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ceres-solver/examples/nist.cc
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Tal Ben-Nun 4f049db7c2 Adaptive numeric differentiation using Ridders' method. 
This method numerically computes function derivatives in different
scales, extrapolating between intermediate results to conserve function
evaluations. Adaptive differentiation is essential to produce accurate
results for functions with noisy derivatives.

Full changelist:
-Created a new type of NumericDiffMethod (RIDDERS).
-Implemented EvaluateRiddersJacobianColumn in NumericDiff.
-Created unit tests with f(x) = x^2 + [random noise] and
 f(x) = exp(x).

Change-Id: I2d6e924d7ff686650272f29a8c981351e6f72091
2015-08-30 14:06:13 +03:00

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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)
//
// 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 <iostream>
#include <iterator>
#include <fstream>
#include "ceres/ceres.h"
#include "gflags/gflags.h"
#include "glog/logging.h"
#include "Eigen/Core"
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);
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) \
: x_(*x), y_(*y) {} \
double x_; \
double y_; \
template <typename T> \
bool operator()(const T* const b, T* residual) const { \
const T y(y_); \
const T x(x_); \
residual[0] = y - (
#define NIST_END ); return true; }};
// y = b1 * (b2+x)**(-1/b3) + e
NIST_BEGIN(Bennet5)
b[0] * pow(b[1] + x, T(-1.0) / b[2])
NIST_END
// y = b1*(1-exp[-b2*x]) + e
NIST_BEGIN(BoxBOD)
b[0] * (T(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) /
(T(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) /
(T(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] * (T(1.0) - exp(-b[1] * x))
NIST_END
// y = b1 * (1-(1+b2*x/2)**(-2)) + e
NIST_BEGIN(Misra1b)
b[0] * (T(1.0) - T(1.0)/ ((T(1.0) + b[1] * x / 2.0) * (T(1.0) + b[1] * x / 2.0))) // NOLINT
NIST_END
// y = b1 * (1-(1+2*b2*x)**(-.5)) + e
NIST_BEGIN(Misra1c)
b[0] * (T(1.0) - pow(T(1.0) + T(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 / (T(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]))/T(kPi)
NIST_END
// y = b1 / (1+exp[b2-b3*x]) + e
NIST_BEGIN(Rat42)
b[0] / (T(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(T(1.0) + exp(b[1] - b[2] * x), T(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) /
(T(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(T(2.0 * kPi) * x / T(12.0)) +
b[2] * sin(T(2.0 * kPi) * x / T(12.0)) +
b[4] * cos(T(2.0 * kPi) * x / b[3]) +
b[5] * sin(T(2.0 * kPi) * x / b[3]) +
b[7] * cos(T(2.0 * kPi) * x / b[6]) +
b[8] * sin(T(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(T(-0.5) * pow((x - b[2])/b[1], 2))
NIST_END
struct Nelson {
public:
Nelson(const double* const x, const double* const y)
: x1_(x[0]), x2_(x[1]), y_(y[0]) {}
template <typename T>
bool operator()(const T* const b, T* residual) const {
// log[y] = b1 - b2*x1 * exp[-b3*x2] + e
residual[0] = T(log(y_)) - (b[0] - b[1] * T(x1_) * exp(-b[2] * T(x2_)));
return true;
}
private:
double x1_;
double x2_;
double y_;
};
static void SetNumericDiffOptions(ceres::NumericDiffOptions* options) {
options->max_num_ridders_extrapolations = FLAGS_ridders_extrapolations;
options->ridders_relative_initial_step_size = FLAGS_ridders_step_size;
}
template <typename Model, int num_residuals, int num_parameters>
int RegressionDriver(const string& filename,
const ceres::Solver::Options& options) {
NISTProblem nist_problem(FLAGS_nist_data_dir + filename);
CHECK_EQ(num_residuals, nist_problem.response_size());
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::Problem problem;
for (int i = 0; i < nist_problem.num_observations(); ++i) {
Model* model = new Model(
predictor.data() + nist_problem.predictor_size() * i,
response.data() + nist_problem.response_size() * i);
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,
num_residuals,
num_parameters>(
model, ceres::TAKE_OWNERSHIP, num_residuals, options);
} else if (FLAGS_numeric_diff_method == "forward") {
cost_function = new NumericDiffCostFunction<Model,
