drake::ad Namespace Reference

Classes
class	AutoDiff
	A scalar type that performs automatic differentiation, similar to Eigen::AutoDiffScalar<Eigen::VectorXd>. More...

Functions
Increment and decrement
https://en.cppreference.com/w/cpp/language/operators#Increment_and_decrement
AutoDiff &	operator++ (AutoDiff &x)
	Standard prefix increment operator (i.e., ++x).
AutoDiff	operator++ (AutoDiff &x, int)
	Standard postfix increment operator (i.e., x++).
AutoDiff &	operator-- (AutoDiff &x)
	Standard prefix decrement operator (i.e., --x).
AutoDiff	operator-- (AutoDiff &x, int)
	Standard postfix decrement operator (i.e., x--).
Arithmetic operators
https://en.cppreference.com/w/cpp/language/operators#Binary_arithmetic_operators
AutoDiff &	operator+= (AutoDiff &a, const AutoDiff &b)
	Standard compound addition and assignment operator.
AutoDiff &	operator+= (AutoDiff &a, double b)
	Standard compound addition and assignment operator.
AutoDiff &	operator-= (AutoDiff &a, const AutoDiff &b)
	Standard compound subtraction and assignment operator.
AutoDiff &	operator-= (AutoDiff &a, double b)
	Standard compound subtraction and assignment operator.
AutoDiff &	operator*= (AutoDiff &a, const AutoDiff &b)
	Standard compound multiplication and assignment operator.
AutoDiff &	operator*= (AutoDiff &a, double b)
	Standard compound multiplication and assignment operator.
AutoDiff &	operator/= (AutoDiff &a, const AutoDiff &b)
	Standard compound division and assignment operator.
AutoDiff &	operator/= (AutoDiff &a, double b)
	Standard compound division and assignment operator.
AutoDiff	operator+ (AutoDiff a, const AutoDiff &b)
	Standard addition operator.
AutoDiff	operator+ (AutoDiff a, double b)
	Standard addition operator.
AutoDiff	operator+ (double a, AutoDiff b)
	Standard addition operator.
AutoDiff	operator+ (AutoDiff x)
	Standard unary plus operator.
AutoDiff	operator- (AutoDiff a, const AutoDiff &b)
	Standard subtraction operator.
AutoDiff	operator- (AutoDiff a, double b)
	Standard subtraction operator.
AutoDiff	operator- (double a, AutoDiff b)
	Standard subtraction operator.
AutoDiff	operator- (AutoDiff x)
	Standard unary minus operator.
AutoDiff	operator* (AutoDiff a, const AutoDiff &b)
	Standard multiplication operator.
AutoDiff	operator* (AutoDiff a, double b)
	Standard multiplication operator.
AutoDiff	operator* (double a, AutoDiff b)
	Standard multiplication operator.
AutoDiff	operator/ (AutoDiff a, const AutoDiff &b)
	Standard division operator.
AutoDiff	operator/ (AutoDiff a, double b)
	Standard division operator.
AutoDiff	operator/ (double a, const AutoDiff &b)
	Standard division operator.
Comparison operators
https://en.cppreference.com/w/cpp/language/operators#Comparison_operators
bool	operator< (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator.
bool	operator<= (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator.
bool	operator> (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator.
bool	operator>= (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator.
bool	operator== (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator.
bool	operator!= (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator.
bool	operator< (const AutoDiff &a, double b)
	Standard comparison operator.
bool	operator<= (const AutoDiff &a, double b)
	Standard comparison operator.
bool	operator> (const AutoDiff &a, double b)
	Standard comparison operator.
bool	operator>= (const AutoDiff &a, double b)
	Standard comparison operator.
bool	operator== (const AutoDiff &a, double b)
	Standard comparison operator.
bool	operator!= (const AutoDiff &a, double b)
	Standard comparison operator.
bool	operator< (double a, const AutoDiff &b)
	Standard comparison operator.
bool	operator<= (double a, const AutoDiff &b)
	Standard comparison operator.
bool	operator> (double a, const AutoDiff &b)
	Standard comparison operator.
