Octave教程
Windows安装Octave
http://wiki.octave.org/Octave_for_Microsoft_Windows
基本操作（Basic Operations）
octave:1> PS1('>> ');
>>
>> path
>> pause
>> clear ; close all; clc
>> fprintf(['test print %%s : %s \n' ...
'test print %%d : %d \n' ...
'test print %%g : %g \n' ...
'test print %%f : %f \n' ...
], 'String', 10, 2.33553e-11, 0.12345678);
test print %s : String
test print %d : 10
test print %g : 2.33553e-11
test print %f : 0.123457
>>
>> 1+2
ans = 3
>> 5*8
ans = 40
>> 1/2
ans = 0.50000
>> 2^6
ans = 64
>> 2^3
ans = 8
>> 1 == 2 % false
ans = 0
>> 1 == 1 % true
ans = 1
>> 1 ~= 2 % true
ans = 1
>> 1 ~= 2 % true
ans = 1
>> 1 ~= 1 % false
ans = 0
>> 1 ~= 1 % false not equal
ans = 0
>> 1 && 0
ans = 0
>> 1 && 0 % AND
ans = 0
>> 1 || 0 % or
ans = 1
>> xor(1,0)
ans = 1
>> xor(1,0) % yi or
ans = 1
>> PS1('>> ');
>> a=3
a = 3
>> a=4;
>> a
a = 4
>> c=(3>=4)
c = 0
>> c
c = 0
>> a=pi
a = 3.1416
>> a=pi;
>> a
a = 3.1416
>> b=e;
>> b
b = 2.7183
>> disp(a);
3.1416
>> disp(sprintf('2 decimals: %0.2f', a))
2 decimals: 3.14
>> disp(sprintf('10 decimals: %0.10f', a))
10 decimals: 3.1415926536
>> disp(sprintf('10 decimals: %0.10f', b))
10 decimals: 2.7182818285
>> format long
>> a
a = 3.141592653589793
>> b
b = 2.718281828459045
>> format short
>> a
a = 3.1416
>> b
b = 2.7183
>> A = [1 2; 3 4; 5 6];
>> A
A =
1 2
3 4
5 6
>> A
A =
1 2
3 4
5 6
>> v=[1 2 3];
>> v =[1; 2; 3]
v =
1
2
3
>> v=1:0.1:2;
>> v
v =
Columns 1 through 7:
1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000
Columns 8 through 11:
1.7000 1.8000 1.9000 2.0000
>> v=1:6;
>> v
v =
1 2 3 4 5 6
>> ones(2,3)
ans =
1 1 1
1 1 1
>> 2 * ones(2,3)
ans =
2 2 2
2 2 2
>> w=ones(1,3)
w =
1 1 1
>> w=zeros(1,3)
w =
0 0 0
>> w=rand(1,3)
w =
0.066378 0.828597 0.569681
>> rand(3,3)
ans =
0.2443954 0.3866398 0.2332407
0.6611382 0.6353541 0.0066938
0.2465706 0.2734220 0.6748704
>> rand(3,3)
ans =
0.71983 0.47680 0.30126
0.19673 0.29252 0.57751
0.99891 0.57380 0.31022
>> rand(3,3)
ans =
0.26842 0.82579 0.22678
0.63709 0.67602 0.11723
0.83274 0.48216 0.26778
>> rand(3,3)
ans =
0.790568 0.666798 0.084361
0.343994 0.482338 0.860989
0.908285 0.967817 0.935013
>> randn(1,3) % gaosi fenbu
ans =
-0.098394 -0.147581 0.085802
>> randn(1,3) % gaosi fenbu
ans =
1.10694 -1.99933 -0.17373
>> w= -6 + sqrt(10) * (randn(1,10000));
>> hist(w)
>> hist(w,50)
>>
>> I = eye(4)
I =
Diagonal Matrix
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
>> help eye
>> help help
移动数据（Moving Data Around）
>> 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
>> size(A, 3)
ans = 1
>> v = [1 2 3 4]
v =
1 2 3 4
>> length(v)
ans = 4
>> length(A)
ans = 3
>> load featuresX.dat
>> load ('priceY.dat')
>> who
Variables in the current scope:
A ans featuresX priceY v
>> whos
Variables in the current scope:
Attr Name Size Bytes Class
==== ==== ==== ===== =====
A 3x2 48 double
ans 1x23 23 char
featuresX 3x1 24 double
priceY 3x1 24 double
v 1x4 32 double
Total is 39 elements using 151 bytes
