# SCILAB (advanced functions)

Scilab is a free software for scientific computing, originally developed in France by INRIA (Institut National de Recherche en Informatique Appliquée) and now maintained by Scilab Entreprise. Scilab allows to work at the highest level (the basic objects are the matrices) and comes with very rich digital processing libraries (linear algebra, signal processing, control, etc.).

This workshop will provide participants with a set of advanced knowledge around the tool SCILAB enabling them to deal with problems related to analysis of digital data, systems modeling and algorithms prototyping.

## Training duration

Three days## Date and place of training

Location: Toulouse (France), dates: contact us

.## Content

#### I - Introduction to Scilab

- Introduction: Applications, description of the background (relative to other applications of calculation)
- Environment: Scilab console, online help, editor,
- Language basics: real and complex numbers, matrices, and vectors, constants, booleans, polynomials and rational functions, standard mathematical functions
- Programming: scripts and functions, control structures, development, input / output files
- Data visualization: 2D and 3D representations, axes and legends
- Tutorial: handling of the environment and language processing through some exercises

#### II - Linear algebra

- Linear Systems: reversible systems, overdetermined, underdetermined, conditionning,
- Resolution in the least squares sense, pseudo inverse
- Eigenvalues and eigenvectors. Matrix decompositions and applications (LU, QR, SVD,...)
- Large size problems

#### III - Statistics

- Probability Distributions / distribution functions
- Congruent generators (limits), common laws, permutations
- Simple statistics: mean, variance, median , quantiles...
- Parameter estimation: maximum likelihood estimation / least squares. Special case: linear regression

#### IV - Signal processing

- Digital Signals: Sampling, Fourier transform
- Representation of linear systems: difference equation, transfer function, state / space representation. Analysis (time, frequency, poles / zeros)
- digital filter design: FIR (windowed, Remez), IIR (from analog prototypes, factoring in second order sections), quantification
- Interpolation: linear interpolations, splines, 2D interpolations
- Spectral Estimation: nonparametric methods (periodogram) / parametric (ARMA)
- Other functions: Hilbert filter, Kalman filter
- Tutorial: around the analysis of a given signal, the design of an FIR filter, its analysis and its simulation.

#### V - Differential calculus / Simulation

- Differential Equations: ODE (first order and higher order), implicit form, particular cases of SLC and SLD, hybrid problems, DAE. Problems with the limit values. Numerical integration
- Optimization problems with fixed constraints: non differentiable functions, differentiable. Special cases: linear and nonlinear least squares
- Problems with linear constraints. Linear and Quadratic Programming
- Solving Nonlinear Equations

#### VI - Other functions (overview)

- Quick Introduction to Xcos graphical tool for the simulation of systems
- A quick tour of a few toolboxes (wavelets, image processing)