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
diff --git a/internal/ceres/numeric_diff_test_utils.h b/internal/ceres/numeric_diff_test_utils.h
index 3ae83fa..2a551d3 100644
--- a/internal/ceres/numeric_diff_test_utils.h
+++ b/internal/ceres/numeric_diff_test_utils.h
@@ -38,6 +38,12 @@
namespace ceres {
namespace internal {
+// Noise factor for randomized cost function.
+static const double kNoiseFactor = 0.01;
+
+// Default random seed for randomized cost function.
+static const unsigned int kRandomSeed = 1234;
+
// 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
@@ -46,7 +52,7 @@
bool operator()(const double* x1, const double* x2, double* residuals) const;
void ExpectCostFunctionEvaluationIsNearlyCorrect(
const CostFunction& cost_function,
- NumericDiffMethod method) const;
+ NumericDiffMethodType method) const;
};
class EasyCostFunction : public SizedCostFunction<3, 5, 5> {
@@ -71,7 +77,7 @@
bool operator()(const double* x1, const double* x2, double* residuals) const;
void ExpectCostFunctionEvaluationIsNearlyCorrect(
const CostFunction& cost_function,
- NumericDiffMethod method) const;
+ NumericDiffMethodType method) const;
};
class TranscendentalCostFunction : public SizedCostFunction<2, 5, 5> {
@@ -85,6 +91,61 @@
TranscendentalFunctor functor_;
};
+// y = exp(x), dy/dx = exp(x)
+class ExponentialFunctor {
+ public:
+ bool operator()(const double* x1, double* residuals) const;
+ void ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function) const;
+};
+
+class ExponentialCostFunction : public SizedCostFunction<1, 1> {
+ public:
+ virtual bool Evaluate(double const* const* parameters,
+ double* residuals,
+ double** /* not used */) const {
+ return functor_(parameters[0], residuals);
+ }
+
+ private:
+ ExponentialFunctor functor_;
+};
+
+// Test adaptive numeric differentiation by synthetically adding random noise
+// to a functor.
+// y = x^2 + [random noise], dy/dx ~ 2x
+class RandomizedFunctor {
+ public:
+ RandomizedFunctor(double noise_factor, unsigned int random_seed)
+ : noise_factor_(noise_factor), random_seed_(random_seed) {
+ }
+
+ bool operator()(const double* x1, double* residuals) const;
+ void ExpectCostFunctionEvaluationIsNearlyCorrect(
+ const CostFunction& cost_function) const;
+
+ private:
+ double noise_factor_;
+ unsigned int random_seed_;
+};
+
+class RandomizedCostFunction : public SizedCostFunction<1, 1> {
+ public:
+ RandomizedCostFunction(double noise_factor, unsigned int random_seed)
+ : functor_(noise_factor, random_seed) {
+ }
+
+ virtual bool Evaluate(double const* const* parameters,
+ double* residuals,
+ double** /* not used */) const {
+ return functor_(parameters[0], residuals);
+ }
+
+ private:
+ RandomizedFunctor functor_;
+};
+
+
} // namespace internal
} // namespace ceres