bool	operator>= (double a, const AutoDiff &b)
	Standard comparison operator.
bool	operator== (double a, const AutoDiff &b)
	Standard comparison operator.
bool	operator!= (double a, const AutoDiff &b)
	Standard comparison operator.
Minimum/maximum operations
https://en.cppreference.com/w/cpp/algorithm#Minimum.2Fmaximum_operations
const AutoDiff &	max (const AutoDiff &a, const AutoDiff &b)
	ADL overload to mimic std::max from <algorithm>.
AutoDiff	max (AutoDiff a, double b)
	ADL overload to mimic std::max from <algorithm>.
AutoDiff	max (double a, AutoDiff b)
	ADL overload to mimic std::max from <algorithm>.
const AutoDiff &	min (const AutoDiff &a, const AutoDiff &b)
	ADL overload to mimic std::min from <algorithm>.
AutoDiff	min (AutoDiff a, double b)
	ADL overload to mimic std::min from <algorithm>.
AutoDiff	min (double a, AutoDiff b)
	ADL overload to mimic std::min from <algorithm>.
Math functions: Basic operations
https://en.cppreference.com/w/cpp/numeric/math#Basic_operations
AutoDiff	abs (AutoDiff x)
	ADL overload to mimic std::abs from <cmath>.
AutoDiff	abs2 (AutoDiff x)
	ADL overload to mimic Eigen::numext::abs2.
Math functions: Exponential and Power functions
https://en.cppreference.com/w/cpp/numeric/math#Exponential_functions https://en.cppreference.com/w/cpp/numeric/math#Power_functions
AutoDiff	exp (AutoDiff x)
	ADL overload to mimic std::exp from <cmath>.
AutoDiff	log (AutoDiff x)
	ADL overload to mimic std::log from <cmath>.
AutoDiff	pow (AutoDiff base, const AutoDiff &exp)
	ADL overload to mimic std::pow from <cmath>.
AutoDiff	pow (double base, const AutoDiff &exp)
	ADL overload to mimic std::pow from <cmath>.
AutoDiff	pow (AutoDiff base, double exp)
	ADL overload to mimic std::pow from <cmath>.
AutoDiff	sqrt (AutoDiff x)
	ADL overload to mimic std::sqrt from <cmath>.
Math functions: Trigonometric functions
https://en.cppreference.com/w/cpp/numeric/math#Trigonometric_functions
AutoDiff	sin (AutoDiff x)
	ADL overload to mimic std::sin from <cmath>.
AutoDiff	cos (AutoDiff x)
	ADL overload to mimic std::cos from <cmath>.
AutoDiff	tan (AutoDiff x)
	ADL overload to mimic std::tan from <cmath>.
AutoDiff	asin (AutoDiff x)
	ADL overload to mimic std::asin from <cmath>.
AutoDiff	acos (AutoDiff x)
	ADL overload to mimic std::acos from <cmath>.
AutoDiff	atan (AutoDiff x)
	ADL overload to mimic std::atan from <cmath>.
AutoDiff	atan2 (AutoDiff a, const AutoDiff &b)
	ADL overload to mimic std::atan2 from <cmath>.
AutoDiff	atan2 (AutoDiff a, double b)
	ADL overload to mimic std::atan2 from <cmath>.
AutoDiff	atan2 (double a, AutoDiff b)
	ADL overload to mimic std::atan2 from <cmath>.
Math functions: Hyperbolic functions
https://en.cppreference.com/w/cpp/numeric/math#Hyperbolic_functions
AutoDiff	sinh (AutoDiff x)
	ADL overload to mimic std::sinh from <cmath>.
AutoDiff	cosh (AutoDiff x)
	ADL overload to mimic std::cosh from <cmath>.
AutoDiff	tanh (AutoDiff x)
	ADL overload to mimic std::tanh from <cmath>.
Math functions: Nearest integer floating point operations
https://en.cppreference.com/w/cpp/numeric/math#Nearest_integer_floating_point_operations https://en.cppreference.com/w/cpp/numeric/math#Floating_point_manipulation_functions
double	ceil (const AutoDiff &x)
	ADL overload to mimic std::ceil from <cmath>.
double	floor (const AutoDiff &x)
	ADL overload to mimic std::floor from <cmath>.
double	round (const AutoDiff &x)
	ADL overload to mimic std::round from <cmath>.
double	nexttoward (const AutoDiff &from, long double to)
	ADL overload to mimic std::nexttoward from <cmath>.
AutoDiff	copysign (const AutoDiff &mag, const AutoDiff &sgn)
	ADL overload to mimic std::copysign from <cmath>.
bool	isfinite (const AutoDiff &x)
	ADL overload to mimic std::isfinite from <cmath>.
bool	isinf (const AutoDiff &x)
	ADL overload to mimic std::isinf from <cmath>.
bool	isnan (const AutoDiff &x)
	ADL overload to mimic std::isnan from <cmath>.

