Understanding Scripts and Functions in Matlab Programming, Study notes of Engineering

Download Understanding Scripts and Functions in Matlab Programming and more Study notes Engineering in PDF only on Docsity! Matlab Programming Gerald W. Recktenwald Department of Mechanical Engineering Portland State University gerry@me.pdx.edu These slides are a supplement to the book Numerical Methods with Matlab: Implementations and Applications, by Gerald W. Recktenwald, c© 2001, Prentice-Hall, Upper Saddle River, NJ. These slides are c© 2001 Gerald W. Recktenwald. The PDF version of these slides may be downloaded or stored or printed only for noncommercial, educational use. The repackaging or sale of these slides in any form, without written consent of the author, is prohibited. The latest version of this PDF file, along with other supplemental material for the book, can be found at www.prenhall.com/recktenwald. Version 0.97 August 28, 2001 Overview • Script m-files
Creating
Side effects • Function m-files
Syntax of I/O parameters
Text output
Primary and secondary functions • Flow control
Relational operators
Conditional execution of blocks
Loops • Vectorization
Using vector operations instead of loops
Preallocation of vectors and matrices
Logical and array indexing • Programming tricks
Variable number of I/O parameters
Indirect function evaluation
Inline function objects
Global variables NMM: Matlab Programming page 1 Script to Plot tan(θ) (1) Enter statements in file called tanplot.m 1. Choose New. . . from File menu 2. Enter lines listed below Contents of tanplot.m: theta = linspace(1.6,4.6); tandata = tan(theta); plot(theta,tandata); xlabel(’\theta (radians)’); ylabel(’tan(\theta)’); grid on; axis([min(theta) max(theta) -5 5]); 3. Choose Save. . . from File menu Save as tanplot.m 4. Run it >> tanplot NMM: Matlab Programming page 4 Script to Plot tan(θ) (2) Running tanplot produces the following plot: 2 2.5 3 3.5 4 4.5 -5 -4 -3 -2 -1 0 1 2 3 4 5 θ (radians) ta n( θ) If the plot needs to be changed, edit the tanplot script and rerun it. This saves the effort of typing in the commands. The tanplot script also provides written documentation of how to create the plot. Example: Put a % character at beginning of the line containing the axis command, then rerun the script NMM: Matlab Programming page 5 Script Side-Effects (1) All variables created in a script file are added to the workplace. This may have undesirable effects because • Variables already existing in the workspace may be overwritten • The execution of the script can be affected by the state variables in the workspace. Example: The easyplot script % easyplot: Script to plot data in file xy.dat % Load the data D = load(’xy.dat’); % D is a matrix with two columns x = D(:,1); y = D(:,2); % x in 1st column, y in 2nd column plot(x,y) % Generate the plot and label it xlabel(’x axis, unknown units’) ylabel(’y axis, unknown units’) title(’Plot of generic x-y data set’) NMM: Matlab Programming page 6 Function m-files (1) • Functions are subprograms:
Functions use input and output parameters to communicate with other functions and the command window
Functions use local variables that exist only while the function is executing. Local variables are distinct from variables of the same name in the workspace or in other functions. • Input parameters allow the same calculation procedure (same algorithm) to be applied to different data. Thus, function m-files are reusable. • Functions can call other functions. • Specific tasks can be encapsulated into functions. This modular approach enables development of structured solutions to complex problems. NMM: Matlab Programming page 9 Function m-files (2) Syntax: The first line of a function m-file has the form: function [outArgs] = funName(inArgs) outArgs are enclosed in [ ] • outArgs is a comma-separated list of variable names • [ ] is optional if there is only one parameter • functions with no outArgs are legal inArgs are enclosed in ( ) • inArgs is a comma-separated list of variable names • functions with no inArgs are legal NMM: Matlab Programming page 10 Function Input and Output (1) Examples: Demonstrate use of I/O arguments • twosum.m — two inputs, no output • threesum.m — three inputs, one output • addmult.m — two inputs, two outputs NMM: Matlab Programming page 11 Function Input and Output Examples (4) Example: Experiments with twosum: >> clear >> x = 4; y = -2; >> twosum(1,2) ans = 3 >> x+y ans = 2 >> disp([x y]) 4 -2 >> who Your variables are: ans x y In this example, the x and y variables defined in the workspace are distinct from the x and y variables defined in twosum. The x and y in twosum are local to twosum. NMM: Matlab Programming page 14 Function Input and Output Examples (5) Example: Experiments with threesum: >> a = threesum(1,2,3) a = 6 >> threesum(4,5,6) ans = 15 >> b = threesum(7,8,9); Note: The last statement produces no output because the assignment expression ends with a semicolon. The value of 24 is stored in b. NMM: Matlab Programming page 15 Function Input and Output Examples (6) Example: Experiments with addmult: >> [a,b] = addmult(3,2) a = 5 b = 6 >> addmult(3,2) ans = 5 >> v = addmult(3,2) v = 5 Note: addmult requires two return variables. Calling addmult with no return variables or with one return variable causes undesired behavior. NMM: Matlab Programming page 16 Prompting for User Input The input function can be used to prompt the user for numeric or string input. >> x = input(’Enter a value for x’); >> yourName = input(’Enter your name’,’s’); Prompting for input betrays the Matlab novice. It is a nuisance to competent users, and makes automation of computing tasks impossible. Free Advice: Avoid using the input function. Rarely is it necessary. All inputs to a function should be provided via the input parameter list. Refer to the demonstration of the inputAbuse function in § 3.3.1. NMM: Matlab Programming page 19 Text Output with disp and fprintf Output to the command window is achieved with either the disp function or the fprintf function. Output to a file requires the fprintf function. disp Simple to use. Provides limited control over appearance of output. fprintf Slightly more complicated than disp. Provides total control over appearance of output. NMM: Matlab Programming page 20 The disp function (1) Syntax: disp(outMatrix) where outMatrix is either a string matrix or a numeric matrix. Examples: Numeric output >> disp(5) 5 >> x = 1:3; disp(x) 1 2 3 >> y = 3-x; disp([x; y]) 1 2 3 2 1 0 >> disp([x y]) 1 2 3 2 1 0 >> disp([x’ y]) ??? All matrices on a row in the bracketed expression must have the same number of rows. Note: The last statement shows that the input to disp must be a legal matrix. NMM: Matlab Programming page 21 The num2str function (2) Although A and S appear to contain the same values, they are not equivalent. A is a numeric matrix, and S is a string matrix. >> clear >> A = eye(3); S = num2str(A); B = str2num(S); >> A-S ??? Error using ==> - Matrix dimensions must agree. >> A-B ans = 0 0 0 0 0 0 0 0 0 >> whos Name Size Bytes Class A 3x3 72 double array B 3x3 72 double array S 3x7 42 char array ans 3x3 72 double array Grand total is 48 elements using 258 bytes NMM: Matlab Programming page 24 Using num2str with disp (1) Combine num2str and disp to print a labeled output of a numeric value >> x = sqrt(2); >> outString = [’x = ’,num2str(x)]; >> disp(outString) x = 1.4142 or, build the input to disp on the fly >> disp([’x = ’,num2str(x)]); x = 1.4142 NMM: Matlab Programming page 25 Using num2str with disp (2) The disp([’x = ’,num2str(x)]); construct works when x is a row vector, but not when x is a column vector or matrix >> z = y’; >> disp([’z = ’,num2str(z)]) ??? All matrices on a row in the bracketed expression must have the same number of rows. Instead, use two disp statements to display column of vectors or matrices >> disp(’z = ’); disp(z) z = 1 2 3 4 NMM: Matlab Programming page 26 The fprintf function (1) Syntax: fprintf(outFormat,outVariables) fprintf(fileHandle,outFormat,outVariables) uses the outFormat string to convert outVariables to strings that are printed. In the first form (no fileHandle) the output is displayed in the command window. In the second form, the output is written to a file referred to by the fileHandle (more on this later). Notes to C programmers: 1. The Matlab fprintf function uses single quotes to define the format string. 