diff --git a/BUILD.bazel b/BUILD.bazel index f0adc5d4..8a474563 100644 --- a/BUILD.bazel +++ b/BUILD.bazel @@ -202,6 +202,7 @@ swift_cc_test( "tests/test_block_utils.cc", "tests/test_call_trace.cc", "tests/test_callers.cc", + "tests/test_chi_squared_versus_gsl.cc", "tests/test_compression.cc", "tests/test_concatenate.cc", "tests/test_conditional_gaussian.cc", diff --git a/WORKSPACE.bazel b/WORKSPACE.bazel index ab62240f..cc08b75b 100644 --- a/WORKSPACE.bazel +++ b/WORKSPACE.bazel @@ -1,12 +1,12 @@ workspace(name = "albatross") load("@bazel_tools//tools/build_defs/repo:http.bzl", "http_archive") - + http_archive( name = "rules_swiftnav", - sha256 = "8e00b694b6dce9c91d811e2e9e13e148af5f1dd329b85b7c5d2d9d2238aa92dc", - strip_prefix = "rules_swiftnav-1c51c97743c9632169dd7e5a228c6ce915893236", - url = "https://github.com/swift-nav/rules_swiftnav/archive/1c51c97743c9632169dd7e5a228c6ce915893236.tar.gz", + sha256 = "2f91790be7845e2eeb746dd33c59d1ba5d6ee85360a3218d2a4a77ead79f81b9", + strip_prefix = "rules_swiftnav-030c1c5050e7541ce66cd82f523939a525b1551c", + url = "https://github.com/swift-nav/rules_swiftnav/archive/030c1c5050e7541ce66cd82f523939a525b1551c.tar.gz", ) load("@rules_swiftnav//cc:repositories.bzl", "register_swift_cc_toolchains", "swift_cc_toolchain") diff --git a/include/albatross/Stats b/include/albatross/Stats index 31fd612b..19bbaf24 100644 --- a/include/albatross/Stats +++ b/include/albatross/Stats @@ -13,6 +13,7 @@ #ifndef ALBATROSS_STATS_H #define ALBATROSS_STATS_H +#include #include #include #include diff --git a/include/albatross/src/stats/chi_squared.hpp b/include/albatross/src/stats/chi_squared.hpp index c5c4f19d..ccf263d5 100644 --- a/include/albatross/src/stats/chi_squared.hpp +++ b/include/albatross/src/stats/chi_squared.hpp @@ -26,11 +26,11 @@ namespace albatross { namespace details { -inline double chi_squared_cdf_unsafe(double x, std::size_t degrees_of_freedom) { - return incomplete_gamma(0.5 * cast::to_double(degrees_of_freedom), 0.5 * x); +inline double chi_squared_cdf_unsafe(double x, double degrees_of_freedom) { + return incomplete_gamma(0.5 * degrees_of_freedom, 0.5 * x); } -inline double chi_squared_cdf_safe(double x, std::size_t degrees_of_freedom) { +inline double chi_squared_cdf_safe(double x, double degrees_of_freedom) { if (std::isnan(x) || x < 0.) { return NAN; @@ -53,7 +53,16 @@ inline double chi_squared_cdf_safe(double x, std::size_t degrees_of_freedom) { } // namespace details -inline double chi_squared_cdf(double x, std::size_t degrees_of_freedom) { +template ::value>> +inline double chi_squared_cdf(double x, IntType degrees_of_freedom) { + // due to implicit argument conversions we can't directly use cast::to_double + // here. + return details::chi_squared_cdf_safe(x, + static_cast(degrees_of_freedom)); +} + +inline double chi_squared_cdf(double x, double degrees_of_freedom) { return details::chi_squared_cdf_safe(x, degrees_of_freedom); } diff --git a/include/albatross/src/stats/incomplete_gamma.hpp b/include/albatross/src/stats/incomplete_gamma.hpp index 262ab9c8..861a3a3a 100644 --- a/include/albatross/src/stats/incomplete_gamma.hpp +++ b/include/albatross/src/stats/incomplete_gamma.hpp @@ -75,32 +75,11 @@ inline double incomplete_gamma_quadrature_recursive(double lb, double ub, inline std::pair incomplete_gamma_quadrature_bounds(double