Real trigonometric Kronecker monomial class. More...

#include <piranha/real_trigonometric_kronecker_monomial.hpp>

Public Types
typedef T	value_type
	Alias for `T`.

typedef ka::size_type	size_type
	Size type. More...

typedef static_vector< value_type, max_size >	v_type
	Vector type used for temporary packing/unpacking.

Public Member Functions
	real_trigonometric_kronecker_monomial ()
	Default constructor. More...

	real_trigonometric_kronecker_monomial (const real_trigonometric_kronecker_monomial &)=default
	Defaulted copy constructor.

	real_trigonometric_kronecker_monomial (real_trigonometric_kronecker_monomial &&)=default
	Defaulted move constructor.

template<typename U , init_list_enabler< U > = 0>
	real_trigonometric_kronecker_monomial (std::initializer_list< U > list, bool flavour=true)
	Constructor from initalizer list. More...

template<typename Iterator , it_ctor_enabler< Iterator > = 0>
	real_trigonometric_kronecker_monomial (const Iterator &start, const Iterator &end, bool flavour=true)
	Constructor from range. More...

	real_trigonometric_kronecker_monomial (const symbol_fset &)
	Constructor from set of symbols. More...

	real_trigonometric_kronecker_monomial (const value_type &n, bool f)
	Constructor from `value_type` and flavour. More...

	real_trigonometric_kronecker_monomial (const real_trigonometric_kronecker_monomial &other, const symbol_fset &)
	Converting constructor. More...

	~real_trigonometric_kronecker_monomial ()
	Trivial destructor.

real_trigonometric_kronecker_monomial &	operator= (const real_trigonometric_kronecker_monomial &other)=default
	Copy assignment operator. More...

real_trigonometric_kronecker_monomial &	operator= (real_trigonometric_kronecker_monomial &&other)=default
	Move assignment operator. More...

void	set_int (const value_type &n)
	Set the internal integer instance. More...

value_type	get_int () const
	Get internal instance. More...

bool	get_flavour () const
	Get flavour. More...

void	set_flavour (bool f)
	Set flavour. More...

bool	canonicalise (const symbol_fset &args)
	Canonicalise. More...

bool	is_compatible (const symbol_fset &args) const noexcept
	Compatibility check. More...

bool	is_zero (const symbol_fset &) const noexcept
	Zero check. More...

real_trigonometric_kronecker_monomial	merge_symbols (const symbol_idx_fmap< symbol_fset > &ins_map, const symbol_fset &args) const
	Merge symbols. More...

bool	is_unitary (const symbol_fset &) const
	Check if monomial is unitary. More...

degree_type	t_degree (const symbol_fset &args) const
	Trigonometric degree. More...

degree_type	t_ldegree (const symbol_fset &args) const
	Low trigonometric degree (equivalent to the trigonometric degree). More...

degree_type	t_degree (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial trigonometric degree. More...

degree_type	t_ldegree (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial low trigonometric degree (equivalent to the partial trigonometric degree). More...

order_type	t_order (const symbol_fset &args) const
	Trigonometric order. More...

order_type	t_lorder (const symbol_fset &args) const
	Low trigonometric order (equivalent to the trigonometric order). More...

order_type	t_order (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial trigonometric order. More...

order_type	t_lorder (const symbol_idx_fset &p, const symbol_fset &args) const
	Partial low trigonometric order (equivalent to the partial trigonometric order). More...

std::size_t	hash () const
	Hash value. More...

bool	operator== (const real_trigonometric_kronecker_monomial &other) const
	Equality operator. More...

bool	operator!= (const real_trigonometric_kronecker_monomial &other) const
	Inequality operator. More...

v_type	unpack (const symbol_fset &args) const
	Unpack internal integer instance. More...

void	print (std::ostream &os, const symbol_fset &args) const
	Print. More...

void	print_tex (std::ostream &os, const symbol_fset &args) const
	Print in TeX mode. More...

std::pair< T, real_trigonometric_kronecker_monomial >	partial (const symbol_idx &p, const symbol_fset &args) const
	Partial derivative. More...

std::pair< T, real_trigonometric_kronecker_monomial >	integrate (const std::string &s, const symbol_fset &args) const
	Integration. More...

template<typename U >
eval_type< U >	evaluate (const std::vector< U > &values, const symbol_fset &args) const
	Evaluation. More...

template<typename U >
std::vector< std::pair< subs_type< U >, real_trigonometric_kronecker_monomial > >	subs (const symbol_idx_fmap< U > &smap, const symbol_fset &args) const
	Substitution. More...

template<typename U >
std::vector< std::pair< t_subs_type< U >, real_trigonometric_kronecker_monomial > >	t_subs (const symbol_idx &idx, const U &c, const U &s, const symbol_fset &args) const
	Trigonometric substitution. More...

