محاضرة بعنوان Octave/Matlab Tutorial

محاضرة بعنوان
Octave/Matlab Tutorial
Kai Arras
Social Robotics Lab
Contents

• Overview
• Start, quit, getting help
• Variables and data types
• Matrices
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• librobotics Matlab
  OctaveOverview
  Octave is the “open-source Matlab”
  Octave is a great gnuplot wrapper
• www.octave.org
• www.mathworks.com
  Octave and Matlab are both, high-level languages and
  mathematical programming environments for:
• Visualization
• Programming, algorithm development
• Numerical computation: linear algebra, optimization,
  control, statistics, signal and image processing, etc.
  Beware: Octave/Matlab programs can be slow.Overview
  Matlab-Octave comparison:
• Matlab is more flexible/advanced/powerful/costly
• Octave is for free (GPL license)
• There are minor differences in syntax
  This tutorial:
• This tutorial applies to Octave and Matlab
  unless stated otherwise!
  Current versions (autumn 2009):
• Octave 3.2.3
• Matlab 7.6Contents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrices
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsStart, Quit, Getting Help
• To start Octave type the shell command octave,
  double-click Octave.app or whatever your OS
  needs.
  You should see the prompt:
  octave:1>
• If you get into trouble, you can interrupt Octave
  by typing Ctrl-C.
• To exit Octave, type quit or exit.Start, Quit, Getting Help
• To get help, type help or doc
• To get help on a specific command (=built-in
  function), type help command
• Examples: help size, help plot, help figure,
  help inv, …
• To get help on the help system, type help help
• Type q to exit help mode (alike man pages)Start, Quit, Getting Help
• In the help text of Matlab functions, function names
  and variables are in capital letters.
  ➛ Don’t get confused! The (case-sensitive) naming
  convention specifies lowercase letters for built-in
  commands. It is just a way to highlight text.
• Example: help round returns
  ROUND Round towards nearest integer.
  ROUND(X) rounds the elements of X to the nearest
  integers.
  See also floor, ceil, fix.
  […]
• Octave texts are mixed, in lower- and uppercase.Contents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrices
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsVariables and Data Types
• Matrices (real and complex)
• Strings (matrices of characters)
• Structures
  ➛  Vectors? It’s a matrix with one column/row
  ➛  Scalars? It’s a matrix of dimension 1×1
  ➛  Integers? It’s a double (you never have to worry)
  ➛  Boolean? It’s an integer (non-null=true, 0=false)
  Almost everything is a matrix!
  Matlab has more types, e.g. OO-classesVariables and Data Types
  Creating a Matrix
• Simply type:
  octave:1> A = [8, 2, 1; 3, -1, 4; 7, 6, -5]
  Octave will respond with a matrix in pretty-print:
  A =
  8 2 1
  3 -1 4
  7 6 -5
  ➛ More on matrices, further down this tutorial.Variables and Data Types
  Creating a Character String
• Simply type:
  octave:4> str = ‘Hello World’
  Opposed to Matlab, Octave can also deal with double
  quotes. For compatibility reasons, use single quotes.
  Creating a Structure
• Type for instance:
  octave:5> data.id = 3;
  octave:6> data.timestamp = 1265.5983;
  octave:7> data.name = ‘sensor 1 front’;Variables and Data Types
  Creating a Array of Structures
• Oh, a new measurement arrives. Extend struct by:
  octave:8> data(2).id = 4;
  octave:9> data(2).timestamp = 1268.9613;
  octave..> data(2).name = ‘sensor 1 front’;
  Octave will respond with:
  data =
  {
  1×2 struct array containing the fields:
  id
  timestamp
  name
  }Variables and Data Types
  Display Variables
• Simply type its name:
  octave:1> a
  a = 4
  Suppress Output
• Add a semicolon:
  octave:2> a;
  octave:3> sin(phi);
  Applies also to function calls.Variables and Data Types
• Variables have no permanent type.
  s = 3 followed by s = ‘octave’ is fine
• Use who (or the more detailed whos ) to list the
  currently defined variables. Example output:
  Variables in the current scope:
  Attr Name Size Bytes Class
  ==== ==== ==== ===== =====
  A 3×3 72 double
  a 1×1 8 double
  ans 21×1 168 double
  s 1×5 5 char
  v 1×21 24 doubleVariables and Data Types
  Numerical Precision
  Variables are stored as double precision numbers in
  IEEE floating point format.
