Class representing a 2D piecewise constant. More...

#include <piecewise.hpp>

Inheritance diagram for graph::piecewise_2D_node< T, SAFE_MATH >:

Public Member Functions
	piecewise_2D_node (const backend::buffer< T > &d, const size_t n, shared_leaf< T, SAFE_MATH > x, const T x_scale, const T x_offset, shared_leaf< T, SAFE_MATH > y, const T y_scale, const T y_offset)
	Construct 2D a piecewise constant node.

size_t	get_num_columns () const
	Get the number of columns.

size_t	get_num_rows () const
	Get the number of columns.

T	get_x_scale () const
	Get x argument scale.

T	get_x_offset () const
	Get x argument offset.

T	get_y_scale () const
	Get y argument scale.

T	get_y_offset () const
	Get y argument offset.

virtual backend::buffer< T >	evaluate ()
	Evaluate the results of the piecewise constant.

virtual shared_leaf< T, SAFE_MATH >	reduce ()
	Reduction method.

virtual shared_leaf< T, SAFE_MATH >	df (shared_leaf< T, SAFE_MATH > x)
	Transform node to derivative.

virtual void	compile_preamble (std::ostringstream &stream, jit::register_map &registers, jit::visiter_map &visited, jit::register_usage &usage, jit::texture1d_list &textures1d, jit::texture2d_list &textures2d, int &avail_const_mem)
	Compile preamble.

virtual shared_leaf< T, SAFE_MATH >	compile (std::ostringstream &stream, jit::register_map &registers, jit::register_map &indices, const jit::register_usage &usage)
	Compile the node.

virtual bool	is_match (shared_leaf< T, SAFE_MATH > x)
	Querey if the nodes match.

virtual void	to_latex () const
	Convert the node to latex.

virtual shared_leaf< T, SAFE_MATH >	to_vizgraph (std::stringstream &stream, jit::register_map &registers)
	Convert the node to vizgraph.

virtual bool	is_constant () const
	Test if node is a constant.

virtual bool	has_constant_zero () const
	Test the constant node has a zero.

virtual bool	is_all_variables () const
	Test if node acts like a variable.

virtual bool	is_power_like () const
	Test if the node acts like a power of variable.

virtual shared_leaf< T, SAFE_MATH >	get_power_base ()
	Get the base of a power.

virtual shared_leaf< T, SAFE_MATH >	get_power_exponent () const
	Get the exponent of a power.

bool	is_arg_match (shared_leaf< T, SAFE_MATH > x)
	Check if the args match.

bool	is_row_match (shared_leaf< T, SAFE_MATH > x)
	Do the rows match.

bool	is_col_match (shared_leaf< T, SAFE_MATH > x)
	Do the columns match.

Public Member Functions inherited from graph::branch_node< T, SAFE_MATH >
	branch_node (shared_leaf< T, SAFE_MATH > l, shared_leaf< T, SAFE_MATH > r, const std::string s)
	Assigns the left and right branches.

	branch_node (shared_leaf< T, SAFE_MATH > l, shared_leaf< T, SAFE_MATH > r, const std::string s, const size_t count, const bool pseudo)
	Assigns the left and right branches.

shared_leaf< T, SAFE_MATH >	get_left ()
	Get the left branch.

shared_leaf< T, SAFE_MATH >	get_right ()
	Get the right branch.

Public Member Functions inherited from graph::leaf_node< T, SAFE_MATH >
	leaf_node (const std::string s, const size_t count, const bool pseudo)
	Construct a basic node.

virtual	~leaf_node ()
	Destructor.

virtual std::shared_ptr< leaf_node< T, SAFE_MATH > >	df (std::shared_ptr< leaf_node< T, SAFE_MATH > > x)=0
	Transform node to derivative.

virtual bool	is_match (std::shared_ptr< leaf_node< T, SAFE_MATH > > x)
	Querey if the nodes match.

bool	is_power_base_match (std::shared_ptr< leaf_node< T, SAFE_MATH > > x)
	Check if the base of the powers match.

virtual void	set (const T d)
	Set the value of variable data.