void	trim_identify (std::vector< char > &trim_mask, const symbol_fset &args) const
	Identify symbols that can be trimmed. More...

real_trigonometric_kronecker_monomial	trim (const std::vector< char > &trim_mask, const symbol_fset &args) const
	Trim. More...

bool	operator< (const real_trigonometric_kronecker_monomial &other) const
	Comparison operator. More...

template<typename Stream , msgpack_pack_enabler< Stream > = 0>
void	msgpack_pack (msgpack::packer< Stream > &packer, msgpack_format f, const symbol_fset &s) const
	Serialize in msgpack format. More...

template<typename U = real_trigonometric_kronecker_monomial, msgpack_convert_enabler< U > = 0>
void	msgpack_convert (const msgpack::object &o, msgpack_format f, const symbol_fset &s)
	Deserialize from msgpack object. More...

Static Public Member Functions
template<typename Cf , multiply_enabler< Cf > = 0>
static void	multiply (std::array< term< Cf, real_trigonometric_kronecker_monomial >, multiply_arity > &res, const term< Cf, real_trigonometric_kronecker_monomial > &t1, const term< Cf, real_trigonometric_kronecker_monomial > &t2, const symbol_fset &args)
	Multiply terms with a trigonometric monomial. More...

Static Public Attributes
static const std::size_t	multiply_arity = 2u
	Arity of the multiply() method.

static const size_type	max_size = 255u
	Maximum monomial size.

Detailed Description

template<typename T = std::make_signed<std::size_t>::type>
class piranha::real_trigonometric_kronecker_monomial< T >

Real trigonometric Kronecker monomial class.

This class represents a multivariate real trigonometric monomial, i.e., functions of the form

\[ \begin{array}{c} \sin \\ \cos \end{array} \left(n_0x_0 + n_1x_1 + \ldots + n_mx_m\right), \]

where the integers \( n_i \) are called multipliers. The values of the multipliers are packed in a signed integer using Kronecker substitution, using the facilities provided by piranha::kronecker_array. The boolean flavour of the monomial indicates whether it represents a cosine (true) or sine (false).

Similarly to an ordinary monomial, this class provides methods to query the trigonometric (partial) (low) degree, defined as if the multipliers were exponents of a regular monomial (e.g., the total trigonometric degree is the sum of the multipliers). Closely related is the concept of trigonometric order, calculated by adding the absolute values of the multipliers.

This class satisfies the piranha::is_key, piranha::key_has_t_degree, piranha::key_has_t_ldegree, piranha::key_has_t_order, piranha::key_has_t_lorder and piranha::key_is_differentiable type traits.

Type requirements

T must be suitable for use in piranha::kronecker_array. The default type for T is the signed counterpart of std::size_t.

Exception safety guarantee

Unless otherwise specified, this class provides the strong exception safety guarantee for all operations.

Move semantics

The move semantics of this class are equivalent to the move semantics of C++ signed integral types.

Definition at line 119 of file real_trigonometric_kronecker_monomial.hpp.

Member Typedef Documentation

◆ size_type

template<typename T = std::make_signed<std::size_t>::type>

typedef ka::size_type piranha::real_trigonometric_kronecker_monomial< T >::size_type

Size type.

Used to represent the number of variables in the monomial. Equivalent to the size type of piranha::kronecker_array.

Definition at line 136 of file real_trigonometric_kronecker_monomial.hpp.

Constructor & Destructor Documentation

◆ real_trigonometric_kronecker_monomial() [1/6]

template<typename T = std::make_signed<std::size_t>::type>

piranha::real_trigonometric_kronecker_monomial< T >::real_trigonometric_kronecker_monomial ( )

inline

Default constructor.

After construction all multipliers in the monomial will be zero, and the flavour will be set to true.

Definition at line 150 of file real_trigonometric_kronecker_monomial.hpp.

◆ real_trigonometric_kronecker_monomial() [2/6]

template<typename T = std::make_signed<std::size_t>::type>

template<typename U , init_list_enabler< U > = 0>

piranha::real_trigonometric_kronecker_monomial< T >::real_trigonometric_kronecker_monomial	(	std::initializer_list< U >	list,
		bool	flavour = `true`
	)

inlineexplicit

Constructor from initalizer list.

Note: This constructor is enabled if U is safely convertible to T.

The values in the initializer list are intended to represent the multipliers of the monomial: they will be safely converted to type T (if T and U are not the same type), encoded using piranha::kronecker_array::encode() and the result assigned to the internal integer instance. The flavour will be set to flavour.

Parameters

list	an initializer list representing the multipliers.
flavour	the flavour that will be assigned to the monomial.

Exceptions

unspecified

any exception thrown by:

Definition at line 181 of file real_trigonometric_kronecker_monomial.hpp.

