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Octave
Vadim Brodsky edited this page Dec 23, 2017
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14 revisions
Like Matlab but free
Basic arithmetic operations
5+5 % ans = 10
3-2 % ans = 1
4*3 % ans = 12
1/3 % ans = 0.33333
2^4 % ans = 16Logical operations
1 == 2 % false ans = 0
1 ~= 2 % true ans = 1
1 && 0 % and ans = 0
1 || 0 % or ans = 1
xor(1,0)Change the prompt
PS1('>> ' ); % changes prompt
a = 3; % semicolon supresses outputVariables
a = 3 % a = 3
b = 'hello';
c = (3>=1); % c = 1
who % shows the variables in the current scope
whos % like who but with more details, sizes, bytes
clear a % clears the a variable
clear % without an argument clears all variablesPrinting output
a = pi % a = 3.1416
a % a = 3.1416
disp(a) % 3.1416
disp(sprintf('2 decimals: %0.2f', a)) % 2 decimals: 3.14
disp(sprintf('2 decimals: %0.6f', a)) % 2 decimals: 3.141593
format long
a % a = 3.14159265358979
format short
a % a = 3.1416Matrices and vectors
A = [1 2; 3 4; 5 6]
% A =
% 1 2
% 3 4
% 5 6
A = [1 2;
> 3 4;
> 5 6]
% A =
% 1 2
% 3 4
% 5 6
V = [1 2 3]
% V =
% 1 2 3
V = [1; 2; 3]
% V =
% 1
% 2
% 3
V = 1:0.1:2
% V =
% Columns 1 through 9:
%
% 1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000
% Columns 10 and 11:
%
% 1.9000 2.0000
V = 1:6
% V =
% 1 2 3 4 5 6
ones(2,3)
% ans =
% 1 1 1
% 1 1 1
c = 2*ones(2,3)
% c =
% 2 2 2
% 2 2 2
w = ones(1,3)
% w =
% 1 1 1
w = zeros(1,3)
% w =
% 0 0 0
I = eye(4)
% I =
% Diagonal Matrix
%
% 1 0 0 0
% 0 1 0 0
% 0 0 1 0
% 0 0 0 1
A = [1 2; 3 4; 5 6]
% A =
% 1 2
% 3 4
% 5 6
size(A)
% ans =
% 3 2
size(A,1) % ans = 3
size(A,2) % ans = 2
v = [1 2 3 4]
% v =
% 1 2 3 4
length(v) % ans = 4
length(A) % size of the longest dimension % ans = 3
length([1;2;3;4;5]) % ans = 5
s = v(1:2) % fist 2 elements of the vector
% s =
% 1
% 2
A = [1 2; 3 4; 5 6]
% A =
% 1 2
% 3 4
% 5 6
A(3,2) % ans = 6
A(2,:) % ":" means every element along that row / column
% ans =
% 3 4
A(:,2)
% ans =
% 2
% 4
% 6
A([1 3], :)
% ans =
% 1 2
% 5 6
A(:,2) = [10; 11; 12] % replaces the first column
% A =
% 1 10
% 3 11
% 5 12
A = [A, [100; 101; 102]] % append another column vector to right
% A =
% 1 10 100
% 3 11 101
% 5 12 102
A(:) % put all elements of A into a single vector
% ans =
% 1
% 3
% 5
% 10
% 11
% 12
% 100
% 101
% 102A = [1 2; 3 4; 5 6]
% A =
% 1 2
% 3 4
% 5 6
B = [11 12; 13 14; 15 16]
% B =
% 11 12
% 13 14
% 15 16
C = [A B]
% C =
% 1 2 11 12
% 3 4 13 14
% 5 6 15 16
C = [A; B]
% C =
% 1 2
% 3 4
% 5 6
% 11 12
% 13 14
% 15 16
C = [A; B]
% C =
% 1 2
% 3 4
% 5 6
% 11 12
% 13 14
% 15 16
size(C)
% ans =
% 6 2
[A B] % same as [A, B]
% ans =
% 1 2 11 12
% 3 4 13 14
% 5 6 15 16Matrix arithmetic
A = [1 2; 3 4; 5 6]
% A =
% 1 2
% 3 4
% 5 6
B = [11 12; 13 14; 15 16]
% B =
% 11 12
% 13 14
% 15 16
C = [1 1; 2 2]
% C =
% 1 1
% 2 2
A*C % matrix multiplication
% ans =
