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Diffstat (limited to 'absl/random/internal/chi_square_test.cc')
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1 files changed, 365 insertions, 0 deletions
diff --git a/absl/random/internal/chi_square_test.cc b/absl/random/internal/chi_square_test.cc new file mode 100644 index 000000000000..5025defac12c --- /dev/null +++ b/absl/random/internal/chi_square_test.cc @@ -0,0 +1,365 @@ +// Copyright 2017 The Abseil Authors. +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// https://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +#include "absl/random/internal/chi_square.h" + +#include <algorithm> +#include <cstddef> +#include <cstdint> +#include <iterator> +#include <numeric> +#include <vector> + +#include "gtest/gtest.h" +#include "absl/base/macros.h" + +using absl::random_internal::ChiSquare; +using absl::random_internal::ChiSquarePValue; +using absl::random_internal::ChiSquareValue; +using absl::random_internal::ChiSquareWithExpected; + +namespace { + +TEST(ChiSquare, Value) { + struct { + int line; + double chi_square; + int df; + double confidence; + } const specs[] = { + // Testing lookup at 1% confidence + {__LINE__, 0, 0, 0.01}, + {__LINE__, 0.00016, 1, 0.01}, + {__LINE__, 1.64650, 8, 0.01}, + {__LINE__, 5.81221, 16, 0.01}, + {__LINE__, 156.4319, 200, 0.01}, + {__LINE__, 1121.3784, 1234, 0.01}, + {__LINE__, 53557.1629, 54321, 0.01}, + {__LINE__, 651662.6647, 654321, 0.01}, + + // Testing lookup at 99% confidence + {__LINE__, 0, 0, 0.99}, + {__LINE__, 6.635, 1, 0.99}, + {__LINE__, 20.090, 8, 0.99}, + {__LINE__, 32.000, 16, 0.99}, + {__LINE__, 249.4456, 200, 0.99}, + {__LINE__, 1131.1573, 1023, 0.99}, + {__LINE__, 1352.5038, 1234, 0.99}, + {__LINE__, 55090.7356, 54321, 0.99}, + {__LINE__, 656985.1514, 654321, 0.99}, + + // Testing lookup at 99.9% confidence + {__LINE__, 16.2659, 3, 0.999}, + {__LINE__, 22.4580, 6, 0.999}, + {__LINE__, 267.5409, 200, 0.999}, + {__LINE__, 1168.5033, 1023, 0.999}, + {__LINE__, 55345.1741, 54321, 0.999}, + {__LINE__, 657861.7284, 654321, 0.999}, + {__LINE__, 51.1772, 24, 0.999}, + {__LINE__, 59.7003, 30, 0.999}, + {__LINE__, 37.6984, 15, 0.999}, + {__LINE__, 29.5898, 10, 0.999}, + {__LINE__, 27.8776, 9, 0.999}, + + // Testing lookup at random confidences + {__LINE__, 0.000157088, 1, 0.01}, + {__LINE__, 5.31852, 2, 0.93}, + {__LINE__, 1.92256, 4, 0.25}, + {__LINE__, 10.7709, 13, 0.37}, + {__LINE__, 26.2514, 17, 0.93}, + {__LINE__, 36.4799, 29, 0.84}, + {__LINE__, 25.818, 31, 0.27}, + {__LINE__, 63.3346, 64, 0.50}, + {__LINE__, 196.211, 128, 0.9999}, + {__LINE__, 215.21, 243, 0.10}, + {__LINE__, 285.393, 256, 0.90}, + {__LINE__, 984.504, 1024, 0.1923}, + {__LINE__, 2043.85, 2048, 0.4783}, + {__LINE__, 48004.6, 48273, 0.194}, + }; + for (const auto& spec : specs) { + SCOPED_TRACE(spec.line); + // Verify all