Adjust blur_width hyperparameter

[adisidev]

cartogram-cpp/src/inset_state/inset_state.cpp

Lines 44 to 73 in 7c9744d

	double InsetState::blur_width() const
	{
	// Blur density to speed up the numerics in flatten_density() below.
	// We slowly reduce the blur width so that the areas can reach their
	// target values. In case of failure during flatten_density, we increase
	// the blur width to avoid the flipped Delaunay triangles.
	// TODO: whenever blur_width hits 0, the maximum area error will start
	// increasing again and eventually lead to an invalid grid
	// cell error when projecting with triangulation. Investigate
	// why. As a temporary fix, we set blur_width to be always
	// positive, regardless of the number of integrations.
	const unsigned int blur_default_pow =
	static_cast<unsigned int>(
	1 + log2(std::max(lx(), ly()) / default_long_grid_length)) +
	n_fails_during_flatten_density_;
	double blur_width =
	std::pow(2.0, blur_default_pow - (0.5 * n_finished_integrations_));
	// NOTE: Read TODO above
	// if (inset_state.n_finished_integrations() < max_integrations) {
	// blur_width =
	// std::pow(2.0, 5 - int(inset_state.n_finished_integrations()));
	// } else {
	// blur_width = 0.0;
	// }
	std::cerr << "blur_width = " << blur_width << std::endl;
	return blur_width;
	}

[adisidev]

I believe the initial blur_width can be adjusted heuristically.

Below is some output of all the countries that had repeat integrations (indicating blur width was too low).

I believe there is a pattern here, and we can come up with a heuristic to increase initial blur_width on said pattern. Although I initially thought it had to just do with max area error and average area error, I believe those don't matter as much as absolute area error (as evidenced by Brazil's low max area error and low average area error, but it still having repeat integrations. Thus, I believe "absolute area error" (calculated as the sum of region_area_error * region_proportion_of_total_area or sum of (region_area_error * region_proportion_of_target_area_to_total_cartogram_area) would be a good heuristic for initial blur_width.

Keep in mind, with blur_width in general, we are trying to balance having a low enough blur width to make actual progress, but also a high enough blur width so the integrator does not fail and so that we get better shape similarity.

ALGERIA
max. area err: 0.999998, GeoDiv: Alger            ⬜⬜                                      0%
average area err: 0.998243
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 80.5311, GeoDiv: Illizi
average area err: 4.23577
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                17%
Integration number 1
max. area err: 26.3797, GeoDiv: Illizi
average area err: 1.8762
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜                               20%
Integration number 2
max. area err: 5.10426, GeoDiv: Illizi
average area err: 0.446879
Integration number 3
max. area err: 2.46791, GeoDiv: Illizi
average area err: 0.168939

BAHAMAS
max. area err: 0.999957, GeoDiv: City of Freeport ⬜⬜                                      0%
average area err: 0.983335
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 50.5531, GeoDiv: Inagua
average area err: 9.42815
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                18%
Integration number 1
max. area err: 48.9825, GeoDiv: Inagua
average area err: 6.97365
Integration number 2                              ⬜⬜⬜⬜⬜⬜                                18%
max. area err: 16.3668, GeoDiv: Rum Cay
average area err: 3.33572



BRAZIL
max. area err: 0.999998, GeoDiv: Federal District ⬜⬜                                      0%
average area err: 0.999891
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 8.17692, GeoDiv: Amazonas
average area err: 1.81109
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜⬜                              23%
Integration number 1
Integration number 1
max. area err: 3.20394, GeoDiv: Roraima
average area err: 0.667096
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                            27%
max. area err: 1.11485, GeoDiv: Roraima
average area err: 0.27623


CHINA
max. area err: 1, GeoDiv: Macao Special Administrative Region                             0%
average area err: 0.999976
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 46.5929, GeoDiv: Tibet Autonomous Region
average area err: 2.87247
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜                               19%
Integration number 1
max. area err: 5.89154, GeoDiv: Tibet Autonomous Region
average area err: 0.506768
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜                             25%
max. area err: 1.11903, GeoDiv: Tibet Autonomous Region
average area err: 0.161027

USA_COUNTY
max. area err: 1, GeoDiv: 0500000US36061          ⬜⬜                                      0%
average area err: 0.999924
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 41.2673, GeoDiv: 0500000US32023
average area err: 1.87969
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜                               19%
Integration number 1
Integration number 1
max. area err: 45.1578, GeoDiv: 0500000US06027
average area err: 1.31477
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜                               19%
max. area err: 21.3945, GeoDiv: 0500000US06027
average area err: 1.02187


USA_COUNTY_2
max. area err: 6.46692, GeoDiv: 0500000US06071    ⬜⬜                                      0%
average area err: 0.882339
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜                             24%
max. area err: 66.706, GeoDiv: 0500000US06071
average area err: 1.00541
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                18%
Integration number 1
max. area err: 13.1023, GeoDiv: 0500000US06073
average area err: 0.406562
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜                              22%
max. area err: 6.14655, GeoDiv: 0500000US04003
average area err: 0.333577


EGYPT_BY_GOVERNATE
max. area err: 0.999996, GeoDiv: Qalyubia Governorate                                     0%
average area err: 0.997887
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 171.478, GeoDiv: New Valley Governorate
average area err: 10.5817
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                16%
Integration number 1
Integration number 1
Integration number 1
Integration number 1
max. area err: 75.6021, GeoDiv: New Valley Governorate
average area err: 7.46942
Integration number 2                              ⬜⬜⬜⬜⬜⬜                                18%


