08-Sep-2022 18:29:59 floyd_test(): MATLAB/Octave version 4.2.2 Test floyd(). floyd_test01(): floyd() uses Floyd's algorithm to find the shortest distance between all pairs of nodes in a directed graph, starting from the initial array of direct node-to-node distances. Node-to-node one-step distance array: 0 2 5 Inf Inf Inf Inf 0 7 1 Inf 8 Inf Inf 0 4 Inf Inf Inf Inf Inf 0 3 Inf Inf Inf 2 Inf 0 3 Inf 5 Inf 2 4 0 Node-to-node shortest total distance array: 0 2 5 3 6 9 Inf 0 6 1 4 7 Inf 15 0 4 7 10 Inf 11 5 0 3 6 Inf 8 2 5 0 3 Inf 5 6 2 4 0 floyd_test02(): Test floyd() on matrices of increasing order N. The work is roughly N^3. N Time (seconds) Time/N^3 1 0.000064 64.134598 2 0.000204 25.480986 4 0.001353 21.141022 8 0.008785 17.158221 16 0.056493 13.792189 32 0.447357 13.652250 64 3.821142 14.576500 128 32.308627 15.405954 256 231.171113 13.778872 floyd_test03() floyd() starts with the adjacency matrix A of a triangulation, determines the pairwise distance matrix B. One-step distance matrix: Columns 1 through 8: 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Columns 9 through 16: 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Columns 17 through 24: Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf 0.00000 1.00000 Inf Inf 1.00000 Inf Inf Inf 1.00000 0.00000 Inf Inf 1.41421 1.00000 Inf Inf Inf Inf 0.00000 1.00000 Inf Inf 1.00000 Inf Inf Inf 1.00000 0.00000 Inf Inf 1.41421 1.00000 1.00000 1.41421 Inf Inf 0.00000 1.00000 Inf Inf Inf 1.00000 Inf Inf 1.00000 0.00000 Inf Inf Inf Inf 1.00000 1.41421 Inf Inf 0.00000 1.00000 Inf Inf Inf 1.00000 Inf Inf 1.00000 0.00000 Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Columns 25 through 32: Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf 0.00000 1.00000 Inf Inf 1.00000 Inf Inf Inf 1.00000 0.00000 Inf Inf 1.41421 1.00000 Inf Inf Inf Inf 0.00000 1.00000 Inf Inf 1.00000 Inf Inf Inf 1.00000 0.00000 Inf Inf 1.41421 1.00000 1.00000 1.41421 Inf Inf 0.00000 1.00000 Inf Inf Inf 1.00000 Inf Inf 1.00000 0.00000 Inf Inf Inf Inf 1.00000 1.41421 Inf Inf 0.00000 1.00000 Inf Inf Inf 1.00000 Inf Inf 1.00000 0.00000 Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Columns 33 through 40: Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 Inf Inf Inf Inf Inf Inf Inf Inf 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 1.41421 Inf Inf Inf Inf Inf Inf Inf 1.00000 Columns 41 through 48: Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf Inf 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 Inf Inf Inf Inf Inf Inf Inf 1.41421 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 Inf Inf Inf Inf Inf Inf Inf Inf 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 1.00000 Inf Inf Inf Inf Inf Inf 1.00000 0.00000 Floyd distance matrix: Columns 1 through 7: 0.00000 1.00000 2.00000 3.00000 4.00000 5.00000 6.00000 1.00000 0.00000 1.00000 2.00000 3.00000 4.00000 5.00000 2.00000 1.00000 0.00000 1.00000 2.00000 3.00000 4.00000 3.00000 2.00000 1.00000 0.00000 1.00000 2.00000 3.00000 4.00000 3.00000 2.00000 1.00000 0.00000 1.00000 2.00000 5.00000 4.00000 3.00000 2.00000 1.00000 0.00000 1.00000 6.00000 5.00000 4.00000 3.00000 2.00000 1.00000 0.00000 7.00000 6.00000 5.00000 4.00000 3.00000 2.00000 1.00000 1.00000 1.41421 2.41421 3.41421 4.41421 5.41421 6.41421 2.00000 1.00000 1.41421 2.41421 3.41421 4.41421 5.41421 3.00000 2.00000 1.00000 1.41421 2.41421 3.41421 4.41421 4.00000 3.00000 2.00000 1.00000 1.41421 2.41421 3.41421 5.00000 4.00000 3.00000 2.00000 1.00000 1.41421 2.41421 6.00000 5.00000 4.00000 3.00000 2.00000 1.00000 1.41421 7.00000 6.00000 5.00000 4.00000 3.00000 2.00000 1.00000 8.00000 7.00000 6.00000 5.00000 4.00000 3.00000 2.00000 2.00000 2.41421 2.82843 3.82843 4.82843 5.82843 6.82843 3.00000 2.00000 2.41421 3.41421 4.41421 5.41421 6.41421 8.00000 7.00000 6.00000 5.00000 4.00000 3.00000 2.00000 9.00000 8.00000 7.00000 6.00000 5.00000 4.00000 3.00000 3.00000 3.41421 3.82843 4.82843 5.82843 6.82843 7.82843 4.00000 3.00000 3.41421 4.41421 5.41421 6.41421 7.41421 9.00000 8.00000 7.00000 6.00000 5.00000 4.00000 3.00000 10.00000 9.00000 8.00000 7.00000 6.00000 5.00000 4.00000 4.00000 4.41421 4.82843 5.82843 6.82843 7.82843 8.82843 5.00000 4.00000 4.41421 5.41421 6.41421 7.41421 8.41421 10.00000 9.00000 8.00000 7.00000 6.00000 5.00000 4.00000 11.00000 10.00000 9.00000 8.00000 7.00000 6.00000 5.00000 5.00000 5.41421 5.82843 6.82843 7.82843 8.82843 9.82843 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11.41421 6.00000 5.00000 6.00000 7.00000 8.00000 9.00000 12.41421 7.00000 6.00000 7.00000 8.00000 9.00000 10.00000 13.41421 8.00000 7.00000 8.00000 9.00000 10.00000 11.00000 8.41421 13.00000 12.00000 11.00000 10.00000 9.00000 8.00000 7.41421 12.00000 11.00000 10.00000 9.00000 8.00000 7.00000 6.41421 11.00000 10.00000 9.00000 8.00000 7.00000 6.00000 6.00000 12.00000 11.00000 10.00000 9.00000 8.00000 7.00000 12.82843 6.00000 6.41421 7.41421 8.41421 9.41421 10.41421 12.41421 7.00000 6.00000 7.00000 8.00000 9.00000 10.00000 13.41421 8.00000 7.00000 8.00000 9.00000 10.00000 11.00000 14.41421 9.00000 8.00000 9.00000 10.00000 11.00000 12.00000 8.82843 13.41421 12.41421 11.41421 10.41421 9.41421 8.41421 7.82843 12.41421 11.41421 10.41421 9.41421 8.41421 7.41421 7.41421 12.00000 11.00000 10.00000 9.00000 8.00000 7.00000 7.00000 13.00000 12.00000 11.00000 10.00000 9.00000 8.00000 Columns 15 through 21: 7.00000 8.00000 2.00000 3.00000 8.00000 9.00000 3.00000 6.00000 7.00000 2.41421 2.00000 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