Kursus Matlab di Jakarta Selatan KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060: GRAPHICS & OTHER MATLAB FEATURES KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

GRAPHICS & OTHER MATLAB FEATURES

% Author: Spike

% Date: 25/3/1999

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function y=mult(varargin)

if nargin>0

y=varargin{1};

for index=2:nargin

y=y.*varargin{index};

end;

>> mult(5,6,7,8)

ans =

1680

>> mult([1 2],[3 4],[5 6])

ans =

15 48

25.16 Sub-functions

• A function existing in its own M-file is visible to all other functions

- can be called by any function (or from main command window)

• At times this global visibility is not desirable:

- some functions are very specific to a particular task and should not be used for anything else

• Matlab allows hiding of functions by placing multiple functions, all in the same file:

- the first function is globally visible (can be called by anyone)

- the 2nd and subsequent functions in the same file can only be called by those functions in that file

• For example the temperature example from the previous lecture might be better with only the main program dailyTemps visible

- change dailyTemps from a script file to a function

- place all the other functions (TempTable etc.) in the dailyTemps.m file after the dailyTemps function

25.17 Review

• Formal vs. actual parameters and returned values

• Pass by value vs. pass by reference

• Function workspaces & scope rules

• Run-time structure & the stack

• Return, error & warning

• Variable numbers of parameters & returned values

• Global variables

• Efficiency issues

• Sub-functions

26 GRAPHICS & OTHER MATLAB FEATURES

• Matlab is a rich environment that has continued to evolve (and grow!) across its lifetime

• This course has concentrated on Matlab as an introductory programming environment for engineers

• Therefore there are many aspects and facets of Matlab that have not been covered during the course

• Today’s lecture briefly highlights a number of Matlab’s major features that have not been covered in the course

- fair emphasis on graphics capabilities

Reference:

For Engineers (Ch. 1, 5, 6, 9, 10, 11)

Mastering (Ch. 12, 18-20, 22-27, 30, 32-33)

Student (Ch. 14-22)

26.1 Motivation

• Matlab is an extremely rich programming language and environment

- many features that could not be adequately covered in such a short course

• Data visualisation is a vital tool of scientists and engineers

- graphical 2D and 3D representation of data

- Matlab incorporates many graphical routines

• Matlab incorporates many in-built functions of high utility to scientists and engineers

- built-in knowledge of problem domains which can be employed with little preparation

- students are likely to employ these additional features of Matlab in future courses and in their careers.

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26.2 2D Graphics –plot

• Most commonly used and versatile function for plotting 2D data is plot()

• plot() has many variants, common forms of usage are:

plot(x_vals,y_vals)

plot(x_vals,y_vals,format)

• Basic form is a line plot connecting values in 2D space.

EDU» x=-2*pi:0.1:2*pi;y=cos(x);z=sin(x);

EDU» plot(x,y,'ms-',x,z,'bp:');

EDU» xlabel('Angle (Radians)'); title('Sine vs. Cosine');

26.3 Axes & Labels

• A useful figure not only contains an image of the raw data but also meaningful labels for the axes, a title and other relevant data.

• Matlab incorporates a number of commands for labelling and modifying existing figures:

title(): Give the figure a title

xlabel(): Label the horizontal axis

ylabel(): Label the vertical axis

grid(): Draw grid-lines on graph

box(): Enclose (or remove enclosing) figure in a box

text(): Place text at the specified location on the figure

gtext(): Interactively (with mouse) place text

legend(): Create a legend box

axis(): Control over axis scaling, range, orientation, appearance, etc.

26.4 Printing Figures

• It is often useful to obtain a hard-copy of a figure or save it as a file for incorporation in other documents

- for example this is how the figures in the lecture slides are done.

