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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2017 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)
+//
+// The National Institute of Standards and Technology has released a
+// set of problems to test non-linear least squares solvers.
+//
+// More information about the background on these problems and
+// suggested evaluation methodology can be found at:
+//
+//   http://www.itl.nist.gov/div898/strd/nls/nls_info.shtml
+//
+// The problem data themselves can be found at
+//
+//   http://www.itl.nist.gov/div898/strd/nls/nls_main.shtml
+//
+// The problems are divided into three levels of difficulty, Easy,
+// Medium and Hard. For each problem there are two starting guesses,
+// the first one far away from the global minimum and the second
+// closer to it.
+//
+// A problem is considered successfully solved, if every components of
+// the solution matches the globally optimal solution in at least 4
+// digits or more.
+//
+// This dataset was used for an evaluation of Non-linear least squares
+// solvers:
+//
+// P. F. Mondragon & B. Borchers, A Comparison of Nonlinear Regression
+// Codes, Journal of Modern Applied Statistical Methods, 4(1):343-351,
+// 2005.
+//
+// The results from Mondragon & Borchers can be summarized as
+//               Excel  Gnuplot  GaussFit  HBN  MinPack
+// Average LRE     2.3      4.3       4.0  6.8      4.4
+//      Winner       1        5        12   29       12
+//
+// Where the row Winner counts, the number of problems for which the
+// solver had the highest LRE.
+
+// In this file, we implement the same evaluation methodology using
+// Ceres. Currently using Levenberg-Marquardt with DENSE_QR, we get
+//
+//               Excel  Gnuplot  GaussFit  HBN  MinPack  Ceres
+// Average LRE     2.3      4.3       4.0  6.8      4.4    9.4
+//      Winner       0        0         5   11        2     41
+
+#include <fstream>
+#include <iostream>
+#include <iterator>
+
+#include "Eigen/Core"
+#include "ceres/ceres.h"
+#include "ceres/tiny_solver.h"
+#include "ceres/tiny_solver_cost_function_adapter.h"
+#include "gflags/gflags.h"
+#include "glog/logging.h"
+
+DEFINE_bool(use_tiny_solver, false, "Use TinySolver instead of Ceres::Solver");
+DEFINE_string(nist_data_dir, "", "Directory containing the NIST non-linear"
+              "regression examples");
+DEFINE_string(minimizer, "trust_region",
+              "Minimizer type to use, choices are: line_search & trust_region");
+DEFINE_string(trust_region_strategy, "levenberg_marquardt",
+              "Options are: levenberg_marquardt, dogleg");
+DEFINE_string(dogleg, "traditional_dogleg",
+              "Options are: traditional_dogleg, subspace_dogleg");
+DEFINE_string(linear_solver, "dense_qr", "Options are: "
+              "sparse_cholesky, dense_qr, dense_normal_cholesky and"
+              "cgnr");
+DEFINE_string(preconditioner, "jacobi", "Options are: "
+              "identity, jacobi");
+DEFINE_string(line_search, "wolfe",
+              "Line search algorithm to use, choices are: armijo and wolfe.");
+DEFINE_string(line_search_direction, "lbfgs",
+              "Line search direction algorithm to use, choices: lbfgs, bfgs");
+DEFINE_int32(max_line_search_iterations, 20,
+             "Maximum number of iterations for each line search.");
+DEFINE_int32(max_line_search_restarts, 10,
+             "Maximum number of restarts of line search direction algorithm.");
+DEFINE_string(line_search_interpolation, "cubic",
+              "Degree of polynomial aproximation in line search, "
+              "choices are: bisection, quadratic & cubic.");
+DEFINE_int32(lbfgs_rank, 20,
+             "Rank of L-BFGS inverse Hessian approximation in line search.");
+DEFINE_bool(approximate_eigenvalue_bfgs_scaling, false,
+            "Use approximate eigenvalue scaling in (L)BFGS line search.");
+DEFINE_double(sufficient_decrease, 1.0e-4,
+              "Line search Armijo sufficient (function) decrease factor.");
+DEFINE_double(sufficient_curvature_decrease, 0.9,
