NumericDiffFunctor.
A wrapper class that takes a variadic functor evaluating a
function, numerically differentiates it and makes it available as a
templated functor so that it can be easily used as part of Ceres'
automatic differentiation framework.
The tests for NumericDiffCostFunction and NumericDiffFunctor have
a lot of stuff that is common, so refactor them to reduce code.
Change-Id: I83b01e58b05e575fb2530d15cbd611928298646a
diff --git a/include/ceres/numeric_diff_functor.h b/include/ceres/numeric_diff_functor.h
new file mode 100644
index 0000000..14adbed
--- /dev/null
+++ b/include/ceres/numeric_diff_functor.h
@@ -0,0 +1,341 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 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 wrapper class that takes a variadic functor evaluating a
+// function, numerically differentiates it and makes it available as a
+// templated functor so that it can be easily used as part of Ceres'
+// automatic differentiation framework.
+//
+// For example:
+//
+// For example, let us assume that
+//
+// struct IntrinsicProjection
+// IntrinsicProjection(const double* observations);
+// bool operator()(const double* calibration,
+// const double* point,
+// double* residuals);
+// };
+//
+// is a functor that implements the projection of a point in its local
+// coordinate system onto its image plane and subtracts it from the
+// observed point projection.
+//
+// Now we would like to compose the action of this functor with the
+// action of camera extrinsics, i.e., rotation and translation, which
+// is given by the following templated function
+//
+// template<typename T>
+// void RotateAndTranslatePoint(const T* rotation,
+// const T* translation,
+// const T* point,
+// T* result);
+//
+// To compose the extrinsics and intrinsics, we can construct a
+// CameraProjection functor as follows.
+//
+// struct CameraProjection {
+// typedef NumericDiffFunctor<IntrinsicProjection, CENTRAL, 2, 5, 3>
+// IntrinsicProjectionFunctor;
+//
+// CameraProjection(double* observation) {
+// intrinsic_projection_.reset(
+// new IntrinsicProjectionFunctor(observation)) {
+// }
+//
+// template <typename T>
+// bool operator(const T* rotation,
+// const T* translation,
+// const T* intrinsics,
+// const T* point,
+// T* residuals) const {
+// T transformed_point[3];
+// RotateAndTranslatePoint(rotation, translation, point, transformed_point);
+// return (*intrinsic_projection_)(intrinsics, transformed_point, residual);
+// }
+//
+// private:
+// scoped_ptr<IntrinsicProjectionFunctor> intrinsic_projection_;
+// };
+//
+// Here, we made the choice of using CENTRAL differences to compute
+// the jacobian of IntrinsicProjection.
+//
+// Now, we are ready to construct an automatically differentiated cost
+// function as
+//
+// CostFunction* cost_function =
+// new AutoDiffCostFunction<CameraProjection, 2, 3, 3, 5>(
+// new CameraProjection(observations));
+//
+// cost_function now seamlessly integrates automatic differentiation
+// of RotateAndTranslatePoint with a numerically differentiated
+// version of IntrinsicProjection.
+
+#include "ceres/numeric_diff_cost_function.h"
+#include "ceres/types.h"
+#include "ceres/cost_function_to_functor.h"
+
+namespace ceres {
+
+template<typename Functor,
+ NumericDiffMethod kMethod = CENTRAL,
+ int kNumResiduals = 0,
+ int N0 = 0, int N1 = 0 , int N2 = 0, int N3 = 0, int N4 = 0,
+ int N5 = 0, int N6 = 0 , int N7 = 0, int N8 = 0, int N9 = 0>
+class NumericDiffFunctor {
+ public:
+ // relative_step_size controls the step size used by the numeric
+ // differentiation process.
