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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 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/schur_jacobi_preconditioner.h"
+
+#include <utility>
+#include <vector>
+#include "Eigen/Dense"
+#include "ceres/block_random_access_sparse_matrix.h"
+#include "ceres/block_sparse_matrix.h"
+#include "ceres/collections_port.h"
+#include "ceres/detect_structure.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/linear_solver.h"
+#include "ceres/schur_eliminator.h"
+#include "glog/logging.h"
+
+namespace ceres {
+namespace internal {
+
+SchurJacobiPreconditioner::SchurJacobiPreconditioner(
+    const CompressedRowBlockStructure& bs,
+    const Preconditioner::Options& options)
+    : options_(options) {
+  CHECK_GT(options_.elimination_groups.size(), 1);
+  CHECK_GT(options_.elimination_groups[0], 0);
+  const int num_blocks = bs.cols.size() - options_.elimination_groups[0];
+  CHECK_GT(num_blocks, 0)
+      << "Jacobian should have atleast 1 f_block for "
+      << "SCHUR_JACOBI preconditioner.";
+
+  block_size_.resize(num_blocks);
+  set<pair<int, int> > block_pairs;
+
+  int num_block_diagonal_entries = 0;
+  for (int i = 0; i < num_blocks; ++i) {
+    block_size_[i] = bs.cols[i + options_.elimination_groups[0]].size;
+    block_pairs.insert(make_pair(i, i));
+    num_block_diagonal_entries += block_size_[i] * block_size_[i];
+  }
+
+  m_.reset(new BlockRandomAccessSparseMatrix(block_size_, block_pairs));
+  InitEliminator(bs);
+}
+
+SchurJacobiPreconditioner::~SchurJacobiPreconditioner() {
+}
+
+// Initialize the SchurEliminator.
+void SchurJacobiPreconditioner::InitEliminator(
+    const CompressedRowBlockStructure& bs) {
+  LinearSolver::Options eliminator_options;
+
+  eliminator_options.elimination_groups = options_.elimination_groups;
+  eliminator_options.num_threads = options_.num_threads;
+
+  DetectStructure(bs, options_.elimination_groups[0],
+                  &eliminator_options.row_block_size,
+                  &eliminator_options.e_block_size,
+                  &eliminator_options.f_block_size);
+
+  eliminator_.reset(SchurEliminatorBase::Create(eliminator_options));
+  eliminator_->Init(options_.elimination_groups[0], &bs);
+}
+
+// Update the values of the preconditioner matrix and factorize it.
+bool SchurJacobiPreconditioner::UpdateImpl(const BlockSparseMatrix& A,
+                                           const double* D) {
+  const int num_rows = m_->num_rows();
+  CHECK_GT(num_rows, 0);
+
+  // We need a dummy rhs vector and a dummy b vector since the Schur
+  // eliminator combines the computation of the reduced camera matrix
+  // with the computation of the right hand side of that linear
+  // system.
+  //
+  // TODO(sameeragarwal): Perhaps its worth refactoring the
+  // SchurEliminator::Eliminate function to allow NULL for the rhs. As
+  // of now it does not seem to be worth the effort.
+  Vector rhs = Vector::Zero(m_->num_rows());
+  Vector b = Vector::Zero(A.num_rows());
+
+  // Compute a subset of the entries of the Schur complement.
+  eliminator_->Eliminate(&A, b.data(), D, m_.get(), rhs.data());
+  return true;
+}
+
+void SchurJacobiPreconditioner::RightMultiply(const double* x,
+                                              double* y) const {
+  CHECK_NOTNULL(x);
+  CHECK_NOTNULL(y);
+
+  const double* lhs_values =
+      down_cast<BlockRandomAccessSparseMatrix*>(m_.get())->matrix()->values();
+
+  // This loop can be easily multi-threaded with OpenMP if need be.
+  for (int i = 0; i < block_size_.size(); ++i) {
+    const int block_size = block_size_[i];
+    ConstMatrixRef block(lhs_values, block_size, block_size);
+
+    VectorRef(y, block_size) =
+        block
+        .selfadjointView<Eigen::Upper>()
+        .ldlt()
+        .solve(ConstVectorRef(x, block_size));
+
+    x += block_size;
+    y += block_size;
+    lhs_values += block_size * block_size;
+  }
+}
+
+int SchurJacobiPreconditioner::num_rows() const {
+  return m_->num_rows();
+}
+
+}  // namespace internal
+}  // namespace ceres