This class implements an automatic differentiation functionality. More...

Public Member Functions
	AutomaticDifferentiationT ()=default
	Creates a new differentiation object without initializing the parameters. More...

	AutomaticDifferentiationT (const T &value)
	Creates a new differentiation object for a given scalar value (not a constant). More...

	AutomaticDifferentiationT (const T &value, const T &derivative)
	Creates a new differentiation object by a given scalar and it's known derivative of the function at the specified location 'value'. More...

	AutomaticDifferentiationT (const T &value, const bool isVariable)
	Creates a new differentiation object by a given scalar or constant value, while a boolean state specifies whether the parameter is a scalar or a constant. More...

const T &	derivative () const
	Returns the actual derivative of this object. More...

const T &	value () const
	Returns the value of this object. More...

const T &	operator() () const
	Returns the actual derivative value of this object. More...

AutomaticDifferentiationT< T, TNumeric >	operator+ (const T &right) const
	Adds a scalar value to this differentiation object. More...

AutomaticDifferentiationT< T, TNumeric > &	operator+= (const T &right)
	Adds a scalar value to this differentiation object. More...

AutomaticDifferentiationT< T, TNumeric >	operator+ (const AutomaticDifferentiationT< T, TNumeric > &right) const
	Adds two differentiation objects and determines the sum derivative. More...

AutomaticDifferentiationT< T, TNumeric > &	operator+= (const AutomaticDifferentiationT< T, TNumeric > &right)
	Adds two differentiation objects and determines the sum derivative. More...

AutomaticDifferentiationT< T, TNumeric >	operator- (const T &right) const
	Subtracts a scalar value from this differentiation object. More...

AutomaticDifferentiationT< T, TNumeric > &	operator-= (const T &right)
	Subtracts a scalar value from this differentiation object. More...

AutomaticDifferentiationT< T, TNumeric >	operator- (const AutomaticDifferentiationT< T, TNumeric > &right) const
	Subtracts two differentiation objects and determines the resulting derivative. More...

AutomaticDifferentiationT< T, TNumeric >	operator- () const
	Unary negation operator returns the negative of this differentiation object. More...

AutomaticDifferentiationT< T, TNumeric > &	operator-= (const AutomaticDifferentiationT< T, TNumeric > &right)
	Subtracts two differentiation objects and determines the resulting derivative. More...

AutomaticDifferentiationT< T, TNumeric >	operator* (const AutomaticDifferentiationT< T, TNumeric > &right) const
	Multiplies two differentiation objects and determines the product derivative. More...

AutomaticDifferentiationT< T, TNumeric > &	operator*= (const AutomaticDifferentiationT< T, TNumeric > &right)
	Multiplies two differentiation objects and determines the product derivative. More...

AutomaticDifferentiationT< T, TNumeric >	operator* (const T &right) const
	Multiplies this differentiation objects with a scalar. More...

AutomaticDifferentiationT< T, TNumeric > &	operator*= (const T &right)
	Multiplies this differentiation objects with a scalar. More...

AutomaticDifferentiationT< T, TNumeric >	operator/ (const AutomaticDifferentiationT< T, TNumeric > &right) const
	Divides two differentiation objects and determines the quotient derivative. More...

AutomaticDifferentiationT< T, TNumeric > &	operator/= (const AutomaticDifferentiationT< T, TNumeric > &right)
	Divides two differentiation objects and determines the quotient derivative. More...

AutomaticDifferentiationT< T, TNumeric >	operator/ (const T &right) const
	Divides this differentiation object by a scalar value. More...

AutomaticDifferentiationT< T, TNumeric > &	operator/= (const T &right)
	Divides this differentiation object by a scalar value. More...

