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Advanced MATLAB

Vectors and matrices

fprintf

Cell arrays

Structures

Flow of control

Vectorization

Functions

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Using an Index to Address Elements of an Array

In the C/C++ programming language, an index starts at 0 and elements of an array are addressed with square brackets [∙]:

8 2 -3 7 -1

x[0] x[1] x[2] x[3] x[4]

↑ ↑ ↑ ↑ ↑

In MATLAB, an index starts at 1 and elements of an array are addressed with parentheses (∙):

8 2 -3 7 -1

x(1) x(2) x(3) x(4) x(5)↑ ↑ ↑ ↑ ↑

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Columns, Rows, and Pagesfor a 2-Dimensional Array (Matrix)

x(m,n)

m is the row numbern is the column number

x(m,n) is the element of the matrix x that is:

in the mth rowin the nth column

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Columns, Rows, and Pagesfor a 3-Dimensional Array

x(m,n,p)

m is the row numbern is the column numberp is the page number

x(m,n,p) is the element of the 3-dimensional array x that is:

in the mth rowin the nth columnon the pth page

% scalars, vectors, matrices, 3-dimensional arrays

a1 = zeros(1,1); % scalardisp(['a1: ',num2str(size(a1))])a2 = zeros(1,4); % vectordisp(['a2: ',num2str(size(a2))])disp(a2)a3 = zeros(2,2); % matrixdisp(['a3: ',num2str(size(a3))])disp(a3)a4 = zeros(2,2,3); % 3-dimensional arraydisp(['a4: ',num2str(size(a4))])

a1: 1 1a2: 1 4 0 0 0 0

a3: 2 2 0 0 0 0

a4: 2 2 3

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Exercise

1. Create a row vector of length 5. Use any values you want for the elements.

2. Display the size of this vector.

3. Create a matrix of all 1s that has 3 rows and 4 columns. (Use the function ones.)

4. Display the size of this matrix.

% Editing arrays with parentheses ()

B = [1 2 3 4; 5 6 7 8];disp('before:')disp(B)b = [0 0]';B(:,4) = b;disp('after:')disp(B)

before: 1 2 3 4 5 6 7 8

after: 1 2 3 0 5 6 7 0

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Exercises

Create a matrix of zeros with 3 rows and 4 columns.

Create a matrix with 2 rows and 2 columns, with all elements equal to 5.

Insert the smaller matrix into the lower right-hand corner of the larger matrix.

Hints: zeros() 5*ones()

% array versus matrix multiplication

a = [1 2; 3 4];disp(a*a) % matrix multiplicationdisp(a.*a) % array multiplication

7 10 15 22

1 4 9 16

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% array multiplication, division, and power

x = [1 4; 9 8];y = [1 2; 3 4];disp(x.*y) % array multiplication: .*disp(x./y) % array division: ./disp(x.^2) % array power: .^

1 8 27 32

1 2 3 2

1 16 81 64

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Exercise

1. Create a row vector containing 4 elements. Use any values you want.

2. Create a second row vector of the same length, using any values you want.

3. Show the result of an array multiplication of these two vectors.

4. Show the result of doing an array division of one of these vectors by the other.

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fprintf Write data to text file

Syntax fprintf(fileID,formatSpec,A1,...,An)

My comments:

fileID not used when printing to Command WindowformatSpec enclosed in single quote marks: ‘string’A1,…,An are variables (or numbers) to be printed

MATLAB Documentation for fprintf

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% print pi to 7 decimal places

fprintf('%9.7f\n',pi)% f fixed-point number% a.b field width = a characters% b digits to the right of decimal point% \n newline

3.1415927

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% print a column of numbers

x = [1.34, -2.45, 0.91];fprintf('%5.2f\n',x) % There can be 2 characters on left.

1.34-2.45 0.91

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Exercise

Print as a fixed-point number to 12 decimal places.

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% print signed integers with field width 4

x = [198, -230, 3];fprintf('%4d\n',x)

198-230 3

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Exercise

Create a vector containing the (integer) elements: 0, -1, 2, -3.

Print these numbers in a column with right justification.

