Primal Dual Algorithm. More...

#include <primal_dual.h>

Classes
struct	Diagnostic
	Values indicating how the algorithm ran. More...

struct	DiagnosticAndResult
	Holds result vector as well. More...

Public Types
using	value_type = SCALAR
	Scalar type. More...

using	Scalar = value_type
	Scalar type. More...

using	Real = typename real_type< Scalar >::type
	Real type. More...

using	t_Vector = Vector< Scalar >
	Type of then underlying vectors. More...

using	t_LinearTransform = LinearTransform< t_Vector >
	Type of the Ψ and Ψ^H operations, as well as Φ and Φ^H. More...

using	t_IsConverged = std::function< bool(const t_Vector &, const t_Vector &)>
	Type of the convergence function. More...

using	t_Constraint = std::function< void(t_Vector &, const t_Vector &)>
	Type of the constraint function. More...

using	t_Random_Updater = std::function< bool()>
	Type of random update function. More...

using	t_Proximal = ProximalFunction< Scalar >
	Type of the convergence function. More...

Public Member Functions
template<typename DERIVED >
	PrimalDual (t_Proximal const &f_proximal, t_Proximal const &g_proximal, Eigen::MatrixBase< DERIVED > const &target)

virtual	~PrimalDual ()

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

	SOPT_MACRO (update_scale, Real)
	Update parameter. More...

	SOPT_MACRO (regulariser_strength, Real)
	γ parameter. More...

	SOPT_MACRO (sigma, Real)
	sigma parameter More...

	SOPT_MACRO (xi, Real)
	xi parameter More...

	SOPT_MACRO (rho, Real)
	rho parameter More...

	SOPT_MACRO (tau, Real)
	tau parameter More...

	SOPT_MACRO (is_converged, t_IsConverged)
	A function verifying convergence. More...

	SOPT_MACRO (constraint, t_Constraint)
	A function applying a simple constraint. More...

	SOPT_MACRO (Phi, t_LinearTransform)
	Measurement operator. More...

	SOPT_MACRO (Psi, t_LinearTransform)
	Wavelet operator. More...

	SOPT_MACRO (f_proximal, t_Proximal)
	First proximal. More...

	SOPT_MACRO (g_proximal, t_Proximal)
	Second proximal. More...

	SOPT_MACRO (random_measurement_updater, t_Random_Updater)
	lambda that determines if to update measurements More...

	SOPT_MACRO (random_wavelet_updater, t_Random_Updater)
	lambda that determines if to update wavelets More...

void	f_proximal (t_Vector &out, Real regulariser_strength, t_Vector const &x) const
	Simplifies calling the proximal of f. More...

void	g_proximal (t_Vector &out, Real regulariser_strength, t_Vector const &x) const
	Simplifies calling the proximal of f. More...

PrimalDual< Scalar > &	is_converged (std::function< bool(t_Vector const &x)> const &func)
	Convergence function that takes only the output as argument. More...

t_Vector const &	target () const
	Vector of target measurements. More...

template<typename DERIVED >
PrimalDual< Scalar > &	target (Eigen::MatrixBase< DERIVED > const &target)
	Sets the vector of target measurements. More...

bool	is_converged (t_Vector const &x, t_Vector const &residual) const
	Facilitates call to user-provided convergence function. More...

Diagnostic	operator() (t_Vector &out) const
	Calls Primal Dual. More...

Diagnostic	operator() (t_Vector &out, std::tuple< t_Vector, t_Vector > const &guess) const
	Calls Primal Dual. More...

Diagnostic	operator() (t_Vector &out, std::tuple< t_Vector const &, t_Vector const & > const &guess) const
	Calls Primal Dual. More...

DiagnosticAndResult	operator() (std::tuple< t_Vector, t_Vector > const &guess) const
	Calls Primal Dual. More...

DiagnosticAndResult	operator() (std::tuple< t_Vector const &, t_Vector const & > const &guess) const
	Calls Primal Dual. More...

DiagnosticAndResult	operator() () const
	Calls Primal Dual. More...

DiagnosticAndResult	operator() (DiagnosticAndResult const &warmstart) const
	Makes it simple to chain different calls to PD. More...