+ NumericDiffFunctor(double relative_step_size = 1e-6)
+ : functor_(new NumericDiffCostFunction<Functor,
+ kMethod,
+ kNumResiduals,
+ N0, N1, N2, N3, N4,
+ N5, N6, N7, N8, N9>(
+ new Functor, relative_step_size)) {
+ }
+
+ NumericDiffFunctor(Functor* functor, double relative_step_size = 1e-6)
+ : functor_(new NumericDiffCostFunction<Functor,
+ kMethod,
+ kNumResiduals,
+ N0, N1, N2, N3, N4,
+ N5, N6, N7, N8, N9>(
+ functor, relative_step_size)) {
+ }
+
+ bool operator()(const double* x0, double* residuals) const {
+ functor_(x0, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ double* residuals) const {
+ return functor_(x0, x1, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ double* residuals) const {
+ return functor_(x0, x1, x2, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ const double* x3,
+ double* residuals) const {
+ return functor_(x0, x1, x2, x3, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ const double* x3,
+ const double* x4,
+ double* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ const double* x3,
+ const double* x4,
+ const double* x5,
+ double* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ const double* x3,
+ const double* x4,
+ const double* x5,
+ const double* x6,
+ double* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ const double* x3,
+ const double* x4,
+ const double* x5,
+ const double* x6,
+ const double* x7,
+ double* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, x7, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ const double* x3,
+ const double* x4,
+ const double* x5,
+ const double* x6,
+ const double* x7,
+ const double* x8,
+ double* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, x7, x8, residuals);
+ }
+
+ bool operator()(const double* x0,
+ const double* x1,
+ const double* x2,
+ const double* x3,
+ const double* x4,
+ const double* x5,
+ const double* x6,
+ const double* x7,
+ const double* x8,
+ const double* x9,
+ double* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0, T* residuals) const {
+ functor_(x0, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ T* residuals) const {
+ return functor_(x0, x1, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ T* residuals) const {
+ return functor_(x0, x1, x2, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ T* residuals) const {
+ return functor_(x0, x1, x2, x3, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ T* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ T* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ T* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ const T* x7,
+ T* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, x7, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ const T* x7,
+ const T* x8,
+ T* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, x7, x8, residuals);
+ }
+
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ const T* x7,
+ const T* x8,
+ const T* x9,
+ T* residuals) const {
+ return functor_(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, residuals);
+ }
+
+
+ private:
+ CostFunctionToFunctor<kNumResiduals,
+ N0, N1, N2, N3, N4,
+ N5, N6, N7, N8, N9> functor_;
+
+};
+
+} // namespace ceres
diff --git a/internal/ceres/CMakeLists.txt b/internal/ceres/CMakeLists.txt
index 193dd63..f9329e9 100644
--- a/internal/ceres/CMakeLists.txt
+++ b/internal/ceres/CMakeLists.txt
@@ -201,7 +201,7 @@
IF (${BUILD_TESTING} AND ${GFLAGS})
ADD_LIBRARY(gtest gmock_gtest_all.cc gmock_main.cc)
- ADD_LIBRARY(test_util test_util.cc)
+ ADD_LIBRARY(test_util test_util.cc numeric_diff_test_utils.cc)
TARGET_LINK_LIBRARIES(gtest ${GFLAGS_LIB} ${GLOG_LIB})
MACRO (CERES_TEST NAME)
@@ -240,6 +240,7 @@
CERES_TEST(minimizer)
CERES_TEST(normal_prior)
CERES_TEST(numeric_diff_cost_function)
+ CERES_TEST(numeric_diff_functor)
CERES_TEST(ordered_groups)
CERES_TEST(parameter_block)
CERES_TEST(parameter_block_ordering)
diff --git a/internal/ceres/numeric_diff_cost_function_test.cc b/internal/ceres/numeric_diff_cost_function_test.cc
index 296cc22..3953ded 100644
--- a/internal/ceres/numeric_diff_cost_function_test.cc
+++ b/internal/ceres/numeric_diff_cost_function_test.cc
@@ -36,8 +36,7 @@
#include <vector>
#include "ceres/internal/macros.h"
#include "ceres/internal/scoped_ptr.h"
-#include "ceres/sized_cost_function.h"
-#include "ceres/stringprintf.h"
+#include "ceres/numeric_diff_test_utils.h"
#include "ceres/test_util.h"
#include "ceres/types.h"
#include "glog/logging.h"
@@ -46,223 +45,109 @@
namespace ceres {
namespace internal {
-// y1 = x1'x2 -> dy1/dx1 = x2, dy1/dx2 = x1
-// y2 = (x1'x2)^2 -> dy2/dx1 = 2 * x2 * (x1'x2), dy2/dx2 = 2 * x1 * (x1'x2)
-// y3 = x2'x2 -> dy3/dx1 = 0, dy3/dx2 = 2 * x2
-struct EasyFunctor {
- bool operator()(const double* x1, const double* x2, double* residuals) const {
- residuals[0] = residuals[1] = residuals[2] = 0;
- for (int i = 0; i < 5; ++i) {
- residuals[0] += x1[i] * x2[i];
- residuals[2] += x2[i] * x2[i];
- }
- residuals[1] = residuals[0] * residuals[0];
- return true;
- }
-};
+TEST(NumericDiffCostFunction, EasyCaseFunctorCentralDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
+ new NumericDiffCostFunction<EasyFunctor,
+ CENTRAL,
+ 3, /* number of residuals */
+ 5, /* size of x1 */
+ 5 /* size of x2 */>(
+ new EasyFunctor));
+ EasyFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+}
-class EasyCostFunction : public SizedCostFunction<3, 5, 5> {
- public:
- virtual bool Evaluate(double const* const* parameters,
- double* residuals,
- double** jacobians) const {
- (void) jacobians; // Ignored.
