Simultaneous-direction method of the multipliers. More...

#include <sdmm.h>

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

struct	DiagnosticAndResult

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 A and A^H operations. More...

using	t_Proximal = ProximalFunction< SCALAR >
	Type of the proximal functions. More...

using	t_IsConverged = ConvergenceFunction< SCALAR >
	Type of the convergence function. More...

Public Member Functions
	SDMM ()

virtual	~SDMM ()

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

	SOPT_MACRO (gamma, Real)
	Gamma. More...

	SOPT_MACRO (conjugate_gradient, ConjugateGradient)
	Conjugate gradient. More...

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

SDMM< SCALAR > &	conjugate_gradient (t_uint itermax, t_real tolerance)
	Helps setup conjugate gradient. More...

template<typename PROXIMAL , typename T >
SDMM< SCALAR > &	append (PROXIMAL proximal, T args)
	Appends a proximal and linear transform. More...

template<typename PROXIMAL >
SDMM< SCALAR > &	append (PROXIMAL proximal)
	Appends a proximal with identity as the linear transform. More...

template<typename PROXIMAL , typename L , typename LADJOINT >
SDMM< SCALAR > &	append (PROXIMAL proximal, L l, LADJOINT ladjoint)
	Appends a proximal with the linear transform as pair of functions. More...

template<typename PROXIMAL , typename L , typename LADJOINT >
SDMM< SCALAR > &	append (PROXIMAL proximal, L l, LADJOINT ladjoint, std::array< t_int, 3 > sizes)
	Appends a proximal with the linear transform as pair of functions. More...

template<typename PROXIMAL , typename L , typename LADJOINT >
SDMM< SCALAR > &	append (PROXIMAL proximal, L l, std::array< t_int, 3 > dsizes, LADJOINT ladjoint, std::array< t_int, 3 > isizes)
	Appends a proximal with the linear transform as pair of functions. More...

Diagnostic	operator() (t_Vector &out, t_Vector const &input) const
	Implements SDMM. More...

DiagnosticAndResult	operator() (t_Vector const &input) const

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

std::vector< t_LinearTransform > const &	transforms () const
	Linear transforms associated with each objective function. More...

std::vector< t_LinearTransform > &	transforms ()
	Linear transforms associated with each objective function. More...

t_LinearTransform const &	transforms (t_uint i) const
	Linear transform associated with a given objective function. More...

t_LinearTransform &	transforms (t_uint i)
	Linear transform associated with a given objective function. More...

std::vector< t_Proximal > const &	proximals () const
	Proximal of each objective function. More...

std::vector< t_Proximal > &	proximals ()
	Linear transforms associated with each objective function. More...

t_Proximal const &	proximals (t_uint i) const
	Proximal associated with a given objective function. More...

t_Proximal &	proximals (t_uint i)
	Proximal associated with a given objective function. More...

template<typename T0 >
proximal::ProximalExpression< t_Proximal const &, T0 >	proximals (t_uint i, Eigen::MatrixBase< T0 > const &x) const
	Lazy call to specific proximal function. More...

t_uint	size () const
	Number of terms. More...

template<typename T0 , typename... T>
auto	conjugate_gradient (T0 &&t0, T &&... args) const -> decltype(this->conjugate_gradient()(std::forward< T0 >(t0), std::forward< T >(args)...))
	Forwards to internal conjugage gradient object. More...

bool	is_converged (t_Vector const &x) const
	Forwards to convergence function parameter. More...

Detailed Description

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

Simultaneous-direction method of the multipliers.

The algorithm is detailed in (doi) 10.1093/mnras/stu202.

Definition at line 23 of file sdmm.h.

Member Typedef Documentation

◆ Real

template<typename SCALAR >

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

Real type.

Definition at line 43 of file sdmm.h.

◆ Scalar

template<typename SCALAR >

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

Scalar type.

Definition at line 41 of file sdmm.h.

◆ t_IsConverged

template<typename SCALAR >

using sopt::algorithm::SDMM< SCALAR >::t_IsConverged = ConvergenceFunction<SCALAR>

Type of the convergence function.

Definition at line 51 of file sdmm.h.

◆ t_LinearTransform

template<typename SCALAR >

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

Type of the A and A^H operations.

Definition at line 47 of file sdmm.h.

◆ t_Proximal

template<typename SCALAR >

using sopt::algorithm::SDMM< SCALAR >::t_Proximal = ProximalFunction<SCALAR>

Type of the proximal functions.

Definition at line 49 of file sdmm.h.