Function Documentation

abs()

AutoDiff abs

(

AutoDiff

x

)

ADL overload to mimic std::abs from <cmath>.

abs2()

AutoDiff abs2

(

AutoDiff

x

)

ADL overload to mimic Eigen::numext::abs2.

acos()

AutoDiff acos

(

AutoDiff

x

)

ADL overload to mimic std::acos from <cmath>.

asin()

AutoDiff asin

(

AutoDiff

x

)

ADL overload to mimic std::asin from <cmath>.

atan()

AutoDiff atan

(

AutoDiff

x

)

ADL overload to mimic std::atan from <cmath>.

atan2() [1/3]

AutoDiff atan2	(	AutoDiff	a,
		const AutoDiff &	b )

ADL overload to mimic std::atan2 from <cmath>.

atan2() [2/3]

AutoDiff atan2	(	AutoDiff	a,
		double	b )

ADL overload to mimic std::atan2 from <cmath>.

atan2() [3/3]

AutoDiff atan2	(	double	a,
		AutoDiff	b )

ADL overload to mimic std::atan2 from <cmath>.

ceil()

double ceil

(

const AutoDiff &

x

)

ADL overload to mimic std::ceil from <cmath>.

The result's derivatives are always zero.

copysign()

AutoDiff copysign	(	const AutoDiff &	mag,
		const AutoDiff &	sgn )

ADL overload to mimic std::copysign from <cmath>.

cos()

AutoDiff cos

(

AutoDiff

x

)

ADL overload to mimic std::cos from <cmath>.

cosh()

AutoDiff cosh

(

AutoDiff

x

)

ADL overload to mimic std::cosh from <cmath>.

exp()

AutoDiff exp

(

AutoDiff

x

)

ADL overload to mimic std::exp from <cmath>.

floor()

double floor

(

const AutoDiff &

x

)

ADL overload to mimic std::floor from <cmath>.

The result's derivatives are always zero.

isfinite()

bool isfinite

(

const AutoDiff &

x

)

ADL overload to mimic std::isfinite from <cmath>.

Because the return type is bool, the derivatives are not preserved.

isinf()

bool isinf

(

const AutoDiff &

x

)

ADL overload to mimic std::isinf from <cmath>.

Because the return type is bool, the derivatives are not preserved.

isnan()

bool isnan

(

const AutoDiff &

x

)

ADL overload to mimic std::isnan from <cmath>.

Because the return type is bool, the derivatives are not preserved.

log()

AutoDiff log

(

AutoDiff

x

)

ADL overload to mimic std::log from <cmath>.

max() [1/3]

AutoDiff max	(	AutoDiff	a,
		double	b )

ADL overload to mimic std::max from <algorithm>.

When a and b are equal, retains the derivatives of a.

max() [2/3]

const AutoDiff & max	(	const AutoDiff &	a,
		const AutoDiff &	b )

ADL overload to mimic std::max from <algorithm>.

Note that like std::max, this function returns a reference to whichever argument was chosen; it does not make a copy. When a and b are equal, retains the derivatives of a (by returning a) unless a has empty derivatives, in which case b is returned.

max() [3/3]

AutoDiff max	(	double	a,
		AutoDiff	b )

ADL overload to mimic std::max from <algorithm>.

