An Introduction to Scilab

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An Introduction to Scilab
Tsing Nam Kiu ??? Department of Mathematics The
University of Hong Kong 2009 January 7
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What is a Scilab?

• Scilab is a mathematical software
• Similar software Matlab, Mathematica, Octave,
  Euler Math Toolbox, Maxima,
• What is special about Scilab free, highly
  supported, powerful, many users,
• Home page of Scilab www.scilab.org
• A short introduction of Scilab
  http//hkumath.hku.hknkt/Scilab/IntroToScilab.htm
  l

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Using Scilab as a calculator

• , , (multiplication), / (division),
  (power)
• Examples
• gt (12.34 0.03) / (2.8 1.2 3)
• gt 23 or 222
• gt 2 3
• gt 2100
• gt ans(1/100)

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Using Scilab as a calculator (2)

• Commonly used functions
• cos, sin, tan, acos, asin, atan, sqrt, exp, log,
  log10
• Solving quadratic equation x2 x10
• gt a 1, b 1, c 1
• gt ( a sqrt(b2 4ac))/(2a)
• gt ( a sqrt(b2 4ac))/(2a)
• A smarter way to find roots of polynomials
• gt p poly(1 1 1,"x","coeff")
• gt roots(p)

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Using Scilab as a calculator (3)

• special constants i, pi, e
• gt tan(pi / 4)
• gt e ( exp(1) )
• gt (1i)(1--i)
• Learning how to use Scilab and getting help
• Click on ? on menu
• gt help command
• See documentation on Scilab website

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Vectors and matrices in Scilab

• Data types (real or complex) numbers, vectors,
  matrices, polynomials, strings, functions,
• Vectors in Scilab
• gt x 0 1 2 3
• gt y 2 4 6 8
• gt z 1 2 3 4
• is conjugate transpose of a matrix
• gt 3x, yz, yz
• gt xy, x1

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Vectors and matrices in Scilab (2)

• Matrices in Scilab
• gt A 0 1 0 1 2 3 4 0
• gt B A
• gt A y, x B, A B, B A, (BA)2
• Special matrices (and vectors)
• gt ones(2,3), zeros(1,2), eye(3,3)
• gt rand, rand(3,2)
• Empty vector or matrix gt a
• Building matrix by blocks
• gt C A 2A, x 9 x 7, a a 1

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Solving linear equations

• 3 x1 2 x2 x3 1
• x1 x3 2
• 2 x1 2 x2 x3 1
• To solve the above system of linear equations
• gt A 3 2 1 1 0 1 2 2 1
• gt b 1 2 1
• gt x inv(A)b (inv is inverse of a matrix)
• gt x A \ b
• Important remark theoretically it does not make
  sense to divide something by a matrix!

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The colon operator

• gt 110, 1100, xx 1100
• Using to suppress answer output
• gt sum(xx)
• gt 1210, 3311, 411, 210,
• gt t 0 0.1 2pi
• gt y sin(t)
• gt plot(t,y), plot(t,sin(t),t,cos(t))
• Task 1 plot the straight lines
• y x 1 and y exp(x) on the same graph, from x
  2 to x 2

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Elements of vectors and matrices

• Example
• gt v rand(4,1)
• gt v(1), v(3), v(2 4), v(4-11), v()
• means the last entry
• Example
• gt A 1 2 3 4 5 6 7 8 9 10
• gt A(2,3), A(1,), A(, 2), A(, 4 2)

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Exercises

• Task 2 simulate tossing of a coin
• 0 head, 1 tail.
• functions to use rand, round,
• Task 3 simulate tossing of 100 coins

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Exercises (2)

• Task 4 simulate throwing 3 dices, each dice has
  outcome from 1 to 6 with equal probabilities
• functions to use rand, floor, ceil,
• Task 5 (challenging!) simulate tossing a coin
  100 times and find the longest run of consecutive
  Hs or Ts in the resulting sequence
• functions to use diff, find, max,

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Programming in Scilab

• Click on menu bar to open Scipad then write your
  scilab function file.
• Format of a function
• function out1, out2, ... name(in1, in2, ...)
  
• (body of function definition may have many
  lines)
• endfunction
• One file may contain more than one function.
• To use the functions, you must load the function
  file by choosing File -gt Execute the file from
  the menu.

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Programming in Scilab (2)

• A simple function to find the n-th term of the
  Fibonnaci sequence 0, 1, 1, 2, 3, 5, 8, 13, 21,
• function k fibo(n)
• if n 1, k 0
• elseif n2, k 1
• else k fibo(n-1) fibo(n-2)
• end
• endfunction
• Save the file as fibo.sci (or any other file
  name).
• Execute it from Scilab menu bar
• Try, say gt fibo(5), fibo(2), fibo(10),
  fibo(100)

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Programming in Scilab (3)

• An improved programme
• function K fibonacci(n)
• //function K fibonacci(n)
• //Gives the n-th term of the Fibonacci sequence
  ,1,1,2,3,5,8,13,... if n1, K 0
• elseif n2, K 1
• elseif ngt2 int(n)n
• // check if n is an integer greater than 2
• K fibonacci(n-1) fibonacci(n-2)
• else disp('error! -- input is not a positive
  integer')
• end
• endfunction

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Programming in Scilab (4)

• Programming Task (challenging!) write a
  programme to automate Task 5, which is to perform
  the following experiment m times. The experiment
  is to simulate tossing a coin n times and find
  the longest run (k) of consecutive Hs or Ts in
  the resulting sequence.
• For each time you do the experiment, youll get a
  number k. Therefore you should get m numbers k1,
  k2, , km at the end.
• Inputs of the function are m, n output is a
  vector k k1 k2 km.

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Recap

• We have discussed and learned the following
• What Scilab is
• Basic usage of Scilab (as a calculator)
• Vectors and Matrices in Scilab
• Solving linear equations
• Simulation of some random events
• Basic Scilab programming