gibson:teaching:fall-2014:math445:lab5
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gibson:teaching:fall-2014:math445:lab5 [2014/11/12 19:16] gibson |
gibson:teaching:fall-2014:math445:lab5 [2015/03/09 13:39] (current) gibson |
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| </code> | </code> | ||
| - | or equivalently | ||
| - | |||
| - | <code> | ||
| - | N=100; | ||
| - | p=(G^N)*p; | ||
| - | </code> | ||
| After that is complete the elements of ''p'' give the probabilities that a random web surfer will end up at the web pages listed in ''U'', and you can rank the pages in ''U'' according to their probabilities in ''p''. Look up the ''sort'' command in the Help menu and find a way to print the list of websites in order of their rank. Turn in the list of the top 10, the fraction of the time a random web surfer would spend in each one of those 10, and your code to complete the Lab. | After that is complete the elements of ''p'' give the probabilities that a random web surfer will end up at the web pages listed in ''U'', and you can rank the pages in ''U'' according to their probabilities in ''p''. Look up the ''sort'' command in the Help menu and find a way to print the list of websites in order of their rank. Turn in the list of the top 10, the fraction of the time a random web surfer would spend in each one of those 10, and your code to complete the Lab. | ||
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| - | Now write a script that tests and times these algorithms on link matrices L of sizes M = 32, 64, 128, 256, 512, and 1024. You can use this Matlab function to produce synthetic data for testing any given value of M | + | Now write a script that tests and times these algorithms on link matrices L of sizes M = 32, 64, 128, 256, ...., up to whatever power of two your computer can handle. It's smart to develop and test your code on a smaller set of M, perhaps just M = 32, 64, 128. As a starting point, here's the code we developed in class to measure execution time of full versus sparse matrices. |
| + | |||
| + | <code matlab> | ||
| + | |||
| + | % script to compare full versus sparse matrix multiplication | ||
| + | |||
| + | for n=1:12 | ||
| + | |||
| + | % set up random M x M Ax=b problem | ||
| + | m = 2^n; | ||
| + | A = randomL(m); | ||
| + | x = randn(m,1); | ||
| + | |||
| + | % measure execution time of sparse matrix multiplication | ||
| + | tic; | ||
| + | b = A*x; | ||
| + | Tsparse(n) = toc; | ||
| + | |||
| + | % measure execution time of full matrix multiplication | ||
| + | A = full(A); | ||
| + | tic; | ||
| + | b = A*x; | ||
| + | Tfull(n) = toc; | ||
| + | |||
| + | M(n) = m; | ||
| + | end | ||
| + | </code> | ||
| + | |||
| + | You can use this Matlab function to produce synthetic data for testing any given value of M | ||
| <code matlab> | <code matlab> | ||
| Line 155: | Line 177: | ||
| L = sparse(M,M); | L = sparse(M,M); | ||
| | | ||
| - | for j=1:M | + | for j=1:M |
| - | i = randi(M, maxlinks, 1); % pick maxlinks random pages | + | i = randi(M, maxlinks, 1); % get vector of random numbers between 1 and M |
| for n = 1:maxlinks | for n = 1:maxlinks | ||
| - | L(i(n),j) = 1; | + | L(i(n),j) = 1; % create links from page j to the random pages i |
| end | end | ||
| end | end | ||
| | | ||
| end | end | ||
| - | <code> | + | </code> |
gibson/teaching/fall-2014/math445/lab5.1415848585.txt.gz · Last modified: 2014/11/12 19:16 by gibson
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