• realmin Smallest positive floating point
  number: 2.23e-308
• realmax Largest positive floating point
  number: 1.80e+308
• eps Relative precision: 2.22e-16Variables and Data Types
  Control Display of Float Variables
• format short Fixed point format with 5 digits
• format long Fixed point format with 15 digits
• format short e Floating point format, 5 digits
• format long e Floating point format, 15 digits
• format short g Best of fixed or floating point
  with 5 digits (good choice)
• format long g Best of fixed or floating point
  with 15 digits
  See help format for more informationVariables and Data Types
  Talking about Float Variables…
• ceil(x) Round to smallest integer
  not less than x
• floor(x) Round to largest integer
  not greater than x
• round(x) Round towards nearest integer
• fix(x) Round towards zero
  If x is a matrix, the functions are applied to each
  element of x.Contents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrices
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsMatrices
  Creating a Matrix
• Simply type:
  octave:1> A = [8, 2, 1; 3, -1, 4; 7, 6, -5]
• To delimit columns, use comma or space
• To delimit rows, use semicolon
  The following expressions are equivalent:
  A = [8 2 1;3 -1 4;7 6 -5]
  A = [8,2,1;3,-1,4;7,6,-5]Matrices
  Creating a Matrix
• Octave will respond with a matrix in pretty-print:
  A =
  8 2 1
  3 -1 4
  7 6 -5
• Alternative Example:
  octave:2> phi = pi/3;
  octave:3> R = [cos(phi) -sin(phi); sin(phi) cos(phi)]
  R =
  0.50000 -0.86603
  0.86603 0.50000Matrices
  Creating a Matrix from Matrices
  octave:1> A = [1 1 1; 2 2 2]; B = [33; 33];
• Column-wise
  octave:2> C = [A B]
  C =
  1 1 1 33
  2 2 2 33
• Row-wise:
  octave:3> D = [A; [44 44 44]]
  D =
  1 1 1
  2 2 2
  44 44 44Matrices
  Indexing
  Always “row before column”!
• aij = A(i,j) Get an element
• r = A(i,:) Get a row
• c = A(:,j) Get a column
• B = A(i:k,j:l) Get a submatrix
• Useful indexing command end :
  octave:1> data = [4 -1 35 9 11 -2];
  octave:2> v = data(3:end)
  v =
  35 9 11 -2Matrices
  Colon ‘:’, two meanings:
• Wildcard to select entire matrix row or column
  A(3,:), B(:,5)
• Defines a range in expressions like
  indices = 1:5 Returns row vector 1,2,3,4,5
  steps = 1:3:61 Returns row vector 1,4,7,…,61
  t = 0:0.01:1 Returns vector 0,0.01,0.02,…,1
• Useful command to define ranges: linspace
  start increment stopMatrices
  Assigning a Row/Column
• All referenced elements are set to the scalar value.
  octave:1> A = [1 2 3 4 5; 2 2 2 2 2; 3 3 3 3 3];
  octave:2> A(3,:) = -3;
  Adding a Row/Column
• If the referenced row/colum doesn’t exist, it’s added.
