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Adaptive numeric differentiation using Ridders' method.

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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
This commit is contained in:
Tal Ben-Nun
2015-05-13 15:43:51 +03:00
parent 070bba4b43
commit 4f049db7c2
14 changed files with 871 additions and 106 deletions
Download Patch File Download Diff File Expand all files Collapse all files
internal/ceres/numeric_diff_cost_function_test.cc
+138 -5
View File
@@ -27,6 +27,7 @@
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: keir@google.com (Keir Mierle)
// tbennun@gmail.com (Tal Ben-Nun)
#include "ceres/numeric_diff_cost_function.h"
@@ -71,6 +72,19 @@ TEST(NumericDiffCostFunction, EasyCaseFunctorForwardDifferences) {
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction, EasyCaseFunctorRidders) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<EasyFunctor,
RIDDERS,
3, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
new EasyFunctor));
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
TEST(NumericDiffCostFunction, EasyCaseCostFunctionCentralDifferences) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
@@ -97,7 +111,21 @@ TEST(NumericDiffCostFunction, EasyCaseCostFunctionForwardDifferences) {
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction, TranscendentalCaseFunctorCentralDifferences) {
TEST(NumericDiffCostFunction, EasyCaseCostFunctionRidders) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<EasyCostFunction,
RIDDERS,
3, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
new EasyCostFunction, TAKE_OWNERSHIP));
EasyFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
TEST(NumericDiffCostFunction,
TranscendentalCaseFunctorCentralDifferences) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<TranscendentalFunctor,
@@ -110,7 +138,8 @@ TEST(NumericDiffCostFunction, TranscendentalCaseFunctorCentralDifferences) {
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction, TranscendentalCaseFunctorForwardDifferences) {
TEST(NumericDiffCostFunction,
TranscendentalCaseFunctorForwardDifferences) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<TranscendentalFunctor,
@@ -123,7 +152,28 @@ TEST(NumericDiffCostFunction, TranscendentalCaseFunctorForwardDifferences) {
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction, TranscendentalCaseCostFunctionCentralDifferences) {
TEST(NumericDiffCostFunction,
TranscendentalCaseFunctorRidders) {
NumericDiffOptions options;
// Using a smaller initial step size to overcome oscillatory function
// behavior.
options.ridders_relative_initial_step_size = 1e-3;
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<TranscendentalFunctor,
RIDDERS,
2, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
new TranscendentalFunctor, TAKE_OWNERSHIP, 2, options));
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
TEST(NumericDiffCostFunction,
TranscendentalCaseCostFunctionCentralDifferences) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<TranscendentalCostFunction,
@@ -136,7 +186,8 @@ TEST(NumericDiffCostFunction, TranscendentalCaseCostFunctionCentralDifferences)
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction, TranscendentalCaseCostFunctionForwardDifferences) {
TEST(NumericDiffCostFunction,
TranscendentalCaseCostFunctionForwardDifferences) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<TranscendentalCostFunction,
@@ -149,6 +200,26 @@ TEST(NumericDiffCostFunction, TranscendentalCaseCostFunctionForwardDifferences)
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, FORWARD);
}
TEST(NumericDiffCostFunction,
TranscendentalCaseCostFunctionRidders) {
NumericDiffOptions options;
// Using a smaller initial step size to overcome oscillatory function
// behavior.
options.ridders_relative_initial_step_size = 1e-3;
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<TranscendentalCostFunction,
RIDDERS,
2, /* number of residuals */
5, /* size of x1 */
5 /* size of x2 */>(
new TranscendentalCostFunction, TAKE_OWNERSHIP, 2, options));
TranscendentalFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, RIDDERS);
}
template<int num_rows, int num_cols>
class SizeTestingCostFunction : public SizedCostFunction<num_rows, num_cols> {
public:
@@ -208,7 +279,8 @@ TEST(NumericDiffCostFunction, EigenRowMajorColMajorTest) {
new EasyFunctor, TAKE_OWNERSHIP, 2));
}
TEST(NumericDiffCostFunction, EasyCaseFunctorCentralDifferencesAndDynamicNumResiduals) {
TEST(NumericDiffCostFunction,
EasyCaseFunctorCentralDifferencesAndDynamicNumResiduals) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<EasyFunctor,
@@ -221,5 +293,66 @@ TEST(NumericDiffCostFunction, EasyCaseFunctorCentralDifferencesAndDynamicNumResi
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function, CENTRAL);
}
TEST(NumericDiffCostFunction, ExponentialFunctorRidders) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<ExponentialFunctor,
RIDDERS,
1, /* number of residuals */
1 /* size of x1 */>(
new ExponentialFunctor));
ExponentialFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
TEST(NumericDiffCostFunction, ExponentialCostFunctionRidders) {
internal::scoped_ptr<CostFunction> cost_function;
cost_function.reset(
new NumericDiffCostFunction<ExponentialCostFunction,
RIDDERS,
1, /* number of residuals */
1 /* size of x1 */>(
new ExponentialCostFunction));
ExponentialFunctor functor;
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
TEST(NumericDiffCostFunction, RandomizedFunctorRidders) {
internal::scoped_ptr<CostFunction> cost_function;
NumericDiffOptions options;
// Larger initial step size is chosen to produce robust results in the
// presence of random noise.
options.ridders_relative_initial_step_size = 10.0;
cost_function.reset(
new NumericDiffCostFunction<RandomizedFunctor,
RIDDERS,
1, /* number of residuals */
1 /* size of x1 */>(
new RandomizedFunctor(kNoiseFactor, kRandomSeed), TAKE_OWNERSHIP,
1, options));
RandomizedFunctor functor (kNoiseFactor, kRandomSeed);
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
TEST(NumericDiffCostFunction, RandomizedCostFunctionRidders) {
internal::scoped_ptr<CostFunction> cost_function;
NumericDiffOptions options;
// Larger initial step size is chosen to produce robust results in the
// presence of random noise.
options.ridders_relative_initial_step_size = 10.0;
cost_function.reset(
new NumericDiffCostFunction<RandomizedCostFunction,
RIDDERS,
1, /* number of residuals */
1 /* size of x1 */>(
new RandomizedCostFunction(kNoiseFactor, kRandomSeed),
TAKE_OWNERSHIP, 1, options));
RandomizedFunctor functor (kNoiseFactor, kRandomSeed);
functor.ExpectCostFunctionEvaluationIsNearlyCorrect(*cost_function);
}
} // namespace internal
} // namespace ceres