Add direct coordinate descent minimizer tests

Cover independent blocks, coupled block ordering, and an excluded
block with analytic residuals. Check automatic ordering and restored
parameter metadata.

Initialize state and metadata before minimizer initialization. Reset
saved state before repeated solves. Check nonzero metadata restoration
in the repeated and exclusion cases.

The isolated test binary compiled against retained CPU libraries.
All eight discovered cases passed.

Issue: https://github.com/ceres-solver/ceres-solver/issues/938

Codex used.

Change-Id: Ice01781aa114e80d867feadd77d4f52da7a46dcc
diff --git a/internal/ceres/CMakeLists.txt b/internal/ceres/CMakeLists.txt
index cc757d5..193d174 100644
--- a/internal/ceres/CMakeLists.txt
+++ b/internal/ceres/CMakeLists.txt
@@ -420,6 +420,7 @@
   ceres_test(conditioned_cost_function)
   ceres_test(conjugate_gradients_solver)
   ceres_test(corrector)
+  ceres_test(coordinate_descent_minimizer)
   ceres_test(cost_function_to_functor)
   ceres_test(covariance)
   ceres_test(cubic_interpolation)
diff --git a/internal/ceres/coordinate_descent_minimizer_test.cc b/internal/ceres/coordinate_descent_minimizer_test.cc
new file mode 100644
index 0000000..518719b
--- /dev/null
+++ b/internal/ceres/coordinate_descent_minimizer_test.cc
@@ -0,0 +1,337 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2026 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.
+
+#include "ceres/coordinate_descent_minimizer.h"
+
+#include <string>
+#include <vector>
+
+#include "ceres/minimizer.h"
+#include "ceres/ordered_groups.h"
+#include "ceres/parameter_block.h"
+#include "ceres/problem_impl.h"
+#include "ceres/program.h"
+#include "ceres/sized_cost_function.h"
+#include "ceres/solver.h"
+#include "gmock/gmock.h"
+#include "gtest/gtest.h"
+
+namespace ceres::internal {
+namespace {
+
+using ::testing::ElementsAre;
+
+constexpr double kStateTolerance = 1e-6;
+// The default inner LM stop can leave endpoint error below 3e-4.
+constexpr double kCoupledOrderingTolerance = 5e-4;
+
+class UnaryResidual final : public SizedCostFunction<1, 1> {
+ public:
+  explicit UnaryResidual(double target) : target_(target) {}
+
+  bool Evaluate(double const* const* parameters,
+                double* residuals,
+                double** jacobians) const override {
+    residuals[0] = parameters[0][0] - target_;
+    if (jacobians != nullptr && jacobians[0] != nullptr) {
+      jacobians[0][0] = 1.0;
+    }
+    return true;
+  }
+
+ private:
+  const double target_;
+};
+
+class BinaryResidual final : public SizedCostFunction<1, 1, 1> {
+ public:
+  explicit BinaryResidual(double target) : target_(target) {}
+
+  bool Evaluate(double const* const* parameters,
+                double* residuals,
+                double** jacobians) const override {
+    residuals[0] = parameters[0][0] + parameters[1][0] - target_;
+    if (jacobians != nullptr) {
+      if (jacobians[0] != nullptr) {
+        jacobians[0][0] = 1.0;
+      }
+      if (jacobians[1] != nullptr) {
+        jacobians[1][0] = 1.0;
+      }
+    }
+    return true;
+  }
+
+ private:
+  const double target_;
+};
+
+struct BlockMetadata {
+  int index;
+  int state_offset;
+  int delta_offset;
+  bool is_constant;
+};
+
+MATCHER_P2(RestoresBlockMetadata,
+           expected,
+           state_data,
+           "restores parameter block metadata") {
+  if (arg->index() != expected.index) {
+    *result_listener << "index is " << arg->index() << ", expected "
+                     << expected.index;
+    return false;
+  }
+  if (arg->state_offset() != expected.state_offset) {
+    *result_listener << "state offset is " << arg->state_offset()
+                     << ", expected " << expected.state_offset;
+    return false;
+  }
+  if (arg->delta_offset() != expected.delta_offset) {
+    *result_listener << "delta offset is " << arg->delta_offset()
+                     << ", expected " << expected.delta_offset;
+    return false;
+  }
+  if (arg->IsConstant() != expected.is_constant) {
+    *result_listener << "constant state is " << arg->IsConstant()
+                     << ", expected " << expected.is_constant;
+    return false;
+  }
