Intro to Scilab
Developed at INRIA, SCILAB has been developed for system control and signal processing applications. It is freely distributed in source code format.
High level scientific computing environments such as Matlab, RLab, Octave and Scilab are an enjoyable way to solve problems numerically.
It is particularly easy to generate some results, draw graphs to look at the interesting features, explore the problem further and manipulate matrices.
Scilab is made of 3 distinct parts
· An interpreter
· Libraries of functions
· Libraries of Fortran and C routines
à - scilab prompt
Up arrow key – to display
// - comment
%pi = 3.1415 //constant pi
clc = clear the screen
clear = clear memory
clear varname = clear specific variable
xbasc() = erase the previous plot
Differences between Matlab and Scilab
à (-1+2+3)*5 – 2/3 //The four arithmetic operations
= 19.33
à 2^3 // Means 2 to the power 3.
= 8
à %pi // The mathematical constant pi
= 3.1415
à exp(sin(%pi/2)) //The usual functions are provided log, log10, cos, tan, asin,…
= 2.7182818
exp – element-wise exponential
Calling sequence:
exp(X)
Parameters
· X : scalar, vector or matrix with real or complex entries.
Description
exp(X) is the (element-wise) exponential of the entries of X.
à %e //The mathematical constant e
Note: Scilab does all calculations correct only to about 16 significant decimal digits. This is enough accuracy for most purposes. Usually only 5 significant digits are displayed on the screen.
Ex.
à %pi
= 3.1415927
à 22/7 //pi is not the same as 22/7
= 3.1428571
à 11*(15/11)-15 //This shows there is round off error when scilab uses fractions.
= 1.776D-15
à cos(%pi/3) //These are familiar trigo functions
= 0.5
à sin(%pi/6) //These are familiar trigo functions
= 0.5
Variable – Scilab also uses variables to store intermediate answers. A variable can have almost any name, but is must begin with a letter.
- Scilab is a case-sensitive language.
Ex.
X = 2+3
Y = 4+5
result = X/Y
; - echo off, suppress unwanted output.
Ex.
à p = 2+3;
à q= 3+5;
à ratio = p/q
= 0.5555556
>> A number of commands can be placed on the one line. Use comma (,) or a semicolon (;)
Ex.
à p1 = 2+3 ; q1 = x+4, ratio1 = p1/q1
q1 =
9
ratio1 =
0.5555556
>>Parentheses can be used to make expressions clearer.
Ex.
à ratio = (2+3)/(x+4)
Complex Numbers - Scilab handles complex numbers as easily as real numbers
- the variable %i stands for 
Ex.
à x=2+3*%i, y=1-1*%i
x = 2 + 3i
y = 1 – i
à z1= x-y, z2 = x*y, z3 = x/y
z1 = 1 + 4 i
z2 = 5 + i
z3 = -0.5 + 2.5i
à abs(x)
= 3.6055513
à real(x)
= 2
à imag(x)
= 3
à sin(x)
= 9.1544991 – 4.168907i
à exp(%pi * %i ) + 1
= 1.225D-16i
PLOTTING LINES AND DATA
- This section shows how to produce simple plots of lines and data.
Ex.
| Xk | .5 | .7 | .9 | 1.3 | 1.7 | 1.8 |
| Yk | .1 | .2 | .75 | 1.5 | 2.1 | 2.4 |
à x=[.5 .7 .9 1.3 1.7 1.8]
à y=[.1 .2 .75 1.5 2.1 2.4]
à plot2d(x,y, style=-1)
Ex.
Y1 = 2X + 4 0 <= x1 <=2
Y2 = x-2 3 <= x2 <=5
à x1 = [0: 0.5: 2];
à x2 = [3: 0.5: 5];
à y1 = (2*x1+4);
à y2 = (x2 – 2);
à plot (x1, y1)
à plot (x2, y2)
à plot (x1, y1, x2, y2)
MATRICES AND VECTORS
Although SciLab is a useful calculator, its main power is that it gives a simple way of working with matrices and vectors.
Matrix Shortcuts
à a = eye(3,3)
à b = ones(4,4)
à c = diag([ 1 2 3 4])
à d = rand(3,3)
à e = [1:5]
à f = [1:3; 4:6; 7:9]
à g = [1:0.1:5]
à h = linspace(-10, 10, 20)
linspace
syntax: linspace(x1, x2,n]
where:
x1, x2 : real or complex scalars
n : integer (no of values) default = 100
Displaying matrix data
à a = [1,2,3; 4,5,6; 7,8,9]; // given data
à a(1,1)
= 1
à a(:, 1) // : is used to denote all entries
= 1
4
7
à a(2, :)
= 4 5 6
à a([1 2], [1 2]) //a([r1, r2], [c1, c2])
= 1 2
4 5
à a([2 3], : )
= 4 5 6
7 8 9
à a([1 2],[2 3])
= 2 3
5 6
MATRIX MANIPULATION
+ addition
- subtraction
* multiplication
/ division
\ left division
^ power
‘ transpose
.* array multiply
./ array division
.^ array power
Addition of Matrices Subtraction of Matrices
A = D = A – B
1 2 3 D =
4 5 6 0 -1 2
7 8 9 3 -2 2
4 3 2
B=
1 3 1 E = B-A
1 7 4 E =
3 5 7 0 1 -2
-3 2 -2
C=A+B -4 -3 -2
C=
2 5 4
5 12 10
10 13 16
F = 3*A G = 2*B
F = G =
3 6 9 2 6 2
12 15 18 2 14 8
21 24 27 6 10 14
H = A’ I = B’
H = I =
1 4 7 1 1 3
2 5 8 3 7 5
3 6 9 1 4 7
Matrix Multiplication Array Multiplication
A= [1 2 3; 4 5 6]; A = [2 4 6 8; 2 3 1 4]
B = [2 4 6 8; 1 2 3 4; 1 3 5 7] B = [1 2 3 4; 2 3 1 4]
à C = A*B à C = A.*B
C = C =
7 17 27 37 2 8 18 32
19 44 69 94 4 9 1 16
à C = B*A à C = A*B
ERROR! Inconsistent multiplication ERROR! Inconsistent multiplication
à C = A.*B
ERROR! Inconsistent multiplication
Matrix Division I
A = [2 4 6 8; 2 4 6 8; 1:4; 5:8]
B = [1 5 1 4; 1 8 3 9; 1 7 9 2; 1 0 5 9]
C = A/B
C=
1.6354 -0.7500 0.2604 0.8542
1.6354 -0.7500 0.2604 0.8542
0.8177 -0.3750 0.1302 0.4271
6.8385 -3.8750 0.4010 1.6354
Inverse of Matrix
C = A*inv(B)
C=
1.6354 -0.7500 0.2604 0.8542
1.6354 -0.7500 0.2604 0.8542
0.8177 -0.3750 0.1302 0.4271
6.8385 -3.8750 0.4010 1.6354
Left Division
Given:
-x1 + x2 + 2x3 = 2
3x1- x2+ x3 = 6
-x1 + 3x2 + 4x3 = 4
à A = [-1 1 2; 3 -1 1; -1 3 4]
à B = [2; 6;4]’
à X = inv(A)*B
X =
1
-1
2
à A\B
X =
1
-1
2