colmap/src/util/math_test.cc

// Copyright (c) 2022, ETH Zurich and UNC Chapel Hill.
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// Author: Johannes L. Schoenberger (jsch-at-demuc-dot-de)

#define TEST_NAME "util/math"
#include "util/testing.h"

#include "util/math.h"

using namespace colmap;

BOOST_AUTO_TEST_CASE(TestSignOfNumber) {
  BOOST_CHECK_EQUAL(SignOfNumber(0), 0);
  BOOST_CHECK_EQUAL(SignOfNumber(-0.1), -1);
  BOOST_CHECK_EQUAL(SignOfNumber(0.1), 1);
  BOOST_CHECK_EQUAL(SignOfNumber(std::numeric_limits<float>::quiet_NaN()), 0);
  BOOST_CHECK_EQUAL(SignOfNumber(std::numeric_limits<float>::infinity()), 1);
  BOOST_CHECK_EQUAL(SignOfNumber(-std::numeric_limits<float>::infinity()), -1);
}

BOOST_AUTO_TEST_CASE(TestIsNaN) {
  BOOST_CHECK(!IsNaN(0.0f));
  BOOST_CHECK(!IsNaN(0.0));
  BOOST_CHECK(IsNaN(std::numeric_limits<float>::quiet_NaN()));
  BOOST_CHECK(IsNaN(std::numeric_limits<double>::quiet_NaN()));
}

BOOST_AUTO_TEST_CASE(TestIsInf) {
  BOOST_CHECK(!IsInf(0.0f));
  BOOST_CHECK(!IsInf(0.0));
  BOOST_CHECK(IsInf(std::numeric_limits<float>::infinity()));
  BOOST_CHECK(IsInf(std::numeric_limits<double>::infinity()));
  BOOST_CHECK(IsInf(-std::numeric_limits<float>::infinity()));
  BOOST_CHECK(IsInf(-std::numeric_limits<double>::infinity()));
}

BOOST_AUTO_TEST_CASE(TestClip) {
  BOOST_CHECK_EQUAL(Clip(0, -1, 1), 0);
  BOOST_CHECK_EQUAL(Clip(0, 0, 1), 0);
  BOOST_CHECK_EQUAL(Clip(0, -1, 0), 0);
  BOOST_CHECK_EQUAL(Clip(0, -1, 1), 0);
  BOOST_CHECK_EQUAL(Clip(0, 1, 2), 1);
  BOOST_CHECK_EQUAL(Clip(0, -2, -1), -1);
  BOOST_CHECK_EQUAL(Clip(0, 0, 0), 0);
}

BOOST_AUTO_TEST_CASE(TestDegToRad) {
  BOOST_CHECK_EQUAL(DegToRad(0.0f), 0.0f);
  BOOST_CHECK_EQUAL(DegToRad(0.0), 0.0);
  BOOST_CHECK_LT(std::abs(DegToRad(180.0f) - M_PI), 1e-6f);
  BOOST_CHECK_LT(std::abs(DegToRad(180.0) - M_PI), 1e-6);
}

BOOST_AUTO_TEST_CASE(TestRadToDeg) {
  BOOST_CHECK_EQUAL(RadToDeg(0.0f), 0.0f);
  BOOST_CHECK_EQUAL(RadToDeg(0.0), 0.0);
  BOOST_CHECK_LT(std::abs(RadToDeg(M_PI) - 180.0f), 1e-6f);
  BOOST_CHECK_LT(std::abs(RadToDeg(M_PI) - 180.0), 1e-6);
}

BOOST_AUTO_TEST_CASE(TestMedian) {
  BOOST_CHECK_EQUAL(Median<int>({1, 2, 3, 4}), 2.5);
  BOOST_CHECK_EQUAL(Median<int>({1, 2, 3, 100}), 2.5);
  BOOST_CHECK_EQUAL(Median<int>({1, 2, 3, 4, 100}), 3);
  BOOST_CHECK_EQUAL(Median<int>({-100, 1, 2, 3, 4}), 2);
  BOOST_CHECK_EQUAL(Median<int>({-1, -2, -3, -4}), -2.5);
  BOOST_CHECK_EQUAL(Median<int>({-1, -2, 3, 4}), 1);
}

