This package contains the implementation of all the introduced algorithms in the course of unconstraint optimization for the 1st year AI engineering student at UM5-ENSIAS, with in addition, the possibility to plot the results of each optimization.
This package requires the following Python 3 libraries :
- numpy
- time
- math
- numdifftools
- scipy
- matplotlib
- mpl_toolkits
- copy
The module matrix.py contains some elementary operations on matrices :
- sum
- product
- transposed
- rows swap
- rows dilatation
- rows transvection
- zeros matrix generator
- identity matrix generator
- printing a matrix
The module gauss.py contains the implementation of the operations :
- Gauss-Jordan pivot
- Inverse of a matrix using Gauss
- Solving a linear system with Gauss pivot
The module deco.py containing the code of the decomposition algorithms :
- Lower-Upper decomposition
- Cholesky's decomposition and also, 2 functions to solve a linear system with the 2 above decompositions.
The module gradient.py contains the code of 3 optimization algorithms for multivariable functions :
- Gradient descent
- Conjugate gradient
- Newton gradient
As for the monovariable unimodal functions, the subfolder unidim contains two modules (elimination.py and interpolation.py) with 10 different methods of optimization :
- unconstrainted search with fixed steps
- unconstrainted search with accelerated steps
- brute force
- binary search
- interval halving method
- Fibonacci method
- Golden section method
- Newton-Rapson method
- Quasi-Newton method
- Secant method
This package is developped with 3 main programs : main.py, main2.py and test_compare.py. They are built-in to help using some of the methods on random functions and data implemented in the file functions.py.