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diff --git a/internal/ceres/implicit_schur_complement_test.cc b/internal/ceres/implicit_schur_complement_test.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// 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/implicit_schur_complement.h"
+
+#include <cstddef>
+#include "Eigen/Dense"
+#include "ceres/block_random_access_dense_matrix.h"
+#include "ceres/block_sparse_matrix.h"
+#include "ceres/casts.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/linear_least_squares_problems.h"
+#include "ceres/linear_solver.h"
+#include "ceres/schur_eliminator.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "ceres/types.h"
+#include "glog/logging.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+using testing::AssertionResult;
+
+const double kEpsilon = 1e-14;
+
+class ImplicitSchurComplementTest : public ::testing::Test {
+ protected :
+  virtual void SetUp() {
+    scoped_ptr<LinearLeastSquaresProblem> problem(
+        CreateLinearLeastSquaresProblemFromId(2));
+
+    CHECK_NOTNULL(problem.get());
+    A_.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
+    b_.reset(problem->b.release());
+    D_.reset(problem->D.release());
+
+    num_cols_ = A_->num_cols();
+    num_rows_ = A_->num_rows();
+    num_eliminate_blocks_ = problem->num_eliminate_blocks;
+  }
+
+  void ReducedLinearSystemAndSolution(double* D,
+                                      Matrix* lhs,
+                                      Vector* rhs,
+                                      Vector* solution) {
+    const CompressedRowBlockStructure* bs = A_->block_structure();
+    const int num_col_blocks = bs->cols.size();
+    vector<int> blocks(num_col_blocks - num_eliminate_blocks_, 0);
+    for (int i = num_eliminate_blocks_; i < num_col_blocks; ++i) {
+      blocks[i - num_eliminate_blocks_] = bs->cols[i].size;
+    }
+
+    BlockRandomAccessDenseMatrix blhs(blocks);
+    const int num_schur_rows = blhs.num_rows();
+
+    LinearSolver::Options options;
+    options.elimination_groups.push_back(num_eliminate_blocks_);
+    options.type = DENSE_SCHUR;
+
+    scoped_ptr<SchurEliminatorBase> eliminator(
+        SchurEliminatorBase::Create(options));
+    CHECK_NOTNULL(eliminator.get());
+    eliminator->Init(num_eliminate_blocks_, bs);
+
+    lhs->resize(num_schur_rows, num_schur_rows);
+    rhs->resize(num_schur_rows);
+
+    eliminator->Eliminate(A_.get(), b_.get(), D, &blhs, rhs->data());
+
+    MatrixRef lhs_ref(blhs.mutable_values(), num_schur_rows, num_schur_rows);
+
+    // lhs_ref is an upper triangular matrix. Construct a full version
+    // of lhs_ref in lhs by transposing lhs_ref, choosing the strictly
+    // lower triangular part of the matrix and adding it to lhs_ref.
+    *lhs = lhs_ref;
+    lhs->triangularView<Eigen::StrictlyLower>() =
+        lhs_ref.triangularView<Eigen::StrictlyUpper>().transpose();
+
+    solution->resize(num_cols_);
+    solution->setZero();
+    VectorRef schur_solution(solution->data() + num_cols_ - num_schur_rows,
+                             num_schur_rows);
+    schur_solution = lhs->selfadjointView<Eigen::Upper>().ldlt().solve(*rhs);
+    eliminator->BackSubstitute(A_.get(), b_.get(), D,
+                               schur_solution.data(), solution->data());
+  }
+
+  AssertionResult TestImplicitSchurComplement(double* D) {
+    Matrix lhs;
+    Vector rhs;
+    Vector reference_solution;
+    ReducedLinearSystemAndSolution(D, &lhs, &rhs, &reference_solution);
+
+    ImplicitSchurComplement isc(num_eliminate_blocks_, true);
+    isc.Init(*A_, D, b_.get());
+
+    int num_sc_cols = lhs.cols();
+
+    for (int i = 0; i < num_sc_cols; ++i) {
+      Vector x(num_sc_cols);
+      x.setZero();
+      x(i) = 1.0;
+
+      Vector y(num_sc_cols);
+      y = lhs * x;
+
+      Vector z(num_sc_cols);
+      isc.RightMultiply(x.data(), z.data());
+
+      // The i^th column of the implicit schur complement is the same as
+      // the explicit schur complement.
+      if ((y - z).norm() > kEpsilon) {
+        return testing::AssertionFailure()
+            << "Explicit and Implicit SchurComplements differ in "
+            << "column " << i << ". explicit: " << y.transpose()
+            << " implicit: " << z.transpose();
+      }
+    }
+
+    // Compare the rhs of the reduced linear system
+    if ((isc.rhs() - rhs).norm() > kEpsilon) {
+      return testing::AssertionFailure()
+            << "Explicit and Implicit SchurComplements differ in "
+            << "rhs. explicit: " << rhs.transpose()
+            << " implicit: " << isc.rhs().transpose();
+    }
+
+    // Reference solution to the f_block.
+    const Vector reference_f_sol =
+        lhs.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
+
+    // Backsubstituted solution from the implicit schur solver using the
+    // reference solution to the f_block.
+    Vector sol(num_cols_);
+    isc.BackSubstitute(reference_f_sol.data(), sol.data());
+    if ((sol - reference_solution).norm() > kEpsilon) {
+      return testing::AssertionFailure()
+          << "Explicit and Implicit SchurComplements solutions differ. "
+          << "explicit: " << reference_solution.transpose()
+          << " implicit: " << sol.transpose();
+    }
+
+    return testing::AssertionSuccess();
+  }
+
+  int num_rows_;
+  int num_cols_;
+  int num_eliminate_blocks_;
+
+  scoped_ptr<BlockSparseMatrix> A_;
+  scoped_array<double> b_;
+  scoped_array<double> D_;
+};
+
+// Verify that the Schur Complement matrix implied by the
+// ImplicitSchurComplement class matches the one explicitly computed
+// by the SchurComplement solver.
+//
+// We do this with and without regularization to check that the
+// support for the LM diagonal is correct.
+TEST_F(ImplicitSchurComplementTest, SchurMatrixValuesTest) {
+  EXPECT_TRUE(TestImplicitSchurComplement(NULL));
+  EXPECT_TRUE(TestImplicitSchurComplement(D_.get()));
+}
+
+}  // namespace internal
+}  // namespace ceres