Package org.hipparchus.analysis.differentiation

Class FieldDerivativeStructure<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.analysis.differentiation.FieldDerivativeStructure<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

DifferentialAlgebra, FieldDerivative<T,FieldDerivativeStructure<T>>, CalculusFieldElement<FieldDerivativeStructure<T>>, FieldElement<FieldDerivativeStructure<T>>

public class FieldDerivativeStructure<T extends CalculusFieldElement<T>>
extends Object
implements FieldDerivative<T,FieldDerivativeStructure<T>>

Class representing both the value and the differentials of a function.

This class is similar to DerivativeStructure except function parameters and value can be any CalculusFieldElement.

Instances of this class are guaranteed to be immutable.

See Also:

• DerivativeStructure
• FDSFactory
• DSCompiler

Method Summary

Modifier and Type	Method	Description
FieldDerivativeStructure<T>	abs()	absolute value.
FieldDerivativeStructure<T>	acos()	Arc cosine operation.
FieldDerivativeStructure<T>	acosh()	Inverse hyperbolic cosine operation.
FieldDerivativeStructure<T>	add(double a)	'+' operator.
FieldDerivativeStructure<T>	add(FieldDerivativeStructure<T> a)	Compute this + a.
FieldDerivativeStructure<T>	asin()	Arc sine operation.
FieldDerivativeStructure<T>	asinh()	Inverse hyperbolic sine operation.
FieldDerivativeStructure<T>	atan()	Arc tangent operation.
FieldDerivativeStructure<T>	atan2(FieldDerivativeStructure<T> x)	Two arguments arc tangent operation.
static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>	atan2(FieldDerivativeStructure<T> y, FieldDerivativeStructure<T> x)	Two arguments arc tangent operation.
FieldDerivativeStructure<T>	atanh()	Inverse hyperbolic tangent operation.
FieldDerivativeStructure<T>	compose(double... f)	Compute composition of the instance by a univariate function.
final FieldDerivativeStructure<T>	compose(T... f)	Compute composition of the instance by a univariate function.
FieldDerivativeStructure<T>	copySign(double sign)	Returns the instance with the sign of the argument.
FieldDerivativeStructure<T>	copySign(FieldDerivativeStructure<T> sign)	Returns the instance with the sign of the argument.
FieldDerivativeStructure<T>	copySign(T sign)	Returns the instance with the sign of the argument.
FieldDerivativeStructure<T>	cos()	Cosine operation.
FieldDerivativeStructure<T>	cosh()	Hyperbolic cosine operation.
FieldDerivativeStructure<T>	differentiate(int varIndex, int differentiationOrder)	Differentiate w.r.t.
FieldDerivativeStructure<T>	divide(double a)	'÷' operator.
FieldDerivativeStructure<T>	divide(FieldDerivativeStructure<T> a)	Compute this ÷ a.
FieldDerivativeStructure<T>	divide(T a)	'÷' operator.
FieldDerivativeStructure<T>	exp()	Exponential.
FieldDerivativeStructure<T>	expm1()	Exponential minus 1.
T[]	getAllDerivatives()	Get all partial derivatives.
FDSFactory<T>	getFactory()	Get the factory that built the instance.
Field<FieldDerivativeStructure<T>>	getField()	Get the Field to which the instance belongs.
int	getFreeParameters()	Get the number of free parameters.
int	getOrder()	Get the maximum derivation order.
T	getPartialDerivative(int... orders)	Get a partial derivative.
FieldDerivativeStructure<T>	getPi()	Get the Archimedes constant π.
T	getValue()	Get the value part of the derivative structure.
FieldDerivativeStructure<T>	hypot(FieldDerivativeStructure<T> y)	Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>	hypot(FieldDerivativeStructure<T> x, FieldDerivativeStructure<T> y)	Returns the hypotenuse of a triangle with sides x and y - sqrt(x2 +y2) avoiding intermediate overflow or underflow.
FieldDerivativeStructure<T>	integrate(int varIndex, int integrationOrder)	Integrate w.r.t.
FieldDerivativeStructure<T>	linearCombination(double[] a, FieldDerivativeStructure<T>[] b)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(double a1, FieldDerivativeStructure<T> b1, double a2, FieldDerivativeStructure<T> b2)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(double a1, FieldDerivativeStructure<T> b1, double a2, FieldDerivativeStructure<T> b2, double a3, FieldDerivativeStructure<T> b3)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(double a1, FieldDerivativeStructure<T> b1, double a2, FieldDerivativeStructure<T> b2, double a3, FieldDerivativeStructure<T> b3, double