• The Matlab command that provides this functionality is print

- print sends the currently active figure to the printer or saves it to a file

• print supports many different formats for images

- different printer manufacturers have different graphics languages

- the most widely supported (standard) is postscript (for stand-alone documents) and encapsulated postscript (for figures that will be included)

• For example:

print % Send the current figure to the

% default printer

print –deps plotex.eps % Save the current

% figure to

% a file called plotex.eps

% & save as encapsulated

% postscript

26.5 Multiple Figures & sub-plots

• It is possible in Matlab to create multiple independent figures, and within a figure to have multiple plots

• By default there is a single figure window

- created the first time any type of plotting is done

- over-written with each new plot (see hold on)

- new figure windows may be created with the figure(n) where n is an integer value

• if figure n window already exists it becomes the active window

• all plots go to the currently active window

• Individual figure windows can be sub-divided into multiple plots with the subplot() command

- subplot(m,n,p) splits the current figure into an m-by-n matrix of plots and makes the p'th plot the active one

- numbering is row-major order

- all plot, label etc. commands modify the p'th plot only

26.6 Other 2D plots

• While plot is the most commonly used 2D plot function there are a number of others available:

- log scale

- area

- pie chart

- error

- bar

- histogram

- polar

- stem

- etc.

- speaker and word recognition error rates for 16 people speaking the TI Digits database.

26.7 Multiple Plots Example

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% multiPlot.m

% An example of the different styles of 2D

% plots and using multiple plots in a single

% figure.

% Employs the datafile /home/student/CS1E/speech.dat

% which contains speaker (1st column) and word

% (2nd column) error rates for 16 speakers on

% the TI Digits speech database.

% Date: 29/3/1999

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Grab speech data and split into separate

% word & speaker error rate vectors.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

load /home/student/CS1E/speech.dat

speaker=speech(:,1);

word=speech(:,2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% First figure: plot, loglog, pie & pareto

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(1);

subplot(2,2,1);

plot(speaker,word,'*');

xlabel('Speaker Recognition Error Rate (%)');

ylabel('Word Recognition Error Rate (%)');

title('Word vs Speaker Error Rate (by Speaker)');

subplot(2,2,2);

loglog(speaker,word,'*');

grid on;

xlabel('Speaker Recognition Error Rate (%)');

ylabel('Word Recognition Error Rate (%)');

title('Log Scale speaker vs Word Error');

subplot(2,2,3);

grid off;

Multiple Plots (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Sort both speaker and word error rates

% (speakers) on the basis of ascending speaker

% recognition error rate.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[speakerS index]=sort(speaker);

wordS=word(index);

pie(speakerS,speakerS>mean(speakerS));

title('Sorted Pie Chart of Speaker Recognition Error');

subplot(2,2,4);

pareto(speaker);

xlabel('Index of Original Order');

title('Pareto Plot');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 2nd figure: bar, bar3, stairs & hist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(2);

subplot(2,2,1);

bar(speech);

title('Bar plot of Speaker & Word Error');

xlabel('Speaker Number');

ylabel('Error Rate (%)');

subplot(2,2,2);

bar3(word);

title('Bar3 plot of Word Error Rate');

xlabel('Speaker Number');

ylabel('Error Rate (%)');

subplot(2,2,3);

stairs(speakerS);

title('Stairs Plot of Speaker Error');

subplot(2,2,4);

hist(word);

xlabel('Word Error Rate');

ylabel('Count (of Speakers)');

title('Histogram of Word Error Rates');

Multiple Plots (Cont)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% 3rd fig: stem, errorbar, polar & rose

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(3);

subplot(2,2,1);

stem(speaker,word);

title('Stem plot of Speaker vs. Word Error');

xlabel('Speaker Error Rate');

ylabel('Word Error Rate');

subplot(2,2,2);

errorbar(speakerS,wordS);

title('Errorbar of Speaker with Word Error Variance');

subplot(2,2,3);

polar(speakerS,wordS);

title('Polar plot of Speaker vs. Word Error');

subplot(2,2,4);

rose(word);

title('Rose plot of Word Error');

%%%%%%%%%%%%%%%%%%%%%%%%

% 4th figure: matrixplot

%%%%%%%%%%%%%%%%%%%%%%%%

figure(4);

plotmatrix(speech);

title('Plotmatrix of speech data matrix');

26.8 2D Plots - Output

2D Plots Output (Cont)

