Description

Generic substitution algorithm.

#include <substitute.hh>

Inheritance diagram for cadabra::substitute:

Classes
class	Rules

Public Member Functions
	substitute (const Kernel &, Ex &tr, Ex &args, bool partial=true)

virtual bool	can_apply (iterator st)
	Match the lhs of the replacement rule to the subtree 'st' under consideration. More...

virtual result_t	apply (iterator &)

Public Member Functions inherited from cadabra::Algorithm
	Algorithm (const Kernel &, Ex &)
	Initialise the algorithm with a reference to the expression tree, but do not yet do anything with this tree. More...

virtual	~Algorithm ()

void	set_progress_monitor (ProgressMonitor *)
	Provide the algorithm with a ProgressMonitor object on which to register (nested) progress information, to be reported out-of-band to a client. More...

result_t	apply_generic (bool deep=true, bool repeat=false, unsigned int depth=0)
	The main entry points for running algorithms, which traverse the tree post-order ('child before parent'). More...

result_t	apply_generic (iterator &, bool deep, bool repeat, unsigned int depth)

result_t	apply_pre_order (bool repeat=false)
	Apply algorithm with alternative traversal: starting from the top node, traverse the tree pre-order ('parent before child') and once the algorithm acts at a given node, do not traverse the subtree below anymore. More...

bool	check_consistency (iterator) const
	Given an expression top node, check index consistency. More...

bool	check_index_consistency (iterator) const

bool	check_degree_consistency (iterator) const
	Given an expression top node, check differential form degree consistency. More...

void	report_progress (const std::string &, int todo, int done, int count=2)

index_iterator	begin_index (iterator it) const

index_iterator	end_index (iterator it) const

unsigned int	number_of_indices (iterator it)

std::string	get_index_set_name (iterator it) const

bool	rename_replacement_dummies (iterator, bool still_inside_algo=false)
	Rename the dummies in the sub-tree starting with head at the given iterator. More...

Public Member Functions inherited from cadabra::IndexClassifier
	IndexClassifier (const Kernel &)

void	fill_index_position_map (Ex::iterator, const index_map_t &, index_position_map_t &) const
	Routines to find and classify all indices in an expression, taking into account sums and products. More...

void	fill_map (index_map_t &, Ex::sibling_iterator, Ex::sibling_iterator) const

void	print_classify_indices (std::ostream &, Ex::iterator) const

void	determine_intersection (index_map_t &one, index_map_t &two, index_map_t &target, bool move_out=false) const
	Determine those indices in 'two' which have a name which is identical to an index name occurring in 'one'. More...

void	classify_add_index (Ex::iterator it, index_map_t &ind_free, index_map_t &ind_dummy) const

void	classify_indices_up (Ex::iterator, index_map_t &ind_free, index_map_t &ind_dummy) const
	Classify indices bottom-up, that is, given a node, it goes up the tree to find. More...

void	classify_indices (Ex::iterator, index_map_t &ind_free, index_map_t &ind_dummy) const
	Classify indices top-down, that is, finds the free indices and all dummy index pairs used in the full subtree below a given node. More...

int	max_numbered_name_one (const std::string &nm, const index_map_t *one) const

int	max_numbered_name (const std::string &, const index_map_t m1, const index_map_t m2=0, const index_map_t m3=0, const index_map_t m4=0, const index_map_t *m5=0) const

Ex	get_dummy (const list_property , const index_map_t m1, const index_map_t m2=0, const index_map_t m3=0, const index_map_t m4=0, const index_map_t m5=0) const

Ex	get_dummy (const list_property *, Ex::iterator) const

Ex	get_dummy (const list_property *, Ex::iterator, Ex::iterator) const

bool	index_in_set (Ex, const index_map_t *) const

void	dumpmap (std::ostream &, const index_map_t &) const

index_map_t::iterator	find_modulo_parent_rel (Ex::iterator it, index_map_t &imap) const
	Find an index in the set, not taking into account index position. More...

Static Public Member Functions
static size_t	cache_size ()
	Return the number of substitution rules which have been pre-processed and sit in the cache. More...

Static Public Member Functions inherited from cadabra::Algorithm
static unsigned int	number_of_indices (const Properties &, iterator it)

static unsigned int	number_of_direct_indices (iterator it)

static bool	is_termlike (iterator)
	Determines whether the indicated node is 'like a term in a sum'. More...

static bool	is_factorlike (iterator)
	Determines whether the indicated node is 'like a factor in a product'. More...

Public Attributes
Ex_comparator	comparator

Public Attributes inherited from cadabra::Algorithm
bool	interrupted

unsigned int	number_of_calls

unsigned int	number_of_modifications

bool	suppress_normal_output

bool	discard_command_node

Stopwatch	index_sw

Stopwatch	get_dummy_sw

Stopwatch	report_progress_stopwatch

Private Attributes
Ex &	args

iterator	use_rule

iterator	conditions

std::map< iterator, bool >	lhs_contains_dummies

std::map< iterator, bool >	rhs_contains_dummies

sort_product	sort_product_

bool	partial

Static Private Attributes
static Rules	replacement_rules = substitute::Rules()

static size_t	cache_hits = 0

static size_t	cache_misses = 0

Additional Inherited Members
Public Types inherited from cadabra::Algorithm
typedef Ex::iterator	iterator

typedef Ex::post_order_iterator	post_order_iterator

typedef Ex::sibling_iterator	sibling_iterator

typedef Ex::result_t	result_t

Public Types inherited from cadabra::IndexClassifier
typedef std::multimap< Ex, Ex::iterator, tree_exact_less_for_indexmap_obj >	index_map_t
	A map from a pattern to the position where it occurs in the tree. More...

typedef std::map< Ex::iterator, int, Ex::iterator_base_less >	index_position_map_t
	A map from the position of each index to the sequential index. More...