- return EasyFunctor()(parameters[0], parameters[1], residuals);
- }
-};
+TEST(NumericDiffCostFunction, EasyCaseFunctorForwardDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
+ new NumericDiffCostFunction<EasyFunctor,
+ FORWARD,
+ 3, /* number of residuals */
+ 5, /* size of x1 */
+ 5 /* size of x2 */>(
+ new EasyFunctor));
+ EasyFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
+}
-TEST(NumericDiffCostFunction, EasyCase) {
- // Try both central and forward difference.
- internal::scoped_ptr<CostFunction> cfs[4];
- cfs[0].reset(
+TEST(NumericDiffCostFunction, EasyCaseCostFunctionCentralDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
new NumericDiffCostFunction<EasyCostFunction,
CENTRAL,
3, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
new EasyCostFunction, TAKE_OWNERSHIP));
+ EasyFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+}
- cfs[1].reset(
+TEST(NumericDiffCostFunction, EasyCaseCostFunctionForwardDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
new NumericDiffCostFunction<EasyCostFunction,
FORWARD,
3, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
new EasyCostFunction, TAKE_OWNERSHIP));
-
- cfs[2].reset(
- new NumericDiffCostFunction< EasyFunctor,
- CENTRAL,
- 3, /* number of residuals */
- 5, /* size of x1 */
- 5 /* size of x2 */>(
- new EasyFunctor));
-
- cfs[3].reset(
- new NumericDiffCostFunction< EasyFunctor,
- FORWARD,
- 3, /* number of residuals */
- 5, /* size of x1 */
- 5 /* size of x2 */>(
- new EasyFunctor));
-
-
- for (int c = 0; c < 4; ++c) {
- CostFunction *cost_function = cfs[c].get();
-
- double x1[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
- double x2[] = { 9.0, 9.0, 5.0, 5.0, 1.0 };
- double *parameters[] = { &x1[0], &x2[0] };
-
- double dydx1[15]; // 3 x 5, row major.
- double dydx2[15]; // 3 x 5, row major.
- double *jacobians[2] = { &dydx1[0], &dydx2[0] };
-
- double residuals[3] = {-1e-100, -2e-100, -3e-100 };
-
- ASSERT_TRUE(cost_function->Evaluate(¶meters[0],
- &residuals[0],
- &jacobians[0]));
-
- EXPECT_EQ(residuals[0], 67);
- EXPECT_EQ(residuals[1], 4489);
- EXPECT_EQ(residuals[2], 213);
-
- for (int i = 0; i < 5; ++i) {
- LOG(INFO) << "c = " << c << " i = " << i;
- const double kEps = c == 0 ? /* central */ 3e-9 : /* forward */ 2e-5;
-
- ExpectClose(x2[i], dydx1[5 * 0 + i], kEps); // y1
- ExpectClose(x1[i], dydx2[5 * 0 + i], kEps);
- ExpectClose(2 * x2[i] * residuals[0], dydx1[5 * 1 + i], kEps); // y2
- ExpectClose(2 * x1[i] * residuals[0], dydx2[5 * 1 + i], kEps);
- ExpectClose(0.0, dydx1[5 * 2 + i], kEps); // y3
- ExpectClose(2 * x2[i], dydx2[5 * 2 + i], kEps);
- }
- }
+ EasyFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
-// y1 = sin(x1'x2)
-// y2 = exp(-x1'x2 / 10)
-//
-// dy1/dx1 = x2 * cos(x1'x2), dy1/dx2 = x1 * cos(x1'x2)
-// dy2/dx1 = -x2 * exp(-x1'x2 / 10) / 10, dy2/dx2 = -x2 * exp(-x1'x2 / 10) / 10
-struct TranscendentalFunctor {
- bool operator()(const double* x1, const double* x2, double* residuals) const {
- double x1x2 = 0;
- for (int i = 0; i < 5; ++i) {
- x1x2 += x1[i] * x2[i];
- }
- residuals[0] = sin(x1x2);
- residuals[1] = exp(-x1x2 / 10);
- return true;
- }
-};
-
-class TranscendentalTestCostFunction : public SizedCostFunction<2, 5, 5> {
- public:
- virtual bool Evaluate(double const* const* parameters,
- double* residuals,
- double** jacobians) const {
- (void) jacobians; // Ignored.
