STAT 391 Handout 1 Making Plots with Matlab Mar 26, 2006

Transcription

1 STAT 39 Handout Making Plots with Matlab Mar 26, 26 c Marina Meilă & Lei Xu mmp@cs.washington.edu This is intended to help you mainly with the graphics in the homework. Matlab is a matrix oriented mathematics package, but it has a nice set of graphics functions that you can use with little extra effort, even if you don t use matlab for the rest of the assignment. Thus, you can do the computations in the homework in your favourite language, then print the data to a file and call matlab to read the file and plot the results. Starting matlab and getting help To start matlab type matlab at the command prompt. The appearance of the matlab >> prompt marks the beginning of the matlab session. If you want to temporarily change the working directory, you need to use cd command in the command window.pwd is the command to get the current working directory path. Below is the example: >> cd( D:\temp ) changing the working directory to the path D:\temp >> pwd ans= D:\temp To get online help you can type help, helpwin, or helpdesk. help prints a summary of help topics. By typing help topic you get a list of functions available in that topic. For example, help graphics lists all available 2-D graphics functions. Typing help help tells you more about the help facilities. help function gives help on a specific function. helpwin opens a window in which you can browse through help topics and demos, see tips, etc.

2 helpdesk starts a browser window where you can find all of the above plus manuals, other product documentation, do full-text search, etc. 2 Variables In matlab, each variable is a matrix. A text is a string characters, all the other variables are matrices of floating point numbers. The assignement sign is = and +, -, *, / have the usual meanings. To get more info about the operators, type help arith for arithmetic operators and help relop for relational operators (i.e,, etc.). Below are some examples: >> A = [ ; ] a matrix A = >> B = [ 2 ] a row vector B = 2 >> C = B the transposes a matrix C = 2 >> >> A(,2) = B( 3) A 2 gets the value of B 3 A = >> A(,:) the first row of A ans = 2

3 2 2 4 >> A(:,2:3) all the rows of A but only columns 2 thru 3 ans = >> x = :8 creates a vector containing the numbers to 8 x = >> y = :.: a vector containing a progression from to with increment. y = Columns through Columns 8 through >> y(2:6) ans = In the following I assume that you have created a data file example.dat containing the results of some experiment and that you want to use matlab to plot these results. An example script is contained in the file h example.m which is reproduced in section 9. Matlab commands can be typed at the prompt or typed in a script file. The standard extension for a script file is.m. tips: Ending a command by semicolon (";"), the result will not print after the command. 3

4 3 Reading files with matlab In Matlab, there are three common methods to read data from text files. 3. Using function textread to read files textread is a function to read data from text files and write to multiple outputs. The syntax is: [A,B,C,...]=textread( filename, format ) or [A,B,C,...]=textread( filename, format,n). This command read data from the specified filename and write to the output [A,B,C,...]. The format string determines the number and types of return arguments. N determines the number of times to reuse the format string. Examples:The data in the file test.dat is Mary Level 45 Jerry Level2 34 Mike Level3 36 Susan Level2 4 >>[names,level,age]=textread( test.dat, %s %s %d ) read the entire file names = Mary, Jerry, Mike, Susan level = Level, Level2, Level3, Level2 age = 45,34,36,4 >>[names,level,age]=textread( test.dat, %s %s %d,) read the first line names= Mary level= Level age= 45 The data file example.dat:

5 Then the code A=textread( example.dat, %d,3) will read the first 3 intergers from the file. The A is a 3-by- column vector. 3.2 Using function textscan When we need to read data from a large text file, or want to read from a specific point of a file, the function textscan will be a better choice. It can read a specified amount of data from a file, and maintain a pointer to the location in the file where the last read operation ended. The function will write the data to a cell array instead of multiple outputs. Cell arrays in MATLAB are multidimensional arrays whose elements are copies of other arrays. Before using this function, we must need to use fopen function to open the file and supply the fid information which is required in the function.for detail descriptions for fopen and fid, you can refer to next section. The syntax for textscan is: C = textscan(fid, format ) or C = textscan(fid, format, N) The format string determines the number and types of return arguments. N determines the number of times to reuse the format string. Examples: The code is to read data from the example.dat described in previous subsection >> fid=fopen( example.dat ); % open the file example.dat >> A=textscan(fid, %d,3); % read the first 3 integers from the file and write into A, then A{} is a 3-by- column vector >> B=textscan(fid, %f ); % this command will read the left numbers and write into the cell array B >> flcose(fid); % close the file 3.3 Using function fscanf to read files First, you need to open the file in order to read the data from it. To open a file use the command fopen: fin = fopen( example.dat, r ); The above command opens the file example.dat for reading, as indicated by the second parameter r. A file identifier is returned in the variable fin. 5

