Squashed 'third_party/ceres/' content from commit e51e9b4

Change-Id: I763587619d57e594d3fa158dc3a7fe0b89a1743b
git-subtree-dir: third_party/ceres
git-subtree-split: e51e9b46f6ca88ab8b2266d0e362771db6d98067
diff --git a/internal/ceres/graph_algorithms_test.cc b/internal/ceres/graph_algorithms_test.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#include "ceres/graph_algorithms.h"
+
+#include <algorithm>
+#include <memory>
+#include <unordered_set>
+
+#include "ceres/graph.h"
+#include "ceres/internal/port.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+using std::vector;
+
+TEST(IndependentSetOrdering, Chain) {
+  Graph<int> graph;
+  graph.AddVertex(0);
+  graph.AddVertex(1);
+  graph.AddVertex(2);
+  graph.AddVertex(3);
+  graph.AddVertex(4);
+
+  graph.AddEdge(0, 1);
+  graph.AddEdge(1, 2);
+  graph.AddEdge(2, 3);
+  graph.AddEdge(3, 4);
+
+  // 0-1-2-3-4
+  // 0, 2, 4 should be in the independent set.
+  vector<int> ordering;
+  int independent_set_size = IndependentSetOrdering(graph, &ordering);
+
+  sort(ordering.begin(), ordering.begin() + 3);
+  sort(ordering.begin() + 3, ordering.end());
+
+  EXPECT_EQ(independent_set_size, 3);
+  EXPECT_EQ(ordering.size(), 5);
+  EXPECT_EQ(ordering[0], 0);
+  EXPECT_EQ(ordering[1], 2);
+  EXPECT_EQ(ordering[2], 4);
+  EXPECT_EQ(ordering[3], 1);
+  EXPECT_EQ(ordering[4], 3);
+}
+
+TEST(IndependentSetOrdering, Star) {
+  Graph<int> graph;
+  graph.AddVertex(0);
+  graph.AddVertex(1);
+  graph.AddVertex(2);
+  graph.AddVertex(3);
+  graph.AddVertex(4);
+
+  graph.AddEdge(0, 1);
+  graph.AddEdge(0, 2);
+  graph.AddEdge(0, 3);
+  graph.AddEdge(0, 4);
+
+  //      1
+  //      |
+  //    4-0-2
+  //      |
+  //      3
+  // 1, 2, 3, 4 should be in the independent set.
+  vector<int> ordering;
+  int independent_set_size = IndependentSetOrdering(graph, &ordering);
+  EXPECT_EQ(independent_set_size, 4);
+  EXPECT_EQ(ordering.size(), 5);
+  EXPECT_EQ(ordering[4], 0);
+  sort(ordering.begin(), ordering.begin() + 4);
+  EXPECT_EQ(ordering[0], 1);
+  EXPECT_EQ(ordering[1], 2);
+  EXPECT_EQ(ordering[2], 3);
+  EXPECT_EQ(ordering[3], 4);
+}
+
+TEST(Degree2MaximumSpanningForest, PreserveWeights) {
+  WeightedGraph<int> graph;
+  graph.AddVertex(0, 1.0);
+  graph.AddVertex(1, 2.0);
+  graph.AddEdge(0, 1, 0.5);
+  graph.AddEdge(1, 0, 0.5);
+
+  std::unique_ptr<WeightedGraph<int> > forest(
+					      Degree2MaximumSpanningForest(graph));
+
+  const std::unordered_set<int>& vertices = forest->vertices();
+  EXPECT_EQ(vertices.size(), 2);
+  EXPECT_EQ(forest->VertexWeight(0), 1.0);
+  EXPECT_EQ(forest->VertexWeight(1), 2.0);
+  EXPECT_EQ(forest->Neighbors(0).size(), 1.0);
+  EXPECT_EQ(forest->EdgeWeight(0, 1), 0.5);
+}
+
+TEST(Degree2MaximumSpanningForest, StarGraph) {
+  WeightedGraph<int> graph;
+  graph.AddVertex(0);
+  graph.AddVertex(1);
+  graph.AddVertex(2);
+  graph.AddVertex(3);
+  graph.AddVertex(4);
+
+  graph.AddEdge(0, 1, 1.0);
+  graph.AddEdge(0, 2, 2.0);
+  graph.AddEdge(0, 3, 3.0);
