Class translotator::DualNumber¶

template <typename Type>

ClassList > translotator > DualNumber

Represents a dual number. More...

#include <DualNumber.hpp>

Inherits the following classes: translotator::MatrixBase

Public Types inherited from translotator::MatrixBase¶

Type	Name
typedef Type	DATATYPE

Public Static Attributes¶

Type	Name
constexpr static ObjectType	OBJECT_TYPE = = ObjectType::DUAL_NUMBER

Public Static Attributes inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
constexpr static size_t	COLS = = M
constexpr static bool	MATRIX_BASE = = true
constexpr static size_t	ROWS = = N

Public Functions¶

Type	Name
Type	Du () const
Type &	Du ()
	DualNumber ()
	DualNumber (const Type & r, const Type & d)
Type	Re () const
Type &	Re ()
void	conjugate () return the conjugate of this dual number
DualNumber< Type >	conjugated () const
DualNumber< Type >	dualNumDiv (const DualNumber< Type > & other) const multiply this dual number with another dual number
void	dualNumDivEq (const DualNumber< Type > & other) return the division of two dual numbers
DualNumber< Type >	dualNumMul (const DualNumber< Type > & other) const divide this dual number with another dual number
void	dualNumMulEq (const DualNumber< Type > & other) return the multiplication of two dual numbers
DualNumber< Type >	inversed () const normalize the real part of this dual number
Type	norm () const return the squared norm of this dual number
Type	normSquared () const conjugate this dual number
void	normalize () return a new DualNumber with normalized real part
DualNumber< Type >	normalized () const return the norm of this dual number
DualNumber< Type >	operator* (const DualNumber< Type > & other) const return the multiplication of two dual numbers
void	*operator= (const DualNumber**< Type > & other)
DualNumber< Type >	operator/ (const DualNumber< Type > & other) const return the division of two dual numbers
void	operator/= (const DualNumber< Type > & other) multiply this dual number with another dual number
Type	operator[] (size_t i) const
Type &	operator[] (size_t i)
SquareMatrix< 2, Type >	toMulMatrix () const return a 2x2 matrix that represents the multiplication of this dual number

Public Functions inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
	MatrixBase () = default Returns the number of columns.
	MatrixBase (const MatrixBase & other) = default
	MatrixBase (const Type data)
	MatrixBase (const Type data)
	MatrixBase (const initializer_list< N M, Type > & list) Initializer list constructor.*
auto	T () const Transpose.
Matrix< P, Q, Type >	block (size_t i, size_t j) const Returns a block of the matrix.
Matrix< P, Q, Type >	block () const Returns a block of the matrix.
ComplexNum< Type >	cast2ComplexNum () const Casts the object to a complex number by copying.
ComplexNum< Type > &	cast2ComplexNumRef () Casts the object to a complex number reference without copying.
DualNumber< Type >	cast2DualNumber () const Casts the object to a dual number by copying.
DualNumber< Type > &	cast2DualNumberRef () Casts the object to a dual number reference without copying.
DualQuaternion< Type >	cast2DualQuaternion () const Casts the object to a dual quaternion by copying.
DualQuaternion< Type > &	cast2DualQuaternionRef () Casts the object to a dual quaternion reference without copying.
Matrix< N, M, Type >	cast2Matrix () const Casts the object to a different matrix type by copying.
Matrix< N, M, Type > &	cast2MatrixRef () Casts the object to a matrix reference without copying.
Quaternion< Type >	cast2Quaternion () const Casts the object to a quaternion by copying.
Quaternion< Type > &	cast2QuaternionRef () Casts the object to a quaternion reference without copying.
SOGroup< N, Type >	cast2SOGroup () const Casts the object to a special orthogonal group by copying.
SOGroup< N, Type > &	cast2SOGroupRef () Casts the object to a special orthogonal group reference without copying.
SquareMatrix< N, Type >	cast2SquareMatrix () const Casts the object to a square matrix by copying.
SquareMatrix< N, Type > &	cast2SquareMatrixRef () Casts the object to a square matrix reference without copying.
UnitComplexNum< Type >	cast2UnitComplexNum () const Casts the object to a unit complex number by copying.
UnitComplexNum< Type > &	cast2UnitComplexNumRef () Casts the object to a unit complex number reference without copying.
UnitDualQuaternion< Type >	cast2UnitDualQuaternion () const Casts the object to a unit dual quaternion by copying.
UnitDualQuaternion< Type > &	cast2UnitDualQuaternionRef () Casts the object to a unit dual quaternion reference without copying.
UnitQuaternion< Type >	cast2UnitQuaternion () const Casts the object to a unit quaternion by copying.
UnitQuaternion< Type > &	cast2UnitQuaternionRef () Casts the object to a unit quaternion reference without copying.
Vector< N, Type >	cast2Vector () const Casts the object to a vector by copying.
Vector< N, Type > &	cast2VectorRef () Casts the object to a vector reference without copying.
NewContainer	castContainer () const Casts the matrix to a different container type by copying.
NewContainer &	castContainerRef () Casts the object to a different container reference without copying.
NewDerived &	castContainerRef ()
auto	castDataType () const Returns the Frobenius norm.
Matrix< N, 1, Type >	col (size_t j) const Returns the j-th column.
void	copyTo (Type * data) const Returns the raw data pointer.
void	fill (const Type & v) Fills the matrix with a value.
Type	frobeniusNorm () const
Type	frobeniusNormSquared () const Returns the squared Frobenius norm.
Type *	getData () const
const Type &	operator() (size_t i, size_t j) const Accesses the element at (i, j)
Type &	operator() (size_t i, size_t j) Accesses the element at (i, j)
auto	operator* (const OtherDerived & other) const Matrix multiplication.
Derived	operator* (const Type & v) const Matrix multiplication by scalar.
void	*operator= (const OtherDerived & other) Matrix** multiplication by scalar.
Derived	operator+ (const OtherDerived & other) const Multiplication by scalar.
void	operator+= (const OtherDerived & other) Matrix division by scalar.
Derived	operator- (const OtherDerived & other) const Matrix subtraction.
Derived	operator- () const Matrix multiplication by scalar.
void	operator-= (const OtherDerived & other) Matrix subtraction by scalar.
Derived	operator/ (Type v) const Division by scalar.
void	operator/= (Type v) Division by scalar.
Derived &	operator= (const Derived & other) Copies the data to the given pointer.
void	print () const Prints the matrix.
Matrix< 1, M, Type >	row (size_t i) const Returns the i-th row.
Derived &	setBlock (size_t i, size_t j, const OtherDerived & block) Sets the element at (i, j)
Derived &	setBlock (const OtherDerived & block) Sets the i-th row.
Derived &	setCol (size_t j, const OtherDerived & col) Sets the j-th column.
Derived &	setCol (const OtherDerived & col) Sets the j-th column.
Derived &	setRow (size_t i, const OtherDerived & row) Sets the i-th row.
Derived &	setRow (const OtherDerived & row) Sets the i-th row.
void	swapCols (size_t j1, size_t j2) Swaps two columns.
void	swapRows (size_t i1, size_t i2) Swaps two rows.
Type	toScalar () const Casts the matrix to a scalar if it is a 1x1 matrix.