values are have at most a 1% relative error. + const double val = ChiSquareValue(spec.df, spec.confidence); + const double err = std::max(5e-6, spec.chi_square / 5e3); // 1 part in 5000 + EXPECT_NEAR(spec.chi_square, val, err) << spec.line; + } + + // Relaxed test for extreme values, from + // http://www.ciphersbyritter.com/JAVASCRP/NORMCHIK.HTM#ChiSquare + EXPECT_NEAR(49.2680, ChiSquareValue(100, 1e-6), 5); // 0.000'005 mark + EXPECT_NEAR(123.499, ChiSquareValue(200, 1e-6), 5); // 0.000'005 mark + + EXPECT_NEAR(149.449, ChiSquareValue(100, 0.999), 0.01); + EXPECT_NEAR(161.318, ChiSquareValue(100, 0.9999), 0.01); + EXPECT_NEAR(172.098, ChiSquareValue(100, 0.99999), 0.01); + + EXPECT_NEAR(381.426, ChiSquareValue(300, 0.999), 0.05); + EXPECT_NEAR(399.756, ChiSquareValue(300, 0.9999), 0.1); + EXPECT_NEAR(416.126, ChiSquareValue(300, 0.99999), 0.2); +} + +TEST(ChiSquareTest, PValue) { + struct { + int line; + double pval; + double chi_square; + int df; + } static const specs[] = { + {__LINE__, 1, 0, 0}, + {__LINE__, 0, 0.001, 0}, + {__LINE__, 1.000, 0, 453}, + {__LINE__, 0.134471, 7972.52, 7834}, + {__LINE__, 0.203922, 28.32, 23}, + {__LINE__, 0.737171, 48274, 48472}, + {__LINE__, 0.444146, 583.1234, 579}, + {__LINE__, 0.294814, 138.2, 130}, + {__LINE__, 0.0816532, 12.63, 7}, + {__LINE__, 0, 682.32, 67}, + {__LINE__, 0.49405, 999, 999}, + {__LINE__, 1.000, 0, 9999}, + {__LINE__, 0.997477, 0.00001, 1}, + {__LINE__, 0, 5823.21, 5040}, + }; + for (const auto& spec : specs) { + SCOPED_TRACE(spec.line); + const double pval = ChiSquarePValue(spec.chi_square, spec.df); + EXPECT_NEAR(spec.pval, pval, 1e-3); + } +} + +TEST(ChiSquareTest, CalcChiSquare) { + struct { + int line; + std::vector<int> expected; + std::vector<int> actual; + } const specs[] = { + {__LINE__, + {56, 234, 76, 1, 546, 1, 87, 345, 1, 234}, + {2, 132, 4, 43, 234, 8, 345, 8, 236, 56}}, + {__LINE__, + {123, 36, 234, 367, 345, 2, 456, 567, 234, 567}, + {123, 56, 2345, 8, 345, 8, 2345, 23, 48, 267}}, + {__LINE__, + {123, 234, 345, 456, 567, 678, 789, 890, 98, 76}, + {123, 234, 345, 456, 567, 678, 789, 890, 98, 76}}, + {__LINE__, {3, 675, 23, 86, 2, 8, 2}, {456, 675, 23, 86, 23, 65, 2}}, + {__LINE__, {1}, {23}}, + }; + for (const auto& spec : specs) { + SCOPED_TRACE(spec.line); + double chi_square = 0; + for (int i = 0; i < spec.expected.size(); ++i) { + const double diff = spec.actual[i] - spec.expected[i]; + chi_square += (diff * diff) / spec.expected[i]; + } + EXPECT_NEAR(chi_square, + ChiSquare(std::begin(spec.actual), std::end(spec.actual), + std::begin(spec.expected), std::end(spec.expected)), + 1e-5); + } +} + +TEST(ChiSquareTest, CalcChiSquareInt64) { + const int64_t data[3] = {910293487, 910292491, 910216780}; + // $ python -c "import scipy.stats + // > print scipy.stats.chisquare([910293487, 910292491, 910216780])[0]" + // 4.25410123524 + double