CS129: Introduction to Matlab (Code)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Introduction to Matlab % (adapted from http://www.stanford.edu/class/cs223b/matlabIntro.html) % % Stefan Roth <roth (AT) cs DOT brown DOT edu>, 09/08/2003 % % Stolen from cs143 for cs129 by % Patrick Doran <pdoran (AT) cs DOT brown DOT edu>, 01/30/2010 % % Last modified: 01/30/2010 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (1) Basics % The symbol "%" is used to indicate a comment (for the remainder of % the line). % When writing a long Matlab statement that becomes to long for a % single line use "..." at the end of the line to continue on the next % line. E.g. A = [1, 2; ... 3, 4]; % A semicolon at the end of a statement means that Matlab will not % display the result of the evaluated statement. If the ";" is omitted % then Matlab will display the result. This is also useful for % printing the value of variables, e.g. A % Matlab's command line is a little like a standard shell: % - Use the up arrow to recall commands without retyping them (and % down arrow to go forward in the command history). % - C-a moves to beginning of line (C-e for end), C-f moves forward a % character and C-b moves back (equivalent to the left and right % arrow keys), C-d deletes a character, C-k deletes the rest of the % line to the right of the cursor, C-p goes back through the % command history and C-n goes forward (equivalent to up and down % arrows), Tab tries to complete a command. % Simple debugging: % If the command "dbstop if error" is issued before running a script % or a function that causes a run-time error, the execution will stop % at the point where the error occurred. Very useful for tracking down % errors. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (2) Basic types in Matlab %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (A) The basic types in Matlab are scalars (usually double-precision % floating point), vectors, and matrices: A = [1 2; 3 4]; % Creates a 2x2 matrix B = [1,2; 3,4]; % The simplest way to create a matrix is % to list its entries in square brackets. % The ";" symbol separates rows; % the (optional) "," separates columns. N = 5 % A scalar v = [1 0 0] % A row vector v = [1; 2; 3] % A column vector v = v' % Transpose a vector (row to column or % column to row) v = 1:.5:3 % A vector filled in a specified range: v = pi*[-4:4]/4 % [start:stepsize:end] % (brackets are optional) v = [] % Empty vector %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (B) Creating special matrices: 1ST parameter is ROWS, % 2ND parameter is COLS m = zeros(2, 3) % Creates a 2x3 matrix of zeros v = ones(1, 3) % Creates a 1x3 matrix (row vector) of ones m = eye(3) % Identity matrix (3x3) v = rand(3, 1) % Randomly filled 3x1 matrix (column % vector); see also randn % But watch out: m = zeros(3) % Creates a 3x3 matrix (!) of zeros %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (C) Indexing vectors and matrices. % Warning: Indices always start at 1 and *NOT* at 0! v = [1 2 3]; v(3) % Access a vector element m = [1 2 3 4; 5 7 8 8; 9 10 11 12; 13 14 15 16] m(1, 3) % Access a matrix element % matrix(ROW #, COLUMN #) m(2, :) % Access a whole matrix row (2nd row) m(:, 1) % Access a whole matrix column (1st column) m(1, 1:3) % Access elements 1 through 3 of the 1st row m(2:3, 2) % Access elements 2 through 3 of the % 2nd column m(2:end, 3) % Keyword "end" accesses the remainder of a % column or row m = [1 2 3; 4 5 6] size(m) % Returns the size of a matrix size(m, 1) % Number of rows size(m, 2) % Number of columns m1 = zeros(size(m)) % Create a new matrix with the size of m who % List variables in workspace whos % List variables w/ info about size, type, etc. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (3) Simple operations on vectors and matrices %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (A) Element-wise operations: % These operations are done "element by element". If two % vectors/matrices are to be added, subtracted, or element-wise % multiplied or divided, they must have the same size. a = [1 2 3 4]'; % A column vector 2 * a % Scalar multiplication a / 4 % Scalar division b = [5 6 7 8]'; % Another column vector a + b % Vector addition a - b % Vector subtraction a .^ 2 % Element-wise squaring (note the ".") a .* b % Element-wise multiplication (note the ".") a ./ b % Element-wise division (note the ".") log([1 2 3 4]) % Element-wise logarithm round([1.5 2; 2.2 3.1]) % Element-wise rounding to nearest integer % Other element-wise arithmetic operations include e.g. : % floor, ceil, ... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (B) Vector Operations % Built-in Matlab functions that operate on vectors a = [1 4 6 3] % A row vector sum(a) % Sum of vector elements mean(a) % Mean of vector elements var(a) % Variance of elements std(a) % Standard deviation max(a) % Maximum min(a) % Minimum % If a matrix is given, then these functions will operate on each column % of the matrix and return a row vector as result a = [1 2 3; 4 5 6] % A matrix mean(a) % Mean of each column max(a) % Max of each column max(max(a)) % Obtaining the max of a matrix mean(a, 2) % Mean of each row (second argument specifies % dimension along which operation is taken) [1 2 3] * [4 5 6]' % 1x3 row vector times a 3x1 column vector % results in a scalar. Known as dot product % or inner product. Note the absence of "." [1 2 3]' * [4 5 6] % 3x1 column vector times a 1x3 row vector % results in a 3x3 matrix. Known as outer % product. Note the absence of "." %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (C) Matrix Operations: a = rand(3,2) % A 3x2 matrix b = rand(2,4) % A 2x4 matrix c = a * b % Matrix product results in a 3x4 matrix a = [1 2; 3 4; 5 6]; % A 3x2 matrix b = [5 6 7]; % A 1x3 row vector b * a % Vector-matrix product results in % a 1x2 row vector c = [8; 9]; % A 2x1 column vector a * c % Matrix-vector product results in % a 3x1 column vector a = [1 3 2; 6 5 4; 7 8 9]; % A 3x3 matrix inv(a) % Matrix inverse of a eig(a) % Vector of eigenvalues of a [V, D] = eig(a) % D matrix with eigenvalues on diagonal; % V matrix of eigenvectors % Example for multiple return values! [U, S, V] = svd(a) % Singular value decomposition of a. % a = U * S * V', singular values are % stored in S % Other matrix operations: det, norm, rank, ... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (D) Reshaping and assembling matrices: a = [1 2; 3 4; 5 6]; % A 3x2 matrix b = a(:) % Make 6x1 column vector by stacking % up columns of a sum(a(:)) % Useful: sum of all elements a = reshape(b, 2, 3) % Make 2x3 matrix out of vector % elements (column-wise) a = [1 2]; b = [3 4]; % Two row vectors c = [a b] % Horizontal concatenation (see horzcat) a = [1; 2; 3]; % Column vector c = [a; 4] % Vertical concatenation (see vertcat) a = [eye(3) rand(3)] % Concatenation for matrices b = [eye(3); ones(1, 3)] b = repmat(5, 3, 2) % Create a 3x2 matrix of fives b = repmat([1 2; 3 4], 1, 2) % Replicate the 2x2 matrix twice in % column direction; makes 2x4 matrix b = diag([1 2 3]) % Create 3x3 diagonal matrix with given % diagonal elements %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % (4) Control statements & vectorization % Syntax of control flow statements: % % for VARIABLE = EXPR % STATEMENT % ... % STATEMENT % end % % EXPR is a vector here, e.g. 1:10 or -1:0.5:1 or [1 4 7] % % % while EXPRESSION % STATEMENTS % end % % if EXPRESSION % STATEMENTS % elseif EXPRESSION % STATEMENTS % else % STATEMENTS % end % % (elseif and else clauses are optional, the "end" is required) % % EXPRESSIONs are usually made of relational clauses, e.g. a < b % The operators are <, >, <=, >=, ==, ~= (almost like in C(++)) % Warning: % Loops run very slowly in Matlab, because of interpretation overhead. % This has gotten somewhat better in version 6.5, but you should % nevertheless try to avoid them by "vectorizing" the computation, % i.e. by rewriting the code in form of matrix operations. This is % illustrated in some examples below. % Examples: for i=1:2:7 % Loop from 1 to 7 in steps of 2 i % Print i end for i=[5 13 -1] % Loop over given vector if (i > 10) % Sample if statement disp('Larger than 10') % Print given string elseif i < 0 % Parentheses are optional disp('Negative value') else disp('Something else') end end % Here is another example: given an mxn matrix A and a 1xn % vector v, we want to subtract v from every row of A. m = 50; n = 10; A = ones(m, n); v = 2 * rand(1, n); % % Implementation using loops: for i=1:m A(i,:) = A(i,:) - v; end % We can compute the same thing using only matrix operations A = ones(m, n) - repmat(v, m, 1); % This version of the code runs % much faster!!! % We can vectorize the computation even when loops contain % conditional statements. % % Example: given an mxn matrix A, create a matrix B of the same size % containing all zeros, and then copy into B the elements of A that % are greater than zero. % Implementation using loops: B = zeros(m,n); for i=1:m for j=1:n if A(i,j)>0 B(i,j) = A(i,j); end end end % All this can be computed w/o any loop! B = zeros(m,n); ind = find(A > 0); % Find indices of positive elements of A % (see "help find" for more