Creation of LTS branch "lts_2019_08_08"

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GitOrigin-RevId: 9ee91d3e430fb33a4590486573792eb0fa146c2d
Change-Id: Ia06e548bc106cc9d136f6c65714be6645317aced

1 files changed, 193 insertions, 0 deletions

diff --git a/absl/random/internal/distribution_test_util_test.cc b/absl/random/internal/distribution_test_util_test.cc
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+// 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/distribution_test_util.h"
+
+#include "gtest/gtest.h"
+
+namespace {
+
+TEST(TestUtil, InverseErf) {
+  const struct {
+    const double z;
+    const double value;
+  } kErfInvTable[] = {
+      {0.0000001, 8.86227e-8},
+      {0.00001, 8.86227e-6},
+      {0.5, 0.4769362762044},
+      {0.6, 0.5951160814499},
+      {0.99999, 3.1234132743},
+      {0.9999999, 3.7665625816},
+      {0.999999944, 3.8403850690566985},  // = log((1-x) * (1+x)) =~ 16.004
+      {0.999999999, 4.3200053849134452},
+  };
+
+  for (const auto& data : kErfInvTable) {
+    auto value = absl::random_internal::erfinv(data.z);
+
+    // Log using the Wolfram-alpha function name & parameters.
+    EXPECT_NEAR(value, data.value, 1e-8)
+        << " InverseErf[" << data.z << "]  (expected=" << data.value << ")  -> "
+        << value;
+  }
+}
+
+const struct {
+  const double p;
+  const double q;
+  const double x;
+  const double alpha;
+} kBetaTable[] = {
+    {0.5, 0.5, 0.01, 0.06376856085851985},
+    {0.5, 0.5, 0.1, 0.2048327646991335},
+    {0.5, 0.5, 1, 1},
+    {1, 0.5, 0, 0},
+    {1, 0.5, 0.01, 0.005012562893380045},
+    {1, 0.5, 0.1, 0.0513167019494862},
+    {1, 0.5, 0.5, 0.2928932188134525},
+    {1, 1, 0.5, 0.5},
+    {2, 2, 0.1, 0.028},
+    {2, 2, 0.2, 0.104},
+    {2, 2, 0.3, 0.216},
+    {2, 2, 0.4, 0.352},
+    {2, 2, 0.5, 0.5},
+    {2, 2, 0.6, 0.648},
+    {2, 2, 0.7, 0.784},
+    {2, 2, 0.8, 0.896},
+    {2, 2, 0.9, 0.972},
+    {5.5, 5, 0.5, 0.4361908850559777},
+    {10, 0.5, 0.9, 0.1516409096346979},
+    {10, 5, 0.5, 0.08978271484375},
+    {10, 5, 1, 1},
+    {10, 10, 0.5, 0.5},
+    {20, 5, 0.8, 0.4598773297575791},
+    {20, 10, 0.6, 0.2146816102371739},
+    {20, 10, 0.8, 0.9507364826957875},
+    {20, 20, 0.5, 0.5},
+    {20, 20, 0.6, 0.8979413687105918},
+    {30, 10, 0.7, 0.2241297491808366},
+    {30, 10, 0.8, 0.7586405487192086},
+    {40, 20, 0.7, 0.7001783247477069},
+    {1, 0.5, 0.1, 0.0513167019494862},
+    {1, 0.5, 0.2, 0.1055728090000841},
+    {1, 0.5, 0.3, 0.1633399734659245},
+    {1, 0.5, 0.4, 0.2254033307585166},
+    {1, 2, 0.2, 0.36},
+    {1, 3, 0.2, 0.488},
+    {1, 4, 0.2, 0.5904},
+    {1, 5, 0.2, 0.67232},
+    {2, 2, 0.3, 0.216},
+    {3, 2, 0.3, 0.0837},
+    {4, 2, 0.3, 0.03078},
+    {5, 2, 0.3, 0.010935},
+
+    // These values test small & large points along the range of the Beta
+    // function.
+    //
+    // When selecting test points, remember that if BetaIncomplete(x, p, q)
+    // returns the same value to within the limits of precision over a large
