imaging_padmm.h

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#ifndef SOPT_L1_PROXIMAL_ADMM_H
#define SOPT_L1_PROXIMAL_ADMM_H
 
#include "sopt/config.h"
#include <limits> // for std::numeric_limits<>
#include <numeric>
#include <tuple>
#include <utility>
#include "sopt/exception.h"
#include "sopt/l1_proximal.h"
#include "sopt/linear_transform.h"
#include "sopt/logging.h"
#include "sopt/padmm.h"
#include "sopt/proximal.h"
#include "sopt/relative_variation.h"
#include "sopt/types.h"
 
namespace sopt::algorithm {
template <typename SCALAR>
class ImagingProximalADMM {
  using PADMM = ProximalADMM<SCALAR>;
 
 public:
  using value_type = typename PADMM::value_type;
  using Scalar = typename PADMM::Scalar;
  using Real = typename PADMM::Real;
  using t_Vector = typename PADMM::t_Vector;
  using t_LinearTransform = typename PADMM::t_LinearTransform;
  using t_Proximal = typename PADMM::t_Proximal;
  using t_IsConverged = typename PADMM::t_IsConverged;
 
  struct Diagnostic : public PADMM::Diagnostic {
    typename proximal::L1<Scalar>::Diagnostic l1_diagnostic;
    Diagnostic(t_uint niters = 0u, bool good = false,
               typename proximal::L1<Scalar>::Diagnostic const &l1diag =
                   typename proximal::L1<Scalar>::Diagnostic())
        : PADMM::Diagnostic(niters, good), l1_diagnostic(l1diag) {}
    Diagnostic(t_uint niters, bool good, typename proximal::L1<Scalar>::Diagnostic const &l1diag,
               t_Vector &&residual)
        : PADMM::Diagnostic(niters, good, std::move(residual)), l1_diagnostic(l1diag) {}
  };
  struct DiagnosticAndResult : public Diagnostic {
    t_Vector x;
  };
 
  template <typename DERIVED>
  ImagingProximalADMM(Eigen::MatrixBase<DERIVED> const &target)
      : l1_proximal_(),
        l2ball_proximal_(1e0),
        tight_frame_(false),
        residual_tolerance_(1e-4),
        relative_variation_(1e-4),
        residual_convergence_(nullptr),
        objective_convergence_(nullptr),
        itermax_(std::numeric_limits<t_uint>::max()),
        regulariser_strength_(1e-8),
        lagrange_update_scale_(0.9),
        is_converged_(),
        Phi_(linear_transform_identity<Scalar>()),
        target_(target) {}
  virtual ~ImagingProximalADMM() {}
 
// Macro helps define properties that can be initialized as in
// auto padmm = ImagingProximalADMM<float>().prop0(value).prop1(value);
#define SOPT_MACRO(NAME, TYPE)                          \
  TYPE const &NAME() const { return NAME##_; }          \
  ImagingProximalADMM<SCALAR> &NAME(TYPE const &(NAME)) { \
    NAME##_ = NAME;                                     \
    return *this;                                       \
  }                                                     \
                                                        \
 protected:                                             \
  TYPE NAME##_;                                         \
                                                        \
 public:
 
  proximal::L1<Scalar> * g_proximal()
  {
    return &l1_proximal_;
  }
 
  SOPT_MACRO(l1_proximal, proximal::L1<Scalar>);
  SOPT_MACRO(l2ball_proximal, proximal::WeightedL2Ball<Scalar>);
  SOPT_MACRO(tight_frame, bool);
  SOPT_MACRO(residual_tolerance, Real);
  SOPT_MACRO(relative_variation, Real);
  SOPT_MACRO(residual_convergence, t_IsConverged);
  SOPT_MACRO(objective_convergence, t_IsConverged);
  SOPT_MACRO(itermax, t_uint);
  SOPT_MACRO(regulariser_strength, Real);
  SOPT_MACRO(lagrange_update_scale, Real);
  SOPT_MACRO(is_converged, t_IsConverged);
  SOPT_MACRO(Phi, t_LinearTransform);
 
#undef SOPT_MACRO
  t_Vector const &target() const { return target_; }
  template <typename DERIVED>
  ImagingProximalADMM<Scalar> &target(Eigen::MatrixBase<DERIVED> const &target) {
    target_ = target;
    return *this;
  }
 
