diff --git a/internal/ceres/local_parameterization.cc b/internal/ceres/local_parameterization.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/local_parameterization.h"
+
+#include <algorithm>
+#include "Eigen/Geometry"
+#include "ceres/householder_vector.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/fixed_array.h"
+#include "ceres/rotation.h"
+#include "glog/logging.h"
+
+namespace ceres {
+
+using std::vector;
+
+LocalParameterization::~LocalParameterization() {
+}
+
+bool LocalParameterization::MultiplyByJacobian(const double* x,
+                                               const int num_rows,
+                                               const double* global_matrix,
+                                               double* local_matrix) const {
+  if (LocalSize() == 0) {
+    return true;
+  }
+
+  Matrix jacobian(GlobalSize(), LocalSize());
+  if (!ComputeJacobian(x, jacobian.data())) {
+    return false;
+  }
+
+  MatrixRef(local_matrix, num_rows, LocalSize()) =
+      ConstMatrixRef(global_matrix, num_rows, GlobalSize()) * jacobian;
+  return true;
+}
+
+IdentityParameterization::IdentityParameterization(const int size)
+    : size_(size) {
+  CHECK_GT(size, 0);
+}
+
+bool IdentityParameterization::Plus(const double* x,
+                                    const double* delta,
+                                    double* x_plus_delta) const {
+  VectorRef(x_plus_delta, size_) =
+      ConstVectorRef(x, size_) + ConstVectorRef(delta, size_);
+  return true;
+}
+
+bool IdentityParameterization::ComputeJacobian(const double* x,
+                                               double* jacobian) const {
+  MatrixRef(jacobian, size_, size_).setIdentity();
+  return true;
+}
+
+bool IdentityParameterization::MultiplyByJacobian(const double* x,
+                                                  const int num_cols,
+                                                  const double* global_matrix,
+                                                  double* local_matrix) const {
+  std::copy(global_matrix,
+            global_matrix + num_cols * GlobalSize(),
+            local_matrix);
+  return true;
+}
+
+SubsetParameterization::SubsetParameterization(
+    int size, const vector<int>& constant_parameters)
+    : local_size_(size - constant_parameters.size()), constancy_mask_(size, 0) {
+  vector<int> constant = constant_parameters;
+  std::sort(constant.begin(), constant.end());
+  CHECK_GE(constant.front(), 0) << "Indices indicating constant parameter must "
+                                   "be greater than equal to zero.";
+  CHECK_LT(constant.back(), size)
+      << "Indices indicating constant parameter must be less than the size "
+      << "of the parameter block.";
+  CHECK(std::adjacent_find(constant.begin(), constant.end()) == constant.end())
+      << "The set of constant parameters cannot contain duplicates";
+  for (int i = 0; i < constant_parameters.size(); ++i) {
+    constancy_mask_[constant_parameters[i]] = 1;
+  }
+}
+
+bool SubsetParameterization::Plus(const double* x,
+                                  const double* delta,
+                                  double* x_plus_delta) const {
+  const int global_size = GlobalSize();
+  for (int i = 0, j = 0; i < global_size; ++i) {
+    if (constancy_mask_[i]) {
+      x_plus_delta[i] = x[i];
+    } else {
+      x_plus_delta[i] = x[i] + delta[j++];
+    }
+  }
+  return true;
+}
+
+bool SubsetParameterization::ComputeJacobian(const double* x,
+                                             double* jacobian) const {
+  if (local_size_ == 0) {
+    return true;
+  }
+
+  const int global_size = GlobalSize();
+  MatrixRef m(jacobian, global_size, local_size_);
+  m.setZero();
+  for (int i = 0, j = 0; i < global_size; ++i) {
+    if (!constancy_mask_[i]) {
+      m(i, j++) = 1.0;
+    }
+  }
+  return true;
+}
+
+bool SubsetParameterization::MultiplyByJacobian(const double* x,
+                                               const int num_rows,
+                                               const double* global_matrix,
+                                               double* local_matrix) const {
+  if (local_size_ == 0) {
+    return true;
+  }
+
+  const int global_size = GlobalSize();
+  for (int row = 0; row < num_rows; ++row) {
+    for (int col = 0, j = 0; col < global_size; ++col) {