When a and b are equal, retains the derivatives of b.

min() [1/3]

AutoDiff min	(	AutoDiff	a,
		double	b )

ADL overload to mimic std::min from <algorithm>.

When a and b are equal, retains the derivatives of a.

min() [2/3]

const AutoDiff & min	(	const AutoDiff &	a,
		const AutoDiff &	b )

ADL overload to mimic std::min from <algorithm>.

Note that like std::min, this function returns a reference to whichever argument was chosen; it does not make a copy. When a and b are equal, retains the derivatives of a (by returning a) unless a has empty derivatives, in which case b is returned.

min() [3/3]

AutoDiff min	(	double	a,
		AutoDiff	b )

ADL overload to mimic std::min from <algorithm>.

When a and b are equal, retains the derivatives of b.

nexttoward()

double nexttoward	(	const AutoDiff &	from,
		long double	to )

ADL overload to mimic std::nexttoward from <cmath>.

The result's derivatives are always zero.

operator!=() [1/3]

bool operator!=	(	const AutoDiff &	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator!=() [2/3]

bool operator!=	(	const AutoDiff &	a,
		double	b )

Standard comparison operator.

Discards the derivatives.

operator!=() [3/3]

bool operator!=	(	double	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator*() [1/3]

AutoDiff operator*	(	AutoDiff	a,
		const AutoDiff &	b )

Standard multiplication operator.

operator*() [2/3]

AutoDiff operator*	(	AutoDiff	a,
		double	b )

Standard multiplication operator.

operator*() [3/3]

AutoDiff operator*	(	double	a,
		AutoDiff	b )

Standard multiplication operator.

operator*=() [1/2]

AutoDiff & operator*=	(	AutoDiff &	a,
		const AutoDiff &	b )

Standard compound multiplication and assignment operator.

operator*=() [2/2]

AutoDiff & operator*=	(	AutoDiff &	a,
		double	b )

Standard compound multiplication and assignment operator.

operator+() [1/4]

AutoDiff operator+	(	AutoDiff	a,
		const AutoDiff &	b )

Standard addition operator.

operator+() [2/4]

AutoDiff operator+	(	AutoDiff	a,
		double	b )

Standard addition operator.

operator+() [3/4]

AutoDiff operator+

(

AutoDiff

x

)

Standard unary plus operator.

operator+() [4/4]

AutoDiff operator+	(	double	a,
		AutoDiff	b )

Standard addition operator.

operator++() [1/2]

AutoDiff & operator++

(

AutoDiff &

x

)

Standard prefix increment operator (i.e., ++x).

operator++() [2/2]

AutoDiff operator++	(	AutoDiff &	x,
		int	)

Standard postfix increment operator (i.e., x++).

operator+=() [1/2]

AutoDiff & operator+=	(	AutoDiff &	a,
		const AutoDiff &	b )

Standard compound addition and assignment operator.

operator+=() [2/2]

AutoDiff & operator+=	(	AutoDiff &	a,
		double	b )

Standard compound addition and assignment operator.

operator-() [1/4]

AutoDiff operator-	(	AutoDiff	a,
		const AutoDiff &	b )

Standard subtraction operator.

operator-() [2/4]

AutoDiff operator-	(	AutoDiff	a,
		double	b )

Standard subtraction operator.

operator-() [3/4]

AutoDiff operator-

(

AutoDiff

x

)

Standard unary minus operator.

operator-() [4/4]

AutoDiff operator-	(	double	a,
		AutoDiff	b )

Standard subtraction operator.

operator--() [1/2]

AutoDiff & operator--

(

AutoDiff &

x

)

Standard prefix decrement operator (i.e., --x).

operator--() [2/2]

AutoDiff operator--	(	AutoDiff &	x,
		int	)

Standard postfix decrement operator (i.e., x--).

operator-=() [1/2]

AutoDiff & operator-=	(	AutoDiff &	a,
		const AutoDiff &	b )

Standard compound subtraction and assignment operator.

operator-=() [2/2]

AutoDiff & operator-=	(	AutoDiff &	a,
		double	b )

