CSCD 409 Scientific Programming. Module 6: Plotting (Chpt 5)

Transcription

1 CSCD 409 Scientific Programming Module 6: Plotting (Chpt 5) , Prentice Hall, Paul Schimpf All rights reserved. No portion of this presentation may be reproduced, in whole or in part, in any form whatsoever, without the express permission of the author. Students enrolled in this class are hereby granted permission to reproduce this presentation for personal use only. XY Plots You can use any variable names

2 Nice things to add see also the axis command Multiple Plots MATLAB overwrites the figure window every time you request a new plot To open a new figure window use the figure function for example: % switch to figure 2 if exists, otherwise create >> figure(2) % create and switch to a new figure >> figure hold on freezes the current plot, so that an additional plot can be overlaid When you use this approach the additional line is also drawn in blue the default drawing color

3 Multiple Plots The hold on command freezes the plot The second line is also drawn in blue, on top of the original plot To unfreeze the plot use the "hold off" command Multiple Plots w/ Single Command Each set of ordered pairs will produce a new line, in a different color

4 Plotting a Vector or Matrix If you just pass a vector, Matlab plots the values versus the index number If you pass a matrix, Matlab plots each column vs. the row number of the entries Multiple Plot Variations If you want to create multiple plots, all with the same x value you can Use alternating sets of ordered pairs plot(x,y1,x,y2,x,y3,x,y4) Or group the y values into a matrix z=[y1,y2,y3,y4] plot(x,z)

5 Plotting a matrix peaks(100) creates 100 Gaussian functions (at various scalings and translations) each with 100 samples, in a 100 x 100 matrix because there are 100 columns, we get 100 plots Line, Color and Mark Style Can specify: line styles line color mark styles >> Help plot for a list of available styles In this example: the style string is: ':ok' : dotted line o circle marks k black color

6 Style Choices Line, Mark and Color Options Line Type Indicator Point Type Indicator Color Indicator solid - point. blue b dotted : circle o green g dash-dot -. x-mark x red r dashed -- plus + cyan c star * magenta m square s yellow y diamond d black k triangle down triangle up v ^ triangle left < triangle right > pentagram hexagram p h Multiple Plots can specify the parameters for each plot after the ordered pair that defines each plot

7 Axis scaling MATLAB automatically scales the plot to completely fill the graph use the axis command to change that axis([xmin,xmax,ymin,ymax]) see also: axis equal, axis square Legends, Titles, Axis Labels You will generally want a title and axis labels Matlab let's you move these annotations around interactively Octave currently does not Octave / GnuPlot gives (x,y) readings of the cursor location but Octave / Qt does not

8 Improving your labels You can use Greek letters by putting a backslash (\) before the name of the letter title( \alpha \beta \gamma ), creates: αβγ To create a superscript use ^, with curly brackets if necessary: title( x^35 ) gives: x 3 5 title( x^{35} ) gives: x 35 use _ for subscript title( x_{35} ) gives: x 35 subplot(2,2,1) Divide the window into a 2x2 grid of plots, and make the first subplot current 2 columns 2 rows

9 Subplot Example Other Types of 2-D Plots Polar Plots Logarithmic Plots Bar Graphs Pie Charts Histograms X-Y graphs with 2 y axes Function Plots

10 Polar Plots Doesn't support multiple argument pairs so you'll have to use "hold on" to superimpose multiple plots Logarithmic Plots A logarithmic scale (base 10) is convenient when a variable ranges over many orders of magnitude and you want to plot the entire range without compressing the smaller values. data varies exponentially plot uses a linear scale on both axes semilogy uses a log 10 scale on the y axis semilogx uses a log 10 scale on the x axis loglog use a log 10 scale on both axes

11 Logarithmic Plots linear linear/log y=x log/linear log/log note the slope of this line What would x 3 look like? what would 5x look like? Bar Graphs and Pie Charts bar(x) vertical bar graph barh(x) horizontal bar graph bar3(x) 3-D vertical bar graph bar3h(x) 3-D horizontal bar graph pie(x) pie chart pie3(x) 3-D pie chart

12 Histograms A histogram is a plot showing the distribution of a set of values X-Y Graphs with Two Y Axes Sometimes it is useful to overlay two x-y plots onto the same figure However, if the order of magnitude of the y values are quite different, it may be difficult to see the behavior of both plots because of scale differences For example:

13 Plotting with two scales plotyy allows you to use two scales Function Plots Function plots allow you to use a function as input to a plot command, instead of a set of ordered pairs of x-y values fplot('sin(x)',[-2*pi,2*pi]) function input as a string range of the independent variable in this case x the function name can be an m-file that takes one argument

14 3D Line Plots These plots require a set of triples (x-y-z values) as input try comet3 here (broken in Octave) Matlab 3D coordinate systems follow the righthand rule Mesh Plots The x and y coordinates are the matrix index numbers often this is NOT what you want displayed care to hazard a guess how I got this? (hint: 1 line of code)

15 Using mesh with 3 variables If you have values of x and y that correspond to the z values, you can show those in the plot instead of the index numbers from the z matrix Can you explain these entries? Surf plots Similar to mesh plots syntax is the same

16 Contour Plots similar input syntax as mesh and surf plots A More Interesting Example We'll compute z as a function of (x,y) 2 2 ( x y ) z xe We could process vectors of x and y input values in a set of nested loops, computing one value of z for each possible (x,y) pair, but that would not take advantage of the matrix manipulation efficiencies of Matlab What we want to do is something as simple as: Z = X.* exp( (X.^2 + Y.^2)) ; In order to compute a 2D grid of Z values using a single algebraic expression, both X and Y have to be 2D grids of the same size Use the meshgrid function to create the x and y input grids: x = [-2 : 0.2 : 2] ; y = [-2 : 0.2 : 2] ; [X, Y] = meshgrid(x,y) ;

17 Meshgrid X(x,y) = x i.e., y is ignored so f(x) = f(x), but over a 2D grid Y(x,y) = y i.e., x is ignored so f(y) = f(y) but over a 2D grid Back to the Example

18 Pseudo Color Plots Similar to contour plots Parametric Plots In a parametric plot, the two plotting coordinates (say x and y) are each functions of a third variable In other words, the two plotting coordinates are actually dependent on a third independent variable Here is an example where x and y are both functions of t: % 100 equally spaced points between 0 and 2*pi t = linspace(0, 2*pi, 100) ; % calculate x and y coords as function of t x = cos(t) ; y = sin(t) ; plot(x,y) ; axis equal ; % Make the scaling the same on both axes

19 Adjusting plots from the menu bar Notice you can add labels, legends, a title and other annotations You can edit axis properties, fonts used, and colormaps You can zoom and rotate the view You can copy the figure to the clipboard You can save to a file Octave has print, copy & save, plus a few style options on the system menu, and you can rotate w/ the mouse