6 The data file is an ASCII file given in section 9 and you can do formatted reading from it. The syntax is similar to the C syntax. [A,COUNT] = fscanf(fid,format,size) reads data from the file specified by file identifier FID, converts it according to the specified FORMAT string, and returns it in matrix A. COUNT is an optional output argument that returns the number of elements successfully read. FID is an integer file identifier obtained from fopen. SIZE is optional; it puts a limit on the number of elements that can be read from the file; if not specified, the entire file is considered; if specified, valid entries are: N read at most N elements into a column vector. inf read to the end of the file. [M,N ] read at most M * N elements filling an M-by-N matrix, in column order. N can be inf (the symbol for infinity), but not M. FORMAT is a string containing C language conversion specifications. fscanf differs from its C language namesake in an important respect - it is vectorized in order to return a matrix argument. The format string is recycled through the file until an end-of-file is reached or the amount of data specified by SIZE is read in. Examples: S = fscanf(fid, %s ) reads (and returns) a character string A = fscanf(fid, %5d ) reads 5-digit decimal integers integer data = fscanf( fin, %d, [, 3 ] ) reads a vector of 3 integers; in the data file, the numbers are separated by blank spaces float data = fscanf( fin, %f, [ 2, 2 ] ) reads a 2 by 2 matrix of blank-separated real numbers When you are finished with a file, close it using the handle and the command fclose: fclose( fin ); Alternatively, you can use the following commands to read in a file. Assume that you have a file called data.txt containing three columns of data (e.g. the weight, height and age of individuals) that are space-delimited dlmread( data.txt, ); %read in the file and store the data in ans weight = ans(:, ); %extract the first column into weight height = ans(:, 2); %extract the second column into height age = ans(:, 3); %extract the third column into age 6

7 plot(weight, height, age); % make use the data e.g. plot a graph 4 Displaying data and inserting comments To display any variable or expression in matlab, type its name at the prompt: integer data prints the vector integer data 3 * ^2 prints the value of the expression Note: if you want an expression to be displayed, do NOT end the statement with ; (semicolon). A semicolon at the end of an expression or statement is optional and its action is to supress the display of the result. The symbol % marks the beginning of a comment. Everything after it in the command line is ignored. Example: x = sort( float data(, : )); % copy row of float data % into x and sort it y = float data( 2, : ); % copy row 2 of float data % into vector y 5 Making a histogram Matlab has the built-in command hist for making a histogram. Its syntax is: hist(y) bins the elements of Y into equally spaced bins. If Y is a matrix, hist works down the columns. hist(y,m), where M is a scalar, uses M bins. Examples: hist( integer data ) histogram with bins hist( integer data, 6 ) histogram with 6 bins 6 Making a plot The function for making plots in matlab is plot. plot(x,y) plots vector Y versus vector X. plot(y) plots the columns of Y versus their index. If Y is complex, plot(y) is equivalent to plot(real(y),imag(y)). 7

8 Various line types, plot symbols and colors may be obtained with plot(x,y,s) wheresis a character string made from one element from any or all the following 3 columns: plot(x,y,s,x2,y2,s2,x3,y3,s3,...) combines the plots defined by the (X,Y,S) triples, where the X s and Y s are vectors or matrices and the S s are strings. color marker type line type y yellow. point - solid m magenta o circle : dotted c cyan x x-mark -. dashdot r red + plus dashed g green * star b blue s square w white d diamond k black v triangle (down) ^ triangle (up) < triangle (left) > triangle (right) p pentagram h hexagram For example: plot(x,y, c+: ) plots a cyan dotted line with a plus at each data point; plot(x,y, bd ) plots blue diamond at each data point but does not draw any line. plot(x,y, y-,x,y, go ) plots the data twice, with a solid yellow line interpolating green circles at the data points. The commands title, xlabel, ylabel let you annotate a plot. title( text ) writes the texttext above the plot as a title. The commandsxlabel( text ), ylabel( text ) label the X and Y axes respectively. For example (see also figure 3): plot( x, y ); % plot y vs x xlabel( x ); ylabel( y ); title( An x-y plot ); To make multiple plots on the same figure, use the command subplot. subplot(m,n,p), or subplot(mnp), breaks the Figure window into an m-by-n matrix of small subplots and selects the p-th subplot for for the current plot. The subplots are counted along the top row of the Figure window, then the second row, etc. For example, subplot(2,3,) % divide the display into 2x3 subplots 8