ceres::FORWARD,
num_residuals,
num_parameters>(
model, ceres::TAKE_OWNERSHIP, num_residuals, options);
} else if (FLAGS_numeric_diff_method == "ridders") {
cost_function = new NumericDiffCostFunction<Model,
ceres::RIDDERS,
num_residuals,
num_parameters>(
model, ceres::TAKE_OWNERSHIP, num_residuals, options);
} else {
LOG(ERROR) << "Invalid numeric diff method specified";
return 0;
}
} else {
cost_function =
new ceres::AutoDiffCostFunction<Model,
num_residuals,
num_parameters>(model);
}
problem.AddResidualBlock(cost_function,
NULL,
initial_parameters.data());
}
ceres::Solver::Summary summary;
Solve(options, &problem, &summary);
// Compute the LRE by comparing each component of the solution
// with the ground truth, and taking the minimum.
Matrix final_parameters = nist_problem.final_parameters();
const double kMaxNumSignificantDigits = 11;
double log_relative_error = kMaxNumSignificantDigits + 1;
for (int i = 0; i < num_parameters; ++i) {
const double tmp_lre =
-std::log10(std::fabs(final_parameters(i) - initial_parameters(i)) /
std::fabs(final_parameters(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)));
}
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 total iterations: %d\n",
start + 1,
log_relative_error < kMinNumMatchingDigits ? "FAILURE" : "SUCCESS",
log_relative_error,
summary.initial_cost,
summary.final_cost,
nist_problem.certified_cost(),
(summary.num_successful_steps + summary.num_unsuccessful_steps));
}
return num_success;
}
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 = 1e-18;
options->gradient_tolerance = 1e-18;
options->parameter_tolerance = 1e-18;
}
void SolveNISTProblems() {
if (FLAGS_nist_data_dir.empty()) {
LOG(FATAL) << "Must specify the directory containing the NIST problems";
}
ceres::Solver::Options options;
SetMinimizerOptions(&options);
cout << "Lower Difficulty\n";
int easy_success = 0;
easy_success += RegressionDriver<Misra1a, 1, 2>("Misra1a.dat", options);
easy_success += RegressionDriver<Chwirut, 1, 3>("Chwirut1.dat", options);
easy_success += RegressionDriver<Chwirut, 1, 3>("Chwirut2.dat", options);
easy_success += RegressionDriver<Lanczos, 1, 6>("Lanczos3.dat", options);
easy_success += RegressionDriver<Gauss, 1, 8>("Gauss1.dat", options);
easy_success += RegressionDriver<Gauss, 1, 8>("Gauss2.dat", options);
easy_success += RegressionDriver<DanWood, 1, 2>("DanWood.dat", options);
easy_success += RegressionDriver<Misra1b, 1, 2>("Misra1b.dat", options);
cout << "\nMedium Difficulty\n";
int medium_success = 0;
medium_success += RegressionDriver<Kirby2, 1, 5>("Kirby2.dat", options);
medium_success += RegressionDriver<Hahn1, 1, 7>("Hahn1.dat", options);
medium_success += RegressionDriver<Nelson, 1, 3>("Nelson.dat", options);
medium_success += RegressionDriver<MGH17, 1, 5>("MGH17.dat", options);
medium_success += RegressionDriver<Lanczos, 1, 6>("Lanczos1.dat", options);
medium_success += RegressionDriver<Lanczos, 1, 6>("Lanczos2.dat", options);
medium_success += RegressionDriver<Gauss, 1, 8>("Gauss3.dat", options);
medium_success += RegressionDriver<Misra1c, 1, 2>("Misra1c.dat", options);
medium_success += RegressionDriver<Misra1d, 1, 2>("Misra1d.dat", options);
medium_success += RegressionDriver<Roszman1, 1, 4>("Roszman1.dat", options);
medium_success += RegressionDriver<ENSO, 1, 9>("ENSO.dat", options);
cout << "\nHigher Difficulty\n";
int hard_success = 0;
hard_success += RegressionDriver<MGH09, 1, 4>("MGH09.dat", options);
hard_success += RegressionDriver<Thurber, 1, 7>("Thurber.dat", options);
hard_success += RegressionDriver<BoxBOD, 1, 2>("BoxBOD.dat", options);
hard_success += RegressionDriver<Rat42, 1, 3>("Rat42.dat", options);
hard_success += RegressionDriver<MGH10, 1, 3>("MGH10.dat", options);
hard_success += RegressionDriver<Eckerle4, 1, 3>("Eckerle4.dat", options);
hard_success += RegressionDriver<Rat43, 1, 4>("Rat43.dat", options);
hard_success += RegressionDriver<Bennet5, 1, 3>("Bennett5.dat", options);
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;
}
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