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C MATLAB PLOTS VERSION OF 20 JUNE 1989 Brought to you by: Jim Locker SofTech Inc. 4443 N. Hyland Ave. Dayton Oh 45424 (513)-429-2771 TABLE OF CONTENTS CHAPTER PAGE 1.0 Introduction 2 2.0 The Main Menu 3 3.0 3-D Plots 5 4.0 X-Y Plots 7 5.0 Polar Plots 10 6.0 Contour Plots 12 7.0 Histograms 13 8.0 Using Matlab as a Data Plotter 14 9.0 Demos 15 1.0 Introduction Matlab Plot is a flexible and comprehensive plot package for Matlab. You may have as many plots on one 16 color hi-res interlace screen as you think you can make sense out of. You may save definitions for as many as 10 of those plots and may display those plots individually or collectively. This manual describes the operation of the plot function and some details about each choice. For more information on some of the choices, you should consult the diglib manual. To enter matlab plot, type "Plot(x);" from matlab, where x is any matrix. This will enter the plot interactive mode. To enter batch mode, type "Plot(x,'filename');" from matlab. In this mode, the filename is the name of a previously saved plot definition file. In batch mode, plot will automagically load the plot file and plot x according to the definitions it finds there, without any other action on your part. When entering Plot interactively from the CLI, you will first be asked if you have set the stack up to at least 100K. Answer yes or no. If you say yes when you should have said no, you will experience a spectacular crash. If you say no, you will exit to Matlab. At this time, save your work, exit Matlab, and set your stack. Then re-enter Matlab to do your plots. A screen will be opened behind the Workbench screen. You should click to and from this screen using the left-Amiga-M and -N options. When a plot is active, the plot window will block the plot screen front/back gadgets. 2.0 The Main Menu After setting your stack and answering yes to the question, you will reach the main menu. This menu says: PLEASE SELECT AN OPTION: 1 3D PLOT 2 X-Y PLOT 3 POLAR PLOT 4 CONTOUR PLOT 5 HISTOGRAM 6 SET BACKGROUND COLOR 7 PLOT BUFFER CONTROL 8 READ PLOT FILE 9 END THE CURRENT PLOT 10 EXIT TO MATLAB Options 1 through 5 will be discussed in the relevant sections of this document. If option 6 is selected, you will be prompted to enter a pen number. Enter a number from 1 to 15. The plot background will be set to the color you select. Sorry...you cannot preview the colors. At a later point I will add that capability. For now, you should just experiment. If you don't select a background color, the default is black. Color 1 is white, color 2 is red, and so forth. Option 8 will prompt you to enter a file name of a previously saved plot definition file. Enter the file name, then sit back and watch. The file will be loaded and the plots will be generated automatically. Option 9 will end the current plot and the program will hang until you click on the close gadget on the plot screen. You may click on the close box at any time, and this release of Matlab will close the window the next time it checks the Intuition message port, which it does frequently. Option 10 exits Plot to matlab. Option 7 is the Plot buffer control. The last 10 plot definitions are stored in a buffer. This option controls how that buffer is handled. When option 7 is selected, the following menu appears: PLEASE CHOOSE THE PLOT BUFFER CONTROL OPTION: 1 CLEAR THE BUFFER 2 DELETE A PLOT 3 SHOW THE PLOT BUFFER 4 DISPLAY ONE OF THE SAVED PLOTS 5 DISPLAY ALL SAVED PLOTS 6 SAVE THE PLOT BUFFER 7 RETURN TO MAIN MENU Choosing option 1 will clear the buffer and eliminate all plot definitions. Choosing option 2 will display the contents of the buffer and prompt you to enter a buffer number to delete. That buffer will be deleted. The buffer handler does not fill holes in the buffer so, for instance, if you delete plot 2 out of a three plot buffer, then define a new plot, that new plot will appear as plot 4 and plot 2 will remain blank. The buffer is a first in-first out (FIFO) buffer with 10 locations. Thus, location 2 would remain blank until enough new definitions had been made to overwrite location 1. Option 3 will show what plots are in the buffer. Option 4 will result in a prompt requesting the plot number to display. Entering