LinearInterpolation< T > Class Template Reference

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 >:

Public Member Functions
	LinearInterpolation (const OptionSet &options)
Public Member Functions inherited from Interpolation< T >
	Interpolation (const OptionSet &options)
Public Member Functions inherited from NonlinearParameter< T >
	NonlinearParameter (const OptionSet &options)
const Variable< T > &	param () const
	Get the nonlinear parameter.
Public Member Functions inherited from Model
	Model (const OptionSet &options)
	Construct a new Model object.
virtual void	diagnose (std::vector< Diagnosis > &) const override
	Check for common problems.
void	diagnose_nl_sys (std::vector< Diagnosis > &diagnoses) const
	Additional diagnostics for a nonlinear system.
virtual bool	is_nonlinear_system () const
	Whether this model defines one or more nonlinear equations to be solved.
std::tuple< const Tensor &, const Tensor &, const Tensor &, const Tensor &, const Tensor & >	get_system_matrices () const
	Get assembled system.
virtual void	reinit (const Tensor &tensor, int deriv_order)
	Allocate storage and setup views for all the variables of this model and recursively all of the sub-models. See the other overload for detailed description.
virtual void	reinit (TensorShapeRef batch_shape={}, int deriv_order=0, const torch::Device &device=default_device(), const torch::Dtype &dtype=default_dtype())
	Allocate storage and setup views for all the variables of this model and recursively all of the sub-models.
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.
virtual std::set< VariableName >	consumed_items () const override
	The variables that this model depends on.
virtual std::set< VariableName >	provided_items () const override
	The variables that this model defines as part of its output.
virtual bool	is_AD_enabled () const override
	Whether AD is enabled.
bool	using_AD_1st_derivative () const
	Whether this model is using AD to get 1st derivatives.
bool	using_AD_2nd_derivative () const
	Whether this model is using AD to get 2nd derivatives.
void	use_AD_derivatives (bool first=true, bool second=true)
	Tell this model to use AD to get derivatives.
void	prepare ()
	Prepare for evaluation.
virtual void	value ()
	Evalute the model.
virtual void	value_and_dvalue ()
	Evalute the model and compute its derivative.
virtual void	dvalue ()
	Evalute the derivative.
virtual void	value_and_dvalue_and_d2value ()
	Evalute the model and compute its first and second derivatives.
virtual void	d2value ()
	Evalute the second derivatives.
virtual void	dvalue_and_d2value ()
	Evalute the first and second derivatives.
virtual LabeledVector	value (const LabeledVector &in)
	Convenient shortcut to construct and return the model value.
virtual std::tuple< LabeledVector, LabeledMatrix >	value_and_dvalue (const LabeledVector &in)
	Convenient shortcut to construct and return the model value and its derivative.
virtual LabeledMatrix	dvalue (const LabeledVector &in)
	Convenient shortcut to construct and return the derivative.
virtual std::tuple< LabeledVector, LabeledMatrix, LabeledTensor3D >	value_and_dvalue_and_d2value (const LabeledVector &in)
	Convenient shortcut to construct and return the model's value, first and second derivative.
virtual LabeledTensor3D	d2value (const LabeledVector &in)
	Convenient shortcut to construct and return the model's second derivative.
virtual std::tuple< LabeledMatrix, LabeledTensor3D >	dvalue_and_d2value (const LabeledVector &in)
	Convenient shortcut to construct and return the model's first and second derivative.
Size	batch_dim () const
TensorShapeRef	batch_sizes () const
	Storage batch shape.
const torch::TensorOptions &	options () const
	Storage tensor options.
torch::Dtype	scalar_type () const
	Storage scalar type.
torch::Device	device () const
	Storage device.
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 (const OptionSet &options)
	Construct a new NEML2Object object.
virtual	~NEML2Object ()=default
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 (const OptionSet &options, NEML2Object *object)
const Storage< std::string, TensorValueBase > &	named_buffers () const
Storage< std::string, TensorValueBase > &	named_buffers ()
template<typename T , typename = typename std::enable_if_t<std::is_base_of_v<TensorBase<T>, T>>>
TensorValue< T > &	get_buffer (const std::string &name)
	}@
Public Member Functions inherited from ParameterStore
	ParameterStore (const OptionSet &options, NEML2Object *object)
const Storage< std::string, TensorValueBase > &	named_parameters () const
Storage< std::string, TensorValueBase > &	named_parameters ()
void	set_parameter (const std::string &, const Tensor &)
	}@
void	set_parameters (const std::map< std::string, Tensor > &)
	Set values for parameters.
