L1 proximal, including linear transform. More...

#include <l1_proximal.h>

Inheritance diagram for sopt::proximal::L1< SCALAR >:

Collaboration diagram for sopt::proximal::L1< SCALAR >:

Classes
class	Breaker

struct	Diagnostic
	How did calling L1 go? More...

struct	DiagnosticAndResult
	Result from calling L1. More...

class	FistaMixing

class	NoMixing

Public Types
using	Scalar = typename L1TightFrame< SCALAR >::Scalar
	Underlying scalar type. More...

using	Real = typename L1TightFrame< SCALAR >::Real
	Underlying real scalar type. More...

Public Member Functions
template<typename T0 >
Diagnostic	operator() (Eigen::MatrixBase< T0 > &out, Real gamma, Vector< Scalar > const &x) const
	Computes proximal for given γ More...

template<typename T0 >
DiagnosticAndResult	operator() (Real const &gamma, Eigen::MatrixBase< T0 > const &x) const
	Lazy version. More...

	L1 ()

	SOPT_MACRO (itermax, t_uint)
	Maximum number of iterations before bailing out. More...

	SOPT_MACRO (tolerance, Real)
	Tolerance criteria. More...

	SOPT_MACRO (positivity_constraint, bool)
	Whether to apply positivity constraints. More...

	SOPT_MACRO (real_constraint, bool)
	Whether the output should be constrained to be real. More...

	SOPT_MACRO (fista_mixing, bool)
	Whether to do fista mixing or not. More...

Vector< Real > const &	weights () const
	Weights of the l1 norm. More...

template<typename T >
L1< Scalar > &	weights (Eigen::MatrixBase< T > const &w)
	Set weights to an array of values. More...

L1< Scalar > &	weights (Real const &w)
	Set weights to a single value. More...

Real	nu () const
	Bounds on the squared norm of the operator Ψ More...

L1< Scalar > &	nu (Real const &nu)
	Sets the bound on the squared norm of the operator Ψ More...

LinearTransform< Vector< Scalar > > const &	Psi () const
	Linear transform applied to input prior to L1 norm. More...

L1< Scalar > &::type	Psi (ARGS &&... args)

template<typename... T>
auto	tight_frame (T &&... args) const -> decltype(this->L1TightFrame< Scalar >::operator()(std::forward< T >(args)...))
	Special case if Ψ ia a tight frame. More...

Detailed Description

template<typename SCALAR>
class sopt::proximal::L1< 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 169 of file l1_proximal.h.

Member Typedef Documentation

◆ Real

template<typename SCALAR >

using sopt::proximal::L1< SCALAR >::Real = typename L1TightFrame<SCALAR>::Real

Underlying real scalar type.

Definition at line 187 of file l1_proximal.h.

◆ Scalar

template<typename SCALAR >

using sopt::proximal::L1< SCALAR >::Scalar = typename L1TightFrame<SCALAR>::Scalar

Underlying scalar type.

Definition at line 185 of file l1_proximal.h.

Constructor & Destructor Documentation

◆ L1()

template<typename SCALAR >

sopt::proximal::L1< SCALAR >::L1 ( )

inline

Definition at line 246 of file l1_proximal.h.

       : L1TightFrame<SCALAR>(),
         itermax_(0),
         tolerance_(1e-8),
         positivity_constraint_(false),
         real_constraint_(false),
         fista_mixing_(true) {}

Member Function Documentation

◆ nu() [1/2]

template<typename SCALAR >

Real sopt::proximal::L1< SCALAR >::nu ( ) const

inline

Bounds on the squared norm of the operator Ψ

Definition at line 294 of file l1_proximal.h.

294 { return L1TightFrame<Scalar>::nu(); }

Referenced by function_l1p(), main(), and sopt::proximal::L1< SCALAR >::nu().

◆ nu() [2/2]

template<typename SCALAR >

L1<Scalar>& sopt::proximal::L1< SCALAR >::nu ( Real const & nu )

inline

Sets the bound on the squared norm of the operator Ψ

Definition at line 296 of file l1_proximal.h.

                                  {
     L1TightFrame<SCALAR>::nu(nu);
     return *this;
   }

References sopt::proximal::L1< SCALAR >::nu().

◆ operator()() [1/2]

template<typename SCALAR >

template<typename T0 >

Diagnostic sopt::proximal::L1< SCALAR >::operator()	(	Eigen::MatrixBase< T0 > &	out,
		Real	gamma,
		Vector< Scalar > const &	x
	)		const

inline

Computes proximal for given γ

Definition at line 215 of file l1_proximal.h.

                                                                                              {
     // Note that we *must* call eval on x, in case it is an expression involving out
     if (gamma <= 0) {
       apply_constraints(out, x);
       return Diagnostic(0, 0, 0.5 * (out - x).squaredNorm(), true);
     }
  
     if (fista_mixing())
       return operator()(out, gamma, x, FistaMixing());
     else
       return operator()(out, gamma, x, NoMixing());
   }

◆ operator()() [2/2]

template<typename SCALAR >

template<typename T0 >

DiagnosticAndResult sopt::proximal::L1< SCALAR >::operator()	(	Real const &	gamma,
		Eigen::MatrixBase< T0 > const &	x
	)		const

inline

Lazy version.

Definition at line 230 of file l1_proximal.h.

