diff --git a/internal/ceres/line_search.cc b/internal/ceres/line_search.cc
new file mode 100644
index 0000000..352c64f
--- /dev/null
+++ b/internal/ceres/line_search.cc
@@ -0,0 +1,878 @@
+// 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/line_search.h"
+
+#include <algorithm>
+#include <cmath>
+#include <iomanip>
+#include <iostream>  // NOLINT
+
+#include "ceres/evaluator.h"
+#include "ceres/function_sample.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/map_util.h"
+#include "ceres/polynomial.h"
+#include "ceres/stringprintf.h"
+#include "ceres/wall_time.h"
+#include "glog/logging.h"
+
+namespace ceres {
+namespace internal {
+
+using std::map;
+using std::ostream;
+using std::string;
+using std::vector;
+
+namespace {
+// Precision used for floating point values in error message output.
+const int kErrorMessageNumericPrecision = 8;
+}  // namespace
+
+ostream& operator<<(ostream &os, const FunctionSample& sample);
+
+// Convenience stream operator for pushing FunctionSamples into log messages.
+ostream& operator<<(ostream &os, const FunctionSample& sample) {
+  os << sample.ToDebugString();
+  return os;
+}
+
+LineSearch::LineSearch(const LineSearch::Options& options)
+    : options_(options) {}
+
+LineSearch* LineSearch::Create(const LineSearchType line_search_type,
+                               const LineSearch::Options& options,
+                               string* error) {
+  LineSearch* line_search = NULL;
+  switch (line_search_type) {
+  case ceres::ARMIJO:
+    line_search = new ArmijoLineSearch(options);
+    break;
+  case ceres::WOLFE:
+    line_search = new WolfeLineSearch(options);
+    break;
+  default:
+    *error = string("Invalid line search algorithm type: ") +
+        LineSearchTypeToString(line_search_type) +
+        string(", unable to create line search.");
+    return NULL;
+  }
+  return line_search;
+}
+
+LineSearchFunction::LineSearchFunction(Evaluator* evaluator)
+    : evaluator_(evaluator),
+      position_(evaluator->NumParameters()),
+      direction_(evaluator->NumEffectiveParameters()),
+      scaled_direction_(evaluator->NumEffectiveParameters()),
+      initial_evaluator_residual_time_in_seconds(0.0),
+      initial_evaluator_jacobian_time_in_seconds(0.0) {}
+
+void LineSearchFunction::Init(const Vector& position,
+                              const Vector& direction) {
+  position_ = position;
+  direction_ = direction;
+}
+
+void LineSearchFunction::Evaluate(const double x,
+                                  const bool evaluate_gradient,
+                                  FunctionSample* output) {
+  output->x = x;
+  output->vector_x_is_valid = false;
+  output->value_is_valid = false;
+  output->gradient_is_valid = false;
+  output->vector_gradient_is_valid = false;
+
+  scaled_direction_ = output->x * direction_;
+  output->vector_x.resize(position_.rows(), 1);
+  if (!evaluator_->Plus(position_.data(),
+                        scaled_direction_.data(),
+                        output->vector_x.data())) {
+    return;
+  }
+  output->vector_x_is_valid = true;
+
+  double* gradient = NULL;
+  if (evaluate_gradient) {
+    output->vector_gradient.resize(direction_.rows(), 1);
+    gradient = output->vector_gradient.data();
+  }
+  const bool eval_status = evaluator_->Evaluate(
+      output->vector_x.data(), &(output->value), NULL, gradient, NULL);
+
+  if (!eval_status || !std::isfinite(output->value)) {
+    return;
+  }
+
+  output->value_is_valid = true;
+  if (!evaluate_gradient) {
+    return;
+  }
+
+  output->gradient = direction_.dot(output->vector_gradient);
+  if (!std::isfinite(output->gradient)) {
+    return;
+  }
+
+  output->gradient_is_valid = true;
+  output->vector_gradient_is_valid = true;
+}
+
+double LineSearchFunction::DirectionInfinityNorm() const {
+  return direction_.lpNorm<Eigen::Infinity>();
+}
+
+void LineSearchFunction::ResetTimeStatistics() {
+  const map<string, CallStatistics> evaluator_statistics =
+      evaluator_->Statistics();
+
+  initial_evaluator_residual_time_in_seconds =
+      FindWithDefault(
+          evaluator_statistics, "Evaluator::Residual", CallStatistics())
+          .time;
+  initial_evaluator_jacobian_time_in_seconds =
+      FindWithDefault(
+          evaluator_statistics, "Evaluator::Jacobian", CallStatistics())
+          .time;
+}
+
+void LineSearchFunction::TimeStatistics(
+    double* cost_evaluation_time_in_seconds,
+    double* gradient_evaluation_time_in_seconds) const {
+  const map<string, CallStatistics> evaluator_time_statistics =
+      evaluator_->Statistics();
+  *cost_evaluation_time_in_seconds =
+      FindWithDefault(
+          evaluator_time_statistics, "Evaluator::Residual", CallStatistics())
+          .time -
+      initial_evaluator_residual_time_in_seconds;
+  // Strictly speaking this will slightly underestimate the time spent
+  // evaluating the gradient of the line search univariate cost function as it
+  // does not count the time spent performing the dot product with the direction
+  // vector.  However, this will typically be small by comparison, and also
+  // allows direct subtraction of the timing information from the totals for
+  // the evaluator returned in the solver summary.