+              "Line search Wolfe sufficient curvature decrease factor.");
+DEFINE_int32(num_iterations, 10000, "Number of iterations");
+DEFINE_bool(nonmonotonic_steps, false, "Trust region algorithm can use"
+            " nonmonotic steps");
+DEFINE_double(initial_trust_region_radius, 1e4, "Initial trust region radius");
+DEFINE_bool(use_numeric_diff, false,
+            "Use numeric differentiation instead of automatic "
+            "differentiation.");
+DEFINE_string(numeric_diff_method, "ridders", "When using numeric "
+              "differentiation, selects algorithm. Options are: central, "
+              "forward, ridders.");
+DEFINE_double(ridders_step_size, 1e-9, "Initial step size for Ridders "
+              "numeric differentiation.");
+DEFINE_int32(ridders_extrapolations, 3, "Maximal number of Ridders "
+             "extrapolations.");
+
+namespace ceres {
+namespace examples {
+
+using Eigen::Dynamic;
+using Eigen::RowMajor;
+typedef Eigen::Matrix<double, Dynamic, 1> Vector;
+typedef Eigen::Matrix<double, Dynamic, Dynamic, RowMajor> Matrix;
+
+using std::atof;
+using std::atoi;
+using std::cout;
+using std::ifstream;
+using std::string;
+using std::vector;
+
+void SplitStringUsingChar(const string& full,
+                          const char delim,
+                          vector<string>* result) {
+  std::back_insert_iterator< vector<string> > it(*result);
+
+  const char* p = full.data();
+  const char* end = p + full.size();
+  while (p != end) {
+    if (*p == delim) {
+      ++p;
+    } else {
+      const char* start = p;
+      while (++p != end && *p != delim) {
+        // Skip to the next occurence of the delimiter.
+      }
+      *it++ = string(start, p - start);
+    }
+  }
+}
+
+bool GetAndSplitLine(ifstream& ifs, vector<string>* pieces) {
+  pieces->clear();
+  char buf[256];
+  ifs.getline(buf, 256);
+  SplitStringUsingChar(string(buf), ' ', pieces);
+  return true;
+}
+
+void SkipLines(ifstream& ifs, int num_lines) {
+  char buf[256];
+  for (int i = 0; i < num_lines; ++i) {
+    ifs.getline(buf, 256);
+  }
+}
+
+class NISTProblem {
+ public:
+  explicit NISTProblem(const string& filename) {
+    ifstream ifs(filename.c_str(), ifstream::in);
+    CHECK(ifs) << "Unable to open : " << filename;
+
+    vector<string> pieces;
+    SkipLines(ifs, 24);
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumResponses = atoi(pieces[1].c_str());
+
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumPredictors = atoi(pieces[0].c_str());
+
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumObservations = atoi(pieces[0].c_str());
+
+    SkipLines(ifs, 4);
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumParameters = atoi(pieces[0].c_str());
+    SkipLines(ifs, 8);
+
+    // Get the first line of initial and final parameter values to
+    // determine the number of tries.
+    GetAndSplitLine(ifs, &pieces);
+    const int kNumTries = pieces.size() - 4;
+
+    predictor_.resize(kNumObservations, kNumPredictors);
+    response_.resize(kNumObservations, kNumResponses);
+    initial_parameters_.resize(kNumTries, kNumParameters);
+    final_parameters_.resize(1, kNumParameters);
+
+    // Parse the line for parameter b1.
+    int parameter_id = 0;
+    for (int i = 0; i < kNumTries; ++i) {
+      initial_parameters_(i, parameter_id) = atof(pieces[i + 2].c_str());
+    }
+    final_parameters_(0, parameter_id) = atof(pieces[2 + kNumTries].c_str());
+
+    // Parse the remaining parameter lines.
+    for (int parameter_id = 1; parameter_id < kNumParameters; ++parameter_id) {
+     GetAndSplitLine(ifs, &pieces);
+     // b2, b3, ....
+     for (int i = 0; i < kNumTries; ++i) {
+       initial_parameters_(i, parameter_id) = atof(pieces[i + 2].c_str());
+     }
+     final_parameters_(0, parameter_id) = atof(pieces[2 + kNumTries].c_str());
+    }
+
+    // Certfied cost
+    SkipLines(ifs, 1);
+    GetAndSplitLine(ifs, &pieces);
+    certified_cost_ = atof(pieces[4].c_str()) / 2.0;
+
+    // Read the observations.
