Operator definitions. More...

Classes
class	Derivative
	Derivative operator. More...

class	IdentityOperator
	Multiplicative identity operator. More...

class	Operator
	Marker interface for operators. More...

class	OperatorProduct
	Represents the product of two operators. More...

class	OperatorSum
	Operator sum. Represents the sum or difference of two operators. More...

class	Position
	Position operator. More...

class	ScalarMultiplication
	Multiplication operator for Operator and scalar. More...

class	SplineOperator
	Operator representation of a Spline. More...

Typedefs
template<size_t n>
using	Dx = Derivative< n >
	Convenient alias for derivative operator.

template<size_t n>
using	X = Position< n >
	Alias for Position operator.

Enumerations
enum class	AdditionOperation { ADDITION , SUBTRACTION }

Functions
template<typename O1 , typename O2 , std::enable_if_t< are_operators_v< O1, O2 >, bool > = true>
OperatorProduct< O1, O2 >	operator* (O1 &&o1, O2 &&o2)
	Operator multiplication operator.

template<typename O1 , typename O2 , std::enable_if_t< are_operators_v< O1, O2 >, bool > = true>
auto	operator+ (O1 &&o1, O2 &&o2)
	Operator sum.

template<typename O1 , typename O2 , std::enable_if_t< are_operators_v< O1, O2 >, bool > = true>
auto	operator- (O1 &&o1, O2 &&o2)
	Operator difference.

template<typename T , size_t order, typename O , std::enable_if_t< is_operator_v< O >, bool > = true>
auto	transformSpline (const O &op, const Spline< T, order > &spline)
	Applies operator to spline.

template<typename O , typename S , std::enable_if_t< is_operator_v< O > &&is_spline_v< S >, bool > = true>
auto	operator* (const O &o, const S &s)
	Applies an operator to a spline.

template<typename S >
	ScalarMultiplication (S s) -> ScalarMultiplication< S, IdentityOperator >
	ScalarMultiplication with default constructed operator.

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>
ScalarMultiplication< S, O >	operator* (const S &s, O &&o)
	Scalar-Opertator multiplication.

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>
ScalarMultiplication< S, O >	operator* (O &&o, const S &s)
	The scalar multiplication operator for an operator.

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>
ScalarMultiplication< S, O >	operator/ (O &&o, const S &s)
	The scalar division operator for an operator.

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>
auto	operator+ (O &&o, const S &s)

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>
auto	operator+ (const S &s, O &&o)
	The scalar addition operator for an operator.

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>
auto	operator- (O &&o, const S &s)
	The scalar subtraction operator for an operator.

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>
auto	operator- (const S &s, O &&o)

template<typename O , std::enable_if_t< is_operator_v< O >, bool > = true>
ScalarMultiplication< int, O >	operator- (O &&o)
	Unitary minus operator.

Variables
template<AdditionOperation operation>
constexpr bool	is_valid_operation_v
	Validates operation.

template<typename O >
constexpr bool	is_operator_v
	Checks whether O is an operator.

template<typename O1 , typename O2 >
constexpr bool	are_operators_v = is_operator_v<O1> &&is_operator_v<O2>
	Checks whether O1 and O2 are operators.

template<typename T , typename O >
constexpr bool	are_scalar_multiplication_types_v
	Validates ScalarOperator template parameters.

Detailed Description

Operator definitions.

Typedef Documentation

◆ Dx

template<size_t n>

using bspline::operators::Dx = typedef Derivative<n>

Convenient alias for derivative operator.

Alias for the derivative operator $\mathrm{d}^n/\mathrm{d}x^n$ .

Template Parameters

n	Order of the derivative.

◆ X

template<size_t n>

using bspline::operators::X = typedef Position<n>

Alias for Position operator.

Alias for the power of the position operator.

Template Parameters

n	Order of the power of the position operator.

Enumeration Type Documentation

◆ AdditionOperation

enum class bspline::operators::AdditionOperation

strong

Indicates which operation the OperatorSum is supposed to perform.