a4, FieldDerivativeStructure<T> b4)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(FieldDerivativeStructure<T>[] a, FieldDerivativeStructure<T>[] b)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(FieldDerivativeStructure<T> a1, FieldDerivativeStructure<T> b1, FieldDerivativeStructure<T> a2, FieldDerivativeStructure<T> b2)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(FieldDerivativeStructure<T> a1, FieldDerivativeStructure<T> b1, FieldDerivativeStructure<T> a2, FieldDerivativeStructure<T> b2, FieldDerivativeStructure<T> a3, FieldDerivativeStructure<T> b3)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(FieldDerivativeStructure<T> a1, FieldDerivativeStructure<T> b1, FieldDerivativeStructure<T> a2, FieldDerivativeStructure<T> b2, FieldDerivativeStructure<T> a3, FieldDerivativeStructure<T> b3, FieldDerivativeStructure<T> a4, FieldDerivativeStructure<T> b4)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(T[] a, FieldDerivativeStructure<T>[] b)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(T a1, FieldDerivativeStructure<T> b1, T a2, FieldDerivativeStructure<T> b2)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(T a1, FieldDerivativeStructure<T> b1, T a2, FieldDerivativeStructure<T> b2, T a3, FieldDerivativeStructure<T> b3)	Compute a linear combination.
FieldDerivativeStructure<T>	linearCombination(T a1, FieldDerivativeStructure<T> b1, T a2, FieldDerivativeStructure<T> b2, T a3, FieldDerivativeStructure<T> b3, T a4, FieldDerivativeStructure<T> b4)	Compute a linear combination.
FieldDerivativeStructure<T>	log()	Natural logarithm.
FieldDerivativeStructure<T>	log10()	Base 10 logarithm.
FieldDerivativeStructure<T>	log1p()	Shifted natural logarithm.
FieldDerivativeStructure<T>	multiply(double a)	'×' operator.
FieldDerivativeStructure<T>	multiply(FieldDerivativeStructure<T> a)	Compute this × a.
FieldDerivativeStructure<T>	multiply(T a)	'×' operator.
FieldDerivativeStructure<T>	negate()	Returns the additive inverse of this element.
FieldDerivativeStructure<T>	newInstance(double value)	Create an instance corresponding to a constant real value.
FieldDerivativeStructure<T>	newInstance(T value)	Create an instance corresponding to a constant Field value.
FieldDerivativeStructure<T>	pow(double p)	Power operation.
static <T extends CalculusFieldElement<T>> FieldDerivativeStructure<T>	pow(double a, FieldDerivativeStructure<T> x)	Compute ax where a is a double and x a FieldDerivativeStructure
FieldDerivativeStructure<T>	pow(int n)	Integer power operation.
FieldDerivativeStructure<T>	pow(FieldDerivativeStructure<T> e)	Power operation.
FieldDerivativeStructure<T>	rebase(FieldDerivativeStructure<T>... p)	Rebase instance with respect to low level parameter functions.
FieldDerivativeStructure<T>	reciprocal()	Returns the multiplicative inverse of this element.
FieldDerivativeStructure<T>	remainder(double a)	IEEE remainder operator.
FieldDerivativeStructure<T>	remainder(FieldDerivativeStructure<T> a)	IEEE remainder operator.
FieldDerivativeStructure<T>	remainder(T a)	IEEE remainder operator.
FieldDerivativeStructure<T>	rootN(int n)	Nth root.
FieldDerivativeStructure<T>	scalb(int n)	Multiply the instance by a power of 2.
FieldDerivativeStructure<T>	sin()	Sine operation.
FieldSinCos<FieldDerivativeStructure<T>>	sinCos()	Combined Sine and Cosine operation.
FieldDerivativeStructure<T>	sinh()	Hyperbolic sine operation.
FieldSinhCosh<FieldDerivativeStructure<T>>	sinhCosh()	Combined hyperbolic sine and cosine operation.
FieldDerivativeStructure<T>	sqrt()	Square root.
FieldDerivativeStructure<T>	square()	Compute this × this.
FieldDerivativeStructure<T>	subtract(double a)	'-' operator.
FieldDerivativeStructure<T>	subtract(FieldDerivativeStructure<T> a)	Compute this - a.
FieldDerivativeStructure<T>	tan()	Tangent operation.
FieldDerivativeStructure<T>	tanh()	Hyperbolic tangent operation.
T	taylor(double... delta)	Evaluate Taylor expansion of a derivative structure.
final T	taylor(T... delta)	Evaluate Taylor expansion of a derivative structure.
FieldDerivativeStructure<T>	toDegrees()	Convert radians to degrees, with error of less than 0.5 ULP
FieldDerivativeStructure<T>	toRadians()	Convert degrees to radians, with error of less than 0.5 ULP
FieldDerivativeStructure<T>	withValue(T value)	Create a new object with new value (zeroth-order derivative, as passed as input) and same derivatives of order one and above.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.hipparchus.CalculusFieldElement

