dual File Reference

Dual number class. More...

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Classes
struct	duals::is_dual< T >
	Check if T is dual<>, match non-duals. More...
struct	duals::is_complex< T >
	Check if T is std::complex<>, match non- std::complex<>. More...
struct	duals::dual_traits< T >
	Dual_traits helper class. More...
struct	std::is_compound< duals::dual< T > >
	Duals are compound types. More...
struct	std::numeric_limits< duals::dual< T > >
class	duals::dual< T >

Macros
#define	CPPDUALS_DUAL
#define	CPPDUALS_HAVE_SIGNGAM   1
	Configure whether system has POSIX extern int signgam;.

Typedefs
typedef dual< float >	duals::dualf
typedef dual< double >	duals::duald
typedef dual< long double >	duals::dualld
typedef dual< dualf >	duals::hyperdualf
typedef dual< duald >	duals::hyperduald
typedef dual< dualld >	duals::hyperdualld
typedef std::complex< dualf >	duals::cdualf
typedef std::complex< duald >	duals::cduald
typedef std::complex< dualld >	duals::cdualld

Functions
template<class T >
T	duals::rpart (const dual< T > &x)
	Get the dual's real part.
template<class T >
T	duals::dpart (const dual< T > &x)
	Get the dual's dual part.
template<class T >
std::complex< T >	duals::rpart (const std::complex< dual< T >> &x)
	R-part of complex<dual<>> is non-dual complex<> (not to be confused with real())
template<class T >
std::complex< T >	duals::dpart (const std::complex< dual< T >> &x)
	Dual part of complex<dual<>> is complex<>
template<class T , CPPDUALS_ENABLE_IF((std::is_arithmetic< T >::value && !std::is_compound< T >::value)||is_complex< T >::value) >
T	duals::rpart (const T &x)
	Get a non-dual's real part.
template<class T , CPPDUALS_ENABLE_IF((std::is_arithmetic< T >::value && !std::is_compound< T >::value)||is_complex< T >::value) >
T	duals::dpart (const T &)
	Get a non-dual's dual part := zero.
template<class T , typename dist = std::uniform_real_distribution<T>, CPPDUALS_ENABLE_IF(!is_complex< T >::value &&!is_dual< T >::value) >
T	duals::randos::random (T a=T(0), T b=T(1))
template<class T , typename dist = std::uniform_real_distribution<T>, CPPDUALS_ENABLE_IF(!is_complex< T >::value &&!is_dual< T >::value) >
T	duals::randos::random2 (T a=T(0), T b=T(1))
template<class DT , CPPDUALS_ENABLE_IF(is_dual< DT >::value) >
DT	duals::randos::random2 (DT a=DT(0, 0), DT b=DT(1, 1))
template<class CT , CPPDUALS_ENABLE_IF(is_complex< CT >::value) >
CT	duals::randos::random2 (CT a=CT(0, 0), CT b=CT(1, 1))
template<class DT , typename dist = std::uniform_real_distribution<typename DT::value_type>, CPPDUALS_ENABLE_IF(is_dual< DT >::value) >
DT	duals::random (DT a=DT(0, 0), DT b=DT(1, 0))
	Random real and dual parts, used by Eigen's Random(), by default.
template<class T >
dual< T >	duals::conj (const dual< T > &x)
	Complex Conjugate of a dual is just the dual.
template<class T , CPPDUALS_ENABLE_IF(!is_dual< T >::value && !is_complex< T >::value && std::is_arithmetic< T >::value) >
T	duals::conj (const T &x)
template<class T >
dual< T >	duals::dconj (const dual< T > &x)
template<class T >
std::complex< T >	duals::dconj (const std::complex< T > &x)
template<class T , CPPDUALS_ENABLE_IF(!is_dual< T >::value && !is_complex< T >::value && std::is_arithmetic< T >::value) >
T	duals::dconj (const T &x)
	Conjugate a thing that's not dual and not complex.
template<class T >
dual< T >	duals::exp (const dual< T > &x)
	Exponential e^x.
template<class T >
dual< T >	duals::log (const dual< T > &x)
	Natural log ln(x)
template<class T >
dual< T >	duals::log10 (const dual< T > &x)
template<class T >
dual< T >	duals::log2 (const dual< T > &x)
template<class T , class U , CPPDUALS_ENABLE_LEQ_DEPTH_AND_COMMON_T(T, U) >
common_t	duals::pow (const dual< T > &x, const U &y)
template<class T , class U , CPPDUALS_ENABLE_LEQ_DEPTH_AND_COMMON_T(T, U) >
common_t	duals::pow (const U &x, const dual< T > &y)
template<class T , class U , CPPDUALS_ENABLE_SAME_DEPTH_AND_COMMON_T(T, U) >
common_t	duals::pow (const dual< T > &f, const dual< U > &g)
template<typename T >
int	duals::utils::sgn (T val)
template<class T >
dual< T >	duals::abs (const dual< T > &x)
template<class T >