◆ t_Vector

template<typename SCALAR >

using sopt::algorithm::SDMM< SCALAR >::t_Vector = Vector<SCALAR>

Type of then underlying vectors.

Definition at line 45 of file sdmm.h.

◆ value_type

template<typename SCALAR >

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

Scalar type.

Definition at line 39 of file sdmm.h.

Constructor & Destructor Documentation

◆ SDMM()

template<typename SCALAR >

sopt::algorithm::SDMM< SCALAR >::SDMM ( )

inline

Definition at line 53 of file sdmm.h.

       : itermax_(std::numeric_limits<t_uint>::max()),
         gamma_(1e-8),
         conjugate_gradient_(std::numeric_limits<t_uint>::max(), 1e-6),
         is_converged_([](t_Vector const &) { return false; }) {}

◆ ~SDMM()

template<typename SCALAR >

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

inlinevirtual

Definition at line 58 of file sdmm.h.

58 {}

Member Function Documentation

◆ append() [1/5]

template<typename SCALAR >

template<typename PROXIMAL >

SDMM<SCALAR>& sopt::algorithm::SDMM< SCALAR >::append ( PROXIMAL proximal )

inline

Appends a proximal with identity as the linear transform.

Definition at line 97 of file sdmm.h.

                                           {
     return append(proximal, linear_transform_identity<Scalar>());
   }

References sopt::algorithm::SDMM< SCALAR >::append().

◆ append() [2/5]

template<typename SCALAR >

template<typename PROXIMAL , typename L , typename LADJOINT >

SDMM<SCALAR>& sopt::algorithm::SDMM< SCALAR >::append	(	PROXIMAL	proximal,
		L	l,
		LADJOINT	ladjoint
	)

inline

Appends a proximal with the linear transform as pair of functions.

Definition at line 102 of file sdmm.h.

                                                                   {
     return append(proximal, linear_transform<t_Vector>(l, ladjoint));
   }

References sopt::algorithm::SDMM< SCALAR >::append().

◆ append() [3/5]

template<typename SCALAR >

template<typename PROXIMAL , typename L , typename LADJOINT >

SDMM<SCALAR>& sopt::algorithm::SDMM< SCALAR >::append	(	PROXIMAL	proximal,
		L	l,
		LADJOINT	ladjoint,
		std::array< t_int, 3 >	sizes
	)

inline

Appends a proximal with the linear transform as pair of functions.

Definition at line 107 of file sdmm.h.

                                                                                             {
     return append(proximal, linear_transform<t_Vector>(l, ladjoint, sizes));
   }

References sopt::algorithm::SDMM< SCALAR >::append().

◆ append() [4/5]

template<typename SCALAR >

template<typename PROXIMAL , typename L , typename LADJOINT >

SDMM<SCALAR>& sopt::algorithm::SDMM< SCALAR >::append	(	PROXIMAL	proximal,
		L	l,
		std::array< t_int, 3 >	dsizes,
		LADJOINT	ladjoint,
		std::array< t_int, 3 >	isizes
	)

inline

Appends a proximal with the linear transform as pair of functions.

Definition at line 112 of file sdmm.h.

                                                   {
     return append(proximal, linear_transform<t_Vector>(l, dsizes, ladjoint, isizes));
   }

References sopt::algorithm::SDMM< SCALAR >::append().

◆ append() [5/5]

template<typename SCALAR >

template<typename PROXIMAL , typename T >

SDMM<SCALAR>& sopt::algorithm::SDMM< SCALAR >::append	(	PROXIMAL	proximal,
		T	args
	)

inline

Appends a proximal and linear transform.

Definition at line 90 of file sdmm.h.

                                                   {
     proximals().emplace_back(proximal);
     transforms().emplace_back(linear_transform(args));
     return *this;
   }

References sopt::linear_transform(), sopt::algorithm::SDMM< SCALAR >::proximals(), and sopt::algorithm::SDMM< SCALAR >::transforms().

Referenced by sopt::algorithm::SDMM< SCALAR >::append(), and TEST_CASE().

◆ conjugate_gradient() [1/2]

template<typename SCALAR >

template<typename T0 , typename... T>

auto sopt::algorithm::SDMM< SCALAR >::conjugate_gradient	(	T0 &&	t0,
		T &&...	args
	)		const -> decltype(this->conjugate_gradient()(std::forward<T0>(t0), std::forward<T>(args)...))

inline

Forwards to internal conjugage gradient object.

Removes the need for ugly extra brackets.

