INTRODUCTION TO MATLAB

INTRODUCTION TO MATLAB

Introduction What is Matlab? MATrix LABoratory.

MATLAB is a numerical computing environment and programming language (initially written in C). MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages.

MATLAB makes mathematical operations with vectors y matrices. As a particular case, it can also work with scalar numbers, both reals and complexes.

It has packages with specialized functions.

Basic elements of Matlab’s desktop

Command Windows: Where all commands and programs are run. Write the command or program name and hit Enter.

Command History: Shows the last commands run on the Command Windows. A command can be recovered clicking twice

Current directory: Shows the directory where work will be done.

Workspace: To see the variables in use and their dimensions (if working with matrices)

Help (can also be called from within the comand windows)

Matlab Editor: All Matlab files must end in the .m extension.

CommandWindows

Current directory

CommandHistory

Basic elements of Matlab’s desktop

Matlab editor There can not be empty spaces in the name of the Matlab files

Use “main_” for the name of the main programs, for example: main_curvature

Write “;” at the end of a line If you don’t want that the intermediate calculus is written in the window while the program is running

Write “%” at the beginning of a line to write a comment in the program

Write “…” at the end of a line if you are writing a very long statement and you want to continue in the next line

Matlab editorDebugger

Set/Clear breakingpoint: Sets or clears a break point in the line the cursor is placed.Clear all breakingpoints: Deletes all breaking points.

Step: Executes the current line of the program.

Step in: Executes the current line of the program, if the line calls to a function, steps into the function.

Step out: Returns from a function you stepped in to its calling function without executing the remaining lines individually.Continue: Continues executing code until the next breaking pointQuit debugging: Stops the debugger

Intro MATLAB

Variable Basicsno declarations needed

mixed data types

semi-colon suppresses output of the calculation’s result

>> 16 + 24ans = 40

>> product = 16 * 23.24product = 371.84

>> product = 16 *555.24;>> productproduct = 8883.8

Intro MATLAB

Variable Basics

complex numbers (i or j) require no special handling

clear removes all variables;

clear x y removes only x and y

save/load are used to

retain/restore workspace variables

>> clear>> product = 2 * 3^3;>> comp_sum = (2 + 3i) + (2 - 3i);>> show_i = i^2;>> save three_things>> clear>> load three_things>> whoYour variables are:comp_sum product show_i >> productproduct = 54>> show_ishow_i = -1

use home to clear screen and put cursor at the top of the screen

Numbers and operationsBasic Arithmetic Operations:

Addition: +, Substraction -

Multiplication: *, Division: /

Power: ^

Priority Order: Power, division and multiplication, and lastly addition and substraction. Use () to change the priority.

Example: main_number_operations.m. Try the Debugger

Numbers and operationsMatlab Functions:

exp(x), log(x) (base e), log2(x) (base 2), log10(x) (base 10), sqrt(x)

Trigonometric functions: sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), atan2(x) (entre –pi y pi)

Hyperbolic functions: sinh(x), cosh(x), tanh(x), asinh(x), acosh(x), atanh(x)

Other functions: abs(x) (absolute value), int(x) (integer part ), round(x) (rounds to the closest integer), sign(x) (sign function)

Functions for complex numbers: real(z) (real part), imag(z) (imaginary part), abs(z) (modulus), angle(z) (angle), conj(z) (conjugated)

Example: main_number_operations.m

Vectors and matricesDefining vectors:

Row vectors; elements separated by spaces or comas >> v =[2 3 4]

Column vectors: elements separated by semicolon (;)>> w =[2;3;4;7;9;8]

Length of a vector w: length(w)

Generating row vectors: Specifying the increment h between the elements v=a:h:b Specifying the dimension n: linspace(a,b,n) (by default n=100) Elements logarithmically spaced logspace(a,b,n) (n points

logarithmically spaced between 10a y 10b. By default n=50)

Example: main_matrix_operations.m

Vectors and matricesDefining matrices: It’s not needed to define their size before hand (a size can be

defined and changed afterwards).

