# randomPD.py
# https://code.activestate.com/recipes/577264-random-numbers-with-arbitrary-probability-distribu/

# Generating N random numbers that probability distribution
# fits to any given function curve
# FB - 201006137

import math
import random


# define any function here!
def f(x):
  return math.sin(x)


# f(x) = 1.0 : for uniform probability distribution


# f(x) = x : for triangular probability distribution
# (math.sqrt(random.random()) would also produce triangular p.d. though.)

# f(x) = math.exp(-x*x/2.0)/math.sqrt(2.0*math.pi) : for std normal p.d.
# (taking average of (last) 2,3,... random.random() values would also
# produce normal probability distributions though.)



# define any xmin-xmax interval here! (xmin < xmax)
xmin = 0.0
xmax = math.pi

# find ymin-ymax
numSteps = 1000000 # bigger the better but slower!
ymin = f(xmin)
ymax = ymin
for i in range(numSteps):
  x = xmin + (xmax - xmin) * float(i) / numSteps
  y = f(x)
  if y < ymin: 
    ymin = y
  if y > ymax: 
    ymax = y

n = 10 # how many random numbers to generate
for i in range(n):
  while True:
    # generate a random number between 0 to 1
    xr = random.random()
    yr = random.random()
    x = xmin + (xmax - xmin) * xr
    y = ymin + (ymax - ymin) * yr
    if y <= f(x):
      print(xr)
      break