26.9 Adding text

• It is possible to place text on 2D & 3D plots with the text() function

• Syntax is:

text(location,string)

Consider the following example:

bar(speaker);

xpos=1:size(speaker,1);

ypos=speaker+0.1;

labels=num2str(round(speaker));

text(xpos,ypos,labels);

26.10 3D Graphics – Line

• The 3D equivalent of the plot() function is plot3()

- functionality extremely similar to that of plot()

• Consider the following example:

theta=-10*pi:0.02:10*pi;

y=sin(theta); z=cos(theta);

plot3(theta,theta.*y,theta.*z);

ylabel(‘x.sin(x)’);

zlabel(‘x.cos(x)’);

title(‘Plot of x.sin(x) vs. x.cos(x)’);

26.11 3D Graphics – Surface

• Matlab has a number of functions for visualising 3D surfaces:

- the following example shows four of the more simple functions

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% pittedDome.m

% Generate a simple pitted dome

% using 2 FOR loops and a random

% function to do the pitting.

% Used to show the surface plotting

% features of Matlab.

% Author: Spike

% Date: 29/3/1999

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

width=50;

pitted=zeros(width,width);

for length=1:width

for breadth=1:width

pitted(length,breadth)=width*width-((length-width/2)^2+...

end;

subplot(2,2,1);

surf(pitted);

title('Surf plot');

subplot(2,2,2);

contour(pitted);

title('Contour plot');

subplot(2,2,3);

pcolor(pitted);

title('Pcolor plot');

subplot(2,2,4);

surfl(pitted);

shading interp;

26.12 3D Surfaces Example

26.13 Polynomials

• Polynomials are extremely important in many areas of science and engineering

• Matlab provides built-in support for their representation and manipulation

- root finding

- reconstruction

- multiplication

- derivative finding

- fitting to data

>> quad=[2 0 -5 12 -73];

>> % y= 2x^4 -5x^2 + 12x -73

>> quadRoots = roots(quad)

quadRoots =

-2.9527

2.4646

0.2440 + 2.2262i

0.2440 - 2.2262i

>> quadRebuilt=poly(quadRoots)

quadRebuilt =

1.0000 -0.0000 -2.5000 6.0000 -36.5000

>> square=[1 3 -9]; %y=x^2+3x-9

>> sixth=conv(quad,square)

sixth =

2 6 -23 -3 8 -327 657

>> % 2x^6 + 6x^5 -23x^4 -3x^3 +8x^2 -327x + 657

>> cubic=polyder(quad) % Derivative

cubic =

8 0 -10 12

Polynomials (Cont)

>> xvals=0:0.1:1;

>> yvals=2*xvals.*xvals-9*xvals+27;

>> yvals=yvals+randn(size(yvals));

>> fitted=polyfit(xvals,yvals,2)

fitted =

5.4375 -11.7186 26.9350

>> xinterp=linspace(0,1,100);

>> yinterp=polyval(fitted,xinterp);

>> plot(xvals,yvals,'-o',xinterp,yinterp,'--');

>> xlabel('X values');

>> ylabel('Y values');

>> title('Binomial function with noise & fitted');

26.14 Interpolation & Splines

• Matlab includes functions for interpolating values between those of a pre-existing set

- 1D, 2D, & multi-dimensional interpolation

- linear, cubic & cubic spline interpolation

• Functions interp1(), interp2(), interpn()

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% interpEx.m

% A simple example of 1D interpolation.

% Author: Spike

% date: 30/3/1999

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%

% y=2x^2-5x+12

%%%%%%%%%%%%%%

originalX=-2:2:6;

originalY=2*originalX.*originalX-5*originalX+12;

interpX=-2:0.05:6;

cubicY=interp1(originalX,originalY,interpX,'cubic');

splineY=interp1(originalX,originalY,interpX,'spline');

plot(originalX,originalY,'-o',interpX,cubicY,'--',interpX,splineY,':');

title('Interpolation Example');

Interpolation (Cont)

• Cubic spline functions also available separate to interp?() functions:

- spline() function fits piecewise cubic splines between data pairs:

• can return polynomial co-efficients, function values etc.