% 5 5
% 11 11
% 17 17
A .* B % element wise multiplication, A .^ B for squaring
% ans =
% 11 24
% 39 56
% 75 96
% v = [1; 2; 3;]
% v =
% 1
% 2
% 3
1 ./ v % element wise reciprocal of a vector
% ans =
% 1.00000
% 0.50000
% 0.33333
log(v) % log of each element
% ans =
% 0.00000
% 0.69315
% 1.09861
exp(v) % exponential of each element
% ans =
% 2.7183
% 7.3891
% 20.0855
abs(v) % absolute value of each element
% ans =
% 1
% 2
% 3
-v % negation of each element
% ans =
% -1
% -2
% -3
v + ones(length(v),1) % increment each value in the vector by one
% ans =
% 2
% 3
% 4
v + 1 % same as above
A' % matrix transpose
% ans =
% 1 3 5
% 2 4 6
(A')' % transpose of a transpose return back A
a = [1 15 2 0.5]
% a =
% 1.00000 15.00000 2.00000 0.50000
val = max(a) % val = 15
[val, indx] = max(a)
% val = 15
% indx = 2
max(A) % column wise maximum
% ans =
% 5 6
a < 3 % element wise comparison
% ans =
% 1 0 1 1
% find(a < 3) % which the index of the elements
% ans =
% 1 3 4
A = magic(3)
% A =
% 8 1 6
% 3 5 7
% 4 9 2
[r, c] = find(A >= 7)
% r =
% 1
% 3
% 2
%
% c =
% 1
% 2
% 3
A(2, 3) % ans = 7
sum(a) % ans = 18.500 % sum(a, 1) by row % sum(a, 2) by column
prod(a) % ans = 15
floor(a)
% ans =
% 1 15 2 0
ceil(a)
% ans =
% 1 15 2 1
max(A, [], 1) % per column maximum
% ans =
% 8 9 7
max(A, [], 2) % per row maxumum
% ans =
% 8
% 7
% 9
max(max(A)) % ans = 9 % of the whole matrix
sum(sum(A .* eye(9))) % sum of the diagonal, using identity
sum(sum(A .* flipud(eye(9)))) % sum of the other diagonal, using flipud
pinv(A) % inverse of the matrix A
% ans =
% 0.147222 -0.144444 0.063889
% -0.061111 0.022222 0.105556
% -0.019444 0.188889 -0.102778
pinv(A) * A % inverse multiplied by inteself yield the identity matrix
% ans =
% 1.00000 0.00000 -0.00000
% -0.00000 1.00000 0.00000
% 0.00000 0.00000 1.00000Random numbers
w = rand(1,3)
% w =
% 0.929673 0.335081 0.071794
w = rand(3,3)
% w =
% 0.169280 0.861922 0.581426
% 0.811334 0.792225 0.879152
% 0.568244 0.019950 0.709208
w = randn(1,3)
% w =
% -0.44849 1.36413 -0.48032Getting help
help rand
help hist
help helpMoving around
pwd % ans = /scripts
ls
cd '/home/'
load featureX.dat
load('featureY.dat')
save hello.mat variable;
save hello.txt variable -ascii % saves as a text fileControl flow
v = zeros(10,1) % create a vector of 10 zeroes
for i=1:10, % for loop
> v(i) = 2^i;
> end;
indices = 1:10; % using premade array
for i=indices,
> disp(i);
> end;
i = 1;
while i <= 5, % while loop
> v(i) = 100;
> i = i + 1;
> end;
i=1;
while true,
> v(i) = 999;
> i = i+1;
> if i == 6, % conditional
> break; % breaking out of the loop
> end;
> end;
v(1) = 2;
if v(1)==1,
> disp('The value is one');
> elseif v(1) == 2,
> disp('The value is two');
> else
> disp('The value is not one or two');
> end;
% The value is twoFunctions
% squareThisNumber.m in the search path
% addpath('/home/octave')