- return TranscendentalFunctor()(parameters[0], parameters[1], residuals);
- }
-};
-
-TEST(NumericDiffCostFunction, TransendentalOperationsInCostFunction) {
- // Try both central and forward difference.
- internal::scoped_ptr<CostFunction> cfs[4];
- cfs[0].reset(
- new NumericDiffCostFunction<TranscendentalTestCostFunction,
- CENTRAL,
- 2, /* number of residuals */
- 5, /* size of x1 */
- 5 /* size of x2 */>(
- new TranscendentalTestCostFunction, TAKE_OWNERSHIP));
-
- cfs[1].reset(
- new NumericDiffCostFunction<TranscendentalTestCostFunction,
- FORWARD,
- 2, /* number of residuals */
- 5, /* size of x1 */
- 5 /* size of x2 */>(
- new TranscendentalTestCostFunction, TAKE_OWNERSHIP));
-
- cfs[2].reset(
+TEST(NumericDiffCostFunction, TranscendentalCaseFunctorCentralDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
new NumericDiffCostFunction<TranscendentalFunctor,
CENTRAL,
2, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
- new TranscendentalFunctor));
+ new TranscendentalFunctor));
+ TranscendentalFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+}
- cfs[3].reset(
+TEST(NumericDiffCostFunction, TranscendentalCaseFunctorForwardDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
new NumericDiffCostFunction<TranscendentalFunctor,
FORWARD,
2, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
- new TranscendentalFunctor));
-
- for (int c = 0; c < 4; ++c) {
- CostFunction *cost_function = cfs[c].get();
-
- struct {
- double x1[5];
- double x2[5];
- } kTests[] = {
- { { 1.0, 2.0, 3.0, 4.0, 5.0 }, // No zeros.
- { 9.0, 9.0, 5.0, 5.0, 1.0 },
- },
- { { 0.0, 2.0, 3.0, 0.0, 5.0 }, // Some zeros x1.
- { 9.0, 9.0, 5.0, 5.0, 1.0 },
- },
- { { 1.0, 2.0, 3.0, 1.0, 5.0 }, // Some zeros x2.
- { 0.0, 9.0, 0.0, 5.0, 0.0 },
- },
- { { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros x1.
- { 9.0, 9.0, 5.0, 5.0, 1.0 },
- },
- { { 1.0, 2.0, 3.0, 4.0, 5.0 }, // All zeros x2.
- { 0.0, 0.0, 0.0, 0.0, 0.0 },
- },
- { { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros.