>> priceY
priceY =
1000
2000
3000
>> featuresX
featuresX =
1234
5678
1235
>> clear featuresX
>>
>> whos
Variables in the current scope:
Attr Name Size Bytes Class
==== ==== ==== ===== =====
A 3x2 48 double
ans 1x23 23 char
priceY 3x1 24 double
v 1x4 32 double
Total is 36 elements using 127 bytes
>> clear
>> whos
>> load ('priceY.dat')
>> v = priceY(2:3)
v =
2000
3000
>> save hello.mat v;
>> clear
>> whos
>> load hello.mat
>> whos
Variables in the current scope:
Attr Name Size Bytes Class
==== ==== ==== ===== =====
v 2x1 16 double
Total is 2 elements using 16 bytes
>> v
v =
2000
3000
>> save hello.txt -ascii % save as text (ASCII)
>> 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
A =
1 2
3 4
5 6
>> A([1 2 3], :)
ans =
1 2
3 4
5 6
>> A(:,2) = [10; 20; 30]
A =
1 10
3 20
5 30
>> A = [A, [100; 101; 102]] % append another column vector to right
A =
1 10 100
3 20 101
5 30 102
>> A = [A; [100 101 102]] % append another column vector to right
A =
1 10 100
3 20 101
5 30 102
100 101 102
>> A(:)
ans =
1
3
5
100
10
20
30
101
100
101
102
102
>> 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 = [A B]
C =
1 2 11 12
3 4 13 14
5 6 15 16
>> [B A]
ans =
11 12 1 2
13 14 3 4
15 16 5 6
>> [A B C]
ans =
1 2 11 12 1 2 11 12
3 4 13 14 3 4 13 14
5 6 15 16 5 6 15 16
>> [A; B]
ans =
1 2
3 4
5 6
11 12
13 14
15 16
>> [A, B]
ans =
1 2 11 12
3 4 13 14
5 6 15 16
计算数据（Computing on Data）
>> 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
ans =
5 5
11 11
17 17
>> A .* B
ans =
11 24
39 56
75 96
>> 3 * A
ans =
3 6
9 12
15 18
>> A*3
ans =
3 6
9 12
15 18
>> A
A =
1 2
3 4
5 6
>> B
B =
11 12
13 14
15 16
>> A.^2
ans =
1 4
9 16
25 36
>> v = [1; 2; 3]
v =
1
2
3
>> 1./v
ans =
1.00000
0.50000
0.33333
>> 1./A
ans =
1.00000 0.50000
0.33333 0.25000
0.20000 0.16667
>> log(v)
ans =
0.00000
0.69315
1.09861
>> exp(v)
ans =
2.7183
7.3891
20.0855
>> abs(v)
ans =
1
2
3
>> abs([-1; 2; -3])
ans =
1
2
3
>> -v
ans =
-1
-2
-3
>> -A
ans =
-1 -2
-3 -4
-5 -6
>> -1*v
ans =
-1
-2
-3
>> v+ones(length(v),1)
ans =
2
3
4
>> ones(length(v),1)
ans =
1
1
1
>> ones(length(v),2)
ans =
1 1
1 1
1 1
>> zeros(length(v),2)
ans =
0 0
0 0
0 0
>> v.+1
ans =
2
3
4
>> v.-1
ans =
0
1
2
>> 1.+v
ans =
2
3
4
>> v+1
ans =
2
3
4
>> v-1
ans =
0
1
2
>> A
A =
1 2
3 4
5 6
>> A'
ans =
1 3 5
2 4 6
>> A''
ans =
1 2
3 4
5 6
>> A''''
ans =
1 2
3 4
5 6
>> a = [1 15 2 0.5]
a =
1.00000 15.00000 2.00000 0.50000
>> val = max(a)
val = 15
>> [val, ind] = max(a)
val = 15
ind = 2
>> max(A)
ans =
5 6
>> a < 3
ans =
1 0 1 1
>> A < 3
ans =
1 1
0 0
0 0
>> find(a<3)
ans =
1 3 4
>> a
a =
1.00000 15.00000 2.00000 0.50000
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
>> magic(4)
ans =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
>> [r,c] = find(A >= 7)
r = [](0x1)
c = [](0x1)
>> A
A =
1 2
3 4
5 6
>> 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
>> [r,c] = find(A >= 2)
r =
1
2
3
2
3
1
2
3
c =
1
1
1
2
2
3
3
3
>> a
a =
1.00000 15.00000 2.00000 0.50000