9 and go % to subplot plot( float data(,: )) % plot something title( float data row ); subplot(232) % now go to second subplot plot( float data(,: ), o ) % plot the same data as before, % but with circles instead of continuous line title( float data row ); subplot(233) % go to third subplot 7 Printing a figure Once a figure is ready, you need to output it by printing it to a file. The print command allows you to do so. print alone sends the current figure to your current printer. print -device -options You can optionally specify a print device (i.e., an output format such as tiff or PostScript or a print driver that controls what is sent to your printer) and options that control various characteristics of the printed file (i.e., the resolution, type of preview, Figure to print etc.). Available devices and options are described by typing help print. print -device -options filename If you specify a filename, matlab directs output to a file instead of a printer. print adds the appropriate file extension if you do not specify one. The implicit format used if you do not specify any device/option is Postscript. When a figure is divided into several subplots, the print command prints all of them in one file.:383 Examples: print histogram.ps saves the current figure into the Postscript file histogram.ps print myfigure saves the current figure into into the Postscript file figure.eps print -depsc -tiff -r3 matilda Saves current Figure at 3 dpi in color EPS to matilda.eps with a TIFF preview (always at 72 dpi). This TIFF preview will show up on screen if matilda.eps is Inserted as a Picture in a Word document, but the EPS will be used if the Word document is printed on a PostScript printer. 9

10 8 Generating random numbers rand and randn are two functions used to generate random numbers in Matlab. rand is used to generate uniformly distributed random numbers and arrays. randn is used to generate normally distributed random numbers and arrays. rand(n) return an n-by-n matrix with random numbers which are from a uniform distribution in the interval (,) rand(m,n) return an m-by-n matrix with random numbers which are from a uniform distribution in the interval (,) randn(n) return an n-by-n matrix with random numbers which are from a normal distribution with mean, variance σ 2 = randn(m,n) return an m-by-n matrix with random numbers which are from a normal distribution with mean, variance σ 2 = >> A=rand(2) return a 2-by-2 matrix A = >> B = rand(,3) return a -by-3 matrix B = >> C = randn(2) random numbers from normal distribution C = >> D=randn(,4) random numbers from normal distribution D =

11 9 An example This is a sequence of matlab commands that reads data from a file, makes some plots and prints them out. The commands are in the file example.m. The data is in file and the printouts are shown in figures, 2, 3. % open file example.dat and read the data fin = fopen( example.dat, r ); integer data = fscanf( fin, %d, [, 3 ] ); % read 3 integers % and store them in the x3 matrix integer data float data = fscanf( fin, %f, [ 2, 2 ] ); % read 4 floating point % numbers and store them in the 2x2 matrix float data fclose( fin ); % display the data integer data float data % make a histogram and print it to file histogram.ps hist( integer data ); xlabel( integer data ); title( histogram of integer data ); print histogram.ps % plot the first row of float data and print the graph to file float data.ps plot( float data(, : ) ); ylabel( float-data row ); print float data.ps % make six plots on one page and print them to file float data.ps subplot(23) % divide the display into 2x3 subplots and go to subplot plot( float data(,: )) % plot the same data as before title( float data row ); subplot(232) % now go to second subplot

12 plot( float data(,: ), o ) % plot the same data as before, but with circles % instead of continuous line title( float data row ); subplot(233) % go to third subplot x = sort( float data(, : )); % copy row of float data into x and sort it y = float data( 2, : ); % copy row 2 of float data into vector y plot( x, y ); % plot y vs x xlabel( x ); ylabel( y ); title( An x-y plot ); subplot( 234 ); % now make same plot with different line style plot( x, y, :, x, y, ^ ); % plots once with dotted line and once with % triangles on the same graph xlabel( x ); ylabel( y ); title( Another x-y plot ); subplot(235) x2 = :.5:; % generate the vector [ ] % with 2 elements y2 = sin( 3 * x2 ); plot( x, y, --, x2, y2, * ); % plot y vs x with dashed line and % y2 vs x2 with * on the same graph xlabel( x, x2 ); ylabel( y, y2 ); title( Two x-y plots on the same graph ); subplot(236) % a histogram of integer data with 6 bins hist( integer data, 6 ); xlabel( integer data ); ylabel( # points ); title( histogram with 6 bins ); print float data.ps The data file example.dat:

13 8 histogram of integer_data integer d ata x 4 Figure : The figure in histogram.ps float data row Figure 2: The figure in float data.ps

14 2 float d ata row 2 float d ata row 2 An x y plot y x 2 Another x y plot Two x y plots on the same graph 2 2 histogram with 6 bins 5 y y, y2 # points x x, x integer_data x 4 Figure 3: The figure in float data.ps. 4