+    SkipLines(ifs, 18 - kNumParameters);
+    for (int i = 0; i < kNumObservations; ++i) {
+      GetAndSplitLine(ifs, &pieces);
+      // Response.
+      for (int j = 0; j < kNumResponses; ++j) {
+        response_(i, j) =  atof(pieces[j].c_str());
+      }
+
+      // Predictor variables.
+      for (int j = 0; j < kNumPredictors; ++j) {
+        predictor_(i, j) =  atof(pieces[j + kNumResponses].c_str());
+      }
+    }
+  }
+
+  Matrix initial_parameters(int start) const { return initial_parameters_.row(start); }  // NOLINT
+  Matrix final_parameters() const  { return final_parameters_; }
+  Matrix predictor()        const { return predictor_;         }
+  Matrix response()         const { return response_;          }
+  int predictor_size()      const { return predictor_.cols();  }
+  int num_observations()    const { return predictor_.rows();  }
+  int response_size()       const { return response_.cols();   }
+  int num_parameters()      const { return initial_parameters_.cols(); }
+  int num_starts()          const { return initial_parameters_.rows(); }
+  double certified_cost()   const { return certified_cost_; }
+
+ private:
+  Matrix predictor_;
+  Matrix response_;
+  Matrix initial_parameters_;
+  Matrix final_parameters_;
+  double certified_cost_;
+};
+
+#define NIST_BEGIN(CostFunctionName)                          \
+  struct CostFunctionName {                                   \
+  CostFunctionName(const double* const x,                     \
+                   const double* const y,                     \
+                   const int n)                               \
+      : x_(x), y_(y), n_(n) {}                                \
+    const double* x_;                                         \
+    const double* y_;                                         \
+    const int n_;                                             \
+    template <typename T>                                     \
+    bool operator()(const T* const b, T* residual) const {    \
+      for (int i = 0; i < n_; ++i) {                          \
+        const T x(x_[i]);                                     \
+        residual[i] = y_[i] - (
+
+#define NIST_END ); } return true; }};
+
+// y = b1 * (b2+x)**(-1/b3)  +  e
+NIST_BEGIN(Bennet5)
+  b[0] * pow(b[1] + x, -1.0 / b[2])
+NIST_END
+
+// y = b1*(1-exp[-b2*x])  +  e
+NIST_BEGIN(BoxBOD)
+  b[0] * (1.0 - exp(-b[1] * x))
+NIST_END
+
+// y = exp[-b1*x]/(b2+b3*x)  +  e
+NIST_BEGIN(Chwirut)
+  exp(-b[0] * x) / (b[1] + b[2] * x)
+NIST_END
+
+// y  = b1*x**b2  +  e
+NIST_BEGIN(DanWood)
+  b[0] * pow(x, b[1])
+NIST_END
+
+// y = b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 )
+//     + b6*exp( -(x-b7)**2 / b8**2 ) + e
+NIST_BEGIN(Gauss)
+  b[0] * exp(-b[1] * x) +
+  b[2] * exp(-pow((x - b[3])/b[4], 2)) +
+  b[5] * exp(-pow((x - b[6])/b[7], 2))
+NIST_END
+
+// y = b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x)  +  e
+NIST_BEGIN(Lanczos)
+  b[0] * exp(-b[1] * x) + b[2] * exp(-b[3] * x) + b[4] * exp(-b[5] * x)
+NIST_END
+
+// y = (b1+b2*x+b3*x**2+b4*x**3) /
+//     (1+b5*x+b6*x**2+b7*x**3)  +  e
+NIST_BEGIN(Hahn1)
+  (b[0] + b[1] * x + b[2] * x * x + b[3] * x * x * x) /
+  (1.0 + b[4] * x + b[5] * x * x + b[6] * x * x * x)
+NIST_END
+
+// y = (b1 + b2*x + b3*x**2) /
+//    (1 + b4*x + b5*x**2)  +  e
+NIST_BEGIN(Kirby2)
+  (b[0] + b[1] * x + b[2] * x * x) /
+  (1.0 + b[3] * x + b[4] * x * x)
+NIST_END
+
+// y = b1*(x**2+x*b2) / (x**2+x*b3+b4)  +  e
+NIST_BEGIN(MGH09)
+  b[0] * (x * x + x * b[1]) / (x * x + x * b[2] + b[3])
+NIST_END
+
+// y = b1 * exp[b2/(x+b3)]  +  e
+NIST_BEGIN(MGH10)
+  b[0] * exp(b[1] / (x + b[2]))
+NIST_END
+
