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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

Engr/Math/Physics 25. Chp3 MATLAB Functions: Part2. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. Learning Goals. Understand the difference Built-In and User-Defined MATLAB Functions Write User Defined Functions

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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  1. Engr/Math/Physics 25 Chp3 MATLABFunctions: Part2 Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. Learning Goals • Understand the difference Built-In and User-Defined MATLAB Functions • Write User Defined Functions • Describe Global and Local Variables • When to use SUBfunctions as opposed to NESTED-Functions • Import Data from an External Data-File • As generated, for example, by an Electronic Data-Acquisition System

  3. Functions (ReDeaux) • MATLAB Has Two Types of Functions • Built-In Functions Provided by the Softeware • e.g.; max, min, median • User-DefinedFunctions are .m-files that can accept InPut Arguments/Parameters and Return OutPut Values

  4. MATLAB will treat a variable as an array automatically. For example, to compute the square roots of 7, 11 and 3-5j, type Array Function Operations >> u = [7, 11, (3-5j)] >> sqrt(u) ans = 2.64583.31662.1013 - 1.1897i

  5. We can write sin2 in text, but MATLAB requires parentheses surrounding the 2 The 2 is called the fcn argument or parameter To evaluate sin2 in MATLAB, type sin(2) The MATLAB function name must be followed by a pair of parentheses that enclose the argument To express in text the sine of the 2nd element of the array x, we would type sin[x(2)]. However, in MATLAB you cannot use square brackets or braces in this way, and you must type sin(x(2)) Expressing Fcn Arguments

  6. Evaluate sin(x2 + 5) → type sin(x.^2 + 5) Evaluate sin(√x+1) → type sin(sqrt(x)+1) Using a function as an argument of another function is called function composition. Check the order of precedence and the number and placement of parentheses when typing such expressions Every left-facing parenthesis requires a right-facing mate. However, this condition does NOT guarantee that the expression is CORRECT! Expressing Fcn Arguments cont

  7. Another common mistake involves expressions like cos2y, which means (cosy)2. In MATLAB write this expression as (cos(y))^2 or cos(y)^2 Do NOT write the Expression as cos^2(y) cos^2y cos(y^2) Expressing Fcn Arguments cont >> cos(pi/1.73) ans = -0.2427 >> (cos(pi/1.73))^2 ans = 0.0589

  8. Built-In Trig Functions • MATLAB trig fcns operate in radian mode • Thus sin(5) returns the sine of 5 rads, NOT the sine of 5°.

  9. Built-In Inverse-Trig Functions TwoaTan’s? • MATLAB trig-1 fcns also operate in radian mode • i.e., They Return Angles in RADIANS

  10. Consider the Situation at Right Why Two aTan’s? • Due to aTan range −/2  y  /2

  11. Calculator Confusion from Why Two aTan’s? cont • MATLAB Solves This problemwith atan2 which allows input of the CoOrds to ID the proper Quadant • MATLAB atan • MATLAB atan2 >> q1 = atan(-3/4) q1 = -0.6435 >> q2 = atan(3/-4) q2 = -0.6435 >> q3 = atan2(-3,4) q3 = -0.6435 >> q4 = atan2(3,-4) q4 = 2.4981

  12. atan2 built into Complex angle >> z1 = 4 - 3j z1 = 4.0000 - 3.0000i >> z2 = -4 + 3j z2 = -4.0000 + 3.0000i >> r1 = abs(z1) r1 = 5 >> r2 = abs(z2) r2 = 5 >> theta1 = atan2(imag(z1),real(z1)) theta1 = -0.6435 >> theta2 = atan2(imag(z2),real(z2)) theta2 = 2.4981 >> z1a = r1 *exp(j *theta1) z1a = 4.0000 - 3.0000i >> z2b = r2 *exp(j *theta2) z2b = -4.0000 + 3.0000i • As noted in the Discussion of Complex numbers converting between the RECTANGULAR & POLAR forms require that we note the Range-Limits of the atan function • MATLAB’s angle function uses atan2