- { 0.0, 0.0, 0.0, 0.0, 0.0 },
- },
- };
- for (int k = 0; k < CERES_ARRAYSIZE(kTests); ++k) {
- double *x1 = &(kTests[k].x1[0]);
- double *x2 = &(kTests[k].x2[0]);
- double *parameters[] = { x1, x2 };
-
- double dydx1[10];
- double dydx2[10];
- double *jacobians[2] = { &dydx1[0], &dydx2[0] };
-
- double residuals[2];
-
- ASSERT_TRUE(cost_function->Evaluate(¶meters[0],
- &residuals[0],
- &jacobians[0]));
- LOG(INFO) << "Ran evaluate for test k=" << k << " c=" << c;
-
- double x1x2 = 0;
- for (int i = 0; i < 5; ++i) {
- x1x2 += x1[i] * x2[i];
- }
-
- for (int i = 0; i < 5; ++i) {
- const double kEps = c == 0 ? /* central */ 3e-9 : /* forward */ 2e-5;
-
- ExpectClose( x2[i] * cos(x1x2), dydx1[5 * 0 + i], kEps);
- ExpectClose( x1[i] * cos(x1x2), dydx2[5 * 0 + i], kEps);
- ExpectClose(-x2[i] * exp(-x1x2 / 10.) / 10., dydx1[5 * 1 + i], kEps);
- ExpectClose(-x1[i] * exp(-x1x2 / 10.) / 10., dydx2[5 * 1 + i], kEps);
- }
- }
- }
+ new TranscendentalFunctor));
+ TranscendentalFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
+TEST(NumericDiffCostFunction, TranscendentalCaseCostFunctionCentralDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
+ new NumericDiffCostFunction<TranscendentalCostFunction,
+ CENTRAL,
+ 2, /* number of residuals */
+ 5, /* size of x1 */
+ 5 /* size of x2 */>(
+ new TranscendentalCostFunction, TAKE_OWNERSHIP));
+ TranscendentalFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+}
+
+TEST(NumericDiffCostFunction, TranscendentalCaseCostFunctionForwardDifferences) {
+ internal::scoped_ptr<CostFunction> cost_function;
+ cost_function.reset(
+ new NumericDiffCostFunction<TranscendentalCostFunction,
+ FORWARD,
+ 2, /* number of residuals */
+ 5, /* size of x1 */
+ 5 /* size of x2 */>(
+ new TranscendentalCostFunction, TAKE_OWNERSHIP));
+ TranscendentalFunctor functor;
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
+}
template<int num_rows, int num_cols>
class SizeTestingCostFunction : public SizedCostFunction<num_rows, num_cols> {
diff --git a/internal/ceres/numeric_diff_functor_test.cc b/internal/ceres/numeric_diff_functor_test.cc
new file mode 100644
index 0000000..a37ceaf
--- /dev/null
+++ b/internal/ceres/numeric_diff_functor_test.cc
@@ -0,0 +1,123 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 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)
+
+#include "ceres/numeric_diff_functor.h"
+
+#include <algorithm>
+#include <cmath>
+#include <string>
+#include <vector>
+#include "ceres/autodiff_cost_function.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/numeric_diff_test_utils.h"
+#include "ceres/test_util.h"
+#include "ceres/types.h"
+#include "glog/logging.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+TEST(NumericDiffCostFunction, EasyCaseCentralDifferences) {
+ typedef NumericDiffFunctor<EasyFunctor, CENTRAL, 3, 5, 5> NumericDiffEasyFunctor;
+
+ internal::scoped_ptr<CostFunction> cost_function;
+ EasyFunctor functor;
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffEasyFunctor, 3, 5, 5>(
+ new NumericDiffEasyFunctor));
+
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffEasyFunctor, 3, 5, 5>(
+ new NumericDiffEasyFunctor(new EasyFunctor)));
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+}
+
+TEST(NumericDiffCostFunction, EasyCaseForwardDifferences) {
+ typedef NumericDiffFunctor<EasyFunctor, FORWARD, 3, 5, 5> NumericDiffEasyFunctor;
+
+ internal::scoped_ptr<CostFunction> cost_function;
+ EasyFunctor functor;
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffEasyFunctor, 3, 5, 5>(
+ new NumericDiffEasyFunctor));
+
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffEasyFunctor, 3, 5, 5>(
+ new NumericDiffEasyFunctor(new EasyFunctor)));
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
+}
+
+TEST(NumericDiffCostFunction, TranscendentalCaseCentralDifferences) {