cbrt, isFinite, isInfinite, isNaN, multiply, norm, round

Methods inherited from interface org.hipparchus.analysis.differentiation.FieldDerivative

add, ceil, floor, getExponent, getReal, rint, sign, subtract, ulp

Methods inherited from interface org.hipparchus.FieldElement

isZero

Method Details

newInstance

public FieldDerivativeStructure<T> newInstance(double value)

Create an instance corresponding to a constant real value.

Specified by:

newInstance in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

value - constant real value

Returns:

instance corresponding to a constant real value

newInstance

public FieldDerivativeStructure<T> newInstance(T value)

Create an instance corresponding to a constant Field value.

This default implementation is there so that no API gets broken by the next release, which is not a major one. Custom inheritors should probably overwrite it.

Specified by:

newInstance in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Parameters:

value - constant value

Returns:

instance corresponding to a constant Field value

withValue

public FieldDerivativeStructure<T> withValue(T value)

Create a new object with new value (zeroth-order derivative, as passed as input) and same derivatives of order one and above.

This default implementation is there so that no API gets broken by the next release, which is not a major one. Custom inheritors should probably overwrite it.

Specified by:

withValue in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Parameters:

value - zeroth-order derivative of new represented function

Returns:

new object with changed value

getFactory

public FDSFactory<T> getFactory()

Get the factory that built the instance.

Returns:

factory that built the instance

getFreeParameters

public int getFreeParameters()

Description copied from interface: DifferentialAlgebra

Get the number of free parameters.

Specified by:

getFreeParameters in interface DifferentialAlgebra

Returns:

number of free parameters

getOrder

public int getOrder()

Description copied from interface: DifferentialAlgebra

Get the maximum derivation order.

Specified by:

getOrder in interface DifferentialAlgebra

Returns:

maximum derivation order

getValue

public T getValue()

Get the value part of the derivative structure.

Specified by:

getValue in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Returns:

value part of the derivative structure

See Also:

• getPartialDerivative(int...)

getPartialDerivative

public T getPartialDerivative(int... orders)
                       throws MathIllegalArgumentException

Get a partial derivative.

Specified by:

getPartialDerivative in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Parameters:

orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)

Returns:

partial derivative

Throws:

MathIllegalArgumentException - if the numbers of variables does not match the instance

See Also:

• FieldDerivative.getValue()

getAllDerivatives

public T[] getAllDerivatives()

Get all partial derivatives.

Returns:

a fresh copy of partial derivatives, in an array sorted according to DSCompiler.getPartialDerivativeIndex(int...)

add

public FieldDerivativeStructure<T> add(double a)

'+' operator.

Specified by:

add in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this+a

add

public FieldDerivativeStructure<T> add(FieldDerivativeStructure<T> a)
                                throws MathIllegalArgumentException

Compute this + a.

Specified by:

add in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - element to add

Returns:

a new element representing this + a

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

subtract

public FieldDerivativeStructure<T> subtract(double a)

'-' operator.

Specified by:

subtract in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this-a

subtract

public FieldDerivativeStructure<T> subtract(FieldDerivativeStructure<T> a)
                                     throws MathIllegalArgumentException

Compute this - a.