BOOST_AUTO_TEST_CASE(TestPercentile) {
  BOOST_CHECK_EQUAL(Percentile<int>({0}, 0), 0);
  BOOST_CHECK_EQUAL(Percentile<int>({0}, 50), 0);
  BOOST_CHECK_EQUAL(Percentile<int>({0}, 100), 0);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1}, 0), 0);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1}, 50), 1);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1}, 100), 1);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 2}, 0), 0);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 2}, 50), 1);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 2}, 100), 2);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 1, 2}, 0), 0);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 1, 2}, 33), 1);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 1, 2}, 50), 1);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 1, 2}, 66), 1);
  BOOST_CHECK_EQUAL(Percentile<int>({0, 1, 1, 2}, 100), 2);
}

BOOST_AUTO_TEST_CASE(TestMean) {
  BOOST_CHECK_EQUAL(Mean<int>({1, 2, 3, 4}), 2.5);
  BOOST_CHECK_EQUAL(Mean<int>({1, 2, 3, 100}), 26.5);
  BOOST_CHECK_EQUAL(Mean<int>({1, 2, 3, 4, 100}), 22);
  BOOST_CHECK_EQUAL(Mean<int>({-100, 1, 2, 3, 4}), -18);
  BOOST_CHECK_EQUAL(Mean<int>({-1, -2, -3, -4}), -2.5);
  BOOST_CHECK_EQUAL(Mean<int>({-1, -2, 3, 4}), 1);
}

BOOST_AUTO_TEST_CASE(TestVariance) {
  BOOST_CHECK_LE(std::abs(Variance<int>({1, 2, 3, 4}) - 1.66666666), 1e-6);
  BOOST_CHECK_LE(std::abs(Variance<int>({1, 2, 3, 100}) - 2401.66666666), 1e-6);
  BOOST_CHECK_LE(std::abs(Variance<int>({1, 2, 3, 4, 100}) - 1902.5), 1e-6);
  BOOST_CHECK_LE(std::abs(Variance<int>({-100, 1, 2, 3, 4}) - 2102.5), 1e-6);
  BOOST_CHECK_LE(std::abs(Variance<int>({-1, -2, -3, -4}) - 1.66666666), 1e-6);
  BOOST_CHECK_LE(std::abs(Variance<int>({-1, -2, 3, 4}) - 8.66666666), 1e-6);
}

BOOST_AUTO_TEST_CASE(TestStdDev) {
  BOOST_CHECK_LE(std::abs(std::sqrt(Variance<int>({1, 2, 3, 4})) -
                          StdDev<int>({1, 2, 3, 4})),
                 1e-6);
  BOOST_CHECK_LE(std::abs(std::sqrt(Variance<int>({1, 2, 3, 100})) -
                          StdDev<int>({1, 2, 3, 100})),
                 1e-6);
}

BOOST_AUTO_TEST_CASE(TestAnyLessThan) {
  BOOST_CHECK(AnyLessThan<int>({1, 2, 3, 4}, 5));
  BOOST_CHECK(AnyLessThan<int>({1, 2, 3, 4}, 4));
  BOOST_CHECK(AnyLessThan<int>({1, 2, 3, 4}, 3));
  BOOST_CHECK(AnyLessThan<int>({1, 2, 3, 4}, 2));
  BOOST_CHECK(!AnyLessThan<int>({1, 2, 3, 4}, 1));
  BOOST_CHECK(!AnyLessThan<int>({1, 2, 3, 4}, 0));
}

BOOST_AUTO_TEST_CASE(TestAnyGreaterThan) {
  BOOST_CHECK(!AnyGreaterThan<int>({1, 2, 3, 4}, 5));
  BOOST_CHECK(!AnyGreaterThan<int>({1, 2, 3, 4}, 4));
  BOOST_CHECK(AnyGreaterThan<int>({1, 2, 3, 4}, 3));
  BOOST_CHECK(AnyGreaterThan<int>({1, 2, 3, 4}, 2));
  BOOST_CHECK(AnyGreaterThan<int>({1, 2, 3, 4}, 1));
  BOOST_CHECK(AnyGreaterThan<int>({1, 2, 3, 4}, 0));
}

