Form of the lagrangian in augmented lagrangian. More...

#include <MatrixLagrangianForm.hpp>

Inheritance diagram for polyfem::solver::MatrixLagrangianForm:

Collaboration diagram for polyfem::solver::MatrixLagrangianForm:

Public Member Functions
	MatrixLagrangianForm (const StiffnessMatrix &A, const Eigen::MatrixXd &b, const StiffnessMatrix &A_proj={}, const Eigen::MatrixXd &b_pro={})
	Construct a new MatrixLagrangianForm object for the constraints Ax = b, where A is sparse.

std::string	name () const override

double	value_unweighted (const Eigen::VectorXd &x) const override
	Compute the value of the form.

void	first_derivative_unweighted (const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const override
	Compute the first derivative of the value wrt x.

void	second_derivative_unweighted (const Eigen::VectorXd &x, StiffnessMatrix &hessian) const override
	Compute the second derivative of the value wrt x.

void	update_lagrangian (const Eigen::VectorXd &x, const double k_al) override

double	compute_error (const Eigen::VectorXd &x) const override

Public Member Functions inherited from polyfem::solver::AugmentedLagrangianForm
	AugmentedLagrangianForm ()

virtual	~AugmentedLagrangianForm ()

void	set_initial_weight (const double k_al)

double	lagrangian_weight () const

const StiffnessMatrix &	constraint_matrix () const

const Eigen::MatrixXd &	constraint_value () const

const StiffnessMatrix &	constraint_projection_matrix () const

const Eigen::MatrixXd &	constraint_projection_vector () const

bool	has_projection () const

virtual bool	can_project () const

virtual void	project_gradient (Eigen::VectorXd &grad) const

virtual void	project_hessian (StiffnessMatrix &hessian) const

void	set_scale (const double scale) override
	sets the scale for the form

Public Member Functions inherited from polyfem::solver::Form
virtual	~Form ()

virtual void	init (const Eigen::VectorXd &x)
	Initialize the form.

virtual void	finish ()

virtual double	value (const Eigen::VectorXd &x) const
	Compute the value of the form multiplied with the weigth.

Eigen::VectorXd	value_per_element (const Eigen::VectorXd &x) const
	Compute the value of the form multiplied with the weigth.

virtual void	first_derivative (const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const
	Compute the first derivative of the value wrt x multiplied with the weigth.

void	second_derivative (const Eigen::VectorXd &x, StiffnessMatrix &hessian) const
	Compute the second derivative of the value wrt x multiplied with the weigth.

virtual bool	is_step_valid (const Eigen::VectorXd &x0, const Eigen::VectorXd &x1) const
	Determine if a step from solution x0 to solution x1 is allowed.

virtual double	max_step_size (const Eigen::VectorXd &x0, const Eigen::VectorXd &x1) const
	Determine the maximum step size allowable between the current and next solution.

virtual void	line_search_begin (const Eigen::VectorXd &x0, const Eigen::VectorXd &x1)
	Initialize variables used during the line search.

virtual void	line_search_end ()
	Clear variables used during the line search.

virtual void	post_step (const polysolve::nonlinear::PostStepData &data)
	Update fields after a step in the optimization.

virtual void	solution_changed (const Eigen::VectorXd &new_x)
	Update cached fields upon a change in the solution.

virtual void	update_quantities (const double t, const Eigen::VectorXd &x)
	Update time-dependent fields.

virtual void	init_lagging (const Eigen::VectorXd &x)
	Initialize lagged fields TODO: more than one step.

virtual void	update_lagging (const Eigen::VectorXd &x, const int iter_num)
	Update lagged fields.

virtual int	max_lagging_iterations () const
	Get the maximum number of lagging iteration allowable.

virtual bool	uses_lagging () const
	Does this form require lagging?

void	set_project_to_psd (bool val)
	Set project to psd.

bool	is_project_to_psd () const
	Get if the form's second derivative is projected to psd.

void	enable ()
	Enable the form.

void	disable ()
	Disable the form.

void	set_enabled (const bool enabled)
	Set if the form is enabled.

bool	enabled () const
	Determine if the form is enabled.

virtual double	weight () const
	Get the form's multiplicative constant weight.

void	set_weight (const double weight)
	Set the form's multiplicative constant weight.

virtual bool	is_step_collision_free (const Eigen::VectorXd &x0, const Eigen::VectorXd &x1) const
	Checks if the step is collision free.

void	set_output_dir (const std::string &output_dir)

Private Attributes
StiffnessMatrix	AtA

Eigen::VectorXd	Atb

Additional Inherited Members
Protected Member Functions inherited from polyfem::solver::AugmentedLagrangianForm
double	L_weight () const

double	A_weight () const

Protected Member Functions inherited from polyfem::solver::Form
std::string	resolve_output_path (const std::string &path) const

virtual Eigen::VectorXd	value_per_element_unweighted (const Eigen::VectorXd &x) const
	Compute the value of the form multiplied per element.

Protected Attributes inherited from polyfem::solver::AugmentedLagrangianForm
double	k_al_
	penalty parameter

Eigen::VectorXd	lagr_mults_
	vector of lagrange multipliers

StiffnessMatrix	A_
	Constraints matrix.

Eigen::MatrixXd	b_
	Constraints value.

StiffnessMatrix	A_proj_
	Constraints projection matrix.

Eigen::MatrixXd	b_proj_
	Constraints projection value.

Protected Attributes inherited from polyfem::solver::Form
bool	project_to_psd_ = false
	If true, the form's second derivative is projected to be positive semidefinite.

double	weight_ = 1
	weight of the form (e.g., AL penalty weight or Δt²)

bool	enabled_ = true
	If true, the form is enabled.

std::string	output_dir_

Detailed Description

Form of the lagrangian in augmented lagrangian.

Definition at line 8 of file MatrixLagrangianForm.hpp.

Constructor & Destructor Documentation

◆ MatrixLagrangianForm()

polyfem::solver::MatrixLagrangianForm::MatrixLagrangianForm	(	const StiffnessMatrix &	A,
		const Eigen::MatrixXd &	b,
		const StiffnessMatrix &	A_proj = `{}`,
		const Eigen::MatrixXd &	b_pro = `{}`
	)