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

std::shared_ptr< 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< std::shared_ptr< 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.

Factory *	factory () const
	Get the factory that created this object.

const Settings &	settings () const
	Settings.

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.

template<typename T >
const T &	resolve_tensor (const std::string &name)
	Resolve a TensorName to a Tensor.

template<class T >
std::shared_ptr< T >	get_object (const std::string &section, const std::string &name)

template<class T = Solver>
std::shared_ptr< T >	get_solver (const std::string &name)
	Get a solver from the factory.

template<class T = Data>
std::shared_ptr< T >	get_data (const std::string &name)
	Get a data from the factory.

template<class T = Model>
std::shared_ptr< T >	get_model (const std::string &name)
	Get a model from the factory.

template<class T = Driver>
std::shared_ptr< T >	get_driver (const std::string &name)
	Get a driver from the factory.

template<class T = WorkScheduler>
std::shared_ptr< T >	get_scheduler (const std::string &name)
	Get a scheduler from the factory.

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

virtual void	clear_derivatives ()

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 ()

template<typename T2 >
static T2	mask (const T2 &in, const Scalar &m)
	Apply the mask tensor `m` on the input `in`.

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

void	check_precision () const
	Check the current default precision and warn if it's not double precision.

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)

Protected Member Functions inherited from BufferStore
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.

Protected Member Functions inherited from ParameterStore
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={}, bool allow_duplicate=false)
	Declare an input variable.

template<typename T >
const Variable< T > &	declare_input_variable (const VariableName &name, TensorShapeRef list_shape={}, bool allow_duplicate=false)
	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.

Protected Member Functions inherited from NonlinearSystem

Protected Attributes
const Scalar &	_X
	The abscissa values of the interpolant.

const Variable< Scalar > &	_x
	Argument of interpolation.

Protected Attributes inherited from Interpolation< T >
const T &	_Y
	The ordinate values of the interpolant.

Variable< T > &	_p
	The interpolated value.

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

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

Protected Attributes inherited from NonlinearSystem
const bool	_autoscale
	If true, do automatic scaling.

const double	_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.

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

Constructor & Destructor Documentation

◆ LinearInterpolation()

template<typename T >

LinearInterpolation ( const OptionSet & options )

Member Function Documentation

◆ expected_options()

template<typename T >

OptionSet expected_options ( )

static

◆ mask()

template<typename T >

template<typename T2 >

T2 mask	(	const T2 &	in,
		const Scalar &	m )

static

Apply the mask tensor m on the input in.

This method additionally handles the necessary expanding and reshaping based on two assumptions:

The mask only selects 1 single batch along the interpolated dimension.
We are always interpolating along the last batch dimension.

So if some day we relax the 2nd assumption, this method need to be adapted accordingly.

◆ 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.

Member Data Documentation

◆ _X

template<typename T >

const Scalar& _X

protected

The abscissa values of the interpolant.

◆ _x

template<typename T >

const Variable<Scalar>& _x

protected

Argument of interpolation.

Detailed Description

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ LinearInterpolation()

Member Function Documentation

◆ expected_options()

◆ mask()

◆ set_value()

Member Data Documentation

◆ _X

◆ _x