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In gaimc, then, we first convert any Matlab sparse matrix input to a com- pressed sparse row data structure for the graph operations. A support func- tion sparse_to_csr performs this simple conversion. All gaimc functions also accept a structure with the compressed sparse row arrays pre-computed. Another advantage of using our own compressed sparse row structure occurs when the graph has edge weights of 0. The Matlab sparse matrix structure removes such entries [Gilbert et al., 1992]. Based on this analysis, we offer some advice to optimize Matlab functions: • donotusefunctioncalls • evaluateperformanceofbuilt-inMatlabfunctions • questionperformanceassumptions. While just-in-time compiled Matlab code may not be as fast as optimized C or C++ code, it need not be slow. 6.4.3 Performance In the previous sections, we have reviewed how to implement a heap structure in Matlab, and optimized the performance of an algorithm using the heap. In this section, we compare the performance of gaimc to MatlabBGL. Writing native Matlab code does not offer the same performance as native C or C++ code and we evaluate gaimc by how much slower the routines are compared with their C++ Boost graph library counterparts. In our tests, we plot the slowdown ratio tgaimc s=, tMatlabBGL where tgaimc is the time of an operation in gaimc and tMatlabBGL is the time of an operation in MatlabBGL. Thus, a slowdown ratio around 1 implies that the routines took roughly the same amount of time. We evaluate the performance of 6 functions: 1. depthfirstsearch(dfs), 2. strongcomponents(scomponents), 3. Dijkstra’ssingle-sourceshortestpaths(dijkstra), 4. directedclusteringcoefficients(dirclustercoeffs), 5. Prim’sminimumspanningtree(prim_mst),and 6. clusteringcoefficients(clustercoeffs), in two cases: • standardMatlabsparsematrixinput(standard),and • “pre-converted”input(fast). In MatlabBGL and gaimc, the input must be transposed or converted to compressed-sparse row arrays, respectively. In the second case, we show the performance with inputs that are already converted, which corresponds to a faster function call. 6.4 ⋅ gaimc 135PDF Image | ALGORITHMS FOR PAGERANK SENSITIVITY DISSERTATION
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