Defining Functions in Matlab

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Misc

Let me know if you prefer a name other than what’s on College rosters, etc.

Questions?

Output vs input variables?

Math has a notion of “input variable” for a function, e.g., in f(x) = x + 3, x represents the “input” value on which the function operates.

For example, the 5 in f(5)

Mathematical functions also implicitly have an output, for example in evaluating f(5) you would calculate that f(5) = 5 + 3 = 8, i.e., the result, or “output,” is 8

Matlab makes you name output as an explicit variable, e.g., output_args

Then you define a function’s output value via a statement of the form output_args = ...

Built-In Functions

We saw a quick example, sin, last time

Almost every mathematical function is available in Matlab, including

• All the trig functions, with their standard mathematical names, in radian and degree versions (e.g., sin (radians) vs sind (degrees))
• Inverse trig functions (e.g., asin, acos, atan, etc.)
• Exponential and logarithmic (e.g., exp (e^x), log (natural log), log10)
• Square roots (sqrt)
• Absolute value (abs)
• And on and on and on. If you need a function and don’t know if it’s in Matlab, look it up online

Some examples

>> sin( 17.9 )
ans =
   -0.8132
>> asin( -0.8132 )
ans =
   -0.9496
>> asind( 1 )
ans =
    90

Defining Functions

Example: Define a pair of functions, both of which take the polar coordinates of a point as arguments, and one of which returns the corresponding x Cartesian coordinate, the other returns the y Cartesian coordinate.

Helpful ideas

• General form: function .... end
• Use new / function to create template
• Suppress output from commands in functions with semicolon
• Remember to save function

Algorithm

• x = r cos(Θ)
• y = r sin(Θ)

Matlab definitions of the functions and some example uses

function [ xCoord ] = f( r, theta )
% Compute x coordinate corresponding to polar coordinates
% r and theta
    xCoord = r * cos( theta );
end

>> f( 1, 0 )
ans =
     1
>> f( 1, 3.14159 )
ans =
   -1.0000

function [ yCoord ] = g( r, theta )
% Compute the y coordinate for polar point (r, theta).
    yCoord = r * sin( theta );
end

>> g( 1, 3.14159 / 2 )
ans =
    1.0000
>> g( 1, 0 )
ans =
     0

It turns out Matlab functions can return more than one result, so you could define both parts of this calculation in a single function:

function [ x, y ] = cartesian( r, theta )
% Compute Cartesian coordinates for polar point (r,theta).
    x = r * cos( theta );
    y = r * sin( theta );
end

Receiving both results requires some new syntax when calling the function though:

>> cartesian( 1, 0 )
ans =
     1
>> [ x, y ] = cartesian( 1, 0 )
x =
     1
y =
     0
>> [ piglet, wombat ] = cartesian( 1, 0 )
piglet =
     1
wombat =
     0

Lab 1

See handout for instructions

Next

Lab day — work on Lab 1

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