Definition at line 166 of file sdmm.h.

                                                                                           {
     return conjugate_gradient()(std::forward<T0>(t0), std::forward<T>(args)...);
   }

References sopt::algorithm::SDMM< SCALAR >::conjugate_gradient().

◆ conjugate_gradient() [2/2]

template<typename SCALAR >

SDMM<SCALAR>& sopt::algorithm::SDMM< SCALAR >::conjugate_gradient	(	t_uint	itermax,
		t_real	tolerance
	)

inline

Helps setup conjugate gradient.

Definition at line 83 of file sdmm.h.

                                                                      {
     conjugate_gradient_.itermax(itermax);
     conjugate_gradient_.tolerance(tolerance);
     return *this;
   }

Referenced by sopt::algorithm::SDMM< SCALAR >::conjugate_gradient(), main(), and TEST_CASE().

◆ is_converged()

template<typename SCALAR >

bool sopt::algorithm::SDMM< SCALAR >::is_converged ( t_Vector const & x ) const

inline

Forwards to convergence function parameter.

Definition at line 172 of file sdmm.h.

172 { return is_converged()(x); }

sopt::algorithm::SDMM::is_converged

bool is_converged(t_Vector const &x) const

Forwards to convergence function parameter.

Definition: sdmm.h:172

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

Referenced by sopt::algorithm::SDMM< SCALAR >::is_converged(), main(), and SCENARIO().

◆ operator()() [1/3]

template<typename SCALAR >

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

inline

Makes it simple to chain different calls to SDMM.

Definition at line 128 of file sdmm.h.

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

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

◆ operator()() [2/3]

template<typename SCALAR >

SDMM< SCALAR >::Diagnostic sopt::algorithm::SDMM< SCALAR >::operator()	(	t_Vector &	out,
		t_Vector const &	input
	)		const

Implements SDMM.

Follows Combettes and Pesquet "Proximal Splitting Methods in Signal Processing", arXiv:0912.3522v4 [math.OC] (2010), equation 65. See therein for notation

Definition at line 196 of file sdmm.h.

                                                                                         {
   sanity_check(input);
   bool convergence = false;
   t_uint niters(0);
   // Figures out where itermax or convergence reached
   auto const has_finished = [&convergence, &niters, this](t_Vector const &out) {
     convergence = is_converged(out);
     return niters >= itermax() or convergence;
   };
  
   SOPT_HIGH_LOG("Performing SDMM ");
   out = input;
   t_Vectors y(transforms().size());
   t_Vectors z(transforms().size());
  
   // Initial step replaces iteration update with initialization
   initialization(y, z, input);
   auto cg_diagnostic = solve_for_xn(out, y, z);
  
   while (not has_finished(out)) {
     SOPT_LOW_LOG("Iteration {}/{}. ", niters, itermax());
     // computes y and z from out and transforms
     update_directions(y, z, out);
     SOPT_LOW_LOG("   - sum z_ij = {}",
                  std::accumulate(z.begin(), z.end(), Scalar(0e0),
                                  [](Scalar const &a, t_Vector const &z) { return a + z.sum(); }));
     // computes x = L^-1 y
     cg_diagnostic = solve_for_xn(out, y, z);
     SOPT_LOW_LOG("   - CG Residual = {} in {}/{} iterations", cg_diagnostic.residual,
                  cg_diagnostic.niters, conjugate_gradient().itermax());
  
     ++niters;
   }
   return {niters, convergence, cg_diagnostic};
 }

References a, SOPT_HIGH_LOG, and SOPT_LOW_LOG.

◆ operator()() [3/3]

template<typename SCALAR >

DiagnosticAndResult sopt::algorithm::SDMM< SCALAR >::operator() ( t_Vector const & input ) const

inline

Definition at line 122 of file sdmm.h.

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

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

◆ proximals() [1/5]

template<typename SCALAR >

std::vector<t_Proximal>& sopt::algorithm::SDMM< SCALAR >::proximals ( )

inline

Linear transforms associated with each objective function.

Definition at line 146 of file sdmm.h.

146 { return proximals_; }

◆ proximals() [2/5]

template<typename SCALAR >

std::vector<t_Proximal> const& sopt::algorithm::SDMM< SCALAR >::proximals ( ) const

inline

Proximal of each objective function.

Definition at line 144 of file sdmm.h.

144 { return proximals_; }

Referenced by sopt::algorithm::SDMM< SCALAR >::append(), sopt::algorithm::SDMM< SCALAR >::proximals(), and sopt::algorithm::SDMM< SCALAR >::size().