+// y = b1 + b2*exp[-x*b4] + b3*exp[-x*b5]
+NIST_BEGIN(MGH17)
+  b[0] + b[1] * exp(-x * b[3]) + b[2] * exp(-x * b[4])
+NIST_END
+
+// y = b1*(1-exp[-b2*x])  +  e
+NIST_BEGIN(Misra1a)
+  b[0] * (1.0 - exp(-b[1] * x))
+NIST_END
+
+// y = b1 * (1-(1+b2*x/2)**(-2))  +  e
+NIST_BEGIN(Misra1b)
+  b[0] * (1.0 - 1.0/ ((1.0 + b[1] * x / 2.0) * (1.0 + b[1] * x / 2.0)))  // NOLINT
+NIST_END
+
+// y = b1 * (1-(1+2*b2*x)**(-.5))  +  e
+NIST_BEGIN(Misra1c)
+  b[0] * (1.0 - pow(1.0 + 2.0 * b[1] * x, -0.5))
+NIST_END
+
+// y = b1*b2*x*((1+b2*x)**(-1))  +  e
+NIST_BEGIN(Misra1d)
+  b[0] * b[1] * x / (1.0 + b[1] * x)
+NIST_END
+
+const double kPi = 3.141592653589793238462643383279;
+// pi = 3.141592653589793238462643383279E0
+// y =  b1 - b2*x - arctan[b3/(x-b4)]/pi  +  e
+NIST_BEGIN(Roszman1)
+  b[0] - b[1] * x - atan2(b[2], (x - b[3])) / kPi
+NIST_END
+
+// y = b1 / (1+exp[b2-b3*x])  +  e
+NIST_BEGIN(Rat42)
+  b[0] / (1.0 + exp(b[1] - b[2] * x))
+NIST_END
+
+// y = b1 / ((1+exp[b2-b3*x])**(1/b4))  +  e
+NIST_BEGIN(Rat43)
+  b[0] / pow(1.0 + exp(b[1] - b[2] * x), 1.0 / b[3])
+NIST_END
+
+// y = (b1 + b2*x + b3*x**2 + b4*x**3) /
+//    (1 + b5*x + b6*x**2 + b7*x**3)  +  e
+NIST_BEGIN(Thurber)
+  (b[0] + b[1] * x + b[2] * x * x  + b[3] * x * x * x) /
+  (1.0 + b[4] * x + b[5] * x * x + b[6] * x * x * x)
+NIST_END
+
+// y = b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 )
+//        + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 )
+//        + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 )  + e
+NIST_BEGIN(ENSO)
+  b[0] + b[1] * cos(2.0 * kPi * x / 12.0) +
+         b[2] * sin(2.0 * kPi * x / 12.0) +
+         b[4] * cos(2.0 * kPi * x / b[3]) +
+         b[5] * sin(2.0 * kPi * x / b[3]) +
+         b[7] * cos(2.0 * kPi * x / b[6]) +
+         b[8] * sin(2.0 * kPi * x / b[6])
+NIST_END
+
+// y = (b1/b2) * exp[-0.5*((x-b3)/b2)**2]  +  e
+NIST_BEGIN(Eckerle4)
+  b[0] / b[1] * exp(-0.5 * pow((x - b[2])/b[1], 2))
+NIST_END
+
+struct Nelson {
+ public:
+  Nelson(const double* const x, const double* const y, const int n)
+      : x_(x), y_(y), n_(n) {}
+
+  template <typename T>
+  bool operator()(const T* const b, T* residual) const {
+    // log[y] = b1 - b2*x1 * exp[-b3*x2]  +  e
+    for (int i = 0; i < n_; ++i) {
+      residual[i] = log(y_[i]) - (b[0] - b[1] * x_[2 * i] * exp(-b[2] * x_[2 * i + 1]));
+    }
+    return true;
+  }
+
+ private:
+  const double* x_;
+  const double* y_;
+  const int n_;
+};
+
+static void SetNumericDiffOptions(ceres::NumericDiffOptions* options) {
+  options->max_num_ridders_extrapolations = FLAGS_ridders_extrapolations;
+  options->ridders_relative_initial_step_size = FLAGS_ridders_step_size;
+}
+
+void SetMinimizerOptions(ceres::Solver::Options* options) {
+  CHECK(
+      ceres::StringToMinimizerType(FLAGS_minimizer, &options->minimizer_type));
+  CHECK(ceres::StringToLinearSolverType(FLAGS_linear_solver,
+                                        &options->linear_solver_type));
+  CHECK(ceres::StringToPreconditionerType(FLAGS_preconditioner,
+                                          &options->preconditioner_type));
+  CHECK(ceres::StringToTrustRegionStrategyType(
+      FLAGS_trust_region_strategy, &options->trust_region_strategy_type));
+  CHECK(ceres::StringToDoglegType(FLAGS_dogleg, &options->dogleg_type));
+  CHECK(ceres::StringToLineSearchDirectionType(
+      FLAGS_line_search_direction, &options->line_search_direction_type));
+  CHECK(ceres::StringToLineSearchType(FLAGS_line_search,
+                                      &options->line_search_type));
+  CHECK(ceres::StringToLineSearchInterpolationType(
+      FLAGS_line_search_interpolation,
