# CMLDA

Repository for the course Computational Mathematics for Learning and Data Analysis.

## Installation
These steps are for MacOS, with [```brew```](brew.sh) and ```python3``` already installed.

### Installing Julia

```sh
brew install julia
```

### Installing JupyterLab and IJulia kernel

#### IJulia kernel

Inside the julia REPL:
```julia
using Pkg
Pkg.add("IJulia")
```

A simple notebook experience can be obtained by simply running ```noteboot()```, which will install in a separate [```conda```](https://docs.conda.io/en/latest/) environment the needed python packages.

#### JupyterLab

A separate environment with [```virtualenv```](https://pypi.org/project/virtualenv/) or [```virtualenvwrapper```](https://pypi.org/project/virtualenvwrapper/) is recommended.

```sh
pip install jupyterlab
```

## Running

To run simply start the notebook with ```jupyter lab``` , the julia kernel should be automatically detected.


# Project 19 (Non-ML)

## Project

In the folder `Project` there is our implementation for the project.

Project description:

> (P) is the linear least squares problem

> $$\min_{w} \lVert \hat{X}w-\hat{y} \rVert$$

> where

> $$\hat{X}= \begin{bmatrix} X^T \newline \lambda I_m \end{bmatrix},\ \ \hat{y} = \begin{bmatrix} y \newline 0 \end{bmatrix},$$

> with $X$ the (tall thin) matrix from the ML-cup dataset by prof. Micheli, $\lambda > 0$ and $y$ is a random vector.

> - (A1) is an algorithm of the class of **limited-memory quasi-Newton methods**.
> - (A2) is **thin QR factorization with Householder reflectors**, in the variant where one does not form the matrix $Q$, but stores the Householder vectors $u_k$ and uses them to perform (implicitly) products with $Q$ and $Q^T$.

## Report

In the folder `Report` there is the latex project for the report of the project.

Run to compile:
```
pdflatex  -file-line-error -shell-escape  --synctex=1 -interaction=nonstopmode main.tex
biber main
pdflatex  -file-line-error -shell-escape  --synctex=1 -interaction=nonstopmode main.tex
```