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Motivation The interactive tools: Drawing commands Interactive figure manipulation The programmer point of view: Introduction to objects and their handles Invoking and manipulating graphics objects

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The interactive tools >> x = -5:0.05:5; % [-5 -4.95 …….4.95 5] >> y = sin(x.^2); >> plot(x,y)

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none

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The axes is contained within the figure. A figure may have more than one axes.

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The plot is contained within the axes. An axes may have more than one plot.

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>> y2= 1./(1+exp(-x)); >> hold Current plot held >> plot(x,y2,'color','k','lineStyle','-.')

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>> y2= 1./(1+exp(-x)); >> hold Current plot held >> plot(x,y2,'color','k','lineStyle','-.') Property-name, property value pair

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>> y2= 1./(1+exp(-x)); >> hold Current plot held >> plot(x,y2,'color','k','lineStyle','-.') Property-name, property value pair

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dash-dot line -. dotted line : dashed line -- solid line (default) - Line Style Specifier six-pointed star (hexagram)h five-pointed star (pentagram)p triangle pointing left< triangle pointing right> triangle pointing downwardv triangle pointing upward^ diamondd squares crossx point. asterisk* circleo Plus sign+ Marker typeSpecifier whitew blackk yellowy magentam cyanc blueb greeng Redr ColorSpecifier

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Alternative format: >> x=[1 2.3 4 10 3 11.3]; >> y=[3.2 5 2 7.4 3 9.4]; >> p2=plot(x,y,'or:’);

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Alternative format: >> x=[1 2.3 4 10 3 11.3]; >> y=[3.2 5 2 7.4 3 9.4]; >> p2=plot(x,y,'or:’); Marker Color LineStyle There are more alternative formats Use MATLAB help. Consult the property inspector.

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Specialized 2D plots Bars Histograpms Stair Stem Scatter Error bars Area Pie charts contour

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Specialized 3D plots plot3 mesh surf Use MATLAB help and demos.

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The programmer’s point of view: Graphic Objects Handles Properties

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Graphic Object (figure, axes, text, line etc.) handle

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Graphic Object (figure, axes, text, line etc.) handle properties

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Many objects may exist simultaneously

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We use the handles to pick an object and manipulate it.

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An object may have more than one handle

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Objects may contain other objects

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Everything inside a figure window is a graphic object The figure window itself is a graphic object All plots in MATLAB are made of graphic objects All graphic objects have properties that control the way they look and behave Graphic object: any element as defined by the set of its properties that constitute part of a figure

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>> t = -pi:0.05:pi; >> x = cos(3*t)*1./(1+exp(-t)); >> y = sin(3*t)*1./(1+exp(-t)); >> p = plot(x,y) p = 158.0055 A handle

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Objects The plot The axes The figure ? Handles p is the plots handle ?

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>>set(p,'color','r') >>set(p,'lineWidth',4) handle

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>>set(p,'color','r') >>set(p,'lineWidth',4) property names

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>>set(p,'color','r') >>set(p,'lineWidth',4) How would I know what properties does the plot have? property values

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>> get(p) Color: [1 0 0] EraseMode: 'normal' LineStyle: '-' LineWidth: 4 Marker: 'none' MarkerSize: 6 MarkerEdgeColor: 'auto' MarkerFaceColor: 'none' XData: [1x126 double] YData: [1x126 double] ZData: [1x0 double] BeingDeleted: 'off' ButtonDownFcn: [] Children: [0x1 double] Clipping: 'on' CreateFcn: [] DeleteFcn: [] BusyAction: 'queue' HandleVisibility: 'on' HitTest: 'on' Interruptible: 'on' Selected: 'off' SelectionHighlight: 'on' Tag: '' Type: 'line' UIContextMenu: [] UserData: [] Visible: 'on' Parent: 157.0059 DisplayName: '' XDataMode: 'manual' XDataSource: '' YDataSource: '' ZDataSource: ''

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>> p_parent=get(p,'parent') p_parent = 157.0059 handle

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property name >> p_parent=get(p,'parent') p_parent = 157.0059

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property value >> p_parent=get(p,'parent') p_parent = 157.0059

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>> p_parent=get(p,'parent') p_parent = 157.0059 p_parent is a handle. Of what? >> get(p_parent,'type') ans = axes

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>> get(p_parent,'children') ??? ans = 158.0063 >> p ans = 158.0063

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>> set(p_parent,'xcolor','b'); >> set(p_parent,'ycolor','b'); What about the title? >> title=get(p_parent,'title') title = 163.0059 >> get(title,'type') ans = text

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>> set(p_parent,'xcolor','b'); >> set(p_parent,'ycolor','b'); What about the title? >> title=get(p_parent,'title') title = 163.0059 >> get(title,'type') ans = text >> set(title,'string','Spiral') >> set(title,'color','b')

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Lets add another line Ooooops… >> x1 = -cos(3*t)*1./(1+exp(-t)); >> y1 = -sin(3*t)*1./(1+exp(-t)); >> plot(x1,y1) >> lines = get(p_parent,'children') lines = 204.0061 158.0063 >> blue=lines(1) blue = 204.0061 >> set(blue,'lineWidth',4)

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Alternatively: >> findobj('color','b') ans = 204.0061

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Who is the title’s parent? Who are the title’s children? Who is the axes` parent? Who is the figure’ parent?

