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MATLAB Functions – Part II Greg Reese, Ph.D Research Computing Support Group Academic Technology Services Miami University September 2013

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MATLAB Functions – Part II © 2010-2013 Greg Reese. All rights reserved 2

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3 Part I Write scripts Run MATLAB functions Write and run our own functions Use our functions in MATLAB plotting and optimization routines Write and use anonymous functions

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4 Part II Document functions Detect number of inputs and outputs Subfunctions Nested functions

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Documentation 5

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6 To find out how to use a MATLAB function you type the command help function_name If you don't know function name, can look for important word in function description with lookfor word We can incorporate our functions in the MATLAB help system so help and lookfor work on custom code

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Documentation 7 Look at results for MATLAB csvread() Try It 1.Type help csvread 2.Type lookfor 'comma separated' 3.Type type csvread

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Documentation 8 >> help csvread CSVREAD Read a comma separated value file. M = CSVREAD('FILENAME') reads a comma separated value formatted file FILENAME. The result is returned in M. The file can only contain numeric values. M = CSVREAD('FILENAME',R,C) reads data from the comma separated value, etc. >> lookfor 'comma separated' lists - Comma separated lists. csvread - Read a comma separated value file. csvwrite - Write a comma separated value file. >> type csvread function m = csvread(filename, r, c, rng) %CSVREAD Read a comma separated value file. % M = CSVREAD('FILENAME') reads a comma separated value formatted file % FILENAME. The result is returned in M. The file can only contain % numeric values. % % M = CSVREAD('FILENAME',R,C) reads data from the comma separated value etc.

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Documentation 9 help displays first group of contiguous comment lines in file Traditionally put right after function line Blank line breaks contiguous group –To display blank, put in line with only a percent sign

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Documentation 10 Example – help output In file doc_check.m function [ result details ] = doc_check( fileName ) % DOC_CHECK Check a function m-file for correct documentation. % % Check that first comment has function name in capital letters and line % ends with a period, that every input and output parameter is documented, % etc. See explanation for "details" output parameter for full list >> help doc_check DOC_CHECK Check a function m-file for correct documentation. Check that first comment has function name in capital letters and line ends with a period, that every input and output parameter is documented, etc. See explanation for "details" output parameter for full list

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Documentation 11 H1 or description line H1 = first line in help description lookfor uses this line –Make line descriptive of function –Include words user would most likely search for

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Documentation 12 Example – lookfor output In file doc_check.m function [ result details ] = doc_check( fileName ) % DOC_CHECK Check a function m-file for correct documentation >> lookfor documentation doc_check - Check a function m-file for correct documentation. builddocsearchdb - Build documentation search database doc - Display HTML documentation in the Help browser. docsearch - Search HTML documentation in the Help browser.

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Documentation 13 Suggestions for documentation H1 line Longer description of functionality Description of parameters Description of errors and how they're handled References

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Documentation 14 H1 line suggestions File name in caps * End in period * Contain words likely to be searched for * MATLAB conventions. Don't know if they have functionality

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Documentation 15 Longer description suggestions Name of algorithm, inputs and outputs, e.g. "Run's Reese's algorithm on the students in the class and produces a list of slackers and hard workers" Don't put in details spelled out further in documentation

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Documentation 16 Parameter suggestions Definition Data type, e.g., scalar, vector, matrix, etc. –For vector, whether row, column or either Units Range –Be careful with > and ≥ Optional or required –Default if optional input

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Documentation 17 Error suggestions Conditions that cause error State of output if error Internal state if error, e.g., "All open files in routine will be closed if there is an error" Error reporting mechanism –error() –errordlg() –Text of message

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Documentation 18 Example In file doc_check.m function [ result details ] = doc_check( fileName ) % DOC_CHECK Check a function m-file for correct documentation. % % Check that first comment has function name in capital letters and line % ends with a period, that every input and output parameter is documented, % etc. See explanation for "details" output parameter for full list % % REQUIRED INPUT % fileName - name of file to check % REQUIRED OUTPUT % result - true if all items checked for are correct, false otherwise % OPTIONAL OUTPUT % details - all values true or false % details(1) - first word of first comment line is function name in caps % details(2) - first comment line ends with a period % etc. % ERRORS % If can't open or read file, calls error() fid = fopen( fileName ); % etc.

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Documentation 19 Example - errors Output for help doc_check.m >> help doc_check DOC_CHECK Check a function m-file for correct documentation. Check that first comment has function name in capital letters and line ends with a period, that every input and output parameter is documented, etc. See explanation for "details" output parameter for full list REQUIRED INPUT fileName - name of file to check REQUIRED OUTPUT result - true if all items checked for are correct, false otherwise OPTIONAL OUTPUT details - all values true or false details(1) - first word of first comment line is function name in caps details(2) - first comment line ends with a period etc. ERRORS If can't open or read file, calls error()

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Documentation 20 References Full citations for books, papers, etc. Web sites –URL –Date downloaded External codes used –MATLAB central –sourceforge.net –university

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21 Documentation Questions?