◆ proximals() [3/5]

template<typename SCALAR >

t_Proximal& sopt::algorithm::SDMM< SCALAR >::proximals ( t_uint i )

inline

Proximal associated with a given objective function.

Definition at line 150 of file sdmm.h.

150 { return proximals_[i]; }

◆ proximals() [4/5]

template<typename SCALAR >

t_Proximal const& sopt::algorithm::SDMM< SCALAR >::proximals ( t_uint i ) const

inline

Proximal associated with a given objective function.

Definition at line 148 of file sdmm.h.

148 { return proximals_[i]; }

◆ proximals() [5/5]

template<typename SCALAR >

template<typename T0 >

proximal::ProximalExpression<t_Proximal const &, T0> sopt::algorithm::SDMM< SCALAR >::proximals	(	t_uint	i,
		Eigen::MatrixBase< T0 > const &	x
	)		const

inline

Lazy call to specific proximal function.

Definition at line 153 of file sdmm.h.

                                                     {
     return {proximals()[i], gamma(), x};
   }

References sopt::algorithm::SDMM< SCALAR >::proximals().

◆ size()

template<typename SCALAR >

t_uint sopt::algorithm::SDMM< SCALAR >::size ( ) const

inline

Number of terms.

Definition at line 159 of file sdmm.h.

159 { return proximals().size(); }

References sopt::algorithm::SDMM< SCALAR >::proximals().

◆ SOPT_MACRO() [1/4]

template<typename SCALAR >

sopt::algorithm::SDMM< SCALAR >::SOPT_MACRO	(	conjugate_gradient	,
		ConjugateGradient
	)

Conjugate gradient.

◆ SOPT_MACRO() [2/4]

template<typename SCALAR >

sopt::algorithm::SDMM< SCALAR >::SOPT_MACRO	(	gamma	,
		Real
	)

Gamma.

◆ SOPT_MACRO() [3/4]

template<typename SCALAR >

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

A function verifying convergence.

◆ SOPT_MACRO() [4/4]

template<typename SCALAR >

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

Maximum number of iterations.

◆ transforms() [1/4]

template<typename SCALAR >

std::vector<t_LinearTransform>& sopt::algorithm::SDMM< SCALAR >::transforms ( )

inline

Linear transforms associated with each objective function.

Definition at line 137 of file sdmm.h.

137 { return transforms_; }

◆ transforms() [2/4]

template<typename SCALAR >

std::vector<t_LinearTransform> const& sopt::algorithm::SDMM< SCALAR >::transforms ( ) const

inline

Linear transforms associated with each objective function.

Definition at line 135 of file sdmm.h.

135 { return transforms_; }

Referenced by sopt::algorithm::SDMM< SCALAR >::append(), and TEST_CASE().

◆ transforms() [3/4]

template<typename SCALAR >

t_LinearTransform& sopt::algorithm::SDMM< SCALAR >::transforms ( t_uint i )

inline

Linear transform associated with a given objective function.

Definition at line 141 of file sdmm.h.

141 { return transforms_[i]; }

◆ transforms() [4/4]

template<typename SCALAR >

t_LinearTransform const& sopt::algorithm::SDMM< SCALAR >::transforms ( t_uint i ) const

inline

Linear transform associated with a given objective function.

Definition at line 139 of file sdmm.h.

139 { return transforms_[i]; }

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

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

Classes

Public Types

Public Member Functions

Detailed Description

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

Member Typedef Documentation

◆ Real

◆ Scalar

◆ t_IsConverged

◆ t_LinearTransform

◆ t_Proximal

◆ t_Vector

◆ value_type

Constructor & Destructor Documentation

◆ SDMM()

◆ ~SDMM()

Member Function Documentation

◆ append() [1/5]

◆ append() [2/5]

◆ append() [3/5]

◆ append() [4/5]

◆ append() [5/5]

◆ conjugate_gradient() [1/2]

◆ conjugate_gradient() [2/2]

◆ is_converged()

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

◆ proximals() [1/5]

◆ proximals() [2/5]

◆ proximals() [3/5]

◆ proximals() [4/5]

◆ proximals() [5/5]

◆ size()

◆ SOPT_MACRO() [1/4]

◆ SOPT_MACRO() [2/4]

◆ SOPT_MACRO() [3/4]

◆ SOPT_MACRO() [4/4]

◆ transforms() [1/4]

◆ transforms() [2/4]

◆ transforms() [3/4]

◆ transforms() [4/4]

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