virtual void	set (const size_t index, const T d)
	Set the value of variable data.

virtual void	set (const std::vector< T > &d)
	Set the value of variable data.

virtual void	set (const backend::buffer< T > &d)
	Set the value of variable data.

bool	is_normal ()
	Test if the result is normal.

size_t	get_hash () const
	Get the hash for the node.

size_t	get_complexity () const
	Get the number of nodes in the subgraph.

virtual bool	has_pseudo () const
	Query if the node contains pseudo variables.

virtual std::shared_ptr< leaf_node< T, SAFE_MATH > >	remove_pseudo ()
	Remove pseudo variable nodes.

virtual void	endline (std::ostringstream &stream, const jit::register_usage &usage) const final
	End a line in the kernel source.

Additional Inherited Members
Public Types inherited from graph::leaf_node< T, SAFE_MATH >
typedef T	base
	Type def to retrieve the backend type.

Static Public Attributes inherited from graph::leaf_node< T, SAFE_MATH >
static thread_local caches_t	caches
	A per thread instance of the cache structure.

Protected Attributes inherited from graph::branch_node< T, SAFE_MATH >
shared_leaf< T, SAFE_MATH >	left
	Left branch of the tree.

shared_leaf< T, SAFE_MATH >	right
	Right branch of the tree.

Protected Attributes inherited from graph::leaf_node< T, SAFE_MATH >
const size_t	hash
	Hash for node.

const size_t	complexity
	Graph complexity.

std::map< size_t, std::shared_ptr< leaf_node< T, SAFE_MATH > > >	df_cache
	Cache derivative terms.

const bool	contains_pseudo
	Node contains pseudo variables.

Detailed Description

template<jit::float_scalar T, bool SAFE_MATH = false>
class graph::piecewise_2D_node< T, SAFE_MATH >

Class representing a 2D piecewise constant.

This class is used to impliment the coefficent terms of bicubic spline interpolation. An function is interpolated using

z(x,y) = Σ_i,3Σ_j,3 c_ij*x^i*y^j (1)

The aguments x and y are assumed to be the normalized arguments

x_norm = (x - xmin)/dx - i (2) y_norm = (y - ymin)/dy - j (3)

To avoid tracking the indices i and j which normaizes x and y to a zero to one interval the coefficients should be normalized to

c00'_ij = Σ_k,3Σ_l,3 (-i)^k*(-j)^l*ckl_ij (4) c10'_ij = Σ_k,3Σ_l,3 k*(-i)^(k-1)*(-j)^l*ckl_ij (5) c01'_ij = Σ_k,3Σ_l,3 l*(-i)^k*(-j)^(l-1)*ckl_ij (6) c20'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*(-i)^(k-2)*(-j)^l*ckl_ij (7) c02'_ij = Σ_k,3Σ_l,3 Max(2*l-3,0)*(-i)^k*(-j)^(l-2)*ckl_ij (8) c30'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*(-i)^(k-3)*(-j)^l*ckl_ij (9) c03'_ij = Σ_k,3Σ_l,3 Max(l-2,0)*(-i)^k*(-j)^(l-3)*ckl_ij (10) c11'_ij = Σ_k,3Σ_l,3 k*l*(-i)^(k-1)*(-j)^(j-1) (11) c21'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*l*(-i)^(k-2)*(-j)^(j-1) (12) c12'_ij = Σ_k,3Σ_l,3 k*Max(2*l-3,0)*(-i)^(k-1)*(-j)^(j-2) (13) c31'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*l*(-i)^(k-3)*(-j)^(j-1) (14) c13'_ij = Σ_k,3Σ_l,3 k*Max(l-2,0)*(-i)^(k-1)*(-j)^(j-3) (15) c22'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*Max(2*l-3,0)*(-i)^(k-2)*(-j)^(j-2) (16) c32'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*Max(2*l-3,0)*(-i)^(k-3)*(-j)^(j-2) (17) c23'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*Max(l-2,0)*(-i)^(k-2)*(-j)^(j-3) (18) c33'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*Max(l-2,0)*(-i)^(k-3)*(-j)^(j-3) (19)

This makes the normalized arguments (6,7) become

x_norm' = (x - xmin)/dx (20) y_norm' = (y - ymin)/dy (21)

Template Parameters

T	Base type of the calculation.
SAFE_MATH	Use Safe Math operations.