+  *gradient_evaluation_time_in_seconds =
+      FindWithDefault(
+          evaluator_time_statistics, "Evaluator::Jacobian", CallStatistics())
+          .time -
+      initial_evaluator_jacobian_time_in_seconds;
+}
+
+void LineSearch::Search(double step_size_estimate,
+                        double initial_cost,
+                        double initial_gradient,
+                        Summary* summary) const {
+  const double start_time = WallTimeInSeconds();
+  CHECK(summary != nullptr);
+  *summary = LineSearch::Summary();
+
+  summary->cost_evaluation_time_in_seconds = 0.0;
+  summary->gradient_evaluation_time_in_seconds = 0.0;
+  summary->polynomial_minimization_time_in_seconds = 0.0;
+  options().function->ResetTimeStatistics();
+  this->DoSearch(step_size_estimate, initial_cost, initial_gradient, summary);
+  options().function->
+      TimeStatistics(&summary->cost_evaluation_time_in_seconds,
+                     &summary->gradient_evaluation_time_in_seconds);
+
+  summary->total_time_in_seconds = WallTimeInSeconds() - start_time;
+}
+
+// Returns step_size \in [min_step_size, max_step_size] which minimizes the
+// polynomial of degree defined by interpolation_type which interpolates all
+// of the provided samples with valid values.
+double LineSearch::InterpolatingPolynomialMinimizingStepSize(
+    const LineSearchInterpolationType& interpolation_type,
+    const FunctionSample& lowerbound,
+    const FunctionSample& previous,
+    const FunctionSample& current,
+    const double min_step_size,
+    const double max_step_size) const {
+  if (!current.value_is_valid ||
+      (interpolation_type == BISECTION &&
+       max_step_size <= current.x)) {
+    // Either: sample is invalid; or we are using BISECTION and contracting
+    // the step size.
+    return std::min(std::max(current.x * 0.5, min_step_size), max_step_size);
+  } else if (interpolation_type == BISECTION) {
+    CHECK_GT(max_step_size, current.x);
+    // We are expanding the search (during a Wolfe bracketing phase) using
+    // BISECTION interpolation.  Using BISECTION when trying to expand is
+    // strictly speaking an oxymoron, but we define this to mean always taking
+    // the maximum step size so that the Armijo & Wolfe implementations are
+    // agnostic to the interpolation type.
+    return max_step_size;
+  }
+  // Only check if lower-bound is valid here, where it is required
+  // to avoid replicating current.value_is_valid == false
+  // behaviour in WolfeLineSearch.
+  CHECK(lowerbound.value_is_valid)
+      << std::scientific << std::setprecision(kErrorMessageNumericPrecision)
+      << "Ceres bug: lower-bound sample for interpolation is invalid, "
+      << "please contact the developers!, interpolation_type: "
+      << LineSearchInterpolationTypeToString(interpolation_type)
+      << ", lowerbound: " << lowerbound << ", previous: " << previous
+      << ", current: " << current;
+
+  // Select step size by interpolating the function and gradient values
+  // and minimizing the corresponding polynomial.
+  vector<FunctionSample> samples;
+  samples.push_back(lowerbound);
+
+  if (interpolation_type == QUADRATIC) {
+    // Two point interpolation using function values and the
+    // gradient at the lower bound.
+    samples.push_back(FunctionSample(current.x, current.value));
+
+    if (previous.value_is_valid) {
+      // Three point interpolation, using function values and the
+      // gradient at the lower bound.
+      samples.push_back(FunctionSample(previous.x, previous.value));
+    }
+  } else if (interpolation_type == CUBIC) {
+    // Two point interpolation using the function values and the gradients.
+    samples.push_back(current);
+
+    if (previous.value_is_valid) {
+      // Three point interpolation using the function values and
+      // the gradients.