  Diagnostic operator()(t_Vector &out) const {
    return operator()(out, PADMM::initial_guess(target(), Phi()));
  }
  Diagnostic operator()(t_Vector &out, std::tuple<t_Vector, t_Vector> const &guess) const {
    return operator()(out, std::get<0>(guess), std::get<1>(guess));
  }
  Diagnostic operator()(t_Vector &out,
                        std::tuple<t_Vector const &, t_Vector const &> const &guess) const {
    return operator()(out, std::get<0>(guess), std::get<1>(guess));
  }
  DiagnosticAndResult operator()(std::tuple<t_Vector, t_Vector> const &guess) const {
    return operator()(std::tie(std::get<0>(guess), std::get<1>(guess)));
  }
  DiagnosticAndResult operator()(
      std::tuple<t_Vector const &, t_Vector const &> const &guess) const {
    DiagnosticAndResult result;
    static_cast<Diagnostic &>(result) = operator()(result.x, guess);
    return result;
  }
  DiagnosticAndResult operator()() const {
    DiagnosticAndResult result;
    static_cast<Diagnostic &>(result) = operator()(result.x,
                                                   PADMM::initial_guess(target(), Phi()));
    return result;
  }
  DiagnosticAndResult operator()(DiagnosticAndResult const &warmstart) const {
    DiagnosticAndResult result = warmstart;
    static_cast<Diagnostic &>(result) = operator()(result.x, warmstart.x, warmstart.residual);
    return result;
  }
 
  template <typename... ARGS>
  typename std::enable_if<sizeof...(ARGS) >= 1, ImagingProximalADMM &>::type Phi(ARGS &&... args) {
    Phi_ = linear_transform(std::forward<ARGS>(args)...);
    return *this;
  }
 
  proximal::L1<Scalar> &l1_proximal() { return l1_proximal_; }
  proximal::WeightedL2Ball<Scalar> &l2ball_proximal() { return l2ball_proximal_; }
 
  t_LinearTransform const &Psi() const { return l1_proximal().Psi(); }
  template <typename... ARGS>
  typename std::enable_if<sizeof...(ARGS) >= 1, ImagingProximalADMM<Scalar> &>::type Psi(
      ARGS &&... args) {
    l1_proximal().Psi(std::forward<ARGS>(args)...);
    return *this;
  }
 
// Forwards get/setters to L1 and L2Ball proximals
// In practice, we end up with a bunch of functions that make it simpler to set or get values
// associated with the two proximal operators.
// E.g.: `paddm.l1_proximal_itermax(100).l2ball_epsilon(1e-2).l1_proximal_tolerance(1e-4)`.
// ~~~
#define SOPT_MACRO(VAR, NAME, PROXIMAL)                                                            \
                                                           \
  decltype(std::declval<proximal::PROXIMAL<Scalar> const>().VAR()) NAME##_proximal_##VAR() const { \
    return NAME##_proximal().VAR();                                                                \
  }                                                                                                \
                                                           \
  ImagingProximalADMM<Scalar> &NAME##_proximal_##VAR(                                              \
      decltype(std::declval<proximal::PROXIMAL<Scalar> const>().VAR()) (VAR)) {                      \
    NAME##_proximal().VAR(VAR);                                                                    \
    return *this;                                                                                  \
  }
  SOPT_MACRO(itermax, l1, L1);
  SOPT_MACRO(tolerance, l1, L1);
  SOPT_MACRO(positivity_constraint, l1, L1);
  SOPT_MACRO(real_constraint, l1, L1);
  SOPT_MACRO(fista_mixing, l1, L1);
  SOPT_MACRO(nu, l1, L1);
  SOPT_MACRO(weights, l1, L1);
  SOPT_MACRO(epsilon, l2ball, WeightedL2Ball);
  SOPT_MACRO(weights, l2ball, WeightedL2Ball);
#ifdef SOPT_MPI
  SOPT_MACRO(communicator, l2ball, WeightedL2Ball);
  SOPT_MACRO(direct_space_comm, l1, L1);
  SOPT_MACRO(adjoint_space_comm, l1, L1);
#endif
#undef SOPT_MACRO
 
  ImagingProximalADMM<Scalar> &residual_convergence(Real const &tolerance) {
    return residual_convergence(nullptr).residual_tolerance(tolerance);
  }
  ImagingProximalADMM<Scalar> &objective_convergence(Real const &tolerance) {
    return objective_convergence(nullptr).relative_variation(tolerance);
  }
  ImagingProximalADMM<Scalar> &is_converged(std::function<bool(t_Vector const &x)> const &func) {
    return is_converged([func](t_Vector const &x, t_Vector const &) { return func(x); });
  }
 
 protected:
  t_Vector target_;
 
