octave syntax

1. tilde equal ~= is in octave, Octave uses bang equal !=

2. Octave uses single quote to present string assignment b = ‘hi’

3. Like Matlab, semicolon suppressing(抑制) output.

4. disp(str) for printing string. disp(sprintf(‘2 decimals: %0.2f’, a)) for printing format string.
5. format long/short
6. row vector [1 2 3]
7. column vector [1; 2; 3]
8. ones(2,3) => initialise matrix
9. rand(1,3) => uniform distribution from 0 to 1: gaussian distribution with mean zero and variance/standard deviation equal to one; gaussian random number/ normal random number.
10. I = eye(5) => Identity Matrix
11. help eye
12. example
    

    1	w = -6 + sqrt(10)*(randn(1,10000000)); hist(w) hist(w,50) => print 50bucket

1. size, length

   1	size(A) = rows columns size(A,1) = rows size(A,2) = columns length(A) = longest dimension

2. load data, find data

3. pwd {show current path}/ cd ‘path’ / ls
4. difference between mat and dat
5. load file.data = load(‘file.dat’)
6. who/ whos{describe the details}
7. clear / clear variable
8. save hello.mat {dat?}
9. v = priceY(1:10) => the first 10 elements, column order

10. I(1:5) / I(1,3)
    octave:47> B = I(1:5)
    B =
    1 0 0 0 1
    octave:48> I
    I =
    Diagonal Matrix

    1 0 0
    0 1 0
    0 0 1

11. save file.mat v; {binary format, compress?}

12. save file.txt v -ascii; % save as text (ASCII)

13. manipulation

14. A(3,2) A(2,:) % “:” means every element along that row/column
15. A([1 3; :]) % all first and third columns
16. Append
    A is a 3 by 2 matrix
    A = [A, [100; 200; 300] ]
    Now, A is 3 by 3
    A = [A; [100, 200, 300]]
    Now, A is 4 by 3
17. A(:) % put all elements of A into a single column vector
    Now, A is a 12 by 1 column vector
18. concatenation

C = [A B] / [A, B]
C = [A; B] % ; means go to the next line

1. element-wise operation
   . .^ ./
   log(v) exp(v) abs(v) -v %equals -1v
   v + 1 % v + ones(length(v),1)

2. Matrix transpose, A = (A’)’

3. Function max

   1	a is a row vector: max(a) [value, index] = max(a) A is a matrix: max(A) % column wise max

4. logic

   1	a = [1 15 2 0.5] a < 3 = [1 0 1 1] find(a < 3) % list the index of element satisfy the given condition ans = [1 3 4]

5. magic(n) => create an N by N magic square, magic(2) is not defined. magic square => each row, each column, and diaglog sum up the same value

   1	octave:64> A A = 8 1 6 3 5 7 4 9 2 octave:65> find(A>=5) {return the index checking by column} ans = 1 5 6 7 8 octave:66> [r c]=find(A>=5) r = 1 2 3 1 2 c = 1 2 2 3 3

6. column-wise & element-wise

   1 2	sum(A) prod(A) {A is matrix, column wise} floor(A)% round down ceil(A)%round up {element-wise}

7. rand(1,3)% create 1 by 3; rand(3)% create 3 by 3

8. max(A,B) % A and B has same size, maximum on element wise

   1

   octave:84> A = magic(3) A = 8 1 6 3 5 7 4 9 2 octave:85> max(A) ans = 8 9 7 octave:86> max(A,[],1) % = max(A), 1 means the first dimension, column ans = 8 9 7 octave:87> max(A,[],2) % 2 means the second dimension, row ans = 8 7 9 octave:89> max(A,5) ans = 8 5 6 5 5 7 5 9 5 octave:90> min(A,5) ans = 5 1 5 3 5 5 4 5 2 find the entire maximum is A: max(max(A)) or max(A(:))

9. Function Sum

   1	A = magic(9) sum(A,1) % sum column sum(A,2) % sum row sum the main diagonal sum(sum(A .* eye(9))) sum the other diagonal: using function flipud, flip up an down sum(sum(A .* flipud(eye(9))))

10. sudep inverse
    pinv(A)

    1

    octave:93> A A = 8 1 6 3 5 7 4 9 2 octave:94> inv(A) ans = 0.147222 -0.144444 0.063889 -0.061111 0.022222 0.105556 -0.019444 0.188889 -0.102778 octave:95> pinv(A) ans = 0.147222 -0.144444 0.063889 -0.061111 0.022222 0.105556 -0.019444 0.188889 -0.102778 octave:96> A*ans ans = 1.0000e+00 -1.2212e-14 6.5503e-15 5.5511e-17 1.0000e+00 -1.1102e-16 -5.8842e-15 1.2434e-14 1.0000e+00 octave:97> inv(A) ans = 0.147222 -0.144444 0.063889 -0.061111 0.022222 0.105556 -0.019444 0.188889 -0.102778 octave:98> A*ans ans = 1.00000 0.00000 -0.00000 -0.00000 1.00000 0.00000 0.00000 0.00000 1.00000

1. Plot 1
   

   1	octave:131> x = [0:0.01:1]; octave:132> plot(x) octave:133> xlabel('x number times') octave:134> ylabel('value of x') octave:135> legend('x') octave:136> title('plot1') octave:137> print -dpng 'plot1.png’

1. Plot 2
   

   1	close figure(1); plot… figure(2); plot…. subplot(1,2,1) %Divides plot a 1x2 grid, access the first element axis([ 0.5 1 - 1 1]); clf; % clear figure

1. Draw Matrix
   

   1 2 3 4 5 6

   octave:173> magic(3) ans = 8 1 6 3 5 7 4 9 2 octave:174> plot(magic(3))

1

imagesc(magic(5)), colorer, colormap gray;     {commands/comma chaining of function }

1. while true,
   break;
2. Octave search path
   addpath(path);
3. function [y1,y2] = …. % return multiple values

numerical and linear algebra library in octave, C++, java

Cost Function Example

Vectorisation Octave Code

Vectorisation C++ Code

Linear Regression Example