Introduction and MATLAB Basics

Transcription

1 Introduction and MATLAB Basics

2 Lecture Computer Room

3 MATLAB MATLAB: Matrix Laboratory, designed for matrix manipulation Pro: Con: Syntax similar to C/C++/Java Automated memory management Dynamic data types Single instructions manipulate entire vectors and matrices A wide range of libraries for signal processing, visualisation, machine learning... Platform independent, inclusion of C/C++/Java/... modules possible Costs money Uses lots of memory Can be slow for certain types of problems Further information in the tutorial: the MATLAB Help System!

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5 Variables a = 5 a = 5 Scalars a = 5; a a = 5 (Semicolon suppresses output) Elements of a row are separated by commas a = [1,2,3] a = Matrices Rows are separated by semicolons a = [1,2,3; 4,5,6] a =

6 Basic Datatypes double: Floating point number, the most common datatype in MATLAB Other numeric datatypes: float, int32, uint8,... rather uncommon a = 1; whos('a'); Name Size Bytes Class a 1x1 8 double array Grand total is 1 element using 8 bytes Complex numbers a = complex(1,-2) a = i a = 1-2*i a = i Warning: i can be redefined (overwritten)! Strings a = ['test123', '456'] a = test123456

7 Advanced Datatypes Cell Arrays: Generalised matrix Elements can have differing datatypes Elements can have different sizes a = {[1,2,3], 'test123'} a = [1x3 double] 'test123' Structures Combine various data in a 'field/value' type structure Fields and associated datatypes do not have to be declared (and can change at run-time) a.b = 2; a.c = [2,3,4]; a a = b: 2 c: [2 3 4]

8 Arithmetic Operators 1 Addition and subtraction a = 5; b=6; a + b 11 a = [1,2,3; 4,5,6]; b = [0,1,2; 3,4,5]; a - b Matrices must have the same size to be added or subtracted Exception: Scalars can be added to matrices a = [1,2; 3,4]; b = [1;2;3]; a + b??? Error using ==> plus Matrix dimensions must agree. a = [1,2; 3,4]; a

9 Arithmetic Operators 2 The * operator is used for matrix multiplication a = 5; b = 6; a * b 30 a = [1,2; 3,4]; a * a = [0,1; 1,0]; b = [1;2]; a * b 2 1 The.* operator multiplies corresponding elements of the operands a = [1; 2]; b = [2; 1]; a.* b 2 2

10 Arithmetic Operators 3 Division with / has the expected effect for scalars a = 2; b = 3; a / b In the case of matrices, the./ operator causes element-wise division a = 2; b = [1,2; 3,4]; a./ b a = [1,2; 3,4]; b = [2,1; 1,2]; a./ b Matrices can also be divided using the / operator. This operation solves the system of linear equations associated with the matrices involved

11 Arithmetic Operators 4 Scalars and matrices can be raised to a power using ^ and.^ respectively a = 5; a ^ 2 25 a = [1,2; 3,4]; a.^ For matrices, the ^ operator is equivalent to repeated matrix multiplication a = [1,2; 3,4]; a ^ 3 a = [1,2; 3,4]; a * a * a

12 Logical Operators In MATLAB, True and False are represented by 1 and 0, repectively The operators {==, ~=} test the operands for equality a = 3; a == 0 a = 3; a ~= The operators{>, <, >=, <=} compare the magnitudes of operands a = 5; a < 3 a = 5; a >= All logical operators can be applied to matrices, where they act on each element a = [1,2; 3,4]; a = [1,2; 3,4]; b = [1,0; 3,0]; a == 3 a > b

13 Working with Matrices 1 Matrices do not have to be created by explicitly listing their contents ones(rows, columns) initialises a matrix of ones zeros(rows, columns) initialises a matrix of zeros ones(2,3) zeros(2,3) zeros and ones can also be used to create higher dimensional (3D,4D etc.) matrices a:b initialises a vector [a, a+1, a+2,..., b] a:c:b initialises a vector [a, a+c, a+2*c,..., b] 1:5 2:-0.5:

14 Working with Matrices 2 MATLAB indices start at 1 a(y,x) is the value of a in row y and column x a = [1,2; 3,4]; a(2,1) 3 Several matrix locations can be accessed simultaneously using lists of indices The special index : accesses an entire dimension of a matrix a = [1,2; 3,4]; a = [1,2; 3,4]; a = [1,2; 3,4]; a([1,2],2) a(1:2,2) a(:,2) Elements in a matrix can be addressed using only a single index (see Linear Indexing in the MATLAB Help system)

15 Working with Matrices 3 The ' operator transposes a matrix and (complex) conjugates each element a = [1,2; 3,4]; a = [1,2; 3,4]; a a' a = The size function determines the size of a matrix a = ones(10,100); size(a) Other important functions include: min, max: Find the minimal/maximal value in a vector sum: Sum the elements of a vector mean, std: Mean and standard deviation in a vector find: Find the indices of elements that satisfy a certain condition abs: Compute the absolute value

16 Flow Control 1 Conditional statements use if if Syntax if logical-value Instruction 1 Instruction 2... else Instruction 3 Instruction 4... end If Example a = 1; if (a >= 0) disp('a ist > 0!'); end a ist > 0! The else part of an if statement is optional A sequence of if statements can often be replaced by a single switch statement (see MATLAB Help!)