Static Public Member Functions
static AutomaticDifferentiationT< T, TNumeric >	sin (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the sinus function. More...

static AutomaticDifferentiationT< T, TNumeric >	cos (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the cosine function. More...

static AutomaticDifferentiationT< T, TNumeric >	tan (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the tangent function. More...

static AutomaticDifferentiationT< T, TNumeric >	sqrt (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the square root function. More...

static AutomaticDifferentiationT< T, TNumeric >	sqr (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the square function. More...

static AutomaticDifferentiationT< T, TNumeric >	exp (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the exponential function. More...

static AutomaticDifferentiationT< T, TNumeric >	log (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the natural logarithm. More...

static AutomaticDifferentiationT< T, TNumeric >	log2 (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the logarithm to the base 2. More...

static AutomaticDifferentiationT< T, TNumeric >	log10 (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the logarithm to the base 10. More...

static AutomaticDifferentiationT< T, TNumeric >	pow (const AutomaticDifferentiationT< T, TNumeric > &x, const T &y)
	Determines the derivative of the power function calculating x to the power of y. More...

static AutomaticDifferentiationT< T, TNumeric >	abs (const AutomaticDifferentiationT< T, TNumeric > &value)
	Determines the derivative of the abs function. More...

static AutomaticDifferentiationT< T, TNumeric >	min (const AutomaticDifferentiationT< T, TNumeric > &value, const T &second)
	Determines the derivative of the min function. More...

static AutomaticDifferentiationT< T, TNumeric >	max (const AutomaticDifferentiationT< T, TNumeric > &value, const T &second)
	Determines the derivative of the max function. More...

Protected Attributes
T	value_ = T(0)
	The scalar value of this object. More...

T	derivative_ = T(0)
	The actual derivative of this object. More...

Friends
template<typename T1 , typename TNumeric1 , typename T2 >
AutomaticDifferentiationT< T1, TNumeric1 >	operator+ (const T2 &left, const AutomaticDifferentiationT< T1, TNumeric1 > &right)

template<typename T1 , typename TNumeric1 , typename T2 >
AutomaticDifferentiationT< T1, TNumeric1 >	operator- (const T2 &left, const AutomaticDifferentiationT< T1, TNumeric1 > &right)

template<typename T1 , typename TNumeric1 , typename T2 >
AutomaticDifferentiationT< T1, TNumeric1 >	operator* (const T2 &left, const AutomaticDifferentiationT< T1, TNumeric1 > &right)

template<typename T1 , typename TNumeric1 , typename T2 >
AutomaticDifferentiationT< T1, TNumeric1 >	operator/ (const T2 &left, const AutomaticDifferentiationT< T1, TNumeric1 > &right)

Detailed Description

template<typename T, typename TNumeric = NumericT<T>>
class Ocean::AutomaticDifferentiationT< T, TNumeric >

This class implements an automatic differentiation functionality.

The automatic differentiation is realized by a pair of two values using the forward mode: the actual value of a function and the corresponding derivative at this location.
Therefore, each object holds the value of x and x' for a given parameter x.
Automatic differentiation is a nice tool for fast prototyping of e.g., non-linear optimization functions.
The accuracy of the resulting derivative is almost ideal and significantly better compared to numerical differentiation.
However, in general the performance of the automatic differentiation (using the forward method) will be at least two times slower than calculating the derivative directory.
The following code snippet shows a simple example how the AutomaticDifferentiation class can be used.

// the following line determines the derivative f'(x) of f(x) = x^2 for x = 5.5
const AutomaticDifferentiation automaticDerivative0 = AutomaticDifferentiation(5.5) * AutomaticDifferentiation(5.5);
const Scalar derivative0 = automaticDerivative0.derivative();
 
// the following line determines the derivative of f'(x) of f(x) = x * sin(x) + 7 for x = 3
const AutomaticDifferentiation automaticDerivative1 = AutomaticDifferentiation(3) * AutomaticDifferentiation::sin(AutomaticDifferentiation(3)) + 7;
const Scalar derivative1 = automaticDerivative1.derivative();

In the case a Jacobian matrix needs to be determined the constructor with additional boolean parameter may be used for calculations:

// we determine the 1x2 Jacobian matrix for f(x, y) = x^2 + 3y + 5
// the Jacobian will have the following layout:
// | df/dx   df/dy |
 
Scalar jacobian[2];
 