Enumerator
ADDITION	Perform addition.
SUBTRACTION	Perform subtraction.

Function Documentation

◆ operator*() [1/4]

template<typename O , typename S , std::enable_if_t< is_operator_v< O > &&is_spline_v< S >, bool > = true>

auto bspline::operators::operator*	(	const O &	o,
		const S &	s
	)

Applies an operator to a spline.

Parameters

o	The operator.
s	The spline.

Template Parameters

O	The type of the operator.
S	The type of the spline.

Returns: The spline resulting from the application of the operator to the spline.

◆ operator*() [2/4]

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>

ScalarMultiplication< S, O > bspline::operators::operator*	(	const S &	s,
		O &&	o
	)

Scalar-Opertator multiplication.

Deduction guide for a ScalarMultiplication of a scalar and an Operator.

Parameters

s	The scalar to be multiplied.
o	The operator to be multiplied.

Template Parameters

S	The type of the scalar.
O	The type of the operator to be multiplied.

Returns: The scaled operator.

◆ operator*() [3/4]

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>

ScalarMultiplication< S, O > bspline::operators::operator*	(	O &&	o,
		const S &	s
	)

The scalar multiplication operator for an operator.

Parameters

o	The operator to be multiplied.
s	The scalar to be multiplied.

Template Parameters

S	The type of the scalar.
O	The type of the operator to be multiplied.

Returns: The scaled operator.

◆ operator*() [4/4]

template<typename O1 , typename O2 , std::enable_if_t< are_operators_v< O1, O2 >, bool > = true>

OperatorProduct< O1, O2 > bspline::operators::operator*	(	O1 &&	o1,
		O2 &&	o2
	)

Operator multiplication operator.

The multiplication operator for two operators, returning an OperatorProduct.

Parameters

o1	The first (left) operator.
o2	The second (right) operator.

Template Parameters

O1	The type of the first (left) operator.
O2	The type of the second (right) operator.

◆ operator+() [1/3]

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>

auto bspline::operators::operator+	(	const S &	s,
		O &&	o
	)

The scalar addition operator for an operator.

Parameters

s	The scalar to be added.
o	The operator to be added.

Template Parameters

S	The type of the scalar.
O	The type of the operator.

Returns: The shifted operator.

◆ operator+() [2/3]

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>

auto bspline::operators::operator+	(	O &&	o,
		const S &	s
	)

The scalar addition operator for an operator.

Parameters

o	The operator to be added.
s	The scalar to be added.

Template Parameters

S	The type of the scalar.
O	The type of the operator.

Returns: The shifted operator.

◆ operator+() [3/3]

template<typename O1 , typename O2 , std::enable_if_t< are_operators_v< O1, O2 >, bool > = true>

auto bspline::operators::operator+	(	O1 &&	o1,
		O2 &&	o2
	)

Operator sum.

The addition operator for two operators, returning an OperatorSum.

Parameters

o1	The first operator.
o2	The second operator.

Template Parameters

O1	The type of the first operator.
O2	The type of the second operator.

Returns: The sum of the two input operators.

◆ operator-() [1/4]

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>

auto bspline::operators::operator-	(	const S &	s,
		O &&	o
	)

The scalar subtraction operator for an operator.

Parameters

s	The scalar.
o	The operator to be subtracted.

Template Parameters

S	The type of the scalar.
O	The type of the operator.

Returns: The shifted and inverted operator.

◆ operator-() [2/4]

template<typename O , std::enable_if_t< is_operator_v< O >, bool > = true>

ScalarMultiplication< int, O > bspline::operators::operator- ( O && o )

Unitary minus operator.

The unitary minus operator for an operator. Returns an ScalarMultiplication<int, O>.

Parameters

o	The operator to be negated.

Template Parameters

O	The type of the operator to be negated.

Returns: The inverted operator.

◆ operator-() [3/4]

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>

auto bspline::operators::operator-	(	O &&	o,
		const S &	s
	)

The scalar subtraction operator for an operator.