  octave:3> A(4,:) = 4
  A =
  1 2 3 4 5
  2 2 2 2 2
  -3 -3 -3 -3 -3
  4 4 4 4 4Matrices
  Deleting a Row/Column
• Assigning an empty matrix [] deletes the
  referenced rows or columns. Examples:
  octave:4> A(2,:) = []
  A =
  1 2 3 4 5
  -3 -3 -3 -3 -3
  4 4 4 4 4
  octave:4> A(:,1:2:5) = []
  A =
  2 4
  2 2
  -3 -3
  4 4Matrices
  Get Size
• nr = size(A,1) Get number of rows of A
• nc = size(A,2) Get number of columns of A
• [nr nc] = size(A) Get both (remember order)
• l = length(A) Get whatever is bigger
• numel(A) Get number of elements in A
• isempty(A) Check if A is empty matrix []
  Octave only:
• nr = rows(A) Get number of rows of A
• nc = columns(A) Get number of columns of AMatrices
  Matrix Operations
• B = 3*A Multiply by scalar
• C = A*B + X – D Add and multiply
• B = A’ Transpose A
• B = inv(A) Invert A
• s = v’Qv Mix vectors and matrices
• d = det(A) Determinant of A
• [v lambda] = eig(A) Eigenvalue decomposition
• [U S V] = svd(A) Sing. value decomposition
• many many more…Matrices
  Vector Operations
  With x being a column vector
• s = x’*x Inner product, result is a scalar
• X = x*x’ Outer product, result is a matrix
• e = x*x Gives an error
  Element-Wise Operations (for vectors/matrices)
• s = x.+x Element-wise addition
• p = x.*x Element-wise multiplication
• q = x./x Element-wise division
• e = x.^3 Element-wise power operatorMatrices
  Useful Vector Functions
• sum(v) Compute sum of elements of v
• cumsum(v) Compute cumulative sum of
  elements of v
• prod(v) Compute product of elements of v
• cumprod(v) Compute cumulative product of
  elements of v
• diff(v) Compute difference of subsequent
  elements [v(2)-v(1) v(3)-v(2) …]
• mean(v) Mean value of elements in v
• std(v) Standard deviation of elementsMatrices
  Useful Vector Functions
• min(v) Return smallest element in v
• max(v) Return largest element in v
• sort(v,’ascend’) Sort in ascending order
• sort(v,’descend’) Sort in descending order
• find(v) Return vector of indices of all nonzero elements in v. Great in combination with vectorized conditions.
  Example:
  ivec = find(datavec == 5).Matrices
  Special Matrices
• A = zeros(m,n) Zero matrix of size m x n
• B = ones(m,n) Matrix of size m x n with all 1’s
• I = eye(n) Identity matrix of size n
• D = diag([a b c]) Diagonal matrix of size 3 x 3
  with a,b,c in the main
  diagonal
  Just for fun
• M = magic(n) Magic square matrix of size
  n x n. (All rows and columns
  sum up to the same number)Matrices
  Random Matrices and Vectors
• R = rand(m,n) Matrix with m x n uniformly
  distributed random numbers
  from interval [0..1]
• N = randn(m,n) Row vector with m x n normally
  distributed random numbers
  with zero mean, unit variance
• v = randperm(n) Row vector with a random
  permutation of the numbers
  1 to nMatrices
  Multi-Dimensional Matrices
  Matrices can have more than two dimensions.
• Create a 3-dimensional matrix by typing, e.g.,
  octave:1> A = ones(2,5,2)
  Octave will respond by
  A =
  ans(:,:,1) =
  1 1 1 1 1
  1 1 1 1 1
  ans(:,:,2) =
  1 1 1 1 1
  1 1 1 1 1Matrices
  Multi-Dimensional Matrices
• All operations to create, index, add, assign,
  delete and get size apply in the same fashion
  Examples:
• [m n l] = size(A)
• A = rand(m,n,l)
• m = min(min(min(A)))
• aijk = A(i,j,k)
• A(:,:,5) = -3Matrices
  Matrix Massage
• reshape(A,m,n) Change size of matrix A to
  have dimension m x n. An
  error results if A does not
  have m x n elements
• circshift(A,[m n]) Shift elements of A m times
  in row dimension and n
  times in column dimension
• shiftdim(A,n) Shift the dimension of A by n.
  Generalizes transpose for
  multi-dimensional matricesMatrices
  Matrix Massage Example
  Let P = [x1; y1; x2; y2; …] be a 2nx1 column vector
  of n (x,y)-pairs. Make it a column vector of
  (x,y,theta)-tuples with all theta values being pi/2:
• Make it a 2xn matrix
  octave:1> P = reshape(P,2,numel(P)/2);
• Add a third row, assign pi/2
  octave:2> P(3,:) = pi/2;
• Reshape it to be a 3nx1 column vector
  octave:3> P = reshape(P,numel(P),1);Strings
  Most Often Used Commands
• strcat Concatenate strings
• int2str Convert integer to a string
• num2str Convert numbers to a string
• sprintf Write formatted data to a string.
  Same as C/C++ fprintf for strings.
• Example
  s = strcat(‘At step ‘,int2str(k),’, p = ‘,num2str(p,4))
  Given that strings are matrices of chars, this is also
  s = [‘At step ‘ int2str(k) ‘, p = ‘ num2str(p,4)]
  Octave responds with
  s = At step 56, p = 0.142Strings
  Octave/Matlab has virtually all common string and
  parsing functions.