function y = squareThisNumber(x)
y = x^2;% squareAndCubeThisNumber.m
% returning 2 values
function [y1, y2] = squareAndCubeThisNumber(x)
y1 = x^2;
y2 = x^3;fuction J = costFunctionJ(X, y, theta)
% X is the "design matrix" containing our training examples
% y is the class labels
m = size(X,1); % number of training examples
predictions = X * theta; % predictions of hypothesis on all m examples
sqErrors = (predictions-y).^2; % squared errors
J = 1/(2*m) * sum(sqErrors);% usage of cost function
X = [1 1; 1 2; 1 3]
% X =
% 1 1
% 1 2
% 1 3
y = [1; 2; 3]
% y =
% 1
% 2
% 3
theta = [0:1]
% theta =
% 0 1
j = costFunctionJ(X, y, theta)function theta = gradientDescent(X, y, theta, alpha, num_iters)
m = length(y); % number of training examples
for iter = 1:num_iters
predictions = X * theta; % hypothesis
errors = predictions - y; % hypothesis - y
delta = (1 / m) * sum(errors .* X(2)); % col1 is 1's
theta = theta - alpha * delta;
endVectorization
% unvectorized implementation
prediction = 0.0;
for j = 1:n+1,
prediction = prediction + theta(j) * x(j)
end;
% vectorized implmentation
prediction = theta' * x;Plotting data
t = [0:0.01:0.98];
y1 = sin(2*pi*4*t);
plot(t,y1)
y2 = cos(2*pi*4*t);
plot(t,y2)
plot(t,y1)
hold on;
plot(t,y2)
xlabel('time')
ylabel('value')
legend('sin','cos')
title('my plot')
print -dpng 'myPlot.png'
close
figure(1): plot(t,y1);
figure(2): plot(t, y2);
subplot(1,2,1);
plot(t, y1)
subplot(1,2,2);
plot(t, y2)
axis([0.5 1 -1 1])
clf;
A = magic(5)
imagesc(A)
imagesc(A), colorbar, colormap gray;Advanced optimization algorithm
function [jVal, gradient] = costFunction(theta)
jVal = (theta(1) - 5)^2 + (theta(2) - 5)^2; % code to compute J(theta)
gradient(1) = 2 * (theta(1) - 5); % derivative for theta_0
gradient(2) = 2 * (theta(2) - 5); % derivative for theta_1
options = optimset('GradObj', 'on', 100);
initialTheta = zeroes(2,1);
% function minimization unconstrained
[optTheta, functionVal, exitFlag] = fminunc(@costFunction, initialTheta, options);Unrolling parameters into a vector
thetaVector = [ Theta1(:); Theta2(:); Theta3(:); ]
deltaVector = [ D1(:); D2(:); D3(:) ]Reshape the matrix back from the unrolled vector
% if the dimensions of Theta1 is 10x11, Theta2 is 10x11 and Theta3 is 1x11
Theta1 = reshape(thetaVector(1:110),10,11)
Theta2 = reshape(thetaVector(111:220),10,11)
Theta3 = reshape(thetaVector(221:231),1,11)Gradient checking
epsilon = 1e-4;
for i = 1:n,
thetaPlus = theta;
thetaPlus(i) += epsilon;
thetaMinus = theta;
thetaMinus(i) -= epsilon;
gradApprox(i) = (J(thetaPlus) - J(thetaMinus))/(2*epsilon)
end;Random initialization: symmetry breaking
% if the dimensions of Theta1 is 10x11, Theta2 is 10x11 and Theta3 is 1x11.
Theta1 = rand(10,11) * (2 * INIT_EPSILON) - INIT_EPSILON;
Theta2 = rand(10,11) * (2 * INIT_EPSILON) - INIT_EPSILON;
Theta3 = rand(1,11) * (2 * INIT_EPSILON) - INIT_EPSILON;