cvt_1d_lumping_test

cvt_1d_lumping_test, a MATLAB program which calls cvt_1d_lumping() to carry out a lumped version of Lloyd's iterative algorithm for the computation of a centroidal Voronoi Tessellation (CVT) in the interval [-1,+1], for a general density function rho(x).

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

cvt_1d_lumping, a MATLAB program which allows the user to carry out a lumped version of Lloyd's iterative algorithm for a centroidal Voronoi Tessellation (CVT() in the interval [-1,+1], and is applied to investigate a relationship between CVT's and the Chebyshev Zero nodes.

Source Code:

• cvt_1d_lumping_test.m, calls all the tests.
• cvt_1d_lumping_test.sh, runs all the tests.
• cvt_1d_lumping_test.txt, the output file.
• density.png, a plot of densities rho(x) and mu(x), truncating values above 10.

The code was run with the Chebyshev Zero Node density function, N = 3, 5, 9, 17, 33, 65, 129 and 255, with the generator values initialized with equaly spaced values (U).

The output files:

• output_003_u.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_005_u.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_009_u.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_017_u.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_033_u.txt, using 750 steps and 100,000 samples and uniform initialization.
• output_065_u.txt, using 2000 steps and 100,000 samples and uniform initialization.
• output_129_u.txt, using 6,000 steps and 200,000 samples and uniform initialization.
• output_257_u.txt , using 15,000 steps and 200,000 samples and uniform initialization.

Data Files:

• chebyzero_005.txt
• chebyzero_009.txt
• chebyzero_017.txt
• chebyzero_033.txt
• chebyzero_065.txt
• chebyzero_129.txt
• chebyzero_257.txt
• cvt_005_c.txt
• cvt_009_c.txt
• cvt_017_c.txt
• cvt_033_c.txt
• cvt_065_c.txt
• cvt_129_c.txt
• cvt_257_c.txt
• cvt_005_r.txt
• cvt_009_r.txt
• cvt_017_r.txt
• cvt_033_r.txt
• cvt_065_r.txt
• cvt_129_r.txt
• cvt_257_r.txt
• cvt_005_u.txt
• cvt_009_u.txt
• cvt_017_u.txt
• cvt_033_u.txt
• cvt_065_u.txt
• cvt_129_u.txt
• cvt_257_u.txt

Files containing the coordinates of the Chebyshev Zero nodes, and the CVT generators initialized by Chebyshev Zero nodes, by random values, or by uniform values:

• chebyzero_005.txt
• chebyzero_009.txt
• chebyzero_017.txt
• chebyzero_033.txt
• chebyzero_065.txt
• chebyzero_129.txt
• chebyzero_257.txt
• cvt_005_c.txt
• cvt_009_c.txt
• cvt_017_c.txt
• cvt_033_c.txt
• cvt_065_c.txt
• cvt_129_c.txt
• cvt_257_c.txt
• cvt_005_r.txt
• cvt_009_r.txt
• cvt_017_r.txt
• cvt_033_r.txt
• cvt_065_r.txt
• cvt_129_r.txt
• cvt_257_r.txt
• cvt_005_u.txt
• cvt_009_u.txt
• cvt_017_u.txt
• cvt_033_u.txt
• cvt_065_u.txt
• cvt_129_u.txt
• cvt_257_u.txt

The plots of energy as a function of iteration step:

• energy_003_u.png
• energy_005_u.png
• energy_009_u.png
• energy_017_u.png
• energy_033_u.png
• energy_065_u.png
• energy_129_u.png
• energy_257_u.png

The plots of the norm of the change in position of the generators as a function of iteration step:

• motion_003_u.png
• motion_005_u.png
• motion_009_u.png
• motion_017_u.png
• motion_033_u.png
• motion_065_u.png
• motion_129_u.png
• motion_257_u.png

The plots of the position of the generators as a function of iteration step:

• evolution_003_u.png
• evolution_005_u.png
• evolution_009_u.png
• evolution_017_u.png
• evolution_033_u.png
• evolution_065_u.png
• evolution_129_u.png
• evolution_257_u.png

The code was run with the Chebyshev Zero Node density function, N = 3, 5, 9, 17, 33, 65, 129 and 255, with the generator values initialized with the Chebyshev Zero Nodes (C). It was expected that, in these runs, the CVT generators would stay near their initial values, so that the motion plots, in particular, would be near vertical.

The output files:

• output_003_c.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_005_c.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_009_c.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_017_c.txt, using 250 steps and 100,000 samples and uniform initialization.
• output_033_c.txt, using 750 steps and 100,000 samples and uniform initialization.
• output_065_c.txt, using 2000 steps and 100,000 samples and uniform initialization.
• output_129_c.txt, using 6,000 steps and 200,000 samples and uniform initialization.
• output_257_c.txt , using 15,000 steps and 200,000 samples and uniform initialization.

The plots of energy as a function of iteration step:

• energy_003_c.png
• energy_005_c.png
• energy_009_c.png
• energy_017_c.png
• energy_033_c.png
• energy_065_c.png
• energy_129_c.png
• energy_257_c.png

The plots of the norm of the change in position of the generators as a function of iteration step:

• motion_003_c.png
• motion_005_c.png
• motion_009_c.png
• motion_017_c.png
• motion_033_c.png
• motion_065_c.png
• motion_129_c.png
• motion_257_c.png

The plots of the position of the generators as a function of iteration step:

• evolution_003_c.png
• evolution_005_c.png
• evolution_009_c.png
• evolution_017_c.png
• evolution_033_c.png
• evolution_065_c.png
• evolution_129_c.png
• evolution_257_c.png