1. Octave Basic operations Arithmeticoperators: >> 5+6 ans
= 11 >> 3-2 ans = 1 >> 5*8 ans = 40 >> 1/2 ans =
0.50000 >> 2^6 ans = 64 Logical operators: (0 meansFalse,1 or
greatermeansTrue) >> 1 == 2 ans = 0 >> 1 ~=2 ans = 1
>> 1 && 0 ans = 0 >> >> 1 || 0 ans = 1
>> >> xor(1,0) ans = 1 Changingcursor:
octave3.2.4.exe:11>PS1(>> ); Semicolonsuppressingoutput:
>> a = 3 a = 3 >> a = 3; >> b = hi; >> c =
(3>=1); >> c c = 1 >> a = pi; >> a a = 3.1416
Functionto displayoutput: >> disp(a); 3.1416 >>
disp(sprint(2decimals:%0.2f,a)) 2 decimals:3.14 2. >>
disp(sprint(6decimals:%0.6f,a)) 6 decimals:3.141593 >>
formatlong >> a a = 3.14159265358979 >> formatshort
>> a a = 3.1416 Matrix: >> A = [1 2 ; 3 4 ; 5 6] A = 1
2 3 4 5 6 Size of matrix: >> size(A) ans = 3 2 Vector:
>> v = [1; 2; 3] v = 1 2 3 >> Range: >> v = 1:6 v
= 1 2 3 4 5 6 >> v = 1:2.5:10 v = 1.0000 3.5000 6.0000 8.5000
Special Matrix functions: >> 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) 3. w = 0 0 0 Randomfunction:
>> w = rand (1, 3) w = 0.91477 0.14359 0.84860 >>
rand(3,3) ans = 0.58714 0.97976 0.72846 0.57976 0.91671 0.87487
0.55249 0.94451 0.90062 GaussianRandom: >> randn(1,3)
Histogram: >> w = -6 + sqrt(10)*(randn(1,4)) w = -10.26499
-6.16161 -3.38088 -0.99144 >> w = -6 + sqrt(10) *
(randn(1,100000) >>hist(w) Histogramwith50 bins >>
hist(w,50) Identitymatrix: >> eye(4) ans = Diagonal Matrix 4.
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 >> >> eye(2,4) ans =
Diagonal Matrix 1 0 0 0 0 1 0 0 >> helpcommand >>
helpeye >> helphelp Moving data around >> A = [1 2; 3
4; 5 6] %a 3 by2 matrix A = 1 2 3 4 5 6 >> size(A) ans = 3 2
size(A) itselfreturns1*2 matrix >> sz = size(A) sz = 3 2
>> size(sz) ans = 1 2 Returns first dimensionofA
(i.e.numberof rows) >> size (A,1) ans = 3 Returns
seconddimensionofA (i.e.number of columns) >> size (A,2) ans
= 3 >> v = [1 2 3 ] v = 1 2 3 Returns size of the
longestdimension >> length(v) ans = 4 %( itis 1 by 4 matrix)
>> length(A) %recall thatA is 3 by2 matrix ans = 3 5.
Usuallylengthfunctionis appliedto vectors >> v = [1;2;3 ] v =
1 2 3 Current directoryor path: >> pwd ans =
D:coursesSP-14MLHumayounex1ex1 >> cd 'D:courses' >> pwd
ans = D:courses You can use otherLinux commandsas well,suchasls,
dir(windowscommand if runningWindows) Loading Data
files(usuallycomma separatedfieldsina record) >>
loadfeaturesX.dat >> loadpriceY.dat Variablesin the current
scope: >> who J_vals ans i m priceY theta0_vals y X data
iterations predict1 t theta1_vals alpha featuresX j predict2 theta
v For detailedviewof variables: >> whos Variablesinthe
currentscope: Attr Name Size Bytes Class ==== ==== ==== ===== =====
J_vals 100x100 80000 double X 97x2 1552 double alpha 1x1 8 double
ans 1x36 36 char featuresX 27x2 432 double . You can clear
variablesby >> clearvariable_name Clear all variables
>> clear You can viewdata: >> featuresX featuresX= 2104
3 1600 3 2400 3 6. 1416 2 3000 4 >> size (featuresX) ans = 47
2 >> size(priceY) ans = 47 1 Selectingdata: >> v =
priceY(1:10) Save first10 elementsinv >> v = priceY(1:10) v =
3999 3299 3690 2320 5399 2999 3149 1989 2120 2425 Saving resultsin
a file: >> save hello.matv; >> loadhello.mat It will
load variable v >> v v = 3999 3299 3690 With>> save
hello.matv, data is saved incompressedformat. You can also save it
in ascii format: 7. >> save hello.txtv ascii >> A [1 2;
3 4 ; 5 6] A = 1 2 3 4 5 6 >> A(3,2) ans = 6 : means
everythinginthat row/column Thirdrow and all columnsinthisrow
>> A(3,:) ans = 5 6 First column >> A(:,1) ans = 1 3 5
Selectmore than one row: First and third row >> A([13], :)
ans = 1 2 5 6 Assigningnewvalues to secondcolumn: >> A(:,2) =
[10; 11; 13] A = 1 10 3 11 5 13 Appendanother column vector to
right >> A = [A,[100; 101; 102]] A = 1 10 100 3 11 101 5 13
102 Put all elementsintoa single vector >> A(:) ans = 1 3 5
10 8. Making a matrix from othermatrices: >> C = [A B]
>> A = [1 2; 3 4] A = 1 2 3 4 >> B = [11 22; 33 44] B =
