Linearly interpolate the parameter along a single axis. More...

Detailed Description

template<typename T>
class neml2::LinearInterpolation< T >

Linearly interpolate the parameter along a single axis.

Currently, this object is hard-coded to always interpolate along the last batch dimension. A few examples of tensor shapes are listed below to demonstrate how broadcasting is handled:

Example 1: unbatched abscissa, unbatched ordinate (of type R2), unbatched input argument, interpolant size 100

abscissa shape: (100; )

ordinate shape: (100; 3, 3)

input shape: ( ; )

output shape: ( ; 3, 3)

Example 2: unbatched abscissa, unbatched ordinate (of type R2), batched input argument (with batch shape (2, 3)), interpolant size 100

abscissa shape: ( 100; )

ordinate shape: ( 100; 3, 3)

input shape: (2, 3 ; )

output shape: (2, 3 ; 3, 3)

Example 3: unbatched abscissa, batched ordinate (of type R2 and with batch shape (5, 1)), batched input argument (with batch shape (2, 5, 2)), interpolant size 100

abscissa shape: ( 100; )

ordinate shape: ( 5, 1, 100; 3, 3)

input shape: (2, 5, 2 ; )

output shape: (2, 5, 2 ; 3, 3)

Example 4: batched abscissa (with batch shape (7, 8, 1)), unbatched ordinate (of type R2), batched input argument (with batch shape (7, 8, 5)), interpolant size 100

abscissa shape: (7, 8, 1, 100; )

ordinate shape: ( 100; 3, 3)

input shape: (7, 8, 5 ; )

output shape: (7, 8, 5 ; 3, 3)

#include <LinearInterpolation.h>

Inheritance diagram for LinearInterpolation< T >:

[legend]

Public Member Functions
	LinearInterpolation (const OptionSet &options)

Public Member Functions inherited from Interpolation< T >
	Interpolation (const OptionSet &options)

Public Member Functions inherited from Model
	Model (const OptionSet &options)
	Construct a new Model object.

void	setup () override
	Setup this object.

void	diagnose () const override
	Check for common problems.

virtual bool	defines_values () const
	Whether this model defines output values.

virtual bool	defines_derivatives () const
	Whether this model defines first derivatives.

virtual bool	defines_second_derivatives () const
	Whether this model defines second derivatives.

virtual bool	is_nonlinear_system () const
	Whether this model defines one or more nonlinear equations to be solved.

virtual bool	is_jit_enabled () const
	Whether JIT is enabled.

virtual void	to (const TensorOptions &options)
	Send model to a different device or dtype.

const std::vector< Model * > &	registered_models () const
	The models that may be used during the evaluation of this model.

Model *	registered_model (const std::string &name) const
	Get a registered model by its name.

void	register_nonlinear_parameter (const std::string &pname, const NonlinearParameter &param)
	Register a nonlinear parameter.

bool	has_nl_param (bool recursive=false) const
	Whether this parameter store has any nonlinear parameter.

const VariableBase *	nl_param (const std::string &) const
	Query the existence of a nonlinear parameter.

virtual std::map< std::string, NonlinearParameter >	named_nonlinear_parameters (bool recursive=false) const
	Get all nonlinear parameters.

std::set< VariableName >	consumed_items () const override
	The variables that this model depends on.

std::set< VariableName >	provided_items () const override
	The variables that this model defines as part of its output.

void	request_AD (VariableBase &y, const VariableBase &u)
	Request to use AD to compute the first derivative of a variable.

void	request_AD (VariableBase &y, const VariableBase &u1, const VariableBase &u2)
	Request to use AD to compute the second derivative of a variable.

void	forward (bool out, bool dout, bool d2out)
	Forward operator without jit.

void	forward_maybe_jit (bool out, bool dout, bool d2out)
	Forward operator with jit.

std::string	variable_name_lookup (const ATensor &var)
	Look up the name of a variable in the traced graph.