PrimalDual &::type	Phi (ARGS &&... args)

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

std::tuple< t_Vector, t_Vector >	initial_guess () const
	Computes initial guess for x and the residual using the targets. More...

Static Public Member Functions
static std::tuple< t_Vector, t_Vector >	initial_guess (t_Vector const &target, t_LinearTransform const &phi)
	Computes initial guess for x and the residual using the targets. More...

Detailed Description

template<typename SCALAR>
class sopt::algorithm::PrimalDual< SCALAR >

Primal Dual Algorithm.

\(\min_{x, z} f(x) + h(z)\) subject to \(Φx + z = y\). \(y\) is a target vector.

Definition at line 24 of file primal_dual.h.

Member Typedef Documentation

◆ Real

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::Real = typename real_type<Scalar>::type

Real type.

Definition at line 31 of file primal_dual.h.

◆ Scalar

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::Scalar = value_type

Scalar type.

Definition at line 29 of file primal_dual.h.

◆ t_Constraint

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::t_Constraint = std::function<void (t_Vector &, const t_Vector &)>

Type of the constraint function.

Definition at line 39 of file primal_dual.h.

◆ t_IsConverged

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::t_IsConverged = std::function<bool (const t_Vector &, const t_Vector &)>

Type of the convergence function.

Definition at line 37 of file primal_dual.h.

◆ t_LinearTransform

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::t_LinearTransform = LinearTransform<t_Vector>

Type of the Ψ and Ψ^H operations, as well as Φ and Φ^H.

Definition at line 35 of file primal_dual.h.

◆ t_Proximal

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::t_Proximal = ProximalFunction<Scalar>

Type of the convergence function.

Definition at line 43 of file primal_dual.h.

◆ t_Random_Updater

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::t_Random_Updater = std::function<bool ()>

Type of random update function.

Definition at line 41 of file primal_dual.h.

◆ t_Vector

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::t_Vector = Vector<Scalar>

Type of then underlying vectors.

Definition at line 33 of file primal_dual.h.

◆ value_type

template<typename SCALAR >

using sopt::algorithm::PrimalDual< SCALAR >::value_type = SCALAR

Scalar type.

Definition at line 27 of file primal_dual.h.

Constructor & Destructor Documentation

◆ PrimalDual()

template<typename SCALAR >

template<typename DERIVED >

sopt::algorithm::PrimalDual< SCALAR >::PrimalDual	(	t_Proximal const &	f_proximal,
		t_Proximal const &	g_proximal,
		Eigen::MatrixBase< DERIVED > const &	target
	)

inline

Setups PrimalDual

Parameters

[in]	f_proximal	proximal operator of the \(f\) function.
[in]	g_proximal	proximal operator of the \(g\) function

Definition at line 69 of file primal_dual.h.

       : itermax_(std::numeric_limits<t_uint>::max()),
         sigma_(1),
         tau_(0.5),
         regulariser_strength_(0.5),
         update_scale_(1),
         xi_(1),
         rho_(1),
         is_converged_(),
         constraint_([](t_Vector &out, t_Vector const &x) { out = x; }),
         Phi_(linear_transform_identity<Scalar>()),
         Psi_(linear_transform_identity<Scalar>()),
         f_proximal_(f_proximal),
         g_proximal_(g_proximal),
         random_measurement_updater_([]() { return true; }),
         random_wavelet_updater_([]() { return true; }),
 #ifdef SOPT_MPI
         v_all_sum_all_comm_(mpi::Communicator()),
         u_all_sum_all_comm_(mpi::Communicator()),
 #endif
         target_(target) {
   }

◆ ~PrimalDual()

template<typename SCALAR >

virtual sopt::algorithm::PrimalDual< SCALAR >::~PrimalDual ( )

inlinevirtual

Definition at line 92 of file primal_dual.h.

92 {}

Member Function Documentation

◆ f_proximal()

template<typename SCALAR >

void sopt::algorithm::PrimalDual< SCALAR >::f_proximal	(	t_Vector &	out,
		Real	regulariser_strength,
		t_Vector const &	x
	)		const

inline

Simplifies calling the proximal of f.