+  graph.AddEdge(0, 4, 4.0);
+
+  std::unique_ptr<WeightedGraph<int> > forest(Degree2MaximumSpanningForest(graph));
+  const std::unordered_set<int>& vertices = forest->vertices();
+  EXPECT_EQ(vertices.size(), 5);
+
+  {
+    const std::unordered_set<int>& neighbors = forest->Neighbors(0);
+    EXPECT_EQ(neighbors.size(), 2);
+    EXPECT_TRUE(neighbors.find(4) != neighbors.end());
+    EXPECT_TRUE(neighbors.find(3) != neighbors.end());
+  }
+
+  {
+    const std::unordered_set<int>& neighbors = forest->Neighbors(3);
+    EXPECT_EQ(neighbors.size(), 1);
+    EXPECT_TRUE(neighbors.find(0) != neighbors.end());
+  }
+
+  {
+    const std::unordered_set<int>& neighbors = forest->Neighbors(4);
+    EXPECT_EQ(neighbors.size(), 1);
+    EXPECT_TRUE(neighbors.find(0) != neighbors.end());
+  }
+
+  {
+    const std::unordered_set<int>& neighbors = forest->Neighbors(1);
+    EXPECT_EQ(neighbors.size(), 0);
+  }
+
+  {
+    const std::unordered_set<int>& neighbors = forest->Neighbors(2);
+    EXPECT_EQ(neighbors.size(), 0);
+  }
+}
+
+TEST(VertexTotalOrdering, TotalOrdering) {
+  Graph<int> graph;
+  graph.AddVertex(0);
+  graph.AddVertex(1);
+  graph.AddVertex(2);
+  graph.AddVertex(3);
+
+  // 0-1
+  //   |
+  // 2-3
+  // 0,1 and 2 have degree 1 and 3 has degree 2.
+  graph.AddEdge(0, 1);
+  graph.AddEdge(2, 3);
+  VertexTotalOrdering<int> less_than(graph);
+
+  for (int i = 0; i < 4; ++i) {
+    EXPECT_FALSE(less_than(i, i)) << "Failing vertex: " << i;
+    for (int j = 0; j < 4; ++j) {
+      if (i != j) {
+        EXPECT_TRUE(less_than(i, j) ^ less_than(j, i))
+            << "Failing vertex pair: " << i << " " << j;
+      }
+    }
+  }
+
+  for (int i = 0; i < 3; ++i) {
+    EXPECT_TRUE(less_than(i, 3));
+    EXPECT_FALSE(less_than(3, i));
+  }
+}
+
+
+TEST(StableIndependentSet, BreakTies) {
+  Graph<int> graph;
+  graph.AddVertex(0);
+  graph.AddVertex(1);
+  graph.AddVertex(2);
+  graph.AddVertex(3);
+
+  graph.AddEdge(0, 1);
+  graph.AddEdge(0, 2);
+  graph.AddEdge(0, 3);
+  graph.AddEdge(1, 2);
+  graph.AddEdge(1, 3);
+  graph.AddEdge(2, 3);
+
+  // Since this is a completely connected graph, the independent set
+  // contains exactly one vertex. StableIndependentSetOrdering
+  // guarantees that it will always be the first vertex in the
+  // ordering vector.
+  {
+    vector<int> ordering;
+    ordering.push_back(0);
+    ordering.push_back(1);
+    ordering.push_back(2);
+    ordering.push_back(3);
+    const int independent_set_size =
+        StableIndependentSetOrdering(graph, &ordering);
+    EXPECT_EQ(independent_set_size, 1);
+    EXPECT_EQ(ordering[0], 0);
+  }
+
+  {
+    vector<int> ordering;
+    ordering.push_back(1);
+    ordering.push_back(0);
+    ordering.push_back(2);
+    ordering.push_back(3);
+    const int independent_set_size =
+        StableIndependentSetOrdering(graph, &ordering);
+    EXPECT_EQ(independent_set_size, 1);
+    EXPECT_EQ(ordering[0], 1);
+  }
+}
+
+}  // namespace internal
+}  // namespace ceres