sopt::proximal::L1TightFrame< SCALAR > Class Template Reference

L1 proximal, including linear transform. More...

#include <l1_proximal.h>

Inheritance diagram for sopt::proximal::L1TightFrame< SCALAR >:

Public Types
using	Scalar = SCALAR
	Underlying scalar type. More...
using	Real = typename real_type< Scalar >::type
	Underlying real scalar type. More...

Public Member Functions
	L1TightFrame ()
	SOPT_MACRO (Psi, LinearTransform< Vector< Scalar >>)
	Linear transform applied to input prior to L1 norm. More...
	SOPT_MACRO (nu, Real)
	Bound on the squared norm of the operator Ψ More...
Vector< Real > const &	weights () const
	Weights of the l1 norm. More...
template<typename T >
L1TightFrame< Scalar > &	weights (Eigen::MatrixBase< T > const &w)
	Weights of the l1 norm. More...
L1TightFrame< Scalar > &	weights (Real const &value)
	Set weights to a single value. More...
L1TightFrame &::type	Psi (ARGS &&... args)
template<typename T0 , typename T1 >
std::enable_if< is_complex< Scalar >::value==is_complex< typename T0::Scalar >::value and is_complex< Scalar >::value==is_complex< typename T1::Scalar >::value >::type	operator() (Eigen::MatrixBase< T0 > &out, Real gamma, Eigen::MatrixBase< T1 > const &x) const
	Computes proximal for given γ More...
template<typename T0 >
ProximalExpression< L1TightFrame< Scalar > const &, T0 >	operator() (Real const &gamma, Eigen::MatrixBase< T0 > const &x) const
	Lazy version. More...
template<typename T0 , typename T1 >
std::enable_if< is_complex< Scalar >::value==is_complex< typename T0::Scalar >::value and is_complex< Scalar >::value==is_complex< typename T1::Scalar >::value, Real >::type	objective (Eigen::MatrixBase< T0 > const &x, Eigen::MatrixBase< T1 > const &z, Real const &gamma) const

Detailed Description

template<typename SCALAR>
class sopt::proximal::L1TightFrame< SCALAR >

L1 proximal, including linear transform.

This function computes the prox operator of the l1 norm for the input vector \(x\). It solves the problem:

\[ min_{z} 0.5||x - z||_2^2 + γ ||Ψ^† z||_w1 \]

where \(Ψ \in C^{N_x \times N_r} \) is the sparsifying operator, and

\[|| ||_w1\]

is the weighted L1 norm.

Definition at line 26 of file l1_proximal.h.

Member Typedef Documentation

Real

template<typename SCALAR >

using sopt::proximal::L1TightFrame< SCALAR >::Real = typename real_type<Scalar>::type

Underlying real scalar type.

Definition at line 31 of file l1_proximal.h.

Scalar

template<typename SCALAR >

using sopt::proximal::L1TightFrame< SCALAR >::Scalar = SCALAR

Underlying scalar type.

Definition at line 29 of file l1_proximal.h.

Constructor & Destructor Documentation

L1TightFrame()

template<typename SCALAR >

sopt::proximal::L1TightFrame< SCALAR >::L1TightFrame ( )

inline

Definition at line 47 of file l1_proximal.h.

      : Psi_(linear_transform_identity<Scalar>()), nu_(1e0), weights_(Vector<Real>::Ones(1)) {}

Member Function Documentation

objective()

template<typename SCALAR >

template<typename T0 , typename T1 >

std::enable_if< is_complex< SCALAR >::value==is_complex< typename T0::Scalar >::value and is_complex< SCALAR >::value==is_complex< typename T1::Scalar >::value, typename real_type< SCALAR >::type >::type sopt::proximal::L1TightFrame< SCALAR >::objective	(	Eigen::MatrixBase< T0 > const &	x,
		Eigen::MatrixBase< T1 > const &	z,
		Real const &	gamma
	)		const

\[ 0.5||x - z||_2^2 + γ||Ψ^† z||_w1 \]

Definition at line 149 of file l1_proximal.h.

                                                         {
#ifdef SOPT_MPI
  auto const adj = gamma * sopt::mpi::l1_norm(static_cast<T1>(Psi().adjoint() * z), weights(),
                                              adjoint_space_comm());
  auto const dir = direct_space_comm().all_sum_all(0.5 * (x - z).squaredNorm());
  return adj + dir;
#else
  return 0.5 * (x - z).squaredNorm() +
         gamma * sopt::l1_norm(static_cast<T1>(Psi().adjoint() * z), weights());
#endif
}

References sopt::l1_norm().