+      samples.push_back(previous);
+    }
+  } else {
+    LOG(FATAL) << "Ceres bug: No handler for interpolation_type: "
+               << LineSearchInterpolationTypeToString(interpolation_type)
+               << ", please contact the developers!";
+  }
+
+  double step_size = 0.0, unused_min_value = 0.0;
+  MinimizeInterpolatingPolynomial(samples, min_step_size, max_step_size,
+                                  &step_size, &unused_min_value);
+  return step_size;
+}
+
+ArmijoLineSearch::ArmijoLineSearch(const LineSearch::Options& options)
+    : LineSearch(options) {}
+
+void ArmijoLineSearch::DoSearch(const double step_size_estimate,
+                                const double initial_cost,
+                                const double initial_gradient,
+                                Summary* summary) const {
+  CHECK_GE(step_size_estimate, 0.0);
+  CHECK_GT(options().sufficient_decrease, 0.0);
+  CHECK_LT(options().sufficient_decrease, 1.0);
+  CHECK_GT(options().max_num_iterations, 0);
+  LineSearchFunction* function = options().function;
+
+  // Note initial_cost & initial_gradient are evaluated at step_size = 0,
+  // not step_size_estimate, which is our starting guess.
+  FunctionSample initial_position(0.0, initial_cost, initial_gradient);
+  initial_position.vector_x = function->position();
+  initial_position.vector_x_is_valid = true;
+
+  const double descent_direction_max_norm = function->DirectionInfinityNorm();
+  FunctionSample previous;
+  FunctionSample current;
+
+  // As the Armijo line search algorithm always uses the initial point, for
+  // which both the function value and derivative are known, when fitting a
+  // minimizing polynomial, we can fit up to a quadratic without requiring the
+  // gradient at the current query point.
+  const bool kEvaluateGradient = options().interpolation_type == CUBIC;
+
+  ++summary->num_function_evaluations;
+  if (kEvaluateGradient) {
+    ++summary->num_gradient_evaluations;
+  }
+
+  function->Evaluate(step_size_estimate, kEvaluateGradient, &current);
+  while (!current.value_is_valid ||
+         current.value > (initial_cost
+                          + options().sufficient_decrease
+                          * initial_gradient
+                          * current.x)) {
+    // If current.value_is_valid is false, we treat it as if the cost at that
+    // point is not large enough to satisfy the sufficient decrease condition.
+    ++summary->num_iterations;
+    if (summary->num_iterations >= options().max_num_iterations) {
+      summary->error =
+          StringPrintf("Line search failed: Armijo failed to find a point "
+                       "satisfying the sufficient decrease condition within "
+                       "specified max_num_iterations: %d.",
+                       options().max_num_iterations);
+      LOG_IF(WARNING, !options().is_silent) << summary->error;
+      return;
+    }
+
+    const double polynomial_minimization_start_time = WallTimeInSeconds();
+    const double step_size =
+        this->InterpolatingPolynomialMinimizingStepSize(
+            options().interpolation_type,
+            initial_position,
+            previous,
+            current,
+            (options().max_step_contraction * current.x),
+            (options().min_step_contraction * current.x));
+    summary->polynomial_minimization_time_in_seconds +=
+        (WallTimeInSeconds() - polynomial_minimization_start_time);
+
+    if (step_size * descent_direction_max_norm < options().min_step_size) {
+      summary->error =
+          StringPrintf("Line search failed: step_size too small: %.5e "
+                       "with descent_direction_max_norm: %.5e.", step_size,
+                       descent_direction_max_norm);
+      LOG_IF(WARNING, !options().is_silent) << summary->error;
+      return;
+    }
+
+    previous = current;
+
+    ++summary->num_function_evaluations;
+    if (kEvaluateGradient) {
+      ++summary->num_gradient_evaluations;
+    }
+
+    function->Evaluate(step_size, kEvaluateGradient, &current);
+  }
+
+  summary->optimal_point = current;
+  summary->success = true;
+}
+
+WolfeLineSearch::WolfeLineSearch(const LineSearch::Options& options)
+    : LineSearch(options) {}
+
+void WolfeLineSearch::DoSearch(const double step_size_estimate,
+                               const double initial_cost,
+                               const double initial_gradient,
+                               Summary* summary) const {
+  // All parameters should have been validated by the Solver, but as
+  // invalid values would produce crazy nonsense, hard check them here.