BOOST_AUTO_TEST_CASE(TestNextCombination) {
  std::vector<int> list{0};
  BOOST_CHECK(!NextCombination(list.begin(), list.begin() + 1, list.end()));
  list = {0, 1};
  BOOST_CHECK(!NextCombination(list.begin(), list.begin() + 2, list.end()));
  BOOST_CHECK_EQUAL(list[0], 0);
  BOOST_CHECK(NextCombination(list.begin(), list.begin() + 1, list.end()));
  BOOST_CHECK_EQUAL(list[0], 1);
  BOOST_CHECK(!NextCombination(list.begin(), list.begin() + 1, list.end()));
  BOOST_CHECK_EQUAL(list[0], 0);
  list = {0, 1, 2};
  BOOST_CHECK_EQUAL(list[0], 0);
  BOOST_CHECK_EQUAL(list[1], 1);
  BOOST_CHECK_EQUAL(list[2], 2);
  BOOST_CHECK(NextCombination(list.begin(), list.begin() + 2, list.end()));
  BOOST_CHECK_EQUAL(list[0], 0);
  BOOST_CHECK_EQUAL(list[1], 2);
  BOOST_CHECK_EQUAL(list[2], 1);
  BOOST_CHECK(NextCombination(list.begin(), list.begin() + 2, list.end()));
  BOOST_CHECK_EQUAL(list[0], 1);
  BOOST_CHECK_EQUAL(list[1], 2);
  BOOST_CHECK_EQUAL(list[2], 0);
  BOOST_CHECK(!NextCombination(list.begin(), list.begin() + 2, list.end()));
  BOOST_CHECK_EQUAL(list[0], 0);
  BOOST_CHECK_EQUAL(list[1], 1);
  BOOST_CHECK_EQUAL(list[2], 2);
}

BOOST_AUTO_TEST_CASE(TestSigmoid) {
  BOOST_CHECK_EQUAL(Sigmoid(0.0), 0.5);
  BOOST_CHECK_CLOSE(Sigmoid(100.0), 1.0, 1e-10);
  BOOST_CHECK_SMALL(Sigmoid(-100.0), 1e-10);
}

BOOST_AUTO_TEST_CASE(TestScaleSigmoid) {
  BOOST_CHECK_CLOSE(ScaleSigmoid(0.5), 0.5, 1e-10);
  BOOST_CHECK_CLOSE(ScaleSigmoid(1.0), 1.0, 1e-10);
  BOOST_CHECK_SMALL(ScaleSigmoid(-1.0), 1e-4);
}

BOOST_AUTO_TEST_CASE(TestNChooseK) {
  BOOST_CHECK_EQUAL(NChooseK(1, 0), 1);
  BOOST_CHECK_EQUAL(NChooseK(2, 0), 1);
  BOOST_CHECK_EQUAL(NChooseK(3, 0), 1);

  BOOST_CHECK_EQUAL(NChooseK(1, 1), 1);
  BOOST_CHECK_EQUAL(NChooseK(2, 1), 2);
  BOOST_CHECK_EQUAL(NChooseK(3, 1), 3);

  BOOST_CHECK_EQUAL(NChooseK(2, 2), 1);
  BOOST_CHECK_EQUAL(NChooseK(2, 3), 0);

  BOOST_CHECK_EQUAL(NChooseK(3, 2), 3);
  BOOST_CHECK_EQUAL(NChooseK(4, 2), 6);
  BOOST_CHECK_EQUAL(NChooseK(5, 2), 10);

  BOOST_CHECK_EQUAL(NChooseK(500, 3), 20708500);
}

BOOST_AUTO_TEST_CASE(TestTruncateCast) {
  BOOST_CHECK_EQUAL((TruncateCast<int, int8_t>(-129)), -128);
  BOOST_CHECK_EQUAL((TruncateCast<int, int8_t>(128)), 127);
  BOOST_CHECK_EQUAL((TruncateCast<int, uint8_t>(-1)), 0);
  BOOST_CHECK_EQUAL((TruncateCast<int, uint8_t>(256)), 255);
  BOOST_CHECK_EQUAL((TruncateCast<int, uint16_t>(-1)), 0);
  BOOST_CHECK_EQUAL((TruncateCast<int, uint16_t>(65536)), 65535);
}