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CIV1900: Engineering Skills
Variables in MATLAB
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Variables allow you to store (intermediate) results
• a variable is a named location in computer memory
• for storing/retrieving one or more values
• created in MATLAB by assignment
radius = 3
• accessed by mentioning the name (or in Workspace)
>>radius
radius =
3
• can be used anywhere a number (literal) can be used
area = pi*radius^2
CIV1900 Engineering Skills: programming in MATLAB 2
3.
Variables in MATLAB
• variables are listed in alphabetical order in the Workspace
• with information about their name, size, type and min/max
• not all information is shown automatically
• use View > Choose Columns when focus is in the Workspace
• MATLAB automatically creates a variable called ans if
needed:
>> 1024^3/8
ans=
134217728
• If you don't want to print out the result add a semi-colon
>> diameter = 2*radius;
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4.
Assignment might look like algebra, but it isn't
• x = x + 1 doesn't sound right
• how can x be equal to x + 1
• why isn't it a logical inconsistency?
• because assignment isn't equality at all
• assignment is a two step process:
• calculate the value on the right hand side (r-value)
• store the result in the variable on the left hand side (l-value)
• So x = x + 1 means:
• evaluate x + 1 first by getting the value out of variable x
• store the result back into variable x
4Engineering Skills: programming in MATLABCIV1900
5.
MATLAB arrays are collections of (like) values
• arrays store multiple elements of one type
• each element can be accessed by position in the array
• called indexing or subscripting the array
• uses the array name and then the index in
parentheses
• most other programming languages index from 0
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6.
1-dimensional arrays are called vectors
• created with square brackets and (optional) commas
pos = [1, 0, -1]
primes = [1 2 3 5 7 11 13]
• accessed with indices e.g. the 6th prime number is?
primes(6)
ans =
11
• notice how vectors appear in the Workspace (e.g. size 1x7)
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Vectors can be created using n:s:m notation
• vectors ranging from n to m with step s can be written n:s:m
e.g. from 1 to 20 stepping by 3:
x = 1:3:20
x =
1 4 7 10 13 16 19
• if the step size is missing, the default is 1:
x = 1:7
x =
1 2 3 4 5 6 7
• the vector goes up to and including the last value
• think about what might happen with negative values!
7Engineering Skills: programming in MATLABCIV1900
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MATLAB has functions to create vectors with fixed sizes
• linspace takes a n and m, and a number of elements:
• e.g. create a vector from 0 to 3 containing 5 values
linspace(0, 3, 5)
ans =
0 0.7500 1.5000 2.2500 3.0000
• zeros and ones create vectors of only zeros and ones
zeros(1, 5)
ans =
0 0 0 0 0
ones(1, 5)
ans =
1 1 1 1 1
8Engineering Skills: programming in MATLABCIV1900
9.
Indexing is used to make vectors longer or shorter
• assigning to an index beyond the length grows the vector
data = [1 2 3];
data(6) = -1
data =
1 2 3 0 0 -1
• zeros are used to fill in the gaps
• assigning an empty vector to an index removes elements
data(2) = []
data =
1 3 0 0 -1
9Engineering Skills: programming in MATLABCIV1900
10.
Boolean vectors can be used to select elements
• booleans are true/false (that is, yes/no values) of type logical
primes = [1 2 3 5 7 11 13];
mask = [true false true false]
mask =
1 0 1 0
primes(mask)
ans =
1 3
• the new vector is the length of the number of true values
• booleans may look like numbers when printed
but they are a different type
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Index vectors can select elements in any order
• each element in the index vector selects an element
primes = [1 2 3 5 7 11 13];
indices = [1 6 4];
primes(indices)
ans =
1 11 5
• the index vector can be of any length
• the new vector has the same length as the index vector
• the index vector can be created using n:s:m range notation
• the special value end can be used in these ranges
11Engineering Skills: programming in MATLABCIV1900
12.
Arrays can store many dimensions
• matrices are two dimensional arrays
• created with semi-colons to separate the rows:
x = [1 2 3; 4 5 6; 7 8 9]
x =
1 2 3
4 5 6
7 8 9
• accessed using a pair of indices (row first, then column)
x(1, 3)
ans =
3
• functions like zeros and ones work too
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13.
Functions apply to arrays in different ways
• some functions apply to all elements of an array
• e.g. min, max, sum, …
values = [0 5 -2];
sum(values)
ans =
3
• others apply to each element one at a time
• e.g. trig functions, absolute value (abs), …
abs(values)
ans =
0 5 2
13Engineering Skills: programming in MATLABCIV1900
14.
Special operators exist for per element calculations
• the regular operators sometimes behave differently on arrays
• e.g. * does not multiply corresponding array elements
[1 2 3]*[4 5 6]
gives the error: Inner matrix dimensions must agree
• because * is matrix multiply (more about this in later weeks)
• we need array multiply which multiplies each pair of elements
to create a new array:
[1 2 3].*[4 5 6]
ans =
4 10 18
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15.
Concatenating and slicing matrices
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>> a=[1 2 3; 5 7 9; 8 9 10]
>> b=[9 8 7; 6 5 4; 1 2 3]
• What would be the result?
