EGR 140 Lab 6: Functions and Function Files Topics to be covered : Practice :

Transcription

1 EGR 140 Lab 6: Functions and Function Files Topics to be covered : Creating a Function File Structure of a Function File Function Definition Line Input and Output Arguments Function Body Local and Global Variables Saving a Function File Using a User-Defined Function Examples of Simple User-Defined Functions Comparison Between Script Files and Function Files Anonymous and Inline Functions Anonymous Functions Inline Functions Function Functions Using Function Handles for Passing a Function into a Function Function Using a Function Name for Passing a Function into a Function Function Practice : ( More 2D graphics)

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6 Using the graphics tools

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8 Lab Exercises : % S C O P E, global and local variables EDU>> M=randi(40,5,5) M = % script called tryme disp(inv(m)); % M is in memory so accessible in the script (global) EDU>> tryscope % now a function called tryme function tryme( A ) disp(inv(m)); EDU>> tryme(m) Undefined function or variable 'M'. Error in tryme (line 2) disp(inv(m)); function tryme( A ) disp(inv(a));

9 EDU>> tryme(m)

10 % faux animation function plotpm(theta) clc; format long g; V0 = 120; g = -9.8; t = 0 : 0.05 : 100; Ax = 0; Ay= g; thisangle = theta *(pi/180); xvelocity = V0 * cos(thisangle); yvelocity = V0 * sin(thisangle); x = xvelocity.* t + (1/2) * Ax.* t.^2; y = yvelocity.* t + (1/2) * Ay.* t.^2; waitingtime=1.0e-40; axis([0,2000,0,800]); grid on; hold on for i=3:length(t) plot(x(i), y(i), 'ro--','linewidth',1); pause(waitingtime); plot(x(i - 1), y(i - 1), 'wo','linewidth',1); if y(i) < 0 break; plot(x(i), y(i), 'ko-','linewidth',1.25); disp('done') function plotmatrix(m,s) plot(m(:,1),m(:,2),s)

11 function matrixout = pascalmatrix(n) M = ones(n); for i = 2:n for j = 2:n M(i,j) = M(i-1,j) + M(i,j-1); matrixout = M;

12 1, 0 < t < T Plot the square wave function f (t ) = 1, T < t < 0 of for T = 1 and t increments Use the subplot command to plot along side of the above function the function F(t) = 4 π 20 k = 0 1 2k + 1 sin ( 2k + 1)πt T for the same increments and values as above. function prob15() % uses functions truesquarewave and approxsqwave subplot(1,2,1); truesquarewave() subplot(1,2,2); approxsqwave(20) function approxsqwave(iterations) T = 1; tinc = 0.01; x = -T:tinc:T; y = []; n = length(x); function truesquarewave() T = 1; x=-t:0.01:t; y=[]; for i=1:length(x) if x(i) < 0 y = [y -1]; else y= [y 1]; plot(x,y) axis([-t T ]) for t = 1:n s = 0; for k=0:iterations s = s + (1 / (2*k + 1))*sin(((2*k+1)*pi*x(t))); Ft = (4/pi)*s; y = [y Ft]; plot(x,y)

13 x = [-1 0 1]; y = [-1 1 1]; stairs (x,y,'r','linewidth',1.5); hold on; approxsqwave(15);

14 ====================================================================== function y = matrixtocolvector(m) % Assume matrix M exists; result col-major order row vector [r c] = size(m); V = [ ]; n = r * c; for i = 1:n V = [V M(i)]; % natural colum major order y = V; O R function y = matrixtocolvector(m) % Assume matrix M exists; result col-major order row vector [r c] = size(m); V = [ ]; for col = 1:c for row = 1:r V(+1) = M(row,col); y = V; function y = matrixtorowlvector(m) % Assume matrix M exists; result col-major order row vector [r c] = size(m); V = [ ]; for row = 1:r for col = 1:c V(+1) = M(row,col); y = V; O R

15 function y = matrixtorowlvector(m) % Assume matrix M exists; result col-major order row vector [r c] = size(m); V = [ ]; M = M ; n = r * c; for i = 1:n V = [V M(i)]; % natural colum major order of transpose y = V; ======================================================================= function y = vectortomatrix(v,r,c) n = length(v); % If n less than (r c ) truncate, if greater pad with 0's k = 0; M = []; for i = 1:r Mrow = []; for j = 1:c k = k + 1; if k <= n Mrow = [Mrow V(k)]; else Mrow = [Mrow 0]; M = [M ; Mrow]; y = M;

16 % OPTIONAL passign a function parameter and contour plotting function tau = Tplate(x,y) % tau is the temperature at <x,y> tau = 100*exp(-.4*((x-1)^2+0.7*(y-3)^2))+80*exp(-.2*(2*(x-5)^2+1.5*(y-1)^2)); function fvals = fongrid(x,y,fn) n = length(x); m = length(y); fvals = zeros(m,n); for j=1:n for i=1:m fvals(i,j) = fn(x(j),y(i)); % Script for contour plot a=0; b=6; n=301; x=linspace(a,b,n); c=0; d=4; m=201; y=linspace(c,d,m); TVals = fongrid(x,y,@tplate); close all v=linspace(5,100,20); contour(x,y,tvals,v); figure TY = fongrid(x,[1 2 3],@Tplate); plot(x,ty(1,:),x,ty(2,:),'--',x,ty(3,:),'-.'); xlabel('x','fontsize',14)' ylabel('temperature','fontsize',14); leg('y=1','y=2','y=3'); shg % show most recent graph window

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18 Assignment : NOTE - due the week after spring break! You are to submit a clean hard copy of the solutions to the following problems. 1. (16 points) 2. (16 points). Construct a function called "howfar" that uses the distance formula to calculate how far the two points are apart. For example, if x = [1 2] and y = [4 6], then disp(howfar(x,y)) should display (16 points) Write a function hitthetarget(angle, xcor) using the projectile motion script above. Use your function to discover what angle should be used as a parameter so as to hit the target. (Note: show the target on your graph as a point on the ground set at x = 1000 )

19 4. (16 points) Two points on the unit circle are randomly selected. What is the probability that the length of the connecting chord is greater than 1? Write a script that simulates the process described in the problem narrative. Run your simulation MANY times to discover the answer. (Note: The equation of the unit circle is x 2 + y 2 = 1. ) 5. (16 points) A stick of length one unit is broken into two pieces. Assume that the "breakpoint" is randomly situated. On the average, how long is the shortest piece? - Write a script that simulates the process described in the problem narrative. Run your simulation MANY times to discover the answer. 6. (20 points)