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- Lecture 2
Lecture 2
MATLAB fundamentals
Variables, Naming Rules,
Arrays (numbers, scalars, vectors, matrices),
Arithmetical Operations,
Defining and manipulating arrays
© 2007 Daniel Valentine. All rights reserved. Published by
Elsevier.
- Variables
Variables
What are variables?
– You name the variables (as the programmer)
and assign them numerical values.
- Variable Naming Rules
Variable Naming Rules
Must begin with a LETTER
May only contain letters, numbers and
underscores ( _ )
No spaces or punctuation marks allowed!
Only the first 63 characters are significant;
beyond that the names are truncated.
Case sensitive (e.g. the variables a and A
are not the same)
- Which variable names are
Which variable names are
valid?
12oclockRock
tertiarySector
blue cows
Eiffel65
red_bananas
This_Variable_Name_Is_Quite_Possibly_Too_L
ong_To_Be_Considered_Good_Practice_Howev
er_It_Will_Work % (the green part is not part of
the recognized name)
- Variable Naming Conventions
Variable Naming Conventions
There are different ways to name variables. The
following illustrate some of the conventions used:
– lowerCamelCase
– UpperCamelCase
– underscore_convention
If a variable is a constant, some programmers use all
caps:
– CONSTANT
It does not matter which convention you choose to work
with; it is up to you.
- Variables as Arrays
In MATLAB, a variable is stored as an array of
variable
numbers. When appropriate, it is interpreted as a
scalar, vector or matrix.
scalar vector matrix
scalar vector matrix
1×1 n × 1 or 1 × n n×m
The size of an array is specified by the number of
The
rows and the number of columns in the array, with
the number of rows indicated first.
the
- Scalars
Scalars are 1×1 arrays.
They contain a single value, for example:
r=6
height = 5.3
width = 9.07
- Vectors
Vectors
A vector is a list of numbers expressed as a 1
vector
dimensional array.
dimensional
A vector can be n×1 or 1×n.
Columns are separated by commas (or spaces):
Columns commas
h = [1, 2, 3]
Rows are separated by semicolons:
Rows semicolons
v = [1; 2; 3]
- Matrices Columns
1 2 3
A matrix is a two
1 3.0 1.8 3.6
dimensional array of
numbers.
2 4.6 2.0 21.3
Rows
3 0.0 6.1 12.8
For example, this is a
4×3 matrix: 4 2.3 0.3 6.1
m = [3.0, 1.8, 3.6; 4.6, -2.0, 21.3; 0.0,
2.0,
-6.1, 12.8; 2.3, 0.3, -6.1]
6.1,
- Indexedlocation of numbers in an
array
Columns
Each item in an array 1 2 3
is located in the
(row, column). 1 3.0 1.8 3.6
m(2,3)
m(2,3) 2 4.6 2.0 21.3
Rows
ans =
ans
21.3000
21.3000 3 0.0 6.1 12.8
4 2.3 0.3 6.1
- Examples
Enter the following into MATLAB:
– Scalar:
a=1
– Vectors:
b = [1, 0, 2]
c = [1 0 2]
– Matrix:
d = [5, 4, 3; 0, 2, 8]
- Examples
Examples
Enter (input) the following matrix into MATLAB:
7 21 6
2 32 0
whiteRabbit =
5 0 18.5
- Scalar Operations
Scalar Operations
Operation Algebraic MATLAB
Syntax Syntax
a + b a+b
Addition
a b a–b
Subtraction
a × b a .* b
Multiplication
a ÷ b a ./ b
Division
ab a .^ b
Exponentiation
- Array Operations
Array Operations
Arrays of numbers in MATLAB can be interpreted as
vectors and matrices if vector or matrix algebra is to be
applied. Recall that matrices are mathematical objects
that can be multiplied by the rules of matrices. To do
matrix multiplication, you need to use the standard *, /,
and ^ operators [without the preceding . (dot)]. They are
operators [without the preceding
not for array multiplication, division and exponentiation.
To deal with arrays on an elementbyelement level we
need to use the following array or dotoperators:
.* , ./ .^
.* ./ and
and
- Array operations & dotoperators
Array operations & dotoperators
.* , ./ .^
./ and
and
Because scalars are equivalent to a 1×1
array, you can either use the standard or
the dotoperators when doing
multiplication, division and exponentiation
of scalars (i.e., of single numbers).
It is okay for you to always use the dot
operators, unless you intend to perform
vector or matrix multiplication or division.
- Array vs. Matrix Operations
Example:
x = [ 2, 1; 3, 4]
y = [ 5, 6; 7, 8]
z = x .* y
results in [10, 6; 21, 32]; this is array multiplication
z=x*y
results in [17, 20; 43, 50]; this is matrix multiplication
So, do NOT forget the dot when doing array
operations! (.* ./ .^)
- Hierarchy of Operations
Hierarchy of Operations
Just like in mathematics the operations are done in the
following order: Left to right doing what is in
Parentheses & Exponents first, followed by
Multiplication & Division, and then
Addition & Subtraction last.
An example:
c = 2+3^2+1/(1+2) 1st c = 2+3^2+1/3
c = 2+3^2+1/(1+2) 2nd c = 2+9+1/3
c = 2+3^2+1/(1+2) 3rd c = 2+9+0.33333
c = 2+3^2+1/(1+2) 4th c = 11+0.33333
11
c = 2+3^2+1/(1+2) 5th c = 11.33333
2+3^2 11.33333
- Handson
Handson
Enter these two arrays into MATLAB:
a= b=
10 5 5 1 0 2
10
2 9 0 0 0 0
6 8 8 1 1 0
Multiply, elementbyelement, a × b.
– Since this is an array operation, the .*
multiplication operation is implied by the
request.
- Defining & manipulating arrays
Defining & manipulating arrays
All variables in MATLAB are arrays!
– Single number array & scalar: 1×1
– Row array & row vector: 1×n
– Column array & column vector: nx1
– Array of n rows x m columns & Matrix: n×m
– Naming rules
– Indexed by (row, column)
Indexed
Remark: vectors and matrices are special
mathematical objects, arrays are lists or
tables of numbers.
tables
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