Monte Carlo Pi estimation

monte_carlo_pi.py

import argparse
import time
import random
import math

parser = argparse.ArgumentParser(description="Approximate digits of Pi using Monte Carlo simulation.")
parser.add_argument("--num-samples", type=int, default=1000000)
parser.add_argument("--parallel", default=False, action="store_true")
parser.add_argument("--distributed", default=False, action="store_true")

SAMPLE_BATCH_SIZE = 100000

def sample(num_samples):
    num_inside = 0
    for _ in range(num_samples):
        x = random.uniform(-1, 1)
        y = random.uniform(-1, 1)
        if math.hypot(x, y) <= 1:
            num_inside += 1

    return num_inside

def approximate_pi(num_samples):
    start = time.time()
    num_inside = sample(num_samples)
    print("pi ~= {}".format((4*num_inside)/num_samples))
    print("Finished in: {:.2f}s".format(time.time()-start))

def approximate_pi_parallel(num_samples):
    from multiprocessing import Pool
    pool = Pool()

    start = time.time()
    num_inside = 0
    for result in pool.map(sample, [SAMPLE_BATCH_SIZE for _ in range(num_samples//SAMPLE_BATCH_SIZE)]):
        num_inside += result

    print("pi ~= {}".format((4*num_inside)/num_samples))
    print("Finished in: {:.2f}s".format(time.time()-start))

def approximate_pi_distributed(num_samples):
    from ray.util.multiprocessing import Pool
    pool = Pool()

    start = time.time()
    num_inside = 0
    for result in pool.map(sample, [SAMPLE_BATCH_SIZE for _ in range(num_samples//SAMPLE_BATCH_SIZE)]):
        num_inside += result

    print("pi ~= {}".format((4*num_inside)/num_samples))
    print("Finished in: {:.2f}s".format(time.time()-start))

if __name__ == "__main__":
    args = parser.parse_args()
    if args.parallel:
        print("Estimating Pi using multiprocessing with {} samples...".format(args.num_samples))
        approximate_pi_parallel(args.num_samples)
    elif args.distributed:
        print("Estimating Pi using ray.util.multiprocessing with {} samples...".format(args.num_samples))
        approximate_pi_distributed(args.num_samples)
    else:
        print("Estimating Pi in one process with {} samples...".format(args.num_samples))
        approximate_pi(args.num_samples)

ray-cluster.yaml

cluster_name: monte_carlo_pi

# The number of worker nodes to launch in addition to the head node.
min_workers: 9
max_workers: 9

provider:
 type: aws
 region: us-west-2
 availability_zone: us-west-2a
 
head_node:
 InstanceType: m4.4xlarge
 ImageId: ami-06d51e91cea0dac8d # Ubuntu 18.04
 
worker_nodes:
 InstanceType: m4.4xlarge
 ImageId: ami-06d51e91cea0dac8d # Ubuntu 18.04

# List of shell commands to run to set up nodes.
setup_commands:
    - wget https://repo.continuum.io/archive/Anaconda3-5.0.1-Linux-x86_64.sh || true
    - bash Anaconda3-5.0.1-Linux-x86_64.sh -b -p $HOME/anaconda3 || true
    - echo 'export PATH="$HOME/anaconda3/bin:$PATH"' >> ~/.bashrc
    - pip install -U https://s3-us-west-2.amazonaws.com/ray-wheels/latest/ray-0.9.0.dev0-cp36-cp36m-manylinux1_x86_64.whl
    - pip install -U ray[dashboard]

NOTE: As of 02/18/2020, this code sample requires installing the nightly Ray wheels.

Example usage:

# Start the cluster and copy the script to it.
> ray up -y ray-cluster.yaml
> ray rsync-up ray-cluster.yaml monte_carlo_pi.py monte_carlo_pi.py

# Attach to a remote shell in the head node and run the script.
> ray attach ray-cluster.yaml
[remote] > RAY_ADDRESS=auto python monte_carlo_pi.py --distributed --num-samples 1_000_000_000
pi ~= 3.141541
Finished in 13.75
[remote] > RAY_ADDRESS=auto python monte_carlo_pi.py --distributed --num-samples 10_000_000_000
pi ~= 3.141599
Finished in 137.19s

# Clean up the cluster.
> ray down -y ray-cluster.yaml