GERMANY
max. area err: 0.999989, GeoDiv: Berlin           ⬜⬜                                      0%
average area err: 0.999799
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 2.1912, GeoDiv: Mecklenburg-Vorpommern
average area err: 0.667218
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                           29%
Integration number 1
Integration number 1
max. area err: 1.2033, GeoDiv: Brandenburg
average area err: 0.383586
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          33%


MALAYSIA
max. area err: 0.999975, GeoDiv: Labuan           ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜        81%
average area err: 0.999388
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜     87%
max. area err: 0.969844, GeoDiv: Labuan
average area err: 0.612628
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜     87%
Integration number 1
max. area err: 0.77951, GeoDiv: Labuan
average area err: 0.333949
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜     88%
max. area err: 0.349194, GeoDiv: Labuan
average area err: 0.12391
Integration number 3                              ⬜⬜⬜


PARIS
max. area err: 0.999999, GeoDiv: Paris            ⬜⬜                                      0%
average area err: 0.999671
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 7.00928, GeoDiv: Lozère
average area err: 1.10541
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜                             24%
Integration number 1
max. area err: 1.69333, GeoDiv: Haute-Corse
average area err: 0.374886
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                           31%
max. area err: 0.821163, GeoDiv: Rhône
average area err: 0.146353

RUSSIA
max. area err: 1, GeoDiv: Moscow City             ⬜⬜                                      0%
average area err: 0.999803
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 118.94, GeoDiv: Chukot
average area err: 3.64016
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                17%
Integration number 1
Integration number 1
max. area err: 75.9413, GeoDiv: Chukot
average area err: 1.91155
Integration number 2                              ⬜⬜⬜⬜⬜⬜                                18%
Integration number 2
max. area err: 37.7918, GeoDiv: Chukot
average area err: 1.19987

SINGAPORE
max. area err: 0.999647, GeoDiv: Choa Chu Kang    ⬜⬜                                      0%
average area err: 0.884153
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 856.364, GeoDiv: North-Eastern Islands
average area err: 76.2376
Integration number 1                              ⬜⬜⬜⬜⬜                                 14%
Integration number 1
Integration number 1
max. area err: 374.614, GeoDiv: North-Eastern Islands
average area err: 43.0859
Integration number 2                              ⬜⬜⬜⬜⬜                                 15%

SWITZERLAND
max. area err: 0.999771, GeoDiv: Basel-City       ⬜⬜                                      0%
average area err: 0.972726
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 8.46291, GeoDiv: Uri
average area err: 1.43089
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜⬜                              23%
Integration number 1
max. area err: 1.99285, GeoDiv: Grisons
average area err: 0.444028
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                           30%
max. area err: 0.653004, GeoDiv: Appenzell Innerrhoden
average area err: 0.158785

TUNISIA
max. area err: 0.999988, GeoDiv: Tunis            ⬜⬜                                      0%
average area err: 0.998756
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 17.2264, GeoDiv: Tataouine
average area err: 1.68936
Integration number 1                              ⬜⬜⬜⬜⬜⬜⬜                               21%
Integration number 1
max. area err: 4.86759, GeoDiv: Tataouine
average area err: 0.497082
Integration number 2                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜                             26%
max. area err: 0.735202, GeoDiv: Tataouine
average area err: 0.118009


WORLD
max. area err: 1, GeoDiv: Macao                   ⬜⬜                                      0%
average area err: 0.999993
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 834.35, GeoDiv: Antarctica
average area err: 5.42833
Integration number 1                              ⬜⬜⬜⬜⬜                                 14%
Integration number 1
Integration number 1
max. area err: 577.985, GeoDiv: Antarctica
average area err: 3.6954
Integration number 2                              ⬜⬜⬜⬜⬜                                 14%


WORLD_w_wo_antarctica_csv
max. area err: 1, GeoDiv: Macao
average area err: 0.999997
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 155.568, GeoDiv: Greenland
average area err: 2.11211
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                16%
Integration number 1
Integration number 1
max. area err: 61.5262, GeoDiv: Greenland
average area err: 1.38395
Integration number 2                              ⬜⬜⬜⬜⬜⬜                                18%
max. area err: 28.645, GeoDiv: Greenland
average area err: 0.992094


WORLD_by_country
max. area err: 1, GeoDiv: MDV                     ⬜⬜                                      0%
average area err: 0.999997
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 155.874, GeoDiv: GRL
average area err: 2.46174
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                16%
Integration number 1
Integration number 1
max. area err: 61.8732, GeoDiv: GRL
average area err: 1.55955
Integration number 2                              ⬜⬜⬜⬜⬜⬜                                18%
max. area err: 24.9938, GeoDiv: GRL
average area err: 1.0906


WORLD_wo_antarctica
max. area err: 1, GeoDiv: Macao                   ⬜⬜                                      0%
average area err: 0.999997
Integration number 0                              ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜                          34%
max. area err: 155.853, GeoDiv: Greenland
average area err: 2.12186
Integration number 1                              ⬜⬜⬜⬜⬜⬜                                16%
Integration number 1
Integration number 1
max. area err: 61.0831, GeoDiv: Greenland
average area err: 1.38242
Integration number 2                              ⬜⬜⬜⬜⬜⬜                                18%
max. area err: 28.2876, GeoDiv: Greenland
average area err: 0.9905