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

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