Constructor & Destructor Documentation

◆ piecewise_2D_node()

template<jit::float_scalar T, bool SAFE_MATH = false>

graph::piecewise_2D_node< T, SAFE_MATH >::piecewise_2D_node	(	const backend::buffer< T > &	d,
		const size_t	n,
		shared_leaf< T, SAFE_MATH >	x,
		const T	x_scale,
		const T	x_offset,
		shared_leaf< T, SAFE_MATH >	y,
		const T	y_scale,
		const T	y_offset
	)

inline

Construct 2D a piecewise constant node.

Parameters

[in]	d	Data to initalize the piecewise constant.
[in]	n	Number of columns.
[in]	x	X Argument.
[in]	x_scale	Scale factor for the xargument.
[in]	x_offset	Offset factor for the x argument.
[in]	y	Y Argument.
[in]	y_scale	Scale factor for the y argument.
[in]	y_offset	Offset factor for the y argument.

Member Function Documentation

◆ compile()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual shared_leaf< T, SAFE_MATH > graph::piecewise_2D_node< T, SAFE_MATH >::compile	(	std::ostringstream &	stream,
		jit::register_map &	registers,
		jit::register_map &	indices,
		const jit::register_usage &	usage
	)

inlinevirtual

Compile the node.

This node first evaluates the value of the argument then chooses the correct piecewise index. This assumes that the argument is

x' = (x - xmin)/dx (1) y' = (y - ymin)/dy (2)

and the spline coefficients are of the form.

c00'_ij = Σ_k,3Σ_l,3 (-i)^k*(-j)^l*ckl_ij (3) c10'_ij = Σ_k,3Σ_l,3 k*(-i)^(k-1)*(-j)^l*ckl_ij (4) c01'_ij = Σ_k,3Σ_l,3 l*(-i)^k*(-j)^(l-1)*ckl_ij (5) c20'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*(-i)^(k-2)*(-j)^l*ckl_ij (6) c02'_ij = Σ_k,3Σ_l,3 Max(2*l-3,0)*(-i)^k*(-j)^(l-2)*ckl_ij (7) c30'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*(-i)^(k-3)*(-j)^l*ckl_ij (8) c03'_ij = Σ_k,3Σ_l,3 Max(l-2,0)*(-i)^k*(-j)^(l-3)*ckl_ij (9) c11'_ij = Σ_k,3Σ_l,3 k*l*(-i)^(k-1)*(-j)^(j-1) (10) c21'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*l*(-i)^(k-2)*(-j)^(j-1) (11) c12'_ij = Σ_k,3Σ_l,3 k*Max(2*l-3,0)*(-i)^(k-1)*(-j)^(j-2) (12) c31'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*l*(-i)^(k-3)*(-j)^(j-1) (13) c13'_ij = Σ_k,3Σ_l,3 k*Max(l-2,0)*(-i)^(k-1)*(-j)^(j-3) (14) c22'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*Max(2*l-3,0)*(-i)^(k-2)*(-j)^(j-2) (15) c32'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*Max(2*l-3,0)*(-i)^(k-3)*(-j)^(j-2) (16) c23'_ij = Σ_k,3Σ_l,3 Max(2*k-3,0)*Max(l-2,0)*(-i)^(k-2)*(-j)^(j-3) (17) c33'_ij = Σ_k,3Σ_l,3 Max(k-2,0)*Max(l-2,0)*(-i)^(k-3)*(-j)^(j-3) (18)

Parameters

[in,out]	stream	String buffer stream.
[in,out]	registers	List of defined registers.
[in,out]	indices	List of defined indices.
[in]	usage	List of register usage count.

Returns: The current node.

Implements graph::leaf_node< T, SAFE_MATH >.