Specified by:

subtract in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

subtract in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - element to subtract

Returns:

a new element representing this - a

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

multiply

public FieldDerivativeStructure<T> multiply(T a)

'×' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this×a

multiply

public FieldDerivativeStructure<T> multiply(double a)

'×' operator.

Specified by:

multiply in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this×a

multiply

public FieldDerivativeStructure<T> multiply(FieldDerivativeStructure<T> a)
                                     throws MathIllegalArgumentException

Compute this × a.

Specified by:

multiply in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - element to multiply

Returns:

a new element representing this × a

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

square

public FieldDerivativeStructure<T> square()

Compute this × this.

Specified by:

square in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

a new element representing this × this

divide

public FieldDerivativeStructure<T> divide(T a)

'÷' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this÷a

divide

public FieldDerivativeStructure<T> divide(double a)

'÷' operator.

Specified by:

divide in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this÷a

divide

public FieldDerivativeStructure<T> divide(FieldDerivativeStructure<T> a)
                                   throws MathIllegalArgumentException

Compute this ÷ a.

Specified by:

divide in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

divide in interface FieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - element to divide by

Returns:

a new element representing this ÷ a

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

remainder

public FieldDerivativeStructure<T> remainder(T a)

IEEE remainder operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)

remainder

public FieldDerivativeStructure<T> remainder(double a)

IEEE remainder operator.

Specified by:

remainder in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a

remainder

public FieldDerivativeStructure<T> remainder(FieldDerivativeStructure<T> a)
                                      throws MathIllegalArgumentException

IEEE remainder operator.

Specified by:

remainder in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

negate

public FieldDerivativeStructure<T> negate()

Returns the additive inverse of this element.

Specified by:

negate in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

the opposite of this.

abs

public FieldDerivativeStructure<T> abs()

absolute value.

Specified by:

abs in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

abs(this)

copySign

public FieldDerivativeStructure<T> copySign(T sign)

Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

Parameters:

sign - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

copySign

public FieldDerivativeStructure<T> copySign(double sign)

Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

Specified by:

copySign in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

sign - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

copySign

public FieldDerivativeStructure<T> copySign(FieldDerivativeStructure<T> sign)

Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

Specified by:

copySign in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

sign - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

scalb

public FieldDerivativeStructure<T> scalb(int n)

Multiply the instance by a power of 2.

Specified by:

scalb in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

n - power of 2

Returns:

this × 2ⁿ

hypot

public FieldDerivativeStructure<T> hypot(FieldDerivativeStructure<T> y)
                                  throws MathIllegalArgumentException

Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.

• If either argument is infinite, then the result is positive infinity.
• else, if either argument is NaN then the result is NaN.

Specified by:

hypot in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

y - a value

Returns:

sqrt(this² +y²)

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

hypot

public static <T extends CalculusFieldElement<T>>
FieldDerivativeStructure<T> hypot(FieldDerivativeStructure<T> x,
 FieldDerivativeStructure<T> y)
                           throws MathIllegalArgumentException

Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +y²) avoiding intermediate overflow or underflow.

• If either argument is infinite, then the result is positive infinity.
• else, if either argument is NaN then the result is NaN.

Type Parameters:

T - the type of the field elements

Parameters:

x - a value

y - a value

Returns:

sqrt(x² +y²)

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

compose

@SafeVarargs
public final FieldDerivativeStructure<T> compose(T... f)
                                          throws MathIllegalArgumentException

Compute composition of the instance by a univariate function.

Parameters:

f - array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).

Returns:

f(this)

Throws:

MathIllegalArgumentException - if the number of derivatives in the array is not equal to order + 1

compose

public FieldDerivativeStructure<T> compose(double... f)
                                    throws MathIllegalArgumentException

Compute composition of the instance by a univariate function.

Parameters:

f - array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).

Returns:

f(this)

Throws:

MathIllegalArgumentException - if the number of derivatives in the array is not equal to order + 1

reciprocal

public FieldDerivativeStructure<T> reciprocal()

Returns the multiplicative inverse of this element.

Specified by:

reciprocal in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

the inverse of this.

sqrt

public FieldDerivativeStructure<T> sqrt()

Square root.

Specified by:

sqrt in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

square root of the instance

rootN

public FieldDerivativeStructure<T> rootN(int n)

N^th root.

Specified by:

rootN in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

n - order of the root

Returns:

n^th root of the instance

getField

public Field<FieldDerivativeStructure<T>> getField()

Get the Field to which the instance belongs.