+      &options->line_search_interpolation_type));
+
+  options->max_num_iterations = FLAGS_num_iterations;
+  options->use_nonmonotonic_steps = FLAGS_nonmonotonic_steps;
+  options->initial_trust_region_radius = FLAGS_initial_trust_region_radius;
+  options->max_lbfgs_rank = FLAGS_lbfgs_rank;
+  options->line_search_sufficient_function_decrease = FLAGS_sufficient_decrease;
+  options->line_search_sufficient_curvature_decrease =
+      FLAGS_sufficient_curvature_decrease;
+  options->max_num_line_search_step_size_iterations =
+      FLAGS_max_line_search_iterations;
+  options->max_num_line_search_direction_restarts =
+      FLAGS_max_line_search_restarts;
+  options->use_approximate_eigenvalue_bfgs_scaling =
+      FLAGS_approximate_eigenvalue_bfgs_scaling;
+  options->function_tolerance = std::numeric_limits<double>::epsilon();
+  options->gradient_tolerance = std::numeric_limits<double>::epsilon();
+  options->parameter_tolerance = std::numeric_limits<double>::epsilon();
+}
+
+string JoinPath(const string& dirname, const string& basename) {
+#ifdef _WIN32
+    static const char separator = '\\';
+#else
+    static const char separator = '/';
+#endif  // _WIN32
+
+  if ((!basename.empty() && basename[0] == separator) || dirname.empty()) {
+    return basename;
+  } else if (dirname[dirname.size() - 1] == separator) {
+    return dirname + basename;
+  } else {
+    return dirname + string(&separator, 1) + basename;
+  }
+}
+
+template <typename Model, int num_parameters>
+CostFunction* CreateCostFunction(const Matrix& predictor,
+                                 const Matrix& response,
+                                 const int num_observations) {
+  Model* model =
+      new Model(predictor.data(), response.data(), num_observations);
+  ceres::CostFunction* cost_function = NULL;
+  if (FLAGS_use_numeric_diff) {
+    ceres::NumericDiffOptions options;
+    SetNumericDiffOptions(&options);
+    if (FLAGS_numeric_diff_method == "central") {
+      cost_function = new NumericDiffCostFunction<Model,
+                                                  ceres::CENTRAL,
+                                                  ceres::DYNAMIC,
+                                                  num_parameters>(
+          model,
+          ceres::TAKE_OWNERSHIP,
+          num_observations,
+          options);
+    } else if (FLAGS_numeric_diff_method == "forward") {
+      cost_function = new NumericDiffCostFunction<Model,
+                                                  ceres::FORWARD,
+                                                  ceres::DYNAMIC,
+                                                  num_parameters>(
+          model,
+          ceres::TAKE_OWNERSHIP,
+          num_observations,
+          options);
+    } else if (FLAGS_numeric_diff_method == "ridders") {
+      cost_function = new NumericDiffCostFunction<Model,
+                                                  ceres::RIDDERS,
+                                                  ceres::DYNAMIC,
+                                                  num_parameters>(
+          model,
+          ceres::TAKE_OWNERSHIP,
+          num_observations,
+          options);
+    } else {
+      LOG(ERROR) << "Invalid numeric diff method specified";
+      return 0;
+    }
+  } else {
+    cost_function =
+        new ceres::AutoDiffCostFunction<Model, ceres::DYNAMIC, num_parameters>(
+            model, num_observations);
+  }
+  return cost_function;
+}
+
+double ComputeLRE(const Matrix& expected, const Matrix& actual) {
+  // Compute the LRE by comparing each component of the solution
+  // with the ground truth, and taking the minimum.
