Introduction to MATLAB Session 3 Simopekka Vänskä, THL 2010

Introduction to MATLABSession 3

Simopekka Vänskä, THL2010

Introduction to MATLAB - Session 3

Contents of this course

Session 1 General

Matrices

M-files

Session 2 Some matrix commands

Logical expressions

Graphics 1

Session 3 My functions + strings, cells

Controlling program flow

Session 4 Function functions

Session 5 Graphics 2

More linear algebra

Starting homework

My functions + strings and cells


FunctionFunctions are m-files starting with command functionA function creates its own variable space that includes

copies of INPUT parameters What the function does for the parameters in the function’s

variable space does not effect to the main variable spaceOwn functions follow the same general syntax as

MATLAB functions[OUTPUT parameters] = functionname(INPUT parameters);

FunctionINPUT

parametersOUTPUT

parameters


Writing a function Save the function to a m-file

whose name is the function

name Begin with the command

function, see the example. Help consisits of the first

connected comment lines. Put information!

Write the command lines. Assign values for all output

variables. Call the function with its name. Help by >> help ftest1

function [b,c] = ftest1(a)

% function [b,c] = ftest1(a)

% Function for learning functions.

% INPUT: a matrix of doubles

% OUTPUT:

% b a short description for

% c the output variables is useful.

% 25.10.2010 Sp Vanska

% This is not seen as help text.

b = a+5; % this is a comment

c = sqrt(a);


Subfunctions

Some routines are practical to put

to subfunctions No need for a separate m-file Start with function –command You can also write

subfunctions in subfunctions. See ”nested functions” of

help for the visibility rules in

this case.

End with end –command (not

obligatory if not nested)

function Z = ftest1(X)

% this is the main function

% with m-file ftest1.m

Y = X+2;

function W = routine1(X,Y)

% this is a subfunction

statements

end % function routine1 ends

Z = X+W;


Variating number of INPUT -variables

Case 1: Optional variables.

function z = ftest(x,p)% p optional parameter, % if p does not exist, then p = 1.

if ~exist(p) p = 1;end

Calling ftest:>> z = ftest(x,p)OR>> z = ftest(x)

Case 2: Free parameter number.

Use ”varargin” command:

function z = ftest(x,varargin)

vn = length(varargin);

for j = 1:vn

eval([’p’,num2str(j),’=varargin{j};’])

end

To understand this, study first

strings and cell arrays. In the same way: varargout


Datatype string String matrix is an array of

chars. String can be created by

>> s = ’abcd’; String array has to be

rectangular (examples right).

Related commands: num2str, str2num: convert

numbers to strings, and vice

versa

eval: executes the string

Try the following:

>> s = [’name’;’age’]

>> s = [’name’;’age1’]

>> a = ’12’;

>> b = 2;

>> a+b

>> s1 = [a,’ + ’,num2str(b)]

>> s2 = str2num(a) + b

>> eval(s1)


Datatype cell array

Element of a cell (-array) is a

matrix of any datatype More precis, a cell element is

a pointer to the matrix.

Create a cell by listing the

elements in curly braces, {}. Refer to the j’th element matrix:

cellname{j} Remark: cellname(j) is just

the pointer to the matrix j

cell(n,m) : creates (n,m) cell

array of empty matrices

Try the following:

>> s = {’name’;’age’}

>> s{1}

>> s(1)

>> c = {rand(3),5,’name’}

>> c(1)

>> c{1}

>> c{1:2}

>> c{1}(2,3)


…back to varargin varargin is a cell array Put varargin the last input

argument Call >> z=ftest(x,q1,q2,q3);

vn is the number of matrices in

varargin

Put the input parameters to p1,

p2, … 1st round string: p1 = varargin{1}; 2nd round string: p2 = varargin{2};

etc.

function z = ftest(x,varargin)

vn = length(varargin);

for j = 1:vn

eval([’p’,num2str(j),’=varargin{j};’])

end

Controlling program flow


Program flow control

Controlling what statements (commands) will be executed next

Conditional control In case A do this, but in case B do that : if

Loop control Repeat the commands this many times: for Repeat the commands until this holds: while


Conditional flow control:if – elseif – else – end

General form of if statement:

if logical expression 1

statements

elseif logical expression 2

statements

elsestatements

end

elseif is optional There can be many elseif

lines within one if-end pair

else is optional Max one else line within if-

end pair

Use indent when writing the if

statement Helps reading the code!

TRUE

FALSE

TRUE

FALSE


Loop flow control: forA simple form of for command:

for k = 1:n statements end

Repeats the statements n times 1st round, k has value 1

2nd round, k has value 2

etc.

A simple generalization of for:for k = v % v vector

statements end

Repeats length(v) times 1st round, k has value v(1)

2nd round, k has value v(2)

etc.

General form of for:for k = expression statements end

Here, k runs through the

columns of the expression.

Try:

>> for k = 1:n

k

end

>> for k = rand(3)

k

end


Loop flow control: while

Form of the while command:

while logical expression

statements

end

Repeats the statements until the

expression is false Avoid infinite loop!

Tip: If the logical expression is

complicated, or has many

conditions, it is often easier to

use extra logical variable:

dothis = 1; loopno = 1;

while dothis statements loopno = loopno+1; if (some given stop condition) dothis=0; elseif loopno>1000 dothis=0; end end

TRUE

FALSE


Break, keyboard, return, continueBREAK terminates the loop (for or

while) and program continues

from end-command In multiple loop case, only the

innermost loop is terminated

CONTINUE terminates this iteration

of the loop and continues from

the next iteration step

KEYBOARD stops executing the file

and gives control to user at that

point. Useful especially when

debugging the code.

for j=1:n … if something

break end

… end statement % here if break

RETURN Returns the program flow to

the invoking m-file Returns the flow to the m-file

from the keyboard mode

(type return + enter)


Some practical tipsLong lines: [1 2 3 4 ... 5 6 7 8];To make the code more readable

Use indents Write comments

Try to use matrices (instead of for-loops e.g.)Use profiling to speed up your programs,

desktopprofiler Some times only one routine takes most of the time improve

it! Do not repeat the same computations Try to minimize the arguments of the functions, e.g. only x

instead of x*ones(1,1000).Keep always in your mind the memory usage.

ProblemsSession 3


Problems

1. Write function Xn = mspolygon(X,x0,a) that scales the INPUT polygon by a (a>0) and moves its center to point x0, and draws both polygons in one image. The polygon is given by matrix X whose columns are the

nodes (corner points) of the polygon. The output Xn is the

nodes of new polygon. Define the centerpoint to be the average of the nodes. Test your function with P of Exercise 1/Session 2.


Problems

2. Write a function Xt = roundt(X,t) that rounds real numbers to grid tZ = (…,-2t,-t,0,t,2t,…) and complex numbers to grid tC = tZ+itZ. The input X can be a matrix and t>0. Test your function (real case) with X = -5:.01:5 and

t=sqrt(2)/2. Draw a picture. Test your function (complex case) with X =

randn(1,5)+2*i*randn(1,5) and t=0.5. Draw a picture.Write both test cases in one m-file.


Problems

3. Continue the Triangle Exercise 7/Session 2.

a) Write a function xn = Qpoints(n) where the input argument n is a vector

n(j) = number of random points in [0,1]x[0,1](e.g. n = 1000:1000:10000)

and xn is a cell array withxn{j} = n(j) random points.

b) Call Qpoints many times to find an approximative error when computing the area of T with different n’s. Represent the results graphically.

>> quit

…to exit MATLAB.

Documents

Introduction to MATLAB Session 3 Simopekka Vänskä, THL 2010