Scalar x = 3; // any value for x
Scalar y = 7; // any value for y
 
for (unsigned int n = 0u; n < 2u; ++n)
{
    const AutomaticDifferentiation dx = AutomaticDifferentiation(x, n == 0u) * AutomaticDifferentiation(x, n == 0u);
    const AutomaticDifferentiation dy = AutomaticDifferentiation(y, n == 1u) * 3;
 
    const AutomaticDifferentiation d = dx + dy + 5;
    jacobian[n] = d(); // or d.derivative();
}

Template Parameters

T	The data type of the scalar
TNumeric	The numeric class providing access to standard mathematical functions like sin, cos, sqrt, etc.

Constructor & Destructor Documentation

◆ AutomaticDifferentiationT() [1/4]

template<typename T , typename TNumeric = NumericT<T>>

Ocean::AutomaticDifferentiationT< T, TNumeric >::AutomaticDifferentiationT ( )

default

Creates a new differentiation object without initializing the parameters.

◆ AutomaticDifferentiationT() [2/4]

template<typename T , typename TNumeric >

Ocean::AutomaticDifferentiationT< T, TNumeric >::AutomaticDifferentiationT ( const T & value )

inlineexplicit

Creates a new differentiation object for a given scalar value (not a constant).

The derivative for the provided scalar value will be set to 1.

Parameters

value The scalar value defining the object

◆ AutomaticDifferentiationT() [3/4]

template<typename T , typename TNumeric >

Ocean::AutomaticDifferentiationT< T, TNumeric >::AutomaticDifferentiationT	(	const T &	value,
		const T &	derivative
	)

inline

Creates a new differentiation object by a given scalar and it's known derivative of the function at the specified location 'value'.

Parameters

value	The scalar value defining the object
derivative	The derivative of the function at location 'value', e.g., 1 for a scalar parameter, 0 for a constant

◆ AutomaticDifferentiationT() [4/4]

template<typename T , typename TNumeric >

Ocean::AutomaticDifferentiationT< T, TNumeric >::AutomaticDifferentiationT	(	const T &	value,
		const bool	isVariable
	)

inline

Creates a new differentiation object by a given scalar or constant value, while a boolean state specifies whether the parameter is a scalar or a constant.

Parameters

value	The scalar or constant value defining the object
isVariable	True, if the provided value is a scalar (with derivative 1); False, if the provided value is a constant (with derivative 0)

Member Function Documentation

◆ abs()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::abs ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the abs function.

Parameters

value The value for which the derivative will be determined

Returns: The resulting derivative value

◆ cos()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::cos ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the cosine function.

Parameters

value The value for which the derivative will be determined, in radians

Returns: The resulting derivative value

◆ derivative()

template<typename T , typename TNumeric >

const T & Ocean::AutomaticDifferentiationT< T, TNumeric >::derivative

inline

Returns the actual derivative of this object.

Returns: The object's derivative

◆ exp()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::exp ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the exponential function.

Parameters

value The value for which the derivative will be determined

Returns: The resulting derivative value

◆ log()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::log ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the natural logarithm.

Parameters

value The value for which the derivative will be determined, with value range (0, infinity)

Returns: The resulting derivative value

◆ log10()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::log10 ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the logarithm to the base 10.

Parameters

value The value for which the derivative will be determined, with value range (0, infinity)

Returns: The resulting derivative value

◆ log2()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::log2 ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the logarithm to the base 2.

Parameters

value The value for which the derivative will be determined, with value range (0, infinity)

Returns: The resulting derivative value

◆ max()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::max	(	const AutomaticDifferentiationT< T, TNumeric > &	value,
		const T &	second
	)

inlinestatic

Determines the derivative of the max function.

Parameters

value	The value for which the derivative will be determined
second	The second scalar value that will be used for maximum comparison

Returns: The resulting derivative value

◆ min()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::min	(	const AutomaticDifferentiationT< T, TNumeric > &	value,
		const T &	second
	)

inlinestatic

Determines the derivative of the min function.

