1. overview 2. plot in 2d 3. plot in 3d 4. other possible charts 5. engineers: label your plots! 6....

1. Overview

2. plot in 2D

3. Plot in 3D

4. Other possible charts

5. Engineers: label your plots!

6. Plots & Polynomial

Plotting

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1. Plots & Charts, overview

Plotting functions

plot(), plot3(), polar(), meshgrid()

Charting functions

pie(), pie3(), bar(), bar3(), bar3h(), hist(), errorbar()

Plot-related functions

polyfit(), polyval(), text(), title(),xlabel(), ylabel()

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2. Plots

Create a graph of y vs. x

plot(x, y) %order of arguments matters

Example: 100 data-points

x = linspace(-pi, pi);y = sin(x);plot(x, y)

By default, plot() connects the data-points with a solid line without markers.

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2. Plots, cont.

Let us try with less data-points:

x = linspace(-pi, pi, 10);y = sin(x);plot(x, y);

Notice that the curve is less smooth

This is another reason why linspace() is friendly to use: easily fixable.

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2. Plots: line specifiers

A third argument can be added in the plot function-call:

plot(x,y, _____)

The third argument must be a string, made of up to three components: One component for the line’s color One component for the line-style And one component for the marker symbol (the symbol at each

data point

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2. Plots: lineSpecs - color

Specify the color only: plot(x, y, ‘r’);

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2. Plots: lineSpecs – line style

Color and line-style: plot(x, y, ‘r:’);

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(none): no line

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2. Plots: lineSpecs - marker Color, type of line and data-marker:

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plot(x, y, ‘r:d’);

2. Plots: line specifier, cont.

If only the data-points must show, leave out the line-style:

plot(x, y, 'rd')

Forgot all the options?

>> doc plot <enter>

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2. Plots: multiple plots

Repeat the series of 3 arguments to combine multiple plots on 1 graph.

Example:X = linspace(-2*pi,2*pi,50);Ysine = sin(X);Ycosine = cos(X);plot(X,Ysine,'r:o',X,Ycosine,'b--d')

The string argument is unnecessary. MATLAB will rotate through the default colors to make sure each plot has a different color. The other 4 arguments are MANDATORY.

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2. Plots: hold on/off

At default mode, the plot() command erases the previous plots before drawing new plots.

If subsequent plots are meant to add to the existing graph, use: hold on, which holds the current plot.

When you are done, use hold off to return to default mode.

hold, by itself, toggles the hold modes.

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>> hold on

>> plot(x1,sin(2*x1),'g’)

2. Plots: hold on/off, cont.

>> x1 = linspace(0,pi,25);

>> plot(x1,sin(x1),'r')

* Range of the axis will be automatically adjusted.

3. Plots: 3 dimensions

plot3() makes a 3D plot – requires x, y, and z data.

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Meshgrid()

Given: x = [1 2 3];y = [4 5];

Evaluate: f(x,y) = x + y

In other words, I need to evaluate (x+y) at every pair of points between x and y.

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Meshgrid(), cont.

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To make a useful plot, it is necessary to match up each x with each y before computing z. The function meshgrid() makes this easy to do.

3. Plots: 3 dimensions, cont.

x = linspace(-pi, pi);y = linspace(-pi, pi);[X, Y] = meshgrid(x, y);Z = sin(X).^3 - cos(Y).^2;plot3(X, Y, Z)

Creates two arrays X, Y where each

value of x is matched with

each value of y

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4. Other Possible Charts

polar() creates polar coordinate plots:

x = linspace(-pi, pi);y = cos(x) - sin(x).^2;polar(x, y)

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4. Other Possible Charts, cont.

pie(), pie3(), bar(), bar3(), bar3h(), hist(), errorbar()

pie3()

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Much like Excel offers:

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>>x = 38 54 8 54 48

>> pie3(x)

4. Other Possible Charts, cont.

pie(), pie3(), bar(), bar3(), bar3h(), hist(), errorbar()

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Much like Excel offers:

bar3h()

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x = 8 9 1 9 6

>> bar3h(x)

4. Other Possible Charts, cont.

pie(), pie3(), bar(), bar3(), bar3h(), hist(), errorbar()

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errorbar()

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4. Other Possible Charts, cont.

As with all the MATLAB possibilities, use…

F1 = Help

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5. Engineers: Complete Plots

The following built-in functions should be applied to any graph created:

title() %title on figurexlabel() %x-axis labelylabel() %y-axis labelzlabel() %z-axis label

Each function takes 1

‘string’ argument only

and has no return-value.

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5. Engineers: Complete Plots

Additional built-in function: text()Example: text(1, -2, -2, 'Cool plot!')

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5. Engineers: Complete Plots

Built-in function: grid onCOMMAND line typed in the script, after a plot command.

It stands alone on one line, requires no arguments, and returns no value.

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5. Engineers: Complete Plots

Additional built-in functions: legend(), xlim, ylim,…

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6. Plotting & Polynomials Plot-related functions that try to find an equation that

links data-points:

polyfit(), polyval()

polyfit() is like linear regression which finds the curve that best fits the data-points. polyfit() attempts to fit a polynomial – not a line. It mainly finds the coefficients of the polynomial that best fits the data given.

polyval() is used to evaluate the polynomial at specified points. It makes use of the coefficients generated by polyfit(). It is frequently used to generate a plot. 2626

6. Plotting & Polynomials, cont.clearclc

%generate tables of x, and y data = [1, 50; 4, 4900; 7, 4600; 10, 3800; 70, 1300; 100, 850; 300, 0.2e9;

700, 1.2e9; 1000, 1.2e9];x = data(:, 1)';y = data(:, 2)'; %plot data points, omit lineplot(x, y, 'd')hold on %combine future plots on this one

%find best-fit polyn. of order 3coeff = polyfit(x, y, 3)px = linspace(min(x), max(x), 100);py = polyval(coeff, px);plot(px, py)

Remember that fitting a curve does NOT mean hitting every data-point! 2727

Wrapping Up Plotting any kind of graphs mostly requires vectors of identical

dimensions: (x,y) (x, y, z) (r, theta, z)... hold on allows multiple plots to be combined together. The independent variable is the first argument. IT IS A COMMON

MISTAKE TO SWAP THEM. All functions are easily explained in the help, usually with examples

that show how to place arguments. As engineer, remember all graphs must be labeled correctly. For mathematical analysis, polyfit() and polyval() allow to fit a curve

through data-points.

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