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Scilab A “Very” Short Introduction

Scilab A “Very” Short Introduction. Math 15 Lecture 7 University of California, Merced. Project #1 – Due 3pm on April 4 th , 2008. Projects can be performed individually or in groups of three, with following rules: Teams turn in one project report and get the same grade.

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Scilab A “Very” Short Introduction

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  1. ScilabA “Very” Short Introduction Math 15 Lecture 7 University of California, Merced

  2. Project #1 – Due 3pm on April 4th, 2008 • Projects can be performed individually or in groups of three, with following rules: • Teams turn in one project report and get the same grade. • A team consists of at most 3 people—no copying between teams! • Team project report must include a title page, where a team describe each team member’s contribution. • 10% bonus for projects done individually • Individual projects must not be copied from anyone else • No late project will be accepted! Project #1 has been posted at UCMCROP. UC Merced 2

  3. Any Questions? UC Merced

  4. Course Lecture Schedule

  5. Outline • Scilab • Getting Started • Simple Operations with Scilab • Simple Plots with Scilab

  6. What is Scilab? • Scilab is a numerical, programming and graphics environment available for free from the French Government’s INRIA (National Institute for Informatics and Automation Research). • It is similar in operation to MATLAB. • It is available for free from the Scilab website • www.scilab.org.

  7. What is Scilab? • Scilab is a software for numerical mathematics and scientific visualization. • It is capable of interactive calculations as well as automation of computations through programming. • It provides all basic operations on matrices through built-in functions so that the trouble of developing and testing code for basic operations are completely • Scilab can help you understand all intermediate steps in solving even complicated problems, as easily as using a calculator.

  8. What Scilab can do:

  9. www.scilab.org

  10. UCM Computer Labs

  11. Scilab Environment • The user enters Scilab commands at the prompt (-->). • Scilab can be used as a simple calculator to perform numerical calculations. • It also has the ability to define variables and store values in them so that they can be used later.

  12. Simple Calculator -->2+3 ans = 5. -->2/3 ans = .6666667 -->2^3 ans = 8. • Evaluate -->s=0.5 s = 0.5 -->log(s^2-2*s*cos(s*%pi/2)+1) ans = - 0.6108426 -->

  13. Loading a Value Into a Variable --> a = 2 a = 2. -->b = 3. b = 3. -->c = a+b c = 5. assignment -->a = 2 Variable Value 2 is assigned to the variable, a.

  14. Variables in Excel • Cell names, such as B1, D1 etc., are variables in Excel. 3 is assigned to Cell B2. = (B1 – D3*B4)/(A1+B2^3) UC Merced - Math 15

  15. Mathematical Operations • Few examples of operations • Arithmetic Operations • Trigonometric Operations sin(), cos(), tan(), asin(), acos(), atan(), sinh, cosh etc. • Exponential and logarithmic operations log(), log10(), exp() etc.

  16. Examples sqrt(3^5-2)/exp(2) 2.1009686 atan(3)/asin(0.6) 1.9410157

  17. Let’s program! But be careful! --> x = 3 --> y = 3x - 3 --> x = 3 --> y = 3x - 3 Missing Operator error >>> --> x = 3 --> y = 3*x - 3 y = 6. UC Merced

  18. Special Constants • SCILAB has a number of special constants: • %i unit imaginary number • %pi ratio of circumference to diameter • %e the base of the natural logarithms • %inf the infinity • %nan not-a-number • %f boolean constant ’false’ • %t boolean constant ’true’ • Etc.

  19. Examples sqrt(3^5-2)/exp(2*%pi) 0.0289905 - 5.3327279 tan(2*%pi/3)/cos(3/%pi) - (sqrt(5)-1)^4

  20. Comments • Comments in SCILAB begin with a double forward slash (//) • a = 2.5 // redefining a <return>

  21. Creating Arrays • Array • You can think as a variable carries series of data • i.e. x = 1, 2, 3, 4, 5 • How to define arrays in SCILAB. • V = [1, 2, 3, 4,5] • V = 1 2 3 4 5 • V = [1:5] // array runs from 1 to 5 by 1. • V = 1 2 3 4 5 • V = 1:2:10 or [1:2:10] // array runs from 1 to 10 by 2. • V = 1 3 5 7 9 • V = linspace(0,10,5) // array has 5 evenly spaced points between 0 and 10. • V= 0 2.5 5.0 7.5 10

  22. Array Operation • Row array with starting value, increment, ending value • x = -10: 0.1: 10; • Applying a function to the array • y = sin(x*%pi/10); • Plotting the function • plot(x,y)

  23. Working with Arrys • X = [1 2 3] • Y = [2;1;5] • b = 2*x • c = 2*y Row array (vector) Column array (vector) 2 4 6 4 2 10

  24. Working with Arrays –cont. • z = [2 1 0]; • a = x + z • b = x + y • c = x .* z 3 3 3 You will get an error. You cannot add (or subtract) a row vector to a column vector 2 2 0 You can multiply (or divide) the elements of two same-size arrays (vectors) term by term with the array operator .* (or ./)

  25. Creating Simple Plots • Let’s plot with Scilab. • First define q as an array • theta = linspace(0,2*%pi,100); • Create a linearly spaced 100 elements between 0 and 2p. • Then, calculate • y = sin(theta); • Then, plot the graph • plot(theta,y)

  26. More on plotting • Let’s plot the following functions on the same graph. theta = linspace(0,2*%pi,100); x = sin(theta); y = cos(theta); plot(theta,x,theta,y,'--')

  27. Teaching Philosophy “I hear and I forget. I see and I remember. I do and I understand.” No Pain! No Gain! Confucius 500 B.C. UC Merced - Math 15

  28. Next Lecture • By using Scilab, we can effortlessly solve systems of equations, such as

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