◆ real_trigonometric_kronecker_monomial() [3/6]

template<typename T = std::make_signed<std::size_t>::type>

template<typename Iterator , it_ctor_enabler< Iterator > = 0>

piranha::real_trigonometric_kronecker_monomial< T >::real_trigonometric_kronecker_monomial	(	const Iterator &	start,
		const Iterator &	end,
		bool	flavour = `true`
	)

inlineexplicit

Constructor from range.

Note: This constructor is enabled if Iterator is an input iterator whose value_type is safely convertible to T.

Will build internally a vector of values from the input iterators, encode it and assign the result to the internal integer instance. The value type of the iterator is converted to T using piranha::safe_cast(). The flavour will be set to flavour.

Parameters

start	beginning of the range.
end	end of the range.
flavour	the flavour that will be assigned to the monomial.

Exceptions

unspecified

any exception thrown by:

Definition at line 215 of file real_trigonometric_kronecker_monomial.hpp.

◆ real_trigonometric_kronecker_monomial() [4/6]

template<typename T = std::make_signed<std::size_t>::type>

piranha::real_trigonometric_kronecker_monomial< T >::real_trigonometric_kronecker_monomial ( const symbol_fset & )

inlineexplicit

Constructor from set of symbols.

After construction all multipliers will be zero and the flavour will be set to true.

Definition at line 228 of file real_trigonometric_kronecker_monomial.hpp.

◆ real_trigonometric_kronecker_monomial() [5/6]

template<typename T = std::make_signed<std::size_t>::type>

piranha::real_trigonometric_kronecker_monomial< T >::real_trigonometric_kronecker_monomial	(	const value_type &	n,
		bool	f
	)

inlineexplicit

Constructor from value_type and flavour.

This constructor will initialise the internal integer instance to n and the flavour to f.

Parameters

n	initializer for the internal integer instance.
f	desired flavour.

Definition at line 237 of file real_trigonometric_kronecker_monomial.hpp.

◆ real_trigonometric_kronecker_monomial() [6/6]

template<typename T = std::make_signed<std::size_t>::type>

piranha::real_trigonometric_kronecker_monomial< T >::real_trigonometric_kronecker_monomial	(	const real_trigonometric_kronecker_monomial< T > &	other,
		const symbol_fset &
	)

inlineexplicit

Converting constructor.

This constructor is for use when converting from one term type to another in piranha::series. It will set the internal integer instance and flavour to the same value of other.

Parameters

other the construction argument.

Definition at line 245 of file real_trigonometric_kronecker_monomial.hpp.

Member Function Documentation

◆ canonicalise()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::canonicalise ( const symbol_fset & args )

inline

Canonicalise.

A monomial is considered to be in canonical form when the first nonzero multiplier is positive. If this is not in canonical form, the method will canonicalise this by switching the signs of all multipliers and return true. Otherwise, this will not be modified and false will be returned.

Parameters

args	the reference piranha::symbol_fset.

Returns: true if the monomial was canonicalised, false otherwise.

Exceptions

unspecified

any exception thrown by:

Definition at line 340 of file real_trigonometric_kronecker_monomial.hpp.

◆ evaluate()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U >

eval_type<U> piranha::real_trigonometric_kronecker_monomial< T >::evaluate	(	const std::vector< U > &	values,
		const symbol_fset &	args
	)		const

inline

Evaluation.

Note: This template method is activated only if U supports the mathematical operations needed to compute the return type.

The return value will be built by applying piranha::math::cos() or piranha::math:sin() to the linear combination of the values in values with the multipliers.

Parameters

values	the values will be used for the evaluation.
args	the reference piranha::symbol_fset.

Returns: the result of evaluating this with the values provided in values.

Exceptions

std::invalid_argument	if the sizes of `values` and `args` differ.
unspecified	any exception thrown by unpack() or by the computation of the return type.

Definition at line 966 of file real_trigonometric_kronecker_monomial.hpp.

◆ get_flavour()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::get_flavour ( ) const

inline

Get flavour.

Returns: flavour of the monomial.

Definition at line 294 of file real_trigonometric_kronecker_monomial.hpp.

◆ get_int()

template<typename T = std::make_signed<std::size_t>::type>

value_type piranha::real_trigonometric_kronecker_monomial< T >::get_int ( ) const

inline

Get internal instance.

Returns: value of the internal integer instance.

Definition at line 286 of file real_trigonometric_kronecker_monomial.hpp.

◆ hash()

template<typename T = std::make_signed<std::size_t>::type>

std::size_t piranha::real_trigonometric_kronecker_monomial< T >::hash ( ) const

inline

Hash value.

Returns: the internal integer instance, cast to std::size_t.

Definition at line 720 of file real_trigonometric_kronecker_monomial.hpp.

◆ integrate()

template<typename T = std::make_signed<std::size_t>::type>

std::pair<T, real_trigonometric_kronecker_monomial> piranha::real_trigonometric_kronecker_monomial< T >::integrate	(	const std::string &	s,
		const symbol_fset &	args
	)		const

inline

Integration.