11 22 33 44 >> C = [A B] C = 1 2 11 22 3 4 33 44 >> C =
[A;B] C = 1 2 3 4 11 22 33 44 Computing on data Matrix
multiplication: >> A * B ans = 77 110 165 242 Elementwise
multiplication >> A .* B Elementwise squaring >> A .^2
>> A .^B Elementwise reciprocal >> 1./A Elementwise log
>>log(A) Exponentiatione^element >>exp(A)
>>abs(-A) >>A >>ones(3,1) ans = 9. 1 1 1 >>
v+ ones(length(v),1) ans = 2 3 4 5 Easy way: >> v+1 Transpose
>> v ans = 1 2 3 4 (v)= v >> (v) Max value: >>max
(v) ans = 4 Value and its index >> [val,ind] = max(v) val = 4
ind= 4 >> A A = 1 2 3 4 >> A> find(A> find(A>
A = magic(3) A = 8 1 6 10. 3 5 7 4 9 2 Sum column wise A = 1 2 3 4
5 6 7 8 9 >> sum(A) ans = 12 15 18 >> v=[1 2 4 5] v = 1
2 4 5 >> sum(v) ans = 12 Other useful matrix functions:
>> ceil(A) >> floor(A) >> rand(3) >>
max(A,B) max elementsfromcorrespondingrowscolumns >>
max(A,[],2) %2for rowmax ans = 8 7 9 >> max(A,[],1) %1
forcolumnmax ans = 8 9 7 >> max(A) %columnmax,bydefault ans =
8 9 7 >> max(max(A)) ans = 9 >>A(:) ans = 8 3 4 1 5 9 6
7 2 >> max(A(:)) 11. ans = 9 >> sum(A,1) %columnwise
ans = 15 15 15 >> sum(A,2) %rowwise ans = 15 15 15
Summingdiagonals: >> A = magic(5) A = 17 24 1 8 15 23 5 7 14
16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 >> eye(5) ans =
Diagonal Matrix 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
>> A.*eye(5) ans = 17 0 0 0 0 0 5 0 0 0 0 0 13 0 0 0 0 0 21 0
0 0 0 0 9 >> sum(sum(A.*eye(5))) ans = 65 >>
flipud(eye(5)) ans = PermutationMatrix 0 0 0 0 1 0 0 0 1 0 0 0 1 0
0 0 1 0 0 0 1 0 0 0 0 Inverse of a matrix (calledpseudoinverse)
>> pinv(A) 12. Plotting data Generate some 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); >> holdon >> plot(t,y2,'r'); >>
xlabel(time) >> ylabel(value) >> legend(sin,cos)
>> title(MyPlot) To close oldplots from memory: >>
close >> figure(1);plot(t,y1); >> figure(2);plot(t,
y2); To plot two figuresin two elementsside byside: 13. Dividesa
plot in 1 by 2 grid >> subplot(1,2,1) % lastone is to
accessthe firstelement >> plot(t,y1) % plotit infirstslot
>> subplot(1,2,2) %lasttwo isto access the secondelement
>> plot(t,y2) To change the axis scale: >> axis[0.51 -1
1] To clear a figure (the openedfigure): >> clf A neat trick
to visualize the matrix: >> A = magic(5) A = 17 24 1 8 15 23
5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 Plotsthe 5 by5
matrix ina 5 by 5 gridof colorswhere the
differentcolorscorrespondtothe differentvaluesinthe matrix A.
>> imagesc(A) See the legend ofthe colorsin the side of the
picture. >> colorbar Three commands together: >>
imagesc(A),colorbar,colormapgray; Visualize a biggerMatrix:
>> imagesc(magic(15)),colorbar,colormapgray; 14. Control
statements:for,while, if statements for loop: >> v=zeros(5,1)
v = 0 0 0 0 0 >> for i=1:5, > v(i) = 2^i; > end;
>> v v = 2 4 8 16 32 >> indices=1:5 indices= 1 2 3 4 5
>> for i=indices, > disp(i); > end; 1 2 3 4 5 while
loop: >> i = 1; 15. >> while i disp(i); > i=i+1;
> end; 1 2 3 4 5 >> i=1; >> while true, > v(i)=i;
> i=i+1; > if i==6, > break; > end; > end; >>
v v = 1 2 3 4 5 >> >> if v(1)==1, > disp('The value
one'); > elseif v(2)==2, > disp('The value istwo'); > else
> disp('The value is notone or two'); > end; The value one
Creatinga function: Create sqrN.mfile inatexteditorandtype inthe
following: functiony= sqrN(x) y = x^2 ; Nowsave the file andwithcd
commandgo to the directorywhere youhave placedit.Now type: 16.
>> sqrN(5) 25 Add a path to Octave search path: >>
addpath(c:Users...ex1) Functionsreturning multiple values:
function[y1,y2] = sqrAndCube(x) y1 = x^2; y2 = x^3; >>
[y1,y2]=sqrAndCube(2) y1 = 4 y2 = 8 Vectorial implementation
>> 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= 17. 0 1 >> j =
costFunctionJ(X,y,theta) j = 0 Update theta: >> theta= [0;0]
theta= 0 0 >> j = costFunctionJ(X,y,theta) j = 2.3333
>> (12 + 22 + 32)/6 = 2.3333 18. >> p r e d i c t i o n
= theta'* x ;