a plot buffer number will result in the display of that plot. Option 5 will immediately generate a plot using all the definitions in the buffer. Option 6 will prompt for a filename. The plot definitions will be stored in this file for later use. At this time, any holes in the buffer will be deleted. Option 7 will return you to the main menu. WARNING...Plot does not check the dimension of an array when plotting from the buffer or from a saved definition file. It is your responsibility to ensure that the array and the definitions in the saved file are compatible. If they are not, there is an excellent chance that you will crash and burn. For instance, do not define a plot for a 50 by 50 array, then try to plot a 10 by 10 array using that definition. This is guaranteed to get you in trouble. 3.0 3-D Plots Upon choosing main menu option 1, you will be presented with the 3-D plot menu. This menu says: PLEASE CHOOSE AN OPTION: 1 CHOOSE PLOT LABELS 2 CHOOSE PLOT VALUES 3 CHOOSE VIEWER PERSPECTIVE 4 CHOOSE HIDDEN LINE OPTIONS 5 CHOOSE PLOT COLOR 6 CHOOSE PLOT SIZE 7 DO THE PLOT 8 END THE CURRENT PLOT 9 EXIT 3-D PLOT If you choose, you may immediately select option 7 (do the plot) because all necessary values for the plot have defaults. Option 1 will ask you to enter strings for the x axis label, the y axis label, the z axis label, and the size (cm) of the characters in the labels. The default is to have no labels. Option 2 will prompt you for x and y limits, and x/z and y/z ratios. The ratios will affect how the plot will appear on the screen. The values default to "good" numbers: the ratios default to 1:1. I suggest you play around to see what works best for you. Option 3 will prompt you to enter a perspective in R, theta, and phi values. Again, experiment. The default places you 45 degrees off the x axis and 30 degrees above the x y plane. Option 4 will provide a small menu of hidden line options. It is fairly self explanatory. The default is no hidden line removal. Option 5 sets the pen color of the plot Option 6 prompts you to enter the space on the screen that the plot is to occupy, in fractions of the total screen size. You are first asked for the origin of the plot (lower left hand corner) on the screen X axis as a fraction of the x axis size. Thus, to start the plot midway across the screen, you would enter 0.5. To start the plot at the left of the screen, you would enter 0. Similarly, for the Y-axis origin, 0 starts the plot at the bottom of the screen and .5 starts it midway up. You are then prompted to enter the fraction of each screen axis that the plot is to occupy. Again, enter a positive decimal number. Please note that if the fraction of the axis defining the start point plus the fraction to be occupied by the plot is greater than 1, there will be clipping of the plot. Example: to place a plot in the lower left quarter of the screen, the x origin is 0, the y origin is 0, the x fraction is .5, and the y fraction is .5. To place the plot in the upper right quarter, the x and y origins are both .5 and the x and y fractions are also .5. The default values generate a full screen plot. Note: the routine that handles keyboard input for Matlab Plot is not very smart. It will accept non-numeric input from you and happily convert it to a number. This leads to unpredictable results. Option 7 will immediately display the plot using the current options. Option 8 will hang the program until you click on the plot close gadget. Option 9 returns to the main menu. 4.0 X-Y Plots This is the most complicated plot option. When you choose main menu option 2, you will encounter a small option menu which says: PLEASE CHOOSE THE X-Y PLOT MODE 1 IMPLICIT X, EXPLICIT Y 2 EXPLICIT X, EXPLICIT Y There are two types of x-y plotting available to you. In option 1, it is assumed that each cell in the matrix contains a y value and the x values are given by the position of the cell in the array. By default, cell location 1 will be assigned the value x=1, location 2 gets x=2, and so forth. This is similar to the 3-D plot, but the plot will be 2 dimensional instead of 3-D. You might use this option if you had made a 3D plot of an array and wanted to also plot specific row or column slices out of the array. As an example, if you are plotting along