#!/usr/bin/env python3
from Crypto.PublicKey import RSA
from multiprocessing import Pool, cpu_count
import numpy as np
import cvxpy as cvx
import pymp

def is_in_convex_hull(arg):
	"""Check whether v lies in the convex hull of point set A, using cvxpy."""
	A,v = arg
	lamb = cvx.Variable(A.shape[1])
	prob = cvx.Problem(cvx.Minimize(0), [A*lamb == v, lamb >= 0])
	prob.solve(solver = cvx.MOSEK)
	return prob.status == 'optimal'

def convex_hull_LP_serial(A):
	"""Compute the convex hull of a point set A with LPs.
	
	In contrast to convex_hull_LP() this function works in a single thread.

	Call:
		indices = convex_hull_LP_serial(A)
	Input:
		A: an (`m` x `n`)-matrix of non-negative integers
	Output:
		indices: list of indices, telling which columns of A form the convex hull
	"""
	return [i for i in range(A.shape[1]) if not is_in_convex_hull((np.delete(A,i,axis=1),A[:,i]))]

def convex_hull_LP(A):
	"""Compute the convex hull of a point set A with LPs.
	
	This function calls a new thread for each point, which creates a large overhead.

	Call:
		indices = convex_hull_LP(A)
	Input:
		A: an (`m` x `n`)-matrix of non-negative integers
	Output:
		indices: list of indices, telling which columns of A form the convex hull
	"""
	pool = Pool(processes = cpu_count())
	res = pool.map(is_in_convex_hull, [(np.delete(A,i,axis=1),A[:,i]) for i in range(A.shape[1])])
	pool.close()
	pool.join()
	return [i for i in range(A.shape[1]) if not res[i]]

if __name__ == '__main__':
	k = RSA.generate(2048)

	print(k.decrypt(17))
	print(pow(17,k.d,k.n))

	def fn(m): 
		return pow(m, k.d, k.n)

	pool = Pool(8)
	l = pool.map(fn, range(100))

	result = pymp.shared.list()
	with pymp.Parallel() as env:
		for m in env.range(100):
			result.append(pow(m, k.d, k.n))

	S = np.random.randint(20, size = (8,100))