Add AutoDiffFirstOrderFunction

This is to FirstOrderFunction, what AutoDiffCostFunction is to CostFunction.
This allows users of GradientSolver to be able to define objective functions
without requiring them to define the derivatives.

The implementation uses the same Jet objects for computing the gradient as
is used by AutoDiffCostFunction.

Change-Id: Ide6e60532a3adab9be9899ba9b368dc267fd2dbb

include/ceres/autodiff_first_order_function.h

@@ -0,0 +1,152 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2019 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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)
+
+
+#ifndef CERES_PUBLIC_AUTODIFF_FIRST_ORDER_FUNCTION_H_
+#define CERES_PUBLIC_AUTODIFF_FIRST_ORDER_FUNCTION_H_
+
+#include <memory>
+
+#include "ceres/first_order_function.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/fixed_array.h"
+#include "ceres/jet.h"
+#include "ceres/types.h"
+
+namespace ceres {
+
+// Create FirstOrderFunctions as needed by the GradientProblem
+// framework, with gradients computed via automatic
+// differentiation. For more information on automatic differentiation,
+// see the wikipedia article at
+// http://en.wikipedia.org/wiki/Automatic_differentiation
+//
+// To get an auto differentiated function, you must define a class
+// with a templated operator() (a functor) that computes the cost
+// function in terms of the template parameter T. The autodiff
+// framework substitutes appropriate "jet" objects for T in order to
+// compute the derivative when necessary, but this is hidden, and you
+// should write the function as if T were a scalar type (e.g. a
+// double-precision floating point number).
+//
+// The function must write the computed value in the last argument
+// (the only non-const one) and return true to indicate
+// success.
+//
+// For example, consider a scalar error e = x'y - a, where both x and y are
+// two-dimensional column vector parameters, the prime sign indicates
+// transposition, and a is a constant.
+//
+// To write an auto-differentiable FirstOrderFunction for the above model, first
+// define the object
+//
+//  class QuadraticCostFunctor {
+//   public:
+//    explicit QuadraticCostFunctor(double a) : a_(a) {}
+//    template <typename T>
+//    bool operator()(const T* const xy, T* cost) const {
+//      const T* const x = xy;
+//      const T* const y = xy + 2;
+//      *cost = x[0] * y[0] + x[1] * y[1] - T(a_);
+//      return true;
+//    }
+//
+//   private:
+//    double a_;
+//  };
+//
+// Note that in the declaration of operator() the input parameters xy come
+// first, and are passed as const pointers to arrays of T. The
+// output is the last parameter.
+//
+// Then given this class definition, the auto differentiated FirstOrderFunction for
+// it can be constructed as follows.
+//
+//    FirstOrderFunction* function =
+//      new AutoDiffFirstOrderFunction<QuadraticCostFunctor, 4>(
+//          new QuadraticCostFunctor(1.0)));
+//
+// In the instantiation above, the template parameters following
+// "QuadraticCostFunctor", "4", describe the functor as computing a
+// 1-dimensional output from a four dimensional vector.
+//
+// WARNING: Since the functor will get instantiated with different types for
+// T, you must convert from other numeric types to T before mixing
+// computations with other variables of type T. In the example above, this is
+// seen where instead of using a_ directly, a_ is wrapped with T(a_).
+
+template <typename FirstOrderFunctor, int kNumParameters>
+class AutoDiffFirstOrderFunction : public FirstOrderFunction {
+ public:
+  // Takes ownership of functor.
+  explicit AutoDiffFirstOrderFunction(FirstOrderFunctor* functor)
+      : functor_(functor) {
+    static_assert(kNumParameters > 0, "kNumParameters must be positive");
+  }
+
+  virtual ~AutoDiffFirstOrderFunction() {}
+
+  virtual bool Evaluate(const double* const parameters,
+                        double* cost,
+                        double* gradient) const {
+    if (gradient == nullptr) {
+      return (*functor_)(parameters, cost);
+    }
+
+    typedef Jet<double, kNumParameters> JetT;
+    internal::FixedArray<JetT, (256 * 7) / sizeof(JetT)> x(kNumParameters);
+    for (int i = 0; i < kNumParameters; ++i) {
+      x[i].a = parameters[i];
+      x[i].v.setZero();
+      x[i].v[i] = 1.0;
+    }
+
+    JetT output;
+    output.a = kImpossibleValue;
+    output.v.setConstant(kImpossibleValue);
+
+    if (!(*functor_)(x.get(), &output)) {
+      return false;
+    }
+
+    *cost = output.a;
+    VectorRef(gradient, kNumParameters) = output.v;
+    return true;
+  }
+
+  int NumParameters() const { return kNumParameters; }
+
+ private:
+  std::unique_ptr<FirstOrderFunctor> functor_;
+};
+
+}  // namespace ceres
+
+#endif  // CERES_PUBLIC_AUTODIFF_FIRST_ORDER_FUNCTION_H_

