## If you have problems with this tutorial, try to download the Notebook.¶

In [ ]:
!wget https://jupyter-jsc.fz-juelich.de/static/files/Dask_JURON.ipynb


This notebook will give you a short introduction into the Dask Extension on JURON. It allows you to run Jobs on the compute nodes, even if your JupyterLab is running interactively on the login node.

# Monte-Carlo Estimate of $\pi$¶

We want to estimate the number $\pi$ using a Monte-Carlo method exploiting that the area of a quarter circle of unit radius is $\pi/4$ and that hence the probability of any randomly chosen point in a unit square to lie in a unit circle centerd at a corner of the unit square is $\pi/4$ as well. So for N randomly chosen pairs $(x, y)$ with $x\in[0, 1)$ and $y\in[0, 1)$, we count the number $N_{circ}$ of pairs that also satisfy $(x^2 + y^2) < 1$ and estimage $\pi \approx 4 \cdot N_{circ} / N$.

## Core Lessons¶

• setting up SLURM (and other jobqueue) clusters
• Scaling clusters

## Set up a Slurm cluster¶

We'll create a SLURM cluster and have a look at the job-script used to start workers on the HPC scheduler.

In [ ]:
import dask
import os

cluster = LSFCluster(
queue="normal",
walltime="60",
ncpus=2,
host="192.168.45.25",
death_timeout="15s",
mem=4 * 1024 * 1024 * 1024,
cores=4,
locals_directory="/tmp",
n_workers=4,
memory="128GB",
usestd_in=True
)

In [ ]:
print(cluster.job_script())

In [ ]:
client = Client(cluster)
client


## You can visit the Dask Dashboard at the following url:¶

https://jupyter-jsc.fz-juelich.de/user/<user_name>/<lab_name>/proxy/<port>/status

Afterwards you can press on the orange buttons to open a new tab in your JupyterLab Environment.

## Scale the cluster to two nodes¶

A look at the Dashboard reveals that there are no workers in the clusetr. Let's start 4 workers (in 2 SLURM jobs).

For the distiction between workers and jobs, see the Dask jobqueue docs.

In [ ]:
cluster.scale(4)  # scale to 4 _workers_


## The Monte Carlo Method¶

In [ ]:
import dask.array as da
import numpy as np

def calc_pi_mc(size_in_bytes, chunksize_in_bytes=200e6):
"""Calculate PI using a Monte Carlo estimate."""

size = int(size_in_bytes / 8)
chunksize = int(chunksize_in_bytes / 8)

xy = da.random.uniform(0, 1, size=(size / 2, 2), chunks=(chunksize / 2, 2))

in_circle = (xy ** 2).sum(axis=-1) < 1
pi = 4 * in_circle.mean()

return pi

def print_pi_stats(size, pi, time_delta, num_workers):
"""Print pi, calculate offset from true value, and print some stats."""
print(
f"{size / 1e9} GB\n"
f"\tMC pi: {pi : 13.11f}"
f"\tErr: {abs(pi - np.pi) : 10.3e}\n"
f"\tWorkers: {num_workers}"
f"\t\tTime: {time_delta : 7.3f}s"
)


## The actual calculations¶

We loop over different volumes of double-precision random numbers and estimate $\pi$ as described above.

In [ ]:
from time import time, sleep

In [ ]:
for size in (1e9 * n for n in (1, 10, 100)):

start = time()
pi = calc_pi_mc(size).compute()
elaps = time() - start

print_pi_stats(
size, pi, time_delta=elaps, num_workers=len(cluster.scheduler.workers)
)


## Scaling the Cluster to twice its size¶

We increase the number of workers by 2 and the re-run the experiments.

In [ ]:
new_num_workers = 2 * len(cluster.scheduler.workers)

print(f"Scaling from {len(cluster.scheduler.workers)} to {new_num_workers} workers.")

cluster.scale(new_num_workers)

sleep(10)

In [ ]:
client


## Re-run same experiments with doubled cluster¶

In [ ]:
for size in (1e9 * n for n in (1, 10, 100)):

start = time()
pi = calc_pi_mc(size).compute()
elaps = time() - start

print_pi_stats(
size, pi, time_delta=elaps, num_workers=len(cluster.scheduler.workers)
)


## Automatically Scaling the Cluster¶

We want each calculation to take only a few seconds. Dask will try to add more workers to the cluster when workloads are high and remove workers when idling.

Watch how the cluster will scale down to the minimum a few seconds after being made adaptive.

In [ ]:
ca = cluster.adapt(minimum=4, maximum=100)

sleep(4)  # Allow for scale-down

In [ ]:
client


## Repeat the calculation from above with larger work loads¶

(And watch the dash board!)

In [ ]:
for size in (n * 1e9 for n in (1, 10, 100)):

start = time()
pi = calc_pi_mc(size, min(size / 1000, 500e6)).compute()
elaps = time() - start

print_pi_stats(
size, pi, time_delta=elaps, num_workers=len(cluster.scheduler.workers)
)

sleep(20)  # allow for scale-down time