Scilab for Engineers and Scientists
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That course will introduce you to Scilab.
Scilab is a powerful scientific computation Software for Engineers and Scientists.
It is free, open source and very similar to Matlab.
The course is a great video based tutorial for any person that is interested in scientific computation : engineers, scientists or anybody curious about applied mathematics.
The structure of the course is the following :
- Section 1 is an overview of Scilab and how to get it.
A Newton method to solve a non-linear equation is given as an example.
- Section 2 covers basic linear algebra using Scilab.
- Section 3 presents Scilab language structures.
As an example, the Newton method is extended to the two dimensional case.
- Section 4 covers the graphic capabilities of Scilab
An example displays natural images, that are given as additional material.
- Section 5 covers advanced topics.
An example shows how to code the wavelet representation of a signal into a single Scilab structured variable. It is then used for compression purposes.
- Section 6 gives a final project and the conclusion.
This project processes images for compression purpose, using a two dimensional wavelets transform.
It is the opportunity to reuse everything learned previously.
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|Section 1: Overview|
This lecture is the introduction to the course, telling the intended audience, engineers and scientists, what the course will bring them.
This lecture is a description of all you need to know about hardware and software requirements, and expecially how to get Scilab for free. After this lesson, you will be ready to start working with Scilab.
This lecture explores in detail a complete example, with many features of Scilab such as vectors, element by element functions, plotting and the control flow that is the 'for' loop. All the Scilab statements and comments (with //) are given in the attached text file 'Newton Cosinus'.
That lecture follows the example of lecture 3 and some more, in order to underline main Scilab features. It announces the rest of the course, the core of it in fact, so that students get teased to watch it.
|Section 2: Get into Scilab : Matrices, Vectors and Scalars|
This course deals with the definition of basic Scilab variable types, that are matrices, line and column vectors, and scalars. The video course is completed with a cool pdf file, that explicits the course with more details, and allows to copy-and-paste the Scilab commands, just to see the result…
This Lecture mainly deals with addition and subtraction of scalars, vectors and matrices of numbers. It does NOT deal with multiplication nor with division, as those are NOT elementary operations with Scilab. They are postponed to the next leacture.
At the end of the course, we give a glance to addition of strings and to Boolean operators, including comparison operators.
An additional pdf file gives some more information about matrices and vectors in Scilab, those elements that are rapidly shown in examples given in the video.
This lecture deals with the multiplication in Scilab in all its extend. This means global or element by element matrices, vectors and scalar products computation.
You will learn the magical power of the star * in Scilab, with the property you MUST fulfill when multiplying a matrix or a vector to another matrix, vector or scalar.
You will also learn to and a dot before the star to muliply element by element. That is the magical power of the "dot-star" (.*). You will learn why it must be separated from the numbers before by a space.
An additional pdf file is a funny application of the multiplication(s) to the drawing of an equilateral triangle using two concurrrent methods.
This lecture deals in detail in putting a square matrix to the power a scalar with the hat ^, globally, and putting elements of a square or rectangular matrix, as well as of a line or column vector to the power a scalar with the dot-hat .^.
Then you will see more rapidly other exponent related topics, with the dot-hat in the reverse order and exponent related functions. An example of element by element and global exponentional function shall be given in lecture 12 about the scripts.
This lecture show the division by a matrix in many different cases: dividing a scalar, a vector or another matrix, in right hand or left hand, whether the dividing matrix is square or rectangular.
It may so be seen that the division operators / and \ only seem to be simple, and that they hide a lot of surprises.
A rapid insight is also made into the element by element division ./. An example with a scalar divided by the elements of a vector hall be given in lecture 14 about the plot function.
|Section 3: Programming in Scilab|
This lecture shows the creation and use of a script to solve a non linear system of 2 equations with 2 variables with a Newton algorithm that solves iteratively the linearized equations.
The script created during the lecture is given as additional attached text file Newton2D.txt that you may copy and paste in Scilab editor Scinotes, and than save as Newton2D.sci or any file name with .sci extension.
Have a look to the video before you use the additional text file.