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Input / Output Arguments 22

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Arguments 23 One function can have different numbers of inputs or outputs. Most MATLAB functions are like this fminbnd Find minimum of single-variable function on fixed interval Syntax x = fminbnd(fun,x1,x2) x = fminbnd(fun,x1,x2,options) [x,fval] = fminbnd(...) [x,fval,exitflag] = fminbnd(...) [x,fval,exitflag,output] = fminbnd(...)

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Arguments 24 Why different number of inputs? Save caller from always entering argument that has commonly used value –e.g., delimiter in tokenizer usually a space Save caller from entering redundant arguments –e.g., correlation( x, y ) computes cross-correlation, for autocorrelation want correlation( x ) instead of correlation( x, x ) Allow caller to enter extra information if available –e.g., pass graph title to plotting routine

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Arguments 25 In a function, get number of arguments passed to function with nargin Example – download scale.m function [ y expansion ] = scale( x, m, b ) % SCALE - linearly scale x so that y = m*x + b % x - unscaled data, row or column vector % Optional input arguments % m - slope, scalar ~= 0, default = 1 % b - y-intercept, scalar, default = 0 % % Required output % y - scaled data, same dimensions as x % Optional output % expansion - optional output, scalar, % expansion = (yMax-yMin)/(xMax-xMin)

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Arguments 26 Typical verification of number of inputs function [ y expansion ] = scale( x, m, b ) % verify right number of input arguments if nargin == 1 m = 1; b = 0; elseif nargin == 2 b = 0; elseif nargin ~= 3 error( 'USAGE: y = scale( x, m, b ) m, b optional' ); end If missing inputs, set them If not max number of inputs, bail out

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Arguments 27 Can verify data type % verify data type if ~isvector( x ) error( 'x must be a vector' ); elseif ~isscalar( m ) | ~isscalar( b ) error( 'm and b must be scalars' ); end

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Arguments 28 Can verify range %verify range if m == 0 error( 'm must not be zero' ); end

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Arguments 29 Try It >> y = scale( magic(3) ) ??? Error using ==> scale at 23 x must be a vector >> y = scale( 1:5, 2 ) y = 2 4 6 8 10 >> y = scale( 1:5, 2, [ 5 6] ) ??? Error using ==> scale at 25 m and b must be scalars >> y = scale( 1:5, 2, 1, 5 ) ??? Error using ==> scale Too many input arguments. >> y = scale( 1:5, 2, 1 ) y = 3 5 7 9 11

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Arguments 30 Why different number of outputs? Provide caller with less important computations –e.g., [R,P]=corrcoef(...) can return main result R (correlation coefficients) and optionally P (p-values) Provide caller with information about processing that took place Provide caller with information for use with other functions Provide caller with information about any errors

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Arguments 31 Example – MATLAB fminbnd() [x,fval] = fminbnd(...) returns the value of the objective function computed in fun at x. [x,fval,exitflag] = fminbnd(...) returns a value exitflag that describes the exit condition of fminbnd: 1fminbnd converged to a solution x based on options.TolX. 0 Maximum number of function evaluations or iterations was reached. -1 Algorithm was terminated by the output function. -2 Bounds are inconsistent (x1 > x2). [x,fval,exitflag,output] = fminbnd(...) returns a structure output that contains information about the optimization: output.algorithmAlgorithm used output.funcCountNumber of function evaluations output.iterationsNumber of iterations output.messageExit message Main results Exit status Processing information

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Arguments 32 In a function, get number of arguments requested by caller with nargout Example – scale.m function [ y expansion ] = scale( x, m, b ) % SCALE - linearly scale x so that y = m*x + b % x - unscaled data, row or column vector % Optional input arguments % m - slope, scalar ~= 0, default = 1 % b - y-intercept, scalar, default = 0 % % Required output % y - scaled data, same dimensions as x % Optional output % expansion - optional output, scalar, % expansion = (yMax-yMin)/(xMax-xMin) Continues on next slide

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Arguments 33 Processing different number of outputs function [ y expansion ] = scale( x, m, b ) % compute main output if nargout == 1 y = m * x + b; elseif nargout == 2 y = m * x + b; expansion = ( max(y) - min(y) ) / ( max(x) - min(x) ); else error( 'USAGE: [ y expansion ] = scale( x, m, b ) m, b optional' ); end If optional output desired, compute it If not max number of inputs, bail out

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Arguments 34 Try It >> scale( 1:5 ) ??? Error using ==> scale at 42 USAGE: [ y expansion ] = scale( x, m, b ) m, b optional >> y = scale( 1:5 ) y = 1 2 3 4 5 >> y = scale( 1:5, 3 ) y = 3 6 9 12 15 >> [ y ratio ] = scale( 1:5, 3 ) y = 3 6 9 12 15 ratio = 3 >> [ y ratio z ] = scale( 1:5, 3 ) ??? Error using ==> scale Too many output arguments.