◆ compile_preamble()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual void graph::piecewise_2D_node< T, SAFE_MATH >::compile_preamble	(	std::ostringstream &	stream,
		jit::register_map &	registers,
		jit::visiter_map &	visited,
		jit::register_usage &	usage,
		jit::texture1d_list &	textures1d,
		jit::texture2d_list &	textures2d,
		int &	avail_const_mem
	)

inlinevirtual

Compile preamble.

Parameters

[in,out]	stream	String buffer stream.
[in,out]	registers	List of defined registers.
[in,out]	visited	List of visited nodes.
[in,out]	usage	List of register usage count.
[in,out]	textures1d	List of 1D textures.
[in,out]	textures2d	List of 2D textures.
[in,out]	avail_const_mem	Available constant memory.

Reimplemented from graph::branch_node< T, SAFE_MATH >.

◆ df()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual shared_leaf< T, SAFE_MATH > graph::piecewise_2D_node< T, SAFE_MATH >::df ( shared_leaf< T, SAFE_MATH > x )

inlinevirtual

Transform node to derivative.

Parameters

[in] x The variable to take the derivative to.

Returns: The derivative of the node.

◆ evaluate()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual backend::buffer< T > graph::piecewise_2D_node< T, SAFE_MATH >::evaluate ( )

inlinevirtual

Evaluate the results of the piecewise constant.

Evaluate functions are only used by the minimization. So this node does not evaluate the argument. Instead this only returs the data as if it were a constant.

Returns: The evaluated value of the node.

Implements graph::leaf_node< T, SAFE_MATH >.

◆ get_num_columns()

template<jit::float_scalar T, bool SAFE_MATH = false>

size_t graph::piecewise_2D_node< T, SAFE_MATH >::get_num_columns ( ) const

inline

Get the number of columns.

Returns: The number of columns in the constant.

◆ get_num_rows()

template<jit::float_scalar T, bool SAFE_MATH = false>

size_t graph::piecewise_2D_node< T, SAFE_MATH >::get_num_rows ( ) const

inline

Get the number of columns.

Returns: The number of columns in the constant.

◆ get_power_base()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual shared_leaf< T, SAFE_MATH > graph::piecewise_2D_node< T, SAFE_MATH >::get_power_base ( )

inlinevirtual

Get the base of a power.

Returns: The base of a power like node.

Reimplemented from graph::leaf_node< T, SAFE_MATH >.

◆ get_power_exponent()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual shared_leaf< T, SAFE_MATH > graph::piecewise_2D_node< T, SAFE_MATH >::get_power_exponent ( ) const

inlinevirtual

Get the exponent of a power.

Returns: The exponent of a power like node.

Reimplemented from graph::branch_node< T, SAFE_MATH >.

◆ get_x_offset()

template<jit::float_scalar T, bool SAFE_MATH = false>

T graph::piecewise_2D_node< T, SAFE_MATH >::get_x_offset ( ) const

inline

Get x argument offset.

Returns: The offset factor for x.

◆ get_x_scale()

template<jit::float_scalar T, bool SAFE_MATH = false>

T graph::piecewise_2D_node< T, SAFE_MATH >::get_x_scale ( ) const

inline

Get x argument scale.

Returns: The scale factor for x.

◆ get_y_offset()

template<jit::float_scalar T, bool SAFE_MATH = false>

T graph::piecewise_2D_node< T, SAFE_MATH >::get_y_offset ( ) const

inline

Get y argument offset.

Returns: The offset factor for x.

◆ get_y_scale()

template<jit::float_scalar T, bool SAFE_MATH = false>

T graph::piecewise_2D_node< T, SAFE_MATH >::get_y_scale ( ) const

inline

Get y argument scale.

Returns: The scale factor for y.

◆ has_constant_zero()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual bool graph::piecewise_2D_node< T, SAFE_MATH >::has_constant_zero ( ) const

inlinevirtual

Test the constant node has a zero.

Returns: True the node has a zero constant value.

Reimplemented from graph::leaf_node< T, SAFE_MATH >.