+      if (!constancy_mask_[col]) {
+        local_matrix[row * local_size_ + j++] =
+            global_matrix[row * global_size + col];
+      }
+    }
+  }
+  return true;
+}
+
+bool QuaternionParameterization::Plus(const double* x,
+                                      const double* delta,
+                                      double* x_plus_delta) const {
+  const double norm_delta =
+      sqrt(delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2]);
+  if (norm_delta > 0.0) {
+    const double sin_delta_by_delta = (sin(norm_delta) / norm_delta);
+    double q_delta[4];
+    q_delta[0] = cos(norm_delta);
+    q_delta[1] = sin_delta_by_delta * delta[0];
+    q_delta[2] = sin_delta_by_delta * delta[1];
+    q_delta[3] = sin_delta_by_delta * delta[2];
+    QuaternionProduct(q_delta, x, x_plus_delta);
+  } else {
+    for (int i = 0; i < 4; ++i) {
+      x_plus_delta[i] = x[i];
+    }
+  }
+  return true;
+}
+
+bool QuaternionParameterization::ComputeJacobian(const double* x,
+                                                 double* jacobian) const {
+  jacobian[0] = -x[1]; jacobian[1]  = -x[2]; jacobian[2]  = -x[3];  // NOLINT
+  jacobian[3] =  x[0]; jacobian[4]  =  x[3]; jacobian[5]  = -x[2];  // NOLINT
+  jacobian[6] = -x[3]; jacobian[7]  =  x[0]; jacobian[8]  =  x[1];  // NOLINT
+  jacobian[9] =  x[2]; jacobian[10] = -x[1]; jacobian[11] =  x[0];  // NOLINT
+  return true;
+}
+
+bool EigenQuaternionParameterization::Plus(const double* x_ptr,
+                                           const double* delta,
+                                           double* x_plus_delta_ptr) const {
+  Eigen::Map<Eigen::Quaterniond> x_plus_delta(x_plus_delta_ptr);
+  Eigen::Map<const Eigen::Quaterniond> x(x_ptr);
+
+  const double norm_delta =
+      sqrt(delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2]);
+  if (norm_delta > 0.0) {
+    const double sin_delta_by_delta = sin(norm_delta) / norm_delta;
+
+    // Note, in the constructor w is first.
+    Eigen::Quaterniond delta_q(cos(norm_delta),
+                               sin_delta_by_delta * delta[0],
+                               sin_delta_by_delta * delta[1],
+                               sin_delta_by_delta * delta[2]);
+    x_plus_delta = delta_q * x;
+  } else {
+    x_plus_delta = x;
+  }
+
+  return true;
+}
+
+bool EigenQuaternionParameterization::ComputeJacobian(const double* x,
+                                                      double* jacobian) const {
+  jacobian[0] =  x[3]; jacobian[1]  =  x[2]; jacobian[2]  = -x[1];  // NOLINT
+  jacobian[3] = -x[2]; jacobian[4]  =  x[3]; jacobian[5]  =  x[0];  // NOLINT
+  jacobian[6] =  x[1]; jacobian[7]  = -x[0]; jacobian[8]  =  x[3];  // NOLINT
+  jacobian[9] = -x[0]; jacobian[10] = -x[1]; jacobian[11] = -x[2];  // NOLINT
+  return true;
+}
+
+HomogeneousVectorParameterization::HomogeneousVectorParameterization(int size)
+    : size_(size) {
+  CHECK_GT(size_, 1) << "The size of the homogeneous vector needs to be "
+                     << "greater than 1.";
+}
+
+bool HomogeneousVectorParameterization::Plus(const double* x_ptr,
+                                             const double* delta_ptr,
+                                             double* x_plus_delta_ptr) const {
+  ConstVectorRef x(x_ptr, size_);
+  ConstVectorRef delta(delta_ptr, size_ - 1);
+  VectorRef x_plus_delta(x_plus_delta_ptr, size_);
+
+  const double norm_delta = delta.norm();
+
+  if (norm_delta == 0.0) {
+    x_plus_delta = x;
+    return true;
+  }
+
+  // Map the delta from the minimum representation to the over parameterized
+  // homogeneous vector. See section A6.9.2 on page 624 of Hartley & Zisserman
+  // (2nd Edition) for a detailed description.  Note there is a typo on Page
+  // 625, line 4 so check the book errata.
+  const double norm_delta_div_2 = 0.5 * norm_delta;
+  const double sin_delta_by_delta = sin(norm_delta_div_2) /
+      norm_delta_div_2;
+
+  Vector y(size_);
+  y.head(size_ - 1) = 0.5 * sin_delta_by_delta * delta;
+  y(size_ - 1) = cos(norm_delta_div_2);
+
+  Vector v(size_);
+  double beta;
+  internal::ComputeHouseholderVector<double>(x, &v, &beta);
+
+  // Apply the delta update to remain on the unit sphere. See section A6.9.3
+  // on page 625 of Hartley & Zisserman (2nd Edition) for a detailed
+  // description.