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Cell Arrays

A cell array can combine different data having different data types all in one array.

A cell within a cell array is referenced by an index.

A cell array is frequently an input argument of a function. This permits a collection of data (even of different data types) to be input to the function using a single argument.

% create a cell array using braces {}

y = {'scores',[73,38,81,55]};y{3} = 'success';celldisp(y)

y{1} = scores y{2} = 73 38 81 55

y{3} = success

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% What is in the second cell of the cell array y?

disp(y(2))

[1x4 double]

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% What values are in the second cell of the cell array y?

disp(y{2})

73 38 81 55

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% print values in the cell array y

fprintf('%s: ',y{1})fprintf('%2d ',y{2})fprintf('\n')

scores: 73 38 81 55

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% create a cell array using the function cell()

x = cell(1,2);x{1} = 'salary';x{2} = 45000;celldisp(x)

x{1} = salary x{2} = 45000

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Exercise

1. Create a cell array that contains three cells: A string containing your first name, An unsigned integer (uint8) containing your age, and A vector containing any two numbers between 0 and 1.

2. Use celldisp to display the contents of the cell array.

3. Extract the string in the first cell.

4. Extract your age.

5. Extract the first number in the vector.

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Structures

A structure can combine different data having different data types under one banner.

Each component of a structure is called a field.

A structure array is an array, each element of which is a structure, and all structures in the structure array have the same set of fields.

% simple structure

a.label = 'x';a.vect = 0:5;disp(a)

label: 'x' vect: [0 1 2 3 4 5]

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Exercise

1. Create a structure that contains two fields: a name (string) and a number. Place any values you want into these fields.

2. Use disp to display the fields of this structure.

% create structure array using function struct()

c = struct('label',{'x','y'},'vect',{0:5,0:10});disp(c)disp(c(1))disp(c(2))

1x2 struct array with fields: label vect

label: 'x' vect: [0 1 2 3 4 5]

label: 'y' vect: [0 1 2 3 4 5 6 7 8 9 10]

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% create 1 x 2 structure array

c = struct('class',{71,72},'language',{'C','MATLAB'});for n = 1:2 fprintf('ECE %2d: %s\n',c(n).class,c(n).language)end

ECE 71: CECE 72: MATLAB

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% structure array

b(1).label = 'x';b(2).label = 'y';b(1).vect = 0:5;b(2).vect = 0:10;disp(b)disp(b(1))disp(b(2))

1x2 struct array with fields: label vect

label: 'x' vect: [0 1 2 3 4 5]

label: 'y' vect: [0 1 2 3 4 5 6 7 8 9 10]

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Exercise

1. Create a 1x2 structure array that contains two fields: a string containing a first name, and a number containing an age (in years)Provide a value for each field of each structure in the structure array.

2. Use a loop and the fprintf function to print the data in the structure array.

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Flow of Control

Redirectionifelseelseif

Loopsfor

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Relational Operators

x == y equal to

x ~= y not equal to

x < y less than

x <= y less than or equal to

x > y greater than

x >= y greater than or equal to

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Logical Operators

&& (short-circuit) and

|| (short-circuit) or

% if

for k = 0:3 if k == 2 disp(k) endend

2

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% if and else

for k = 0:3 if k >= 2 disp(k) else disp([num2str(k),' < 2']) endend

0 < 21 < 2 2

3

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% elseif

for k = 0:3 if k < 2 disp([num2str(k),' < 2']) elseif k == 2 disp(k) else disp([num2str(k),' > 2']) endend

0 < 21 < 2 2

3 > 2

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% or

for k = 0:4 if k < 2 || k > 3 disp(k) endend

0

1

4

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% and (input number is 3)

x = input('number: ');if x >= 1 && x <= 5 disp('between 1 and 5')end

between 1 and 5

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Exercise

Create a script that does the following:

1. Get a number (x) from the user.2. If x is less than or equal to 3, set y to 3.3. If x is greater than or equal to 6, set y to 6.4. Otherwise, set y to x.5. Display y.

