08_GENN004m_VectorizedCode

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GENN004: Introduction to Computers 09-Feb-

Vectorized Code

Vectorized Code

Outline

Operations on Vectors and Matrices

Vectors and Matrices as Function Arguments

Logical Vectors


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Vectorized Code

Operations on Vectors and Matrices

v=[3 7 2 1]

for i = 1:length(v)

v(i) =v(i) * 3;

End

v= [3 7 2 1];

>> v=v*3

9 27 6 3

mat = [4:6; 3:1:1]

mat =

4 5 6

3 2 1

>> mat * 2

ans =

8 10 12

6 4 2

Scalar OperationsOperation Algebraic Form MATLAB Form

Addition a + b a + b

Subtraction a b a b

Multiplication a b a * b

Divisiona

ba / b or b \ a

Exponentiation ab a ^ b

Note that b \ a is called left divisionThis is equal to a / b


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Vectorized Code

Array Operations

Operation MATLAB form Comments

Addition a + b Adds each element in a to the element with the same

index in b

Subtraction a b Subtracts from each element in a the element with the

same index in b

Multiplication a .* b Multiplies each element in a with the element in b

having the same index

Either a or b can be a scalar

Right Division a ./ b Element by element division ofa and b:

a(i,j) / b(i,j) provided a, b have same shape


Left Division a .\ b Element by element division ofa and b:

b(i,j) / a(i,j) provided a, b have same shape


Exponentiation a .^ b Element by element exponentiation ofa and b:

a(i,j) ^ b(i,j) provided a, b have same shape


Array and Matrix Operations

Array Operations are performed element-by-element Both arrays must have the same number of rows and

columns

Matrix Operations follow rules of linear algebra These rules are specific to each operation

Useful after Linear Algebra Course

Be careful not to confuse these two operation sets Since a matrix is an array in MATLAB, many times picking

the wrong operation wont produce an error as it istechnically valid but logically incorrect


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Vectorized Code

Operations Rules Examples

v=[3 7 2 1];

>> v ^ 2

??? Error using ==> mpower

Inputs must be a scalar and a square matrix.

To compute elementwise POWER, use POWER (.^)instead.

>> v .^ 2

ans =9 49 4 1

Operations Rules Examples

v1 = 2:5;

v2 = [33 11 5 1];

>> v1 * v2 %Error why

>> v1*v2 % what is the output

>> v1 .* v2 % v1 and v2 must have same size


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Vectorized Code

Vectors and Matrices as Function

Arguments Many functions accept scalars as input

Some functions work on arrays

Most scalar functions accept arrays as well The function is performed on each element in the array

individually

Try x = pi/2; y = sin(x) in MATLAB

Now try

x = [0 pi/2 pi 3*pi/2 2*pi];y = sin(x)

Functions Examples

v1=[1 3 2 7 4 -2]

v2=[5 3 4 1 2 -2]

[mx mxi]=max(v1) 7 4

v=v1-v2 -4 0 -2 6 2 0

v=sign(v1-v2) -1 0 -1 1 1 0

x=sum(v1) 15

v=find(v1>3) 4 5


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Vectorized Code

Logical Vectors

v1=[1 3 2 7 4 -2]

v2=[5 3 -4 -1 2 -2]

v=v1>0 1 1 1 1 1 0

v=v2>0 1 1 0 0 1 0

a=vec(v) 5 3 2

x=sum(v2>0) 3

v=true(1,5) 1 1 1 1 1

v=false(1,5) 0 0 0 0 0

x=all(v) 1 (are all ones?)

y=any(v) 0 (any one?)

Example: Vertical Motion

% Vertical motion under gravity

g = 9.81; % acceleration due to gravity

u = 60; % initial velocity in metres/sec

t = 0 : 0.1 : 12.3; % time in seconds

s = u * t g / 2 * t . 2; % vertical displacementin metres

plot(t, s), title( Vertical motion under gravity )

xlabel( time ), ylabel( vertical displacement )

grid

disp( [t s] ) % display a table

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08_GENN004m_VectorizedCode