dual< T >	duals::fabs (const dual< T > &x)
template<class T >
duals::dual< T >	duals::copysign (const duals::dual< T > &x, const duals::dual< T > &y)
template<class T >
duals::dual< T >	duals::hypot (const duals::dual< T > &x, const duals::dual< T > &y)
template<class T >
duals::dual< T >	duals::scalbn (const duals::dual< T > &arg, int ex)
template<class T >
duals::dual< T >	duals::logb (const duals::dual< T > &x)
template<class T >
int()	duals::fpclassify (const duals::dual< T > &d)
template<class T >
bool()	duals::isfinite (const duals::dual< T > &d)
template<class T >
bool()	duals::isnormal (const duals::dual< T > &d)
template<class T >
bool()	duals::isinf (const duals::dual< T > &d)
template<class T >
bool()	duals::isnan (const duals::dual< T > &d)
template<class T >
bool()	duals::signbit (const duals::dual< T > &d)
template<class T >
dual< T >	duals::sqrt (const dual< T > &x)
template<class T >
dual< T >	duals::cbrt (const dual< T > &x)
template<class T >
dual< T >	duals::sin (const dual< T > &x)
template<class T >
dual< T >	duals::cos (const dual< T > &x)
template<class T >
dual< T >	duals::tan (const dual< T > &x)
template<class T >
dual< T >	duals::asin (const dual< T > &x)
template<class T >
dual< T >	duals::acos (const dual< T > &x)
template<class T >
dual< T >	duals::atan (const dual< T > &x)
template<class T >
dual< T >	duals::atan2 (const dual< T > &y, const dual< T > &x)
template<class T , class U , CPPDUALS_ENABLE_LEQ_DEPTH_AND_COMMON_T(T, U) >
common_t	duals::atan2 (const dual< T > &y, const U &x)
template<class T , class U , CPPDUALS_ENABLE_LEQ_DEPTH_AND_COMMON_T(T, U) >
common_t	duals::atan2 (const U &y, const dual< T > &x)
template<class T >
dual< T >	duals::sinh (const dual< T > &x)
template<class T >
dual< T >	duals::cosh (const dual< T > &x)
template<class T >
dual< T >	duals::tanh (const dual< T > &x)
template<class T >
dual< T >	duals::asinh (const dual< T > &x)
template<class T >
dual< T >	duals::acosh (const dual< T > &x)
template<class T >
dual< T >	duals::atanh (const dual< T > &x)
template<class T >
dual< T >	duals::log1p (const dual< T > &x)
template<class T >
dual< T >	duals::expm1 (const dual< T > &x)
template<class T >
dual< T >	duals::erf (const dual< T > &x)
template<class T >
dual< T >	duals::erfc (const dual< T > &x)
	Error function complement (1 - erf()).
template<class T >
dual< T >	duals::tgamma (const dual< T > &x)
	Gamma function. Approximation of the dual part.
template<class T >
dual< T >	duals::lgamma (const dual< T > &x)
	Log of absolute value of gamma function. Approximation of the dual part.
template<class T , class _CharT , class _Traits >
std::basic_ostream< _CharT, _Traits > &	duals::operator<< (std::basic_ostream< _CharT, _Traits > &os, const dual< T > &x)
	Putto operator.
template<class T , class CharT , class Traits >
std::basic_istream< CharT, Traits > &	duals::operator>> (std::basic_istream< CharT, Traits > &is, dual< T > &x)
	Stream reader.

Detailed Description

Dual number class.

Definition in file dual.

Function Documentation

conj()

template<class T , CPPDUALS_ENABLE_IF(!is_dual< T >::value && !is_complex< T >::value && std::is_arithmetic< T >::value) >

T duals::conj

(

const T &

x

)

Conjugate a thing that's not dual and not complex – it has no complex value so just return it. This is different from std::conj() which promotes the T to a std::complex<T>.

Definition at line 827 of file dual.

dconj() [1/2]

template<class T >

dual<T> duals::dconj

(

const dual< T > &

x

)

Dual Conjugate, such that x*dconj(x) = rpart(x)^2. Different function name from complex conjugate conj().

Definition at line 831 of file dual.

dconj() [2/2]

template<class T >

std::complex<T> duals::dconj

(

const std::complex< T > &

x

)

Dual Conjugate of a complex, such that x*dconj(x) = rpart(x)^2. Different function name from complex conjugate conj().

Definition at line 837 of file dual.

erf()

template<class T >

dual<T> duals::erf

(

const dual< T > &

x

)

The error function. Make sure to #include <math.h> before #include <duals/dual> to use this function.

Definition at line 1110 of file dual.