                                                                                         {
     DiagnosticAndResult result;
     static_cast<Diagnostic &>(result) = operator()(result.proximal, gamma, x);
     return result;
   }

References sopt::proximal::L1< SCALAR >::DiagnosticAndResult::proximal.

◆ Psi() [1/2]

template<typename SCALAR >

LinearTransform<Vector<Scalar> > const& sopt::proximal::L1< SCALAR >::Psi ( ) const

inline

Linear transform applied to input prior to L1 norm.

Definition at line 302 of file l1_proximal.h.

302 { return L1TightFrame<Scalar>::Psi(); }

sopt::proximal::L1TightFrame::Psi

L1TightFrame &::type Psi(ARGS &&... args)

Definition: l1_proximal.h:93

References sopt::proximal::L1TightFrame< SCALAR >::Psi().

Referenced by sopt::algorithm::ImagingProximalADMM< SCALAR >::Psi(), and sopt::algorithm::L1GProximal< SCALAR >::Psi().

◆ Psi() [2/2]

template<typename SCALAR >

L1<Scalar>& ::type sopt::proximal::L1< SCALAR >::Psi ( ARGS &&... args )

inline

Definition at line 305 of file l1_proximal.h.

                                                                                      {
     L1TightFrame<Scalar>::Psi(std::forward<ARGS>(args)...);
     return *this;
   }

References sopt::proximal::L1TightFrame< SCALAR >::Psi().

◆ SOPT_MACRO() [1/5]

template<typename SCALAR >

sopt::proximal::L1< SCALAR >::SOPT_MACRO	(	fista_mixing	,
		bool
	)

Whether to do fista mixing or not.

◆ SOPT_MACRO() [2/5]

template<typename SCALAR >

sopt::proximal::L1< SCALAR >::SOPT_MACRO	(	itermax	,
		t_uint
	)

Maximum number of iterations before bailing out.

0 means algorithm breaks only if convergence is reached.

◆ SOPT_MACRO() [3/5]

template<typename SCALAR >

sopt::proximal::L1< SCALAR >::SOPT_MACRO	(	positivity_constraint	,
		bool
	)

Whether to apply positivity constraints.

◆ SOPT_MACRO() [4/5]

template<typename SCALAR >

sopt::proximal::L1< SCALAR >::SOPT_MACRO	(	real_constraint	,
		bool
	)

Whether the output should be constrained to be real.

◆ SOPT_MACRO() [5/5]

template<typename SCALAR >

sopt::proximal::L1< SCALAR >::SOPT_MACRO	(	tolerance	,
		Real
	)

Tolerance criteria.

◆ tight_frame()

template<typename SCALAR >

template<typename... T>

auto sopt::proximal::L1< SCALAR >::tight_frame ( T &&... args ) const -> decltype(this->L1TightFrame<Scalar>::operator()(std::forward<T>(args)...))

inline

Special case if Ψ ia a tight frame.

See also: L1TightFrame

Definition at line 313 of file l1_proximal.h.

                                                                                 {
     return this->L1TightFrame<Scalar>::operator()(std::forward<T>(args)...);
   }

References sopt::proximal::L1TightFrame< SCALAR >::operator()().

◆ weights() [1/3]

template<typename SCALAR >

Vector<Real> const& sopt::proximal::L1< SCALAR >::weights ( ) const

inline

Weights of the l1 norm.

Definition at line 280 of file l1_proximal.h.

280 { return L1TightFrame<Scalar>::weights(); }

sopt::proximal::L1TightFrame::weights

Vector< Real > const & weights() const

Weights of the l1 norm.

Definition: l1_proximal.h:74

References sopt::proximal::L1TightFrame< SCALAR >::weights().

◆ weights() [2/3]

template<typename SCALAR >

template<typename T >

L1<Scalar>& sopt::proximal::L1< SCALAR >::weights ( Eigen::MatrixBase< T > const & w )

inline

Set weights to an array of values.

Definition at line 283 of file l1_proximal.h.

                                                    {
     L1TightFrame<Scalar>::weights(w);
     return *this;
   }

References sopt::proximal::L1TightFrame< SCALAR >::weights().

◆ weights() [3/3]

template<typename SCALAR >

L1<Scalar>& sopt::proximal::L1< SCALAR >::weights ( Real const & w )

inline

Set weights to a single value.

Definition at line 288 of file l1_proximal.h.

                                      {
     L1TightFrame<Scalar>::weights(w);
     return this;
   }

References sopt::proximal::L1TightFrame< SCALAR >::weights().

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

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

Classes

Public Types

Public Member Functions

Detailed Description

template<typename SCALAR> class sopt::proximal::L1< SCALAR >

Member Typedef Documentation

◆ Real

◆ Scalar

Constructor & Destructor Documentation

◆ L1()

Member Function Documentation

◆ nu() [1/2]

◆ nu() [2/2]

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ Psi() [1/2]

◆ Psi() [2/2]

◆ SOPT_MACRO() [1/5]

◆ SOPT_MACRO() [2/5]

◆ SOPT_MACRO() [3/5]

◆ SOPT_MACRO() [4/5]

◆ SOPT_MACRO() [5/5]

◆ tight_frame()

◆ weights() [1/3]

◆ weights() [2/3]

◆ weights() [3/3]

template<typename SCALAR>
class sopt::proximal::L1< SCALAR >