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). More...
AutoDiff	operator++ (AutoDiff &x, int)
	Standard postfix increment operator (i.e., x++). More...
AutoDiff &	operator-- (AutoDiff &x)
	Standard prefix decrement operator (i.e., --x). More...
AutoDiff	operator-- (AutoDiff &x, int)
	Standard postfix decrement operator (i.e., x--). More...
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. More...
AutoDiff &	operator+= (AutoDiff &a, double b)
	Standard compound addition and assignment operator. More...
AutoDiff &	operator-= (AutoDiff &a, const AutoDiff &b)
	Standard compound subtraction and assignment operator. More...
AutoDiff &	operator-= (AutoDiff &a, double b)
	Standard compound subtraction and assignment operator. More...
AutoDiff &	operator *= (AutoDiff &a, const AutoDiff &b)
	Standard compound multiplication and assignment operator. More...
AutoDiff &	operator *= (AutoDiff &a, double b)
	Standard compound multiplication and assignment operator. More...
AutoDiff &	operator/= (AutoDiff &a, const AutoDiff &b)
	Standard compound division and assignment operator. More...
AutoDiff &	operator/= (AutoDiff &a, double b)
	Standard compound division and assignment operator. More...
AutoDiff	operator+ (AutoDiff a, const AutoDiff &b)
	Standard addition operator. More...
AutoDiff	operator+ (AutoDiff a, double b)
	Standard addition operator. More...
AutoDiff	operator+ (double a, AutoDiff b)
	Standard addition operator. More...
AutoDiff	operator+ (AutoDiff x)
	Standard unary plus operator. More...
AutoDiff	operator- (AutoDiff a, const AutoDiff &b)
	Standard subtraction operator. More...
AutoDiff	operator- (AutoDiff a, double b)
	Standard subtraction operator. More...
AutoDiff	operator- (double a, AutoDiff b)
	Standard subtraction operator. More...
AutoDiff	operator- (AutoDiff x)
	Standard unary minus operator. More...
AutoDiff	operator * (AutoDiff a, const AutoDiff &b)
	Standard multiplication operator. More...
AutoDiff	operator * (AutoDiff a, double b)
	Standard multiplication operator. More...
AutoDiff	operator * (double a, AutoDiff b)
	Standard multiplication operator. More...
AutoDiff	operator/ (AutoDiff a, const AutoDiff &b)
	Standard division operator. More...
AutoDiff	operator/ (AutoDiff a, double b)
	Standard division operator. More...
AutoDiff	operator/ (double a, const AutoDiff &b)
	Standard division operator. More...
Comparison operators
https://en.cppreference.com/w/cpp/language/operators#Comparison_operators
bool	operator< (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator<= (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator> (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator>= (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator== (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator!= (const AutoDiff &a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator< (const AutoDiff &a, double b)
	Standard comparison operator. More...
bool	operator<= (const AutoDiff &a, double b)
	Standard comparison operator. More...
bool	operator> (const AutoDiff &a, double b)
	Standard comparison operator. More...
bool	operator>= (const AutoDiff &a, double b)
	Standard comparison operator. More...
bool	operator== (const AutoDiff &a, double b)
	Standard comparison operator. More...
bool	operator!= (const AutoDiff &a, double b)
	Standard comparison operator. More...