virtual ValueMap	value (const ValueMap &in)
	Convenient shortcut to construct and return the model value.

virtual ValueMap	value (ValueMap &&in)

virtual std::tuple< ValueMap, DerivMap >	value_and_dvalue (const ValueMap &in)
	Convenient shortcut to construct and return the model value and its derivative.

virtual std::tuple< ValueMap, DerivMap >	value_and_dvalue (ValueMap &&in)

virtual DerivMap	dvalue (const ValueMap &in)
	Convenient shortcut to construct and return the derivative.

virtual DerivMap	dvalue (ValueMap &&in)

virtual std::tuple< ValueMap, DerivMap, SecDerivMap >	value_and_dvalue_and_d2value (const ValueMap &in)
	Convenient shortcut to construct and return the model's value, first and second derivative.

virtual std::tuple< ValueMap, DerivMap, SecDerivMap >	value_and_dvalue_and_d2value (ValueMap &&in)

virtual SecDerivMap	d2value (const ValueMap &in)
	Convenient shortcut to construct and return the model's second derivative.

virtual SecDerivMap	d2value (ValueMap &&in)

virtual std::tuple< DerivMap, SecDerivMap >	dvalue_and_d2value (const ValueMap &in)
	Convenient shortcut to construct and return the model's first and second derivative.

virtual std::tuple< DerivMap, SecDerivMap >	dvalue_and_d2value (ValueMap &&in)

Public Member Functions inherited from Data
	Data (const OptionSet &options)
	Construct a new Data object.

const std::vector< Data * > &	registered_data () const
	All the registered data objects.

Public Member Functions inherited from NEML2Object
	NEML2Object ()=delete

	NEML2Object (NEML2Object &&)=delete

	NEML2Object (const NEML2Object &)=delete

NEML2Object &	operator= (NEML2Object &&)=delete

NEML2Object &	operator= (const NEML2Object &)=delete

virtual	~NEML2Object ()=default

	NEML2Object (const OptionSet &options)
	Construct a new NEML2Object object.

const OptionSet &	input_options () const

const std::string &	name () const
	A readonly reference to the object's name.

const std::string &	type () const
	A readonly reference to the object's type.

const std::string &	path () const
	A readonly reference to the object's path.

const std::string &	doc () const
	A readonly reference to the object's docstring.

template<typename T = NEML2Object>
const T *	host () const
	Get a readonly pointer to the host.

template<typename T = NEML2Object>
T *	host ()
	Get a writable pointer to the host.

Public Member Functions inherited from BufferStore
	BufferStore (NEML2Object *object)

	BufferStore (const BufferStore &)=delete

	BufferStore (BufferStore &&)=delete

BufferStore &	operator= (const BufferStore &)=delete

BufferStore &	operator= (BufferStore &&)=delete

virtual	~BufferStore ()=default

const std::map< std::string, std::unique_ptr< TensorValueBase > > &	named_buffers () const

std::map< std::string, std::unique_ptr< TensorValueBase > > &	named_buffers ()

const TensorValueBase &	get_buffer (const std::string &name) const
	}@

TensorValueBase &	get_buffer (const std::string &name)
	Get a writable reference of a buffer.

Public Member Functions inherited from ParameterStore
	ParameterStore (Model *object)

	ParameterStore (const ParameterStore &)=delete

	ParameterStore (ParameterStore &&)=delete

ParameterStore &	operator= (const ParameterStore &)=delete

ParameterStore &	operator= (ParameterStore &&)=delete

virtual	~ParameterStore ()=default

const std::map< std::string, std::unique_ptr< TensorValueBase > > &	named_parameters () const

std::map< std::string, std::unique_ptr< TensorValueBase > > &	named_parameters ()

const TensorValueBase &	get_parameter (const std::string &name) const
	}@

TensorValueBase &	get_parameter (const std::string &name)
	Get a writable reference of a parameter.

void	set_parameter (const std::string &, const Tensor &)
	Set the value for a parameter.

void	set_parameters (const std::map< std::string, Tensor > &)
	Set values for parameters.