include/ceres/first_order_function.h

@@ -0,0 +1,55 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2019 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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)
+
+
+#ifndef CERES_PUBLIC_FIRST_ORDER_FUNCTION_H_
+#define CERES_PUBLIC_FIRST_ORDER_FUNCTION_H_
+
+#include "ceres/internal/port.h"
+
+namespace ceres {
+
+// A FirstOrderFunction object implements the evaluation of a function
+// and its gradient.
+class CERES_EXPORT FirstOrderFunction {
+ public:
+  virtual ~FirstOrderFunction() {}
+
+  // cost is never null. gradient may be null. The return value
+  // indicates whether the evaluation was successful or not.
+  virtual bool Evaluate(const double* const parameters,
+                        double* cost,
+                        double* gradient) const = 0;
+  virtual int NumParameters() const = 0;
+};
+
+}  // namespace ceres
+
+#endif  // CERES_PUBLIC_FIRST_ORDER_FUNCTION_H_

include/ceres/gradient_problem.h

@@ -33,6 +33,7 @@
 
 #include <memory>
 #include "ceres/internal/port.h"
+#include "ceres/first_order_function.h"
 #include "ceres/local_parameterization.h"
 
 namespace ceres {
@@ -109,18 +110,6 @@ class CERES_EXPORT GradientProblem {
   std::unique_ptr<double[]> scratch_;
 };
 
-// A FirstOrderFunction object implements the evaluation of a function
-// and its gradient.
-class CERES_EXPORT FirstOrderFunction {
- public:
-  virtual ~FirstOrderFunction() {}
-  // cost is never NULL. gradient may be null.
-  virtual bool Evaluate(const double* const parameters,
-                        double* cost,
-                        double* gradient) const = 0;
-  virtual int NumParameters() const = 0;
-};
-
 }  // namespace ceres
 
 #endif  // CERES_PUBLIC_GRADIENT_PROBLEM_H_

include/ceres/internal/autodiff.h

@@ -1,5 +1,5 @@
 // Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2015 Google Inc. All rights reserved.
+// Copyright 2019 Google Inc. All rights reserved.
 // http://ceres-solver.org/
 //
 // Redistribution and use in source and binary forms, with or without

internal/ceres/CMakeLists.txt

@@ -392,6 +392,7 @@ if (BUILD_TESTING AND GFLAGS)
 
   ceres_test(array_utils)
   ceres_test(autodiff)
+  ceres_test(autodiff_first_order_function)
   ceres_test(autodiff_cost_function)
   ceres_test(autodiff_local_parameterization)
   ceres_test(block_jacobi_preconditioner)

internal/ceres/autodiff_cost_function_test.cc

@@ -1,5 +1,5 @@
 // Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2015 Google Inc. All rights reserved.
+// Copyright 2019 Google Inc. All rights reserved.
 // http://ceres-solver.org/
 //
 // Redistribution and use in source and binary forms, with or without
@@ -30,7 +30,6 @@
 
 #include "ceres/autodiff_cost_function.h"
 
-#include <cstddef>
 #include <memory>
 
 #include "gtest/gtest.h"
@@ -74,7 +73,7 @@ TEST(AutodiffCostFunction, BilinearDifferentiationTest) {
 
   double residuals = 0.0;
 
-  cost_function->Evaluate(parameters, &residuals, NULL);
+  cost_function->Evaluate(parameters, &residuals, nullptr);
   EXPECT_EQ(10.0, residuals);
 
   cost_function->Evaluate(parameters, &residuals, jacobians);
@@ -128,7 +127,7 @@ TEST(AutodiffCostFunction, ManyParameterAutodiffInstantiates) {
 
   double residuals = 0.0;
 
-  cost_function->Evaluate(parameters, &residuals, NULL);
+  cost_function->Evaluate(parameters, &residuals, nullptr);
   EXPECT_EQ(45.0, residuals);
 
   cost_function->Evaluate(parameters, &residuals, jacobians);

internal/ceres/autodiff_first_order_function_test.cc

@@ -0,0 +1,77 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2019 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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/autodiff_first_order_function.h"
+
+#include <memory>
+
+#include "ceres/array_utils.h"
+#include "ceres/first_order_function.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+class QuadraticCostFunctor {
+ public:
+  explicit QuadraticCostFunctor(double a) : a_(a) {}
+  template <typename T>
+  bool operator()(const T* const x, T* cost) const {
+    cost[0] = x[0] * x[1] + x[2] * x[3] - T(a_);
+    return true;
+  }
+
+ private:
+  double a_;
+};
+
+TEST(AutoDiffFirstOrderFunction, BilinearDifferentiationTest) {
+  std::unique_ptr<FirstOrderFunction> function(
+      new AutoDiffFirstOrderFunction<QuadraticCostFunctor, 4>(
+          new QuadraticCostFunctor(1.0)));
+
+  double parameters[4] = {1.0, 2.0, 3.0, 4.0};
+  double gradient[4];
+  double cost;
+
+  function->Evaluate(parameters, &cost, nullptr);
+  EXPECT_EQ(cost, 13.0);
+
+  cost = -1.0;
+  function->Evaluate(parameters, &cost, gradient);
+  EXPECT_EQ(cost, 13.0);
+  EXPECT_EQ(gradient[0], parameters[1]);
+  EXPECT_EQ(gradient[1], parameters[0]);
+  EXPECT_EQ(gradient[2], parameters[3]);
+  EXPECT_EQ(gradient[3], parameters[2]);
+}
+
+}  // namespace internal
+}  // namespace ceres