Writing MATLAB Programs

Transcription

1 Outlines September 14, 2004

2 Outlines Part I: Review of Previous Lecture Part II: Review of Previous Lecture

3 Outlines Part I: Review of Previous Lecture Part II: Control Structures If/Then/Else For Loops While Loops Vectorized Loops Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots

4 Part I Review of Previous Lecture

5 Review of Previous Lecture Starting MATLAB, exiting MATLAB, getting help Major elements of the MATLAB environment Command window Workspace Command history Current directory selector MATLAB as a calculator Writing functions

6 Part II

7 Introduction In their simplest form, MATLAB programs are like functions without the function header line. They are simple text files that contain several MATLAB commands to be run in a consistent fashion. For example: % Calculate projectile positions at a given time initialvelocity =5; % m/ s launchangle =45*( pi / 180); % radians time =2; % seconds [ xposition, yposition ]=... computeprojectileposition ( initialvelocity,... launchangle, time )

8 If/Then/Else For Loops While Loops Vectorized Loops Control Structures Control structures are ways of making programs do something other than simply execute lines of the program in order. Control structures allow programs to make decisions, and to repeat calculations while certain conditions are met.

9 If/Then/Else For Loops While Loops Vectorized Loops If/Then/Else Structures If/Then/Else structures allow your program to make decisions based on calculations or other information. Their general form is if a condition is met, do this. Otherwise, do something else. You ve already used this type of logic in previous homework problems. For example, on the bisection method, one of the steps reads if sgn(f (a)) = sgn(f (b)), stop, the program is set up wrong. Otherwise, continue on.

10 If/Then/Else For Loops While Loops Vectorized Loops MATLAB If/Then/Else Example width =0; height =5; depth =3; density =10; volume = width * height * depth ; if ( volume <=0) error ( How did I get a non - positive volume? ); else weight = density * volume ; end

11 If/Then/Else For Loops While Loops Vectorized Loops For Loops For loops are used when you want to repeat a calculation a specific number of times. Your first programming assignment used a construct like that: loop times, adding 1.0/3.0 to result each time.

12 If/Then/Else For Loops While Loops Vectorized Loops For Loop Example result =9; for n =1: result = result +1.0/3.0; end for n =1: result = result -1.0/3.0; end fprintf ( result =%.15 f\n,result );

13 If/Then/Else For Loops While Loops Vectorized Loops While Loops While loops are used when you want to repeat a calculation until a particular criteria is met. Normally, you don t know exactly how many loops will be required to meet that criteria beforehand. The incremental search method used constructs like that: repeat the previous steps as long as sgn(f (x)) = sgn(f (x + x)).

14 If/Then/Else For Loops While Loops Vectorized Loops While Loop Example x =0; dx =0.1; while ( sign ( myfunction (x)) == sign ( myfunction (x+dx ))) x=x+dx; end fprintf ( Found a root on the interval (%f,%f)\n,... x,x+dx );

15 If/Then/Else For Loops While Loops Vectorized Loops Vectorized Loops One of MATLAB s advantages over other languages is that it does not require you to predefine every variable with a type and a size before using it. You can add extra elements to an array or vector anytime during the variable s lifetime. However, this flexibility comes at a price. When MATLAB has to resize an array, it has to find new memory for the larger array, allocate that memory, copy the existing array into the new memory location, and add the new array element onto the end. All these operations add on to your total time required to solve a problem. When you repeat this operation tens or hundreds of thousands of times, it can really slow things down.

16 If/Then/Else For Loops While Loops Vectorized Loops Non-Vectorized Loop Example clear all tic for n =1: x(n)= log (n); end toc This code required 196 seconds to run on a Pentium 4 Xeon 2.8 GHz system, and would probably require even more time on a normal PC.

17 If/Then/Else For Loops While Loops Vectorized Loops Better Non-Vectorized Loop Example How much difference would it make if we preallocated the memory for the x variable rather than resizing it on each run through the loop? clear all tic x= zeros (1,100000); for n =1: x(n)= log (n); end toc This code required only 0.29 seconds to run on the same 2.8 GHz Xeon system, required 0.40 seconds to run on a normal PC, and yields identical results compared to the first example.

18 If/Then/Else For Loops While Loops Vectorized Loops Vectorized Loop Example What s the code for and the effect of a vectorized loop? clear all tic n =1: ; x= log (n); toc This version of the loop required only 0.02 seconds to run on the Xeon, and only 0.05 seconds to run on a more typical PC.