+ typedef NumericDiffFunctor<TranscendentalFunctor, CENTRAL, 2, 5, 5>
+ NumericDiffTranscendentalFunctor;
+
+ internal::scoped_ptr<CostFunction> cost_function;
+ TranscendentalFunctor functor;
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffTranscendentalFunctor, 2, 5, 5>(
+ new NumericDiffTranscendentalFunctor));
+
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffTranscendentalFunctor, 2, 5, 5>(
+ new NumericDiffTranscendentalFunctor(new TranscendentalFunctor)));
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
+}
+
+TEST(NumericDiffCostFunction, TranscendentalCaseForwardDifferences) {
+ typedef NumericDiffFunctor<TranscendentalFunctor, FORWARD, 2, 5, 5>
+ NumericDiffTranscendentalFunctor;
+
+ internal::scoped_ptr<CostFunction> cost_function;
+ TranscendentalFunctor functor;
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffTranscendentalFunctor, 2, 5, 5>(
+ new NumericDiffTranscendentalFunctor));
+
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
+
+ cost_function.reset(
+ new AutoDiffCostFunction<NumericDiffTranscendentalFunctor, 2, 5, 5>(
+ new NumericDiffTranscendentalFunctor(new TranscendentalFunctor)));
+ functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
+}
+
+} // namespace internal
+} // namespace ceres
diff --git a/internal/ceres/numeric_diff_test_utils.cc b/internal/ceres/numeric_diff_test_utils.cc
new file mode 100644
index 0000000..6786ac9
--- /dev/null
+++ b/internal/ceres/numeric_diff_test_utils.cc
@@ -0,0 +1,130 @@
+#include "ceres/numeric_diff_test_utils.h"
+
+#include <algorithm>
+#include <cmath>
+#include "ceres/cost_function.h"
+#include "ceres/internal/macros.h"
+#include "ceres/test_util.h"
+#include "ceres/types.h"
+#include "gtest/gtest.h"
+
+
+namespace ceres {
+namespace internal {
+
+bool EasyFunctor::operator()(const double* x1,
+ const double* x2,
+ double* residuals) const {
+ residuals[0] = residuals[1] = residuals[2] = 0;
+ for (int i = 0; i < 5; ++i) {
+ residuals[0] += x1[i] * x2[i];
+ residuals[2] += x2[i] * x2[i];
+ }
+ residuals[1] = residuals[0] * residuals[0];
+ return true;
+}
+
+void EasyFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function,
+ NumericDiffMethod method) const {
+ double x1[] = { 1.0, 2.0, 3.0, 4.0, 5.0 };
+ double x2[] = { 9.0, 9.0, 5.0, 5.0, 1.0 };
+ double *parameters[] = { &x1[0], &x2[0] };
+
+ double dydx1[15]; // 3 x 5, row major.
+ double dydx2[15]; // 3 x 5, row major.
+ double *jacobians[2] = { &dydx1[0], &dydx2[0] };
+
+ double residuals[3] = {-1e-100, -2e-100, -3e-100 };
+
+ ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
+ &residuals[0],
+ &jacobians[0]));
+
+ EXPECT_EQ(residuals[0], 67);
+ EXPECT_EQ(residuals[1], 4489);
+ EXPECT_EQ(residuals[2], 213);
+
+ const double tolerance = (method == CENTRAL)? 3e-9 : 2e-5;
+
+ for (int i = 0; i < 5; ++i) {
+ ExpectClose(x2[i], dydx1[5 * 0 + i], tolerance); // y1
+ ExpectClose(x1[i], dydx2[5 * 0 + i], tolerance);
+ ExpectClose(2 * x2[i] * residuals[0], dydx1[5 * 1 + i], tolerance); // y2
+ ExpectClose(2 * x1[i] * residuals[0], dydx2[5 * 1 + i], tolerance);
+ ExpectClose(0.0, dydx1[5 * 2 + i], tolerance); // y3
+ ExpectClose(2 * x2[i], dydx2[5 * 2 + i], tolerance);
+ }
+}
+
+bool TranscendentalFunctor::operator()(const double* x1,
+ const double* x2,
+ double* residuals) const {
+ double x1x2 = 0;
+ for (int i = 0; i < 5; ++i) {
+ x1x2 += x1[i] * x2[i];
+ }
+ residuals[0] = sin(x1x2);
+ residuals[1] = exp(-x1x2 / 10);
+ return true;
+}
+
+void TranscendentalFunctor::ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function,
+ NumericDiffMethod method) const {
+ struct {
+ double x1[5];
+ double x2[5];
+ } kTests[] = {
+ { { 1.0, 2.0, 3.0, 4.0, 5.0 }, // No zeros.
+ { 9.0, 9.0, 5.0, 5.0, 1.0 },
+ },
+ { { 0.0, 2.0, 3.0, 0.0, 5.0 }, // Some zeros x1.
+ { 9.0, 9.0, 5.0, 5.0, 1.0 },
+ },
+ { { 1.0, 2.0, 3.0, 1.0, 5.0 }, // Some zeros x2.