Public Member Functions inherited from VariableStore
	VariableStore (Model *object)

	VariableStore (const VariableStore &)=delete

	VariableStore (VariableStore &&)=delete

VariableStore &	operator= (const VariableStore &)=delete

VariableStore &	operator= (VariableStore &&)=delete

virtual	~VariableStore ()=default

LabeledAxis &	declare_axis (const std::string &name)

virtual void	setup_layout ()
	Setup the layout of all the registered axes.

const TensorOptions &	variable_options () const
	Current tensor options for variables.

LabeledAxis &	input_axis ()

const LabeledAxis &	input_axis () const

LabeledAxis &	output_axis ()

const LabeledAxis &	output_axis () const

VariableStorage &	input_variables ()

const VariableStorage &	input_variables () const

VariableStorage &	output_variables ()

const VariableStorage &	output_variables () const

VariableBase &	input_variable (const VariableName &)

const VariableBase &	input_variable (const VariableName &) const

VariableBase &	output_variable (const VariableName &)

const VariableBase &	output_variable (const VariableName &) const

void	assign_input (const ValueMap &vals)

void	assign_input (ValueMap &&vals)
	Assign input variable values.

void	assign_output (const ValueMap &vals)
	Assign output variable values.

void	assign_output_derivatives (const DerivMap &derivs)
	Assign variable derivatives.

ValueMap	collect_input () const

ValueMap	collect_output () const

DerivMap	collect_output_derivatives () const
	Collect variable derivatives.

SecDerivMap	collect_output_second_derivatives () const
	Collect variable second derivatives.

Public Member Functions inherited from NonlinearSystem
	NonlinearSystem (const NonlinearSystem &)=default

	NonlinearSystem (NonlinearSystem &&) noexcept=default

NonlinearSystem &	operator= (const NonlinearSystem &)=delete

NonlinearSystem &	operator= (NonlinearSystem &&)=delete

virtual	~NonlinearSystem ()=default

	NonlinearSystem (const OptionSet &options)

virtual void	init_scaling (const Sol< false > &x, const bool verbose=false)
	Compute algebraic Jacobian-based automatic scaling following https://cs.stanford.edu/people/paulliu/files/cs517-project.pdf.

Res< true >	scale (const Res< false > &r) const
	Apply scaling to the residual.

Res< false >	unscale (const Res< true > &r) const
	Remove scaling to the residual.

Jac< true >	scale (const Jac< false > &J) const
	Apply scaling to the Jacobian.

Jac< false >	unscale (const Jac< true > &J) const
	Remove scaling to the Jacobian.

Sol< true >	scale (const Sol< false > &u) const
	Apply scaling to the solution.

Sol< false >	unscale (const Sol< true > &u) const
	Remove scaling to the solution.

void	set_guess (const Sol< true > &x)
	Set the current guess.

template<bool scaled>
Res< scaled >	residual ()
	Assemble and return the residual.

template<bool scaled>
Res< scaled >	residual (const Sol< scaled > &x)
	Convenient shortcut to set the current guess, assemble and return the residual.

template<bool scaled>
Jac< scaled >	Jacobian ()
	Assemble and return the Jacobian.

template<bool scaled>
Jac< scaled >	Jacobian (const Sol< scaled > &x)
	Convenient shortcut to set the current guess, assemble and return the Jacobian.

template<bool scaled>
std::tuple< Res< scaled >, Jac< scaled > >	residual_and_Jacobian ()
	Assemble and return the residual and Jacobian.

template<bool scaled>
std::tuple< Res< scaled >, Jac< scaled > >	residual_and_Jacobian (const Sol< scaled > &x)
	Convenient shortcut to set the current guess, assemble and return the residual and Jacobian.

