5+6 % adding
3-2 % substrating
5*8 % multiplication
1/2 % division
2^6 % power
quit % exit octave
exit % exit octave
1 == 2 % equals, evals to 0 which means false
1 ~= 2 % not equals, evals to 1 which means true
1 && 0 % logical and
1 || 0 % logical or
xor(1,0) % logical xor
PS1('>> ')
a = 3 % assign 3 to variable a
a = 3; % semicolon prevents printing result
b = 'hi'; % string assignment
c = (3>=1); % c = 1
a = pi; % assign pi number to variable a
disp(a); % for more complex printing or debug in functions
disp(sprintf('2 decimals: %0.2f', pi)) % advanced c-like string formatting
disp(sprintf('6 decimals: %0.6f', pi)) % advanced c-like string formatting
format long % print long version of numbers
format short % print short version of numbers
a=1, b=2, c=3; % comma-chaining multiple commands
A = [1 2; 3 4; 5 6]; % declare a matrix
% A =
%
% 1 2
% 3 4
% 5 6
A = [1 2;
3 4;
5 6] % declare matrix multi-line
v = [1 2 3] % a row vector
v = [1; 2; 3] % a column vector
v = 1:0.1:2
% [1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0]
v = 1:6
% [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
eye(4)
% ans =
% 1 0 0 0
% 0 1 0 0
% 0 0 1 0
% 0 0 0 1
eye(6)
% ans =
% 1 0 0 0 0 0
% 0 1 0 0 0 0
% 0 0 1 0 0 0
% 0 0 0 1 0 0
% 0 0 0 0 1 0
% 0 0 0 0 0 1
eye(3)
% ans =
% 1 0 0
% 0 1 0
% 0 0 1
w = rand(1,3) % generate 1x3 random number [0,1) matrix
rand(3,3) % generate 3x3 random number [0,1) matrix
w = randn(1,3) % generate 1x3 gaussian distribution matrix
hist(-6 + sqrt(10)*(randn(1,10000))) % plot histogram of vector
hist(-6 + sqrt(10)*(randn(1,10000)),50) % plot histogram of vector with 50 buckets
help eye % get help about identity function
help rand % get help about rand
help help % get help about help
size(A)
% ans =
% 3 2
% this shows that matrix is a 3x2 matrix (3 rows 2 columns)
size(size(A))
% ans =
% 1 2
size(A, 1) % get number of rows
size(A, 2) % get number of columns
length([1 2 3 4]) % gives size of longest dimention, in this case 4
pwd % get current working directory
cd '/path' % change directory to path
ls % list files in pwd
load file.dat % load file.dat into variable file
load('file.dat') % load file.dat into variable file
who % list variables
whos % list variables with their sizes
clear file % delete variable file
save hello.mat v % save variable v into file hello.mat in a compressed format
save hello.txt v -ascii % save variable v into file hello.txt in a human readable format
A(3,2) % return cell at row 3, column 2
v(1:10) % returns first 10 rows of data
A(2,:) % fetch everything in the second row
A(:,2) % everything in the second column
A([1 3],:) % first and third row only
A(:,2) = [10; 11; 12] % assign 10,11,12 to second column
A = [A, [1; 2; 3;]]; % append a new column vector to the right
A(:) % put all elements of A inside a column vector
C = [A B] % concatenate A and B together from right of A
C = [A, B] % concatenate A and B together from right of A
C = [A; B] % concatenate A and B together from bottom of A
A * C % multiply matrices A, C
A .* B % multiply matrices A, B element-wise instead of normal matrix multiplication
A .^ 2 % element-wise squaring of A
1 ./ v % element-wise inverse
a < 3 % element-wise comparison
find(a < 3) % returns a vector of indices, where a was < 3
log(v) % element-wise logarithm
exp(v) % element-wise exponentiotion
abs(v) % element-wise absolute value
-v % same as -1 * v
v + ones(length(v),1) % increment each element of vector v by 1
v + 1 % increment each element of vector v by 1, much simpler version!