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Graph Objects Phylogeny This hierarchy is based on the interdependency of objects. A line can only be plotted inside an Axes. A figure contains Axes and so on.

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Graph Objects Phylogeny parent

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Graph Objects Phylogeny children

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…in the beginning there is only the root object…. Hello, I am the root object Although I am the root I always got a 0 as my handle I know and control many important things… Type get(0) to see all my properties

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What is the difference between a handle and “simple variable”? >> a = [1 2 3 4 5]; >> b = a; >> b(3)=9 b = 1 2 9 4 5 >> a a = 1 2 3 4 5 >> get(title,'String') ans = Spiral >> ttt = title; >> set(ttt,'string','Red wide spiral') >> get(title,'String') ans = Red wide spiral

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handle right_handle = handle

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The subplot command Present simultaneously several pieces of information that when displayed on a single plot may confuse the reader Display and image and quantification Let’s see an example

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x=linspace(0,3,500); plot(x,1./(x-1).^2+3./(x-2).^2) grid on %Change zooming ylim([0 50])

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>>x=linspace(0,3,500); >>a(1)=subplot(1,2,1);%1 rows, 2 cols use first axis >>plot(x,1./(x-1).^2+3./(x-2).^2) >>a(2)=subplot(1,2,2 );%1 rows, 2 cols use second axis >>plot(x,1./(x-1).^2+3./(x-2).^2) >>ylim([0 50]) >>set(a,'XGrid','on','YGrid','on')

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The general synopsis of subplot is subplot (n,m,p) where n is the number of rows m is the number of columns p identifies the specific subplot. Starting from the top left axes and counting across rows How to use the subplot command >>subplot(1,2,2)

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MATLAB has an text interpreter named T E X very similar to LAT E X. format mathematical expressions and Greek letters to display nicely both in the screen and in printed material we use a backslash “\” followed by either a symbol identifier, or a string modifier We can limit the extent of string formatting by placing the string inside curly braces {…} To create the following formatted string f()=sin() We write: {\itf(\tetha)}=sin{\it(\tetha)}

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A little more elaborated example: The most useful string modifiers are: \it changes text to italics \rmchanges text to normal ^superscript _underscript

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Bar plots bar and barh create vertical and horizontal bar graph respectively When you use bar(Y) where Y is a matrix, rows are treated as groups. Use bar(x,Y) to center the bars at the places specified by x

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>>x=[10,20,30]; >>y=[5 3 10 2 7 10 3 7 10 10 2 2]; >>bar(x,y) >>title('Vertical bar graph');

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>>bar(x,y,'stacked')

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Histograms Use hist(X,[bins]) to create an histogram (one per column of X) By default the count of the data is done in 10 bins You can change this by passing a second argument to hist –Scalar => tells the number of bins –Vector => tell the center of each bin

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Y(:,1)=randn(10000,1); Y(:,2)=randn(10000,1)+10; hist(Y,20) title('histogram with 20 bins');

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As we saw hist plots the count (i.e. the number of elements in each category) What if we want to plot the frequencies instead? Use [n,x]=hist(X,[bins]) –n will hold the # of elements of each bin –x will hold the center value of each bin

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>> [n,x]=hist(Y,20) >> freqN=n./repmat(sum(n),length(n),1) % freqN=n/10000 >> bar (x,freqN)

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Stair plots Commonly used in digital signal processing and statistical analysis When we sample data at a given rate, we have no information about what is going on between two consecutive samples

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>> x=-2:0.1:2; >> y=normpdf([-2:0.1:2],0,1); >> stairs(x,y) >> title('Stair graph')

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Error bars Error bars can be added to plots with the help of the errorbar function. The synopsis of this function is errorbar(x,y,l,u,[formatting string]) x,y,l,u are all vertors of the same size draws a marker on the point specified by the x,y and add bars of the size [ y+u(i) y-l(i)]

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>> x=1:10; >> y=2*x+5; >> noise=rand(1,1)*x.^2; >> errorbar(x,y,noise,'ok:') >> xlim([0 11]) >> title('Errorbars')

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Pie charts among the less recommend though common use a lot of graphics to represent very low data density Still, if you want to use them it is easily done

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pie(x,[outline]): –x is a vector with the value of each data –Outline is a vector of 1s and 0s the same size of x that states which pie slices should be outlined (1) or held together (0)

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>> x=[10 1 3 0.5 7] >> outline=x>5; % = [1 0 0 0 1] >> pie(x,outline) >> title('Pie chart')

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