19 If/Then/Else For Loops While Loops Vectorized Loops Other Vectorized Examples n =1; while ( n <=1999) x(n )=( n *5)+5; y(n)=x(n )^2; n=n +1; end for n =1: 1999 x(n )=( n *5)+5; y(n)=x(n )^2; end x =10:5:10000; y=x.^2;

20 If/Then/Else For Loops While Loops Vectorized Loops Vectorized Loop Warning Since vectors in MATLAB are actually single-row or single-column matrices, MATLAB treats them according to the rules of matrix algebra. The most common problem with vector calculations are with multiplication or division operations, since matrix algebra rules require that matrices multiplied or divided together must be of a particular size. Plus, the required sizes almost never show up in vectorized loops.

21 If/Then/Else For Loops While Loops Vectorized Loops Vectorized Loop Solution Put a period before any multiplication, division, or power symbol in a vectorized calculation: >> x =0:5:25 x = >> y=x^2??? Error using == > ^ Matrix must be square. >> >> x =0:5:25 x = >> y=x.^2 y = >>

22 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Saving Data to a Text File If you need to save the results of some MATLAB calculations to avoid the need to repeat the same calculations over and over, you can save any MATLAB variable into a text file: >> x =0:10; >> y=x.^2; >> save - ascii parabola. txt y

23 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Loading Data from a Text File Similarly, you can load previously-calculated results from a text file. It doesn t matter whether the text file contains results from MATLAB or from another program, as long as it s formatted properly: >> clear all >> load - ascii parabola. txt >> whos Name Size Bytes Class parabola 1 x11 88 double array Grand total is 11 elements using 88 bytes >> parabola parabola = >> y= parabola ;

24 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Text File Advantages Very easy to exchange data between MATLAB and other applications, such as Excel, LabVIEW, Tecplot, etc. Very easy to exchange data between MATLAB and custom C, C++, or FORTRAN programs. Data can be examined, created, or modified with a text editor such as Notepad.

25 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Text File Disadvantages Only one variable may be stored per text file. Only 8 digits of precision are stored in the text file. Slow performance on loading or saving very large data sets.

26 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Saving Data to a MATLAB Binary File >> x =0:10; >> y=x.^2; >> save parabola. mat

27 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Loading Data from a MATLAB Binary File >> clear all >> load parabola >> whos Name Size Bytes Class x 1 x11 88 double array y 1 x11 88 double array Grand total is 22 elements using 176 bytes

28 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots MATLAB Binary File Advantages Multiple variables may be stored in a single.mat file, even the entire MATLAB workspace. No precision is lost in the transfer. Variables are not truncated at the eighth decimal place. Fast performance on loading or saving very large data sets.

29 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots MATLAB Binary File Disadvantages More difficult to exchange data between MATLAB and other applications, such as Excel, LabVIEW, Tecplot, etc. More difficult to exchange data between MATLAB and custom C, C++, or FORTRAN programs.

30 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Basic X-Y Plots Assuming you already have a set of x and y data (or x and t data, etc.), the plot command can plot them against each other. >> t =0:0.01:1; >> x= exp (-t ).* sin (5* pi*t); >> plot (t,x)

31 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots X-Y Plot Result

32 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Multiple Traces on One Graph >> t =0:0.01:1; >> x= exp (-t ).* sin (5* pi*t); >> plot (t,x) >> x2=exp ( -2*t).* sin (4* pi*t); >> plot (t,x,t,x2)

33 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots X-Y Plot Result

34 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots Graph Labels, Titles, and Legends >> t =0:0.01:1; >> x= exp (-t ).* sin (5* pi*t); >> plot (t,x) >> x2=exp ( -2*t).* sin (4* pi*t); >> plot (t,x,t,x2) >> xlabel ( Time (s) ); >> ylabel ( Displacement (mm) ); >> title ( Motion Observed at Tip of Beam ); >> legend ( Beam 1, Beam 2 );

35 Loading and Saving Data with Text Files Loading and Saving Data with MATLAB Binary Files X-Y Plots X-Y Plot Result

36 Update your projectile motion calculators to accept a vector of times, rather than a single value. For example, the following code should calculate a series of (x, y) values: >> v0 =5; >> theta =pi /4; >> t =0:0.01:1; >> [x,y]= computeprojectileposition (v0, theta,t); Plot the (x, y) position of a projectile launched with the above v 0 and θ parameters. Label the axes, title the graph, and place a legend on it.