This method will return the antiderivative of this with respect to the symbol s. The result is a pair consisting of the multiplier associated to s and a copy of the monomial. The sign of the multiplier and the flavour of the resulting monomial are set according to the standard integration formulas for elementary trigonometric functions. If s is not in args or if the multiplier associated to it is zero, the returned pair will be (0,real_trigonometric_kronecker_monomial{args}).

Parameters

s	the symbol with respect to which the integration will be calculated.
args	the reference piranha::symbol_fset.

Returns: the result of the integration.

Exceptions

unspecified any exception thrown by unpack().

Definition at line 900 of file real_trigonometric_kronecker_monomial.hpp.

◆ is_compatible()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::is_compatible ( const symbol_fset & args ) const

inlinenoexcept

Compatibility check.

A monomial is considered incompatible if any of these conditions holds:

the size of args is zero and the internal integer is not zero,
the size of args is equal to or larger than the size of the output of piranha::kronecker_array::get_limits(),
the internal integer is not within the limits reported by piranha::kronecker_array::get_limits(),
the first nonzero element of the vector of multipliers represented by the internal integer is negative.

Otherwise, the monomial is considered to be compatible for insertion.

Parameters

args	the reference piranha::symbol_fset.

Returns: compatibility flag for the monomial.

Definition at line 365 of file real_trigonometric_kronecker_monomial.hpp.

◆ is_unitary()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::is_unitary ( const symbol_fset & ) const

inline

Check if monomial is unitary.

Returns: true if all the multipliers are zero and the flavour is true, false otherwise.

Definition at line 444 of file real_trigonometric_kronecker_monomial.hpp.

◆ is_zero()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::is_zero ( const symbol_fset & ) const

inlinenoexcept

Zero check.

A trigonometric monomial is zero if all multipliers are zero and the flavour is false.

Returns: ignorability flag.

Definition at line 403 of file real_trigonometric_kronecker_monomial.hpp.

◆ merge_symbols()

template<typename T = std::make_signed<std::size_t>::type>

real_trigonometric_kronecker_monomial piranha::real_trigonometric_kronecker_monomial< T >::merge_symbols	(	const symbol_idx_fmap< symbol_fset > &	ins_map,
		const symbol_fset &	args
	)		const

inline

Merge symbols.

This method will return a copy of this in which the value 0 has been inserted at the positions specified by ins_map. Specifically, before each index appearing in ins_map a number of zeroes equal to the size of the mapped piranha::symbol_fset will be inserted.

For instance, given a piranha::real_trigonometric_kronecker_monomial containing the values [1,2,3,4], a symbol set args containing ["c","e","g","h"] and an insertion map ins_map containing the pairs [(0,["a","b"]),(1,["d"]),(2,["f"]),(4,["i"])], the output of this method will be [0,0,1,0,2,0,3,4,0]. That is, the symbols appearing in ins_map are merged into this with a value of zero at the specified positions. The original flavour of this will be preserved in the return value.

Parameters

ins_map	the insertion map.
args	the reference symbol set for `this`.

Returns: a piranha::real_trigonometric_kronecker_monomial resulting from inserting into this zeroes at the positions specified by ins_map.

Exceptions

std::invalid_argument	in the following cases: the size of `ins_map` is zero, the last index in `ins_map` is greater than the size of `args`.
unspecified	any exception thrown by: unpack(), piranha::static_vector::push_back(), piranha::kronecker_array::encode().

Definition at line 434 of file real_trigonometric_kronecker_monomial.hpp.

◆ msgpack_convert()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U = real_trigonometric_kronecker_monomial, msgpack_convert_enabler< U > = 0>

void piranha::real_trigonometric_kronecker_monomial< T >::msgpack_convert	(	const msgpack::object &	o,
		msgpack_format	f,
		const symbol_fset &	s
	)

inline

Deserialize from msgpack object.

Note: This method is activated only if the T, bool and piranha::real_trigonometric_kronecker_monomial::v_type satisfy piranha::has_msgpack_convert.

This method will deserialize o into this. In binary mode, no check is performed on the content of o, and calling this method will result in undefined behaviour if o does not contain a monomial serialized via msgpack_pack(). This method provides the basic exception safety guarantee.

Parameters

o	msgpack object that will be deserialized.
f	serialization format.
s	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if the size of the deserialized array differs from the size of `s`.
unspecified	any exception thrown by: the constructor of piranha::kronecker_monomial from a container, the public interface of `msgpack::object`, piranha::msgpack_convert().

Definition at line 1372 of file real_trigonometric_kronecker_monomial.hpp.

◆ msgpack_pack()

template<typename T = std::make_signed<std::size_t>::type>

template<typename Stream , msgpack_pack_enabler< Stream > = 0>

void piranha::real_trigonometric_kronecker_monomial< T >::msgpack_pack	(	msgpack::packer< Stream > &	packer,
		msgpack_format	f,
		const symbol_fset &	s
	)		const

inline

Serialize in msgpack format.

