Scilab

Chapter 3. Scilab as a calculator

Chapter 3.1 Introduction
Scilab, like every programming language, has its own instructions, e.g. addition, subtraction, sin(x)… etc.
Scilab’s Console-basic window is ideal for testing them.
You simply enter e.g.:
2+2
and you immediately get the result 4.
With this approach, Scilab, or more precisely, its Console, acts as an ordinary calculator. On the one hand, it is a degradation for a serious programming language. On the other hand, it is an ideal method of learning new instructions. For example, mathematical ones, such as 4 bacic operations, sine, cosine logarithm… We will learn about the remaining instructions, i.e. control, input-output, in the next chapters.

Chapter 3.3 Basic Math Instruction
Choose the most convenient method for reading the course and testing it immediately.
In the previous chapter I chose the method from Chapter 2.5, that is
small course and Scilab windows at the same time,
you will mostly test the instructions without the animation, which I will leave for less typical cases.
We’ll start with the simplest action
Addition
2+2=4
You already know how to do it from the previous chapter. Just in case, I’ll show you this in the animation in Fig.3-1.

Fig.3-1
2+2
1. Open Scilab by clicking its icon
2. Type into the Console window
2+2
3. Enter–>The result will appear 4
4. Type clear; clc//instructions to clean up the Variable Browser and Console.
Always do this when testing subsequent instructions, i.e. Subtraction, Multiplication…

You can check other instructions in the same way
Subtraction
5-3=2

Multiplication
5*3=15

Division
20/4=5

Absolute value
abs(-2)
–> abs(-2)
ans =2.

Complex operations, e.g. with brackets and division
(3+5*7)/(2+3*4)+4=6.7142857

Exponentiation
2^3=8

Root
sqrt(9)=3
sqrt(10)=3.1622777…

Nth degree root
nthroot(27,3)
ans =
3.
Correct. The third root of 27 is 3.
Let’s check again
nthroot(2,2)
ans =
1.4142136
and exponentiation
2^0.5
ans =
1.4142136
Sine
sin(%pi/2) (enter the data in radians)
ans =
1.

Cosine
cos(%pi/2)
ans =
6.123D-17
What’s up? It should be 0! And so it is. Note that 6.123D-17 is a very, very small number!
Scilab calculated it this way by decomposing cos(x) into a polynomial. It then treats this number as 0.
Check e.g. that
1+6.123D-17=1

Tangent
tan(%pi/4)
ans =
1.0000000

Cotangent
cotg(%pi/4)
ans =
1.0000000

If you want to treat trigonometric functions in a human way, i.e. in degrees, add the letter d.
So there will be sind(x), cosd(x), tand(x) and cotg(x)
Let’s check, for example, sin(30º)
sind(30)
ans =
0.5000000

Let’s also check the claim
sin²(x)+cos²(x)=1
for x=30º
–> [sind(x)]^2+[cosd(x)]^2
ans =
1.

4 important mathematical constants π, e
%pi=3.1415927…
%e=2.7182818…
%eps=2.220D-16=”almost zero”
Sometimes Scilab gives a very small number “almost zero” in its calculations instead of zero. It is known, for example, that cos(0) = 0 and in Scilab the output will be cos(0) = “almost zero”.

%i=0. + i –>imaginary number i

Complex number 2+3i
2+3*%i=2. + 3.i

Note:
In this chapter, you tested instructions as regular operations, e.g. 2+2. Here, the result of 2 was assigned to a specific ans variable. So ans=2+2=4. If you then entered e.g. 2+3 into the console, the result 5 would also be in the same variable ans=2+3=5. What if you used addition with assignment to a variable with a specific address in memory, e.g. x=2+2 and y=2+3? Then it could make our job easier by calculating z=x*y=4*5=20.

Defining a vector
After entering it into the console
x=[1,2,3]
and clicking Enter, the text will appear
x =
1. 2. 3.
In this way, the variable x was created as a vector with the following values 1, 2, 3.
Note:
The first element of this vector is x(1)=1, not x(0)=1.

Conclusion:
Vector indexing in Scilab. It starts from 1, not 0! I spent a lot of time looking for errors while testing the program. Remember that!
A vector, as well as matrices, do not have to consist only of numbers. They can also be made of strings (writings).
x=[‘Warsaw’, ‘Kraków’, ‘Suwałki’]
Check in the console

x=[‘Warsaw’, ‘Kraków’, ‘Suwałki’]
x =
“Warsaw” “Kraków” “Suwałki”

Transposing a vector

x=[1,2,3]
y=x’
y =

1.
2.
3.
A new vector y was created, which from a “horizontal” x vector became a “vertical” y vector

Dot product of 2 vectors
x=[1,2,3]
y=[4,5,6]
z=x*y’–>spatial product – note the ‘ sign
After pressing Enter, the scalar product of these vectors was calculated as

x=[1,2,3]
x =
1. 2. 3.
–> y=[4,5,6]
y =
4. 5. 6.
–> z=x*y’
z =
32.
Please note that the scalar product of 2 vectors is number = 32, otherwise it is a scalar and not a vector!
I will check manually.
1*4+2*5+3*6=32
Correct!

Matrix
A matrix is a generalization of a vector and its example is e.g.
A=[2,2,4;5,2,3;4,2,7]
This looks strange. Check it in the Scilab console

A=[2,2,4;5,2,3;4,2,7]
A =

2. 2. 4.
5. 2. 3.
4. 2. 7.
You can perform addition, subtraction, multiplication and division operations on matrices.
e.g.

–> B=[1,2,5;-3,2,-2;-1,2,3]
B =

1. 2. 5.
-3. 2. -2.
-1. 2. 3.
There is no problem with addition and subtraction
A+B
ans =

3. 4. 9.
2. 4. 1.
3. 4. 10.
But when it comes to multiplication, you need to remember the theory.
–> A*B
ans =

-8. 16. 18.
-4. 20. 30.
-9. 26. 37.

How to create a matrix whose every element is squared?
A=[2,2,4;5,2,3;4,2,7]
A =

2. 2. 4.
5. 2. 3.
4. 2. 7.

–> A.^2(note the dot next to A)
ans =

4. 4. 16.
25. 4. 9.
16. 4. 49.

Each element of matrix A multiplied by the corresponding element of matrix B
Note:
This is not a multiplication of matrices A and B

A=[2,2,4;5,2,3;4,2,7]
A =

2. 2. 4.
5. 2. 3.
4. 2. 7.

B=[1,2,5;-3,2,-2;-1,2,3]
B =

1. 2. 5.
-3. 2. -2.
-1. 2. 3.

A.*B (note the dot next to A)
ans =

2. 4. 20.
-15. 4. -6.
-4. 4. 21.

Other mathematical operations instructions
I have provided only the most necessary Scilab instructions. You will find every math instruction in the help.

e.g. Prime factorization
factor(20)
ans =
2. 2. 5.
Indeed, 20=2*2*5