17 Flow Control 2 for Syntax for Variable = List Instruction 1 Instruction 2... end for Loops for Example 1 for i=[2,4,6] disp(i); end while Loops for Example 2 for i=1:3 disp(2*i); end while Example whlie Syntax while Condition Instruction 1 Instruction 2... end a = 6; while (a > 0) disp(a); a = a-4; end 6 2

18 Writing Functions 1 New (user defined) functions are defined in.m files The file name has to correspond to the function name E.g. the function myfunc is defined in myfunc.m New.m Files can be created using the menu item File -> New -> M-File Several functions can be defined in a single.m file, however only the main program is visible to the outside Important MATLAB will only find your.m file if the directory containing it is either set as the Current Directory in the main window or is permanently added to the search path using File -> Set Path...

19 Writing Functions 2 A function begins with a declaration that contains the function name and lists inputs (parameters) and outputs: function [output1, output2, output3,... ]=Name(input1, input2,... ) output1, output2...: The outputs, or results, of the function input1, input2...: The input parameters to the function Name: The name of the function A very simple MATLAB function could be the following: % Function test1: % Computes the sum of in1 and in2 function [out]=test1(in1, in2) out = in1 + in2; end Comments in MATLAB Programms begin with %, as shown above

20 Writing Functions 3 Functions can be executed in the MATLAB main window total = test1(5,6); total 11 Several outputs are possible by simply assigning values to all output variables: % Function test2: % Computes the sum and the difference of in1 und in2 function [out1, out2]=test2(in1, in2) out1 = in1 + in2; out2 = in1 - in2; end Not all outputs of a function have to be used (assigned) by the caller summe = test2(5,6); [summe, diff] = test2(5,6);

21 Graphics The figure command opens a new window for graphical output figure The close command closes the currently active figure

22 plot plot([-5:5].^2) title('parabola') xlabel('x') ylabel('y') legend('x^2') x = cos(0:0.1:2*pi) y = sin(0:0.1:2*pi) plot(x,y)

23 imshow imshow(diag(0:200),[ ]) colorbar imshow displays matrices as images The empty square braces indicate that intensities are automatically scaled (minimum and maximum become black and white, respectively) The example above displays a matrix with the values [0:200] on the diagonal imshow can also display colour images

24 imread & subplot rgb = imread('img/desert.jpg'); grau = rgb2gray(rgb); subplot(2,1,1) imshow(rgb) subplot(2,1,2) imshow(grau) imread reads an image from a file In the case of colour images, the result is a 3D matrix with RGB values rgb2gray converts colour images to grayscale subplot is used to display several graphics outputs in a single window For image processing and analysis, it is almost always necessary to cast grayscale values to the 'double' datatype: rgb = imread('img/desert.jpg'); grau = double(rgb2gray(rgb));

25 Breakpoints The execution of a function can be halted at arbitrary points using breakpoints The contents of variables at the breakpoint in the function can be viewed and changed This is often usefull when debugging functions test1([1,2], ones(2))??? Error using ==> plus Matrix dimensions must agree. Breakpoints are enabled by clicking on the '-' marker at the beginning of a line Error in ==> test1 at 5 out = in1 + in2; test1([1,2], ones(2)) 5 out = in1 + in2; K in1, in2 in1 = 1 2 in2 =

26 Automatically Switching to Debug Mode MATLAB can be configured to switch to debug mode automatically, as soon as an error occurs Usefull when there are several potential sources of errors (The Debug menu in the main window) (Enable the debug mode automatically in case of an error)

27 Exercises MATLAB is optimised for the manipulation of matrices Loops in which elements of a matrix are processed individually are very slow Good MATLAB programs therefore avoid loops all together Surprisingly many problems can be solved by manipulating entire matrices without explicit iteration, even when the solution is sometimes more memory intensive The aim of this exercise is, therefore, to solve a number of simple and not so simple tasks without using explicit loops over matrices (i.e. no for or while loops allowed!) The following slides describe the prototypes of the functions to be implemented

28 function splitshow(imga,imgb) A processed image (imgb) is to be compared with the original (imga) Both images are cut in half and concatenated to make their comparison easy Both intensities in both images need to be scaled such that their gray values lie in the same range before the two image halves are concatenated imga = imread('img/desert.jpg'); imga = double(rgb2gray(imga)); imgb = edge(imga,'canny'); splitshow(imga,imgb)

29 function [n]=matchcount(a,num) Function matchcount counts how often a given number num occurs in matrix A A = [1,2; 2,3] A = matchcount(a,2) A = [1,2; 2,3] A = matchcount(a,1) 2 1

30 function [A]=replicate(vect, num) The vector vect is repeated num times to produce matrix A vect can be a row-vector or a column-vector Do not use the MATLAB repmat function! a = [1,2,3,4] a = replicate(a,5) a = [1;2;3;4] a = replicate(a,5)

31 function [circ]=circle(radius) circle computes a quadratic matrix circ with (2*radius+1) rows and columns circ contains a region of 1s in the shape of a circle (of radius radius) Hint: Begin by computing a matrix of distances to the centre element of the matrix circle(4) The replicate function could come in handy Example Distances for radius = imshow(circle(100),[])