Note: This method is activated only if Stream satisfies piranha::is_msgpack_stream and T, bool and piranha::real_trigonometric_kronecker_monomial::v_type satisfy piranha::has_msgpack_pack.

This method will pack this into packer.

Parameters

packer	the target packer.
f	the serialization format.
s	the reference piranha::symbol_fset.

Exceptions

unspecified

any exception thrown by:

the public interface of msgpack::packer,
piranha::msgpack_pack().

Definition at line 1339 of file real_trigonometric_kronecker_monomial.hpp.

◆ multiply()

template<typename T = std::make_signed<std::size_t>::type>

template<typename Cf , multiply_enabler< Cf > = 0>

static void piranha::real_trigonometric_kronecker_monomial< T >::multiply	(	std::array< term< Cf, real_trigonometric_kronecker_monomial< T > >, multiply_arity > &	res,
		const term< Cf, real_trigonometric_kronecker_monomial< T > > &	t1,
		const term< Cf, real_trigonometric_kronecker_monomial< T > > &	t2,
		const symbol_fset &	args
	)

inlinestatic

Multiply terms with a trigonometric monomial.

Note

This method is enabled only if the following conditions hold:

Cf satisfies piranha::has_mul3,
Cf is divisible in-place by int,
Cf is copy-assignable and it satisfies piranha::has_negate.

This method will compute the result of the multiplication of the two terms t1 and t2 with trigonometric key. The result is stored in the two terms of res and it is computed using basic trigonometric formulae. Note however that this method will not perform the division by two implied by Werner's formulae. Also, in case Cf is an instance of piranha::mp_rational, only the numerators of the coefficients will be multiplied.

Parameters

res	result of the multiplication.
t1	first argument.
t2	second argument.
args	the reference piranha::symbol_fset.

Exceptions

std::overflow_error	if the computation of the result overflows type `value_type`.
unspecified	any exception thrown by: piranha::kronecker_array::encode(), unpack(), piranha::static_vector::push_back(), piranha::math::mul3(), copy-assignment on the coefficient type, piranha::math::negate().

Definition at line 661 of file real_trigonometric_kronecker_monomial.hpp.

◆ operator!=()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::operator!= ( const real_trigonometric_kronecker_monomial< T > & other ) const

inline

Inequality operator.

Parameters

other the comparison argument.

Returns: the opposite of operator==().

Definition at line 741 of file real_trigonometric_kronecker_monomial.hpp.

◆ operator<()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::operator< ( const real_trigonometric_kronecker_monomial< T > & other ) const

inline

Comparison operator.

The values of the internal integral instances are used for comparison. If the values are the same, the flavours of the monomials are compared to break the tie.

Parameters

other comparison argument.

Returns: true if this is less than other, false otherwise.

Definition at line 1300 of file real_trigonometric_kronecker_monomial.hpp.

◆ operator=() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

real_trigonometric_kronecker_monomial& piranha::real_trigonometric_kronecker_monomial< T >::operator= ( const real_trigonometric_kronecker_monomial< T > & other )

default

Copy assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ operator=() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

real_trigonometric_kronecker_monomial& piranha::real_trigonometric_kronecker_monomial< T >::operator= ( real_trigonometric_kronecker_monomial< T > && other )

default

Move assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ operator==()

template<typename T = std::make_signed<std::size_t>::type>

bool piranha::real_trigonometric_kronecker_monomial< T >::operator== ( const real_trigonometric_kronecker_monomial< T > & other ) const

inline

Equality operator.

Parameters

other the comparison argument.

Returns: true if the internal integral instance and the flavour of this are the same of other, false otherwise.

Definition at line 731 of file real_trigonometric_kronecker_monomial.hpp.

◆ partial()

template<typename T = std::make_signed<std::size_t>::type>

std::pair<T, real_trigonometric_kronecker_monomial> piranha::real_trigonometric_kronecker_monomial< T >::partial	(	const symbol_idx &	p,
		const symbol_fset &	args
	)		const

inline

Partial derivative.

This method will return the partial derivative of this with respect to the symbol at the position indicated by p. The result is a pair consisting of the multiplier at the position p and a copy of the monomial. The sign of the multiplier and the flavour of the resulting monomial are set according to the standard differentiation formulas for elementary trigonometric functions. If p is not smaller than the size of args or if its corresponding multiplier is zero, the returned pair will be (0,real_trigonometric_kronecker_monomial{args}).

Parameters

p	the position of the symbol with respect to which the differentiation will be calculated.
args	the reference piranha::symbol_fset.

Returns: the result of the differentiation.

Exceptions

unspecified any exception thrown by unpack().