+  CHECK_GE(step_size_estimate, 0.0);
+  CHECK_GT(options().sufficient_decrease, 0.0);
+  CHECK_GT(options().sufficient_curvature_decrease,
+           options().sufficient_decrease);
+  CHECK_LT(options().sufficient_curvature_decrease, 1.0);
+  CHECK_GT(options().max_step_expansion, 1.0);
+
+  // Note initial_cost & initial_gradient are evaluated at step_size = 0,
+  // not step_size_estimate, which is our starting guess.
+  FunctionSample initial_position(0.0, initial_cost, initial_gradient);
+  initial_position.vector_x = options().function->position();
+  initial_position.vector_x_is_valid = true;
+  bool do_zoom_search = false;
+  // Important: The high/low in bracket_high & bracket_low refer to their
+  // _function_ values, not their step sizes i.e. it is _not_ required that
+  // bracket_low.x < bracket_high.x.
+  FunctionSample solution, bracket_low, bracket_high;
+
+  // Wolfe bracketing phase: Increases step_size until either it finds a point
+  // that satisfies the (strong) Wolfe conditions, or an interval that brackets
+  // step sizes which satisfy the conditions.  From Nocedal & Wright [1] p61 the
+  // interval: (step_size_{k-1}, step_size_{k}) contains step lengths satisfying
+  // the strong Wolfe conditions if one of the following conditions are met:
+  //
+  //   1. step_size_{k} violates the sufficient decrease (Armijo) condition.
+  //   2. f(step_size_{k}) >= f(step_size_{k-1}).
+  //   3. f'(step_size_{k}) >= 0.
+  //
+  // Caveat: If f(step_size_{k}) is invalid, then step_size is reduced, ignoring
+  // this special case, step_size monotonically increases during bracketing.
+  if (!this->BracketingPhase(initial_position,
+                             step_size_estimate,
+                             &bracket_low,
+                             &bracket_high,
+                             &do_zoom_search,
+                             summary)) {
+    // Failed to find either a valid point, a valid bracket satisfying the Wolfe
+    // conditions, or even a step size > minimum tolerance satisfying the Armijo
+    // condition.
+    return;
+  }
+
+  if (!do_zoom_search) {
+    // Either: Bracketing phase already found a point satisfying the strong
+    // Wolfe conditions, thus no Zoom required.
+    //
+    // Or: Bracketing failed to find a valid bracket or a point satisfying the
+    // strong Wolfe conditions within max_num_iterations, or whilst searching
+    // shrank the bracket width until it was below our minimum tolerance.
+    // As these are 'artificial' constraints, and we would otherwise fail to
+    // produce a valid point when ArmijoLineSearch would succeed, we return the
+    // point with the lowest cost found thus far which satsifies the Armijo
+    // condition (but not the Wolfe conditions).
+    summary->optimal_point = bracket_low;
+    summary->success = true;
+    return;
+  }
+
+  VLOG(3) << std::scientific << std::setprecision(kErrorMessageNumericPrecision)
+          << "Starting line search zoom phase with bracket_low: "
+          << bracket_low << ", bracket_high: " << bracket_high
+          << ", bracket width: " << fabs(bracket_low.x - bracket_high.x)
+          << ", bracket abs delta cost: "
+          << fabs(bracket_low.value - bracket_high.value);
+
+  // Wolfe Zoom phase: Called when the Bracketing phase finds an interval of
+  // non-zero, finite width that should bracket step sizes which satisfy the
+  // (strong) Wolfe conditions (before finding a step size that satisfies the
+  // conditions).  Zoom successively decreases the size of the interval until a
+  // step size which satisfies the Wolfe conditions is found.  The interval is
+  // defined by bracket_low & bracket_high, which satisfy:
+  //
+  //   1. The interval bounded by step sizes: bracket_low.x & bracket_high.x
+  //      contains step sizes that satsify the strong Wolfe conditions.
+  //   2. bracket_low.x is of all the step sizes evaluated *which satisifed the
+  //      Armijo sufficient decrease condition*, the one which generated the
+  //      smallest function value, i.e. bracket_low.value <
+  //      f(all other steps satisfying Armijo).
+  //        - Note that this does _not_ (necessarily) mean that initially
+  //          bracket_low.value < bracket_high.value (although this is typical)
+  //          e.g. when bracket_low = initial_position, and bracket_high is the
+  //          first sample, and which does not satisfy the Armijo condition,
+  //          but still has bracket_high.value < initial_position.value.
+  //   3. bracket_high is chosen after bracket_low, s.t.
+  //      bracket_low.gradient * (bracket_high.x - bracket_low.x) < 0.
+  if (!this->ZoomPhase(initial_position,
+                       bracket_low,
+                       bracket_high,
+                       &solution,
+                       summary) && !solution.value_is_valid) {
+    // Failed to find a valid point (given the specified decrease parameters)
+    // within the specified bracket.