◆ is_all_variables()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual bool graph::piecewise_2D_node< T, SAFE_MATH >::is_all_variables ( ) const

inlinevirtual

Test if node acts like a variable.

Returns: True if the node acts like a variable.

Reimplemented from graph::branch_node< T, SAFE_MATH >.

◆ is_arg_match()

template<jit::float_scalar T, bool SAFE_MATH = false>

bool graph::piecewise_2D_node< T, SAFE_MATH >::is_arg_match ( shared_leaf< T, SAFE_MATH > x )

inline

Check if the args match.

Parameters

[in] x Node to match.

Returns: True if the arguments match.

◆ is_col_match()

template<jit::float_scalar T, bool SAFE_MATH = false>

bool graph::piecewise_2D_node< T, SAFE_MATH >::is_col_match ( shared_leaf< T, SAFE_MATH > x )

inline

Do the columns match.

The number of rows is the column dimension.

Parameters

[in] x Node to match.

Returns: True if the column arguments match.

◆ is_constant()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual bool graph::piecewise_2D_node< T, SAFE_MATH >::is_constant ( ) const

inlinevirtual

Test if node is a constant.

Returns: True if the node is a constant.

Reimplemented from graph::leaf_node< T, SAFE_MATH >.

◆ is_match()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual bool graph::piecewise_2D_node< T, SAFE_MATH >::is_match ( shared_leaf< T, SAFE_MATH > x )

inlinevirtual

Querey if the nodes match.

Assumes both arguments are either set or not set.

Parameters

[in] x Other graph to check if it is a match.

Returns: True if the nodes are a match.

◆ is_power_like()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual bool graph::piecewise_2D_node< T, SAFE_MATH >::is_power_like ( ) const

inlinevirtual

Test if the node acts like a power of variable.

Returns: True.

Reimplemented from graph::leaf_node< T, SAFE_MATH >.

◆ is_row_match()

template<jit::float_scalar T, bool SAFE_MATH = false>

bool graph::piecewise_2D_node< T, SAFE_MATH >::is_row_match ( shared_leaf< T, SAFE_MATH > x )

inline

Do the rows match.

Parameters

[in] x Node to match.

Returns: True if the row arguments match.

◆ reduce()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual shared_leaf< T, SAFE_MATH > graph::piecewise_2D_node< T, SAFE_MATH >::reduce ( )

inlinevirtual

Reduction method.

If all the values in the data buffer are the same. Reduce to a single constant.

Returns: A reduced representation of the node.

Implements graph::leaf_node< T, SAFE_MATH >.

◆ to_latex()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual void graph::piecewise_2D_node< T, SAFE_MATH >::to_latex ( ) const

inlinevirtual

Convert the node to latex.

Assumes both arguments are either set or not set.

Implements graph::leaf_node< T, SAFE_MATH >.

◆ to_vizgraph()

template<jit::float_scalar T, bool SAFE_MATH = false>

virtual shared_leaf< T, SAFE_MATH > graph::piecewise_2D_node< T, SAFE_MATH >::to_vizgraph	(	std::stringstream &	stream,
		jit::register_map &	registers
	)

inlinevirtual

Convert the node to vizgraph.

Parameters

[in,out]	stream	String buffer stream.
[in,out]	registers	List of defined registers.

Returns: The current node.

Implements graph::leaf_node< T, SAFE_MATH >.

The documentation for this class was generated from the following file:

graph_framework/piecewise.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ piecewise_2D_node()

Member Function Documentation

◆ compile()

◆ compile_preamble()

◆ df()

◆ evaluate()

◆ get_num_columns()

◆ get_num_rows()

◆ get_power_base()

◆ get_power_exponent()

◆ get_x_offset()

◆ get_x_scale()

◆ get_y_offset()

◆ get_y_scale()

◆ has_constant_zero()

◆ is_all_variables()

◆ is_arg_match()

◆ is_col_match()

◆ is_constant()

◆ is_match()

◆ is_power_like()

◆ is_row_match()

◆ reduce()

◆ to_latex()

◆ to_vizgraph()