  13. “Degree” Trig Functions • MATLAB now has Trig Functions that Operate on angles in DEGREES (º) • Example: Y = cosd(θ) • Where is Measured in Degrees NO atan2d(y)though(we’llmake one) • cosd(θ) • sind(θ) • tand(θ) • cotd(θ) • cscd(θ) • secd(θ) • acosd(y) • asind(y) • atand(y) • acotd(y) • acscd(y) • asecd(y)

  14. Built-In Hyperbolic Functions

  15. Built-In Inverse-Hyp Functions >> asinh(37) ans = 4.3042 >> asinh(-37) ans = -4.3042 >> acosh(37) ans = 4.3039 >> acosh(-37) ans = 4.3039 + 3.1416i

  16. The first line in a function file must begin with a FUNCTION DEFINITION LINE that has a list of inputs & outputs. This line distinguishes a function m-file from a script m-file. The 1st Line Syntax: User-Defined Functions (UDFs) function [output variables] = name(input variables) • Note that the OUTPUT variables are enclosed in SQUARE BRACKETS, while the input variables must be enclosed with parentheses. • The function name (here, name) should be the same as the file name in which it is saved (with the .m extension).

  17. The Active m-File Lines UDF Example function ave3 = avg3(a, b, c) TriTot = a+b+c; ave3 = TriTot/3; • Note the use of a semicolon at the end of the lines. This prevents the values of TriTot and ave3 from being displayed

  18. “Call” this Function with its OutPut Agrument UDF Example cont >> TriAve = avg3(7,13,-3) TriAve = 5.6667 • To Determine TriAve the Function takes • a = 7 • b = 13 • c = −3

  19. Call the avg3 function withOUT its output argument and try to access its internal value, avg3. You will see an error message. UDF Example cont >> avg3(-23,19,29) ans = 8.3333 >> ave3 ??? Undefined function or variable 'ave3'. • The variable ave3 is LOCAL to the UDF • It’s Value is NOT defined OutSide the UDF

  20. The variables a, b, & c are local to the function avg3, so unless you pass their values by naming them in the command window, their values will not be available in the workspace outside the function. The variable TriTot is also local to the function. UDF Example cont >> a=-37; b=73; c=19; >> s = avg3(a,b,c); >> a a = -37 >> b b = 73 >> c c = 19 >> TriTot ??? Undefined function or variable 'TriTot'.

  21. New Function UDF – 2nd Example • Write Function DecayCos with inputs of t & ω function ecos = DecayCos(t,w) % Calc the decay of a cosine % Bruce Mayer, PE • ENGR25 • 28Jun05 % INPUTS: % t = time (sec) % w = angular frequency (rads/s) % Calculation section: ePart = exp(t/6); ecos =cos(w.*t)./ePart; w & t can be Arrays

  22. Pass Arrays to DecayCos UDF – 2nd Example cont >> p = DecayCos([1:3],[11:13]) p = 0.0037 0.3039 0.1617 • Note that in MATLAB • [11:13]  [11:1:13] = [ 11, 12, 13]

  23. A function may have more than one output. These are enclosed in square brackets [ ] The OUPput is on the LEFT-hand side of the “=“ sign in the “function definition” line For example, the function Res computes the Electrical Current, Ires, and Power-Dissipated, Pres, in an Electrical Resistor given its Resistance, R, and Voltage-Drop, v,as input arguments UDF – Multiple Outputs

  24. Calling the function Res for 4.7Ω and 28 V Res has 2-INputs & 2-OUTputs UDF – Multiple Outputs cont >> [I1 P1] = res(4.7,28) I1 = 5.9574 P1 = 166.8085

  25. One input, one output: Examples of Fcn Def Lines function [area_square] = square(side) Vector-Brackets are optional for one output: function area_square = square(side) Three inputs, one output (Brackets Optional): function [volume_box] = box(height,width,length) One input, Two outputs (Vector-Brackets Reqd): function [area_circle,circumf] = circle(radius) Output can be a Plot as well as number(s) function sqplot(side)