Definition at line 147 of file primal_dual.h.

                                                                                      {
     f_proximal()(out, regulariser_strength, x);
   }

◆ g_proximal()

template<typename SCALAR >

void sopt::algorithm::PrimalDual< SCALAR >::g_proximal	(	t_Vector &	out,
		Real	regulariser_strength,
		t_Vector const &	x
	)		const

inline

Simplifies calling the proximal of f.

Definition at line 151 of file primal_dual.h.

                                                                                      {
     g_proximal()(out, regulariser_strength, x);
   }

◆ initial_guess() [1/2]

template<typename SCALAR >

std::tuple<t_Vector, t_Vector> sopt::algorithm::PrimalDual< SCALAR >::initial_guess ( ) const

inline

Computes initial guess for x and the residual using the targets.

with y the vector of measurements

x = Φ^T y / nu = Φ^T y / (Φ_norm^2)
residuals = Φ x - y

Definition at line 233 of file primal_dual.h.

                                                      {
     return PrimalDual<SCALAR>::initial_guess(target(), Phi());
   }

References sopt::algorithm::PrimalDual< SCALAR >::Phi(), and sopt::algorithm::PrimalDual< SCALAR >::target().

Referenced by sopt::algorithm::ImagingPrimalDual< SCALAR >::operator()(), sopt::algorithm::PrimalDual< SCALAR >::operator()(), and sopt::algorithm::TVPrimalDual< SCALAR >::operator()().

◆ initial_guess() [2/2]

template<typename SCALAR >

static std::tuple<t_Vector, t_Vector> sopt::algorithm::PrimalDual< SCALAR >::initial_guess	(	t_Vector const &	target,
		t_LinearTransform const &	phi
	)

inlinestatic

Computes initial guess for x and the residual using the targets.

with y the vector of measurements

x = Φ^T y / nu = Φ^T y / (Φ_norm^2)
residuals = Φ x - y

This function simplifies creating overloads for operator() in PD wrappers.

Definition at line 243 of file primal_dual.h.

                                                                                     {
     std::tuple<t_Vector, t_Vector> guess;
     std::get<0>(guess) = static_cast<t_Vector>(phi.adjoint() * target) / phi.sq_norm();
     std::get<1>(guess) = target;
     return guess;
   }

References sopt::LinearTransform< VECTOR >::adjoint(), sopt::LinearTransform< VECTOR >::sq_norm(), and sopt::algorithm::PrimalDual< SCALAR >::target().

◆ is_converged() [1/2]

template<typename SCALAR >

PrimalDual<Scalar>& sopt::algorithm::PrimalDual< SCALAR >::is_converged ( std::function< bool(t_Vector const &x)> const & func )

inline

Convergence function that takes only the output as argument.

Definition at line 156 of file primal_dual.h.

                                                                                      {
     return is_converged([func](t_Vector const &x, t_Vector const &) { return func(x); });
   }

Referenced by sopt::algorithm::PrimalDual< SCALAR >::is_converged(), and TEST_CASE().

◆ is_converged() [2/2]

template<typename SCALAR >

bool sopt::algorithm::PrimalDual< SCALAR >::is_converged	(	t_Vector const &	x,
		t_Vector const &	residual
	)		const

inline

Facilitates call to user-provided convergence function.

Definition at line 170 of file primal_dual.h.

                                                                        {
     return static_cast<bool>(is_converged()) and is_converged()(x, residual);
   }

References sopt::algorithm::PrimalDual< SCALAR >::is_converged().

◆ operator()() [1/7]

template<typename SCALAR >

DiagnosticAndResult sopt::algorithm::PrimalDual< SCALAR >::operator() ( ) const

inline

Calls Primal Dual.

Parameters

[in] guess initial guess

Definition at line 205 of file primal_dual.h.

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

References sopt::algorithm::PrimalDual< SCALAR >::initial_guess(), and sopt::algorithm::PrimalDual< SCALAR >::DiagnosticAndResult::x.

Referenced by sopt::algorithm::PrimalDual< SCALAR >::operator()().