Rows in Matrix X which is an M by N array, then if you plot along row M1 such that 1 > M1 < M, then the location X(M1,1) contains Y1 and the corresponding x value is assigned the value of 1. Location X(M1,2) contains Y2 and is assigned x=2, and so forth up to X(M1,N) which contains YN and is assigned x=N. In option 2, it is assumed that the data in the array is arranged in ordered pairs, with a Y value in a cell corresponding to an x value in another cell. You may have an array with one row containing the x values and all other rows containing y values that correspond to the x value in the x row at the same column location. The minimum array dimension for this option is 2 by N or M by 2 because this option requires ordered pairs. Again as an example, if you are plotting X(M,N) along rows such that X(1,N) contains all x values, and X(2,N) contains corresponding Y values, then you would select option 2. The array could be arranged so that X(3,N) contains new x values, and X(4,N) contains the corresponding Y values, X(5,N) contains x, X(6,N) the corresponding Y, and so forth. You must have at least one set of x and one set of y values, but you may have as many of each as you choose, arranged in any fashion you see fit. After choosing one option or the other, you will be informed that you are plotting from an M row by N column array (M and N given as the appropriate numbers) and you are asked whether to plot along rows or columns. In other words, tell Plot how you want the data organized. Choosing rows will result in a plot of successive column locations in the same row. Choosing columns will result in a plot of successive row locations in the same column. After choosing rows or columns, you will be asked how many lines will be placed on the plot. You may plot from one to ten sets of ordered pairs, or Y values if the implicit x option was chosen. After choosing the number of lines, you will be prompted to enter the row (or column) number of the x and y components of each line. If the implicit x option was chosen, you will be prompted for y components only. You may choose the same row (or column) as many times as you wish. After entering this information, you will finally reach the main menu. This menu says: PLEASE CHOOSE AN OPTION: 1 SELECT THE TYPES OF PLOT AXES 2 SELECT THE X AND Y GRID MARKINGS 3 SELECT THE X AND Y AXIS TICK MARK OPTIONS 4 SELECT THE LINE OPTIONS 5 SELECT THE PLOT COLORS 6 SELECT THE BACKGROUND COLOR 7 SELECT THE AXIS SCALES 8 CHOOSE THE PLOT SIZE 9 CHOOSE THE PLOT LABELS 10 DO THE PLOT 11 END THE CURRENT PLOT 12 EXIT XYPLOT At this point, sufficient information to do a plot has been provided, and you may immediately choose option 10 if you wish. Choosing option 1 will result in another menu giving various log and linear options which are self explanatory. You may also choose to place a second Y axis on the right side of the plot. If you choose that option, another menu will appear with appropriate choices for that axis. Option 2 will result in a menu to determine the types of grid markings to be applied. Option 3 will let you choose axis tick mark options. These options are cumulative. You should not choose any options for a second y axis tick marks if you have previously chosen a second y axis from the axis menu. Option 4 leads through successive menus to determine line and symbol types and sizes. Four line types are available and four symbols are available. You may also choose the symbol spacing (ie every data point, every third data point, etc.) When choosing symbol size, enter your values in centimeters, or fractions thereof. Option 5 enables you to set the color of any or all of the plot lines, by pen number. Option 6 lets you set the background color for the plot. Option 7 lets you set the axis scales if for some reason the default values, which are selected so that all your data will plot on screen, are not acceptable. When choosing the Implicit X option, if you do not change the x-axis scale, the plot will be labeled starting with x=1 and going to x=M or N. Option 8 lets you choose the plot size in the same fashion as the 3-D plot. If you use a plot title label, you must leave room for it at the top of the plot. This means that you should set the y axis size somewhat shorter than if there was no