casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations Struct Reference

Implements all mathematical operators and functions for AutoDiff. More...

#include <AutoDiffMath.h>

List of all members.

Public Member Functions
template<class T >
AutoDiff< T >	operator+ (const AutoDiff< T > &other)
	Unary arithmetic operators.
template<class T >
AutoDiff< T >	operator- (const AutoDiff< T > &other)
template<class T >
AutoDiff< T >	operator+ (const AutoDiff< T > &left, const AutoDiff< T > &right)
	Arithmetic on two AutoDiff objects, returning an AutoDiff object.
template<class T >
AutoDiff< T >	operator- (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
AutoDiff< T >	operator* (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
AutoDiff< T >	operator/ (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
AutoDiff< T >	operator+ (const AutoDiff< T > &left, const T &right)
	Arithmetic on an AutoDiff and a scalar, returning an AutoDiff.
template<class T >
AutoDiff< T >	operator- (const AutoDiff< T > &left, const T &right)
template<class T >
AutoDiff< T >	operator* (const AutoDiff< T > &left, const T &right)
template<class T >
AutoDiff< T >	operator/ (const AutoDiff< T > &left, const T &right)
template<class T >
AutoDiff< T >	operator+ (const T &left, const AutoDiff< T > &right)
	Arithmetic between a scalar and an AutoDiff returning an AutoDiff.
template<class T >
AutoDiff< T >	operator- (const T &left, const AutoDiff< T > &right)
template<class T >
AutoDiff< T >	operator* (const T &left, const AutoDiff< T > &right)
template<class T >
AutoDiff< T >	operator/ (const T &left, const AutoDiff< T > &right)
template<class T >
AutoDiff< T >	acos (const AutoDiff< T > &ad)
	Transcendental functions.
template<class T >
AutoDiff< T >	asin (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	atan (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	atan2 (const AutoDiff< T > &y, const AutoDiff< T > &x)
template<class T >
AutoDiff< T >	cos (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	cosh (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	exp (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	log (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	log10 (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	erf (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	erfc (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	pow (const AutoDiff< T > &a, const AutoDiff< T > &b)
template<class T >
AutoDiff< T >	pow (const AutoDiff< T > &a, const T &b)
template<class T >
AutoDiff< T >	square (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	cube (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	sin (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	sinh (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	sqrt (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	tan (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	tanh (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	abs (const AutoDiff< T > &ad)
template<class T >
AutoDiff< T >	fmod (const AutoDiff< T > &x, const T &c)
	Floating-point remainder of x/c, with the same sign as x, where c is a constant.
template<class T >
AutoDiff< T >	fmod (const AutoDiff< T > &x, const AutoDiff< T > &c)
template<class T >
AutoDiff< T >	floor (const AutoDiff< T > &ad)
	Floor and ceil of values.
template<class T >
AutoDiff< T >	ceil (const AutoDiff< T > &ad)
template<class T >
Bool	operator> (const AutoDiff< T > &left, const AutoDiff< T > &right)
	Comparison operators.
template<class T >
Bool	operator< (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
Bool	operator>= (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
Bool	operator<= (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
Bool	operator== (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
Bool	operator!= (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
Bool	near (const AutoDiff< T > &left, const AutoDiff< T > &right)
template<class T >
Bool	near (const AutoDiff< T > &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	allnear (const AutoDiff< T > &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	nearAbs (const AutoDiff< T > &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	allnearAbs (const AutoDiff< T > &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	operator> (const AutoDiff< T > &left, const T &right)
	Compare an AutoDiff and a constant.
template<class T >
Bool	operator< (const AutoDiff< T > &left, const T &right)
template<class T >
Bool	operator>= (const AutoDiff< T > &left, const T &right)
template<class T >
Bool	operator<= (const AutoDiff< T > &left, const T &right)
template<class T >
Bool	operator== (const AutoDiff< T > &left, const T &right)
template<class T >
Bool	operator!= (const AutoDiff< T > &left, const T &right)
template<class T >
Bool	near (const AutoDiff< T > &left, const T &right)
template<class T >
Bool	near (const AutoDiff< T > &left, const T &right, const Double tol)
template<class T >
Bool	allnear (const AutoDiff< T > &left, const T &right, const Double tol)
template<class T >
Bool	nearAbs (const AutoDiff< T > &left, const T &right, const Double tol)
template<class T >
Bool	allnearAbs (const AutoDiff< T > &left, const T &right, const Double tol)
template<class T >
Bool	operator> (const T &left, const AutoDiff< T > &right)
	Compare a constant and an AutoDiff.
template<class T >
Bool	operator< (const T &left, const AutoDiff< T > &right)
template<class T >
Bool	operator>= (const T &left, const AutoDiff< T > &right)
template<class T >
Bool	operator<= (const T &left, const AutoDiff< T > &right)
template<class T >
Bool	operator== (const T &left, const AutoDiff< T > &right)
template<class T >
Bool	operator!= (const T &left, const AutoDiff< T > &right)
template<class T >
Bool	near (const T &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	allnear (const T &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	nearAbs (const T &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	allnearAbs (const T &left, const AutoDiff< T > &right, const Double tol)
template<class T >
Bool	isNaN (const AutoDiff< T > &val)
	Test special values.
template<class T >
Bool	isInf (AutoDiff< T > &val)
template<class T >
AutoDiff< T >	min (const AutoDiff< T > &left, const AutoDiff< T > &right)
	Minimum/maximum.
template<class T >
AutoDiff< T >	max (const AutoDiff< T > &left, const AutoDiff< T > &right)