info) B(ind) = A(ind); % Copies into B only the elements of A % that are > 0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %(5) Saving your work save myfile % Saves all workspace variables into % file myfile.mat save myfile a b % Saves only variables a and b clear a b % Removes variables a and b from the % workspace clear % Clears the entire workspace load myfile % Loads variable(s) from myfile.mat %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %(6) Creating scripts or functions using m-files: % % Matlab scripts are files with ".m" extension containing Matlab % commands. Variables in a script file are global and will change the % value of variables of the same name in the environment of the current % Matlab session. A script with name "script1.m" can be invoked by % typing "script1" in the command window. % Functions are also m-files. The first line in a function file must be % of this form: % function [outarg_1, ..., outarg_m] = myfunction(inarg_1, ..., inarg_n) % % The function name should be the same as that of the file % (i.e. function "myfunction" should be saved in file "myfunction.m"). % Have a look at myfunction.m and myotherfunction.m for examples. % % Functions are executed using local workspaces: there is no risk of % conflicts with the variables in the main workspace. At the end of a % function execution only the output arguments will be visible in the % main workspace. a = [1 2 3 4]; % Global variable a b = myfunction(2 * a) % Call myfunction which has local % variable a a % Global variable a is unchanged [c, d] = ... myotherfunction(a, b) % Call myotherfunction with two return % values %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %(7) Plotting x = [0 1 2 3 4]; % Basic plotting plot(x); % Plot x versus its index values pause % Wait for key press plot(x, 2*x); % Plot 2*x versus x axis([0 8 0 8]); % Adjust visible rectangle figure; % Open new figure x = pi*[-24:24]/24; plot(x, sin(x)); xlabel('radians'); % Assign label for x-axis ylabel('sin value'); % Assign label for y-axis title('dummy'); % Assign plot title figure; subplot(1, 2, 1); % Multiple functions in separate graphs plot(x, sin(x)); % (see "help subplot") axis square; % Make visible area square subplot(1, 2, 2); plot(x, 2*cos(x)); axis square; figure; plot(x, sin(x)); hold on; % Multiple functions in single graph plot(x, 2*cos(x), '--'); % '--' chooses different line pattern legend('sin', 'cos'); % Assigns names to each plot hold off; % Stop putting multiple figures in current % graph figure; % Matrices vs. images m = rand(64,64); imagesc(m) % Plot matrix as image colormap gray; % Choose gray level colormap axis image; % Show pixel coordinates as axes axis off; % Remove axes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %(8) Working with (gray level) images I = imread('cit.png'); % Read a PNG image figure imagesc(I) % Display it as gray level image colormap gray; colorbar % Turn on color bar on the side pixval % Display pixel values interactively truesize % Display at resolution of one screen % pixel per image pixel truesize(2*size(I)) % Display at resolution of two screen % pixels per image pixel I2 = imresize(I, 0.5, 'bil'); % Resize to 50% using bilinear % interpolation I3 = imrotate(I2, 45, ... % Rotate 45 degrees and crop to 'bil', 'crop'); % original size I3 = double(I2); % Convert from uint8 to double, to allow % math operations imagesc(I3.^2) % Display squared image (pixel-wise) imagesc(log(I3)) % Display log of image (pixel-wise) I3 = uint8(I3); % Convert back to uint8 for writing imwrite(I3, 'test.png') % Save image as PNG figure; g = [1 2 1]' * [1 2 1] / 16; % 3x3 Gaussian filter mask I2 = double(I); % Convert image to floating point I3 = conv2(I2, g); % Convolve image with filter mask I3 = conv2(I2, g, 'same'); % Convolve image, but keep original size subplot(1, 2, 1) % Display original and filtered image imagesc(I); % side-by-side axis square; colormap gray; subplot(1, 2, 2) imagesc(I3); axis square; colormap gray; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%myfunction.m
function y = myfunction(x) % Function of one argument with one return value a = [-2 -1 0 1]; % Have a global variable of the same name y = a + x;myotherfunction.m
function [y, z] = myotherfunction(a, b) % Function of two arguments with two return values y = a + b; z = a - b;
1 komentar:
Baccarat: What's the game of Bet on the Go with Betway!
In the game of Baccarat, the objective is septcasino to beat the dealer 바카라사이트 in the casino's head by matching the bet slip, and then 1xbet korean matching the bet slip. In this
Post a Comment and Don't Spam!