Parameters

value	The value for which the derivative will be determined
second	The second scalar value that will be used for minimum comparison

Returns: The resulting derivative value

◆ operator()()

template<typename T , typename TNumeric >

const T & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator()

inline

Returns the actual derivative value of this object.

Returns: The object's derivative value

◆ operator*() [1/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator* ( const AutomaticDifferentiationT< T, TNumeric > & right ) const

inline

Multiplies two differentiation objects and determines the product derivative.

Parameters

right The right differentiation object

Returns: The product derivative

◆ operator*() [2/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator* ( const T & right ) const

inline

Multiplies this differentiation objects with a scalar.

Parameters

right The right scalar value

Returns: The resulting differentiation object

◆ operator*=() [1/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator*= ( const AutomaticDifferentiationT< T, TNumeric > & right )

inline

Multiplies two differentiation objects and determines the product derivative.

Parameters

right The right differentiation object

Returns: The reference to this object

◆ operator*=() [2/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator*= ( const T & right )

inline

Multiplies this differentiation objects with a scalar.

Parameters

right The right scalar value

Returns: The reference to this object

◆ operator+() [1/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator+ ( const AutomaticDifferentiationT< T, TNumeric > & right ) const

inline

Adds two differentiation objects and determines the sum derivative.

Parameters

right The right differentiation object

Returns: The sum derivative

◆ operator+() [2/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator+ ( const T & right ) const

inline

Adds a scalar value to this differentiation object.

Parameters

right The scalar value

Returns: The differentiation object with added scalar

◆ operator+=() [1/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator+= ( const AutomaticDifferentiationT< T, TNumeric > & right )

inline

Adds two differentiation objects and determines the sum derivative.

Parameters

right The right differentiation object

Returns: The reference to this object

◆ operator+=() [2/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator+= ( const T & right )

inline

Adds a scalar value to this differentiation object.

Parameters

right The scalar value

Returns: The reference to this object

◆ operator-() [1/3]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator-

inline

Unary negation operator returns the negative of this differentiation object.

Returns: The negative differentiation object

◆ operator-() [2/3]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator- ( const AutomaticDifferentiationT< T, TNumeric > & right ) const

inline

Subtracts two differentiation objects and determines the resulting derivative.

Parameters

right The right differentiation object

Returns: The resulting derivative

◆ operator-() [3/3]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator- ( const T & right ) const

inline

Subtracts a scalar value from this differentiation object.

Parameters

right The scalar value

Returns: The differentiation object with subtracted scalar

◆ operator-=() [1/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator-= ( const AutomaticDifferentiationT< T, TNumeric > & right )

inline

Subtracts two differentiation objects and determines the resulting derivative.

Parameters

right The right differentiation object

Returns: The reference to this object

◆ operator-=() [2/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator-= ( const T & right )

inline

Subtracts a scalar value from this differentiation object.

Parameters

right The scalar value

Returns: The reference to this object

◆ operator/() [1/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator/ ( const AutomaticDifferentiationT< T, TNumeric > & right ) const

inline

Divides two differentiation objects and determines the quotient derivative.

Parameters

right The right differentiation object, while the object's value must not be zero

Returns: The quotient derivative

◆ operator/() [2/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::operator/ ( const T & right ) const

inline

Divides this differentiation object by a scalar value.

Parameters

right The right scalar value, must not be zero

Returns: The resulting differentiation object

◆ operator/=() [1/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator/= ( const AutomaticDifferentiationT< T, TNumeric > & right )

inline

Divides two differentiation objects and determines the quotient derivative.

Parameters

right The right differentiation object, while the object's value must not be zero

Returns: The reference to this object

◆ operator/=() [2/2]

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > & Ocean::AutomaticDifferentiationT< T, TNumeric >::operator/= ( const T & right )

inline

Divides this differentiation object by a scalar value.

Parameters

right The right scalar value, must not be zero

Returns: The reference to this object

◆ pow()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::pow	(	const AutomaticDifferentiationT< T, TNumeric > &	x,
		const T &	y
	)

inlinestatic

Determines the derivative of the power function calculating x to the power of y.

