# SP4E - Homework 1

## General info

This file provides a brief documentation and information related to the first Homework of the course Scientific Programming for Engineers, fall 2019.
This homework is done by **O. Ashtari** and **A. Sieber**
Last update: 16.10.2019

## Project Description
This project is intended to solve a minimization problem on n-dimensional quadratic functions defined as S(X)= X<sup>T</sup>AX - X<sup>T</sup>b, where X<sup>T</sup>=[x, y], T represents the transpose,  A is an n by n square matrix and b a column vector.
	
## Setup
The project is created with Python 3.7. It moreover requires the following libraries to be installed:
* numpy
* scipy
* matplotlib
* sys
	
## Use

### optimizer.py

This script solves minimization problems using the scipy.optimize.minimize routine. The minimization solver can be specified as an input argumeent by entering the following command line:

```
$ python3 optimizer.py method
```
Where the variable  method is one of the following:

* Nelder-Mead
* Powell
* CG (default)
* BFGS
* L-BFGS-B
* TNC
* SLSQP

The initial guess of the minimization process has to be specified directly in the optimizer.py file by changing the value of the variable X0. The matrix A and vector B can also be modified directly in the file.

### conjugate_gradient.py

### post_processing.py

Post-processing file that takes as inputs the value of A, B as well as the intermediate solutions of the iterative minimization process and the method used. The file generates a 3D plot displaying the function to be minimized as well as the intermediate solutions.