  26. Example  Free Fall • Consider an object with arbitrary mass, m, falling downward • under the acceleration of gravity • with negligible air-resistance (drag) • With original velocity v0 • Take DOWN as POSITIVE direction

  27. Example  Free Fall cont • Use Newtonian Mechanics to analyze the Ballistics of the falling Object • The Velocity and Distance-Traveled as a function of time & Original Velocity

  28. Free Fall/Drop MATLAB Fcn function [dist, vel] = drop(g, v0, t); % Calc Speed and distance-traveled by % dropped object subject to accel of gravity % Bruce Mayer, PE ENGR25 27Jun05 % % Parameter/Argument List % g = accel of gravity % v0 = velocity at drop point (zero-pt) % t = falling time % % Calculation section: vel = g*t + v0; dist = 0.5*g*t.^2 + v0*t;

  29. The variable names used in the function definition may, but need not, be used when the function is called: Calling Function drop >> a = 32.17; % ft/s^2 >> v_zero = -17; % ft/s >> tf = 4.3; % s >> [dist_ft, spd_fps] = drop(a, v_zero, tf) dist_ft = 224.3117 spd_fps = 121.3310

  30. The input variables need not be assigned values outside the function prior to the function call: Calling Function drop cont >> [ft_dist, fps_spd] = drop(32.17, -17, 4.3) ft_dist = 224.3117 fps_spd = 121.3310

  31. The inputs and outputs may be arrays: Calling Function drop cont Time For Live Demo

  32. The names of the input variables given in the function definition line are local to that function i.e., the Function sets up a PRIVATE Workspace This means that other variable names can be used when you call the function All variables inside a function are erased after the function finishes executing, except when the same variable names appear in the output variable list used in the function call. Local Variables

  33. The global command declares certain variables global, and therefore their values are available to the basic workspace and to other functions that declare these variables global The syntax to declare the variables a, x, and q as GLOBAL is: global a x q Any assignment to those variables, in any function or in the base workspace, is available to all the other functions declaring them global. Global Variables

  34. Private WorkSpace CommandWindow Cmd WindowWorkSpace OUTPUTS fromFunction-1 INPUTS toFunction-1 Function1 Function-1WorkSpace

  35. Make “atan2d” Function function Q = atan2d(Y,X); % Bruce Mayer, PE * 8Sep10 % ENGR25 * Fcn Lecture % % Modifies Built-in Function atan2 to return answer in DEGREES % Q = (180/pi)*atan2(Y,X); >> a2 = atan2d(-3,4) a2 = -36.8699 >> a1 = atan2d(3,-4) a1 = 143.1301

  36. All Done for Today Thisworkspacefor rent

  37. Engr/Math/Physics 25 Appendix Time For Live Demo Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  38. Calling Function drop – 1 • Make as current directory • C:\Working_Files_Laptop_0505\BMayer\Chabot_Engineering\ENGR-25_Comp-Meth\E25_Demo • Use FILE => NEW => M-FILE to open m-file editor • To Slide-28 and Copy the “drop” Text • Paste drop-Text into m-file editor and save-as drop.m

  39. Calling Function drop - 2 • Test drop using SI units >> [y_m, s_mps] = drop(9.8, 2.3, .78) y_m = 4.7752 s_mps = 9.9440>>

  40. The inputs and outputs may be arrays: Calling Function drop - 3 >> [ft_fall, fps_vel] = drop(32.17,-17, [0:.5:2.5]) ft_fall = 0 -4.4787 -0.9150 10.6913 30.3400 58.0313 fps_vel = -17.0000 -0.9150 15.1700 31.2550 47.3400 63.4250 • This function call produces the arrays ft_fall and fps_vel, each with six values corresponding to the six values of time in the array t.

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