>> sum(a)
ans = 18.500
>> prod(a)
ans = 15
>> floor(a)
ans =
1 15 2 0
>> ceil(a)
ans =
1 15 2 1
>> rand(3)
ans =
0.43298 0.41511 0.89855
0.21145 0.15275 0.96643
0.67367 0.31471 0.15306
>> max(rand(3), rand(3))
ans =
0.99326 0.98554 0.83527
0.78799 0.71117 0.92512
0.99326 0.98996 0.34543
>> A
A =
8 1 6
3 5 7
4 9 2
>> max(A, [], 1)
ans =
8 9 7
>> max(A, [], 2)
ans =
8
7
9
>> max(A)
ans =
8 9 7
>> max(max(A))
ans = 9
>> A(:)
ans =
8
3
4
1
5
9
6
7
2
>> max(A(:))
ans = 9
>>
>>
>>
>> A = magic(9)
A =
47 58 69 80 1 12 23 34 45
57 68 79 9 11 22 33 44 46
67 78 8 10 21 32 43 54 56
77 7 18 20 31 42 53 55 66
6 17 19 30 41 52 63 65 76
16 27 29 40 51 62 64 75 5
26 28 39 50 61 72 74 4 15
36 38 49 60 71 73 3 14 25
37 48 59 70 81 2 13 24 35
>> sum(A,1)
ans =
369 369 369 369 369 369 369 369 369
>> sum(A,2)
ans =
369
369
369
369
369
369
369
369
369
>> eye(9)
ans =
Diagonal Matrix
1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1
>> A .* eye(9)
ans =
47 0 0 0 0 0 0 0 0
0 68 0 0 0 0 0 0 0
0 0 8 0 0 0 0 0 0
0 0 0 20 0 0 0 0 0
0 0 0 0 41 0 0 0 0
0 0 0 0 0 62 0 0 0
0 0 0 0 0 0 74 0 0
0 0 0 0 0 0 0 14 0
0 0 0 0 0 0 0 0 35
>> sum(A .* eye(9))
ans =
47 68 8 20 41 62 74 14 35
>> sum(sum(A .* eye(9)))
ans = 369
>> flipud(eye(9))
ans =
Permutation Matrix
0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 1 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
>> sum(sum(A .* flipud(eye(9))))
ans = 369
>>
>>
>>
>>
>> A = magic(3)
A =
8 1 6
3 5 7
4 9 2
>> pinv(A) % pseudoinverse
ans =
0.147222 -0.144444 0.063889
-0.061111 0.022222 0.105556
-0.019444 0.188889 -0.102778
>> inv(A)
ans =
0.147222 -0.144444 0.063889
-0.061111 0.022222 0.105556
-0.019444 0.188889 -0.102778
>> temp = pinv(A)
temp =
0.147222 -0.144444 0.063889
-0.061111 0.022222 0.105556
-0.019444 0.188889 -0.102778
>> temp * A
ans =
1.00000 0.00000 -0.00000
-0.00000 1.00000 0.00000
0.00000 0.00000 1.00000
>> abs(temp * A)
ans =
1.00000 0.00000 0.00000
0.00000 1.00000 0.00000
0.00000 0.00000 1.00000
数据绘制（Plotting Data）
>> t=[0:0.01:0.98];
>> t
t =
Columns 1 through 11:
0.00000 0.01000 0.02000 0.03000 0.04000 0.05000 0.06000 0.07000 0.08000 0.09000 0.10000
Columns 12 through 22:
0.11000 0.12000 0.13000 0.14000 0.15000 0.16000 0.17000 0.18000 0.19000 0.20000 0.21000
Columns 23 through 33:
0.22000 0.23000 0.24000 0.25000 0.26000 0.27000 0.28000 0.29000 0.30000 0.31000 0.32000
Columns 34 through 44:
0.33000 0.34000 0.35000 0.36000 0.37000 0.38000 0.39000 0.40000 0.41000 0.42000 0.43000
Columns 45 through 55:
0.44000 0.45000 0.46000 0.47000 0.48000 0.49000 0.50000 0.51000 0.52000 0.53000 0.54000
Columns 56 through 66:
0.55000 0.56000 0.57000 0.58000 0.59000 0.60000 0.61000 0.62000 0.63000 0.64000 0.65000
Columns 67 through 77:
0.66000 0.67000 0.68000 0.69000 0.70000 0.71000 0.72000 0.73000 0.74000 0.75000 0.76000
Columns 78 through 88:
0.77000 0.78000 0.79000 0.80000 0.81000 0.82000 0.83000 0.84000 0.85000 0.86000 0.87000