TensorValueBase &	get_parameter (const std::string &name)
	Get a writable reference of a parameter.
const TensorValueBase &	get_parameter (const std::string &name) const
	Get a read-only reference of a parameter.
bool	has_nl_param () 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, const VariableBase * >	named_nonlinear_parameters (bool recursive=false) const
	Get all nonlinear parameters.
virtual std::map< std::string, Model * >	named_nonlinear_parameter_models (bool recursive=false) const
	Get all nonlinear parameters' models.
Public Member Functions inherited from VariableStore
	VariableStore (const OptionSet &options, Model *object)
LabeledAxis &	declare_axis (const std::string &name)
virtual void	setup_layout ()
	Setup the layouts of all the registered axes.
VariableBase *	input_variable (const VariableName &)
	Get the view of an input variable.
VariableBase *	output_variable (const VariableName &)
	Get the view of an output variable.
TensorType	input_type (const VariableName &) const
	Get the variable type of an input variable.
TensorType	output_type (const VariableName &) const
	Get the variable type of an output variable.
template<typename T = Tensor>
Variable< T > &	get_input_variable (const VariableName &name)
template<typename T = Tensor>
const Variable< T > &	get_input_variable (const VariableName &name) const
template<typename T = Tensor>
const Variable< T > &	get_output_variable (const VariableName &name)
template<typename T = Tensor>
const Variable< T > &	get_output_variable (const VariableName &name) const
LabeledAxis &	input_axis ()
const LabeledAxis &	input_axis () const
LabeledAxis &	output_axis ()
const LabeledAxis &	output_axis () const
Storage< VariableName, VariableBase > &	input_variables ()
const Storage< VariableName, VariableBase > &	input_variables () const
Storage< VariableName, VariableBase > &	output_variables ()
const Storage< VariableName, VariableBase > &	output_variables () const
LabeledVector &	input_storage ()
const LabeledVector &	input_storage () const
LabeledVector &	output_storage ()
const LabeledVector &	output_storage () const
LabeledMatrix &	derivative_storage ()
const LabeledMatrix &	derivative_storage () const
LabeledTensor3D &	second_derivative_storage ()
const LabeledTensor3D &	second_derivative_storage () const
Public Member Functions inherited from NonlinearSystem
	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.
Tensor	scale_residual (const Tensor &r) const
	Apply scaling to the residual.
Tensor	scale_Jacobian (const Tensor &J) const
	Apply scaling to the Jacobian.
Tensor	scale_direction (const Tensor &p) const
	Remove scaling from the search direction, i.e. \( J^{-1} r \).
virtual Tensor	solution () const
	Get the solution vector.
Tensor	residual (const Tensor &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.
Tensor	Jacobian (const Tensor &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< Tensor, Tensor >	residual_and_Jacobian (const Tensor &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 Tensor &	get_residual () const
const Tensor &	get_Jacobian () const
Tensor	residual_norm () const
	The residual norm.
virtual bool	is_AD_disabled () const final
	Whether AD is disabled.
Public Member Functions inherited from DiagnosticsInterface
	DiagnosticsInterface (NEML2Object *object)
template<typename... Args>
void	diagnostic_assert (std::vector< Diagnosis > &diagnoses, bool assertion, Args &&... args) const
void	diagnostic_assert_state (std::vector< Diagnosis > &diagnoses, const VariableBase &v) const
void	diagnostic_assert_old_state (std::vector< Diagnosis > &diagnoses, const VariableBase &v) const
void	diagnostic_assert_force (std::vector< Diagnosis > &diagnoses, const VariableBase &v) const
void	diagnostic_assert_old_force (std::vector< Diagnosis > &diagnoses, const VariableBase &v) const
void	diagnostic_assert_residual (std::vector< Diagnosis > &diagnoses, const VariableBase &v) const
void	diagnostic_check_input_variable (std::vector< Diagnosis > &diagnoses, const VariableBase &v) const
void	diagnostic_check_output_variable (std::vector< Diagnosis > &diagnoses, const VariableBase &v) const

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 NonlinearParameter< 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
virtual void	setup () override
	Setup this model.
virtual void	check_AD_limitation () const
void	check_inplace_dbg ()
	Check for potential in-place operation.
virtual void	check_input (const LabeledVector &in) const
	Check if the input has valid shape.