Matrices are defined by rows; the elements of one row are separated by spaces or comas. Rows are separated by semicolon (;).

» M=[3 4 5; 6 7 8; 1 -1 0]

Empty matrix: M=[ ];

Information about an element: M(1,3), a row M(2,:), a column M(:,3).

Changing the value of an element: M(2,3)=1;

Deleting a column: M(:,1)=[ ], a row: M(2,:)=[ ];

Example: main_matrix_operations.m

Intro MATLAB

Durer’s Matrix: Creation

» durer1N2row = [16 3 2 13; 5 10 11 8];» durer3row = [9 6 7 12];» durer4row = [4 15 14 1];» durerBy4 = [durer1N2row;durer3row;durer4row];» durerBy4

durerBy4 =

16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

Intro MATLAB

Easier Way...durerBy4 = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

» durerBy4r2 = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

durerBy4r2 =

16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

Intro MATLAB

Set FunctionsArrays are ordered sets:

>> a = [1 2 3 4 5]a = 1 2 3 4 5>> b = [3 4 5 6 7]b = 3 4 5 6 7

>> isequal(a,b)ans = 0>> ismember(a,b)ans = 0 0 1 1 1

returns true (1) if arrays are the same size and have the same values

returns 1 where a is in b and 0 otherwise

Intro MATLAB

>> durer = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1]

durer = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

>> % durer's matrix is "magic" in that all rows, columns,>> % and main diagonals sum to the same number>> column_sum = sum(durer) % MATLAB operates column-wise

column_sum = 34 34 34 34

Matrix OperationsMATLAB also hasmagic(N) (N >

2)function

Intro MATLAB

Dot Operator Example>> A = [1 5 6; 11 9 8; 2 34 78]A = 1 5 6 11 9 8 2 34 78>> B = [16 4 23; 8 123 86; 67 259 5]B = 16 4 23 8 123 86 67 259 5

Vectors and matricesDefining matrices:

Generating de matrices:

Generating a matrix full of zeros, zeros(n,m) Generating a matrix full of ones, ones(n,m) Initializing an identity matrix eye(n,m) Generating a matrix with random elements rand(n,m)

Adding matrices: [X Y] columns, [X; Y] rows

Example: main_matrix_operations.m

Operations with vectors and matricesOperating vectors and matrices with scalars:

v: vector, k: scalar:

v+k addition v-k sustraction v*k product v/k divides each element of v by k k./v divides k by each element of v v.^k powers each element of v to the k-power k.^v powers k to each element of v

Example: main_matrix_operations.m

Operations with vectors and matricesOperating vectors and matrices

+ addition – subtraction * matrix product .* product element by element ^ power .^ power element by element \ left-division / right-division ./ y .\ right and left division element by element Transposed matrix: B=A’ (in complex numbers, it returns the

conjugated transposed, to get only the trasposed: B=A.’)

Example: main_matrix_operations.m

Functions for vectors and matrices sum(v) adds the elements of a vector

prod(v) product of the elements of a vector

dot(v,w) vectors dot product

cross(v,w) cross product

mean(v) (gives the average)

diff(v) (vector whose elements are the differenceof the elements of v)

[y,k]=max(v) maximum value of the elements of a vector (k gives the position), min(v) (minimum value). The maximum value of a matrix M is obtained with max(max(M)) and the minimum with min(min(v))

Some of these operations applied to matrices, give the result by columns.

Functions for vectors and matrices [n,m]=size(M) gives the number of rows and columns

Inverted matrix: B=inv(M), rank: rank(M)

diag(M): gives the diagonal of a matrix. sum(diag(M)) sums the elements of the diagonal of M. diag(M,k) gives the k-th diagonal.

norm(M) norm of a matrix (maximum value of the absolute values of the elements of M)

flipud(M) reorders the matrix, making it symmetrical over an horizontal axis. fliplr(M) ) reorders the matrix, making it symmetrical over a vertical axis.