Public Member Functions inherited from DependencyDefinition< VariableName >
	DependencyDefinition ()=default

	DependencyDefinition (DependencyDefinition &&)=delete

	DependencyDefinition (const DependencyDefinition &)=delete

DependencyDefinition &	operator= (const DependencyDefinition &)=delete

DependencyDefinition &	operator= (DependencyDefinition &&)=delete

virtual	~DependencyDefinition ()=default

Public Member Functions inherited from DiagnosticsInterface
	DiagnosticsInterface ()=delete

	DiagnosticsInterface (NEML2Object *object)

	DiagnosticsInterface (DiagnosticsInterface &&)=delete

	DiagnosticsInterface (const DiagnosticsInterface &)=delete

DiagnosticsInterface &	operator= (const DiagnosticsInterface &)=delete

DiagnosticsInterface &	operator= (DiagnosticsInterface &&)=delete

virtual	~DiagnosticsInterface ()=default

const NEML2Object &	object () const
	Get the object.

Static Public Member Functions
static OptionSet	expected_options ()

Static Public Member Functions inherited from Interpolation< T >
static OptionSet	expected_options ()

Static Public Member Functions inherited from Model
static OptionSet	expected_options ()

Static Public Member Functions inherited from Data
static OptionSet	expected_options ()

Static Public Member Functions inherited from NEML2Object
static OptionSet	expected_options ()

Static Public Member Functions inherited from NonlinearSystem
static OptionSet	expected_options ()

static void	disable_automatic_scaling (OptionSet &options)

static void	enable_automatic_scaling (OptionSet &options)

Protected Member Functions
void	set_value (bool out, bool dout_din, bool d2out_din2) override
	The map between input -> output, and optionally its derivatives.

Protected Member Functions inherited from Model
void	diagnostic_assert_state (const VariableBase &v) const

void	diagnostic_assert_old_state (const VariableBase &v) const

void	diagnostic_assert_force (const VariableBase &v) const

void	diagnostic_assert_old_force (const VariableBase &v) const

void	diagnostic_assert_residual (const VariableBase &v) const

void	diagnostic_check_input_variable (const VariableBase &v) const

void	diagnostic_check_output_variable (const VariableBase &v) const

void	diagnose_nl_sys () const
	Additional diagnostics for a nonlinear system.

virtual void	link_input_variables ()

virtual void	link_input_variables (Model *submodel)

virtual void	link_output_variables ()

virtual void	link_output_variables (Model *submodel)

void	clear_input () override

void	clear_output () override

void	zero_input () override

void	zero_output () override

virtual void	request_AD ()

template<typename T = Model, typename = typename std::enable_if_t<std::is_base_of_v<Model, T>>>
T &	register_model (const std::string &name, bool nonlinear=false, bool merge_input=true)
	Register a model that the current model may use during its evaluation.

void	assign_input_stack (jit::Stack &stack)

jit::Stack	collect_input_stack () const

void	set_guess (const Sol< false > &) override
	Set the unscaled current guess.

void	assemble (Res< false > , Jac< false > ) override
	Compute the unscaled residual and Jacobian.

Protected Member Functions inherited from Data
template<typename T, typename = typename std::enable_if_t<std::is_base_of_v<Data, T>>>
T &	register_data (const std::string &name)

virtual void	send_buffers_to (const TensorOptions &options)
	Send all buffers to `options`.

template<typename T, typename = typename std::enable_if_t<std::is_base_of_v<TensorBase<T>, T>>>
const T &	declare_buffer (const std::string &name, const T &rawval)
	Declare a buffer.

template<typename T, typename = typename std::enable_if_t<std::is_base_of_v<TensorBase<T>, T>>>
const T &	declare_buffer (const std::string &name, const TensorName< T > &tensorname)
	Declare a buffer.

template<typename T, typename = typename std::enable_if_t<std::is_base_of_v<TensorBase<T>, T>>>
const T &	declare_buffer (const std::string &name, const std::string &input_option_name)
	Declare a buffer.