◆ operator()() [2/7]

template<typename SCALAR >

DiagnosticAndResult sopt::algorithm::PrimalDual< SCALAR >::operator() ( DiagnosticAndResult const & warmstart ) const

inline

Makes it simple to chain different calls to PD.

Definition at line 211 of file primal_dual.h.

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

References sopt::algorithm::PrimalDual< SCALAR >::Diagnostic::residual, and sopt::algorithm::PrimalDual< SCALAR >::DiagnosticAndResult::x.

◆ operator()() [3/7]

template<typename SCALAR >

DiagnosticAndResult sopt::algorithm::PrimalDual< SCALAR >::operator() ( std::tuple< t_Vector const &, t_Vector const & > const & guess ) const

inline

Calls Primal Dual.

Parameters

[in] guess initial guess

Definition at line 197 of file primal_dual.h.

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

References sopt::algorithm::PrimalDual< SCALAR >::DiagnosticAndResult::x.

◆ operator()() [4/7]

template<typename SCALAR >

DiagnosticAndResult sopt::algorithm::PrimalDual< SCALAR >::operator() ( std::tuple< t_Vector, t_Vector > const & guess ) const

inline

Calls Primal Dual.

Parameters

[in] guess initial guess

Definition at line 192 of file primal_dual.h.

                                                                                   {
     return operator()(std::tie(std::get<0>(guess), std::get<1>(guess)));
   }

References sopt::algorithm::PrimalDual< SCALAR >::operator()().

◆ operator()() [5/7]

template<typename SCALAR >

Diagnostic sopt::algorithm::PrimalDual< SCALAR >::operator() ( t_Vector & out ) const

inline

Calls Primal Dual.

Parameters

[out] out Output vector x

Definition at line 176 of file primal_dual.h.

176 { return operator()(out, initial_guess()); }

References sopt::algorithm::PrimalDual< SCALAR >::initial_guess(), and sopt::algorithm::PrimalDual< SCALAR >::operator()().

Referenced by sopt::algorithm::PrimalDual< SCALAR >::operator()().

◆ operator()() [6/7]

template<typename SCALAR >

Diagnostic sopt::algorithm::PrimalDual< SCALAR >::operator()	(	t_Vector &	out,
		std::tuple< t_Vector const &, t_Vector const & > const &	guess
	)		const

inline

Calls Primal Dual.

Parameters

[out]	out	Output vector x
[in]	guess	initial guess

Definition at line 186 of file primal_dual.h.

                                                                                          {
     return operator()(out, std::get<0>(guess), std::get<1>(guess));
   }

References sopt::algorithm::PrimalDual< SCALAR >::operator()().

◆ operator()() [7/7]

template<typename SCALAR >

Diagnostic sopt::algorithm::PrimalDual< SCALAR >::operator()	(	t_Vector &	out,
		std::tuple< t_Vector, t_Vector > const &	guess
	)		const

inline

Calls Primal Dual.

Parameters

[out]	out	Output vector x
[in]	guess	initial guess

Definition at line 180 of file primal_dual.h.

                                                                                         {
     return operator()(out, std::get<0>(guess), std::get<1>(guess));
   }

References sopt::algorithm::PrimalDual< SCALAR >::operator()().

◆ Phi()

template<typename SCALAR >

PrimalDual& ::type sopt::algorithm::PrimalDual< SCALAR >::Phi ( ARGS &&... args )

inline

Definition at line 218 of file primal_dual.h.

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

References sopt::linear_transform().

Referenced by sopt::algorithm::PrimalDual< SCALAR >::initial_guess().

◆ Psi()

template<typename SCALAR >

PrimalDual& ::type sopt::algorithm::PrimalDual< SCALAR >::Psi ( ARGS &&... args )

inline

Definition at line 224 of file primal_dual.h.

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

References sopt::linear_transform().

◆ SOPT_MACRO() [1/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	constraint	,
		t_Constraint
	)

A function applying a simple constraint.

◆ SOPT_MACRO() [2/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	f_proximal	,
		t_Proximal
	)

First proximal.

◆ SOPT_MACRO() [3/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	g_proximal	,
		t_Proximal
	)

Second proximal.