+  const double kMaxNumSignificantDigits = 11;
+  double log_relative_error = kMaxNumSignificantDigits + 1;
+  for (int i = 0; i < expected.cols(); ++i) {
+    const double tmp_lre = -std::log10(std::fabs(expected(i) - actual(i)) /
+                                       std::fabs(expected(i)));
+    // The maximum LRE is capped at 11 - the precision at which the
+    // ground truth is known.
+    //
+    // The minimum LRE is capped at 0 - no digits match between the
+    // computed solution and the ground truth.
+    log_relative_error =
+        std::min(log_relative_error,
+                 std::max(0.0, std::min(kMaxNumSignificantDigits, tmp_lre)));
+  }
+  return log_relative_error;
+}
+
+template <typename Model, int num_parameters>
+int RegressionDriver(const string& filename) {
+  NISTProblem nist_problem(JoinPath(FLAGS_nist_data_dir, filename));
+  CHECK_EQ(num_parameters, nist_problem.num_parameters());
+
+  Matrix predictor = nist_problem.predictor();
+  Matrix response = nist_problem.response();
+  Matrix final_parameters = nist_problem.final_parameters();
+
+  printf("%s\n", filename.c_str());
+
+  // Each NIST problem comes with multiple starting points, so we
+  // construct the problem from scratch for each case and solve it.
+  int num_success = 0;
+  for (int start = 0; start < nist_problem.num_starts(); ++start) {
+    Matrix initial_parameters = nist_problem.initial_parameters(start);
+    ceres::CostFunction* cost_function = CreateCostFunction<Model, num_parameters>(
+        predictor, response,  nist_problem.num_observations());
+
+    double initial_cost;
+    double final_cost;
+
+    if (!FLAGS_use_tiny_solver) {
+      ceres::Problem problem;
+      problem.AddResidualBlock(cost_function, NULL, initial_parameters.data());
+      ceres::Solver::Summary summary;
+      ceres::Solver::Options options;
+      SetMinimizerOptions(&options);
+      Solve(options, &problem, &summary);
+      initial_cost = summary.initial_cost;
+      final_cost = summary.final_cost;
+    } else {
+      ceres::TinySolverCostFunctionAdapter<Eigen::Dynamic, num_parameters> cfa(
+          *cost_function);
+      typedef ceres::TinySolver<
+          ceres::TinySolverCostFunctionAdapter<Eigen::Dynamic, num_parameters> >
+          Solver;
+      Solver solver;
+      solver.options.max_num_iterations = FLAGS_num_iterations;
+      solver.options.gradient_tolerance =
+          std::numeric_limits<double>::epsilon();
+      solver.options.parameter_tolerance =
+          std::numeric_limits<double>::epsilon();
+
+      Eigen::Matrix<double, num_parameters, 1> x;
+      x = initial_parameters.transpose();
+      typename Solver::Summary summary = solver.Solve(cfa, &x);
+      initial_parameters = x;
+      initial_cost = summary.initial_cost;
+      final_cost = summary.final_cost;
+      delete cost_function;
+    }
+
+    const double log_relative_error = ComputeLRE(nist_problem.final_parameters(),
+                                                 initial_parameters);
+    const int kMinNumMatchingDigits = 4;