Definition at line 868 of file real_trigonometric_kronecker_monomial.hpp.

◆ print()

template<typename T = std::make_signed<std::size_t>::type>

void piranha::real_trigonometric_kronecker_monomial< T >::print	(	std::ostream &	os,
		const symbol_fset &	args
	)		const

inline

Print.

Thie method will print to stream a human-readable representation of the monomial.

Parameters

os	target stream.
args	the reference piranha::symbol_fset.

Exceptions

unspecified any exception thrown by unpack() or by streaming instances of value_type.

Definition at line 771 of file real_trigonometric_kronecker_monomial.hpp.

◆ print_tex()

template<typename T = std::make_signed<std::size_t>::type>

void piranha::real_trigonometric_kronecker_monomial< T >::print_tex	(	std::ostream &	os,
		const symbol_fset &	args
	)		const

inline

Print in TeX mode.

This method will print to stream a TeX representation of the monomial.

Parameters

os	target stream.
args	the reference piranha::symbol_fset.

Exceptions

unspecified any exception thrown by unpack() or by streaming instances of value_type.

Definition at line 816 of file real_trigonometric_kronecker_monomial.hpp.

◆ set_flavour()

template<typename T = std::make_signed<std::size_t>::type>

void piranha::real_trigonometric_kronecker_monomial< T >::set_flavour ( bool f )

inline

Set flavour.

Parameters

f	value to which the flavour will be set.

Definition at line 302 of file real_trigonometric_kronecker_monomial.hpp.

◆ set_int()

template<typename T = std::make_signed<std::size_t>::type>

void piranha::real_trigonometric_kronecker_monomial< T >::set_int ( const value_type & n )

inline

Set the internal integer instance.

Parameters

n	value to which the internal integer instance will be set.

Definition at line 278 of file real_trigonometric_kronecker_monomial.hpp.

◆ subs()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U >

std::vector<std::pair<subs_type<U>, real_trigonometric_kronecker_monomial> > piranha::real_trigonometric_kronecker_monomial< T >::subs	(	const symbol_idx_fmap< U > &	smap,
		const symbol_fset &	args
	)		const

inline

Substitution.

Note: This template method is activated only if U supports the mathematical operations needed to compute the return type.

This method will substitute the symbols at the positions specified in the keys of smap with the mapped values. The return value is a vector of two pairs computed according to the standard angle sum identities. That is, given a monomial of the form

\[ \begin{array}{c} \sin \\ \cos \end{array} \left(na + mb + c\right) \]

in which the symbols \( a \) and \( b \) are to be substituted with \( x \) and \( y \), the result of the substitution will be one of

\[ \left\{\left[\sin \left(nx+my\right),\cos c \right],\left[\cos \left(nx+my\right),\sin c \right]\right\} \]

or

\[ \left\{\left[\cos \left(nx+my\right),\cos c \right],\left[-\sin \left(nx+my\right),\sin c \right]\right\} \]

where \( \cos c \) and \( \sin c \) are returned as monomials, and \( \cos \left(nx+my\right) \) and \( \sin \left(nx+my\right) \) are computed via piranha::math::cos() and piranha::math::sin(). If s is not in args, \( \cos \left(nx+my\right) \) will be initialised to 1 and \( \sin \left(nx+my\right) \) to 0. If, after the substitution, the first nonzero multiplier in \( c \) is negative, \( c \) will be negated and the other signs changed accordingly.

Parameters

smap	the map relating the positions of the symbols to be substituted to the values they will be substituted with.
args	the reference piranha::symbol_fset.

Returns: the result of the substitution.

Exceptions

std::invalid_argument	if the last element of the substitution map is not smaller than the size of `args`.
unspecified	any exception thrown by unpack(), the computation of the return value or memory errors in standard containers.

Definition at line 1050 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_degree() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::real_trigonometric_kronecker_monomial< T >::t_degree ( const symbol_fset & args ) const

inline

Trigonometric degree.

The type returned by this method is the type resulting from the addition of two instances of T.

Parameters

args	the reference symbol set for `this`.

Returns: the trigonometric degree of the monomial.

Exceptions

std::overflow_error	if the computation of the degree overflows.
unspecified	any exception thrown by unpack().

Definition at line 466 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_degree() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::real_trigonometric_kronecker_monomial< T >::t_degree	(	const symbol_idx_fset &	p,
		const symbol_fset &	args
	)		const

inline

Partial trigonometric degree.

Partial trigonometric degree of the monomial: only the symbols at the positions specified by p are considered. The type returned by this method is the type resulting from the addition of two instances of T.

Parameters

p	the positions of the symbols to be considered in the calculation of the degree.
args	the reference piranha::symbol_fset.

Returns: the summation of the multipliers of the monomial at the positions specified by p.

Exceptions

std::invalid_argument	if the last element of `p`, if existing, is not less than the size of `args`.
std::overflow_error	if the computation of the degree overflows.
unspecified	any exception thrown by unpack().