+    return;
+  }
+  // Ensure that if we ran out of iterations whilst zooming the bracket, or
+  // shrank the bracket width to < tolerance and failed to find a point which
+  // satisfies the strong Wolfe curvature condition, that we return the point
+  // amongst those found thus far, which minimizes f() and satisfies the Armijo
+  // condition.
+
+  if (!solution.value_is_valid || solution.value > bracket_low.value) {
+    summary->optimal_point = bracket_low;
+  } else {
+    summary->optimal_point = solution;
+  }
+
+  summary->success = true;
+}
+
+// Returns true if either:
+//
+// A termination condition satisfying the (strong) Wolfe bracketing conditions
+// is found:
+//
+// - A valid point, defined as a bracket of zero width [zoom not required].
+// - A valid bracket (of width > tolerance), [zoom required].
+//
+// Or, searching was stopped due to an 'artificial' constraint, i.e. not
+// a condition imposed / required by the underlying algorithm, but instead an
+// engineering / implementation consideration. But a step which exceeds the
+// minimum step size, and satsifies the Armijo condition was still found,
+// and should thus be used [zoom not required].
+//
+// Returns false if no step size > minimum step size was found which
+// satisfies at least the Armijo condition.
+bool WolfeLineSearch::BracketingPhase(
+    const FunctionSample& initial_position,
+    const double step_size_estimate,
+    FunctionSample* bracket_low,
+    FunctionSample* bracket_high,
+    bool* do_zoom_search,
+    Summary* summary) const {
+  LineSearchFunction* function = options().function;
+
+  FunctionSample previous = initial_position;
+  FunctionSample current;
+
+  const double descent_direction_max_norm =
+      function->DirectionInfinityNorm();
+
+  *do_zoom_search = false;
+  *bracket_low = initial_position;
+
+  // As we require the gradient to evaluate the Wolfe condition, we always
+  // calculate it together with the value, irrespective of the interpolation
+  // type.  As opposed to only calculating the gradient after the Armijo
+  // condition is satisifed, as the computational saving from this approach
+  // would be slight (perhaps even negative due to the extra call).  Also,
+  // always calculating the value & gradient together protects against us
+  // reporting invalid solutions if the cost function returns slightly different
+  // function values when evaluated with / without gradients (due to numerical
+  // issues).
+  ++summary->num_function_evaluations;
+  ++summary->num_gradient_evaluations;
+  const bool kEvaluateGradient = true;
+  function->Evaluate(step_size_estimate, kEvaluateGradient, &current);
+  while (true) {
+    ++summary->num_iterations;
+
+    if (current.value_is_valid &&
+        (current.value > (initial_position.value
+                          + options().sufficient_decrease
+                          * initial_position.gradient
+                          * current.x) ||
+         (previous.value_is_valid && current.value > previous.value))) {
+      // Bracket found: current step size violates Armijo sufficient decrease
+      // condition, or has stepped past an inflection point of f() relative to
+      // previous step size.
+      *do_zoom_search = true;
+      *bracket_low = previous;
+      *bracket_high = current;
+      VLOG(3) << std::scientific
+              << std::setprecision(kErrorMessageNumericPrecision)
+              << "Bracket found: current step (" << current.x
+              << ") violates Armijo sufficient condition, or has passed an "
+              << "inflection point of f() based on value.";
+      break;
+    }
+
+    if (current.value_is_valid &&
+        fabs(current.gradient) <=
+        -options().sufficient_curvature_decrease * initial_position.gradient) {
+      // Current step size satisfies the strong Wolfe conditions, and is thus a
+      // valid termination point, therefore a Zoom not required.
+      *bracket_low = current;
+      *bracket_high = current;
+      VLOG(3) << std::scientific
+              << std::setprecision(kErrorMessageNumericPrecision)
+              << "Bracketing phase found step size: " << current.x
+              << ", satisfying strong Wolfe conditions, initial_position: "
+              << initial_position << ", current: " << current;
+      break;
+
+    } else if (current.value_is_valid && current.gradient >= 0) {
+      // Bracket found: current step size has stepped past an inflection point
+      // of f(), but Armijo sufficient decrease is still satisfied and
+      // f(current) is our best minimum thus far.  Remember step size
+      // monotonically increases, thus previous_step_size < current_step_size
+      // even though f(previous) > f(current).
+      *do_zoom_search = true;
+      // Note inverse ordering from first bracket case.
