Download User Functions & Vectorized Arithmetic in CS1112 Lecture 9 (2008/9/25) and more Study notes Computer Science in PDF only on Docsity!
Previous Lecture:
Finite/inexact arithmetic
Discrete vs. continuous
Today’s Lecture:
User-defined functions
Announcement:
Prelim 1 tonight at 7:30pm
September 25, 2008 Lecture 9 3
Vectorized
element-by-element arithmetic operations
on arrays
.* ./
A dot (. ) is necessary in front of these math operators
.^
September 25, 2008 Lecture 9 4
Shift
x
= z^5 4 3.5^11
Matlab code: z= x + y
September 25, 2008 Lecture 9 5
Reciprocate
x
/ y
= z .5^12.
Matlab code: z= x ./ y
September 25, 2008 Lecture 9 6
./
A dot (.) is necessary in front of these math operators
Vectorized
element-by-element arithmetic operations between an
array and a scalar
/
.^ .^
The dot in .^ , .^ , ./ not necessary but OK
September 25, 2008 Lecture 9 7
−6 −4 −2 0 2 4 6
−
−
−
−
0
1
2
3
4
major axis = 5, minor axis = 3
Estimate the perimeter of an ellipse
Different methods based on different ways to “average” the major and minor axes
September 25, 2008 Lecture 9 10
How many errors are there in the following
statement given that
x = linspace(0,1,100)?
Y = (3*x .+ 1)/(1 + x^2)
A: 1 B: 2 C: 3 D: 4
September 25, 2008 Lecture 9 11
Plotting an Ellipse
⎟^ =
b
y
a
x
( a cos( t ), b sin( t ))
Easier representation for plotting:
0 <= t <= 2 π
September 25, 2008 Lecture 9 14
Convert from polar to Cartesian coordinates
θ
r (^) y
x
Polar coordinates Cartesian coordinates
September 25, 2008 Lecture 9 15
% Convert polar coordinates (r,theta) to % Cartesian coordinates (x,y). % theta is in degrees.
r= input(‘Enter radius: ’); theta= input(‘Enter angle in degrees: ’);
rads= thetapi/180; % radian x= rcos(rads); y= r*sin(rads);
September 25, 2008 Lecture 9 16
dotsScript.m
function [x, y] = polar2xy(r,theta) % Convert polar coordinates (r,theta) to % Cartesian coordinates (x,y). % theta is in degrees.
rads= thetapi/180; % radian x= rcos(rads); y= r*sin(rads);
r= input(‘Enter radius: ’); theta= input(‘Enter angle in degrees: ’);
rads= thetapi/180; % radian x= rcos(rads); y= r*sin(rads);
A function file polar2xy.m
(Part of) a script file
September 25, 2008 Lecture 9 25
Software Management
Today:
I write a function
EPerimeter(a,b)
that computes the perimeter of the ellipse
2 2
b
y
a
x
September 25, 2008 Lecture 9 26
Software Management
During this year :
You write software that makes extensive use of
EPerimeter(a,b)
Imagine hundreds of programs each with several
lines that reference EPerimeter
September 25, 2008 Lecture 9 27
Software Management
Next year:
I discover a more efficient way to approximate
ellipse perimeters. I change the implementation of
EPerimeter(a,b)
You do not have to change your software at all.
function [x, y] = polar2xy(r,theta) % Convert polar coordinates (r,theta) to % Cartesian coordinates (x,y). % theta is in degrees.
rads= thetapi/180; % radian x= rcos(rads); y= r*sin(rads);
r= input(‘Enter radius: ’); theta= input(‘Enter angle in degrees: ’);
rads= thetapi/180; % radian x= rcos(rads); y= r*sin(rads);
A function file polar2xy.m
(Part of) a script file
September 25, 2008 Lecture 9 30
function [x, y] = polar2xy(r,theta)
Output parameter list
Function name (This file’s name is polar2xy.m)
Input parameter list
September 25, 2008 Lecture 9 32
Function header is the “contract” for how the function will be used (called)
function [x, y] = polar2xy(r, theta)
% Convert polar coordinates (r, theta) to
% Cartesian coordinates (x,y). Theta in degrees.
% Convert polar (r1,t1) to Cartesian (x1,y1)
r1= 1; t1= 30;
[x1, y1]= polar2xy(r1, t1);
plot(x1, y1, ‘*’)
You have this function:
Code to call the above function:
September 25, 2008 Lecture 9 33
Function header is the “contract” for how the function will be used (called)
function [x, y] = polar2xy(r, theta)
% Convert polar coordinates (r,theta) to
% Cartesian coordinates (x,y). Theta in degrees.
% Convert polar (r1,t1) to Cartesian (x1,y1)
r1= 1; t1= 30;
[x1, y1]= polar2xy(r1, t1);
plot(x1, y1, ‘*’)
You have this function:
Code to call the above function:
September 25, 2008 Lecture 9 34
General form of a user-defined function
function [ out1 , out2 , …]= functionName ( in1 , in2 , …) % 1-line comment to describe the function % Additional description of function
Executable code that at some point assigns values to output parameters out1 , out2 , …
in1 , in2 , … are defined when the function begins execution. Variables in1 , in2 , … are called function parameters and they hold the function arguments used when the function is invoked (called). out1 , out2 , … are not defined until the executable code in the function assigns values to them.
September 25, 2008 Lecture 9 35
Comments in functions
Block of comments after the function header is
printed whenever a user types help
functionName at the Command Window
The 1st^ line of this comment block is searched
whenever a user types lookfor someWord at
the Command Window
Every function should have a comment block
after the function header:
1 st^ line succinctly describes what the function does
Additional lines for more detail, if necessary
f= …; n= …;
d= convertLength(f,n);
d= convertLength(f*12+n);
d= convertLength(f+n/12);
x= min(convertLength(f,n), 1);
y= convertLength(pi*(f+n/12)^2);
A: 1 B: 2 C: 3 D: 4
function m = convertLength(ft,in) % Convert length from feet (ft) and inches (in) % to meters (m).
...
Given this function:
How many proper calls to convertLength are shown below?
E: 5 or 0
September 25, 2008 Lecture 9 37
dotsInCircles.m
(functions with multiple input parameters)
(functions with a single output parameter)
(functions with multiple output parameters)
(functions with no output parameter)
Accessing your functions
For now*, put your related functions and scripts
in the same directory.
dotsInCircles.m
randDouble.m
polar2xy.m
drawColorDot.m
*The path function gives greater flexibility. Not required in CS1112.
MyDirectory
Any script/function that
calls polar2xy.m