• You are encouraged to browse through the list of
  commands or simply type help command :
  strcmp, strncmp, strmatch, char, ischar,
  findstr, strfind, str2double, str2num,
  num2str, strvcat, strtrim, strtok, upper,
  lower,
  and many more…Contents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrices
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsPlotting
  Plotting in 2D
• plot(x,cos(x)) Display x,y-plot
  Creates automatically a figure window. Octave uses
  gnuplot to handle graphics.
• figure(n) Create figure window ‘n’
  If the figure window already exists, brings it into the
  foreground (= makes it the current figure)
• figure Create new figure window with
  identifier incremented by 1.Plotting
  Several Plots
• Series of x,y-patterns: plot(x1,y1,x2,y2,…)
  e.g. plot(x,cos(x),x,sin(x),x,x.^2)
• Add legend to plot: command legend
  legend(‘cos(x)’,’sin(x)’,’x^2′)
• Alternatively, hold on does the same job:
  octave:1> hold on; plot(x,cos(x));
  octave:2> plot(x,sin(x));
  octave:3> plot(x,x.^2);Plotting
  Frequent Commands
• clf Clear figure
• hold on Hold axes. Don’t replace plot with
  new plot, superimpose plots
• grid on Add grid lines
• grid off Remove grid lines
• title(‘Exp1’) Set title of figure window
• xlabel(‘time’) Set label of x-axis
• ylabel(‘prob’) Set label of y-axis
• subplot Put several plot axes into figurePlotting
  Controlling Axes
• axis equal Set equal scales for x-/y-axes
• axis square Force a square aspect ratio
• axis tight Set axes to the limits of the data
• a = axis Return current axis limits
  [xmin xmax ymin ymax]
• axis([-1 1 2 5]) Set axis limits (freeze axes)
• axis off Turn off tic marks
• box on Adds a box to the current axes
• box off Removes boxPlotting
  Choosing Symbols and Colors
• In plot(x,cos(x),’r+’) the format expression
  ‘r+’ means red cross.
• There are a number of line styles and colors,
  see help plot.
  Example:
  octave:1> x = linspace(0,2*pi,100);
  octave:2> plot(x,cos(x),’r+’,x,sin(x),’bx’);
  produces this plot:Plotting
  plot(x,cos(x),’r+’,x,sin(x),’bx’);Plotting
• Adjusting the axes
  octave:3> axis([0 2*pi -1 1])
  (try also axis tight )
• Adding a legend, labels and a title
  octave:4> legend(‘cos(x)’,’sin(x)’,
  ‘Location’,’Southwest’)
  octave:5> title(‘Trigonometric Functions’)
  octave:6> xlabel(‘x’)
  octave:7> ylabel(‘y’)Plotting
  plot(x,cos(x),’r+’,x,sin(x),’bx’);
  *) Title and x-label
  wrongly cut off.
  This seems to be a
  Octave-AquaTerm
  on Mac problem.
  Should work in
  general.
  *)Plotting
  Uhm…, don’t like it. New try:
  octave:1> clf;
• Controlling Color and Marker Size
  octave:2> plot(x,cos(x),’r+’,x,sin(x),’-x’,…
  ‘Color’,[1 .4 .8],’MarkerSize’,2)
  octave:3> axis tight
• Adding Text
  octave:4> text(1,-0.5,’cos(\phi)’)
  octave:5> text(3,0.5,’sin(\phi)’)
  Note the LateX syntax!Plotting
  plot(x,cos(x),’r+’,x,sin(x),’-x’,’Color’,[1 .4 .8],’MarkerSize’,2)Plotting
  Yepp, I like it… Get hardcopy!
  Exporting Figures
• print –deps myPicBW.eps Export B/W .eps file
• print –depsc myPic.eps Export color .eps file
• print –djpeg –r80 myPic.jpg Export .jpg in 80 ppi
• print –dpng –r100 myPic.png Export .png in 100 ppi
  See help print for more devices including
  specialized ones for Latex.
• print can also be called as a function. Then, it
  takes arguments and options as a comma-separated list. E.g.: print(‘-dpng’,’-r100′,’myPic.png’);Plotting
  This tutorial cannot cover the huge variety of
  graphics commands in Octave/Matlab.