>> c=[a b]
c = 1 2 3 9 8 7
5 7 9 6 5 4
8 9 10 1 2 3
>> d=[a; b]
d = 1 2 3
5 7 9
8 9 10
9 8 7
6 5 4
1 2 3
>> e=a(1,:)
e = 1 2 3
“1” means “the first row”
“:” means “all columns”
>> f=a(:,1)
f = 1
5
8
“:” means “all rows”
“1” means “the first column”
Engineering Skills: programming in MATLABCIV1900
16.
Deleting rows and columns
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• Easy, by using []
>>c
c = 1 2 3 9 8 7
5 7 9 6 5 4
8 9 10 1 2 3
• To delete the second column:
>> c(:,2)=[]
c = 1 3 9 8 7
5 9 6 5 4
8 10 1 2 3
• To further delete the second row:
>> c(2,:)=[]
c = 1 3 9 8 7
8 10 1 2 3
Engineering Skills: programming in MATLABCIV1900
17.
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Transpose of a matrix
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• If a is a m x n matrix, then the transpose of a, denoted with a’,
is a n x m matrix whose first column is the first row of a, whose
second column is the second row of a, and so on
• In Matlab we can compute the transpose of a matrix using the
dot-apostrophe operator „
>>a=[1 2 3 4; 5 7 9 3; 8 9 10 12]
a = 1 2 3 4
5 7 9 3
8 9 10 12
>> a'
ans = 1 5 8
2 7 9
3 9 10
4 3 12
3 x 4
4 x 3
Engineering Skills: programming in MATLABCIV1900
18.
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Generating basic matrices
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• zeros() – all elements are 0
>> zeros(2,3)
ans = 0 0 0
0 0 0
• ones() – all elements are 1
>> ones(2,3)
ans = 1 1 1
1 1 1
• rand() – uniformly distributed
random elements from (0,1)
>> rand(2,3)
ans = 0.8147 0.1270 0.6324
0.9058 0.9134 0.0975
• eye() – identity matrix
>> eye(3)
>>ans =
1 0 0
0 1 0
0 0 1
>> eye(5)
ans =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
CIV1900 Engineering Skills: programming in MATLAB
19.
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• Done element by element
• Matrices must have the same dimensions
>> a=[1,2,3; 5,7,9; 8,9,10]
a = 1 2 3
5 7 9
8 9 10
>> b=[9,8,7; 6,5,4; 1,2,3]
b = 9 8 7
6 5 4
1 2 3
• What would be the result?
>> c=a+b
c = 10 10 10
11 12 13
9 11 13
Adding and subtracting matrices
>> d=a-b
d = -8 -6 -4
-1 2 5
7 7 7
Engineering Skills: programming in MATLABCIV1900
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• Each matrix element is multiplied by the scalar
>> a=[1,2,3; 5,7,9; 8,9,10]
a = 1 2 3
5 7 9
8 9 10
>> b=a*6
b = 6 12 18
30 42 54
48 54 60
• Do we need to use .* instead of * ?
Multiplying a matrix with a scalar
Engineering Skills: programming in MATLABCIV1900
21.
Calculating the inverse matrix
• Let a, b and c are square matrices, a*b=c and
we are given a and c and need to find b
>> a=[9 2 7; 6 1 4; 1 6 3]
>> c=[1 2 3; 5 7 9; 8 9 10]
• Let‟s do it analytically:
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• In Matlab we can use inv():
>> b=inv(a)*c
b = 5.9643 7.8214 9.6786
4.7857 5.9286 7.0714
-8.8929 -11.4643 -14.0357
cab
caaba
cab
1
1 1
multiply both sides on theleft by 1
a
, where I is the identity matrixIaa
1
Engineering Skills: programming in MATLABCIV1900
22.
Matlab can manipulate not only numbers but also strings
• A character string or simply string is an ordered sequence of
characters (i.e. symbols and digits)
• In Matlab strings are enclosed in single quotes
>> s1 = 'Hello!'
s1 = Hello!
>> s2 = 'I am 20 years old.'
s2 = I am 20 years old.
• Single quotes can be included in the strings with double quotes
>> s4 = 'You''re smart'
s4 = You're smart
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23.
Matlab treats strings as arrays of characters
• We can apply the vector manipulation functions
• What is the result?
>> s1 = 'James';
>> size(s1)
ans = 1 5
>> length(s1)
ans = 5
>> s1(3)
ans = m
>> s1(6)
??? Attempted to access s1(6); index out of bounds
because numel(s1)=5.
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24.
Displaying string variables with disp()
• We already have seen how to use disp()
• num2str() must be used to convert numbers intro strings,
which are then concatenated with other strings in disp()
>> disp(6)
6
>> disp(['My favourite number is ', a])
My favourite number is
>> disp(['My favourite number is ', int2str(a)])
My favourite number is 6
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25.
Displaying string variables with fprintf()
• There are other display and print functions which do not require
numbers to be converted to strings to display information, e.g.
fprintf()
>> fprintf('My favourite number is %d n', a);
My favourite number is 6
%d – print the value of the variable a as an integer
n – the cursor goes to a new line
Other useful formatting symbols:
%f – float point number
%s – string
t – insert tab
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