Columns 89 through 99:
0.88000 0.89000 0.90000 0.91000 0.92000 0.93000 0.94000 0.95000 0.96000 0.97000 0.98000
>> 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,'r');
>> xlabel('time');
>> ylabel('value');
>> legend('sin','cos');
>> legend('cos','sin');
>> legend('sin','cos');
>> title('my plot');
>> print -dpng 'myPolt.png'
>> close
>> figure(1); plot(t,y1);
>> figure(2); plot(t,y2,'r');
>> subplot(1,2,1);
>> plot(t,y1)
>> subplot(1,2,2)
>> plot(t,y2,'r')
>> title myPlot
>> axis([0.5 1 -1 1])
>> clf;
>> A=magic(5);
>> imagesc(A);
>> imagesc(A), colorbar, colormap gray;
>> imagesc(magic(15)), colorbar, colormap gray;
控制语句：for，while，if语句（Control Statements）
>> v=zeros(10,1)
v =
0
0
0
0
0
0
0
0
0
0
>> for i=1:10
> v(i) = 2^i;
> end
>> v
v =
2
4
8
16
32
64
128
256
512
1024
>> indices=1:10
indices =
1 2 3 4 5 6 7 8 9 10
>> for i=indices
> disp(i)
> end
1
2
3
4
5
6
7
8
9
10
>>
>> v
v =
2
4
8
16
32
64
128
256
512
1024
>> i=1
i = 1
>> while i <=5
> v(i) = 100;
> i = i +1;
> end;
>> v
v =
100
100
100
100
100
64
128
256
512
1024
>> i=1;
>> while true
> v(i)=999;
> i = i + 1;
> if i==6,
> break;
> end;
> end;
>> v
v =
999
999
999
999
999
64
128
256
512
1024
>> v(1)
ans = 999
>> 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 two
函数的定义和使用（Defining and using functions）
>> function y = squareThisNumber(x);
> y = x^2;
> end;
>>
>> squareThisNumber(5)
ans = 25
>> % octave serch path (advanced/optional)
>> addpath('C:\users\');
>> % you can also put the function into the 'suareThisNumber.m' file under addpath
>> % then you can invoke this function use 'squareThisNumber(5)'
>> function [y1,y2] = squareAndCubeThisNumber(x);
> y1 = x^2;
> y2 = x^3;
> end;
>> squareAndCubeThisNumber(3)
y1 = 9
y2 = 27
ans = 9
>> [a,b]=squareAndCubeThisNumber(3)
y1 = 9
y2 = 27
a = 9
b = 27
>> a
a = 9
>> b
b = 27
>> 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
>> function J = costFunctionJ(X, y, theta)
> % X is the "design matrix" containing out training examples.
> % y is the class labels
>
> m = size(X, 1); % number of traning examples
> predictions = X * theta; % predictions of hypothesis on all m examples
> sqrErrors = (predictions - y).^2; % squared errors
>
> J = 1/(2*m) * sum(sqrErrors);
> end;
>> j=costFunctionJ(X,y,theta)
j = 0
>> size(X,1)
ans = 3
>> X*theta
ans =
1
2
3
>> sum(X)
ans =
3 6
>> A = magic(9)
A =
47 58 69 80 1 12 23 34 45
57 68 79 9 11 22 33 44 46
67 78 8 10 21 32 43 54 56
77 7 18 20 31 42 53 55 66
6 17 19 30 41 52 63 65 76
16 27 29 40 51 62 64 75 5
26 28 39 50 61 72 74 4 15
36 38 49 60 71 73 3 14 25
37 48 59 70 81 2 13 24 35
>> sum(A,1)
ans =
369 369 369 369 369 369 369 369 369
>> sum(A,2)
ans =
369
369
369
369
369
369
369
369
369
>> sum(A)
ans =
369 369 369 369 369 369 369 369 369
>> sum(sum(A))
ans = 3321
>> theta=[0;0]
theta =
0
0
>> j=costFunctionJ(X,y,theta)
j = 2.3333
>> (1^2 + 2^2 + 3^2)/(2*3)
ans = 2.3333
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