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35 Arguments Questions?

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Subfunctions 36

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Subfunctions 37 A function m-file can contain more than one function. All functions other that the first one are called subfunctions. Subfunctions –Used mainly to carry out tasks that should be separated from primary function but unlikely to be used by other m-files – Help avoid having a lot of m-files – Override (used in place of) other functions of same name

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Subfunctions 38 Subfunctions in a file Start with a function line End at next function line or at end of file Are only visible (usable) by the primary function or the other subfunctions Can come in any order as long as primary function comes first Cannot access variables in other subfunctions or in the primary function

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Subfunctions 39 Example – download newstats.m function [avg, med] = newstats(u) % Primary function % NEWSTATS Find mean and median with internal functions. % From MATLAB help on subfunction n = length(u); % Note subfunction mean() gets called, not MATLAB's mean() avg = mean(u, n); med = my_median(u, n); function a = mean(v, n) % Subfunction % Calculate average. a = sum(v)/n; function m = my_median(v, n) % Subfunction % Calculate median. w = sort(v); if rem(n, 2) == 1 m = w((n+1) / 2); else m = (w(n/2) + w(n/2+1)) / 2; end

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Subfunctions 40 Try It Call primary function >> [ av med ] = newstats( 1:11 ) av = 6 med = 6 Call subfunction >> med2 = my_median( 1:11, 11 ) ??? Undefined function or method 'my_median' for input arguments of type 'double'.

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Subfunctions 41 Try It Verify overridden mean() called by putting line disp( 'In newstats mean' ); in subfunction mean() >> [ av med ] = newstats( 1:11 ) In newstats mean av = 6 med = 6

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Subfunctions 42 Strange but True Although you can't access subfunctions from outside their file, you can get help on them! 1.Write normal help stuff for subfunction 2.On command line type help filename>subfunction_name where filename is the name of the file (without the.m) that the subfunction is in

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Subfunctions 43 Try It After the function line for my_median put some help lines and print them by using the help command on the command line function m = my_median(v, n) % This is my median % Land that I love >> help newstats>my_median This is my median Land that I love

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44 Subfunctions Questions?

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Nested Functions 45 function1 function2 function3

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Nested Functions 46 A nested function is a function defined within another function Nested functions often passed by function handle to functions that manipulate other functions – e.g., ezplot(), fminbnd(), etc. – Can be used instead of anonymous functions if function has more than one expression

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Nested Functions 47 To define a nested function, just write it within another function Example function outer( a, b, c )... function inner( a )... end... end Nested function

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Nested Functions 48 Nested functions Can be nested within other nested functions Cannot be inside any MATLAB program control statement, i.e., if, else, elseif, switch, for, while, try, or catch statement Must always be terminated by an end statement

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49 Nested Functions MATLAB Help says: "M-file functions don't normally require a terminating end statement. This rule does not hold, however, when you nest functions. If an M-file contains one or more nested functions, you must terminate all functions (including subfunctions) in the M-file with end, whether or not they contain nested functions."

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Nested Functions 50 You can call a nested function From the level immediately above it. (In the following code, function A can call B or D, but not C or E.) From a function nested at the same level within the same parent function. (Function B can call D, and D can call B.) From a function at any lower level. (Function C can call B or D, but not E.) You can also call a subfunction from any nested function in the same M-file. function A(x, y) % Primary function B(x, y); D(y); function B(x, y) % Nested in A C(x); D(y); function C(x) % Nested in B D(x); end function D(x) % Nested in A E(x); function E(x) % Nested in D... end

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Nested Functions 51 The scope of a variable is the range of functions that have direct access to the variable. When define a variable in a function, scope normally that function alone Calling function cannot access called function's variables A subfunction cannot access another subfunction's variables

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Nested Functions 52 Big power of nested functions: A nested function has access to the variables in all functions in which it is nested

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Nested Functions 53 A variable that has a value assigned to it by the primary function can be read or overwritten by a function nested at any level within the primary A variable that is assigned in a nested function can be read or overwritten by any of the functions containing that function

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Nested Functions 54 Example – download and run nested_fibonacci.m function nested_fibonacci % primary function % nested function function sum = print_and_sum( ix ) if ix < 3 sum = 1; else % nested function can access "indexes" % variable in containing function sum = indexes(ix-1) + indexes(ix-2); fprintf( '%d = %d + %d\n', sum,... indexes(ix-1), indexes(ix-2) ); end indexes = 1:8; % apply print_and_sum to every element of numbers, % save results in a vector and display the vector fib = arrayfun( @print_and_sum, indexes ); fib end % end of nested_fibonacci

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55 Nested Functions Questions?

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56 The End

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