Definition at line 505 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_ldegree() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::real_trigonometric_kronecker_monomial< T >::t_ldegree ( const symbol_fset & args ) const

inline

Low trigonometric degree (equivalent to the trigonometric degree).

Parameters

args	the reference symbol set for `this`.

Returns: the output of t_degree(const symbol_fset &) const.

Exceptions

unspecified any exception thrown by t_degree(const symbol_fset &) const.

Definition at line 485 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_ldegree() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

degree_type piranha::real_trigonometric_kronecker_monomial< T >::t_ldegree	(	const symbol_idx_fset &	p,
		const symbol_fset &	args
	)		const

inline

Partial low trigonometric degree (equivalent to the partial trigonometric degree).

Parameters

p	the positions of the symbols to be considered in the calculation of the degree.
args	the reference piranha::symbol_fset.

Returns: the output of t_degree(const symbol_idx_fset &, const symbol_fset &) const.

Exceptions

unspecified any exception thrown by t_degree(const symbol_idx_fset &, const symbol_fset &) const.

Definition at line 531 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_lorder() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

order_type piranha::real_trigonometric_kronecker_monomial< T >::t_lorder ( const symbol_fset & args ) const

inline

Low trigonometric order (equivalent to the trigonometric order).

Parameters

args	the reference piranha::symbol_fset.

Returns: the output of t_order(const symbol_fset &) const.

Exceptions

unspecified any exception thrown by t_order(const symbol_fset &) const.

Definition at line 573 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_lorder() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

order_type piranha::real_trigonometric_kronecker_monomial< T >::t_lorder	(	const symbol_idx_fset &	p,
		const symbol_fset &	args
	)		const

inline

Partial low trigonometric order (equivalent to the partial trigonometric order).

Parameters

p	positions of the symbols to be considered.
args	the reference piranha::symbol_fset.

Returns: the output of t_order(const symbol_idx_fset &, const symbol_fset &) const.

Exceptions

unspecified any exception thrown by t_order(const symbol_idx_fset &, const symbol_fset &) const.

Definition at line 620 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_order() [1/2]

template<typename T = std::make_signed<std::size_t>::type>

order_type piranha::real_trigonometric_kronecker_monomial< T >::t_order ( const symbol_fset & args ) const

inline

Trigonometric order.

The type returned by this method is the type resulting from the addition of the absolute values of two instances of T.

Parameters

args	the reference piranha::symbol_fset.

Returns: the trigonometric order of the monomial.

Exceptions

std::overflow_error	if the computation of the order overflows.
unspecified	any exception thrown by unpack().

Definition at line 553 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_order() [2/2]

template<typename T = std::make_signed<std::size_t>::type>

order_type piranha::real_trigonometric_kronecker_monomial< T >::t_order	(	const symbol_idx_fset &	p,
		const symbol_fset &	args
	)		const

inline

Partial trigonometric order.

Partial trigonometric order of the monomial: only the symbols at the positions specified by p are considered. The type returned by this method is the type resulting from the addition of the absolute values of two instances of T.

Parameters

p	the positions of the symbols to be considered in the calculation of the order.
args	the reference piranha::symbol_fset.

Returns: the partial trigonometric order of the monomial.

Exceptions

std::invalid_argument	if the last element of `p`, if existing, is not less than the size of `args`.
std::overflow_error	if the computation of the degree overflows.
unspecified	any exception thrown by unpack().

Definition at line 593 of file real_trigonometric_kronecker_monomial.hpp.

◆ t_subs()

template<typename T = std::make_signed<std::size_t>::type>

template<typename U >

std::vector<std::pair<t_subs_type<U>, real_trigonometric_kronecker_monomial> > piranha::real_trigonometric_kronecker_monomial< T >::t_subs	(	const symbol_idx &	idx,
		const U &	c,
		const U &	s,
		const symbol_fset &	args
	)		const

inline

Trigonometric substitution.

Note: This method is enabled only if U supports the operations needed to compute the result.

This method will substitute the cosine and sine of the symbol at the position idx with, respectively, c and s. The substitution is performed using standard trigonometric formulae, and it will result in a list of two (substitution result, new monomial) pairs. If idx is not smaller than the size of this, the result of the substitution will be the original monomial unchanged.

Parameters

idx	the index of the symbol whose cosine and sine will be substituted.
c	the quantity that will replace the cosine of the symbol at the position `idx`.
s	the quantity that will replace the sine of the symbol at the position `idx`.
args	the reference piranha::symbol_fset.

Returns: the result of the substitution.

Exceptions

unspecified

any exception thrown by:

unpack(),
construction, assignment and arithmetics on the return value and on the intermediary values invovled in the computation,
piranha::kronecker_array::encode().

Definition at line 1175 of file real_trigonometric_kronecker_monomial.hpp.