---

Detailed Description

Implements all mathematical operators and functions for AutoDiff.

Review Status

Reviewed By:

UNKNOWN

Date Reviewed:

before2004/08/25

Test programs:

tAutoDiff

Prerequisite

• AutoDiff class

Etymology

Implements all mathematical operators and functions for AutoDiff.

To Do

• nothing I know of

Definition at line 60 of file AutoDiffMath.h.

---

Member Function Documentation

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::abs

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::acos

(

const AutoDiff< T > &

ad

)

Transcendental functions.

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::allnear	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::allnear	(	const AutoDiff< T > &	left,
		const T &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::allnear	(	const T &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::allnearAbs	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::allnearAbs	(	const AutoDiff< T > &	left,
		const T &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::allnearAbs	(	const T &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::asin

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::atan

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::atan2	(	const AutoDiff< T > &	y,
		const AutoDiff< T > &	x
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::ceil

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::cos

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::cosh

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::cube

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::erf

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::erfc

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::exp

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::floor

(

const AutoDiff< T > &

ad

)

Floor and ceil of values.

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::fmod	(	const AutoDiff< T > &	x,
		const T &	c
	)

Floating-point remainder of x/c, with the same sign as x, where c is a constant.

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::fmod	(	const AutoDiff< T > &	x,
		const AutoDiff< T > &	c
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::isInf

(

AutoDiff< T > &

val

)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::isNaN

(

const AutoDiff< T > &

val

)

Test special values.

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::log

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::log10

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::max	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::min	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

Minimum/maximum.

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::near	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::near	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::near	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::near	(	const AutoDiff< T > &	left,
		const T &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::near	(	const T &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::nearAbs	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::nearAbs	(	const AutoDiff< T > &	left,
		const T &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::nearAbs	(	const T &	left,
		const AutoDiff< T > &	right,
		const Double	tol
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator!=	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator!=	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator!=	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator*	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator*	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator*	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator+

(

const AutoDiff< T > &

other

)

Unary arithmetic operators.

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator+	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

Arithmetic on two AutoDiff objects, returning an AutoDiff object.

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator+	(	const AutoDiff< T > &	left,
		const T &	right
	)

Arithmetic on an AutoDiff and a scalar, returning an AutoDiff.

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator+	(	const T &	left,
		const AutoDiff< T > &	right
	)

Arithmetic between a scalar and an AutoDiff returning an AutoDiff.

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator-

(

const AutoDiff< T > &

other

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator-	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator-	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator-	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator/	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator/	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator/	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator<	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator<	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator<	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator<=	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator<=	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator<=	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator==	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator==	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator==	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator>	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

Comparison operators.

Only the values are compared: in the actual functions, comparisons are used to decide on algorithms. To check if two AutoDiff values are equal, use comparison for both value and derivatives.
Tip: To check if two AutoDiff values are equal, use the member method equals() (e;g; for debugging and testing);

Compare two AutoDiff's

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator>	(	const AutoDiff< T > &	left,
		const T &	right
	)

Compare an AutoDiff and a constant.

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator>	(	const T &	left,
		const AutoDiff< T > &	right
	)

Compare a constant and an AutoDiff.

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator>=	(	const AutoDiff< T > &	left,
		const AutoDiff< T > &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator>=	(	const AutoDiff< T > &	left,
		const T &	right
	)

template<class T >

Bool casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::operator>=	(	const T &	left,
		const AutoDiff< T > &	right
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::pow	(	const AutoDiff< T > &	a,
		const AutoDiff< T > &	b
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::pow	(	const AutoDiff< T > &	a,
		const T &	b
	)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::sin

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::sinh

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::sqrt

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::square

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::tan

(

const AutoDiff< T > &

ad

)

template<class T >

AutoDiff<T> casa::AutoDiffMath_global_functions_AutoDiff_mathematical_operations::tanh

(

const AutoDiff< T > &

ad

)

---

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

• casacore/scimath/Mathematics/AutoDiffMath.h