+ { 0.0, 9.0, 0.0, 5.0, 0.0 },
+ },
+ { { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros x1.
+ { 9.0, 9.0, 5.0, 5.0, 1.0 },
+ },
+ { { 1.0, 2.0, 3.0, 4.0, 5.0 }, // All zeros x2.
+ { 0.0, 0.0, 0.0, 0.0, 0.0 },
+ },
+ { { 0.0, 0.0, 0.0, 0.0, 0.0 }, // All zeros.
+ { 0.0, 0.0, 0.0, 0.0, 0.0 },
+ },
+ };
+
+ for (int k = 0; k < CERES_ARRAYSIZE(kTests); ++k) {
+ double *x1 = &(kTests[k].x1[0]);
+ double *x2 = &(kTests[k].x2[0]);
+ double *parameters[] = { x1, x2 };
+
+ double dydx1[10];
+ double dydx2[10];
+ double *jacobians[2] = { &dydx1[0], &dydx2[0] };
+
+ double residuals[2];
+
+ ASSERT_TRUE(cost_function.Evaluate(¶meters[0],
+ &residuals[0],
+ &jacobians[0]));
+ double x1x2 = 0;
+ for (int i = 0; i < 5; ++i) {
+ x1x2 += x1[i] * x2[i];
+ }
+
+ const double tolerance = (method == CENTRAL)? 3e-9 : 2e-5;
+
+ for (int i = 0; i < 5; ++i) {
+ ExpectClose( x2[i] * cos(x1x2), dydx1[5 * 0 + i], tolerance);
+ ExpectClose( x1[i] * cos(x1x2), dydx2[5 * 0 + i], tolerance);
+ ExpectClose(-x2[i] * exp(-x1x2 / 10.) / 10., dydx1[5 * 1 + i], tolerance);
+ ExpectClose(-x1[i] * exp(-x1x2 / 10.) / 10., dydx2[5 * 1 + i], tolerance);
+ }
+ }
+}
+
+} // namespace internal
+} // namespace ceres
diff --git a/internal/ceres/numeric_diff_test_utils.h b/internal/ceres/numeric_diff_test_utils.h
new file mode 100644
index 0000000..1a43df2
--- /dev/null
+++ b/internal/ceres/numeric_diff_test_utils.h
@@ -0,0 +1,56 @@
+#include "ceres/cost_function.h"
+#include "ceres/sized_cost_function.h"
+#include "ceres/types.h"
+
+namespace ceres {
+namespace internal {
+
+// y1 = x1'x2 -> dy1/dx1 = x2, dy1/dx2 = x1
+// y2 = (x1'x2)^2 -> dy2/dx1 = 2 * x2 * (x1'x2), dy2/dx2 = 2 * x1 * (x1'x2)
+// y3 = x2'x2 -> dy3/dx1 = 0, dy3/dx2 = 2 * x2
+class EasyFunctor {
+ public:
+ bool operator()(const double* x1, const double* x2, double* residuals) const;
+ void ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function,
+ NumericDiffMethod method) const;
+};
+
+class EasyCostFunction : public SizedCostFunction<3, 5, 5> {
+ public:
+ virtual bool Evaluate(double const* const* parameters,
+ double* residuals,
+ double** /* not used */) const {
+ return functor_(parameters[0], parameters[1], residuals);
+ }
+
+ private:
+ EasyFunctor functor_;
+};
+
+// y1 = sin(x1'x2)
+// y2 = exp(-x1'x2 / 10)
+//
+// dy1/dx1 = x2 * cos(x1'x2), dy1/dx2 = x1 * cos(x1'x2)
+// dy2/dx1 = -x2 * exp(-x1'x2 / 10) / 10, dy2/dx2 = -x2 * exp(-x1'x2 / 10) / 10
+class TranscendentalFunctor {
+ public:
+ bool operator()(const double* x1, const double* x2, double* residuals) const;
+ void ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function,
+ NumericDiffMethod method) const;
+};
+
+class TranscendentalCostFunction : public SizedCostFunction<2, 5, 5> {
+ public:
+ virtual bool Evaluate(double const* const* parameters,
+ double* residuals,
+ double** /* not used */) const {
+ return functor_(parameters[0], parameters[1], residuals);
+ }
+ private:
+ TranscendentalFunctor functor_;
+};
+
+} // namespace internal
+} // namespace ceres