Parameters

x	The value for which the derivative will be determined, with value range [0, infinity)
y	The exponent, with range (-infinity, infinity)

Returns: The resulting derivative value

◆ sin()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::sin ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the sinus function.

Parameters

value The value for which the derivative will be determined, in radians

Returns: The resulting derivative value

◆ sqr()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::sqr ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the square function.

Parameters

value The value for which the derivative will be determined

Returns: The resulting derivative value

◆ sqrt()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::sqrt ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the square root function.

Parameters

value The value for which the derivative will be determined, with value range [0, infinity)

Returns: The resulting derivative value

◆ tan()

template<typename T , typename TNumeric >

AutomaticDifferentiationT< T, TNumeric > Ocean::AutomaticDifferentiationT< T, TNumeric >::tan ( const AutomaticDifferentiationT< T, TNumeric > & value )

inlinestatic

Determines the derivative of the tangent function.

Parameters

value The value for which the derivative will be determined, in radian

Returns: The resulting derivative value

◆ value()

template<typename T , typename TNumeric >

const T & Ocean::AutomaticDifferentiationT< T, TNumeric >::value

inline

Returns the value of this object.

Returns: The object's value

Friends And Related Function Documentation

◆ operator*

template<typename T , typename TNumeric = NumericT<T>>

template<typename T1 , typename TNumeric1 , typename T2 >

AutomaticDifferentiationT<T1, TNumeric1> operator*	(	const T2 &	left,
		const AutomaticDifferentiationT< T1, TNumeric1 > &	right
	)

friend

◆ operator+

template<typename T , typename TNumeric = NumericT<T>>

template<typename T1 , typename TNumeric1 , typename T2 >

AutomaticDifferentiationT<T1, TNumeric1> operator+	(	const T2 &	left,
		const AutomaticDifferentiationT< T1, TNumeric1 > &	right
	)

friend

◆ operator-

template<typename T , typename TNumeric = NumericT<T>>

template<typename T1 , typename TNumeric1 , typename T2 >

AutomaticDifferentiationT<T1, TNumeric1> operator-	(	const T2 &	left,
		const AutomaticDifferentiationT< T1, TNumeric1 > &	right
	)

friend

◆ operator/

template<typename T , typename TNumeric = NumericT<T>>

template<typename T1 , typename TNumeric1 , typename T2 >

AutomaticDifferentiationT<T1, TNumeric1> operator/	(	const T2 &	left,
		const AutomaticDifferentiationT< T1, TNumeric1 > &	right
	)

friend

Field Documentation

◆ derivative_

template<typename T , typename TNumeric = NumericT<T>>

T Ocean::AutomaticDifferentiationT< T, TNumeric >::derivative_ = T(0)

protected

The actual derivative of this object.

◆ value_

template<typename T , typename TNumeric = NumericT<T>>

T Ocean::AutomaticDifferentiationT< T, TNumeric >::value_ = T(0)

protected

The scalar value of this object.

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

AutomaticDifferentiation.h

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

template<typename T, typename TNumeric = NumericT<T>> class Ocean::AutomaticDifferentiationT< T, TNumeric >

Constructor & Destructor Documentation

◆ AutomaticDifferentiationT() [1/4]

◆ AutomaticDifferentiationT() [2/4]

◆ AutomaticDifferentiationT() [3/4]

◆ AutomaticDifferentiationT() [4/4]

Member Function Documentation

◆ abs()

◆ cos()

◆ derivative()

◆ exp()

◆ log()

◆ log10()

◆ log2()

◆ max()

◆ min()

◆ operator()()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ pow()

◆ sin()

◆ sqr()

◆ sqrt()

◆ tan()

◆ value()

Friends And Related Function Documentation

◆ operator*

◆ operator+

◆ operator-

◆ operator/

Field Documentation

◆ derivative_

◆ value_

template<typename T, typename TNumeric = NumericT<T>>
class Ocean::AutomaticDifferentiationT< T, TNumeric >