2. The fprintf function is vectorized. (See examples below.) Example: >> x = 3; >> fprintf(’Square root of %g is %8.6f\n’,x,sqrt(x)); The square root of 3 is 1.732051 NMM: Matlab Programming page 29 The fprintf function (2) The outFormat string specifies how the outVariables are converted and displayed. The outFormat string can contain any text characters. It also must contain a conversion code for each of the outVariables. The following table shows the basic conversion codes. Code Conversion instruction %s format as a string %d format with no fractional part (integer format) %f format as a floating-point value %e format as a floating-point value in scientific notation %g format in the most compact form of either %f or %e \n insert newline in output string \t insert tab in output string NMM: Matlab Programming page 30 The fprintf function (3) In addition to specifying the type of conversion (e.g. %d, %f, %e) one can also specify the width and precision of the result of the conversion. Syntax: %wd %w.pf %w.pe where w is the number of characters in the width of the final result, and p is the number of digits to the right of the decimal point to be displayed. Examples: Format String Meaning %14.5f use floating point format to convert a numerical value to a string 14 characters wide with 5 digits after the decimal point %12.3e use scientific notation format to convert numerical value to a string 12 characters wide with 3 digits after the decimal point. The 12 characters for the string include the e+00 or e-00 (or e+000 or e-000 on WindowsTM) NMM: Matlab Programming page 31 The fprintf function (6) Vectorized fprintf cycles through the outVariables by columns. This can also lead to unintended results >> A = [1 2 3; 4 5 6; 7 8 9] A = 1 2 3 4 5 6 7 8 9 >> fprintf(’%8.2f %8.2f %8.2f\n’,A) 1.00 4.00 7.00 2.00 5.00 8.00 3.00 6.00 9.00 NMM: Matlab Programming page 34 How to print a table with fprintf (1) Many times a tabular display of results is desired. The boxSizeTable function listed below, shows how the fprintf function creates column labels and formats numeric data into a tidy tabular display. The for loop construct is discussed later in these slides. function boxSizeTable % boxSizeTable Demonstrate tabular output with fprintf % --- labels and sizes for shiping containers label = char(’small’,’medium’,’large’,’jumbo’); width = [5; 5; 10; 15]; height = [5; 8; 15; 25]; depth = [15; 15; 20; 35]; vol = width.*height.*depth/10000; % volume in cubic meters fprintf(’\nSizes of boxes used by ACME Delivery Service\n\n’); fprintf(’size width height depth volume\n’); fprintf(’ (cm) (cm) (cm) (m^3)\n’); for i=1:length(width) fprintf(’%-8s %8d %8d %8d %9.5f\n’,... label(i,:),width(i),height(i),depth(i),vol(i)) end Note: length is a built-in function that returns the number of elements in a vector. width, height, and depth are local variables in the boxSizeTable function. NMM: Matlab Programming page 35 How to print a table with fprintf (2) Example: Running boxSizeTable gives >> boxSizeTable Sizes of boxes used by ACME Delivery Service size width height depth volume (cm) (cm) (cm) (m^3) small 5 5 15 0.03750 medium 5 8 15 0.06000 large 10 15 20 0.30000 jumbo 15 25 35 1.31250 NMM: Matlab Programming page 36 Relational Operators (1) Relational operators are used in comparing two values. Operator Meaning < less than <= less than or equal to > greater than >= greater than or equal to ~= not equal to The result of applying a relational operator is a logical value, i.e. the result is either true or false. In Matlab any nonzero value, including a non-empty string, is equivalent to true. Only zero is equivalent to false. Note: The <=, >=, and ~= operators have “=” as the second character. =<, => and =~ are not valid operators. NMM: Matlab Programming page 39 Relational Operators (2) The result of a relational operation is a true or false value. Examples: >> a = 2; b = 4; >> aIsSmaller = a < b aIsSmaller = 1 >> bIsSmaller = b < a bIsSmaller = 0 Relational operations can also be performed on matrices of the same shape, e.g., >> x = 1:5; y = 5:-1:1; >> z = x>y z = 0 0 0 1 1 NMM: Matlab Programming page 40 Logical Operators Logical operators are used to combine logical expressions (with “and” or “or”), or to change a logical value with “not” Operator Meaning & and | or ~ not Examples: >> a = 2; b = 4; >> aIsSmaller = a < b; >> bIsSmaller = b < a; >> bothTrue = aIsSmaller & bIsSmaller bothTrue = 0 >> eitherTrue = aIsSmaller | bIsSmaller eitherTrue = 1 >> ~eitherTrue ans = 0 NMM: Matlab Programming page 41 if Constructs Syntax: if expression block of statements end The block of statements is executed only if the expression is true. Example: if a < 0 disp(’a is negative’); end One line format uses comma after if expression if a < 0, disp(’a is negative’); end NMM: Matlab Programming page 44 if. . . else Multiple choices are allowed with if. . . else and if. . . elseif constructs if x < 0 error(’x is negative; sqrt(x) is imaginary’); else r = sqrt(x); end NMM: Matlab Programming page 45 if. . . elseif It’s a good idea to include a default else to catch cases that don’t match preceding if and elseif blocks if x > 0 disp(’x is positive’); elseif x < 0 disp(’x is negative’); else disp(’x is exactly zero’); end NMM: Matlab Programming page 46 for loops for loops are most often used when each element in a vector or matrix is to be processed. Syntax: for index = expression block of statements end Example: Sum of elements in a vector x = 1:5; % create a row vector sumx = 0; % initialize the sum for k = 1:length(x) sumx = sumx + x(k); end NMM: Matlab Programming page 49 for loop variations Example: A loop with an index incremented by two for k = 1:2:n ... end Example: A loop with an index that counts down for k = n:-1:1 ... end Example: A loop with non-integer increments for x = 0:pi/15:pi fprintf(’%8.2f %8.5f\n’,x,sin(x)); end Note: In the last example, x is a scalar inside the loop. Each time through the loop, x is set equal to one of the columns of 0:pi/15:pi. NMM: Matlab Programming page 50 while loops (1) while loops are most often used when an iteration is repeated until some termination criterion is met. Syntax: while expression block of statements end The block of statements is executed as long as expression is true. Example: Newton’s method for evaluating √ x rk = 1 2 ( rk−1 + x rk−1 ) r = ... % initialize rold = ... while abs(rold-r) > delta rold = r; r = 0.5*(rold + x/rold); end NMM: Matlab Programming page 51 The break command Example: Escape from a while loop function k = breakDemo(n) % breakDemo Show how the "break" command causes % exit from a while loop. % Search a random vector to find index % of first element greater than 0.8. % % Synopsis: k = breakDemo(n) % % Input: n = size of random vector to be generated % % Output: k = first (smallest) index in x such that x(k)>0.8 x = rand(1,n); k = 1; while k<=n if x(k)>0.8 break end k = k + 1; end fprintf(’x(k)=%f for k = %d n = %d\n’,x(k),k,n); % What happens if loop terminates without finding x(k)>0.8 ? NMM: Matlab Programming page 54 The return command Example: Return from within the body of a function function k = returnDemo(n) % returnDemo Show how the "return" command % causes exit from a function. % Search a random vector to find % index of first element greater than 0.8. % % Synopsis: k = returnDemo(n) % % Input: n = size of random vector to be generated % % Output: k = first (smallest) index in x % such that x(k)>0.8 x = rand(1,n); k = 1; while k<=n if x(k)>0.8 return end k = k + 1; end % What happens if loop terminates without finding x(k)>0.8 ? NMM: Matlab Programming page 55 Comparison of break and return break is used to escape the current while or for