+      *bracket_low = current;
+      *bracket_high = previous;
+      VLOG(3) << "Bracket found: current step (" << current.x
+              << ") satisfies Armijo, but has gradient >= 0, thus have passed "
+              << "an inflection point of f().";
+      break;
+
+    } else if (current.value_is_valid &&
+               fabs(current.x - previous.x) * descent_direction_max_norm
+               < options().min_step_size) {
+      // We have shrunk the search bracket to a width less than our tolerance,
+      // and still not found either a point satisfying the strong Wolfe
+      // conditions, or a valid bracket containing such a point. Stop searching
+      // and set bracket_low to the size size amongst all those tested which
+      // minimizes f() and satisfies the Armijo condition.
+      LOG_IF(WARNING, !options().is_silent)
+          << "Line search failed: Wolfe bracketing phase shrank "
+          << "bracket width: " << fabs(current.x - previous.x)
+          <<  ", to < tolerance: " << options().min_step_size
+          << ", with descent_direction_max_norm: "
+          << descent_direction_max_norm << ", and failed to find "
+          << "a point satisfying the strong Wolfe conditions or a "
+          << "bracketing containing such a point. Accepting "
+          << "point found satisfying Armijo condition only, to "
+          << "allow continuation.";
+      *bracket_low = current;
+      break;
+
+    } else if (summary->num_iterations >= options().max_num_iterations) {
+      // Check num iterations bound here so that we always evaluate the
+      // max_num_iterations-th iteration against all conditions, and
+      // then perform no additional (unused) evaluations.
+      summary->error =
+          StringPrintf("Line search failed: Wolfe bracketing phase failed to "
+                       "find a point satisfying strong Wolfe conditions, or a "
+                       "bracket containing such a point within specified "
+                       "max_num_iterations: %d", options().max_num_iterations);
+      LOG_IF(WARNING, !options().is_silent) << summary->error;
+      // Ensure that bracket_low is always set to the step size amongst all
+      // those tested which minimizes f() and satisfies the Armijo condition
+      // when we terminate due to the 'artificial' max_num_iterations condition.
+      *bracket_low =
+          current.value_is_valid && current.value < bracket_low->value
+          ? current : *bracket_low;
+      break;
+    }
+    // Either: f(current) is invalid; or, f(current) is valid, but does not
+    // satisfy the strong Wolfe conditions itself, or the conditions for
+    // being a boundary of a bracket.
+
+    // If f(current) is valid, (but meets no criteria) expand the search by
+    // increasing the step size.  If f(current) is invalid, contract the step
+    // size.
+    //
+    // In Nocedal & Wright [1] (p60), the step-size can only increase in the
+    // bracketing phase: step_size_{k+1} \in [step_size_k, step_size_k * factor].
+    // However this does not account for the function returning invalid values
+    // which we support, in which case we need to contract the step size whilst
+    // ensuring that we do not invert the bracket, i.e, we require that:
+    // step_size_{k-1} <= step_size_{k+1} < step_size_k.
+    const double min_step_size =
+        current.value_is_valid
+        ? current.x : previous.x;
+    const double max_step_size =
+        current.value_is_valid
+        ? (current.x * options().max_step_expansion) : current.x;
+
+    // We are performing 2-point interpolation only here, but the API of
+    // InterpolatingPolynomialMinimizingStepSize() allows for up to
+    // 3-point interpolation, so pad call with a sample with an invalid
+    // value that will therefore be ignored.
+    const FunctionSample unused_previous;
+    DCHECK(!unused_previous.value_is_valid);
+    // Contracts step size if f(current) is not valid.
+    const double polynomial_minimization_start_time = WallTimeInSeconds();
+    const double step_size =
+        this->InterpolatingPolynomialMinimizingStepSize(
+            options().interpolation_type,
+            previous,
+            unused_previous,
+            current,
+            min_step_size,
+            max_step_size);
+    summary->polynomial_minimization_time_in_seconds +=
+        (WallTimeInSeconds() - polynomial_minimization_start_time);
+    if (step_size * descent_direction_max_norm < options().min_step_size) {
+      summary->error =
+          StringPrintf("Line search failed: step_size too small: %.5e "
+                       "with descent_direction_max_norm: %.5e", step_size,
+                       descent_direction_max_norm);
+      LOG_IF(WARNING, !options().is_silent) << summary->error;
+      return false;
+    }
+
+    // Only advance the lower boundary (in x) of the bracket if f(current)
+    // is valid such that we can support contracting the step size when
+    // f(current) is invalid without risking inverting the bracket in x, i.e.
+    // prevent previous.x > current.x.
+    previous = current.value_is_valid ? current : previous;
+    ++summary->num_function_evaluations;
+    ++summary->num_gradient_evaluations;
+    function->Evaluate(step_size, kEvaluateGradient, &current);
+  }
+
+  // Ensure that even if a valid bracket was found, we will only mark a zoom
+  // as required if the bracket's width is greater than our minimum tolerance.