title. How much shorter depends upon the size of the title. Option 9 lets you select plot labels for the x axis, the y axis, the second y axis, and the plot title. You do not have to select the label size on this plot; that feature defaults to auto-sizing. However, you may choose the size if you wish. Option 10 will immediately do the plot using the selected options. Option 11 hangs the program until the plot close gadget is selected. Option 12 returns to the main menu. 5.0 Polar Plots This release of Matlab supports a complete polar plotting function. Selecting main menu option 3 will get you there. When you enter the polar plot function, you are immediately asked to define the plot mode. You have two choices: R-Theta (type real) mode, in which case the data in the array is arranged as ordered pairs of radial-angle information; or X+IY (Complex) mode, in which the data in the array contains imaginary components. After choosing a mode, you are given a display similar to that in the XYPLOT routine, asking you to choose plotting along rows or columns. Pick one. You are then asked how many data lines to plot. You may choose up to 10 on one plot. If you chose the R-Theta plot option, you will then be prompted, for each line to be plotted, to enter the R and Theta row or column numbers. If you chose complex plots, you will be prompted to enter the row or column number of the complex number data to be plotted. Then you reach the main menu. This menu says: PLEASE CHOOSE AN OPTION 1 DEFINE THE PLOT LABEL 2 CHOOSE PLOT AXIS TYPE 3 CHOOSE LINE OPTIONS 4 CHOOSE PLOT AXIS AND TICK MARK OPTIONS 5 CHOOSE THE BACKGROUND COLOR 6 CHOOSE THE PLOT COLOR 7 CHOOSE THE PLOT SIZE 8 DO THE PLOT 9 END THE CURRENT PLOT 10 EXIT POLAR PLOTS. Option 1 enables you to define a plot label. Option 2 lets you choose among the alternative radius types. Two choices are available. LINEAR does the plot with a linear radius. LOGARITHMIC does the plot with a logarithmic radius scale. Option 3 lets you choose data line options. Option 4 defines plot axis/tick mark options. You may choose the number of range rings to draw, and the line styles to use when drawing them. The number of range rings to be drawn is the total number of range rings if you are in the linear radius mode, or the number of range rings per decade in logarithmic radius mode. Option 5 lets you set the background color. This does a SetRast() and will wipe out any other plots which are currently displayed. Those plots remain defined in the plot buffer, however. Option 6 lets you choose the color of the axis, range rings, and labels Option 7 lets you choose the size of the plot. An improper selection of aspect ratio here will result in a distorted graph. The polar plotting routine won't correct aspect ratio. Option 8 does the plot. You may select this option as soon as you reach the main menu. Option 9 hangs the program until you click on the close gadget. Option 10 returns to the main plot menu. 6.0 Contour Plots When you enter the Contour plot function, you immediately encounter the main menu. It presents the following display: PLEASE SELECT AN OPTION: 1 CHOOSE PLOT LABELS 2 CHOOSE PLOT VALUES 3 CHOOSE NUMBER OF CONTOURS 4 CHOOSE CONTOUR LEVELS 5 SET THE BACKGROUND COLOR 6 CHOOSE PLOT COLOR 7 CHOOSE PLOT SIZE 8 DO THE PLOT 9 END THE CURRENT PLOT 10 EXIT CONTOUR PLOTS Option 1 enables you to define x and y axis labels for the plot. Option 2 enables you to define the minimum and maximum x and y values to be displayed on the plot. By default, this is an implicit value and ranges from X=0, Y=0 to X=M,Y=N where the input array is dimensioned M by N. Choose this option if the default is not acceptable. Option 3 enables you to choose the number of contour lines to be plotted. The default is 20 contours. Option 4 enables you to choose at what values contour lines will be drawn. By default, they are drawn at equal intervals in the data. This option enables the user to force contour drawing at specified data values. Option 5 enables you to set the background color. This does a SetRast() and therefore obliterates all other plots currently being displayed. The plot definitions remain in the plot buffer. Option 6 lets you choose the color of the plot. Option 7 lets you define the size of the plot on the screen. Option 