More Function Examples

Example 1

· Here is a function you will use! It converts an angle in degrees to radians. Copy-and-paste this into a new m-file (deg2rad.m). Be sure to remove those unwanted spaces between the comment lines on top in your m-file.

function rad=deg2rad(deg)

%

% rad=deg2rad(deg)

%

% Converts an angle in degrees to radians

% deg – input angle in degrees

% rad – angle converted to radians

%

% Author: …

% Date: …

% 360 degrees = 2 pi radians

rad=(deg/360)*2*pi;

· Test it at the command prompt like so...

>> r1=deg2rad(180)

>> r2=deg2rad(360)

>> r3=deg2rad(0)

· Now, write a new function that converts the other way called rad2deg( ). This should be in a new m-file called rad2deg.m. Model it after the function code above (copy this code into a new m-file). Be sure, however, to modify the function line, comment lines, and the actual mathematical expression inside the function.

· Test it like so at the command prompt…

>> rad2deg(deg2rad(45))

· What should the output be?

Example 2

· The following function computes some parameters for a circle, given its radius

function [a,c,d]=circle(r)

%

% [a,c,d]=circle(r)

%

% Computes the area, circumference, and diameter of

% a circle with radius r.

%

% a – output area of circle

% c – output circumference of circle

% d – output diameter of circle

% r – input radius of circle

%

% Author: …

% Date: …

a=pi*r^2;

c=2*pi*r;

d=r*2;

· Modify this scalar function so that it will work with an array input r then try this at the command prompt…

>> r=linspace(0,10,1000);

>> [a,c,d]=circle(r);

>> plot(r,a,r,c,r,d)

>> legend('Area', 'Circumference', 'Diameter');

>> xlabel('Radius');

Example 3

· This function compute the distance and velocity of a dropped object

function [dist,vel]=drop(g,v0,t)

%

% function [dist,vel]=drop(g,v0,t)

%

% Computes the distance and velocity of a dropped object

% given the acceleration due to gravity, initial velocity, and time after drop.

% Neglects air resistance!

%

% dist – output distance traveled after drop

% vel – output velocity of object at time t

% g – input acceleration due to gravity: g=32 ft/s^2 or g=9.8 m/s^2.

% v0 – input initial velocity

% t – input time after drop (can be scalar or vector).

%

% Author: …

% Date: …

% velocity is integral (with respect to t) of acceleration + initial velocity

vel=g*t+v0;

% distance is integral of velocity (with respect to t)

dist=.5*g*t.^2+v0*t;

· Let’s take our function for a spin… If you drop a coin off a building and it takes 3.2 seconds to hit the ground, how tall was the building? How fast was it going when it hit the ground?

>> [height,velocity]=drop(32,0,3.2)

· Let’s go farther…

>> t=linspace(0,10,1000);

>> [d,v]=drop(32,0,t);

>> figure(1)

>> plot(t,v)

>> xlabel('Time (s) '); ylabel('Velocity (ft/s) ');

>> figure(2)

>> plot(t,d)

>> xlabel('Time (s) '); ylabel('Distance (ft) ');

Notes…

· The variables you use inside a function are local to that function and are not “known” to the calling m-file or workspace (if calling the function from the command line). The calling m-file or workspace will only “know” about the variables specifically declared as output variables in the function statement.

· When you call a function, the output variables can be named anything, as can the input variables. It is the order only that matters.