+  if (arg->state() != state_data + expected.state_offset) {
+    *result_listener << "state pointer does not match offset "
+                     << expected.state_offset;
+    return false;
+  }
+  return true;
+}
+
+class CoordinateDescentMinimizerTest : public ::testing::Test {
+ protected:
+  bool InitMinimizer(const ParameterBlockOrdering& ordering) {
+    problem_.mutable_program()->SetParameterOffsetsAndIndex();
+    state_.resize(problem_.program().NumParameters());
+    problem_.program().ParameterBlocksToStateVector(state_.data());
+    initial_state_ = state_;
+    metadata_.clear();
+    for (ParameterBlock* block : problem_.program().parameter_blocks()) {
+      metadata_.push_back({block->index(),
+                           block->state_offset(),
+                           block->delta_offset(),
+                           block->IsConstant()});
+    }
+    return minimizer_.Init(
+        problem_.program(), problem_.parameter_map(), ordering, &error_);
+  }
+
+  void ResetState() { state_ = initial_state_; }
+
+  void Minimize(int num_threads = 1) {
+    Minimizer::Options options;
+    options.num_threads = num_threads;
+    problem_.context()->EnsureMinimumThreads(num_threads);
+    Solver::Summary summary;
+    minimizer_.Minimize(options, state_.data(), &summary);
+  }
+
+  double x_ = 0.0;
+  double y_ = 0.0;
+  double z_ = 0.0;
+  std::vector<double> state_;
+  std::vector<double> initial_state_;
+  std::vector<BlockMetadata> metadata_;
+  std::string error_;
+  ProblemImpl problem_;
+  CoordinateDescentMinimizer minimizer_{problem_.context()};
+};
+
+TEST(CoordinateDescentMinimizerOrdering, RejectsCoupledParametersInSameGroup) {
+  double x = 0.0;
+  double y = 0.0;
+  ProblemImpl problem;
+  problem.AddResidualBlock(new BinaryResidual(3.0), nullptr, &x, &y);
+  ParameterBlockOrdering ordering;
+  ordering.AddElementToGroup(&x, 0);
+  ordering.AddElementToGroup(&y, 0);
+  std::string error;
+
+  EXPECT_FALSE(CoordinateDescentMinimizer::IsOrderingValid(
+      problem.program(), ordering, &error));
+  EXPECT_FALSE(error.empty());
+}
+
+TEST(CoordinateDescentMinimizerOrdering,
+     AcceptsCoupledParametersInSeparateGroups) {
+  double x = 0.0;
+  double y = 0.0;
+  ProblemImpl problem;
+  problem.AddResidualBlock(new BinaryResidual(3.0), nullptr, &x, &y);
+  ParameterBlockOrdering ordering;
+  ordering.AddElementToGroup(&x, 0);
+  ordering.AddElementToGroup(&y, 1);
+  std::string error;
+
+  EXPECT_TRUE(CoordinateDescentMinimizer::IsOrderingValid(
+      problem.program(), ordering, &error))
+      << error;
+}
+
+TEST(CoordinateDescentMinimizerOrdering,
+     AutomaticOrderingSeparatesCoupledParameters) {
+  double x = 0.0;
+  double y = 0.0;
+  double z = 0.0;
+  ProblemImpl problem;
+  problem.AddResidualBlock(new BinaryResidual(3.0), nullptr, &x, &y);
+  problem.AddResidualBlock(new UnaryResidual(1.0), nullptr, &z);
+  const auto ordering =
+      CoordinateDescentMinimizer::CreateOrdering(problem.program());
+  std::string error;
+
+  ASSERT_NE(nullptr, ordering);
+  EXPECT_TRUE(ordering->IsMember(&x));
+  EXPECT_TRUE(ordering->IsMember(&y));
+  EXPECT_TRUE(ordering->IsMember(&z));
+  EXPECT_EQ(3, ordering->NumElements());
+  EXPECT_EQ(2, ordering->NumGroups());
+  const int first_group = ordering->MinNonZeroGroup();
+  EXPECT_EQ(1, ordering->GroupSize(first_group));
+  EXPECT_EQ(2, ordering->GroupSize(first_group + 1));
+  EXPECT_NE(ordering->GroupId(&x), ordering->GroupId(&y));
+  EXPECT_TRUE(CoordinateDescentMinimizer::IsOrderingValid(
+      problem.program(), *ordering, &error))
+      << error;
+}
+
+TEST_F(CoordinateDescentMinimizerTest, IndependentBlocksAreOptimized) {
+  problem_.AddResidualBlock(new UnaryResidual(2.0), nullptr, &x_);
+  problem_.AddResidualBlock(new UnaryResidual(-3.0), nullptr, &y_);
+  ParameterBlockOrdering ordering;
+  ordering.AddElementToGroup(&x_, 0);
+  ordering.AddElementToGroup(&y_, 0);
+  ASSERT_TRUE(InitMinimizer(ordering)) << error_;
+  ASSERT_EQ(problem_.program().NumParameters(), state_.size());
+
+  // Minimize requests up to one thread per problem in an independent group.
+  for (int num_threads : {1, 2}) {
+    ResetState();
+    Minimize(num_threads);