bool	operator< (double a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator<= (double a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator> (double a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator>= (double a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator== (double a, const AutoDiff &b)
	Standard comparison operator. More...
bool	operator!= (double a, const AutoDiff &b)
	Standard comparison operator. More...
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>. More...
AutoDiff	max (AutoDiff a, double b)
	ADL overload to mimic std::max from <algorithm>. More...
AutoDiff	max (double a, AutoDiff b)
	ADL overload to mimic std::max from <algorithm>. More...
const AutoDiff &	min (const AutoDiff &a, const AutoDiff &b)
	ADL overload to mimic std::min from <algorithm>. More...
AutoDiff	min (AutoDiff a, double b)
	ADL overload to mimic std::min from <algorithm>. More...
AutoDiff	min (double a, AutoDiff b)
	ADL overload to mimic std::min from <algorithm>. More...
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>. More...
AutoDiff	abs2 (AutoDiff x)
	ADL overload to mimic Eigen::numext::abs2. More...
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>. More...
AutoDiff	log (AutoDiff x)
	ADL overload to mimic std::log from <cmath>. More...
AutoDiff	pow (AutoDiff base, const AutoDiff &exp)
	ADL overload to mimic std::pow from <cmath>. More...
AutoDiff	pow (double base, const AutoDiff &exp)
	ADL overload to mimic std::pow from <cmath>. More...
AutoDiff	pow (AutoDiff base, double exp)
	ADL overload to mimic std::pow from <cmath>. More...
AutoDiff	sqrt (AutoDiff x)
	ADL overload to mimic std::sqrt from <cmath>. More...
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>. More...
AutoDiff	cos (AutoDiff x)
	ADL overload to mimic std::cos from <cmath>. More...
AutoDiff	tan (AutoDiff x)
	ADL overload to mimic std::tan from <cmath>. More...
AutoDiff	asin (AutoDiff x)
	ADL overload to mimic std::asin from <cmath>. More...
AutoDiff	acos (AutoDiff x)
	ADL overload to mimic std::acos from <cmath>. More...
AutoDiff	atan (AutoDiff x)
	ADL overload to mimic std::atan from <cmath>. More...
AutoDiff	atan2 (AutoDiff a, const AutoDiff &b)
	ADL overload to mimic std::atan2 from <cmath>. More...
AutoDiff	atan2 (AutoDiff a, double b)
	ADL overload to mimic std::atan2 from <cmath>. More...
AutoDiff	atan2 (double a, AutoDiff b)
	ADL overload to mimic std::atan2 from <cmath>. More...
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>. More...
AutoDiff	cosh (AutoDiff x)
	ADL overload to mimic std::cosh from <cmath>. More...
AutoDiff	tanh (AutoDiff x)
	ADL overload to mimic std::tanh from <cmath>. More...
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
AutoDiff	ceil (AutoDiff x)
	ADL overload to mimic std::ceil from <cmath>. More...
AutoDiff	floor (AutoDiff x)
	ADL overload to mimic std::floor from <cmath>. More...
AutoDiff	round (AutoDiff x)
	ADL overload to mimic std::round from <cmath>. More...
AutoDiff	nexttoward (AutoDiff from, long double to)
	ADL overload to mimic std::nexttoward from <cmath>. More...
bool	isfinite (const AutoDiff &x)
	ADL overload to mimic std::isfinite from <cmath>. More...
bool	isinf (const AutoDiff &x)
	ADL overload to mimic std::isinf from <cmath>. More...
bool	isnan (const AutoDiff &x)
	ADL overload to mimic std::isnan from <cmath>. More...
Miscellaneous functions
std::ostream &	operator<< (std::ostream &s, const AutoDiff &x)
	Outputs the value() part of x to the stream. More...