◆ SOPT_MACRO() [4/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	is_converged	,
		t_IsConverged
	)

A function verifying convergence.

It takes as input two arguments: the current solution x and the current residual.

◆ SOPT_MACRO() [5/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	itermax	,
		t_uint
	)

Maximum number of iterations.

◆ SOPT_MACRO() [6/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	Phi	,
		t_LinearTransform
	)

Measurement operator.

◆ SOPT_MACRO() [7/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	Psi	,
		t_LinearTransform
	)

Wavelet operator.

◆ SOPT_MACRO() [8/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	random_measurement_updater	,
		t_Random_Updater
	)

lambda that determines if to update measurements

◆ SOPT_MACRO() [9/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	random_wavelet_updater	,
		t_Random_Updater
	)

lambda that determines if to update wavelets

◆ SOPT_MACRO() [10/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	regulariser_strength	,
		Real
	)

γ parameter.

◆ SOPT_MACRO() [11/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	rho	,
		Real
	)

rho parameter

◆ SOPT_MACRO() [12/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	sigma	,
		Real
	)

sigma parameter

◆ SOPT_MACRO() [13/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	tau	,
		Real
	)

tau parameter

◆ SOPT_MACRO() [14/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	update_scale	,
		Real
	)

Update parameter.

◆ SOPT_MACRO() [15/15]

template<typename SCALAR >

sopt::algorithm::PrimalDual< SCALAR >::SOPT_MACRO	(	xi	,
		Real
	)

xi parameter

◆ target() [1/2]

template<typename SCALAR >

t_Vector const& sopt::algorithm::PrimalDual< SCALAR >::target ( ) const

inline

Vector of target measurements.

Definition at line 161 of file primal_dual.h.

161 { return target_; }

Referenced by sopt::algorithm::PrimalDual< SCALAR >::initial_guess(), and sopt::algorithm::PrimalDual< SCALAR >::target().

◆ target() [2/2]

template<typename SCALAR >

template<typename DERIVED >

PrimalDual<Scalar>& sopt::algorithm::PrimalDual< SCALAR >::target ( Eigen::MatrixBase< DERIVED > const & target )

inline

Sets the vector of target measurements.

Definition at line 164 of file primal_dual.h.

                                                                      {
     target_ = target;
     return *this;
   }

References sopt::algorithm::PrimalDual< SCALAR >::target().

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

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

Classes

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

template<typename SCALAR> class sopt::algorithm::PrimalDual< SCALAR >

Member Typedef Documentation

◆ Real

◆ Scalar

◆ t_Constraint

◆ t_IsConverged

◆ t_LinearTransform

◆ t_Proximal

◆ t_Random_Updater

◆ t_Vector

◆ value_type

Constructor & Destructor Documentation

◆ PrimalDual()

◆ ~PrimalDual()

Member Function Documentation

◆ f_proximal()

◆ g_proximal()

◆ initial_guess() [1/2]

◆ initial_guess() [2/2]

◆ is_converged() [1/2]

◆ is_converged() [2/2]

◆ operator()() [1/7]

◆ operator()() [2/7]

◆ operator()() [3/7]

◆ operator()() [4/7]

◆ operator()() [5/7]

◆ operator()() [6/7]

◆ operator()() [7/7]

◆ Phi()

◆ Psi()

◆ SOPT_MACRO() [1/15]

◆ SOPT_MACRO() [2/15]

◆ SOPT_MACRO() [3/15]

◆ SOPT_MACRO() [4/15]

◆ SOPT_MACRO() [5/15]

◆ SOPT_MACRO() [6/15]

◆ SOPT_MACRO() [7/15]

◆ SOPT_MACRO() [8/15]

◆ SOPT_MACRO() [9/15]

◆ SOPT_MACRO() [10/15]

◆ SOPT_MACRO() [11/15]

◆ SOPT_MACRO() [12/15]

◆ SOPT_MACRO() [13/15]

◆ SOPT_MACRO() [14/15]

◆ SOPT_MACRO() [15/15]

◆ target() [1/2]

◆ target() [2/2]

template<typename SCALAR>
class sopt::algorithm::PrimalDual< SCALAR >