+    EXPECT_THAT(
+        problem_.program().parameter_blocks(),
+        ElementsAre(RestoresBlockMetadata(metadata_[0], state_.data()),
+                    RestoresBlockMetadata(metadata_[1], state_.data())));
+    EXPECT_NEAR(2.0, state_[0], kStateTolerance);
+    EXPECT_NEAR(-3.0, state_[1], kStateTolerance);
+  }
+}
+
+TEST_F(CoordinateDescentMinimizerTest, UsesUpdatedXWhenMinimizingY) {
+  problem_.AddResidualBlock(new BinaryResidual(3.0), nullptr, &x_, &y_);
+  problem_.AddResidualBlock(new UnaryResidual(1.0), nullptr, &y_);
+  ParameterBlockOrdering ordering;
+  ordering.AddElementToGroup(&x_, 0);
+  ordering.AddElementToGroup(&y_, 1);
+  ASSERT_TRUE(InitMinimizer(ordering)) << error_;
+  ASSERT_EQ(problem_.program().NumParameters(), state_.size());
+
+  Minimize();
+  EXPECT_THAT(problem_.program().parameter_blocks(),
+              ElementsAre(RestoresBlockMetadata(metadata_[0], state_.data()),
+                          RestoresBlockMetadata(metadata_[1], state_.data())));
+  // X reaches 3 first. The single Y sweep then minimizes both residuals.
+  EXPECT_NEAR(3.0, state_[0], kCoupledOrderingTolerance);
+  EXPECT_NEAR(0.5, state_[1], kCoupledOrderingTolerance);
+}
+
+TEST_F(CoordinateDescentMinimizerTest, UsesUpdatedYWhenMinimizingX) {
+  problem_.AddResidualBlock(new BinaryResidual(3.0), nullptr, &x_, &y_);
+  problem_.AddResidualBlock(new UnaryResidual(1.0), nullptr, &y_);
+  ParameterBlockOrdering ordering;
+  ordering.AddElementToGroup(&x_, 1);
+  ordering.AddElementToGroup(&y_, 0);
+  ASSERT_TRUE(InitMinimizer(ordering)) << error_;
+  ASSERT_EQ(problem_.program().NumParameters(), state_.size());
+
+  Minimize();
+  EXPECT_THAT(problem_.program().parameter_blocks(),
+              ElementsAre(RestoresBlockMetadata(metadata_[0], state_.data()),
+                          RestoresBlockMetadata(metadata_[1], state_.data())));
+  // Y reaches 2 first. The single X sweep then minimizes the binary residual.
+  EXPECT_NEAR(1.0, state_[0], kCoupledOrderingTolerance);
+  EXPECT_NEAR(2.0, state_[1], kCoupledOrderingTolerance);
+}
+
+TEST_F(CoordinateDescentMinimizerTest,
+       RepeatedMinimizationRestoresMetadataAfterStateReset) {
+  problem_.AddResidualBlock(new UnaryResidual(2.0), nullptr, &x_);
+  problem_.AddResidualBlock(new UnaryResidual(-3.0), nullptr, &y_);
+  ParameterBlockOrdering ordering;
+  ordering.AddElementToGroup(&x_, 0);
+  ordering.AddElementToGroup(&y_, 1);
+  ASSERT_TRUE(InitMinimizer(ordering)) << error_;
+  ASSERT_EQ(1, metadata_[1].index);
+  ASSERT_EQ(1, metadata_[1].state_offset);
+  ASSERT_EQ(1, metadata_[1].delta_offset);
+  ASSERT_EQ(problem_.program().NumParameters(), state_.size());
+
+  Minimize();
+  EXPECT_THAT(problem_.program().parameter_blocks(),
+              ElementsAre(RestoresBlockMetadata(metadata_[0], state_.data()),
+                          RestoresBlockMetadata(metadata_[1], state_.data())));
+  EXPECT_NEAR(2.0, state_[0], kStateTolerance);
+  EXPECT_NEAR(-3.0, state_[1], kStateTolerance);
+
+  ResetState();
+  Minimize();
+  EXPECT_THAT(problem_.program().parameter_blocks(),
+              ElementsAre(RestoresBlockMetadata(metadata_[0], state_.data()),
+                          RestoresBlockMetadata(metadata_[1], state_.data())));
+  EXPECT_NEAR(2.0, state_[0], kStateTolerance);
+  EXPECT_NEAR(-3.0, state_[1], kStateTolerance);
+}
+
+TEST_F(CoordinateDescentMinimizerTest, KeepsExcludedParameterBlockFixed) {
+  x_ = 1.0;
+  problem_.AddResidualBlock(new BinaryResidual(5.0), nullptr, &x_, &z_);
+  ParameterBlockOrdering ordering;
+  ordering.AddElementToGroup(&z_, 0);
+  ASSERT_TRUE(InitMinimizer(ordering)) << error_;
+  ASSERT_EQ(1, metadata_[1].index);
+  ASSERT_EQ(1, metadata_[1].state_offset);
+  ASSERT_EQ(1, metadata_[1].delta_offset);
+  ASSERT_EQ(problem_.program().NumParameters(), state_.size());
+
+  Minimize();
+  EXPECT_THAT(problem_.program().parameter_blocks(),
+              ElementsAre(RestoresBlockMetadata(metadata_[0], state_.data()),
+                          RestoresBlockMetadata(metadata_[1], state_.data())));
+  EXPECT_DOUBLE_EQ(1.0, state_[0]);
+  EXPECT_NEAR(4.0, state_[1], kStateTolerance);
+}
+
+}  // namespace
+}  // namespace ceres::internal