+  if (*do_zoom_search &&
+      fabs(bracket_high->x - bracket_low->x) * descent_direction_max_norm
+      < options().min_step_size) {
+    *do_zoom_search = false;
+  }
+
+  return true;
+}
+
+// Returns true iff solution satisfies the strong Wolfe conditions. Otherwise,
+// on return false, if we stopped searching due to the 'artificial' condition of
+// reaching max_num_iterations, solution is the step size amongst all those
+// tested, which satisfied the Armijo decrease condition and minimized f().
+bool WolfeLineSearch::ZoomPhase(const FunctionSample& initial_position,
+                                FunctionSample bracket_low,
+                                FunctionSample bracket_high,
+                                FunctionSample* solution,
+                                Summary* summary) const {
+  LineSearchFunction* function = options().function;
+
+  CHECK(bracket_low.value_is_valid && bracket_low.gradient_is_valid)
+      << std::scientific << std::setprecision(kErrorMessageNumericPrecision)
+      << "Ceres bug: f_low input to Wolfe Zoom invalid, please contact "
+      << "the developers!, initial_position: " << initial_position
+      << ", bracket_low: " << bracket_low
+      << ", bracket_high: "<< bracket_high;
+  // We do not require bracket_high.gradient_is_valid as the gradient condition
+  // for a valid bracket is only dependent upon bracket_low.gradient, and
+  // in order to minimize jacobian evaluations, bracket_high.gradient may
+  // not have been calculated (if bracket_high.value does not satisfy the
+  // Armijo sufficient decrease condition and interpolation method does not
+  // require it).
+  //
+  // We also do not require that: bracket_low.value < bracket_high.value,
+  // although this is typical. This is to deal with the case when
+  // bracket_low = initial_position, bracket_high is the first sample,
+  // and bracket_high does not satisfy the Armijo condition, but still has
+  // bracket_high.value < initial_position.value.
+  CHECK(bracket_high.value_is_valid)
+      << std::scientific << std::setprecision(kErrorMessageNumericPrecision)
+      << "Ceres bug: f_high input to Wolfe Zoom invalid, please "
+      << "contact the developers!, initial_position: " << initial_position
+      << ", bracket_low: " << bracket_low
+      << ", bracket_high: "<< bracket_high;
+
+  if (bracket_low.gradient * (bracket_high.x - bracket_low.x) >= 0) {
+    // The third condition for a valid initial bracket:
+    //
+    //   3. bracket_high is chosen after bracket_low, s.t.
+    //      bracket_low.gradient * (bracket_high.x - bracket_low.x) < 0.
+    //
+    // is not satisfied.  As this can happen when the users' cost function
+    // returns inconsistent gradient values relative to the function values,
+    // we do not CHECK_LT(), but we do stop processing and return an invalid
+    // value.
+    summary->error =
+        StringPrintf("Line search failed: Wolfe zoom phase passed a bracket "
+                     "which does not satisfy: bracket_low.gradient * "
+                     "(bracket_high.x - bracket_low.x) < 0 [%.8e !< 0] "
+                     "with initial_position: %s, bracket_low: %s, bracket_high:"
+                     " %s, the most likely cause of which is the cost function "
+                     "returning inconsistent gradient & function values.",
+                     bracket_low.gradient * (bracket_high.x - bracket_low.x),
+                     initial_position.ToDebugString().c_str(),
+                     bracket_low.ToDebugString().c_str(),
+                     bracket_high.ToDebugString().c_str());
+    LOG_IF(WARNING, !options().is_silent) << summary->error;
+    solution->value_is_valid = false;
+    return false;
+  }
+
+  const int num_bracketing_iterations = summary->num_iterations;
+  const double descent_direction_max_norm = function->DirectionInfinityNorm();
+
+  while (true) {
+    // Set solution to bracket_low, as it is our best step size (smallest f())
+    // found thus far and satisfies the Armijo condition, even though it does
+    // not satisfy the Wolfe condition.
+    *solution = bracket_low;
+    if (summary->num_iterations >= options().max_num_iterations) {
+      summary->error =
+          StringPrintf("Line search failed: Wolfe zoom phase failed to "
+                       "find a point satisfying strong Wolfe conditions "
+                       "within specified max_num_iterations: %d, "
+                       "(num iterations taken for bracketing: %d).",
+                       options().max_num_iterations, num_bracketing_iterations);
+      LOG_IF(WARNING, !options().is_silent) << summary->error;
+      return false;
+    }
+    if (fabs(bracket_high.x - bracket_low.x) * descent_direction_max_norm
+        < options().min_step_size) {
+      // Bracket width has been reduced below tolerance, and no point satisfying
+      // the strong Wolfe conditions has been found.