• You are encouraged to browse through the list of
  commands or simply type help command :
  hist, bar, pie, area, fill, contour, quiver,
  scatter, compass, rose, semilogx, loglog,
  stem, stairs, image, imagesc
  and many more…Plotting
  Plotting in 3D
• plot3 Plot lines and points in 3d
• mesh 3D mesh surface plot
• surf 3D colored surface plot
  Most 2d plot commands have a 3D sibling. Check
  out, for example,
  bar3, pie3, fill3, contour3, quiver3,
  scatter3, stem3Contents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrices
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsProgramming
  Programming in Octave/Matlab is Super Easy.
  However, keep the following facts in mind:
• Indices start with 1 !!!
  octave:1> v = 1:10
  octave:2> v(0)
  error: subscript indices must be either positive
  integers or logicals.
• Octave/Matlab is case-sensitive.
  Text Editors
• Use an editor with m-file syntax highlighting/
  coloring.Programming
  Control Structures
• if Statement
  if condition,
  then-body;
  elseif condition,
  elseif-body;
  else
  else-body;
  end
  The else and elseif clauses are optional.
  Any number of elseif clauses may exist.Programming
  Control Structures
• switch Statement
  switch expression
  case label
  command-list;
  case label
  command-list;
  …
  otherwise
  command-list;
  end
  Any number of case labels are possible.Programming
  Control Structures
• while Statement
  while condition,
  body;
  end
• for statement
  for var = expression,
  body;
  endProgramming
  Interrupting and Continuing Loops
• break
  Jumps out of the innermost for or while loop that
  encloses it.
• continue
  Used only inside for or while loops. It skips over
  the rest of the loop body, causing the next cycle to
  begin. Use with care.Programming
  Increment Operators (Octave only!)
  Increment operators increase or decrease the value of
  a variable by 1.
• i++ Increment scalar i by 1
• i– Decrement scalar i by 1
• A++ Increment all elements of matrix A by 1
• v– Decrement all elements of vector v by 1
  There are the C/C++ equivalent operators ++i , –A .Programming
  Comparison Operators
• All of comparison operators return a value of 1 if
  the comparison is true, or 0 if it is false.
  Examples: i == 6, cond1 = (d > theta)
• For the matrix-to-matrix case, the comparison is
  made on an element-by-element basis. Example:
  [1 2; 3 4] == [1 3; 2 4] returns [1 0; 0 1]
• For the matrix-to-scalar case, the scalar is
  compared to each element in turn. Example:
  [1 2; 3 4] == 2 returns [0 1; 0 0]Programming
  Comparison Operators
• any(v) Returns 1 if any element of
  vector v is non-zero (e.g. 1)
• all(v) Returns 1 if all elements in
  vector v are non-zero (e.g. 1)
  For matrices, any and all return a row vector with
  elements corresponding to the columns of the matrix.
• any(any(C)) Returns 1 if any element of
  matrix C is non-zero (e.g. 1)
• all(all(C)) Returns 1 if all elements in
  matrix C are non-zero (e.g. 1)Programming
  Relational Operators
• x < y True if x is less than y
• x <= y True if x is less than or equal to y
• x == y True if x is equal to y
• x >= y True if x is greater than or equal to y
• x > y True if x is greater than y
• x ~= y True if x is not equal to y
• x != y True if x is not equal to y (Octave only)
• x <> y True if x is not equal to y (Octave only)Programming
  Boolean Expressions
• B1 & B2 Element-wise logical and
• B1 | B2 Element-wise logical or
• ~B Element-wise logical not
• !B Element-wise logical not (Octave only)
  Short-circuit operations: evaluate expression only
  as long as needed (more efficient).
• B1 && B2 Short-circuit logical and
• B1 || B2 Short-circuit logical orProgramming
  Recommended Naming Conventions
• Underscore-separated or lowercase notation for
  functions
  Examples: intersect_line_circle.m,
  drawrobot.m, calcprobability.m
• UpperCamelCase for scripts
  Examples: LocalizeRobot.m, MatchScan.m
• Note: Matlab/Octave commands are all in
  lowercase notation (no underscores or dashes)
  Examples: continue, int2str, isnumericContents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrix arithmetic
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsFunctions and Scripts
  Functions
  Complicated Octave/Matlab programs can often be
  simplified by defining functions. Functions are
  typically defined in external files, and can be called
  just like built-in functions.
