = (first + last) // 2
if seq[midpoint] == item:
first = midpoint
found = True
else:
if item < seq[midpoint]:
last = midpoint - 1
else:
first = midpoint + 1
return first
Which gives identical results:
all(bin_search(gen_seq, i) == np.searchsorted(gen_seq, i) for i in range(100))
# True
Incidentally, this is also WAY faster:
gen_seq = GeneratorSequence(lambda x: x ** 2, 1000000)
%timeit np.searchsorted(gen_seq, 10000)
# 1 loop, best of 3: 1.23 s per loop
%timeit bin_search(gen_seq, 10000)
# 100000 loops, best of 3: 16.1 µs per loop

Answer 2

Inspired by #norok2 comment, I think you can use something like this:
def f(i):
return i*2 # Just an example
class MySeq(Sequence):
def __init__(self, f, maxi):
self.maxi = maxi
self.f = f
def __getitem__(self, x):
if x < 0 or x > self.maxi:
raise IndexError()
return self.f(x)
def __len__(self):
return self.maxi + 1
In this case f is your function while maxi is the maximum index. This of course only works if the function f return values in sorted order.
At this point you can use an object of type MySeq inside np.searchsorted.