Standard compound subtraction and assignment operator.

operator/() [1/3]

AutoDiff operator/	(	AutoDiff	a,
		const AutoDiff &	b )

Standard division operator.

operator/() [2/3]

AutoDiff operator/	(	AutoDiff	a,
		double	b )

Standard division operator.

operator/() [3/3]

AutoDiff operator/	(	double	a,
		const AutoDiff &	b )

Standard division operator.

operator/=() [1/2]

AutoDiff & operator/=	(	AutoDiff &	a,
		const AutoDiff &	b )

Standard compound division and assignment operator.

operator/=() [2/2]

AutoDiff & operator/=	(	AutoDiff &	a,
		double	b )

Standard compound division and assignment operator.

operator<() [1/3]

bool operator<	(	const AutoDiff &	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator<() [2/3]

bool operator<	(	const AutoDiff &	a,
		double	b )

Standard comparison operator.

Discards the derivatives.

operator<() [3/3]

bool operator<	(	double	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator<=() [1/3]

bool operator<=	(	const AutoDiff &	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator<=() [2/3]

bool operator<=	(	const AutoDiff &	a,
		double	b )

Standard comparison operator.

Discards the derivatives.

operator<=() [3/3]

bool operator<=	(	double	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator==() [1/3]

bool operator==	(	const AutoDiff &	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator==() [2/3]

bool operator==	(	const AutoDiff &	a,
		double	b )

Standard comparison operator.

Discards the derivatives.

operator==() [3/3]

bool operator==	(	double	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator>() [1/3]

bool operator>	(	const AutoDiff &	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator>() [2/3]

bool operator>	(	const AutoDiff &	a,
		double	b )

Standard comparison operator.

Discards the derivatives.

operator>() [3/3]

bool operator>	(	double	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator>=() [1/3]

bool operator>=	(	const AutoDiff &	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

operator>=() [2/3]

bool operator>=	(	const AutoDiff &	a,
		double	b )

Standard comparison operator.

Discards the derivatives.

operator>=() [3/3]

bool operator>=	(	double	a,
		const AutoDiff &	b )

Standard comparison operator.

Discards the derivatives.

pow() [1/3]

AutoDiff pow	(	AutoDiff	base,
		const AutoDiff &	exp )

ADL overload to mimic std::pow from <cmath>.

The resulting partial derivative ∂/∂vᵢ is undefined (i.e., NaN) for all of the following cases:

• ∂base/∂vᵢ is non-zero and either:
  • base, exp, or pow(base, exp) not finite, or
  • base is 0 and exp < 0
• ∂exp/∂vᵢ is non-zero and either:
  • base, exp, or pow(base, exp) not finite, or
  • base is < 0

In all other cases, if the base and exp partial derivatives were well-defined then the resulting partial derivatives will also be well-defined.

pow() [2/3]

AutoDiff pow	(	AutoDiff	base,
		double	exp )

ADL overload to mimic std::pow from <cmath>.

Refer to pow(AutoDiff,const AutoDiff&) for an explanation of special cases.

pow() [3/3]

AutoDiff pow	(	double	base,
		const AutoDiff &	exp )

ADL overload to mimic std::pow from <cmath>.

Refer to pow(AutoDiff,const AutoDiff&) for an explanation of special cases.

round()

double round

(

const AutoDiff &

x

)

ADL overload to mimic std::round from <cmath>.

The result's derivatives are always zero.

sin()

AutoDiff sin

(

AutoDiff

x

)

ADL overload to mimic std::sin from <cmath>.

sinh()

AutoDiff sinh

(

AutoDiff

x

)

ADL overload to mimic std::sinh from <cmath>.

sqrt()

AutoDiff sqrt

(

AutoDiff

x

)

ADL overload to mimic std::sqrt from <cmath>.

tan()

AutoDiff tan

(

AutoDiff

x

)

ADL overload to mimic std::tan from <cmath>.

tanh()

AutoDiff tanh

(

AutoDiff

x

)

ADL overload to mimic std::tanh from <cmath>.