• In its simplest form, the definition of a function
  named name looks like this:
  function name
  body
  end
• Get used to the principle to define one function
  per file (text files called m-file or .m-file)Functions and Scripts
  Passing Parameters to/from Functions
• Simply write
  function [ret-var] = name(arg-list)
  body
  end
• arg-list is a comma-separated list of
  input arguments arg1, arg2, …, argn
• ret-var is a comma-separated list of
  output arguments. Note that ret-var is a vector
  enclosed in square brackets [arg1, arg2, …, argm].Functions and Scripts
  Example Functions:
  function [mu sigma] = calcmoments(data)
  mu = mean(data);
  sigma = std(data);
  end
  function [haspeaks i] = findfirstpeak(data, thresh)
  indices = find(data > thresh);
  if isempty(indices),
  haspeaks = 0; i = [];
  else
  haspeaks = 1; i = indices(1);
  end
  endFunctions and Scripts
  Local Variables, Variable Number of Arguments
• Of course, all variables defined within the body of
  the function are local variables.
• varargin Collects all input argument in a cell
  array. Get them with varargin{i}
• varargout Collects all output argument in a cell
  array. Get them with varargout{i}
• nargin Get the number of input args.
• nargout Get the number of output args.
  See help varargin, help varargout for details.Functions and Scripts
  Functions and their m-File
• When putting a function into its m-file, the name of
  that file must be the same as the function name
  plus the .m extension.
  Examples: calcmoments.m, findfirstpeak.m
• To call a function, type its name without the .m
  extension. Example:
  [bool i] = findfirstpeak(myreadings, 0.3);
• Comments in Octave/Matlab start with % . Make
  use of them!Functions and Scripts
  Scripts
• The second type of m-files is called script. Again,
  Octave/Matlab scripts are text files with an
  .m extension.
• Scripts contain executable code. They are basically
  the “main” programs.
• Execute a script by typing its name without
  the .m extension!
  Example: octave:1> LocalizeRobot
• Comments in Octave/Matlab start with % .
  (I can’t repeat this often enough ;-)Functions and Scripts
  Document your Function/Script
• You can add a help text to your own functions
  or scripts that appears upon help command.
• The first block of comment lines in the
  beginning of an m-file is defined to be help text.
  Example:
  %NORMANGLE Put angle into a two-pi interval.
  % AN = NORMANGLE(A,MIN) puts angle A into the interval
  % [MIN..MIN+2*pi[. If A is Inf, Inf is returned.
  % v.1.0, Dec. 2003, Kai Arras.
  function an = normangle(a,mina);
  if a < Inf,
  […]
  help textFunctions and Scripts
  Setting Paths
• path Print search path list
• addpath(‘dir’) Prepend the specified directory
  to the path list
• rmpath(‘dir’) Remove the specified directory
  from the path list
• savepath Save the current path listContents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrix arithmetic
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsFiles I/O
  Save Variables
  After a complex of lengthy computation, it is recommended to save variables on the disk.
• save my_vars.mat
  Saves all current variables into file my_vars.mat
• save results.mat resultdata X Y
  Saves variables resultdata, X and Y in file results.mat
• save … -ascii
  Saves variables in ASCII format
• save … -mat
  Saves variables in binary MAT formatFiles I/O
  Load Variables
  The corresponding command is load.
• load my_vars.mat
  Retrieves all variables from the file my_vars.mat
• load results.mat X Y
  Retrieves only X and Y from the file results.mat
  An ASCII file that contains numbers in a matrix
  format (columns separated by spaces, rows separated
  by new lines), can be simply read in by
• A = load(‘data.txt’)Files I/O
  Open, Write, Close Files
• fopen Open or create file for writing/reading
• fclose Close file
• fprintf Write formatted data to file. C/C++
  format syntax.
  Example:
  v = randn(1000,1);
  fid = fopen(‘gauss.txt’,’w’);
  for i = 1:length(v),
  fprintf(fid,’%7.4f\n’,v(i));
  end
  fclose(fid);Files I/O
  Attention, Popular Bug
• If your program writes to and reads from files,
  floating point precision of fprintf is crucial!
• Be sure to always write floating point numbers into
  files using the appropriate precision.