+    if (log_relative_error > kMinNumMatchingDigits) {
+      ++num_success;
+    }
+
+    printf(
+        "start: %d status: %s lre: %4.1f initial cost: %e final cost:%e "
+        "certified cost: %e\n",
+        start + 1,
+        log_relative_error < kMinNumMatchingDigits ? "FAILURE" : "SUCCESS",
+        log_relative_error,
+        initial_cost,
+        final_cost,
+        nist_problem.certified_cost());
+  }
+  return num_success;
+}
+
+
+void SolveNISTProblems() {
+  if (FLAGS_nist_data_dir.empty()) {
+    LOG(FATAL) << "Must specify the directory containing the NIST problems";
+  }
+
+  cout << "Lower Difficulty\n";
+  int easy_success = 0;
+  easy_success += RegressionDriver<Misra1a, 2>("Misra1a.dat");
+  easy_success += RegressionDriver<Chwirut, 3>("Chwirut1.dat");
+  easy_success += RegressionDriver<Chwirut, 3>("Chwirut2.dat");
+  easy_success += RegressionDriver<Lanczos, 6>("Lanczos3.dat");
+  easy_success += RegressionDriver<Gauss, 8>("Gauss1.dat");
+  easy_success += RegressionDriver<Gauss, 8>("Gauss2.dat");
+  easy_success += RegressionDriver<DanWood, 2>("DanWood.dat");
+  easy_success += RegressionDriver<Misra1b, 2>("Misra1b.dat");
+
+  cout << "\nMedium Difficulty\n";
+  int medium_success = 0;
+  medium_success += RegressionDriver<Kirby2, 5>("Kirby2.dat");
+  medium_success += RegressionDriver<Hahn1, 7>("Hahn1.dat");
+  medium_success += RegressionDriver<Nelson, 3>("Nelson.dat");
+  medium_success += RegressionDriver<MGH17, 5>("MGH17.dat");
+  medium_success += RegressionDriver<Lanczos, 6>("Lanczos1.dat");
+  medium_success += RegressionDriver<Lanczos, 6>("Lanczos2.dat");
+  medium_success += RegressionDriver<Gauss, 8>("Gauss3.dat");
+  medium_success += RegressionDriver<Misra1c, 2>("Misra1c.dat");
+  medium_success += RegressionDriver<Misra1d, 2>("Misra1d.dat");
+  medium_success += RegressionDriver<Roszman1, 4>("Roszman1.dat");
+  medium_success += RegressionDriver<ENSO, 9>("ENSO.dat");
+
+  cout << "\nHigher Difficulty\n";
+  int hard_success = 0;
+  hard_success += RegressionDriver<MGH09, 4>("MGH09.dat");
+  hard_success += RegressionDriver<Thurber, 7>("Thurber.dat");
+  hard_success += RegressionDriver<BoxBOD, 2>("BoxBOD.dat");
+  hard_success += RegressionDriver<Rat42, 3>("Rat42.dat");
+  hard_success += RegressionDriver<MGH10, 3>("MGH10.dat");
+  hard_success += RegressionDriver<Eckerle4, 3>("Eckerle4.dat");
+  hard_success += RegressionDriver<Rat43, 4>("Rat43.dat");
+  hard_success += RegressionDriver<Bennet5, 3>("Bennett5.dat");
+
+  cout << "\n";
+  cout << "Easy    : " << easy_success << "/16\n";
+  cout << "Medium  : " << medium_success << "/22\n";
+  cout << "Hard    : " << hard_success << "/16\n";
+  cout << "Total   : " << easy_success + medium_success + hard_success
+       << "/54\n";
+}
+
+}  // namespace examples
+}  // namespace ceres
+
+int main(int argc, char** argv) {
+  CERES_GFLAGS_NAMESPACE::ParseCommandLineFlags(&argc, &argv, true);
+  google::InitGoogleLogging(argv[0]);
+  ceres::examples::SolveNISTProblems();
+  return 0;
+}