+  x_plus_delta = x.norm() * (y -  v * (beta * (v.transpose() * y)));
+
+  return true;
+}
+
+bool HomogeneousVectorParameterization::ComputeJacobian(
+    const double* x_ptr, double* jacobian_ptr) const {
+  ConstVectorRef x(x_ptr, size_);
+  MatrixRef jacobian(jacobian_ptr, size_, size_ - 1);
+
+  Vector v(size_);
+  double beta;
+  internal::ComputeHouseholderVector<double>(x, &v, &beta);
+
+  // The Jacobian is equal to J = 0.5 * H.leftCols(size_ - 1) where H is the
+  // Householder matrix (H = I - beta * v * v').
+  for (int i = 0; i < size_ - 1; ++i) {
+    jacobian.col(i) = -0.5 * beta * v(i) * v;
+    jacobian.col(i)(i) += 0.5;
+  }
+  jacobian *= x.norm();
+
+  return true;
+}
+
+ProductParameterization::ProductParameterization(
+    LocalParameterization* local_param1,
+    LocalParameterization* local_param2) {
+  local_params_.push_back(local_param1);
+  local_params_.push_back(local_param2);
+  Init();
+}
+
+ProductParameterization::ProductParameterization(
+    LocalParameterization* local_param1,
+    LocalParameterization* local_param2,
+    LocalParameterization* local_param3) {
+  local_params_.push_back(local_param1);
+  local_params_.push_back(local_param2);
+  local_params_.push_back(local_param3);
+  Init();
+}
+
+ProductParameterization::ProductParameterization(
+    LocalParameterization* local_param1,
+    LocalParameterization* local_param2,
+    LocalParameterization* local_param3,
+    LocalParameterization* local_param4) {
+  local_params_.push_back(local_param1);
+  local_params_.push_back(local_param2);
+  local_params_.push_back(local_param3);
+  local_params_.push_back(local_param4);
+  Init();
+}
+
+ProductParameterization::~ProductParameterization() {
+  for (int i = 0; i < local_params_.size(); ++i) {
+    delete local_params_[i];
+  }
+}
+
+void ProductParameterization::Init() {
+  global_size_ = 0;
+  local_size_ = 0;
+  buffer_size_ = 0;
+  for (int i = 0; i < local_params_.size(); ++i) {
+    const LocalParameterization* param = local_params_[i];
+    buffer_size_ = std::max(buffer_size_,
+                            param->LocalSize() * param->GlobalSize());
+    global_size_ += param->GlobalSize();
+    local_size_ += param->LocalSize();
+  }
+}
+
+bool ProductParameterization::Plus(const double* x,
+                                   const double* delta,
+                                   double* x_plus_delta) const {
+  int x_cursor = 0;
+  int delta_cursor = 0;
+  for (int i = 0; i < local_params_.size(); ++i) {
+    const LocalParameterization* param = local_params_[i];
+    if (!param->Plus(x + x_cursor,
+                     delta + delta_cursor,
+                     x_plus_delta + x_cursor)) {
+      return false;
+    }
+    delta_cursor += param->LocalSize();
+    x_cursor += param->GlobalSize();
+  }
+
+  return true;
+}
+
+bool ProductParameterization::ComputeJacobian(const double* x,
+                                              double* jacobian_ptr) const {
+  MatrixRef jacobian(jacobian_ptr, GlobalSize(), LocalSize());
+  jacobian.setZero();
+  internal::FixedArray<double> buffer(buffer_size_);
+
+  int x_cursor = 0;
+  int delta_cursor = 0;
+  for (int i = 0; i < local_params_.size(); ++i) {
+    const LocalParameterization* param = local_params_[i];
+    const int local_size = param->LocalSize();
+    const int global_size = param->GlobalSize();
+
+    if (!param->ComputeJacobian(x + x_cursor, buffer.get())) {
+      return false;
+    }
+    jacobian.block(x_cursor, delta_cursor, global_size, local_size)
+        = MatrixRef(buffer.get(), global_size, local_size);
+
+    delta_cursor += local_size;
+    x_cursor += global_size;
+  }
+
+  return true;
+}
+
+}  // namespace ceres