% Compare 2 methods of printing a vector

ticfor k = 0:9 % within this loop, k is a scalar fprintf('%1d ',k)endfprintf('\n')toc

ticm = 0:9;fprintf('%1d ',m) % This is preferred. It is faster.fprintf('\n')toc

0 1 2 3 4 5 6 7 8 9 Elapsed time is 0.000264 seconds.0 1 2 3 4 5 6 7 8 9 Elapsed time is 0.000077 seconds.

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% Add all even integers 0 through 100

x = 0;for m = 2:2:100 % even integers, 2 through 100 x = x + m;endfprintf('%4d\n',x)

2550

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Exercise

Calculate the sum of all odd integers from 1 through 101.

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Vectorization

Preallocation of memory

Vectorizing Loops

% Preallocation of memory

tic % SLOW: frequent lengthening of xx(1) = 1;x(2) = 1;for n = 3:100000 x(n) = x(n-1)*x(n-2);endtoc

tic % FAST: preallocation of memory for xy = ones(1,100000);for n = 3:10000 y(n) = y(n-1)*y(n-2);endtoc

Elapsed time is 0.526046 seconds.Elapsed time is 0.021451 seconds.

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% Vectorizing a loop: linspace

tic % slowphi = 0;dphi = 2*pi/100;g = zeros(1,1001);for n = 1:1001 g(n) = sin(phi); phi = phi + dphi;endtoc

tic % fastphi = linspace(0,20*pi,1001);h = sin(phi);toc

Elapsed time is 0.002522 seconds.Elapsed time is 0.000136 seconds.

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Exercise

Here is one way to generate samples of a sinewave:

for n = 1:8 x(n) = sin(pi*(n-1)/4);end

Enter the above code and display the results. Then vectorize this code and verify that your vectorized code gives the same results.

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Functions

Function m-file

Local variables

Functions with multiple inputs/outputs

function v = sphereVol(r)% calculates the volume of a sphere% input r = radius% output v = volumec = 4/3;v = c*pi*(r^3);end % sphereVol

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Local Variables

Variables appearing in a function are local. These local variables do not appear in the MATLAB workspace and are not visible outside of the function in which they occur. For example, a variable c in the MATLAB workspace will be unaffected by a (local) variable c that appears within a function. Within the function, the local c is recognized and the workspace c is not. When the function returns, the local c is forgotten and the workspace c is again recognized.

The input arguments of a function have local names. When the function returns, these local names are forgotten.

The output variables of a function have local names. The values of these output variables are returned to the caller; however, the local names of these output variables are forgotten.

% Script that calls the function sphereVol

c = 2;radius = 1;vol = sphereVol(radius);fprintf('c = %3.1f, vol = %5.2f\n',c,vol)whos

c = 2.0, vol = 4.19 Name Size Bytes Class Attributes

c 1x1 8 double radius 1x1 8 double vol 1x1 8 double

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Exercise

1. Create a function m-file that computes the surface area of a sphere. There will be one input, the radius, and one output, the surface area.

2. Create a script m-file that calls your function m-file.

function [radius, angle] = rect2polar(x, y)% converts the (x,y) coordinates to polar coordinates% inputs: rectangular coordinates x and y% outputs:% radius = distance from origin% angle = angle (rad) measured counterclockwise from x axisradius = sqrt(x.^2 + y.^2);angle = atan2(y,x);end % rect2polar

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% Rectangular to polar coordinate conversions

x = linspace(1,0,5);y = linspace(0,1,5);[r,theta] = rect2polar(x,y);table = [x; y; r; theta];fprintf(' x y r theta\n')fprintf('%5.2f %5.2f %5.3f %5.3f\n',table)

x y r theta 1.00 0.00 1.000 0.000 0.75 0.25 0.791 0.322 0.50 0.50 0.707 0.785 0.25 0.75 0.791 1.249 0.00 1.00 1.000 1.571

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Exercise

1. Create a function m-file that takes two inputs and produces two outputs, where the inputs are the polar coordinates ( and ) of a point in 2-dimensional space and the outputs are the rectangular coordinates ( and ).

2. Make sure to include some comment lines, including an H1 line.

3. Create a script m-file that calls your function m-file.