Function Documentation

abs()

AutoDiff drake::ad::abs

(

AutoDiff

x

)

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

abs2()

AutoDiff drake::ad::abs2

(

AutoDiff

x

)

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

acos()

AutoDiff drake::ad::acos

(

AutoDiff

x

)

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

asin()

AutoDiff drake::ad::asin

(

AutoDiff

x

)

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

atan()

AutoDiff drake::ad::atan

(

AutoDiff

x

)

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

atan2() [1/3]

AutoDiff drake::ad::atan2	(	AutoDiff	a,
		const AutoDiff &	b
	)

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

atan2() [2/3]

AutoDiff drake::ad::atan2	(	AutoDiff	a,
		double	b
	)

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

atan2() [3/3]

AutoDiff drake::ad::atan2	(	double	a,
		AutoDiff	b
	)

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

ceil()

AutoDiff drake::ad::ceil

(

AutoDiff

x

)

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

The result's derivatives are always zero.

cos()

AutoDiff drake::ad::cos

(

AutoDiff

x

)

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

cosh()

AutoDiff drake::ad::cosh

(

AutoDiff

x

)

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

exp()

AutoDiff drake::ad::exp

(

AutoDiff

x

)

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

floor()

AutoDiff drake::ad::floor

(

AutoDiff

x

)

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

The result's derivatives are always zero.

isfinite()

bool drake::ad::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 drake::ad::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 drake::ad::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 drake::ad::log

(

AutoDiff

x

)

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

max() [1/3]

const AutoDiff& drake::ad::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() [2/3]

AutoDiff drake::ad::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() [3/3]

AutoDiff drake::ad::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]

const AutoDiff& drake::ad::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() [2/3]

AutoDiff drake::ad::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() [3/3]

AutoDiff drake::ad::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()

AutoDiff drake::ad::nexttoward	(	AutoDiff	from,
		long double	to
	)

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

The result's derivatives are always zero.

operator *() [1/3]

AutoDiff drake::ad::operator *	(	AutoDiff	a,
		const AutoDiff &	b
	)

Standard multiplication operator.

operator *() [2/3]

AutoDiff drake::ad::operator *	(	AutoDiff	a,
		double	b
	)

Standard multiplication operator.

operator *() [3/3]

AutoDiff drake::ad::operator *	(	double	a,
		AutoDiff	b
	)

Standard multiplication operator.

operator *=() [1/2]

AutoDiff& drake::ad::operator *=	(	AutoDiff &	a,
		const AutoDiff &	b
	)

Standard compound multiplication and assignment operator.

operator *=() [2/2]

AutoDiff& drake::ad::operator *=	(	AutoDiff &	a,
		double	b
	)

Standard compound multiplication and assignment operator.

operator!=() [1/3]

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

Standard comparison operator.

Discards the derivatives.

operator!=() [2/3]

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

Standard comparison operator.

Discards the derivatives.

operator!=() [3/3]

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

Standard comparison operator.

Discards the derivatives.

operator+() [1/4]

AutoDiff drake::ad::operator+	(	AutoDiff	a,
		const AutoDiff &	b
	)

Standard addition operator.

operator+() [2/4]

AutoDiff drake::ad::operator+	(	AutoDiff	a,
		double	b
	)

Standard addition operator.

operator+() [3/4]

AutoDiff drake::ad::operator+	(	double	a,
		AutoDiff	b
	)

Standard addition operator.

operator+() [4/4]

AutoDiff drake::ad::operator+

(

AutoDiff

x

)

Standard unary plus operator.

operator++() [1/2]

AutoDiff& drake::ad::operator++

(

AutoDiff &

x

)

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

operator++() [2/2]

AutoDiff drake::ad::operator++	(	AutoDiff &	x,
		int
	)

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

operator+=() [1/2]

AutoDiff& drake::ad::operator+=	(	AutoDiff &	a,
		const AutoDiff &	b
	)

Standard compound addition and assignment operator.

operator+=() [2/2]

AutoDiff& drake::ad::operator+=	(	AutoDiff &	a,
		double	b
	)

Standard compound addition and assignment operator.

operator-() [1/4]

AutoDiff drake::ad::operator-	(	AutoDiff	a,
		const AutoDiff &	b
	)

Standard subtraction operator.

operator-() [2/4]

AutoDiff drake::ad::operator-	(	AutoDiff	a,
		double	b
	)

Standard subtraction operator.

operator-() [3/4]

AutoDiff drake::ad::operator-	(	double	a,
		AutoDiff	b
	)

Standard subtraction operator.

operator-() [4/4]

AutoDiff drake::ad::operator-

(

AutoDiff

x

)

Standard unary minus operator.

operator--() [1/2]

AutoDiff& drake::ad::operator--

(

AutoDiff &

x

)

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

operator--() [2/2]