a, double z) { - - if (a > 800) { - return std::make_pair(std::max(0., std::min(z, a) - 11 * sqrt(a)), - std::min(z, a + 10 * sqrt(a))); - } else if (a > 300) { - return std::make_pair(std::max(0., std::min(z, a) - 10 * sqrt(a)), - std::min(z, a + 9 * sqrt(a))); - } else if (a > 90) { - return std::make_pair(std::max(0., std::min(z, a) - 9 * sqrt(a)), - std::min(z, a + 8 * sqrt(a))); - } else if (a > 70) { - return std::make_pair(std::max(0., std::min(z, a) - 8 * sqrt(a)), - std::min(z, a + 7 * sqrt(a))); - } else if (a > 50) { - return std::make_pair(std::max(0., std::min(z, a) - 7 * sqrt(a)), - std::min(z, a + 6 * sqrt(a))); - } else if (a > 40) { - return std::make_pair(std::max(0., std::min(z, a) - 6 * sqrt(a)), - std::min(z, a + 5 * sqrt(a))); - } else if (a > 30) { - return std::make_pair(std::max(0., std::min(z, a) - 5 * sqrt(a)), - std::min(z, a + 4 * sqrt(a))); - } else { - return std::make_pair(std::max(0., std::min(z, a) - 4 * sqrt(a)), - std::min(z, a + 4 * sqrt(a))); - } + // NOTE: GCEM uses a large conditional block to select tighter bounds, but in + // practice those bounds were not tight enough, particularly on the upper + // bound, so we've modified this function to be more conservative + return std::make_pair(std::max(0., std::min(z, a) - 12 * sqrt(a)), + std::min(z, a + 13 * sqrt(a + 1))); } inline double incomplete_gamma_quadrature(double a, double z) { diff --git a/tests/test_chi_squared_versus_gsl.cc b/tests/test_chi_squared_versus_gsl.cc new file mode 100644 index 00000000..51a22ea7 --- /dev/null +++ b/tests/test_chi_squared_versus_gsl.cc @@ -0,0 +1,5742 @@ +/* + * Copyright (C) 2024 Swift Navigation Inc. + * Contact: Swift Navigation + * + * This source is subject to the license found in the file 'LICENSE' which must + * be distributed together with this source. All other rights reserved. + * + * THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, + * EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED + * WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A PARTICULAR PURPOSE. + */ + +#include +#include + +#include + +namespace albatross { + +/* + What follows is a long list of spot checks of our incomplete gamma + implementation. The function is critical for the evaluation of the chi squared + percentiles and since those values often factor in to outlier detection we + need to be sure we have good precision on the tails. What follows were a bunch + of comparisons to the GSL implementations which were generated using: + + #include + + double dof = 1.0; + while (dof < 2000) { + const double a = 0.5 * dof; + + const auto bounds = + details::incomplete_gamma_quadrature_bounds(a, 100 * sqrt(a)); + const double lowest = 2. * bounds.first; + const double highest = 2. * bounds.second; + + auto gsl_chi_squared = [](double x, double dof) { + return gsl_sf_gamma_inc_P(0.5 * dof, 0.5 * x); + }; + + // The bounds provided should correspond to the z argument which corresponds + // to near zero and near one evaluations of the incomplete gamma + EXPECT_NEAR(chi_squared_cdf_non_integer_dof(lowest, dof), 0., 1e-8); + EXPECT_NEAR(chi_squared_cdf_non_integer_dof(highest, dof), 1., 1e-8); + + for (const auto &x : linspace(lowest, highest, 101)) { + const double actual = chi_squared_cdf_non_integer_dof(x, dof); + const double expected = gsl_chi_squared(x, dof); + std::cout << std::setprecision(12); + // std::cout << "UNITTEST: EXPECT_NEAR(chi_squared_cdf_non_integer_dof(" + << x << ", " << dof + // << "), " << expected << ", 1e-6);" << std::endl; + std::cout << "UNITTEST: {" << x << ", " << dof << ", " << expected << "}," + << std::endl; + } + + // explore the lower degrees of freedom better + if (dof > 50) { + dof *= 2; + } else { + dof += 1; + } + } + +*/ + +struct ChiSquaredCdfTestCase { + double x; + double dof; + double expected; +}; + +TEST(test_stats, test_chi_squared_matches_gsl) { + + const std::vector test_cases = { + {0, 1, 0}, + {0.328433666562, 1, 0.433417139218}, + {0.656867333124, 1, 0.582331924206}, + {0.985300999685, 1, 0.679106430429}, + {1.31373466625, 1, 0.748280414629}, + {1.64216833281, 1, 0.799971776317}, + {1.97060199937, 1, 0.839616022372}, + {2.29903566593, 1, 0.870545651282}, + {2.62746933249, 1, 0.894971004504}, + {2.95590299906, 1, 0.914435503447}, + {3.28433666562, 1, 0.930056113705}, + {3.61277033218, 1, 0.942662468229}, + {3.94120399874, 1, 0.952882956205}, + {4.2696376653, 1, 0.961200797031}, + {4.59807133187, 1, 0.96799205511}, + {4.92650499843, 1, 0.973552243887}, + {5.25493866499, 1, 0.978115427339}, + {5.58337233155, 1, 0.981868224344}, + {5.91180599811, 1, 0.984960254525}, + {6.24023966467, 1, 0.987512042433}, + {6.56867333124, 1, 0.989621071018}, + {6.8971069978, 1, 0.991366465278}, + {7.22554066436, 1, 0.992812647776}, + {7.55397433092, 1, 0.994012213126}, + {7.88240799748, 1, 0.995008202997}, + {8.21084166405, 1, 0.995835916842}, + {8.53927533061, 1, 0.996524360197}, + {8.86770899717, 1, 0.99709740814}, + {9.19614266373, 1, 0.99757474352}, + {9.52457633029, 1, 0.997972616137}, + {9.85300999685, 1, 0.998304458906}, + {10.1814436634, 1, 0.998581389333}, + {10.50987733, 1, 0.998812618625}, + {10.8383109965, 1, 0.99900578621}, + {11.1667446631, 1, 0.999167233805}, + {11.4951783297, 1, 0.999302230367}, + {11.8236119962, 1, 0.999415157045}, + {12.1520456628, 1, 0.999509659472}, + {12.4804793293, 1, 0.999588773334}, + {12.8089129959, 1, 0.999655028057}, + {13.1373466625, 1, 0.999710532504}, + {13.465780329, 1, 0.999757045903}, + {13.7942139956, 1, 0.999796036591}, + {14.1226476622, 1, 0.999828730736}, + {14.4510813287, 1, 0.999856152753}, + {14.7795149953, 1, 0.99987915889}, + {15.1079486618, 1, 0.999898465134}, + {15.4363823284, 1, 0.999914670426}, + {15.764815995, 1, 0.999928275987}, + {16.0932496615, 1, 0.999939701413}, + {16.4216833281, 1, 0.999949298087}, + {16.7501169947, 1, 0.999957360365}, + {17.0785506612, 1, 0.999964134908}, + {17.4069843278, 1, 0.999969828472}, + {17.7354179943, 1, 0.999974614413}, + {18.0638516609, 1, 0.999978638119}, + {18.3922853275, 1, 0.999982021559}, + {18.720718994, 1, 0.999984867076}, + {19.0491526606, 1, 0.999987260567}, + {19.3775863271, 1, 0.999989274145}, + {19.7060199937, 1, 0.99999096836}, + {20.0344536603, 1, 0.999992394065}, + {20.3628873268, 1, 0.99999359398}, + {20.6913209934, 1, 0.999994603997}, + {21.01975466, 1, 0.999995454278}, + {21.3481883265, 1, 0.999996170175}, + {21.6766219931, 1, 0.999996772999}, + {22.0050556596, 1, 0.999997280668}, + {22.3334893262, 1, 0.999997708251}, + {22.6619229928, 1, 0.999998068421}, + {22.9903566593, 1, 0.999998371839}, + {23.3187903259, 1, 0.999998627474}, + {23.6472239925, 1, 0.999998842873}, + {23.975657659, 1, 