sum = std::accumulate(std::begin(data), std::end(data), double{0}); + size_t n = std::distance(std::begin(data), std::end(data)); + double a = ChiSquareWithExpected(std::begin(data), std::end(data), sum / n); + EXPECT_NEAR(4.254101, a, 1e-6); + + // ... Or with known values. + double b = + ChiSquareWithExpected(std::begin(data), std::end(data), 910267586.0); + EXPECT_NEAR(4.254101, b, 1e-6); +} + +TEST(ChiSquareTest, TableData) { + // Test data from + // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm + // 0.90 0.95 0.975 0.99 0.999 + const double data[100][5] = { + /* 1*/ {2.706, 3.841, 5.024, 6.635, 10.828}, + /* 2*/ {4.605, 5.991, 7.378, 9.210, 13.816}, + /* 3*/ {6.251, 7.815, 9.348, 11.345, 16.266}, + /* 4*/ {7.779, 9.488, 11.143, 13.277, 18.467}, + /* 5*/ {9.236, 11.070, 12.833, 15.086, 20.515}, + /* 6*/ {10.645, 12.592, 14.449, 16.812, 22.458}, + /* 7*/ {12.017, 14.067, 16.013, 18.475, 24.322}, + /* 8*/ {13.362, 15.507, 17.535, 20.090, 26.125}, + /* 9*/ {14.684, 16.919, 19.023, 21.666, 27.877}, + /*10*/ {15.987, 18.307, 20.483, 23.209, 29.588}, + /*11*/ {17.275, 19.675, 21.920, 24.725, 31.264}, + /*12*/ {18.549, 21.026, 23.337, 26.217, 32.910}, + /*13*/ {19.812, 22.362, 24.736, 27.688, 34.528}, + /*14*/ {21.064, 23.685, 26.119, 29.141, 36.123}, + /*15*/ {22.307, 24.996, 27.488, 30.578, 37.697}, + /*16*/ {23.542, 26.296, 28.845, 32.000, 39.252}, + /*17*/ {24.769, 27.587, 30.191, 33.409, 40.790}, + /*18*/ {25.989, 28.869, 31.526, 34.805, 42.312}, + /*19*/ {27.204, 30.144, 32.852, 36.191, 43.820}, + /*20*/ {28.412, 31.410, 34.170, 37.566, 45.315}, + /*21*/ {29.615, 32.671, 35.479, 38.932, 46.797}, + /*22*/ {30.813, 33.924, 36.781, 40.289, 48.268}, + /*23*/ {32.007, 35.172, 38.076, 41.638, 49.728}, + /*24*/ {33.196, 36.415, 39.364, 42.980, 51.179}, + /*25*/ {34.382, 37.652, 40.646, 44.314, 52.620}, + /*26*/ {35.563, 38.885, 41.923, 45.642, 54.052}, + /*27*/ {36.741, 40.113, 43.195, 46.963, 55.476}, + /*28*/ {37.916, 41.337, 44.461, 48.278, 56.892}, + /*29*/ {39.087, 42.557, 45.722, 49.588, 58.301}, + /*30*/ {40.256, 43.773, 46.979, 50.892, 59.703}, + /*31*/ {41.422, 44.985, 48.232, 52.191, 61.098}, + /*32*/ {42.585, 46.194, 49.480, 53.486, 62.487}, + /*33*/ {43.745, 47.400, 50.725, 54.776, 63.870}, + /*34*/ {44.903, 48.602, 51.966, 56.061, 65.247}, + /*35*/ {46.059, 49.802, 53.203, 57.342, 66.619}, + /*36*/ {47.212, 50.998, 54.437, 58.619, 67.985}, + /*37*/ {48.363, 52.192, 55.668, 59.893, 69.347}, + /*38*/ {49.513, 53.384, 56.896, 61.162, 70.703}, + /*39*/ {50.660, 54.572, 58.120, 62.428, 72.055}, + /*40*/ {51.805, 55.758, 59.342, 63.691, 73.402}, + /*41*/ {52.949, 56.942, 60.561, 64.950, 74.745}, + /*42*/ {54.090, 58.124, 61.777, 66.206, 76.084}, + /*43*/ {55.230, 59.304, 62.990, 67.459, 77.419}, + /*44*/ {56.369, 60.481, 64.201, 68.710, 78.750}, + /*45*/ {57.505, 61.656, 65.410, 69.957, 80.077}, + /*46*/ {58.641, 62.830, 66.617, 71.201, 81.400}, + /*47*/ {59.774, 64.001, 67.821, 72.443, 82.720}, + /*48*/ {60.907, 65.171, 69.023, 73.683, 84.037}, + /*49*/ {62.038, 66.339, 70.222, 74.919, 85.351}, + /*50*/ {63.167, 67.505, 71.420, 76.154, 86.661}, + /*51*/ {64.295, 68.669, 72.616, 77.386, 87.968}, + /*52*/ {65.422, 69.832, 73.810, 78.616, 89.272}, + /*53*/ {66.548, 70.993, 75.002, 79.843, 90.573}, + /*54*/ {67.673, 72.153, 76.192, 81.069, 91.872}, + /*55*/ {68.796, 73.311, 77.380, 82.292, 93.168}, + /*56*/ {69.919, 74.468, 78.567, 83.513, 94.461}, + /*57*/ {71.040, 75.624, 79.752, 84.733, 95.751}, + /*58*/ {72.160, 76.778, 80.936, 85.950, 97.039}, + /*59*/ {73.279, 77.931, 82.117, 87.166, 98.324}, + /*60*/ {74.397, 79.082, 83.298, 88.379, 99.607}, + /*61*/ {75.514, 80.232, 84.476, 89.591, 100.888}, + /*62*/ {76.630, 81.381, 85.654, 90.802, 102.166}, + /*63*/ {77.745, 82.529, 86.830, 92.010, 103.442}, + /*64*/ {78.860, 83.675, 88.004, 93.217, 104.716}, + /*65*/ {79.973, 84.821, 89.177, 94.422, 105.988}, + /*66*/ {81.085, 85.965, 90.349, 95.626, 107.258}, + /*67*/ {82.197, 87.108, 91.519, 96.828, 108.526}, + /*68*/ {83.308, 88.250, 92.689, 98.028, 109.791}, + /*69*/ {84.418, 89.391, 93.856, 99.228, 111.055}, + /*70*/ {85.527, 90.531, 95.023, 100.425, 112.317}, + /*71*/ {86.635, 91.670, 96.189, 101.621, 113.577}, + /*72*/ {87.743, 92.808, 97.353, 102.816, 114.835}, + /*73*/ {88.850, 93.945, 98.516, 104.010, 116.092}, + /*74*/ {89.956, 95.081, 99.678, 105.202, 117.346}, + /*75*/ {91.061, 96.217, 100.839, 106.393, 118.599}, + /*76*/ {92.166, 97.351, 101.999, 107.583, 119.850}, + /*77*/ {93.270, 98.484, 103.158, 108.771, 121.100}, + /*78*/ {94.374, 99.617, 104.316, 109.958, 122.348}, + /*79*/ {95.476, 100.749, 105.473, 111.144, 123.594}, + /*80*/ {96.578, 101.879, 106.629, 112.329, 124.839}, + /*81*/ {97.680, 103.010, 107.783, 113.512, 126.083}, + /*82*/ {98.780, 104.139, 108.937, 114.695, 127.324}, + /*83*/ {99.880, 105.267, 110.090, 115.876, 128.565}, + /*84*/ {100.980, 106.395, 111.242, 117.057, 129.804}, + /*85*/ {102.079, 107.522, 112.393, 118.236, 131.041}, + /*86*/ {103.177, 108.648, 113.544, 119.414, 132.277}, + /*87*/ {104.275, 109.773, 114.693, 120.591, 133.512}, + /*88*/ {105.372, 110.898, 115.841, 121.767, 134.746}, + /*89*/ {106.469, 112.022, 116.989, 122.942, 135.978}, + /*90*/ {107.565, 113.145, 118.136, 124.116, 137.208}, + /*91*/ {108.661, 114.268, 119.282, 125.289, 138.438}, + /*92*/ {109.756, 115.390, 120.427, 126.462, 139.666}, + /*93*/ {110.850, 116.511, 121.571, 127.633, 140.893}, + /*94*/ {111.944, 117.632, 122.715, 128.803, 142.119}, + /*95*/ {113.038, 118.752, 123.858, 129.973, 143.344}, + /*96*/ {114.131, 119.871, 125.000, 131.141, 144.567}, + /*97*/ {115.223, 120.990, 126.141, 132.309, 145.789}, + /*98*/ {116.315, 122.108, 127.282, 133.476, 147.010}, + /*99*/ {117.407, 123.225, 