• In the above example, with ‘%7.4f\n’ as the
  format definition, this file is going to be poor
  source of Gaussian random numbers.Files I/O
  Reading Files (more advanced stuff)
• textread Read formatted data from text file
• fscanf Read formatted data from text file
• fgetl Read line from file
• fread Read binary data file
  Read/write images
• imread Read image from file (many formats)
• imwrite Write image to file (many formats)Contents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrix arithmetic
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsMisc
  Cleaning Up
• clear A Clear variable A
• clear frame* Clear all variables whose names
  start with frame…
• clear Clear all variables
• clear all Clear everything: variables,
  globals, functions, links, etc.
• close Close foreground figure window
• close all Close all open figure windows
• clc Clear command window (shell)Misc
  Displaying (Pretty) Messages
• disp(A) Display matrix A without
  printing the matrix name
• disp(str) Display string str without
  printing the string name
  Example: when typing
  octave:1> disp(‘done’)
  Octave will respond with
  done
  instead of
  ans = done
  from sprintf(‘done’) or simply ‘done’.Misc
  Command History
• Navigate up and down the command history using
  the up/down arrow keys.
• The command history is start-letter sensitive.
  Type one or more letters and use the arrow keys to
  navigate up and down the history of commands
  that start with the letters you typed.
  Tab completion
• Octave/Matlab have tab completion. Type some
  letters followed by tab to get a list of all commands
  that start with the letters you typed.Misc
  Built-in Unix Commands
• pwd Display current working directory
• ls List directory. See also dir .
• cd Change directory
• mkdir Make new directory
• rmdir Delete directory
  Related Commands
• movefile Move file
• copyfile Copy fileMisc
  Random Seeds
• rand and randn obtain their initial seeds from the
  system clock.
• To generate identical/repeatable sequences, set the
  random generator seeds manually.
  To set the random seeds:
• rand(‘seed’,value) Set seed to scalar
  integer value value.
• randn(‘seed’,value) Set seed to scalar
  integer value value.Contents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrix arithmetic
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• libroboticsOctave/Matlab in Practice
  Useful Stuff in Practice
• Generating output from a C/C++/Python/
  Java/… program in Octave syntax
• Making animations
• Calling unix/dos functions from within Octave
  programs
• Increasing speedOctave/Matlab in Practice
  Output Files in Octave Syntax
• Data written in a matrix format. Example:
  filtered_readings.txt
  0.792258 0.325823 0.957683 0.647680 0.498282
  0.328679 0.414615 0.270472 0.975753 0.043852
  0.601800 0.062914 0.837494 0.621332 0.870605
  0.940364 0.036513 0.843801 0.806506 0.804710
  0.937506 0.872248 0.134889 0.042745 0.228380
• Read in using the command load .
  Example: A = load(‘filtered_readings.txt’);Output Files in Octave Syntax
• File contains code snippets. Example:
  PlotFilteredReadings.m
  A = [
  0.792258 0.325823 0.957683 0.647680 0.498282
  0.328679 0.414615 0.270472 0.975753 0.043852
  0.601800 0.062914 0.837494 0.621332 0.870605
  0.940364 0.036513 0.843801 0.806506 0.804710
  ];
  figure(1); clf; hold on;
  plot(1:size(A,1),A(:,1));
• Must have the .m extension. It’s a script.
• Simply execute by typing PlotFilteredReadings
  Octave/Matlab in PracticeMaking Animations
• Matlab has commands such as getframe and
  movie to make animated movies from plots.
• Octave, being free of charge, does not (yet)
  support these commands.
• Never mind! Here is a pretty obvious way to make
  movies:
  Export plots to a “frames” directory using print
  from within a loop. Then compose frames to a
  movie using tools such as ImageMagick or
  Quicktime Pro.
  Octave/Matlab in PracticeMaking Animations. Example:
• Let data.txt contain data in matrix format, we
  want to plot each column and save it as a frame.
  A = load(‘data.txt’);
  [m n] = size(A);
  figure(1);
  for i = 1:n,
  plot(1:m,A(:,i));
  fname = sprintf(‘frames/frame%04d.png’,i);
  print(‘-dpng’,’-r100′,fname);
  end
• Problem: axis limits change for each plot/frame.
  Octave/Matlab in PracticeMaking Animations. Example:
• To freeze the axes over the entire animation, use
  the command axis([xmin xmax ymin ymax])
  after the plot command.
