Chapters 6-7. User-Defined Functions

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1 Chapters 6-7 User-Defined Functions User-Defined Functions, Iteration, and Debugging Strategies Learning objectives: 1. Write simple program modules to implement single numerical methods and algorithms 2. Test program output for accuracy using hand calculations and debugging techniques Topics/Outline: 1. Functions: purpose and definition 2. Examples 3. Pass by value and local memory 4. Debugging Chapter 6-7: User-Defined Functions 1

2 User-Defined Functions Good programs: Never type the same code twice Solutions: 1. Iteration structure (loops) 2. Put code you need to reuse in a function We already constructed several simple user-defined functions in Chapters 3 and 4 MATLAB Script File A collection of MATLAB statements (M-files) that are stored in a file Script file produces the same result as if all commands had been typed directly into the Command Window Script files share the Command Window s workspace All variables defined before the start of script file or created by the script file remain in the workspace A script file has no input arguments and returns no results, but can communicate with other script files through the data left behind in the workspace Chapter 6-7: User-Defined Functions 2

3 MATLAB Functions A special type of M-file that runs in its own independent workspace Receives input data through an input argument list Returns results to the call through output argument list A function may contain multiple input and multiple output arguments MATLAB Built-In Functions We already know how to use MATLAB built-in functions y = sqrt(x) output can have any name input can have any name function theta = atan2(y,x) single output function multiple inputs [max_a,index_a] = max(a) multiple outputs function single input Chapter 6-7: User-Defined Functions 3

4 User-Defined Functions One output variable function y = mname(input arguments) More than one output variables function [y1, y2, ] = mname(input arguments) Both functions and scripts are M-files Differences between scripts and functions Scripts share variables with the main workspace Functions do not User-Defined Functions Special.m-files The first executable line must be function [output1,output2, ] = mname (input1, input2, ) square brackets name of the.m-file parentheses The.m filename must be the same as the function name (including capitalization): mname.m May contain multiple input and multiple output arguments Input and output arguments can be any name The bracket can be dropped if only one output argument or only the first output is desired Chapter 6-7: User-Defined Functions 4

5 User-Defined Functions function [output1,output2, ] = mname (input1, input2, ) Examples: function y = my_func(x) y = x.^3 + 3*x.^2-5*x + 2; function [r,theta] = rect2polar(x,y) r = sqrt(x.^2 + y.^2); theta = 180/pi * atan2(y,x); function [x,y] = polar2rect(r,theta) x = r * cos(theta * pi/180); y = r * sin(theta * pi/180); User-Defined Function Example: equipment.m Prompt for interactive input Optional end Chapter 6-7: User-Defined Functions 5

6 User-Defined Function Example: equipment.m Prompt for input at Command Window >> equipment Current temperature in degree Fahrenheit: 130 Too hot - equipment malfunctioning. >> equipment Current temperature in degree Fahrenheit: 100 Normal operating range. >> equipment Current temperature in degree Fahrenheit: 78 Normal operating range. >> equipment Current temperature in degree Fahrenheit: 68 Temperature below desired operating range. >> equipment Current temperature in degree Fahrenheit: 45 Too Cold - turn off equipment User-Defined Function Example: equipment2.m One input argument, no output argument Chapter 6-7: User-Defined Functions 6

7 User-Defined Function Example: equipment2.m Specific temperature in the input argument >> equipment2(130) Too hot - equipment malfunctioning. >> equipment2(100) Normal operating range. >> equipment2(78) Normal operating range. >> equipment2(68) Temperature below desired operating range. >> equipment2(45) Too Cold - turn off equipment. Anything you wish to pass to the main program should be specified in the output argument list Example: average.m Create function average.m to evaluate the mean of any variable Try which mean in command window to open the MATLAB built-in mean.m file Type help mean and see the help block Construct a user-defined function average.m (avoid using mean.m) function [xbar] = average(x) Chapter 6-7: User-Defined Functions 7

Example: average.m Include a data dictionary for user-defined function Return the mean value xbar Example: average.m >> y = [1-3 4 7 5-6 9 12 2]; >> [ym] = average(y) ym = 3.