[V, landa]=eig(M) gives a diagonal matrix landa with the eigenvalues, and another V whose columns are the eigenvectors of M

Example: main_matrix_operations.m

Data input and output

Saving to files and recovering data:

save –mat file_name matrix1_name, matrix2_name

load –mat file_name matrix1_name, matrix2_name

save file_name matrix1_name –ascii (saves 8 figures after the decimal point)

save file_name matrix1_name –ascii –double (saves 16 figures after the decimal point)

Example: main_matrix_operations.m

Matlab Files Program files: Scripts

They are built with a series of commands. The main file will be named main_name.m

Function files

To create your own functions. They are called from within the scripts.

The first line is executable and starts with the word function as showed:

function [output_arg1, output_arg2]=function_name(input_arg1, input_arg2, …, parameters)

The file must be saved as function_name.m

Example: main_plot_sine.m. Use “Step in” in Debugger to enter this function

Intro MATLAB

Vectorization Example*>> type slow.mtic;x=0.1;for k=1:199901 y(k)=besselj(3,x) +

log(x); x=x+0.001;endtoc;>> slowElapsed time is 17.092999 seconds.

*times measured on this laptop

>> type fast.mtic;x=0.1:0.001:200;y=besselj(3,x) + log(x);toc;>> fastElapsed time is 0.551970 seconds.

Roughly 31 times faster without use of for loop

Intro MATLAB

Easy 2-D Graphics>> x = [0: pi/100: pi]; % [start: increment: end]>> y = sin(x);>> plot(x,y), title('Simple Plot')

Intro MATLAB

Adding Another Curve

Line color, style, marker type, all within single quotes; type

>> doc LineSpec

for all available line properties

>> z = cos(x);>> plot(x,y,'g.',x,z,'b-.'),title('More complicated')

Intro MATLAB

You can save and run the file/function/script in one step by clicking here

Tip: semi-colons suppress printing, commas (and semi-colons) allow multiple commands on one line, and 3 dots (…) allow continuation of lines without execution

m-file Editor Window

Intro MATLAB

function [a b c] = myfun(x, y)b = x * y; a = 100; c = x.^2;

>> myfun(2,3) % called with zero outputsans = 100>> u = myfun(2,3) % called with one outputu = 100>> [u v w] = myfun(2,3) % called with all outputsu = 100v = 6w = 4

Functions – First ExampleWrite these two lines to a file myfun.m and save it on MATLAB’s path

Any return value which is not stored in an output variable is simply discarded

ProgrammingLoops

for k=n1:incre:n2

end

for k=vector_column

end

while

end

Example: main_loops

Intro MATLAB

for Loop>> for i = 2:5 for j = 3:6 a(i,j) = (i + j)^2 end end>> aa = 0 0 0 0 0 0 0 0 25 36 49 64 0 0 36 49 64 81 0 0 49 64 81 100 0 0 64 81 100 121

Intro MATLAB

while Loop>> b = 4; a = 2.1; count = 0;>> while b - a > 0.01 a = a + 0.001; count = count + 1; end>> countcount = 1891

ProgrammingConditional control structures

Logical operators: >, <, >=,<=,== (equal) | (or), &(and) ~ (no), ~= (not equal)

Example: main_conditional

ifend

ifelseend

ifelseifelseend

Intro MATLAB

if/elseif/else Statement>> A = 2; B = 3;>> if A > B 'A is bigger' elseif A < B 'B is bigger' elseif A == B 'A equals B' else error('Something odd is happening') endans =B is bigger

ProgrammingStructures of control condicionated: switch

switch is similar to a sequence of if...elseif

Example: main_conditional

switch_expresion=case_expr3 %example

switch switch_expresion

case case_expr1,actions1

case {case_expr2, case_expr3,case_expr4,...}actions2

otherwise, % option by defaultactions3

end

Intro MATLAB

switch Statement>> n = 8n = 8>> switch(rem(n,3)) case 0 m = 'no remainder' case 1 m = ‘the remainder is one' case 2 m = ‘the remainder is two' otherwise error('not possible') endm =the remainder is two