Protected Types inherited from cadabra::Algorithm
typedef std::pair< sibling_iterator, sibling_iterator >	range_t
	Finding objects in sets. More...

typedef std::vector< range_t >	range_vector_t

Protected Member Functions inherited from cadabra::Algorithm
int	index_parity (iterator) const

bool	contains (sibling_iterator from, sibling_iterator to, sibling_iterator arg)

void	find_argument_lists (range_vector_t &, bool only_comma_lists=true) const

template<class Iter >
range_vector_t::iterator	find_arg_superset (range_vector_t &, Iter st, Iter nd)

range_vector_t::iterator	find_arg_superset (range_vector_t &, sibling_iterator it)

unsigned int	locate_single_object (Ex::iterator obj_to_find, Ex::iterator st, Ex::iterator nd, std::vector< unsigned int > &store)

bool	locate_object_set (const Ex &objs, Ex::iterator st, Ex::iterator nd, std::vector< unsigned int > &store)

bool	is_single_term (iterator)
	Take a single non-product node in a sum and wrap it in a product node, so it can be handled on the same footing as a proper product. More...

bool	is_nonprod_factor_in_prod (iterator)

bool	prod_wrap_single_term (iterator &)

bool	prod_unwrap_single_term (iterator &)

bool	sum_wrap_single_term (iterator &)

bool	sum_unwrap_single_term (iterator &)

void	force_node_wrap (iterator &, std::string)
	Wrap a term in a product or sum in a node with indicated name, irrespective of its parent (it usually makes more sense to call the safer prod_wrap_single_term or sum_wrap_single_term above). More...

bool	separated_by_derivative (iterator, iterator, iterator check_dependence) const
	Figure out whether two objects (commonly indices) are separated by a derivative operator, as in. More...

void	pushup_multiplier (iterator)

template<class BinaryPredicate >
unsigned int	intersection_number (sibling_iterator, sibling_iterator, sibling_iterator, sibling_iterator, BinaryPredicate) const
	Determine the number of elements in the first range which also occur in the second range. More...

void	node_zero (iterator)

void	node_one (iterator)

void	node_integer (iterator, int)

Static Protected Member Functions inherited from cadabra::Algorithm
static bool	less_without_numbers (nset_t::iterator, nset_t::iterator)

static bool	equal_without_numbers (nset_t::iterator, nset_t::iterator)

static bool	compare_ (const str_node &, const str_node &)

Protected Attributes inherited from cadabra::Algorithm
Ex &	tr

ProgressMonitor *	pm

bool	traverse_ldots

Protected Attributes inherited from cadabra::IndexClassifier
const Kernel &	kernel

Constructor & Destructor Documentation

◆ substitute()

substitute::substitute	(	const Kernel &	k,
		Ex &	tr,
		Ex &	args,
		bool	partial = `true`
	)

Member Function Documentation

◆ apply()

Algorithm::result_t substitute::apply ( iterator & st )

virtual

Implements cadabra::Algorithm.

◆ cache_size()

size_t substitute::cache_size ( )

static

Return the number of substitution rules which have been pre-processed and sit in the cache.

◆ can_apply()

bool substitute::can_apply ( iterator st )

virtual

Match the lhs of the replacement rule to the subtree 'st' under consideration.

This will fill the replacement_map giving a map from objects appearing in the rule to what they matched to.

For F_{m n} -> G_{m n}, position-free indices and the expression F^{m n}, we would get a replacement map

 _m  -> ^m
 _n  -> ^n

(Note how it is important that despite these indices being position-free, the rules in the replacement map do not ignore sub/superscript information). In the apply member, we then replace all of 'st' with the rhs of the rule, and scan through the rule (with a basic replacement_map.find based on simple tree comparison logic, not pattern matching) for replacements to be made.

Implements cadabra::Algorithm.

Member Data Documentation

◆ args

Ex& cadabra::substitute::args

private

◆ cache_hits

size_t substitute::cache_hits = 0

staticprivate

◆ cache_misses

size_t substitute::cache_misses = 0

staticprivate

◆ comparator

Ex_comparator cadabra::substitute::comparator

◆ conditions

iterator cadabra::substitute::conditions

private

◆ lhs_contains_dummies

std::map<iterator, bool> cadabra::substitute::lhs_contains_dummies

private

◆ partial

bool cadabra::substitute::partial

private

◆ replacement_rules

substitute::Rules substitute::replacement_rules = substitute::Rules()

staticprivate

◆ rhs_contains_dummies

std::map<iterator, bool> cadabra::substitute::rhs_contains_dummies

private

◆ sort_product_

sort_product cadabra::substitute::sort_product_

private

◆ use_rule

iterator cadabra::substitute::use_rule

private

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

core/algorithms/substitute.hh
core/algorithms/substitute.cc

Description

Classes

Public Member Functions

Static Public Member Functions

Public Attributes

Private Attributes

Static Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ substitute()

Member Function Documentation

◆ apply()

◆ cache_size()

◆ can_apply()

Member Data Documentation

◆ args

◆ cache_hits

◆ cache_misses

◆ comparator

◆ conditions

◆ lhs_contains_dummies

◆ partial

◆ replacement_rules

◆ rhs_contains_dummies

◆ sort_product_

◆ use_rule