Example code for cubic interpolation.
Example code demonstrates how a sampled function can be
minimized. Also, in the process uncovered some deficiencies
in the CubicInterpolator and BicubicInterpolator interfaces and
fixed them.
Change-Id: I18c8f670fbee076bf1e94d1f45c7477fd71640e8
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index 62df0c0..cd53a1c 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -65,10 +65,12 @@
ADD_EXECUTABLE(robust_curve_fitting robust_curve_fitting.cc)
TARGET_LINK_LIBRARIES(robust_curve_fitting ceres)
-ADD_EXECUTABLE(simple_bundle_adjuster
- simple_bundle_adjuster.cc)
+ADD_EXECUTABLE(simple_bundle_adjuster simple_bundle_adjuster.cc)
TARGET_LINK_LIBRARIES(simple_bundle_adjuster ceres)
+ADD_EXECUTABLE(sampled_function sampled_function.cc)
+TARGET_LINK_LIBRARIES(sampled_function ceres)
+
IF (GFLAGS)
# The CERES_GFLAGS_NAMESPACE compile definition is NOT stored in
# CERES_COMPILE_OPTIONS (and thus config.h) as Ceres itself does not
diff --git a/examples/sampled_function.cc b/examples/sampled_function.cc
new file mode 100644
index 0000000..700ef6d
--- /dev/null
+++ b/examples/sampled_function.cc
@@ -0,0 +1,88 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2014 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+//
+// A simple example of optimizing a sampled function by using cubic
+// interpolation.
+
+#include "ceres/ceres.h"
+#include "ceres/cubic_interpolation.h"
+#include "glog/logging.h"
+
+using ceres::CubicInterpolator;
+using ceres::AutoDiffCostFunction;
+using ceres::CostFunction;
+using ceres::Problem;
+using ceres::Solver;
+using ceres::Solve;
+
+// A simple cost functor that interfaces an interpolated table of
+// values with automatic differentiation.
+struct InterpolatedCostFunctor {
+ explicit InterpolatedCostFunctor(const CubicInterpolator& interpolator)
+ : interpolator_(interpolator) {
+ }
+
+ template<typename T> bool operator()(const T* x, T* residuals) const {
+ return interpolator_.Evaluate(*x, residuals);
+ }
+
+ static CostFunction* Create(const CubicInterpolator& interpolator) {
+ return new AutoDiffCostFunction<InterpolatedCostFunctor, 1, 1>(
+ new InterpolatedCostFunctor(interpolator));
+ }
+
+ private:
+ const CubicInterpolator& interpolator_;
+};
+
+int main(int argc, char** argv) {
+ google::InitGoogleLogging(argv[0]);
+
+ // Evaluate the function f(x) = (x - 4.5)^2;
+ const int kNumSamples = 10;
+ double values[kNumSamples];
+ for (int i = 0; i < 10; ++i) {
+ values[i] = (i - 4.5) * (i - 4.5);
+ }
+
+ CubicInterpolator interpolator(values, kNumSamples);
+
+ double x = 1.0;
+ Problem problem;
+ CostFunction* cost_function = InterpolatedCostFunctor::Create(interpolator);
+ problem.AddResidualBlock(cost_function, NULL, &x);
+
+ Solver::Options options;
+ options.minimizer_progress_to_stdout = true;
+ Solver::Summary summary;
+ Solve(options, &problem, &summary);
+ std::cout << summary.BriefReport() << "\n";
+ return 0;
+}
diff --git a/include/ceres/cubic_interpolation.h b/include/ceres/cubic_interpolation.h
index 2ade679..7e477c8 100644
--- a/include/ceres/cubic_interpolation.h
+++ b/include/ceres/cubic_interpolation.h
@@ -70,7 +70,13 @@
// derivative. Returns false if x is out of bounds.
bool Evaluate(double x, double* f, double* dfdx) const;
- // Overload for Jets, which automatically accounts for the chain rule.
+ // The following two Evaluate overloads are needed for interfacing
+ // with automatic differentiation. The first is for when a scalar
+ // evaluation is done, and the second one is for when Jets are used.
+ bool Evaluate(const double& x, double* f) const {
+ return Evaluate(x, f, NULL);
+ }
+
template<typename JetT> bool Evaluate(const JetT& x, JetT* f) const {
double dfdx;
if (!Evaluate(x.a, &f->a, &dfdx)) {
@@ -117,7 +123,13 @@
bool Evaluate(double r, double c,
double* f, double* dfdr, double* dfdc) const;
- // Overload for Jets, which automatically accounts for the chain rule.
+ // The following two Evaluate overloads are needed for interfacing
+ // with automatic differentiation. The first is for when a scalar
+ // evaluation is done, and the second one is for when Jets are used.
+ bool Evaluate(const double& r, const double& c, double* f) const {
+ return Evaluate(r, c, f, NULL, NULL);
+ }
+
template<typename JetT> bool Evaluate(const JetT& r,
const JetT& c,
JetT* f) const {