  Diagnostic operator()(t_Vector &out, t_Vector const &guess, t_Vector const &res) const;
 
  template <typename T0, typename T1>
  typename proximal::L1<Scalar>::Diagnostic l1_proximal(Eigen::MatrixBase<T0> &out, Real regulariser_strength,
                                                        Eigen::MatrixBase<T1> const &x) const {
    return l1_proximal_real_constraint()
               ? call_l1_proximal(out, regulariser_strength, x.real().template cast<typename T1::Scalar>())
               : call_l1_proximal(out, regulariser_strength, x);
  }
 
  template <typename T0, typename T1>
  typename proximal::L1<Scalar>::Diagnostic call_l1_proximal(Eigen::MatrixBase<T0> &out, Real regulariser_strength,
                                                             Eigen::MatrixBase<T1> const &x) const {
    if (tight_frame()) {
      l1_proximal().tight_frame(out, regulariser_strength, x);
      return {0, 0, l1_proximal().objective(x, out, regulariser_strength), true};
    }
    return l1_proximal()(out, regulariser_strength, x);
  }
 
  bool residual_convergence(t_Vector const &x, t_Vector const &residual) const;
 
  bool objective_convergence(ScalarRelativeVariation<Scalar> &scalvar, t_Vector const &x,
                             t_Vector const &residual) const;
 
  bool is_converged(ScalarRelativeVariation<Scalar> &scalvar, t_Vector const &x,
                    t_Vector const &residual) const;
};
 
template <typename SCALAR>
typename ImagingProximalADMM<SCALAR>::Diagnostic ImagingProximalADMM<SCALAR>::operator()(
    t_Vector &out, t_Vector const &guess, t_Vector const &res) const {
  SOPT_HIGH_LOG("Performing Proximal ADMM with L1 and L2 operators");
  // The f proximal is an L1 proximal that stores some diagnostic result
  Diagnostic result;
  auto const f_proximal = [this, &result](t_Vector &out, Real regulariser_strength, t_Vector const &x) {
    result.l1_diagnostic = this->l1_proximal(out, regulariser_strength, x);
  };
  auto const g_proximal = [this](t_Vector &out, Real regulariser_strength, t_Vector const &x) {
    this->l2ball_proximal()(out, regulariser_strength, x);
  };
  ScalarRelativeVariation<Scalar> scalvar(relative_variation(), relative_variation(),
                                          "Objective function");
  auto const convergence = [this, scalvar](t_Vector const &x, t_Vector const &residual) mutable {
    return this->is_converged(scalvar, x, residual);
  };
  auto const padmm = PADMM(f_proximal, g_proximal, target())
                         .itermax(itermax())
                         .regulariser_strength(regulariser_strength())
                         .lagrange_update_scale(lagrange_update_scale())
                         .Phi(Phi())
                         .is_converged(convergence);
  static_cast<typename PADMM::Diagnostic &>(result) = padmm(out, std::tie(guess, res));
  return result;
}
 
template <typename SCALAR>
bool ImagingProximalADMM<SCALAR>::residual_convergence(t_Vector const &x,
                                                       t_Vector const &residual) const {
  if (static_cast<bool>(residual_convergence())) return residual_convergence()(x, residual);
  if (residual_tolerance() <= 0e0) return true;
  auto const residual_norm = sopt::l2_norm(residual, l2ball_proximal_weights());
  SOPT_LOW_LOG("    - [PADMM] Residuals: {} <? {}", residual_norm, residual_tolerance());
  return residual_norm < residual_tolerance();
}
 
template <typename SCALAR>
bool ImagingProximalADMM<SCALAR>::objective_convergence(ScalarRelativeVariation<Scalar> &scalvar,
                                                        t_Vector const &x,
                                                        t_Vector const &residual) const {
  if (static_cast<bool>(objective_convergence())) return objective_convergence()(x, residual);
  if (scalvar.relative_tolerance() <= 0e0) return true;
  auto const current =
      sopt::l1_norm(static_cast<t_Vector>(Psi().adjoint() * x), l1_proximal_weights());
  return scalvar(current);
}
 
template <typename SCALAR>
bool ImagingProximalADMM<SCALAR>::is_converged(ScalarRelativeVariation<Scalar> &scalvar,
                                               t_Vector const &x, t_Vector const &residual) const {
  auto const user = static_cast<bool>(is_converged()) == false or is_converged()(x, residual);
  auto const res = residual_convergence(x, residual);
  auto const obj = objective_convergence(scalvar, x, residual);
  // beware of short-circuiting!
  // better evaluate each convergence function everytime, especially with mpi
  return user and res and obj;
}
} // namespace sopt::algorithm
#endif