128.422, 134.642, 148.230}, + /*100*/ {118.498, 124.342, 129.561, 135.807, 149.449} + /**/}; + + // 0.90 0.95 0.975 0.99 0.999 + for (int i = 0; i < ABSL_ARRAYSIZE(data); i++) { + const double E = 0.0001; + EXPECT_NEAR(ChiSquarePValue(data[i][0], i + 1), 0.10, E) + << i << " " << data[i][0]; + EXPECT_NEAR(ChiSquarePValue(data[i][1], i + 1), 0.05, E) + << i << " " << data[i][1]; + EXPECT_NEAR(ChiSquarePValue(data[i][2], i + 1), 0.025, E) + << i << " " << data[i][2]; + EXPECT_NEAR(ChiSquarePValue(data[i][3], i + 1), 0.01, E) + << i << " " << data[i][3]; + EXPECT_NEAR(ChiSquarePValue(data[i][4], i + 1), 0.001, E) + << i << " " << data[i][4]; + + const double F = 0.1; + EXPECT_NEAR(ChiSquareValue(i + 1, 0.90), data[i][0], F) << i; + EXPECT_NEAR(ChiSquareValue(i + 1, 0.95), data[i][1], F) << i; + EXPECT_NEAR(ChiSquareValue(i + 1, 0.975), data[i][2], F) << i; + EXPECT_NEAR(ChiSquareValue(i + 1, 0.99), data[i][3], F) << i; + EXPECT_NEAR(ChiSquareValue(i + 1, 0.999), data[i][4], F) << i; + } +} + +TEST(ChiSquareTest, ChiSquareTwoIterator) { + // Test data from http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm + // Null-hypothesis: This data is normally distributed. + const int counts[10] = {6, 6, 18, 33, 38, 38, 28, 21, 9, 3}; + const double expected[10] = {4.6, 8.8, 18.4, 30.0, 38.2, + 38.2, 30.0, 18.4, 8.8, 4.6}; + double chi_square = ChiSquare(std::begin(counts), std::end(counts), + std::begin(expected), std::end(expected)); + EXPECT_NEAR(chi_square, 2.69, 0.001); + + // Degrees of freedom: 10 bins. two estimated parameters. = 10 - 2 - 1. + const int dof = 7; + // The critical value of 7, 95% => 14.067 (see above test) + double p_value_05 = ChiSquarePValue(14.067, dof); + EXPECT_NEAR(p_value_05, 0.05, 0.001); // 95%-ile p-value + + double p_actual = ChiSquarePValue(chi_square, dof); + EXPECT_GT(p_actual, 0.05); // Accept the null hypothesis. +} + +TEST(ChiSquareTest, DiceRolls) { + // Assume we are testing 102 fair dice rolls. + // Null-hypothesis: This data is fairly distributed. + // + // The dof value of 4, @95% = 9.488 (see above test) + // The dof value of 5, @95% = 11.070 + const int rolls[6] = {22, 11, 17, 14, 20, 18}; + double sum = std::accumulate(std::begin(rolls), std::end(rolls), double{0}); + size_t n = std::distance(std::begin(rolls), std::end(rolls)); + + double a = ChiSquareWithExpected(std::begin(rolls), std::end(rolls), sum / n); + EXPECT_NEAR(a, 4.70588, 1e-5); + EXPECT_LT(a, ChiSquareValue(4, 0.95)); + + double p_a = ChiSquarePValue(a, 4); + EXPECT_NEAR(p_a, 0.318828, 1e-5); // Accept the null hypothesis. + + double b = ChiSquareWithExpected(std::begin(rolls), std::end(rolls), 17.0); + EXPECT_NEAR(b, 4.70588, 1e-5); + EXPECT_LT(b, ChiSquareValue(5, 0.95)); + + double p_b = ChiSquarePValue(b, 5); + EXPECT_NEAR(p_b, 0.4528180, 1e-5); // Accept the null hypothesis. +} + +} // namespace |