CS 175 Project in AI Discussion -- matlab Yutian Chen

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

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

Matrix Indexing end, find exercise: Subscripted Indexing (1-based) A = [11 14 17; ... % use “…” to continue on the next line 12 15 18; ... 13 16 19]; A(2:3,2) Linear Indexing (matrix is store by column) A([3,1,8]) Logical Indexing A(logical([0 0 1 0 1])) 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 15 A(A>15)

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

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 [1 1 1 1 1 2 2 2 2 2] [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 [1 2 3 4; 5 6 7 8] A = reshape(A',4,2)'

Flow Control if, else, switch for loop while loop continue break for i = [1 3 5 6]; H(i) = 1/i; end while loop continue break

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

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')

Vectorization For simplicity and speed Vector dot product A=[1 2 3 4 5]; B=[5 4 3 2 1]; p = 0; for i=1:5 p=p+A(i)*B(i); end Or p = A*B'; p = sum(A.*B);

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

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) ))

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)

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

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