26.15 Optimisation

• Matlab has a number of functions for optimising numeric functions:

- finding their zeros

• generalises to finding where they meet any particular values

- minimisation

+ finding function peaks and valleys

>> x=-40:0.1:40;

>> y=0.2*x.^4+6*x.^3-8*x.^2+7.2*x-10.1-x.^5/200;

>> plot(x,y); title('Optimisation Example');

>> minX=fmin('0.2*x.^4+6*x.^3-8*x.^2+7.2*x-10.1-x.^5/200',-30,0)

minX =

-15.8967

>> line([minX minX],[max(y) min(y)]);

26.16 Integration, Differentiation & Ordinary Differential Equations

• Matlab implements functions for the numeric solution of integration, differentiation, and ordinary differential equation problems

• Details of the functions and their appropriate usage is beyond the scope of this course

- take a course on numerical analysis

• Functions include:

Integration: quad(), quad8(), dblquad(), trapz(), cumtrapz()

Differentiation: ployfit(), polyder(), diff(), gradient(), del2()

ODEs: ode23(), ode45(), ode113(), ode23s(), ode15s(), odeset(), odeget(), odefile()

26.17 Data-structures

• Matlab provides limited support for more complex data-structures

- quite limited and weak support compared to most general purpose 3rd generation programming languages

• Cell Array

- An array, whose individual elements can be any type or size (including other cell arrays)

>> cellEx{1,1}=[1 2; 3 4];

>> cellEx{1,2}='1st row, 2nd column';

>> cellEx{2,1}=6.4-5.1i;

>> cellEx{2,2}=eye(3);

>> cellEx

cellEx =

[2x2 double] '1st row, 2nd column'

[6.4000- 5.1000i] [3x3 double]

>> celldisp(cellEx);

cellEx{1,1} =

1 2

3 4

cellEx{2,1} =

6.4000 - 5.1000i

cellEx{1,2} =

1st row, 2nd column

cellEx{2,2} =

1 0 0

0 1 0

0 0 1

Data-Structures (Cont)

• Structures

- A collection of (usually) disparate types of information, each with a name

>> unit.name='Sherman Tank';

>> unit.attack=20;

>> unit.armour=12;

>> unit.health=30;

>> unit(2).name='Alpha Squad';

>> unit(2).attack=14;

>> unit(2).armour=0;

>> unit(2).health=20;

>> unit

unit =

1x2 struct array with fields:

name

attack

armour

health

>> unit(1)

ans =

name: 'Sherman Tank'

attack: 20

armour: 12

health: 30

>> fieldnames(unit)

ans =

'name'

'attack'

'armour'

'health'

26.18 Object Oriented

• Recent versions of Matlab have supported object oriented programming:

- classes

- objects

- methods

- inheritance

- aggregation

• Unfortunately the hybrid design of procedural syntax with tacked-on objects leads to a number of difficulties

- method invocation (precedence rules rather than explicit user indication of object that invokes)

- requirement to explicitly list other classes in constructor’s superiorto(), inferiorto() calls means forward compatibility with new classes is an on-going problem

26.19 GUI Design

• Matlab provides sophisticated tools for building GUIs

- for instance the Matlab demos which were constructed with Matlab’s GUI functions

• GUI – Graphical User Interface

• Provides support for:

- menus

- text boxes

- buttons

- sliders

- figures

- typefaces

- pointer & mouse events

- dialog boxes

• Also has a built-in set of constructor tools to allow the user to visually design the GUI

26.20 Toolboxes

• Matlab’s functionality may be expanded modularly with the addition of toolboxes

• Toolboxes are a suite of functions related to a specific problem area

- signal processing

- image processing

- neural networks

- communications

- fuzzy logic

- wavelets

- optimisation

- splines

- etc.

Kursus Matlab di Jakarta Selatan KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

Selasa, 13 Januari 2015

GRAPHICS & OTHER MATLAB FEATURES KURSUS MATLAB ONLINE Skripsi, Tesis, DISERTASI 081219449060

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