% Vectors and matrices
  % Row-vectors are defined as:
  a=[1 2 3 4 5 6 7],
  % For sequences of values, you can use a colon form:
  a=1:7,
  b=1:2:7,
  c=7:-1:1,
  % Column-vectors are:
  ac=[1;2;3;4;5;6;7],
  % Transpose and complex-conjugate transpose are .' and ', respectively:
  ac=[1;2;3;4;5;6;7].',
  % Matrices are defined similarly:
  A = [1 2 3 4;5 6 7 8;9 10 11 12];
 
  % Several useful constructors for matrices:
  A0 = zeros(3,4);           % create a 3x4 matrix of all zeros
  A1 = ones(3,4);            % create a 3x4 matrix of all ones
  Ru = rand(2,2);            % create a 2x2 matrix of uniform random numbers, in [0,1)
  Rn = randn(3,2);           % create a 3x2 matrix of Gaussian random numbers, mean 0 variance 1
  B = repmat(b,[3,2]);       % create a matrix by "tiling" copies of b (3 copies down and 2 across)

  % Arithmetic operations are defined for vectors and matrices, i.e.,
  a=a+2,
  % adds the scalar value 2 to every entry of a; similarly for *,-,/, etc.
 
  % You can add two vectors if they are the same size:
  a+2*c,
  % but you cannot add two vectors that are not the same size (unless one is a scalar):
  a+b,
 
  % To access an entry in a vector, use parentheses:
  c(2),
  c(2)=20,
  % For matrices, use two arguments
  A(3,1),
  A(3,1)=20,
  % These basic operations also generalize to n-dimensional arrays
 
  % Arithemetic operations are defined for vectors and matrices, so that
  a*c.'    % The dot product between vectors a and c
  A*b.'    % The matrix-vector product of A and  c
 
  % Element-wise versions of times and divide are specified by .* and ./ :
  a.*c,    % The vector given by the elementwise product
 
  % Matrix powers are ^ while elementwise powers are .^
  R=A^2,    % The matrix product R=A*A:    R(i,j)=\sum_k A(i,k)*A(k,j)
  R=A.^2,   % The elementwise square of A: R(i,j)=A(i,j)^2

  a = [0 1 2]; b = [0 0 2]; 
  a==b,     % test a(i)=b(i): returns logical vector [ 1 0 1 ] 
  a~=b,     % test a(i)!=b(i): logical vector [ 0 1 0 ] 
  a<2,      % test a(i)<2: logical vector [ 1 1 0 ] 

  any( a~=b ),   % true if any a(i)!=b(i) for some i 
  all( a==b ),   % true if all a(i)=b(i) for every i 

  M=[0 1 ; 0 0]; 
  any( M ),      % acts on individual columns of M; returns a logical row vector 

  if (any(a)),   %Best to be sure that test condition is a scalar! 
    fprintf('Some elements of a are true\n'); 
  end; 

  %While-loops behave normally; again best if test condition is a scalar 
  while (i<15), 
    fprintf('While iter %d \n',i); i=i+1; 
  end; 

  %For-loops: step through the code with each value in a series
  for i=1:10,         
    fprintf('Iteration %d \n',i); 
    i=i+2;                        %Note: changing i will not affect the next iteration! 
  end; 
  for i=[7 2 9 13], fprintf('%d\n',i); end;  % can step through any arbitrary series

  %For line plots, use vectors of the x-values and y-values:
  x=[1 1.5 2 3 3.5 4]; y=[0 2 0 4 4 3];         
  plot(x,y,'b-o');      % b=blue, -=solid line, o=circles at points 
  hold on;              % plot over the current plot 
  plot(x,log(x),'r--'); % r=red, --=dashed line 

%Data are plotted and connected in the order they are given:

  x=[1 3 1.5 2 3.5 4]; y=[0 4 2 0 4 3];         
  plot(x,y,'g-.');      % plot the same points but in a different order 

  %Matlab has some useful pre-defined plotting & drawing functions, such as
  %  hist : compute and plot histograms
  %  bar  : bar graphs  (bar3 = 3D bar graph)
  %  surf, mesh: surface and mesh-frame surfaces
  %  contour: contour plot (contour3 = 3D contour)
  %  quiver : "quiver" or vector flow plot
  %  image: display an image (imagesc: with scaling)
  %Finally, "colormap" sets the value-to-color interpretation in plots

  You can access the internals of vectors with indices, or with logical vectors of the same size 
  a = [0 -1 2 -1]; 
  idx=find( a < 0 ),    % returns a list of indices where condition is true: idx=[2 4] 
  b = a( find(a>=0) ),  % extracts subseries where condition is true: b=[0 2] 
  a( find(a<0) )=0,     % replace negative entries with zero 

  a = [0 -1 2 -1];      % Here's an equivalent way to do the same thing using logical indexing: 
  b=a; b(b<0)=[];       % remove (replace with empty) positions where b < 0 
  a( a < 0 ) = 0,       % replace negative entries with zero 

  %Basics 
  u = rand(1,10);             % 10 uniformly distributed random numbers in [0,1) 
  x = randn(2,10);           % 2x10 "standard Gaussian" (independent, variance 1) draws 
  pi = randperm(10);        % random permutation (reordering) of 1:10 
  s = ceil(10*rand(1,10));  % random re-sampling (bootstrap) from 1:10 
  % Seeds: often it is useful to have reproducible random numbers 
  rand('state',seed);   % use "state" random # generator, with initial seed "seed" 
  randn('state',seed);  % same idea, for the Gaussian random # generator

  % Cell arrays store collections of mismatched objects (different in type or in size) 
  c{1} = rand(1,5); c{2} = rand(1,10); c{3} = uint32(1:5); 
  
  % Structs can also hold collections, but use names rather than vector/matrix indexing 
  s.myRandom = rand(1,5); s.myZeros = zeros(3,3); 

  % Command history 
  diary on;             % record input & output to file diary
  diary myFile.txt;     % record input & output to file myFile.txt
  diary off;            % stop recording 
  % Saving and Loading 
  save file.mat;      % save all variables to file.mat 
  load file.mat;      % restore variables from file.mat 
  save file.txt var -ASCII;   % save variable "var" to "file.txt" in ascii format 
  var = load('file.txt');    % load a single variable from a text file