CheeseZH: Octave basic commands

 1.Basic Operations
 5+6
 3-2
 5*8
 1/2
 2^6
 1 == 2 %false  ans = 0
 1 ~= 2 %true ans = 1
 1 && 0 %AND ans = 0
 1 || 0 %OR ans = 1
 xor(1,0) %ans = 1
 PS1('>> '); %change the command prompt info
 a = 3 %show a = 3 in screen
 a = 3 %not show a = 3 in screen
 b = 'hi'
 c = (3>=1)
 a = pi; %a = 3.1416
 disp(sprintf('2 decimals: %0.2f',a)) %2 decimals: 3.14
 disp(sprintf('6 decimals: %0.6f',a)) %2 decimals: 3.141593
 format long  %a = 3.14159265358979
 format short %a = 3.1416

 2. Matrices and Vectors
 A = [1 2; 3 4; 5 6]
 v = [ 1 2 3]
 v = [1; 2; 3]
 v = 1:0.1:2 %1.0 1.1 1.2 ... 2.0
 v = 1:6
 v = ones(2,3)
 c = 2*ones(2,3)
 w = ones(1,3)
 w = zeros(1,3)
 w = rand(1,3)
 w = rand(3,3)
 w = randn(1,3) %Gossian distribution
 w = -6 + sqrt(10)*(randn(1,10000))
 hist(w) %draw a histogram
 hist(w,50)
 I = eye(4)
 help eye
 help rand
 help help

 3.Moving data around
 A = [1 2; 3 4; 5 6]
 size(A) %ans = 3 2
 size(A,1) %ans = 3
 size(A,2) %ans = 2
 A(3,2) %ans = 6
 A(2,:) %the second row, ':' means every elements along that row/column
 A(:,2) %the second column
 A([1 3],:) %the first and the third row
 A(:,2) = [10; 11; 12]
 A = [A, [100; 101; 102]] %append another column vector to right
 A(:) %put all elements of A into a single vector
 A = [1 2; 3 4; 5 6]
 B = [11 12; 13 14; 15 16]
 C = [A B] %3 * 4
 C = [A; B] %6 * 2

 v = [1 2 3 4]
 length(v) %ans = 4
 length(A) %ans = 3
 length([1;2;3;4;5]) %ans = 5

 pwd %current path
 cd 'path...'
 ls

 load featuresX.dat
 load priceY.dat
 load('featuresX.dat')
 load('priceY.dat')

 who %show the variables in current scope
 whos %show the variables detail in current scope
 size(featuresX) %ans = 47 2

 v = priceY(1:10)

 save hello.mat v; %save v into a file named "hello.mat"(BINARY)
 save hello.txt v; %txt format can be understood by human(ASCII)
 clear featuresX %delete featuresX from current scope
 clear %delete all variables in current scope

 4.Computing on data
 A = [1 2; 3 4; 5 6]
 B = [11 12; 13 14; 15 16]
 C = [1 1; 2 2]
 A*C
 A.*B %'.' element operation
 A.^2
 v = [1; 2; 3]
 1./v
 log(v)
 exp(v)
 abs(v)
 -v %-1*v
 v + ones(length(v),1) % v + 1, v + ones(3,1)
 A' %transpose

 a = [1 15 2 0.5]
 val = max(a) %val = 15
 [val, ind] = max(a) %val=15 ind(ex)=2
 max(A) %ans = 5 6
 a < 3 %element wise comparison: ans = 1 0 1 1
 find(a<3) %ans = 1 3 4
 A = magic(3)
 [r, c] = find(A>=7) % r = 1; 3; 2   c = 1; 2; 3 ==>A(1,1) A(3,2) A(2,3) are greater than 7
 help find
 sum(a)
 prod(a)
 floor(a)
 ceil(a)
 max(rand(3),rand(3))
 max(A,[],1) %the maximum element in each column
 max(A,[],2) %the maximum element in each row
 max(A) %ans = 8 9 7
 max(max(A)) %ans = 9
 max(A(:)) %ans = 9
 A = magic(9)
 sum(A,1) %sum up each column
 sum(A,2) %sum up each row
 sum(sum(A.*eye(9))) %sum up the main diagonal
 sum(sum(A.*flipud(eye(9)))) %sum up the other diagonal
 pinv(A) %pseudo inverse

 5. Plotting Data
 t = [0:0.01:0.98]
 y1 = sin(2*pi*4*t)
 plot(t,y1);%sin function
 y2 = cos(2*pi*4*t)
 hold on; %put figures in one window
 plot(t,y2,'r') %change the color of cos to red
 xlabel('time')
 ylabel('value')
 legend('sin','cos')
 title('my plot')
 cd '/home/zhanghe';
 print -dpng 'myPlot.png'
 close
 figure(1);plot(t,y1);
 figure(2);plot(t,y2);
 subplot(1,2,1) %%divides plot into 1*2 grid access first element
 plot(t,y1);
 subplot(1,2,2) %%divides plot into 1*2 grid access second element
 plot(t,y2);
 axis([0.5 1 -1 1])
 clf;
 A = magic(5)
 imagesc(A)
 imagesc(A),colorbar,colormap

 6. Control statements
 v = zeros(10,1)
 for i=1:10,
   v(i) = 2^i;
 end;
 indices = 1:10;
 for i=indices,
   disp(i);
 end;
 i = 1;
 while i<=5,
   v(i) = 100;
   i = i+1;
 end;
 while true,
   v(i) = 999;
   i = i+1;
   if i==6,
     break;
   end;
 end;
 v(1) = 2;
 if v(1) == 1,
   disp('One');
 elseif v(1) == 2,
   disp('Two');
 else
   disp('Else');
 end;

 %Octave search path (advanced/optional)
 addpath('/home/zhanghe/ml/ex1')

 %Example of CostFunction
 predictions = X*theta;
 sqrErrors = (predictions-y).^2;
 J = 1/(2*m) * sum(sqrErrors);

 7.Vectorization
 % Hypothesis Function
 % Unvectorized implementation
 prediction = 0.0;
 for j = 1:n+1,
   prediction = prediction + theta(j) * x(j)
 end;
 % Vectorized implementation
 prediction = theta' * x

 % Gradient descent(Simultaneous updates)
 % Vectorized implementation
 delta = 1/m*((hypothesis-y)*x)
 theta = theta - alpha*delta