Public Static Functions¶

Type	Name
DualNumber< Type >	sqrt (const DualNumber< Type > & dn) divide this dual number with another dual number

Public Static Functions inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
Derived	NaN () Returns a matrix filled with NaN.
constexpr static size_t	colSize () Returns the number of rows.
Derived	eye () Returns an identity matrix.
Derived	ones () Returns a matrix filled with ones.
constexpr static size_t	rowSize ()
Derived	zeros () Returns a matrix filled with zeros.

Protected Attributes inherited from translotator::MatrixBase¶

See translotator::MatrixBase

Type	Name
Type	data_

Detailed Description¶

DualNumber

Template parameters:

Type floating point type

A dual number is a pair of real numbers, where one is the real part and the other is the dual part. The dual part is a number that squares to zero, i.e., e^2 = 0. It is used to represent infinitesimal quantities.

Note:

Data structure : [real, dual], (2 x 1)

Public Static Attributes Documentation¶

variable OBJECT_TYPE¶

constexpr static ObjectType translotator::DualNumber< Type >::OBJECT_TYPE;

Public Functions Documentation¶

function Du [1/2]¶

inline Type translotator::DualNumber::Du () const

function Du [2/2]¶

inline Type & translotator::DualNumber::Du ()

function DualNumber [1/2]¶

inline translotator::DualNumber::DualNumber ()

function DualNumber [2/2]¶

inline translotator::DualNumber::DualNumber (
    const Type & r,
    const Type & d
)

function Re [1/2]¶

inline Type translotator::DualNumber::Re () const

accessors

function Re [2/2]¶

inline Type & translotator::DualNumber::Re ()

function conjugate¶

inline void translotator::DualNumber::conjugate ()

function conjugated¶

inline DualNumber < Type > translotator::DualNumber::conjugated () const

utils

function dualNumDiv¶

inline DualNumber < Type > translotator::DualNumber::dualNumDiv (
    const DualNumber < Type > & other
) const

function dualNumDivEq¶

inline void translotator::DualNumber::dualNumDivEq (
    const DualNumber < Type > & other
)

function dualNumMul¶

inline DualNumber < Type > translotator::DualNumber::dualNumMul (
    const DualNumber < Type > & other
) const

function dualNumMulEq¶

inline void translotator::DualNumber::dualNumMulEq (
    const DualNumber < Type > & other
)

function inversed¶

inline DualNumber < Type > translotator::DualNumber::inversed () const

function norm¶

inline Type translotator::DualNumber::norm () const

function normSquared¶

inline Type translotator::DualNumber::normSquared () const

function normalize¶

inline void translotator::DualNumber::normalize ()

function normalized¶

inline DualNumber < Type > translotator::DualNumber::normalized () const

function operator*¶

inline DualNumber < Type > translotator::DualNumber::operator* (
    const DualNumber < Type > & other
) const

function operator*=¶

inline void translotator::DualNumber::operator*= (
    const DualNumber < Type > & other
)

function operator/¶

inline DualNumber < Type > translotator::DualNumber::operator/ (
    const DualNumber < Type > & other
) const

function operator/=¶

inline void translotator::DualNumber::operator/= (
    const DualNumber < Type > & other
)

function operator[]¶

inline Type translotator::DualNumber::operator[] (
    size_t i
) const

function operator[]¶

inline Type & translotator::DualNumber::operator[] (
    size_t i
)

function toMulMatrix¶

return a 2x2 matrix that represents the multiplication of this dual number

inline SquareMatrix < 2, Type > translotator::DualNumber::toMulMatrix () const

casts

Public Static Functions Documentation¶

function sqrt¶

divide this dual number with another dual number

static inline DualNumber < Type > translotator::DualNumber::sqrt (
    const DualNumber < Type > & dn
)

static functions return the square root of a dual number. Re > 0 is required

The documentation for this class was generated from the following file include/translotator/objects/DualNumber.hpp