+    // domain of the input, x, then BetaIncompleteInv(alpha, p, q) may return an
+    // essentially arbitrary value where BetaIncomplete(x, p, q) =~ alpha.
+
+    // BetaRegularized[x, 0.00001, 0.00001],
+    // For x in {~0.001 ... ~0.999}, => ~0.5
+    {1e-5, 1e-5, 1e-5, 0.4999424388184638311},
+    {1e-5, 1e-5, (1.0 - 1e-8), 0.5000920948389232964},
+
+    // BetaRegularized[x, 0.00001, 10000].
+    // For x in {~epsilon ... 1.0}, => ~1
+    {1e-5, 1e5, 1e-6, 0.9999817708130066936},
+    {1e-5, 1e5, (1.0 - 1e-7), 1.0},
+
+    // BetaRegularized[x, 10000, 0.00001].
+    // For x in {0 .. 1-epsilon}, => ~0
+    {1e5, 1e-5, 1e-6, 0},
+    {1e5, 1e-5, (1.0 - 1e-6), 1.8229186993306369e-5},
+};
+
+TEST(BetaTest, BetaIncomplete) {
+  for (const auto& data : kBetaTable) {
+    auto value = absl::random_internal::BetaIncomplete(data.x, data.p, data.q);
+
+    // Log using the Wolfram-alpha function name & parameters.
+    EXPECT_NEAR(value, data.alpha, 1e-12)
+        << " BetaRegularized[" << data.x << ", " << data.p << ", " << data.q
+        << "]  (expected=" << data.alpha << ")  -> " << value;
+  }
+}
+
+TEST(BetaTest, BetaIncompleteInv) {
+  for (const auto& data : kBetaTable) {
+    auto value =
+        absl::random_internal::BetaIncompleteInv(data.p, data.q, data.alpha);
+
+    // Log using the Wolfram-alpha function name & parameters.
+    EXPECT_NEAR(value, data.x, 1e-6)
+        << " InverseBetaRegularized[" << data.alpha << ", " << data.p << ", "
+        << data.q << "]  (expected=" << data.x << ")  -> " << value;
+  }
+}
+
+TEST(MaxErrorTolerance, MaxErrorTolerance) {
+  std::vector<std::pair<double, double>> cases = {
+      {0.0000001, 8.86227e-8 * 1.41421356237},
+      {0.00001, 8.86227e-6 * 1.41421356237},
+      {0.5, 0.4769362762044 * 1.41421356237},
+      {0.6, 0.5951160814499 * 1.41421356237},
+      {0.99999, 3.1234132743 * 1.41421356237},
+      {0.9999999, 3.7665625816 * 1.41421356237},
+      {0.999999944, 3.8403850690566985 * 1.41421356237},
+      {0.999999999, 4.3200053849134452 * 1.41421356237}};
+  for (auto entry : cases) {
+    EXPECT_NEAR(absl::random_internal::MaxErrorTolerance(entry.first),
+                entry.second, 1e-8);
+  }
+}
+
+TEST(ZScore, WithSameMean) {
+  absl::random_internal::DistributionMoments m;
+  m.n = 100;
+  m.mean = 5;
+  m.variance = 1;
+  EXPECT_NEAR(absl::random_internal::ZScore(5, m), 0, 1e-12);
+
+  m.n = 1;
+  m.mean = 0;
+  m.variance = 1;
+  EXPECT_NEAR(absl::random_internal::ZScore(0, m), 0, 1e-12);
+
+  m.n = 10000;
+  m.mean = -5;
+  m.variance = 100;
+  EXPECT_NEAR(absl::random_internal::ZScore(-5, m), 0, 1e-12);
+}
+
+TEST(ZScore, DifferentMean) {
+  absl::random_internal::DistributionMoments m;
+  m.n = 100;
+  m.mean = 5;
+  m.variance = 1;
+  EXPECT_NEAR(absl::random_internal::ZScore(4, m), 10, 1e-12);
+
+  m.n = 1;
+  m.mean = 0;
+  m.variance = 1;
+  EXPECT_NEAR(absl::random_internal::ZScore(-1, m), 1, 1e-12);
+
+  m.n = 10000;
+  m.mean = -5;
+  m.variance = 100;
+  EXPECT_NEAR(absl::random_internal::ZScore(-4, m), -10, 1e-12);
+}
+}  // namespace