loop. return is used to escape the current function. function k = demoBreak(n) ... while k<=n if x(k)>0.8 break; end k = k + 1; end function k = demoReturn(n) ... while k<=n if x(k)>0.8 return; end k = k + 1; end jump to end of enclosing “while ... end” block return to calling function NMM: Matlab Programming page 56 Preallocate Memory The following loop increases the size of s on each pass. y = ... % some computation to define y for j=1:length(y) if y(j)>0 s(j) = sqrt(y(j)); else s(j) = 0; end end Preallocate s before assigning values to elements. y = ... % some computation to define y s = zeros(size(y)); for j=1:length(y) if y(j)>0 s(j) = sqrt(y(j)); end end NMM: Matlab Programming page 59 Vectorized Indexing and Logical Functions (1) Thorough vectorization of code requires use of array indexing and logical indexing. Array Indexing: Use a vector or matrix as the “subscript” of another matrix: >> x = sqrt(0:4:20) x = 0 2.0000 2.8284 3.4641 4.0000 4.47210 >> i = [1 2 5]; >> y = x(i) y = 0 2 4 The x(i) expression selects the elements of x having the indices in i. The expression y = x(i) is equivalent to k = 0; for i = [1 2 5] k = k + 1; y(k) = x(i); end NMM: Matlab Programming page 60 Vectorized Indexing and Logical Functions (2) Logical Indexing: Use a vector or matrix as the mask to select elements from another matrix: >> x = sqrt(0:4:20) x = 0 2.0000 2.8284 3.4641 4.0000 4.47210 >> j = find(rem(x,2)==0) j = 1 2 5 >> z = x(j) z = 0 2 4 The j vector contains the indices in x that correspond to elements in x that are integers. NMM: Matlab Programming page 61 Vectorized Copy Operations (2) Example: Copy and transform submatrices Scalar Code for j=2:3 B(1,j) = A(j,3); end Vectorized Code B(1,2:3) = A(2:3,3)’ NMM: Matlab Programming page 64 Deus ex Machina Matlab has features to solve some recurring programming problems: • Variable number of I/O parameters • Indirect function evaluation with feval • In-line function objects (Matlab version 5.x) • Global Variables NMM: Matlab Programming page 65 Variable Input and Output Arguments (1) Each function has internal variables, nargin and nargout. Use the value of nargin at the beginning of a function to find out how many input arguments were supplied. Use the value of nargout at the end of a function to find out how many input arguments are expected. Usefulness: • Allows a single function to perform multiple related tasks. • Allows functions to assume default values for some inputs, thereby simplifying the use of the function for some tasks. NMM: Matlab Programming page 66 Indirect Function Evaluation (2) >> fsum(’sin’,0,pi,5) ans = 2.4142 >> fsum(’cos’,0,pi,5) ans = 0 NMM: Matlab Programming page 69 Use of feval function s = fsum(fun,a,b,n) % FSUM Computes the sum of function values, f(x), at n equally % distributed points in an interval a <= x <= b % % Synopsis: s = fsum(fun,a,b,n) % % Input: fun = (string) name of the function to be evaluated % a,b = endpoints of the interval % n = number of points in the interval x = linspace(a,b,n); % create points in the interval y = feval(fun,x); % evaluate function at sample points s = sum(y); % compute the sum function y = sincos(x) % SINCOS Evaluates sin(x)*cos(x) for any input x % % Synopsis: y = sincos(x) % % Input: x = angle in radians, or vector of angles in radians % % Output: y = value of product sin(x)*cos(x) for each element in x y = sin(x).*cos(x); NMM: Matlab Programming page 70 Inline Function Objects Matlab version 5.x introduced object-oriented programming extensions. Though OOP is an advanced and somewhat subtle way of programming, in-line function objects are simple to use and offer great program flexibility. Instead of function y = myFun(x) y = x.^2 - log(x); Use myFun = inline( ’x.^2 - log(x)’ ); Both definitions of myFun allow expressions like z = myFun(3); s = linspace(1,5); t = myFun(s); Usefulness: • Eliminates need to write separate m-files for functions that evaluate a simple formula. • Useful in all situations where feval is used. NMM: Matlab Programming page 71