0.999999024386}, + {24.3040913256, 1, 0.999999177359}, + {24.6325249921, 1, 0.99999930629}, + {24.9609586587, 1, 0.99999941497}, + {25.2893923253, 1, 0.999999506585}, + {25.6178259918, 1, 0.999999583823}, + {25.9462596584, 1, 0.999999648945}, + {26.2746933249, 1, 0.999999703856}, + {26.6031269915, 1, 0.999999750161}, + {26.9315606581, 1, 0.999999789211}, + {27.2599943246, 1, 0.999999822147}, + {27.5884279912, 1, 0.999999849926}, + {27.9168616578, 1, 0.999999873359}, + {28.2452953243, 1, 0.999999893126}, + {28.5737289909, 1, 0.999999909802}, + {28.9021626574, 1, 0.999999923872}, + {29.230596324, 1, 0.999999935744}, + {29.5590299906, 1, 0.999999945761}, + {29.8874636571, 1, 0.999999954214}, + {30.2158973237, 1, 0.999999961347}, + {30.5443309902, 1, 0.999999967368}, + {30.8727646568, 1, 0.999999972449}, + {31.2011983234, 1, 0.999999976738}, + {31.5296319899, 1, 0.999999980358}, + {31.8580656565, 1, 0.999999983414}, + {32.1864993231, 1, 0.999999985994}, + {32.5149329896, 1, 0.999999988172}, + {32.8433666562, 1, 0.999999990011}, + {0, 2, 0}, + {0.387695526217, 2, 0.176216695067}, + {0.775391052434, 2, 0.321381066514}, + {1.16308657865, 2, 0.440965052183}, + {1.55078210487, 2, 0.539476343115}, + {1.93847763109, 2, 0.620628299931}, + {2.3261731573, 2, 0.68747992712}, + {2.71386868352, 2, 0.742551181505}, + {3.10156420974, 2, 0.787917961449}, + {3.48925973595, 2, 0.825290357366}, + {3.87695526217, 2, 0.856077113187}, + {4.26465078839, 2, 0.881438728646}, + {4.6523463146, 2, 0.902331204047}, + {5.04004184082, 2, 0.919542076481}, + {5.42773736704, 2, 0.933720105855}, + {5.81543289326, 2, 0.945399729751}, + {6.20312841947, 2, 0.955021208924}, + {6.59082394569, 2, 0.962947222836}, + {6.97851947191, 2, 0.969476540771}, + {7.36621499812, 2, 0.974855283878}, + {7.75391052434, 2, 0.979286202651}, + {8.14160605056, 2, 0.982936319562}, + {8.52930157677, 2, 0.985943224935}, + {8.91699710299, 2, 0.98842026338}, + {9.30469262921, 2, 0.990460806297}, + {9.69238815543, 2, 0.992141771485}, + {10.0800836816, 2, 0.993526522543}, + {10.4677792079, 2, 0.994667257346}, + {10.8554747341, 2, 0.995606975632}, + {11.2431702603, 2, 0.996381099868}, + {11.6308657865, 2, 0.997018810489}, + {12.0185613127, 2, 0.997544145852}, + {12.4062568389, 2, 0.997976908353}, + {12.7939523652, 2, 0.998333410877}, + {13.1816478914, 2, 0.998627091704}, + {13.5693434176, 2, 0.998869021067}, + {13.9570389438, 2, 0.999068318437}, + {14.34473447, 2, 0.999232496283}, + {14.7324299962, 2, 0.999367743251}, + {15.1201255225, 2, 0.999479157446}, + {15.5078210487, 2, 0.999570938599}, + {15.8955165749, 2, 0.999646546381}, + {16.2832121011, 2, 0.99970883081}, + {16.6709076273, 2, 0.999760139682}, + {17.0586031535, 2, 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{27.5263823614, 2, 0.999998946288}, + {27.9140778876, 2, 0.999999131969}, + {28.3017734138, 2, 0.999999284931}, + {28.6894689401, 2, 0.999999410938}, + {29.0771644663, 2, 0.999999514741}, + {29.4648599925, 2, 0.999999600251}, + {29.8525555187, 2, 0.999999670694}, + {30.2402510449, 2, 0.999999728723}, + {30.6279465711, 2, 0.999999776527}, + {31.0156420974, 2, 0.999999815906}, + {31.4033376236, 2, 0.999999848347}, + {31.7910331498, 2, 0.999999875071}, + {32.178728676, 2, 0.999999897085}, + {32.5664242022, 2, 0.999999915221}, + {32.9541197284, 2, 0.99999993016}, + {33.3418152547, 