Parameters

o	The operator.
s	The scalar to be subtracted.

Template Parameters

S	The type of the scalar.
O	The type of the operator.

Returns: The shifted operator.

◆ operator-() [4/4]

template<typename O1 , typename O2 , std::enable_if_t< are_operators_v< O1, O2 >, bool > = true>

auto bspline::operators::operator-	(	O1 &&	o1,
		O2 &&	o2
	)

Operator difference.

The subtraction operator for two operators, returning an OperatorSum.

Parameters

o1	The first operator.
o2	The second operator.

Template Parameters

O1	The type of the first operator.
O2	The type of the second operator.

Returns: the difference of the two input operators.

◆ operator/()

template<typename S , typename O , std::enable_if_t< are_scalar_multiplication_types_v< S, O >, bool > = true>

ScalarMultiplication< S, O > bspline::operators::operator/	(	O &&	o,
		const S &	s
	)

The scalar division operator for an operator.

Parameters

o	The operator to be divided.
s	The divisor.

Template Parameters

S	The type of the scalar.
O	The type of the operator to be divided.

Returns: The scaled operator.

◆ ScalarMultiplication()

template<typename S >

bspline::operators::ScalarMultiplication ( S s ) -> ScalarMultiplication< S, IdentityOperator >

ScalarMultiplication with default constructed operator.

Deduction guide for a ScalarMultiplication constructed from a scalar alone.

Template Parameters

S	The type of the scalar.

◆ transformSpline()

template<typename T , size_t order, typename O , std::enable_if_t< is_operator_v< O >, bool > = true>

auto bspline::operators::transformSpline	(	const O &	op,
		const Spline< T, order > &	spline
	)

Applies operator to spline.

Helper method that applies an operator to a spline based on the transformation of the coefficients on a single interval.

Parameters

op	The operator to apply to the spline.
spline	The spline to apply the operator to.

Template Parameters

T	The datatype of the input and output splines.
order	The order of the input spline.
O	The type of the operator.

Returns: The spline resulting from the application of this operator to the spline.

Variable Documentation

◆ are_operators_v

template<typename O1 , typename O2 >

constexpr bool bspline::operators::are_operators_v = is_operator_v<O1> &&is_operator_v<O2>

inlineconstexpr

Checks whether O1 and O2 are operators.

Indicates whether both template parameters are operator types.

Template Parameters

O1	First template parameter.
O2	Second template parameter.

◆ are_scalar_multiplication_types_v

template<typename T , typename O >

constexpr bool bspline::operators::are_scalar_multiplication_types_v

inlineconstexpr

Initial value:

=

!is_spline_v<T> && !is_operator_v<T> && is_operator_v<O>

Validates ScalarOperator template parameters.

Indicates whether the argument types may be arguments of a scalar multiplication (i.e. a scalar multiplied with an operator).

Template Parameters

T	Scalar type.
O	Operator type.

◆ is_operator_v

template<typename O >

constexpr bool bspline::operators::is_operator_v

inlineconstexpr

Initial value:

=

std::is_base_of_v<Operator, std::remove_cv_t<std::remove_reference_t<O>>>

Checks whether O is an operator.

Indicates whether the template parameter is an operator type.

Template Parameters

O	Template parameter.

◆ is_valid_operation_v

template<AdditionOperation operation>

constexpr bool bspline::operators::is_valid_operation_v

inlineconstexpr

Initial value:

= (operation ==
                                              AdditionOperation::ADDITION) ||
                                             (operation ==
                                              AdditionOperation::SUBTRACTION)

Validates operation.

Checks whether the operation is a valid oeration for OperatorSum.

Template Parameters

operation The operation type to be checked.

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ Dx

◆ X

Enumeration Type Documentation

◆ AdditionOperation

Function Documentation

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator/()

◆ ScalarMultiplication()

◆ transformSpline()

Variable Documentation

◆ are_operators_v

◆ are_scalar_multiplication_types_v

◆ is_operator_v

◆ is_valid_operation_v