A' % transpose of matrix A
max(a) % maximum of vector a
[val, ind] = max(a) % maximum of vector a and it's column
max(A) % column-wise maximum of A
magic(4) % return a 4x4 "magic" matrix
[r, c] = find(A >= 7) % return r,c as column vectors holding indices of locations A >=7
sum(a) % adds all elements of vector a
sum(A,1) % take column-wise sum of matrix A
sum(A,2) % take row-wise sum of matrix A
prod(a) % product of all elements of vector a
floor(a) % element-wise floor
ceil(a) % element-wise ceiling
max(A, B) % take element-wise maximum of two matrices
max(A,[],1) % take column-wise maximum of A
max(A) % take column-wise maximum of A
max(A, [], 2) % take row-wise maximum of A
max(max(A)) % maximum element in matrix A
sum(sum(A .* eye(9))) % sum main diagonal
flipud(A) % flip up-down matrix
sum(sum(A .* flipud(eye(9)))) % sum secondary diagonal
pinv(A) % return inverse of matrix A
std(a) % standard deviation of vector a
t =[0:0.1:1];
y1=sin(2*pi*4*t);
y1=cos(2*pi*4*t); % suppose we have these variables
plot(t, y1); % plot sin(x)
plot(t, y2, 'r'); % plot cos(x) in red color
plot(t, y1);
hold on; % plot y1, y2 on each other
plot(t, y2, 'r');
xlabel('time'); % label horizontal axis
ylabel('value'); % label vertical axis
legend('sin', 'cos'); % add legend to plot
title('my plot'); % gives a title to entire plot
print -dpng 'myPlot.png' % save plot in png format
close % close open plot
figure(1);
plot(t, y1);
figure(2);
plot(t, y2); % don't override previous plot, simply open a new window instead
subplot(2, 1, 1); % divide plot into 2x1 grid and start accessing first element
plot(t, y1); % plot in first element of grid
subplot(2, 1, 2); % access second element
plot(t, y2); % plot in second element of grid
axis(0.5 1 -1 1); % change axis: x-range and y-range of plot
clf % clears the figure
A=magic(5);
imagesc(A); % show a colorful heatmap of A
imagesc(A), colorbar, colorbar gray; % show a grayscale heatmap of A
plot(t, y1, 'rx'); % plot data in scattered mode using * sign
plot(t, y1, 'rx', 'MarkerSize', 10); % plot data in scattered mode and with custom marker size
plot(t, y1, 'k+'); % plot data in scattered using + sign
plot(t, y1, 'ko'); % plot data in scattered using o sign
plot(t, y1, 'LineWidth', 2); % adjust border size
plot(t, y1, 'MarkerFaceColor', 'y'); % set color of sign to yellow
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;
if v(1) == 1,
disp('The value is 1');
elseif v(1) == 2,
disp('The value is 2');
else,
disp('The value is neither 1 or 2');
end;
To define function squareThisNumber we have to put definition inside file squareThisNumber.m and it should be accessible via:
- either
pwdwhich can be navigated bycd - search directory which can be appended by
addpath('path')
function y = squareThisNumber(x)
y = x ^ 2;
function [y1,y2] = squareAndCubeThisNumber(x)
y1 = x^2;
y2 = x^3;
This declaration can be invoked using:
[a, b] = squareAndCubeThisNumber(5);
function J = function(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
sqrErrors = (predictions - y).^2 % squared errors
J = 1/(2*m) * sum(sqrErrors)
Use fminunc function.
options = optimset('GradObj', 'on', 'MaxIter', 100);
initialTheta = zeros(size(data,2),1);
[optTheta, functionVal, exitFlag] = fminunc(@(t)(costFunction(t, X, y)), initialTheta, options);
Use fmincg function.
options = optimset('GradObj', 'on', 'MaxIter', 100);
initialTheta = zeros(size(data,2),1);
[optTheta, functionVal, exitFlag] = fmincg(@(t)(costFunction(t, X, y)), initialTheta, options);
thetaVec = [ Theta1(:); Theta2(:); Theta3(:) ]
Theta1 = reshape(thetaVec(1:110), 10, 11)
Theta2 = reshape(thetaVec(111:220), 10, 11)
Theta3 = reshape(thetaVec(221:231), 1, 11)