Specified by:

getField in interface FieldElement<T extends CalculusFieldElement<T>>

Returns:

Field to which the instance belongs

pow

public static <T extends CalculusFieldElement<T>>
FieldDerivativeStructure<T> pow(double a,
 FieldDerivativeStructure<T> x)

Compute a^x where a is a double and x a FieldDerivativeStructure

Type Parameters:

T - the type of the field elements

Parameters:

a - number to exponentiate

x - power to apply

Returns:

a^x

pow

public FieldDerivativeStructure<T> pow(double p)

Power operation.

Specified by:

pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

p - power to apply

Returns:

this^p

pow

public FieldDerivativeStructure<T> pow(int n)

Integer power operation.

Specified by:

pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

n - power to apply

Returns:

thisⁿ

pow

public FieldDerivativeStructure<T> pow(FieldDerivativeStructure<T> e)
                                throws MathIllegalArgumentException

Power operation.

Specified by:

pow in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

pow in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Parameters:

e - exponent

Returns:

this^e

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

exp

public FieldDerivativeStructure<T> exp()

Exponential.

Specified by:

exp in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

exponential of the instance

expm1

public FieldDerivativeStructure<T> expm1()

Exponential minus 1.

Specified by:

expm1 in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

exponential minus one of the instance

log

public FieldDerivativeStructure<T> log()

Natural logarithm.

Specified by:

log in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

logarithm of the instance

log1p

public FieldDerivativeStructure<T> log1p()

Shifted natural logarithm.

Specified by:

log1p in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

logarithm of one plus the instance

log10

public FieldDerivativeStructure<T> log10()

Base 10 logarithm.

Specified by:

log10 in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

log10 in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Returns:

base 10 logarithm of the instance

cos

public FieldDerivativeStructure<T> cos()

Cosine operation.

Specified by:

cos in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

cos(this)

sin

public FieldDerivativeStructure<T> sin()

Sine operation.

Specified by:

sin in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

sin(this)

sinCos

public FieldSinCos<FieldDerivativeStructure<T>> sinCos()

Combined Sine and Cosine operation.

Specified by:

sinCos in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

[sin(this), cos(this)]

tan

public FieldDerivativeStructure<T> tan()

Tangent operation.

Specified by:

tan in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

tan(this)

acos

public FieldDerivativeStructure<T> acos()

Arc cosine operation.

Specified by:

acos in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

acos in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Returns:

acos(this)

asin

public FieldDerivativeStructure<T> asin()

Arc sine operation.

Specified by:

asin in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

asin(this)

atan

public FieldDerivativeStructure<T> atan()

Arc tangent operation.

Specified by:

atan in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

atan(this)

atan2

public FieldDerivativeStructure<T> atan2(FieldDerivativeStructure<T> x)
                                  throws MathIllegalArgumentException

Two arguments arc tangent operation.

Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.

Specified by:

atan2 in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

x - second argument of the arc tangent

Returns:

atan2(this, x)

Throws:

MathIllegalArgumentException - if number of free parameters or orders are inconsistent

atan2

public static <T extends CalculusFieldElement<T>>
FieldDerivativeStructure<T> atan2(FieldDerivativeStructure<T> y,
 FieldDerivativeStructure<T> x)
                           throws MathIllegalArgumentException

Two arguments arc tangent operation.

Type Parameters:

T - the type of the field elements

Parameters:

y - first argument of the arc tangent

x - second argument of the arc tangent

Returns:

atan2(y, x)

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

cosh

public FieldDerivativeStructure<T> cosh()

Hyperbolic cosine operation.

Specified by:

cosh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

cosh in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Returns:

cosh(this)

sinh

public FieldDerivativeStructure<T> sinh()

Hyperbolic sine operation.

Specified by:

sinh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Specified by:

sinh in interface FieldDerivative<T extends CalculusFieldElement<T>,FieldDerivativeStructure<T extends CalculusFieldElement<T>>>

Returns:

sinh(this)

sinhCosh

public FieldSinhCosh<FieldDerivativeStructure<T>> sinhCosh()

Combined hyperbolic sine and cosine operation.

Specified by:

sinhCosh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

[sinh(this), cosh(this)]

tanh

public FieldDerivativeStructure<T> tanh()

Hyperbolic tangent operation.