Referenced by sopt::proximal::L1< SCALAR >::Breaker::Breaker(), and sopt::proximal::L1< SCALAR >::Breaker::operator()().

operator()() [1/2]

template<typename SCALAR >

template<typename T0 , typename T1 >

std::enable_if< is_complex< SCALAR >::value==is_complex< typename T0::Scalar >::value and is_complex< SCALAR >::value==is_complex< typename T1::Scalar >::value >::type sopt::proximal::L1TightFrame< SCALAR >::operator()	(	Eigen::MatrixBase< T0 > &	out,
		Real	gamma,
		Eigen::MatrixBase< T1 > const &	x
	)		const

Computes proximal for given γ

Definition at line 128 of file l1_proximal.h.

                                                                     {
  Vector<Scalar> const psit_x = Psi().adjoint() * x;
  if (weights().size() == 1)
    out = static_cast<Vector<Scalar>>(
              Psi() * (soft_threshhold(psit_x, nu() * gamma * weights()(0)) - psit_x)) /
              nu() +
          x;
  else
    out = static_cast<Vector<Scalar>>(
              Psi() * (soft_threshhold(psit_x, nu() * gamma * weights()) - psit_x)) /
              nu() +
          x;
  SOPT_LOW_LOG("Prox L1: objective = {}", objective(x, out, gamma));
}

References sopt::soft_threshhold(), and SOPT_LOW_LOG.

Referenced by sopt::proximal::L1< SCALAR >::tight_frame().

operator()() [2/2]

template<typename SCALAR >

template<typename T0 >

ProximalExpression<L1TightFrame<Scalar> const &, T0> sopt::proximal::L1TightFrame< SCALAR >::operator() ( Real const &  gamma, Eigen::MatrixBase< T0 > const &  x  ) const

inline

Lazy version.

Definition at line 106 of file l1_proximal.h.

                                                             {
    return {*this, gamma, x};
  }

Psi()

template<typename SCALAR >

L1TightFrame& ::type sopt::proximal::L1TightFrame< SCALAR >::Psi ( ARGS &&...  args )

inline

Definition at line 93 of file l1_proximal.h.

                                                                                       {
    Psi_ = linear_transform(std::forward<ARGS>(args)...);
    return *this;
  }

References sopt::linear_transform().

Referenced by sopt::proximal::L1< SCALAR >::Psi().

SOPT_MACRO() [1/2]

template<typename SCALAR >

sopt::proximal::L1TightFrame< SCALAR >::SOPT_MACRO	(	nu	,
		Real
	)

Bound on the squared norm of the operator Ψ

SOPT_MACRO() [2/2]

template<typename SCALAR >

sopt::proximal::L1TightFrame< SCALAR >::SOPT_MACRO	(	Psi	,
		LinearTransform< Vector< Scalar >>
	)

Linear transform applied to input prior to L1 norm.

weights() [1/3]

template<typename SCALAR >

Vector<Real> const& sopt::proximal::L1TightFrame< SCALAR >::weights ( ) const

inline

Weights of the l1 norm.

Definition at line 74 of file l1_proximal.h.

{ return weights_; }

Referenced by sopt::proximal::L1< SCALAR >::weights().

weights() [2/3]

template<typename SCALAR >

template<typename T >

L1TightFrame<Scalar>& sopt::proximal::L1TightFrame< SCALAR >::weights ( Eigen::MatrixBase< T > const &  w )

inline

Weights of the l1 norm.

Definition at line 77 of file l1_proximal.h.

                                                             {
    if ((w.array() < 0e0).any()) SOPT_THROW("Weights cannot be negative");
    if (w.stableNorm() < 1e-12) SOPT_THROW("Weights cannot be null");
    weights_ = w;
    return *this;
  }

References SOPT_THROW.

weights() [3/3]

template<typename SCALAR >

L1TightFrame<Scalar>& sopt::proximal::L1TightFrame< SCALAR >::weights ( Real const &  value )

inline

Set weights to a single value.

Definition at line 85 of file l1_proximal.h.

                                                   {
    if (value <= 0e0) SOPT_THROW("Weight cannot be negative or null");
    weights_ = Vector<Real>::Ones(1) * value;
    return *this;
  }

References SOPT_THROW.

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The documentation for this class was generated from the following file:

• /home/runner/work/sopt/sopt/cpp/sopt/l1_proximal.h