1. Overview 2. plot in 2D 3. Plot in 3D 4. Other possible charts 5. Engineers: label your plots! 6. Plots & Polynomial Plotting 11

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() 22

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. 33

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. 44

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 55

2. Plots: lineSpecs - color Specify the color only: plot(x, y, ‘r’); 66

2. Plots: lineSpecs – line style Color and line-style: plot(x, y, ‘r:’); 7 (none): no line 7

2. Plots: lineSpecs - marker Color, type of line and data-marker: 8 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 99

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. 10

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. 11

>> hold on >> plot(x1,sin(2*x1),'g’) 2. Plots: hold on/off, cont. 12 >> 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. 13

Meshgrid() 14 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.

Meshgrid(), cont. 15 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 16

4. Other Possible Charts polar() creates polar coordinate plots: x = linspace(-pi, pi); y = cos(x) - sin(x).^2; polar(x, y) 17

4. Other Possible Charts, cont. pie(), pie3(), bar(), bar3(), bar3h(), hist(), errorbar() pie3() 18 Much like Excel offers: 18 >> x = >> pie3(x)

4. Other Possible Charts, cont. pie(), pie3(), bar(), bar3(), bar3h(), hist(), errorbar() 19 Much like Excel offers: bar3h() 19 x = >> bar3h(x)

4. Other Possible Charts, cont. pie(), pie3(), bar(), bar3(), bar3h(), hist(), errorbar() 20 errorbar() 20

4. Other Possible Charts, cont. As with all the MATLAB possibilities, use… F1 = Help 21

5. Engineers: Complete Plots The following built-in functions should be applied to any graph created: title() %title on figure xlabel() %x-axis label ylabel() %y-axis label zlabel() %z-axis label Each function takes 1 ‘string’ argument only and has no return-value. 22

5. Engineers: Complete Plots Additional built-in function: text() Example: text(1, -2, -2, 'Cool plot!') 23

5. Engineers: Complete Plots Built-in function: grid on COMMAND line typed in the script, after a plot command. It stands alone on one line, requires no arguments, and returns no value. 24

5. Engineers: Complete Plots Additional built-in functions: legend(), xlim, ylim,… 25

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. 26

6. Plotting & Polynomials, cont. clear clc %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 line plot(x, y, 'd') hold on %combine future plots on this one %find best-fit polyn. of order 3 coeff = 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! 27

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. 28