Hessian.hpp

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// Copyright (c) Sleipnir contributors
 
#pragma once
 
#include <utility>
 
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <wpi/SmallVector.h>
 
#include "sleipnir/autodiff/ExpressionGraph.hpp"
#include "sleipnir/autodiff/Jacobian.hpp"
#include "sleipnir/autodiff/Profiler.hpp"
#include "sleipnir/autodiff/Variable.hpp"
#include "sleipnir/autodiff/VariableMatrix.hpp"
#include "sleipnir/util/SymbolExports.hpp"
 
namespace sleipnir {
 
/**
 * This class calculates the Hessian of a variable with respect to a vector of
 * variables.
 *
 * The gradient tree is cached so subsequent Hessian calculations are faster,
 * and the Hessian is only recomputed if the variable expression is nonlinear.
 */
class SLEIPNIR_DLLEXPORT Hessian {
 public:
  /**
   * Constructs a Hessian object.
   *
   * @param variable Variable of which to compute the Hessian.
   * @param wrt Vector of variables with respect to which to compute the
   *   Hessian.
   */
  Hessian(Variable variable, const VariableMatrix& wrt) noexcept
      : m_jacobian{
            [&] {
              wpi::SmallVector<detail::ExpressionPtr> wrtVec;
              wrtVec.reserve(wrt.size());
              for (auto& elem : wrt) {
                wrtVec.emplace_back(elem.expr);
              }
 
              auto grad =
                  detail::ExpressionGraph{variable.expr}.GenerateGradientTree(
                      wrtVec);
 
              VariableMatrix ret{wrt.Rows()};
              for (int row = 0; row < ret.Rows(); ++row) {
                ret(row) = Variable{std::move(grad[row])};
              }
              return ret;
            }(),
            wrt} {}
 
  /**
   * Returns the Hessian as a VariableMatrix.
   *
   * This is useful when constructing optimization problems with derivatives in
   * them.
   */
  VariableMatrix Get() const { return m_jacobian.Get(); }
 
  /**
   * Evaluates the Hessian at wrt's value.
   */
  const Eigen::SparseMatrix<double>& Value() { return m_jacobian.Value(); }
 
  /**
   * Returns the profiler.
   */
  Profiler& GetProfiler() { return m_jacobian.GetProfiler(); }
 
 private:
  Jacobian m_jacobian;
};
 
}  // namespace sleipnir