NonlinearSystem Class Reference

Definition of a nonlinear system of equations. More...

Detailed Description

Definition of a nonlinear system of equations.

#include <NonlinearSystem.h>

Inheritance diagram for NonlinearSystem:

Public Member Functions
	NonlinearSystem (const OptionSet &options)
virtual void	init_scaling (const bool verbose=false)
	Compute algebraic Jacobian-based automatic scaling following https://cs.stanford.edu/people/paulliu/files/cs517-project.pdf.
BatchTensor	scale_residual (const BatchTensor &r) const
	Apply scaling to the residual.
BatchTensor	scale_Jacobian (const BatchTensor &J) const
	Apply scaling to the Jacobian.
BatchTensor	scale_direction (const BatchTensor &p) const
	Remove scaling from the search direction, i.e. \( J^{-1} r \).
virtual void	set_solution (const BatchTensor &x)
	Set the solution vector.
virtual BatchTensor	solution () const
	Get the solution vector.
BatchTensor	residual (const BatchTensor &x)
	Convenient shortcut to set the current solution, assemble and return the system residual.
void	residual ()
	Convenient shortcut to assemble and return the system residual.
BatchTensor	Jacobian (const BatchTensor &x)
	Convenient shortcut to set the current solution, assemble and return the system Jacobian.
void	Jacobian ()
	Convenient shortcut to assemble and return the system Jacobian.
std::tuple< BatchTensor, BatchTensor >	residual_and_Jacobian (const BatchTensor &x)
	Convenient shortcut to set the current solution, assemble and return the system residual and Jacobian.
void	residual_and_Jacobian ()
	Convenient shortcut to assemble and return the system residual and Jacobian.
const BatchTensor &	residual_view () const
const BatchTensor &	Jacobian_view () const
BatchTensor	residual_norm () const
	The residual norm.

Static Public Member Functions
static OptionSet	expected_options ()
static void	disable_automatic_scaling (OptionSet &options)
static void	enable_automatic_scaling (OptionSet &options)

Protected Member Functions
virtual void	assemble (bool residual, bool Jacobian)=0
	Compute the residual and Jacobian.

Protected Attributes
TorchSize	_ndof
	Number of degrees of freedom.
BatchTensor	_solution
	View for the solution of this nonlinear system.
BatchTensor	_residual
	View for the residual of this nonlinear system.
BatchTensor	_Jacobian
	View for the Jacobian of this nonlinear system.
BatchTensor	_scaled_residual
BatchTensor	_scaled_Jacobian
const bool	_autoscale
	If true, do automatic scaling.
const Real	_autoscale_tol
	Tolerance for convergence check of the iterative automatic scaling algorithm.
const unsigned int	_autoscale_miter
	Maximum number of iterations allowed for the iterative automatic scaling algorithm.
bool	_scaling_matrices_initialized
	Flag to indicate whether scaling matrices have been computed.
BatchTensor	_row_scaling
	Row scaling "matrix" – since it's a batched diagonal matrix, we are only storing its diagonals.
BatchTensor	_col_scaling
	Column scaling "matrix" – since it's a batched diagonal matrix, we are only storing its diagonals.

Constructor & Destructor Documentation

NonlinearSystem()

NonlinearSystem

(

const OptionSet &

options

)

Member Function Documentation

assemble()

virtual void assemble ( bool residual, bool Jacobian )

protectedpure virtual

Compute the residual and Jacobian.

Parameters

residual	Whether residual is requested
Jacobian	Whether Jacobian is requested

Implemented in Model, and TrustRegionSubProblem.

disable_automatic_scaling()

void disable_automatic_scaling ( OptionSet & options )

static

enable_automatic_scaling()

void enable_automatic_scaling ( OptionSet & options )

static

expected_options()

OptionSet expected_options ( )

static

init_scaling()

void init_scaling ( const bool verbose = false )

virtual

Compute algebraic Jacobian-based automatic scaling following https://cs.stanford.edu/people/paulliu/files/cs517-project.pdf.

Parameters

verbose

Print automatic scaling convergence information

Jacobian() [1/2]

void Jacobian

(

)

Convenient shortcut to assemble and return the system Jacobian.

Jacobian() [2/2]

BatchTensor Jacobian

(

const BatchTensor &

x

)

Convenient shortcut to set the current solution, assemble and return the system Jacobian.

Jacobian_view()

const BatchTensor & Jacobian_view ( ) const

inline

residual() [1/2]

void residual

(

)

Convenient shortcut to assemble and return the system residual.

residual() [2/2]

BatchTensor residual

(

const BatchTensor &

x

)

Convenient shortcut to set the current solution, assemble and return the system residual.

residual_and_Jacobian() [1/2]

void residual_and_Jacobian

(

)

Convenient shortcut to assemble and return the system residual and Jacobian.

residual_and_Jacobian() [2/2]

std::tuple< BatchTensor, BatchTensor > residual_and_Jacobian

(

const BatchTensor &

x

)

Convenient shortcut to set the current solution, assemble and return the system residual and Jacobian.

residual_norm()

BatchTensor residual_norm

(

)

const

The residual norm.

residual_view()

const BatchTensor & residual_view ( ) const

inline

scale_direction()

BatchTensor scale_direction

(

const BatchTensor &

p

)

const

Remove scaling from the search direction, i.e. \( J^{-1} r \).

scale_Jacobian()

BatchTensor scale_Jacobian

(

const BatchTensor &

J

)

const

Apply scaling to the Jacobian.

scale_residual()

BatchTensor scale_residual

(

const BatchTensor &

r

)

const

Apply scaling to the residual.

set_solution()

void set_solution ( const BatchTensor & x )

virtual

Set the solution vector.

Reimplemented in Model.

solution()

virtual BatchTensor solution ( ) const

inlinevirtual

Get the solution vector.

Member Data Documentation

_autoscale

const bool _autoscale

protected

If true, do automatic scaling.

_autoscale_miter

const unsigned int _autoscale_miter

protected

Maximum number of iterations allowed for the iterative automatic scaling algorithm.

_autoscale_tol

const Real _autoscale_tol

protected

Tolerance for convergence check of the iterative automatic scaling algorithm.

_col_scaling

BatchTensor _col_scaling

protected

Column scaling "matrix" – since it's a batched diagonal matrix, we are only storing its diagonals.

_Jacobian

BatchTensor _Jacobian

protected

View for the Jacobian of this nonlinear system.

_ndof

TorchSize _ndof

protected

Number of degrees of freedom.

_residual

BatchTensor _residual

protected

View for the residual of this nonlinear system.

_row_scaling

BatchTensor _row_scaling

protected

Row scaling "matrix" – since it's a batched diagonal matrix, we are only storing its diagonals.

_scaled_Jacobian

BatchTensor _scaled_Jacobian

protected

_scaled_residual

BatchTensor _scaled_residual

protected

_scaling_matrices_initialized

bool _scaling_matrices_initialized

protected

Flag to indicate whether scaling matrices have been computed.

_solution

BatchTensor _solution

protected

View for the solution of this nonlinear system.