Specified by:

tanh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

tanh(this)

acosh

public FieldDerivativeStructure<T> acosh()

Inverse hyperbolic cosine operation.

Specified by:

acosh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

acosh(this)

asinh

public FieldDerivativeStructure<T> asinh()

Inverse hyperbolic sine operation.

Specified by:

asinh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

asin(this)

atanh

public FieldDerivativeStructure<T> atanh()

Inverse hyperbolic tangent operation.

Specified by:

atanh in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

atanh(this)

toDegrees

public FieldDerivativeStructure<T> toDegrees()

Convert radians to degrees, with error of less than 0.5 ULP

Specified by:

toDegrees in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

instance converted into degrees

toRadians

public FieldDerivativeStructure<T> toRadians()

Convert degrees to radians, with error of less than 0.5 ULP

Specified by:

toRadians in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

instance converted into radians

integrate

public FieldDerivativeStructure<T> integrate(int varIndex,
 int integrationOrder)

Integrate w.r.t. one independent variable.

Rigorously, if the derivatives of a function are known up to order N, the ones of its M-th integral w.r.t. a given variable (seen as a function itself) are actually known up to order N+M. However, this method still casts the output as a DerivativeStructure of order N. The integration constants are systematically set to zero.

Parameters:

varIndex - Index of independent variable w.r.t. which integration is done.

integrationOrder - Number of times the integration operator must be applied. If non-positive, call the differentiation operator.

Returns:

DerivativeStructure on which integration operator has been applied a certain number of times.

Since:

2.2

differentiate

public FieldDerivativeStructure<T> differentiate(int varIndex,
 int differentiationOrder)

Differentiate w.r.t. one independent variable.

Rigorously, if the derivatives of a function are known up to order N, the ones of its M-th derivative w.r.t. a given variable (seen as a function itself) are only known up to order N-M. However, this method still casts the output as a DerivativeStructure of order N with zeroes for the higher order terms.

Parameters:

varIndex - Index of independent variable w.r.t. which differentiation is done.

differentiationOrder - Number of times the differentiation operator must be applied. If non-positive, call the integration operator instead.

Returns:

DerivativeStructure on which differentiation operator has been applied a certain number of times

Since:

2.2

taylor

@SafeVarargs
public final T taylor(T... delta)
               throws MathRuntimeException

Evaluate Taylor expansion of a derivative structure.

Parameters:

delta - parameters offsets (Δx, Δy, ...)

Returns:

value of the Taylor expansion at x + Δx, y + Δy, ...

Throws:

MathRuntimeException - if factorials becomes too large

taylor

public T taylor(double... delta)
         throws MathRuntimeException

Evaluate Taylor expansion of a derivative structure.

Parameters:

delta - parameters offsets (Δx, Δy, ...)

Returns:

value of the Taylor expansion at x + Δx, y + Δy, ...

Throws:

MathRuntimeException - if factorials becomes too large

rebase

public FieldDerivativeStructure<T> rebase(FieldDerivativeStructure<T>... p)

Rebase instance with respect to low level parameter functions.

The instance is considered to be a function of n free parameters up to order o \(f(p_0, p_1, \ldots p_{n-1})\). Its partial derivatives are therefore \(f, \frac{\partial f}{\partial p_0}, \frac{\partial f}{\partial p_1}, \ldots \frac{\partial^2 f}{\partial p_0^2}, \frac{\partial^2 f}{\partial p_0 p_1}, \ldots \frac{\partial^o f}{\partial p_{n-1}^o}\). The free parameters \(p_0, p_1, \ldots p_{n-1}\) are considered to be functions of \(m\) lower level other parameters \(q_0, q_1, \ldots q_{m-1}\).

\( \begin{align} p_0 & = p_0(q_0, q_1, \ldots q_{m-1})\\ p_1 & = p_1(q_0, q_1, \ldots q_{m-1})\\ p_{n-1} & = p_{n-1}(q_0, q_1, \ldots q_{m-1}) \end{align}\)

This method compute the composition of the partial derivatives of \(f\) and the partial derivatives of \(p_0, p_1, \ldots p_{n-1}\), i.e. the partial derivatives of the value returned will be \(f, \frac{\partial f}{\partial q_0}, \frac{\partial f}{\partial q_1}, \ldots \frac{\partial^2 f}{\partial q_0^2}, \frac{\partial^2 f}{\partial q_0 q_1}, \ldots \frac{\partial^o f}{\partial q_{m-1}^o}\).