◆ trim()

template<typename T = std::make_signed<std::size_t>::type>

real_trigonometric_kronecker_monomial piranha::real_trigonometric_kronecker_monomial< T >::trim	(	const std::vector< char > &	trim_mask,
		const symbol_fset &	args
	)		const

inline

Trim.

This method is used in piranha::series::trim(). The input mask trim_mask is a vector of boolean flags signalling (with nonzero values) elements of this to be removed. The method will return a copy of this in which the specified elements have been removed.

For instance, if this contains the values [0,5,3,0,4] and trim_mask contains the values [false,false,false,true,false], then the output of this method will be the array of values [0,5,3,4] (that is, the fourth element has been removed as indicated by a true value in trim_mask's fourth element).

Parameters

trim_mask	a mask indicating which element will be removed.
args	the reference piranha::symbol_fset.

Returns: a trimmed copy of this.

Exceptions

std::invalid_argument	if the size of `trim_mask` differs from the size of `args`.
unspecified	any exception thrown by unpack() or piranha::static_vector::push_back().

Definition at line 1287 of file real_trigonometric_kronecker_monomial.hpp.

◆ trim_identify()

template<typename T = std::make_signed<std::size_t>::type>

void piranha::real_trigonometric_kronecker_monomial< T >::trim_identify	(	std::vector< char > &	trim_mask,
		const symbol_fset &	args
	)		const

inline

Identify symbols that can be trimmed.

This method is used in piranha::series::trim(). The input parameter trim_mask is a vector of boolean flags (i.e., a mask) which signals which elements in args are candidates for trimming (i.e., a zero value means that the symbol at the corresponding position in args is not a candidate for trimming, while a nonzero value means that the symbol is a candidate for trimming). This method will set to zero those values in trim_mask for which the corresponding element in this is nonzero.

For instance, if this contains the values [0,5,3,0,4] and trim_mask originally contains the values [1,1,0,1,0], after a call to this method trim_mask will contain [1,0,0,1,0] (that is, the second element was set from 1 to 0 as the corresponding element in this has a value of 5 and thus must not be trimmed).

Parameters

trim_mask	a mask signalling candidate elements for trimming.
args	the reference piranha::symbol_fset.

Exceptions

std::invalid_argument	if the size of `trim_mask` differs from the size of `args`.
unspecified	any exception thrown by unpack().

Definition at line 1263 of file real_trigonometric_kronecker_monomial.hpp.

◆ unpack()

template<typename T = std::make_signed<std::size_t>::type>

v_type piranha::real_trigonometric_kronecker_monomial< T >::unpack ( const symbol_fset & args ) const

inline

Unpack internal integer instance.

This method will decode the internal integral instance into a piranha::static_vector of size equal to the size of args.

Parameters

args	the reference piranha::symbol_fset.

Returns: a piranha::static_vector containing the result of decoding the internal integral instance via piranha::kronecker_array.

Exceptions

std::invalid_argument	if the size of `args` is larger than the maximum size of piranha::static_vector.
unspecified	any exception thrown by piranha::kronecker_array::decode().

Definition at line 758 of file real_trigonometric_kronecker_monomial.hpp.

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

real_trigonometric_kronecker_monomial.hpp

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

template<typename T = std::make_signed<std::size_t>::type> class piranha::real_trigonometric_kronecker_monomial< T >

Type requirements

Exception safety guarantee

Move semantics

Member Typedef Documentation

◆ size_type

Constructor & Destructor Documentation

◆ real_trigonometric_kronecker_monomial() [1/6]

◆ real_trigonometric_kronecker_monomial() [2/6]

◆ real_trigonometric_kronecker_monomial() [3/6]

◆ real_trigonometric_kronecker_monomial() [4/6]

◆ real_trigonometric_kronecker_monomial() [5/6]

◆ real_trigonometric_kronecker_monomial() [6/6]

Member Function Documentation

◆ canonicalise()

◆ evaluate()

◆ get_flavour()

◆ get_int()

◆ hash()

◆ integrate()

◆ is_compatible()

◆ is_unitary()

◆ is_zero()

◆ merge_symbols()

◆ msgpack_convert()

◆ msgpack_pack()

◆ multiply()

◆ operator!=()

◆ operator<()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ partial()

◆ print()

◆ print_tex()

◆ set_flavour()

◆ set_int()

◆ subs()

◆ t_degree() [1/2]

◆ t_degree() [2/2]

◆ t_ldegree() [1/2]

◆ t_ldegree() [2/2]

◆ t_lorder() [1/2]

◆ t_lorder() [2/2]

◆ t_order() [1/2]

◆ t_order() [2/2]

◆ t_subs()

◆ trim()

◆ trim_identify()

◆ unpack()

template<typename T = std::make_signed<std::size_t>::type>
class piranha::real_trigonometric_kronecker_monomial< T >