8 Example: average.m Include a data dictionary for user-defined function Return the mean value xbar Example: average.m >> y = [ ]; >> [ym] = average(y) ym = >> ym = average(y) ym = bracket can be neglected if there is only one output or only the first output is desired >> who Your variables are: y ym >> mean(y) ans = local memory destroyed: (x,n,i,sumx,xbar) MATLAB built-in function Function average.m produces identical result as mean.m Chapter 6-7: User-Defined Functions 8

9 Example: average.m >> y = 1:0.2:12; >> [ysq_bar] = average(y.^2) User-defined function ysq_bar = >> mean(y.^2) ans = MATLAB built-in function Note: use square brackets for output, and parentheses for input MATLAB function receives VALUES, not VARIABLES Pass-by-Value MATLAB functions receive VALUES, not VARIABLES Values are passed to function through input (i.e., [ ], etc.) Variables (i.e., y, y.^2, etc.) are NOT Similar operations for output Local Memory: any variable created or modified inside a function is cleared (i.e., destroyed) when the function ends Chapter 6-7: User-Defined Functions 9

10 Pass-by-Value Scheme >> a = 2; b = [6 4]; >> fprintf('before sample: a = %f, b= %f %f\n',a,b); Before sample: a = , b = >> pass_by_value(a,b); In sample: a = , b = In sample: a = , b = >> fprintf('after sample: a = %f, b= %f %f\n',a,b); After sample: a = , b = Pass-by-Value Scheme >> a = 2; b = [6 4]; Before sample: a = , b= In sample: a = , b= In sample: a = , b= After sample: a = , b= (a,b) were changed from (2,[6,4]) to (10,[60,40]) inside the pass_by_value function But the original (a,b) values were restored after the completion of the function execution Function pass_by_value has no effect on the calling program Chapter 6-7: User-Defined Functions 10

11 Function Outputs Everything you want returned by a function must be listed as an output [output1, output2, ] = function(input1, input2, ) If there is only one output, or only the first output is desired: [output1] = function(input1, input2, ) or output1 = function(input1, input2, ) If second output is desired, then it is necessary to list all outputs Function Debugging The variables inside function do not show in Workspace To view values as function executes: insert break point (in Editor Window) This allows MATLAB to temporarily convert function to program so all variables stay in Workspace Use Workspace to debug problems in function (select Debug tab in MATLAB desktop) Chapter 6-7: User-Defined Functions 11

Set breakpoint and step through index i You may set multiple

12 Function Debugging Use average.m as an example Step through index i Set breakpoint Function Debugging Set breakpoint and step through index i You may set multiple breakpoints Click Step (or press F10) to step through the code one line at a time Chapter 6-7: User-Defined Functions 12

Function Debugging Use continue in Debug tab to step through index i = 1, 2, K>> clear all K>> y = [1-3 4 7 5-6 9 12 2]; K>> ym = average(y); 9 sumx = sumx + x(i); K>> i i = 1 K>> sumx sumx = 0 K>> i

13 Function Debugging Use continue in Debug tab to step through index i = 1, 2, K>> clear all K>> y = [ ]; K>> ym = average(y); 9 sumx = sumx + x(i); K>> i i = 1 K>> sumx sumx = 0 K>> i i = 2 K>> sumx sumx = 1 K>> i i = 3 K>> sumx sumx = -2 K>> i i = 4 K>> sumx sumx = 2 K>> i i = 5 K>> sumx sumx = 9 K>> who Your variables are: i n sumx x (Function variables stay in workspace) User-Defined Function Example Lab Assignment #1 (extract dates and prices) Chapter 6-7: User-Defined Functions 13

14 User-Defined Function Example Lab assignment #1 >> [year,month,supply] = mgsupply(mgs_vec); Year Month Production User-Defined Function Multiple inputs and multiple outputs: average_temperature.m Chapter 6-7: User-Defined Functions 14

User-Defined Function Multiple inputs and multiple outputs: average_temperature.m >> dates = [20041215; 20061215; 20081215; 20101215]; >> tps = [45.3; 55.8; 63.1; 39.

15 User-Defined Function Multiple inputs and multiple outputs: average_temperature.m >> dates = [ ; ; ; ]; >> tps = [45.3; 55.8; 63.1; 39.5]; >> [year,month,date,tp,tp_avg] = average_temperature(dates,tps); Year Month Date Temperature Average temperature = Nested: call another user-defined function within a user-defined function function [xbar] = average(x) User-Defined Function Interactive inputs: average_temperature2.m Chapter 6-7: User-Defined Functions 15