  A = load(‘data.txt’);
  [m n] = size(A);
  figure(1);
  for i = 1:n,
  plot(1:m,A(:,i));
  axis([1 m min(min(A)) max(max(A))]);
  fname = sprintf(‘frames/frame%04d.png’,i);
  print(‘-dpng’,’-r100′,fname);
  end
  Octave/Matlab in PracticeCalling unix/dos Functions
• For Unix/Linux/MacOSX systems, there is the
  command unix to execute system commands and
  return the result. Examples:
  unix(‘ls -al’)
  unix(‘ftp < ftp_script’)
  unix(‘./myprogram’)
• For PCs, there is the equivalent command dos .
• These commands allow for powerful and handy
  combinations with other programs or system
  commands.
  Octave/Matlab in PracticeSpeed!
• The lack of speed of Octave/Matlab programs is
  widely recognized to be their biggest drawback.
• Mostly it’s your program that is slow, not the
  built-in functions!
• This brings us to the following guidelines:
• For-loops are evil
• Vectorization is good
• Preallocation is good
• Prefer struct of arrays over arrays of struct
  Octave/Matlab in PracticeSpeed: Vectorization
• Given phi = linspace(0,2*pi,100000);
  The code
  for i = 1:length(phi),
  sinphi(i) = sin(phi(i));
  end;
  is significantly slower than simply
  sinphi = sin(phi);
• Nearly all built-in commands are vectorized.
  Think vectorized!
  Octave/Matlab in PracticeSpeed: Preallocation
• If a for- or while-loop cannot be avoided, do not
  grow data structures in the loop, preallocate
  them if you can. Instead of, e.g.,
  for i = 1:100,
  A(i,:) = rand(1,50);
  end;
  Write:
  A = zeros(100,50); % preallocate matrix
  for i = 1:100,
  A(i,:) = rand(1,50);
  end;
  Octave/Matlab in PracticeSpeed: Structure of Arrays
• Always prefer a struct of arrays over a array of
  structs. It requires significantly less memory
  and has a corresponding speed benefit.
• Structure of arrays
  data.x = linspace(0,2*pi,100);
  data.y = sin(data.x);
• Array of structure
  people(1).name = ‘Polly J Harvey’;
  people(1).age = 32;
  people(2).name = ‘Monica Lebowski’;
  people(2).age = 27;
  Octave/Matlab in PracticeContents
• Overview
• Start, quit, getting help
• Variables and data types
• Matrix arithmetic
• Plotting
• Programming
• Functions and scripts
• Files I/O
• Misc
• Octave and Matlab in practice
• librobotics- librobotics is a small library with frequently used
  Octave/Matlab functions in Robotics, especially for
  visualization.
  chi2invtable.m drawrawdata.m j2comp.m
  compound.m drawreference.m jinv.m
  diffangle.m drawrobot.m mahalanobis.m
  drawarrow.m drawrect.m meanwm.m
  drawellipse.m drawtransform.m normangle.m
  drawlabel.m icompound.m
  drawprobellipse.m j1comp.m
• Download from SRL Homepage:
  srl.informatik.uni-freiburg.de/downloads
  libroboticsCommand drawreference.m
  libroboticsCommand drawrect.m
  libroboticsCommand drawarrow.m
  libroboticsCommand drawlabel.m
  libroboticsCommand drawprobellipse.m
  libroboticsCommand drawtransform.m
  libroboticsCommand drawrobot.m
  libroboticsExample Figure
  librobotics- All commands are fully documented, just type
  help command.
• Note the command chi2invtable.m . It returns
  values of the cumulative chi square distribution, typically used for gating and hypothesis
  testing. It replaces the chi2inv function from the
  Matlab statistics toolbox (which is a costly addition
  to Matlab) while being much faster, too.
• librobotics is compatible with both, Matlab and
  Octave.
• It’s open source, feel free to distribute and
  extend.
  libroboticsMore Information
  Full Octave online documentation:
  http://www.octave.org
  ➛ Docs
  ➛ 575 page manual
  (directly: www.gnu.org/software/octave/doc/interpreter)
  Full Matlab online documentation:
  http://www.mathworks.com
  ➛ Products & Services
  ➛ Product List
  ➛ MATLAB
  ➛ DocumentationThanks and Enjoy!
  Kai Arras
  Social Robotics Lab

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