AutoDiff drake::ad::operator--	(	AutoDiff &	x,
		int
	)

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

operator-=() [1/2]

AutoDiff& drake::ad::operator-=	(	AutoDiff &	a,
		const AutoDiff &	b
	)

Standard compound subtraction and assignment operator.

operator-=() [2/2]

AutoDiff& drake::ad::operator-=	(	AutoDiff &	a,
		double	b
	)

Standard compound subtraction and assignment operator.

operator/() [1/3]

AutoDiff drake::ad::operator/	(	AutoDiff	a,
		const AutoDiff &	b
	)

Standard division operator.

operator/() [2/3]

AutoDiff drake::ad::operator/	(	AutoDiff	a,
		double	b
	)

Standard division operator.

operator/() [3/3]

AutoDiff drake::ad::operator/	(	double	a,
		const AutoDiff &	b
	)

Standard division operator.

operator/=() [1/2]

AutoDiff& drake::ad::operator/=	(	AutoDiff &	a,
		const AutoDiff &	b
	)

Standard compound division and assignment operator.

operator/=() [2/2]

AutoDiff& drake::ad::operator/=	(	AutoDiff &	a,
		double	b
	)

Standard compound division and assignment operator.

operator<() [1/3]

bool drake::ad::operator<	(	const AutoDiff &	a,
		const AutoDiff &	b
	)

Standard comparison operator.

Discards the derivatives.

operator<() [2/3]

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

Standard comparison operator.

Discards the derivatives.

operator<() [3/3]

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

Standard comparison operator.

Discards the derivatives.

operator<<()

std::ostream& drake::ad::operator<<	(	std::ostream &	s,
		const AutoDiff &	x
	)

Outputs the value() part of x to the stream.

To output the derivatives use << x.derivatives().transpose().

operator<=() [1/3]

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

Standard comparison operator.

Discards the derivatives.

operator<=() [2/3]

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

Standard comparison operator.

Discards the derivatives.

operator<=() [3/3]

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

Standard comparison operator.

Discards the derivatives.

operator==() [1/3]

bool drake::ad::operator==	(	const AutoDiff &	a,
		const AutoDiff &	b
	)

Standard comparison operator.

Discards the derivatives.

operator==() [2/3]

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

Standard comparison operator.

Discards the derivatives.

operator==() [3/3]

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

Standard comparison operator.

Discards the derivatives.

operator>() [1/3]

bool drake::ad::operator>	(	const AutoDiff &	a,
		const AutoDiff &	b
	)

Standard comparison operator.

Discards the derivatives.

operator>() [2/3]

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

Standard comparison operator.

Discards the derivatives.

operator>() [3/3]

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

Standard comparison operator.

Discards the derivatives.

operator>=() [1/3]

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

Standard comparison operator.

Discards the derivatives.

operator>=() [2/3]

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

Standard comparison operator.

Discards the derivatives.

operator>=() [3/3]

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

Standard comparison operator.

Discards the derivatives.

pow() [1/3]

AutoDiff drake::ad::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 is NaN
• exp is NaN
• pow(base, exp) is NaN
• ∂base/∂vᵢ is non-zero and either:
  • base is zero or not finite, or
  • exp is not finite
• ∂exp/∂vᵢ is non-zero and either:
  • base is not positive-finite, or
  • exp is not finite

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 drake::ad::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.

pow() [3/3]

AutoDiff drake::ad::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.

round()

AutoDiff drake::ad::round

(

AutoDiff

x

)

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

The result's derivatives are always zero.

sin()

AutoDiff drake::ad::sin

(

AutoDiff

x

)

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

sinh()

AutoDiff drake::ad::sinh

(

AutoDiff

x

)

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

sqrt()

AutoDiff drake::ad::sqrt

(

AutoDiff

x

)

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

tan()

AutoDiff drake::ad::tan

(

AutoDiff

x

)

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

tanh()

AutoDiff drake::ad::tanh

(

AutoDiff

x

)

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