16 User-Defined Function Interactive inputs: average_temperature2.m >> [year,month,date,tp,tp_avg] = average_temperature2; Enter selected dates in YYYYMMDD format = [ ; ; ; ] Enter daily temperature = [55.24; 78.50; 85.36; 38.71] Year Month Date Temperature Average temperature = Enter dates and daily temperatures directly at the command prompt Function: Evaluate CVEN 302 Grade Chapter 6-7: User-Defined Functions 16

17 User-Defined Function if elseif Structure >> cven302_grade Enter Student Name: Jane Doe Enter Student ID: Enter Homework Average (30%): 96 Enter Exam I score (20%): 88 Enter Exam II score (20%): 92 Enter Final Exam score (30%): 85 Your Semester Average is: Your Semester Grade is : A >> cven302_grade Enter Student Name: John Doe Enter Student ID: Enter Homework Average (30%): 62 Enter Exam I score (20%): 84 Enter Exam II score (20%): 80 Enter Final Exam score (30%): 91 Your Semester Average is: Your Semester Grade is : C Benefits of Functions Independent testing of sub-tasks (unit testing) Reusable code (e.g., average.m) Isolation from unintended side effects (local variables) We will program most of the numerical methods learned as reusable functions e.g., Once you have a linear regression module, you may apply it to any dataset Chapter 6-7: User-Defined Functions 17

18 Optional Arguments Functions can be more flexible if we let the users decide the number of input and output arguments How does MATLAB decide what to do with different number of input arguments? >> A = zeros(10); >> A = zeros(10,4); >> A = zeros(10,4,3); >> help zeros ZEROS Zeros array. ZEROS(N) is an N-by-N matrix of zeros. ZEROS(M,N) or ZEROS([M,N]) is an M-by-N matrix of zeros. ZEROS(M,N,P,...) or ZEROS([M N P...]) is an M-by-N-by-P-by-... array of zeros. ZEROS(SIZE(A)) is the same size as A and all zeros. ZEROS with no arguments is the scalar 0. ZEROS(M,N,...,CLASSNAME) or ZEROS([M,N,...],CLASSNAME) is an M-by-N-by-... array of zeros of class CLASSNAME. Note: The size inputs M, N, and P... should be nonnegative integers. Negative integers are treated as 0. Optional Output Arguments >> A = zeros(10,4,3); >> size(a) ans = >> size(a,1) ans = 10 >> size(a,2) ans = 4 >> size(a,3) ans = 3 >> m = size(a) m = >> A = zeros(10,4,3); >> [m,n] = size(a) m = 10 n = 12 >> [m,n,p] = size(a) m = 10 n = 4 p = 3 >> [m,n,p,q] = size(a) m = 10 n = 4 p = 3 q = 1 The answer depends on the number (0-4) of output arguments Chapter 6-7: User-Defined Functions 18

Optional Input Arguments We may call the built-in function plot with as few as two elements or as many as seven input arguments How does MATLAB decide what to do with optional arguments?

19 Optional Input Arguments We may call the built-in function plot with as few as two elements or as many as seven input arguments How does MATLAB decide what to do with optional arguments? (Color/symbol/line type, LineWidth, MarkerSize, MarkerEdgeColor, MarkerFaceColor) Optional Input Arguments Customize plot using optional arguments: Color/symbol/line type, LineWidth, MarkerSize, MarkerEdgeColor, MarkerFaceColor Chapter 6-7: User-Defined Functions 19

20 Special Functions for Functions Use the following six special functions to get information about optional arguments and to report errors in those arguments nargin nargout nargchk error return the number of actual input arguments used to call the function return the number of actual output arguments used to call the function return error if the function is called with too few or too many arguments display error message and abort the function execution. Used for fatal errors. warning display warning message and continue function execution. Used for non-fatal errors. inputname returns the actual name of the variable that corresponds to a particular function number Optional Arguments [output1,output2] = size(input1) if nargin == 1 if nargout == 1 statements elseif nargout == 2 another statements else error( too many output arguments ) end another statements end Chapter 6-7: User-Defined Functions 20

21 Optional Arguments: animal_population.m Optional Arguments: animal_population.m inputname, nargchk, nargin, error, warning >> dog = 23; cat = 15; rabbit = 57; pig = 46; tiger = 1; mouse = 0; >> animal_population;??? Error using ==> animal_population at 5 Not enough input arguments. >> animal_population(dog); The first argument is named "dog". Total animal population = 23 nargin = 0 nargin = 1 >> animal_population(dog,rabbit); The first argument is named "dog". The second argument is named "rabbit". Total animal population = 80 >> animal_population(rabbit,cat,dog); The first argument is named "rabbit". The second argument is named "cat". The third argument is named "dog". Total animal population = 95 nargin = 2 nargin = 3 Chapter 6-7: User-Defined Functions 21

