Back-substitute on NO_CONVERGENCE in SchurComplementSolver

When ITERATIVE_SCHUR is used with use_explicit_schur_complement = true, ExplicitSchurComplementSolver inherits from SchurComplementSolver. Previously, SchurComplementSolver::SolveImpl only performed back-substitution when SolveReducedLinearSystem returned SUCCESS. When ConjugateGradientsSolver hit max_num_iterations and returned NO_CONVERGENCE, the eliminated parameter blocks were left at zero instead of being back-substituted from the approximate reduced solution, unlike IterativeSchurComplementSolver.

Thanks to @1784174022-ops for reporting this.

Fixes https://github.com/ceres-solver/ceres-solver/issues/1215

Change-Id: Ic879f1d6ad429d0ee054f8101c13a858d53b02c4

internal/ceres/schur_complement_solver.cc

diff --git a/internal/ceres/schur_complement_solver.cc b/internal/ceres/schur_complement_solver.cc
index 4a2fbba..7683633 100644
--- a/internal/ceres/schur_complement_solver.cc
+++ b/internal/ceres/schur_complement_solver.cc
@@ -149,7 +149,8 @@
       SolveReducedLinearSystem(per_solve_options, reduced_solution);
   event_logger.AddEvent("ReducedSolve");
 
-  if (summary.termination_type == LinearSolverTerminationType::SUCCESS) {
+  if (summary.termination_type == LinearSolverTerminationType::SUCCESS ||
+      summary.termination_type == LinearSolverTerminationType::NO_CONVERGENCE) {
     eliminator_->BackSubstitute(
         BlockSparseMatrixData(*A), b, per_solve_options.D, reduced_solution, x);
     event_logger.AddEvent("BackSubstitute");

internal/ceres/schur_complement_solver_test.cc

diff --git a/internal/ceres/schur_complement_solver_test.cc b/internal/ceres/schur_complement_solver_test.cc
index 18b79f3..349f6b1 100644
--- a/internal/ceres/schur_complement_solver_test.cc
+++ b/internal/ceres/schur_complement_solver_test.cc
@@ -193,6 +193,48 @@
       4, true, ITERATIVE_SCHUR, EIGEN, NO_SPARSE, OrderingType::NATURAL);
 }
 
+TEST_F(SchurComplementSolverTest,
+       ExplicitIterativeSchurBackSubstitutesOnNoConvergence) {
+  SetUpFromProblemId(2);
+  LinearSolver::Options options;
+  options.elimination_groups.push_back(num_eliminate_blocks);
+  options.elimination_groups.push_back(A->block_structure()->cols.size() -
+                                       num_eliminate_blocks);
+  options.type = ITERATIVE_SCHUR;
+  options.preconditioner_type = SCHUR_JACOBI;
+  options.max_num_iterations = 1;
+  ContextImpl context;
+  options.context = &context;
+  DetectStructure(*A->block_structure(),
+                  num_eliminate_blocks,
+                  &options.row_block_size,
+                  &options.e_block_size,
+                  &options.f_block_size);
+
+  LinearSolver::PerSolveOptions per_solve_options;
+  per_solve_options.r_tolerance = 0.0;
+  per_solve_options.q_tolerance = 0.0;
+  per_solve_options.D = D.get();
+
+  options.use_explicit_schur_complement = false;
+  std::unique_ptr<LinearSolver> implicit_solver(LinearSolver::Create(options));
+  Vector x_implicit(num_cols);
+  LinearSolver::Summary implicit_summary = implicit_solver->Solve(
+      A.get(), b.get(), per_solve_options, x_implicit.data());
+  ASSERT_EQ(implicit_summary.termination_type,
+            LinearSolverTerminationType::NO_CONVERGENCE);
+
+  options.use_explicit_schur_complement = true;
+  std::unique_ptr<LinearSolver> explicit_solver(LinearSolver::Create(options));
+  Vector x_explicit(num_cols);
+  LinearSolver::Summary explicit_summary = explicit_solver->Solve(
+      A.get(), b.get(), per_solve_options, x_explicit.data());
+  ASSERT_EQ(explicit_summary.termination_type,
+            LinearSolverTerminationType::NO_CONVERGENCE);
+
+  EXPECT_NEAR((x_implicit - x_explicit).norm() / num_cols, 0.0, 1e-10);
+}
+
 #ifndef CERES_NO_LAPACK
 TEST_F(SchurComplementSolverTest, DenseSchurWithLAPACKSmallProblem) {
   ComputeAndCompareSolutions(