This lecture shows in detail the programing topics that are control flows, namely conditional stateùents and loops.
Very simple examples are given, just in order to illustrate the purpose.
More elaborated examples shall be given in further lectures.
This Lecture is the first one about Programing in Scilab. It shows an example of script writing and executing, with two methods for the execution, one at once after writing and one for later processing.
The script wrote is attached as text file .txt. You may copy and paste it in Scinotes, the in-built Scilab text-editor and use it when saved with a .sce extension.
This Lecture is the top of Programming in Scilab, as it shows how to create a Library made of Functions and how to use the Library later on.
It follows the first example of Lecture 3, redoing it with a clean Library.
The sources of the library created are given in the attached zip file.
|Section 4: Graphics and Images|
|This lecture deals with Scilab 2D graphical capabilities. It points out two functions: plot and xpoly, that allow to draw curves and polygons. The attached text file contains the commands to draw several regular polygons very easily.|
This lecture teaches 3D graphic functions, param3d for curves, and surf and contour for surfaces and contour plot.
The way to define and draw real functions of one or two real variables are illustrated in the video and explained more precisely in the attached pdf file.
This lecture is about images and this is cool.
It relies on the additional zip file. When uzipped, you havr a folder where there are 4 files : 2 images in RGB colors and 2 conversion functions.
You will be invited to load the images, draw them, and obtain and draw the grayscale version of them.
The manipulations are shown in the video for one image and explained in the pdf file for the other image.
|Section 5: Advanced Topics|
This Lecture enters into advanced variable types that are structures, lists and cells. These are objects that allow to put together in a sole variable heterogenous elements.
An application of a mix of strucres and lists is shown, with the sources given in the attached zip file. It is a signal compression algorithm, based on wavelets transforms computation.
That lecture is a recapitulation of the way to navigate in Scilab and use it by the way of menus, Unix commands in the console, and double-cliquing in the left window.
It deals with the problem of language, Scilab language being the language of the OS, so that you may have a interface language different than the French of the course.
It could be useful to have a look at that lecture and the very beginning of the course.
This is a somewhat conclusive Lecture, dealing with additional information to open the perspective on Scilab.
|Section 6: Make an End|
The final project uses many features of Scilab in a cool application of image compression with 2D wavelets.
It shows you an advanced mathematical tool with quite simple, short, Scilab code.
This lecture is the first part, grayscale image compressing.
The whole Scilab code, including a set of function to generate a library, is given in the attaches zip file.
This the part 2 of our final project, adding the color information.
It shows the difference between processing the grayscale information (luminance) and processing the colorization information (two chrominance channels), that may be very simpler and more compressed in fact.
The whole code is given in the attached zip file. The two "Wavelets2D" folders, given in the previous and in the present lecture, are exactly the same. It is the library for 2D Wavelets image compression.
It is time to say good bye, good practice of Scilab and… see you for our forthcoming series of courses on practical mathematics!
Fabienne Chaplais is 57, and lives in Paris, France.
She is married and has three children.
She obtained the French highest degree to teach mathematics at undergraduate level. This means that she is very accurate in mathematics and in teaching them to anyone from the beginners to the undergraduate level.
She then turned to an Engineer’s career for about 30 years.
She became an expert in R&D, especially when using applied mathematics and scientific programming in high level languages such as Matlab and Scilab.
She notably worked on satellites guidance, shuttle accosting and reentry .She applied her exoertise to implementing various complex algorithms such as Kalman filters and fuzzy logic.
After that, she worked in the railway industry, on automatic urban transportation systems for Paris and New York. After various R&D projects including error correcting Viterbi encoding and decoding as well as formal method based B language, she became an expert in safety analysis involving many specialized sharp inductive and deductive approach, including probability calculations.
She then founded Mathedu with her husband, a Researcher in Control Science.
Mathedu aims to teach mathematics from a practical point of view.
The idea is to let the students be in action with a very pragmatic approach, using its computer with Scilab installed as a laboratory.
Then and only then, the link with theory is done, in a very progressive way.
Learning maths with us will let you find the subject easy, so that you will no more understand why mathematics were so hard to understand before…