2, 0.999999942467}, + {33.7295107809, 2, 0.999999952605}, + {34.1172063071, 2, 0.999999960957}, + {34.5049018333, 2, 0.999999967837}, + {34.8925973595, 2, 0.999999973505}, + {35.2802928857, 2, 0.999999978174}, + {35.667988412, 2, 0.99999998202}, + {36.0556839382, 2, 0.999999985188}, + {36.4433794644, 2, 0.999999987798}, + {36.8310749906, 2, 0.999999989948}, + {37.2187705168, 2, 0.99999999172}, + {37.606466043, 2, 0.999999993179}, + {37.9941615693, 2, 0.999999994381}, + {38.3818570955, 2, 0.999999995371}, + {38.7695526217, 2, 0.999999996187}, + {0, 3, 0}, + {0.441096095822, 3, 0.0683719176834}, + {0.882192191644, 3, 0.170277022924}, + {1.32328828747, 3, 0.276389389219}, + {1.76438438329, 3, 0.377284211807}, + {2.20548047911, 3, 0.469130305381}, + {2.64657657493, 3, 0.550617481935}, + {3.08767267075, 3, 0.621695689713}, + {3.52876876658, 3, 0.682949968161}, + {3.9698648624, 3, 0.73526337928}, + {4.41096095822, 3, 0.779628798706}, + {4.85205705404, 3, 0.81704363119}, + {5.29315314986, 3, 0.848452709675}, + {5.73424924568, 3, 0.874719773319}, + {6.17534534151, 3, 0.896615955789}, + {6.61644143733, 3, 0.914818262462}, + {7.05753753315, 3, 0.929913707735}, + {7.49863362897, 3, 0.942406429717}, + {7.93972972479, 3, 0.952726127942}, + {8.38082582062, 3, 0.961236820866}, + {8.82192191644, 3, 0.968245334906}, + {9.26301801226, 3, 0.974009201085}, + {9.70411410808, 3, 0.978743802479}, + {10.1452102039, 3, 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1632, 0.999999999992}, + {2060.84056803, 1632, 0.999999999998}, + {2075.1279744, 1632, 1}, + {2089.41538077, 1632, 1}, + {2103.70278715, 1632, 1}, + {2117.99019352, 1632, 1}, + {2132.2775999, 1632, 1}, + {2146.56500627, 1632, 1}, + {2160.85241264, 1632, 1}, + {2175.13981902, 1632, 1}, + {2189.42722539, 1632, 1}, + {2203.71463177, 1632, 1}, + {2218.00203814, 1632, 1}, + {2232.28944451, 1632, 1}, + {2246.57685089, 1632, 1}, + {2260.86425726, 1632, 1}, + {2275.15166364, 1632, 1}, + {2289.43907001, 1632, 1}, + {2303.72647638, 1632, 1}, + {2318.01388276, 1632, 1}, + {2332.30128913, 1632, 1}, + {2346.58869551, 1632, 1}, + {2360.87610188, 1632, 1}, + {2375.16350825, 1632, 1}, + }; + + ASSERT_TRUE(test_cases.size() > 0); + for (const auto &test_case : test_cases) { + EXPECT_NEAR(chi_squared_cdf(test_case.x, test_case.dof), test_case.expected, + 1e-6); + } +} + +} // namespace albatross diff --git a/tests/test_stats.cc b/tests/test_stats.cc index c927c4f7..45b9b584 100644 --- a/tests/test_stats.cc +++ b/tests/test_stats.cc @@ -117,6 +117,25 @@ TEST(test_stats, test_chi_squared_cdf) { EXPECT_LT(ks, 0.05); } +TEST(test_stats, test_chi_squared_cdf_bounds) { + + for (std::size_t dof = 1; dof < 50; ++dof) { + const double a = 0.5 * cast::to_double(dof); + const auto bounds = + details::incomplete_gamma_quadrature_bounds(a, 100 * sqrt(a)); + + // low/high for the chi squared will be double low/high for the incomplete + // gamma + const double lowest = 2. * bounds.first; + const double highest = 2. * bounds.second; + + // The bounds provided should correspond to the z argument which corresponds + // to near zero and near one evaluations of the incomplete gamma + EXPECT_NEAR(chi_squared_cdf(lowest, dof), 0., 1e-8); + EXPECT_NEAR(chi_squared_cdf(highest, dof), 1., 1e-8); + } +} + TEST(test_stats, test_chi_squared_cdf_monotonic) { Eigen::Index k = 5;