void	assign_buffer_stack (jit::Stack &stack)
	Assign stack to buffers.

jit::Stack	collect_buffer_stack () const
	Collect stack from buffers.

virtual void	send_parameters_to (const TensorOptions &options)
	Send parameters to options.

template<typename T, typename = typename std::enable_if_t<std::is_base_of_v<TensorBase<T>, T>>>
const T &	declare_parameter (const std::string &name, const T &rawval)
	Declare a parameter.

template<typename T, typename = typename std::enable_if_t<std::is_base_of_v<TensorBase<T>, T>>>
const T &	declare_parameter (const std::string &name, const TensorName< T > &tensorname, bool allow_nonlinear)
	Declare a parameter.

template<typename T, typename = typename std::enable_if_t<std::is_base_of_v<TensorBase<T>, T>>>
const T &	declare_parameter (const std::string &name, const std::string &input_option_name, bool allow_nonlinear=false)
	Declare a parameter.

void	assign_parameter_stack (jit::Stack &stack)
	Assign stack to parameters.

jit::Stack	collect_parameter_stack () const
	Collect stack from parameters.

Protected Member Functions inherited from VariableStore
virtual void	send_variables_to (const TensorOptions &options)
	Send padding variables to options.

template<typename T>
const Variable< T > &	declare_input_variable (const char *name, TensorShapeRef list_shape={})
	Declare an input variable.

template<typename T>
const Variable< T > &	declare_input_variable (const VariableName &name, TensorShapeRef list_shape={})
	Declare an input variable.

template<typename T>
Variable< T > &	declare_output_variable (const char *name, TensorShapeRef list_shape={})
	Declare an output variable.

template<typename T>
Variable< T > &	declare_output_variable (const VariableName &name, TensorShapeRef list_shape={})
	Declare an output variable.

const VariableBase *	clone_input_variable (const VariableBase &var, const VariableName &new_name={})
	Clone a variable and put it on the input axis.

VariableBase *	clone_output_variable (const VariableBase &var, const VariableName &new_name={})
	Clone a variable and put it on the output axis.

void	assign_input_stack (jit::Stack &stack)
	Assign stack to input variables.

void	assign_output_stack (jit::Stack &stack, bool out, bool dout, bool d2out)
	Assign stack to output variables and derivatives.

jit::Stack	collect_input_stack () const
	Collect stack from input variables.

jit::Stack	collect_output_stack (bool out, bool dout, bool d2out) const
	Collect stack from output variables and derivatives.

Additional Inherited Members
Public Types inherited from VariableStore
using	VariableStorage = std::map<VariableName, std::unique_ptr<VariableBase>>

Protected Attributes inherited from Interpolation< T >
const Scalar &	_X
	The abscissa values of the interpolant.

const T &	_Y
	The ordinate values of the interpolant.

const Variable< Scalar > &	_x
	Argument of interpolation.

Variable< T > &	_p
	The interpolated value.

Protected Attributes inherited from Model
std::vector< Model * >	_registered_models
	Models this model may use during its evaluation.

Protected Attributes inherited from Data
std::vector< Data * >	_registered_data
	Registered Data objects.

Protected Attributes inherited from NonlinearSystem
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 = false
	Flag to indicate whether scaling matrices have been computed.

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

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

Constructor & Destructor Documentation

◆ LinearInterpolation()

template<typename T>

LinearInterpolation ( const OptionSet & options )

Member Function Documentation

◆ expected_options()

template<typename T>

OptionSet expected_options ( )

static

◆ set_value()

template<typename T>

void set_value	(	bool	out,
		bool	dout_din,
		bool	d2out_din2 )

overrideprotectedvirtual

The map between input -> output, and optionally its derivatives.

Implements Model.

Detailed Description

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ LinearInterpolation()

Member Function Documentation

◆ expected_options()

◆ set_value()