The number of parameters must match getFreeParameters() and the derivation orders of the instance and parameters must also match.

Parameters:

p - base parameters with respect to which partial derivatives were computed in the instance

Returns:

derivative structure with partial derivatives computed with respect to the lower level parameters used in the \(p_i\)

Since:

2.2

linearCombination

public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T>[] a,
 FieldDerivativeStructure<T>[] b)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

linearCombination

public FieldDerivativeStructure<T> linearCombination(T[] a,
 FieldDerivativeStructure<T>[] b)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

public FieldDerivativeStructure<T> linearCombination(double[] a,
 FieldDerivativeStructure<T>[] b)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

linearCombination

public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T> a1,
 FieldDerivativeStructure<T> b1,
 FieldDerivativeStructure<T> a2,
 FieldDerivativeStructure<T> b2)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

See Also:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

public FieldDerivativeStructure<T> linearCombination(T a1,
 FieldDerivativeStructure<T> b1,
 T a2,
 FieldDerivativeStructure<T> b2)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

Throws:

MathIllegalArgumentException - if number of free parameters or orders are inconsistent

See Also:

• linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
• linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)

linearCombination

public FieldDerivativeStructure<T> linearCombination(double a1,
 FieldDerivativeStructure<T> b1,
 double a2,
 FieldDerivativeStructure<T> b2)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

See Also:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

linearCombination

public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T> a1,
 FieldDerivativeStructure<T> b1,
 FieldDerivativeStructure<T> a2,
 FieldDerivativeStructure<T> b2,
 FieldDerivativeStructure<T> a3,
 FieldDerivativeStructure<T> b3)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

See Also:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

public FieldDerivativeStructure<T> linearCombination(T a1,
 FieldDerivativeStructure<T> b1,
 T a2,
 FieldDerivativeStructure<T> b2,
 T a3,
 FieldDerivativeStructure<T> b3)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

Throws:

MathIllegalArgumentException - if number of free parameters or orders are inconsistent

See Also:

• linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
• linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)

linearCombination

public FieldDerivativeStructure<T> linearCombination(double a1,
 FieldDerivativeStructure<T> b1,
 double a2,
 FieldDerivativeStructure<T> b2,
 double a3,
 FieldDerivativeStructure<T> b3)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

See Also:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

linearCombination

public FieldDerivativeStructure<T> linearCombination(FieldDerivativeStructure<T> a1,
 FieldDerivativeStructure<T> b1,
 FieldDerivativeStructure<T> a2,
 FieldDerivativeStructure<T> b2,
 FieldDerivativeStructure<T> a3,
 FieldDerivativeStructure<T> b3,
 FieldDerivativeStructure<T> a4,
 FieldDerivativeStructure<T> b4)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

See Also:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

public FieldDerivativeStructure<T> linearCombination(T a1,
 FieldDerivativeStructure<T> b1,
 T a2,
 FieldDerivativeStructure<T> b2,
 T a3,
 FieldDerivativeStructure<T> b3,
 T a4,
 FieldDerivativeStructure<T> b4)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the third term

b4 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

Throws:

MathIllegalArgumentException - if number of free parameters or orders are inconsistent

See Also:

• linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure)
• linearCombination(double, FieldDerivativeStructure, double, FieldDerivativeStructure, double, FieldDerivativeStructure)

linearCombination

public FieldDerivativeStructure<T> linearCombination(double a1,
 FieldDerivativeStructure<T> b1,
 double a2,
 FieldDerivativeStructure<T> b2,
 double a3,
 FieldDerivativeStructure<T> b3,
 double a4,
 FieldDerivativeStructure<T> b4)
                                              throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

Throws:

MathIllegalArgumentException - if number of free parameters or orders do not match

See Also:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)

getPi

public FieldDerivativeStructure<T> getPi()

Get the Archimedes constant π.

Archimedes constant is the ratio of a circle's circumference to its diameter.

Specified by:

getPi in interface CalculusFieldElement<T extends CalculusFieldElement<T>>

Returns:

Archimedes constant π