virtual LabeledVector	get_output ()
virtual LabeledMatrix	get_doutput_dinput ()
virtual LabeledTensor3D	get_d2output_dinput2 ()
template<typename T , typename = typename std::enable_if_t<std::is_base_of_v<Model, T>>>
T &	register_model (const std::string &name, int extra_deriv_order=0, bool nonlinear=false, bool merge_input=true)
	Register a model that the current model may use during its evaluation.
virtual void	reinit (bool in, bool out)
	Allocate storage and setup views for all the variables of this model and recursively all of the sub-models. See the other overload for detailed description.
virtual void	cache (TensorShapeRef batch_shape, int deriv_order, const torch::Device &device, const torch::Dtype &dtype)
bool	requires_grad () const
	Whether derivative has been requested for this model.
bool	requires_2nd_grad () const
	Whether 2nd derivative has been requested for this model.
virtual void	allocate_variables (bool in, bool out)
	Call VariableStore::allocate_variables recursively on all submodels.
virtual void	setup_input_views (VariableStore *host=nullptr) override
	Call VariableStore::setup_input_views recursively on all submodels.
virtual void	setup_submodel_input_views (VariableStore *host)
virtual void	setup_output_views ()
virtual void	setup_submodel_output_views ()
virtual void	setup_nonlinear_system ()
virtual void	cache (TensorShapeRef batch_shape)
	Cache the variable's batch shape.
virtual void	allocate_variables (TensorShapeRef batch_shape, const torch::TensorOptions &options, bool in, bool out, bool dout_din, bool d2out_din2)
	Allocate variable storages given the batch shape and tensor options.
virtual void	setup_output_views (bool out, bool dout_din, bool d2out_din2)
	Call VariableStore::setup_output_views recursively on all submodels.
virtual void	zero ()
virtual void	set_input (const LabeledVector &in)
	Set in to be the input of this model.
virtual void	set_solution (const Tensor &x) override
	Set x as the current solution of the nonlinear system.
virtual void	assemble (bool residual, bool Jacobian) override
	Compute the residual and Jacobian.
virtual void	zero (bool dout_din, bool d2out_din2)
	Zero out derivative and second derivative storage.
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 torch::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 std::string &input_option_name)
	Declare a buffer.
Protected Member Functions inherited from ParameterStore
virtual void	send_parameters_to (const torch::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 std::string &input_option_name, bool allow_nonlinear=false)
	Declare a parameter.
Protected Member Functions inherited from VariableStore
template<typename T , typename... S>
const Variable< T > &	declare_input_variable (S &&... name)
	Declare an input variable.
template<typename... S>
const Variable< Tensor > &	declare_input_variable (Size sz, TensorType t, S &&... name)
	Declare an input variable (with unknown base shape at compile time)
template<typename T , typename... S>
const Variable< Tensor > &	declare_input_variable_list (Size list_size, S &&... name)
	Declare an input variable that is a list of tensors of fixed size.
template<typename T , typename... S>
Variable< T > &	declare_output_variable (S &&... name)
	Declare an output variable.
template<typename... S>
Variable< Tensor > &	declare_output_variable (Size sz, TensorType t, S &&... name)
	Declare an input variable (with unknown base shape at compile time)
template<typename T , typename... S>
Variable< Tensor > &	declare_output_variable_list (Size list_size, S &&... name)
	Declare an output variable that is a list of tensors of fixed size.
template<typename T >
VariableName	declare_variable (LabeledAxis &axis, const VariableName &var) const
	Declare an item recursively on an axis.
VariableName	declare_variable (LabeledAxis &axis, const VariableName &var, Size sz) const
	Declare an item (with known storage size) recursively on an axis.
VariableName	declare_subaxis (LabeledAxis &axis, const VariableName &subaxis) const
	Declare a subaxis recursively on an axis.

Additional Inherited Members
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.
Protected Attributes inherited from NonlinearParameter< T >
Variable< T > &	_p
	The nonlinear parameter.
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 ParameterStore
std::map< std::string, const VariableBase * >	_nl_params
	Map from nonlinear parameter names to their corresponding variable views.
std::map< std::string, Model * >	_nl_param_models
	Map from nonlinear parameter names to models which evaluate them.
Protected Attributes inherited from NonlinearSystem
Size	_ndof
	Number of degrees of freedom.
Tensor	_solution
	View for the solution of this nonlinear system.
Tensor	_residual
	View for the residual of this nonlinear system.
Tensor	_Jacobian
	View for the Jacobian of this nonlinear system.
Tensor	_scaled_residual
Tensor	_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.
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.