# Quantitative Julia Problems

Justin Napolitano

2022-05-24 01:30:32.169 +0000 UTC

# Table of Contents

# Series

This is a post in the
**Quantitative Analysis in Julia** series.

Other posts in this series:

## Introduction

In my previous post, I demonstrated how to configure Rocky Linux and RHEL distributions for quantitative analysis.

In this post, I include a few sample programs to test your installation.

## How to run the programs

I saved them to a folder within the project directory.

### Activate the Project

```
using Pkg
Pkg.activate(".")
#cd("<sub-directory-containing-files>) optional
```

### Run a program

```
include("path/to/script-name.jl")
```

## Estimate the Value of Pi

Use the Monte Carlo method to estimate the value of pi.

### Solution

We estimate the area by sampling bivariate uniforms and looking at the fraction that fall into the unit circle.

```
# Number of iterations
n = 1000000
#counter variable
count = 0
for i in 1:n # for i in the range of 1 to n
global count # make count global to reference within the loop. Otherwise the the variable will be understood to be a local within the for loop
#rand(2) Returns a two element vector.
#Can be read as let u be equal to the first index of the vector and let v be equal to the second
u, v = rand(2)
d = sqrt((u - 0.5)^2 + (v - 0.5)^2) # distance from middle of square
if d < 0.5
count += 1
end
end
area_estimate = count / n
print(area_estimate * 4) # dividing by radius**2
```

## Use QuadGk to Aproximate an integral

The trapezoidal rule can be used to aproximate an integral.

```
using QuadGK
f(x) = x^8 # The Function
value, accuracy = quadgk(f, 0.0, 1.0) # pass the function, the lower bound and the upper bound
```

# Series

This is a post in the
**Quantitative Analysis in Julia** series.

Other posts in this series: