intro duca om at lab

7/29/2019 Intro Duca Om at Lab

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Breve Introduo Programao em MATLAB

Aulas Prticas de Aprendizagem Automtica

Ano Lectivo 2006/2007

Susana Nascimento

Departamento de Informtica

[email protected]


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Introduo MatLab AA-0607 2

Introduo ao MatLabO ambiente de trabalho das aulas prticas: MATLAB.

O MATLAB um ambiente de programao de alto nvel paraaplicaes Cientficas e de Engenharia.

Facilidades

Oferece um leque alargado de bibliotecas de funes pr-

definidas.

Muito amigvel em funcionalidades grficas para Visualizao de

Dados.

Largamente divulgado em Universidades e Laboratrios de

Investigao.

Muito conveniente para o desenvolvimento efics de prottipos.
http://www.mathworks.com/http://www.mathworks.com/


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MATLAB the Language

of Technical Computing

Simulink for Model-based and

System-Level Design

Site para Consulta da Linguagem:http://www.mathworks.com/access/helpdesk/help/techdoc/learn_matlab/learn_matlab.shtml
http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/access/helpdesk/help/techdoc/learn_matlab/learn_matlab.shtmlhttp://www.mathworks.com/access/helpdesk/help/techdoc/learn_matlab/learn_matlab.shtmlhttp://www.mathworks.com/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/http://www.mathworks.com/products/


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Sumrio

Tipos de dados arrays: caracteres, numricos, estruturados,

Operadores

aritmtica, relacionais, lgicos.

Fluxo de Controlo condicionais, case, while, etc.

M-functions

sintaxe

Exemplos e funes simples


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Tipos de Dados em MatLab

Array

Char Numeric Structure Cell

a image.width = 120

image.name = face1

Uint8

(8 bit unsigned integer,from 0 to 255,

e.g., image gray scales)

Double

e.g., 3.2567

(8 bytes)


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Uint8 e Doubles

Double

Maioria funes MATLAB

doubles como argumento de entrada

return double


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Uint8 e Doubles

Double

Maioria funes MATLAB

doubles como argumento de entrada

return double e.g.,

Necessidade de converter uint8 para

double antes de realizar operaomatemtica

a = 1:10

a =

1 2 3 4 5 6 7 8 9 10

b = uint8(a)

b =

1 2 3 4 5 6 7 8 9 10 whos

Name Size Bytes Class

a 1x10 80 double array

b 1x10 10 uint8 array

b*2

??? Error using ==> *Function '*' not defined for variables of class 'uint8'.

(double(b))*2

ans =

2 4 6 8 10 12 14 16 18 20


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Tipo Char

c = ['hello'];

whos


c 1x5 10 char array

Grand total is 5 elements using 10 bytes

c(1)

ans =

h


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Tipo de Dados Char

c = ['hello'];

whos


c 1x5 10 char array


c(1)

ans =

h

d = [c,' again'];

d

d =

hello again

b = ['hello';'again']; size(b)

ans =

2 5

b

b =

hello

again


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Tipo de Dados Struct

image.name = 'Tom';

image.height = 3;

image.width = 3;

image.data = [8 10 2; 22 7 22; 2 4 7];

whos


image 1x1 590 struct array



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Tipo de dados Arrays de Estruturas

image(1) = image;

image(2).name = 'Mary'

image(2).width = 4;

image(2).height = 4;

whos




image

image =

1x2 struct array with fields:

name

height

width

data


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Arrays de Estruturas image(1) = image;

image(2).name = 'Mary'

image(2).width = 4;

image(2).height = 4;

whos




image

image =

1x2 struct array with fields:

name

height

width

data

image(2)

ans =

name: 'Mary'

height: 4

width: 4data: []

image(1)

ans =

name: 'Tom'height: 3

width: 3

data: [3x3 double]


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Operadores

Aritmticos

Computao numrica, e.g., 2^10

Relacional Comparao quantitativa de operandos

e.g., a < b

Lgico AND, OR, NOT

Devolve varivel Booleana, 1 (TRUE) ou 0 (FALSE)


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Operadores Aritmticos

Transpose, a

Power, a^2

Addition, multiplication, division

a(1)*b(2) a*b

works if a and b are matriceswith appropriate dimensions(columns(a) = rows(b))

a.*b (element by element)

except for matrix operations, mostoperands must be of the same size,unless one is a scalar


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Operadores Aritmticos

Transpose, a

Power, a^2

Addition, multiplication, division

a(1)*b(2) a*b

works if a and b are matriceswith appropriate dimensions(columns(a) = rows(b))

a.*b (element by element)

except for matrix operations,operands must be of the same size,unless one is a scalar

a = [2 3];

b = [4 5];

a(1)*b(2)

ans =

10

a*b??? Error using ==> *

Inner matrix dimensions must agree.

a*b'

ans =

23

a.*bans =

8 15

b/2

ans =

2.0000 2.5000


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Operadores Relacionais

=, ==, ~=

compare corresponding elements

of arrays with same dimensions

if one is scalar, one is not, the scalaris compared with each element

result is, element by element, 1 or 0


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Operadores Relacionais

=, ==, ~=

compare corresponding elements

of arrays with same dimensions

if one is scalar, one is not, the scalaris compared with each element

result is element by element 1 or 0

a

a =

2 3

b

b =

4 5

a > b

ans =

0 0

b > a

ans =1 1

a > 2

ans =

0 1


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Fluxo de Controlo

If, else, endif

if index


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Programao em MATLAB

File with MATLAB code: M file, e.g., sort.m

Two kinds of M-files

scripts

no input arguments supplied no output arguments returned

operates on data in workspace

functions

can accept input arguments and return output arguments

internal variables local to function by default

useful for extending functionality of MATLAB


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Exemplo de Script MATLAB

% script randVect

% Script simples para gerar um vector de n n. aleatrios.

% ilustar aplicando:

% (a) loops for, and (b) chamada directa a uma funo.

%

%

Comentar o cdigo


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% script randVect% Script simples para gerar um vector de n n. aleatrios.



%

%

n = 100000; % the number of points for the "for loop

y = zeros(n,1); % preallocate memory for yfprintf('Simulating %d random numbers.....\n\n',n);

Inicializao de variveis

Print de informao para o ecran


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% script randVect% Script simples para gerar um vector de n n. aleatrios.



n = 100000; % the number of points for the "for loop

y = zeros(n,1); % preallocate memory for yfprintf('Simulating %d random numbers.....\n\n',n);

% first do the calculation using a "for loop"

fprintf('For loop calculations.....\n');

tic % set the timer

for i=1:n

y(i) = rand(1);

endtotal = sum(y);

fprintf('Sum of %d random numbers = %f\n',n,total);

t1 = toc; % read the time elapsed since "tic" (in seconds)

fprintf('Time taken, using for loop = %6.5f microseconds\n\n', (t1)*1000);

...

(1) Calcula n n. aleatrios

e correspondente soma usando loop for;

(2) Calcular tempo execuo;

(3) mostrar resultado


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% now do the calculation using vectorization

fprintf('Vectorization calculations.....\n');

tic % reset the timer

z = rand(n,1);total = sum(z);

fprintf('Sum of %d random numbers = %f\n',n,total);

t2 = toc; % read the time elapsed since "tic" (in seconds)

fprintf('Time taken, using vectorization = %6.5f microseconds\n', (t2)*1000);

(1) Calcula n n. aleatrios

e correspondente soma usando funo rand;(2) Calcular tempo execuo;

(3) mostrar resultado


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Gerador de Nmeros (pseudo)aleatrios

em MatLab Gera sequncia (of length n) de ns pseudoaleatrios:

Gerao da sequncia: x(i) = mod(a * x(i-1), m)

Inicializao com valor (seed)

help rand

RAND Uniformly distributed random numbers.

RAND produces pseudo-random numbers. The sequence of numbers

generated is determined by the state of the generator. Since MATLAB

resets the state at start-up, the sequence of numbers generated will

be the same unless the state is changed.

S = RAND('state') is a 35-element vector containing the current stateof the uniform generator. RAND('state',S) resets the state to S.

RAND('state',0) resets the generator to its initial state.

RAND('state',J), for integer J, resets the generator to its J-th state.

RAND('state',sum(100*clock)) resets it to a different state each time.

This generator can generate all the floating point numbers in the

closed interval [2^(-53), 1-2^(-53)]. Theoretically, it can generate

over 2^1492 values before repeating itself.


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Exemplo de Funo MATLAB

function [meanr, stdr, z] = simulate(n);

Identificador de funo

Lista de valores de output devolvidos

Nome

funo

Lista de argumentos de entrada,

(separados por vrgula)


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Funo MATLAB

Definio de linha de funo

required of all functions

Lista de inputs e outputs

comma delimited: [y, z] = average(a, b, c)

for more than one output, outputs enclosed in square brackets Variveis de entrada

function variables are local to the function

input variables are readable to the function: local copies are made if theinputs need to be changed

Escopo MATLAB searches in this order:

variable name, subfunction, current directory, MATLAB search path


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function [meanr, stdr, z] = simulate(n);%

% Funo que simula um vector de n valores uniformemente distribuidos

% calcula e devolve: mdia e desvio padro dos nmeros.

%

%

% INPUTS:

% n: number (inteiro) de ns (pseudo)aleatrios a gerar.

%% OUTPUTS:

% meanr: mdia dos n ns (pseudo)aleatrios

% stdr: desvio padro dos ns (pseudo)aleatrios

% z: array n x 1 de ns (pseudo)aleatrios

Funes comentadas


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function [meanr, stdr, z] = simulate(n);%

% Funo que simula um vector de n valores uniformemente distribuidos

% calcula e devolve: mdia e desvio padro dos nmeros.

%

%

% INPUTS:


%% OUTPUTS:




% simple error checking to check n is a positive integerif (rem(n,1)~=0) | n


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fprintf('Simulating %d random numbers.....\n\n',n);

% generate the n random numbers

z = rand(n,1);

% calculate the mean and standard deviationmeanr= mean(z);

fprintf('Mean of the %d random numbers = %f\n',n,meanr);

stdr= std(z);

fprintf('Standard deviation of the %d random numbers = %f\n',n,stdr);

Simular os nmeros aleatrios.

No necessita de funo return explcita

Valores no devolvidos so locais funo


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Chamada da Funo MATLAB

[m, s] = simulate(1000000);

Simulating 1000000 random numbers.....

Mean of the 1000000 random numbers = 0.499702

Standard deviation of the 1000000 random numbers = 0.499702

[m, s] = simulate(1000000);

Simulating 1000000 random numbers.....

Mean of the 1000000 random numbers = 0.499684

Standard deviation of the 1000000 random numbers = 0.288456

m

m =

0.4997

s

s =

0.2885


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Outra Funo MATLABfunction [meanr, stdr, z] = simplot(n,plotflag);

%% Funo que simula um vector de n valores uniformemente distribuidos

% calcula e devolve: mdia e desvio padro dos nmeros. Se

% var plotflag for 1 feito o plotting do histogram dos ns gerados.

%

% INPUTS:


% plotflag: se plotflag=1, desenhar histograma de z,% c.c. no.

%

% OUTPUTS:




% simple error checking to check n is a positive integer

if (rem(n,1)~=0) | n


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Simplot.m (cont.)

fprintf('Simulating %d random numbers.....\n\n',n);

% generate the n random numbers

z = rand(n,1);

% calculate the mean and standard deviation

meanr= mean(z);

fprintf('Mean of the %d random numbers = %f\n',n,meanr);stdr= std(z);

fprintf('Standard deviation of the %d random numbers = %f\n',n,stdr);

if nargin>1 & plotflag==1

figure

hist(z, max(n/100,10))

end Novo cdigo

Nargin n. de argumentos de entrada

sintaxe: hist(data vector, number of bins)


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Fazer o plotting da mdia amostral

em funo de n

Extender simplot.m

Para cada valor i = 1 n, calcular

mean(i) = [sum (x(i) x(i)) ]/I

mean(i) deve convergir para true mean0.5 para n>>>

Lei dos grandes nmeros da estatstica

Fazer plot para visualizar

Caractersticas de plotting acrescidas

grids, log axes, labels, titles


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Cdigo acrescentado ao simplot.m

if nargin>1 & plotflag==1

figure % figure for a histogram to see how uniform the numbers are

hist(z,max(n/100,10))

figure % figure to see visually how the sample mean converges to 0.5

cs = cumsum(z); % generate a vector of cumulative sums

ns = 1:n; % generate a vector of sample sizes

runningmean = cs./ns; % calculate the running meanplot(ns,runningmean);

%runningmean = cs./ns';

%semilogx(ns,runningmean);

%grid;

%axis([1 n 0 1]);

%xlabel('Number of random numbers generated');

%ylabel('Mean value');%title('Convergence of sample mean to true mean');

end


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Exerccios


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1 - Para as matrizes A e B, definidas a baixo, execute as seguintesoperaes e interprete os resultados.

a) A+B b) A*B c) A.*B d) A.^2e) A^2 f) A*A g) inv(A) h) inv(A)*A

i) A\A j) A/A k) A/Aeye(3)

l) A*inv(A)eye(3)

073

110013

113

210321

BA


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2Utilizando as funes zeros, onese eyeconstrua as seguintesmatrizes:

10

01

1

1

111

111111

0000

0000

0000

0000

DCBA

zeros(4) ones(3) ones(2,1) eye(2)


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3A partir das matrizes A e B do exerccio 2 e D = [A B]verifique quais so as operaes vlidas.

a) A*D b) D*A c) D*A d) A*D*B

e) A*B*D f) A*D g) D(:,1:3)*A

h) D(1:3,:)*A


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4A partir de um conjunto 500 de valores aleatrios comdistribuio normal (mdia 10 e desvio padro 2)determine a percentagem de valores:

a) superiores a 10b) entre 8 e 12;

c) entre 6 e 14;

d) entre 6 e 14;

e) superiores a 15.

5- Represente graficamente a funo de densidade de

probabilidade da distribuio normal reduzida, nointervalo de -3 a 3.

2

2

2

1)(

x

exf


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I d M L b AA 0607 41

6 A partir de um conjunto de 100 valores aleatrios com mdia 500 e desviopadro 100, representando uma srie de valores anuais de precipitao entre1900 e 1999, elabore um programa que:

a) Represente graficamente esta srie temporal (Figura 1).

b) Conte o nmero de ocorrncias em que a precipitao excedeu o valor mdio mais duasvezes o desvio padro (valores considerados anmalos).

c) Represente no grfico, atravs de crculos pretos, os valores anteriores.

d) Utilizando a funo hist, construa um histograma, com 20 classes, que represente a

distribuio da precipitao (Figura 2).

1900 1920 1940 1960 1980 2000250

300

350

400

450

500

550

600

650

700

750

i

i

Figura 1

250 300 350 400 450 500 550 600 650 7000

2

4

6

8

10

12

14

Figura 2

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