What is a Function? EF102 - Spring, A&S Lecture 4 Matlab Functions

Transcription

1 What is a Function? EF102 - Spring, 2002 A&S Lecture 4 Matlab Functions What is a M-file? Matlab Building Blocks Matlab commands Built-in commands (if, for, ) Built-in functions sin, cos, max, min Matlab defined function files (plot, mean, ) You can view these commands type mean Script files Inline functions User-defined function files Toolboxes collection of functions

2 Built-in Functions Rounding Functions Example sin(x) cos(x) tan(x) asin(x) acos(x) atan(x) atan2(y,x) max(x) [m,i]=max(x) min(x) [m,i]=min(x) mean(x) median(x) std(x) sum(x) prod(x) sort(x) abs(x) sqrt(x) exp(x) log(x) log10(x) rand(m,n) randn(m,n) round(x) fix(x) floor(x) ceil(x) sign(x) rem(x/y) abs(x) Absolute value round(x) Round to nearest integer fix(x) Truncate to nearest integer towards 0 floor(x) Rounds to lower integer ceil(x) Rounds to higher integer sign(x) Positive, negative or zero rem(x,y) Remainder of x/y (sometimes referred to as modulus) x = abs(x)= round(x)= fix(x)= floor(x)= ceil(x)= sign(x)= rem(5,3) = 2 Inline Function Definition inline(expr) constructs an inline function object from the MATLAB expression contained in the string EXPR. The input argument is automatically determined by searching EXPR for an isolated lower case alphabetic character, other than 'i' or j If you have more than one input variable, you must to specify them as additional parameters Useful for one-liners Examples: cosd = inline( cos(a.*pi./180) ) z1 = inline( 3.*x 2.*y, x, y ) Inline Function Example» z = inline('2.*x+3.*y','x','y') z = Inline function: z(x,y) = 2.*x+3.*y» z(1,2) ans = 8» xxx=1:10 x = » yyy=2:2:20 y = » z(xxx,yyy) ans =

3 Matlab Script and Function Overview Matlab Script List of Matlab commands in a.m file Uses the workspace for variable storage This is what we have used so far Matlab Function Also stored in a.m file Starts with the command function Allows input and output parameters Has its own variable space - does NOT use the workspace for variable storage Can contain sub-functions Function Example function [r1,r2] = myfunc(p1) % myfunc calculate average and std dev of a list % Usage: [r1,r2] = myfunc(p1) % Input: p1 - list of numbers % Output: r1, r2 - average and std deviation of the list % DO NOT use clear all in a function!!! n = length(p1); r1 = sum(p1)./n; % Calculate the average r2 = sqrt(sum((p1 - r1).^2)./n); % Calculate the std dev ; %not required, but helps mark the end of function Using the Function» help myfunc myfunc calculate average and std dev of a list Usage: [r1,r2] = myfunc(p1) Input: p1 - list of numbers Output: r1, r2 - average and std deviation of the list» x = 1:1:10 x = » a1 = myfunc(x) a1 = » [wsavg,wsstd] = myfunc(x) wsavg = wsstd = » r1??? Undefined function or variable 'r1'. Function Guidelines Always starts with the keyword function Function name should match filename the filename is the true function name Don t use clear all All comments up to first blank line are displayed by help Comments should describe the input and output parameters Input and output parameters are just placeholders All input parameters are passed by value, i.e. the function gets a copy of them and any modifications to input parameters are lost when the function s. Main program s variables are NOT available If there is more than one value to be ed, the values must be enclosed in [ ] brackets

4 Function Guidelines (con t) Beginning comments are shown when you display help for that function Internal variables are NOT retained Variables from the calling program are not accessible Be sure to always define the output variables Returns to calling program when End of file is reached Return command Another function definition is encountered File must be in the Matlab path to use it Name your function uniquely!!! Function Notes Usually used to perform a single task Used to modularize and standardize code Used to generalize operations Avoid cut & paste of similar sections of code More Function Details nargin and nargout variables automatically defined by Matlab for every function Can be used to check if the function was called with the correct number of inputs and outputs A function.m file can contain subfunctions Defined after the first function Only accessible from that file Variables in the calling program can be accessed if defined as global y F6 x A C Coefficient Matrix Notes F 5 F4 B F1 F1 3920N cosd for x sind for y same angle no signs 4 entries/member 2 entries/reaction 180 difference

5 Building a Matrix by Components Planning J1 J2 J3 jmcoef = zeros(6,6); jmcoef(1,2) = cosd(270); jmcoef(1,3) = cosd(300); jmcoef(1,4) = cosd(0); jmcoef(1,5) = cosd(90); jmcoef(2,2) = sind(270); etc... J1 y x A F5 F4 J2 B F1 F1 3920N F6 C J3 coef = addforce(coef, forcenum, jointnum, angle) coef = addmember(coef, forcenum, jn1, jn2, angle) loads = addload(loads, jointnum, mag, angle) Addforce Details Addmember Details function m2 = addforce(m1,fn,jn,ang) %Purpose: Add loads to a load matrix %Input: % m1: input load matrix % fn: force number % jn: joint number % ang: force angle %Output: % m2: new coef matrix with two terms added if (nargin ~=4), ; end; if (jn<=0 jn>length(m1)), ; end; row = jn*2-1; m2 = m1; m2(row, fn) = cos(ang*pi/180); m2(row+1,fn) = sin(ang*pi/180); ; function m2 = addmember(m1,fn,j1,j2,ang) %Purpose: Add member forces to a coefficient matrix %Input: % m1: input coefficient matrix % fn: force number % j1,j2: joint numbers % ang: force angle from j1 to j2 %Output: % m2: new coefficient matrix with four terms added if (nargin ~=5), ; end; if (j1<=0 j1>length(m1)), ; end; if (j2<=0 j2>length(m1)), ; end; m2 = m1; m2 = addforce(m2,fn,j1,ang); m2 = addforce(m2,fn,j2,ang+180); ;

6 Addload Details Final Program (4 files) function m2 = addload(m1,jn,mag,ang) %Purpose: Add loads to a load matrix %Input: % m1: input load matrix % jn: joint number % mag: magnitude of the force % ang: force angle %Output: % m2: new load matrix with two terms added if (nargin ~=4), ; end; if (jn<=0 jn>length(m1)), ; end; row = jn*2-1; m2 = m1; m2(row, 1) = mag.*cos(ang*pi/180); m2(row+1,1) = mag.*sin(ang*pi/180); ; %header clear all coef = zeros(6,6); loads = zeros(6,1); % m1 fn j1 j2 ang coef = addmember(coef, 1, 2, 3,-150); coef = addmember(coef, 2, 1, 3,-90); coef = addmember(coef, 3, 1, 2,-60); % m1 fn jn ang coef = addforce(coef, 4, 1, 0); coef = addforce(coef, 5, 1,90); coef = addforce(coef, 6, 3, 0); % m1 jn mag ang loads = addload(loads, 2, 3920, -90); U = coef \ (-loads) F A 5 F4 y x B F1 F1 3920N F6 C Final Program (1 file with subfunctions) function main %because subfunctions cannot be used in script files %remove clear all % main program here function m2 = addforce(m1,fn,jn,ang)... function m2 = addmember(m1,fn,j1,j2,ang)... function m2 = addload(m1,jn,mag,ang)... Debugging Two types of errors: Syntax Logic Editor hints Auto-indent Goto Syntax highlighting Read error messages Make incremental changes Checking program flow and intermediate results Omit semi-colons Add fprintf statements Pause Debugger