22 Optional Arguments: animal_population.m inputname, nargchk, nargin, error, warning >> dog = 23; cat = 15; rabbit = 70; pig = 46; tiger = 1; mouse = 0; >> animal_population(dog,cat,mouse,pig); The first argument is named "dog". The second argument is named "cat". The third argument is named "mouse". nargin = 4 Warning: Zero or negative animal population > In animal_population at 20 The fourth argument is named "pig". Total animal population = 84 >> animal_population(cat,dog,tiger,rabbit); The first argument is named "cat". The second argument is named "dog". The third argument is named "tiger". The fourth argument is named "rabbit". Total animal population = 109 nargin = 4 >> animal_population(dog,cat,tiger,rabbit,pig);??? Error using ==> animal_population Too many input arguments. nargin = 5 Global Memory Sharing data using global memory, accessible from any workspace Makes values in global variables available and modifiable by all functions and programs If necessary, make global variables ALL CAPS and avoid modifying them in functions global GRAVITY, VAR2, VAR3 GRAVITY = function [ ] = fname( ) global GRAVITY, VAR2, VAR3 weight = mass * GRAVITY; end Chapter 6-7: User-Defined Functions 22

23 Persistent Memory Preserving data between calls to a function Memory in functions is LOCAL, and is destroyed when function ends Sometimes you need a function to remember a value, such as how many times it has been called If such a counter were destroyed every time the function exited, the count would never exceed 1 Declare these variables: persistent var1 var2 var3 persistent n % number of input values persistent sum_x % running sum of values persistent sum_x2 % running sum of values squared Function Functions Functions whose input argument include the names of other functions (used during function s execution) Passing functions to functions What if the input to a function needs to be a function name? Example: want a built-in MATLAB function to do something with a user-defined function >> root = fzero('cos',[0 pi]) root = >> x = 0:0.1:10; >> y = feval(inline('sin(x)+exp(-x)'),x); We will use inline function and feval later when testing various numerical methods Chapter 6-7: User-Defined Functions 23

24 Subfunctions You may put more than one function in a.m file Subfunctions are only available when the main function is used. File mystates.m mystats Function mystats is accessible from outside the file mean_udf median_udf Functions mean_udf and median_udf are only accessible from inside the file Subfunctions Subfunctions mean_udf & median_udf are only accessible from inside the file mystats.m Chapter 6-7: User-Defined Functions 24

25 Private Functions Functions that reside in subdirectories with the special name private They are only visible to other functions in the private directory or to functions in the parent directory Private functions are restricted to the private directory and to the parent directory that contains it Since private functions are invisible outside of the parent directory, the same function names can be used in other directories Nested Functions Defined entirely within the body of the host function Visible only to the host function and the other nested functions embedded at the same level within the same host function host_function nested_function_1 end % nested_function_1 nested_function_2 end % nested_function_2 end % host_function Variables defined in host function are visible inside any nested functions Variables defined within nested functions are not visible in the host functions nested_function_1 can be called by host_function or nested_function_2 nested_function_2 can be called by host_function or nested_function_1 Chapter 6-7: User-Defined Functions 25

26 Order of Function Evaluation MATLAB locates functions in the following order: 1. Nested function with the specified name 2. Subfunction with the specified name 3. Private function with the specified name 4. Function in the current directory with the specified name 5. The first function found within the specified name of the MATLAB path Top-Down Program Design State the problem clearly Describe input and desired output, and any equations needed Work a hand-calculation Develop an algorithm to solve the problem Code the algorithm Test code against hand-calculation results Work on optimizations for speed Finalize comments and documentation Chapter 6-7: User-Defined Functions 26

27 Code Optimization Identify modules (functions) and separate them from the programs Keep program/functions as short as possible (split into smaller modules if possible) Write for clarity Look for orange hints in text editor Use built-in function if it exist Vectorize array operations Remove unnecessary debbuging calculations Chapter 6-7: User-Defined Functions 27

Chapter 6 User-Defined Functions. dr.dcd.h CS 101 /SJC 5th Edition 1

Chapter 6 User-Defined Functions dr.dcd.h CS 101 /SJC 5th Edition 1 MATLAB Functions M-files are collections of MATLAB statements that stored in a file, called a script file. Script files share the command