1. CS 175 Project in AI Discussion -- matlab
Yutian Chen

2. help
help
help help
Documentation
doc help

3. Useful functions
who, whos
size, length
clear
clc
sum, max, min

4. Matrix Allocation Enter an explicit list of elements. Colon operator
Generate matrices using built-in functions.
linspace, logspace, zeros, ones, eye, rand
Tips: Pre-allocation avoids reallocation of matrices

5. Matrix Indexing end, find exercise: Subscripted Indexing (1-based)
A = [ ; % use “…” to continue on the next line
; ... ];
A(2:3,2)
Linear Indexing (matrix is store by column)
A([3,1,8])
Logical Indexing
A(logical([ ]))
end, find
exercise:
last column of A A(:,end)
diagonal of A diag(A) or A(logical(eye(size(A))))
Find all the elements greater than A(A>15)

6. Matrix Manipulation
Transpose A=A'
A(:)
repmat
reshape []
Cat

7. Matrix Manipulation cont.
exercise:
A=ones(2,2); B=rand(2); concatenate A and B along the 1st, 2nd, 3rd dimension
1st: [A;B] or cat(1,A,B)
2nd: [A,B] or cat(2,A,B)
3rd: cat(3,A,B)
generate [ ]
[ones(1,5),2*ones(1,5)] or reshape(repmat([1, 2],5,1),1,10)
transform A=[1 2; 3 4; 5 6; 7 8] to [ ; ]
A = reshape(A',4,2)'

8. Flow Control if, else, switch for loop while loop continue break
for i = [ ]; H(i) = 1/i; end
while loop
continue
break

9. Logical operators Element-wise operator &, |, ~
<, <=, >, >=, ==, ~=
A=ones(2,2); B=A;
A==B
Some functions to reduce the results of matrix comparisons to scalar conditions:
isequal, isempty, all, any

10. Save/Load save load save a.mat save a.mat x y save('a.mat','x','y')
load a.mat
load a.mat x
load('a.mat','x')

11. Vectorization For simplicity and speed Vector dot product
A=[ ]; B=[ ];
p = 0;
for i=1:5
p=p+A(i)*B(i);
end Or
p = A*B';
p = sum(A.*B);

12. Vectorization cont. Matrix multiplication A=ones(5); B=eye(5);
p = zeros(size(A,1),size(B,2));
for i=1:size(p,1)
for j=1:size(p,2)
for k=1:size(p,2)
p=p+A(i,k)*B(k,j);
end Or
p = A*B
Compare the multiplication of two 100x100 matrix to see the difference

13. Vectorization cont. Exercise
A is a row vector, C=A(1)*A(2)+A(2)*A(3)+...+A(N- 1)*A(N);
C = A(1:end-1)*A(2:end) '
polynomial evaluation: a0+a1*x+...+ak*x^k
y = A*2.^(0:k) ';
sigmoid(x,W,b) (x: dims:1xD, W: 1xD, b:1x1)
1/(1+exp( -(W*x‘+b) ))
sigmoid(x,W,b) (x: NxD, W: 1xD, b:1x1)
1./(1+exp( -(W*x‘+b) ))

14. Vectorization cont. Exercise weight update in logistic regression
y is a Nx1 row vector of labels
x is a NxD matrix of data
W is a 1XD row vector
W = W + rate * x' *(y-1./(1+exp( -(W*x' +b) )))
(Be careful to match the inner dimension of matrix multiplications)

15. Plot plot line type, color, symbol
plot(x,y); plot(y); plot(A)
line type, color, symbol
title, xlabel, legend, xlim, hold on/off
log-scale: semilogx, semilogy, loglog
hist, bar, stem, surf, scatter

16. Script/Function Script Function Debugging
a batch of commands grouped in a .m file
share the same workspace with the command line
Function
keyword: function
input, output
function name determined by the file name
useful functions: nargin, nargout, exist
Debugging