+      summary->error =
+          StringPrintf("Line search failed: Wolfe zoom bracket width: %.5e "
+                       "too small with descent_direction_max_norm: %.5e.",
+                       fabs(bracket_high.x - bracket_low.x),
+                       descent_direction_max_norm);
+      LOG_IF(WARNING, !options().is_silent) << summary->error;
+      return false;
+    }
+
+    ++summary->num_iterations;
+    // Polynomial interpolation requires inputs ordered according to step size,
+    // not f(step size).
+    const FunctionSample& lower_bound_step =
+        bracket_low.x < bracket_high.x ? bracket_low : bracket_high;
+    const FunctionSample& upper_bound_step =
+        bracket_low.x < bracket_high.x ? bracket_high : bracket_low;
+    // We are performing 2-point interpolation only here, but the API of
+    // InterpolatingPolynomialMinimizingStepSize() allows for up to
+    // 3-point interpolation, so pad call with a sample with an invalid
+    // value that will therefore be ignored.
+    const FunctionSample unused_previous;
+    DCHECK(!unused_previous.value_is_valid);
+    const double polynomial_minimization_start_time = WallTimeInSeconds();
+    const double step_size =
+        this->InterpolatingPolynomialMinimizingStepSize(
+            options().interpolation_type,
+            lower_bound_step,
+            unused_previous,
+            upper_bound_step,
+            lower_bound_step.x,
+            upper_bound_step.x);
+    summary->polynomial_minimization_time_in_seconds +=
+        (WallTimeInSeconds() - polynomial_minimization_start_time);
+    // No check on magnitude of step size being too small here as it is
+    // lower-bounded by the initial bracket start point, which was valid.
+    //
+    // As we require the gradient to evaluate the Wolfe condition, we always
+    // calculate it together with the value, irrespective of the interpolation
+    // type.  As opposed to only calculating the gradient after the Armijo
+    // condition is satisifed, as the computational saving from this approach
+    // would be slight (perhaps even negative due to the extra call).  Also,
+    // always calculating the value & gradient together protects against us
+    // reporting invalid solutions if the cost function returns slightly
+    // different function values when evaluated with / without gradients (due
+    // to numerical issues).
+    ++summary->num_function_evaluations;
+    ++summary->num_gradient_evaluations;
+    const bool kEvaluateGradient = true;
+    function->Evaluate(step_size, kEvaluateGradient, solution);
+    if (!solution->value_is_valid || !solution->gradient_is_valid) {
+      summary->error =
+          StringPrintf("Line search failed: Wolfe Zoom phase found "
+                       "step_size: %.5e, for which function is invalid, "
+                       "between low_step: %.5e and high_step: %.5e "
+                       "at which function is valid.",
+                       solution->x, bracket_low.x, bracket_high.x);
+      LOG_IF(WARNING, !options().is_silent) << summary->error;
+      return false;
+    }
+
+    VLOG(3) << "Zoom iteration: "
+            << summary->num_iterations - num_bracketing_iterations
+            << ", bracket_low: " << bracket_low
+            << ", bracket_high: " << bracket_high
+            << ", minimizing solution: " << *solution;
+
+    if ((solution->value > (initial_position.value
+                            + options().sufficient_decrease
+                            * initial_position.gradient
+                            * solution->x)) ||
+        (solution->value >= bracket_low.value)) {
+      // Armijo sufficient decrease not satisfied, or not better
+      // than current lowest sample, use as new upper bound.
+      bracket_high = *solution;
+      continue;
+    }
+
+    // Armijo sufficient decrease satisfied, check strong Wolfe condition.
+    if (fabs(solution->gradient) <=
+        -options().sufficient_curvature_decrease * initial_position.gradient) {
+      // Found a valid termination point satisfying strong Wolfe conditions.
+      VLOG(3) << std::scientific
+              << std::setprecision(kErrorMessageNumericPrecision)
+              << "Zoom phase found step size: " << solution->x
+              << ", satisfying strong Wolfe conditions.";
+      break;
+
+    } else if (solution->gradient * (bracket_high.x - bracket_low.x) >= 0) {
+      bracket_high = bracket_low;
+    }
+
+    bracket_low = *solution;
+  }
+  // Solution contains a valid point which satisfies the strong Wolfe
+  // conditions.
+  return true;
+}
+
+}  // namespace internal
+}  // namespace ceres