8 draws the picture immediately. You may select this option as soon as you reach the main menu. Option 9 hangs the program until you click on the window close box. Option 10 returns to the main menu. 7.0 Histograms The histogram function is relatively immature. In the June 20 release, what is here works, but you may find it too limiting for many applications. Try it, if it's useful to you, use it. Upon selecting option 5 on the main menu, you will encounter the histogram main menu: PLEASE SELECT AN OPTION: 1 CHOOSE THE BAR GRAPH TYPE 2 CHOOSE BAR GRAPH AXIS TYPE 3 CHOOSE BAR GRAPH AXIS COLORS 4 CHOOSE BAR GRAPH LABELS 5 SET THE BAR GRAPH COLORS 6 SET THE BACKGROUND COLOR 7 SET THE PLOT SIZE 8 DO THE PLOT 9 END THE CURRENT PLOT 10 EXIT TO MAIN MENU You may immediately choose option 8 if you desire; all necessary values default. The histogram is somewhat more limited in options than the x-y plot. You do not get to choose whether to plot columns or rows; histograms are done along rows only. Furthermore, the first 8 rows of the array will be histogrammed, one histogram per row, with axis scales set to include all histograms. If there are fewer than 8 rows, then only that many rows will be histogrammed. Thus, to get one histogram, you must input a 1 by N array, with N less than or equal to 512. Option 1 allows you to choose the histogram type. Two types are available: statistical and occurence count. In Statistical (the default) the histogram will be normalized to one. Thus, the maximum possible value on the y axis is 1, if all events fall into the same bin. This is for use in statistical distributions. In Occurence Count, the histogram is not normalized. The Y axis will reflect the number of events in each cell. All other Histogram features work as described in previous sections. 8.0 Using Matlab as a data plotter I have been asked how you do this. Really it is quite simple. I presume you have an ASCII data file which represents your data, in an appropriate format. To bring it into Matlab, you must edit the data file to place the data in a format that Matlab will recognize, then EXECute the file from within Matlab. For instance, suppose you have the following data pairs that represent data you have collected/generated. This data represents X-Y ordered pairs: ***start of dummy ASCII file*** x y 3 2 5 6 47.5 13.2 ***end of dummy ASCII file*** You would edit the file and remove all extraneous stuff, such as the header, the footer, and the x and y labels. You would take the data and re-format it like this: x = < 3 2; 5 6; 47.5 13.2; > Then, from within matlab, type: EXEC('MYDATAFILE') You have just entered a generalized ASCII data file into Matlab and may plot it as you choose. 9.0 Demos A demonstration of the plot features is provided on the distribution disk. The demo will take a previously calculated 2 dimensional Sinc function (sin(x)/x * sin(y)/y) and plot it 3 ways. To run the demo, at the CLI prompt CD to the disk containing Matlab. Increase your stack to 100000. Enter "Matlab" (You should not enter the double quotes) When the Matlab intro is complete and the Matlab prompt ( <> ) appears, enter: "Load('sinc.sav')" After the load operation is complete, enter: "Plot(z);" when asked if the stack is set to 90K, enter: "Y" (unless, of course, you didn't set the stack) You now reach the main menu. Choose option 8. When prompted for a file name, enter: "sinc2.plt" (do not enter the quotes, just the name) Now click to the back screen and watch the plotting happen. It will take about 45 seconds to begin; the 3-D plot has been selected with hidden line removal activated and that takes some calculation. You may also start Matlab from Workbench. After starting it from Workbench, you must load and plot the demo files as described above. You may execute the script file testit2.exe to see an example of plotting from batch mode. Other demo files may be on the disk: those labeled with the suffix .exe are script files for Matlab which will cause calculations (sometimes lengthy) to occur, those with the suffix .sav are saved variables which may be directly plotted after being loaded, and those labeled .plt are plot definition files. There is nothing magic about these suffixes; I simply use them to keep track of things. I suggest that you do to.