Package org.hipparchus.analysis.differentiation

Class FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.analysis.differentiation.FieldUnivariateDerivative<T,FieldUnivariateDerivative2<T>>

org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2<T>

Type Parameters:

T - the type of the function parameters and value

All Implemented Interfaces:

DifferentialAlgebra, FieldDerivative<T,FieldUnivariateDerivative2<T>>, CalculusFieldElement<FieldUnivariateDerivative2<T>>, FieldElement<FieldUnivariateDerivative2<T>>

public class FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>
extends FieldUnivariateDerivative<T,FieldUnivariateDerivative2<T>>

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

This class is a stripped-down version of FieldDerivativeStructure with only one free parameter and derivation order limited to two. It should have less overhead than FieldDerivativeStructure in its domain.

This class is an implementation of Rall's numbers. Rall's numbers are an extension to the real numbers used throughout mathematical expressions; they hold the derivative together with the value of a function.

FieldUnivariateDerivative2 instances can be used directly thanks to the arithmetic operators to the mathematical functions provided as methods by this class (+, -, *, /, %, sin, cos ...).

Implementing complex expressions by hand using Derivative-based classes (or in fact any CalculusFieldElement class) is a tedious and error-prone task but has the advantage of not requiring users to compute the derivatives by themselves and allowing to switch for one derivative implementation to another as they all share the same filed API.

Instances of this class are guaranteed to be immutable.

Since:

1.7

See Also:

• DerivativeStructure
• UnivariateDerivative1
• UnivariateDerivative2
• Gradient
• FieldDerivativeStructure
• FieldUnivariateDerivative1
• FieldGradient

Constructor Summary

Constructors

Constructor	Description
FieldUnivariateDerivative2(FieldDerivativeStructure<T> ds)	Build an instance from a FieldDerivativeStructure.
FieldUnivariateDerivative2(T f0, T f1, T f2)	Build an instance with values and derivative.

Method Summary

Modifier and Type	Method	Description
FieldUnivariateDerivative2<T>	abs()	absolute value.
FieldUnivariateDerivative2<T>	acos()	Arc cosine operation.
FieldUnivariateDerivative2<T>	acosh()	Inverse hyperbolic cosine operation.
FieldUnivariateDerivative2<T>	add(double a)	'+' operator.
FieldUnivariateDerivative2<T>	add(FieldUnivariateDerivative2<T> a)	Compute this + a.
FieldUnivariateDerivative2<T>	asin()	Arc sine operation.
FieldUnivariateDerivative2<T>	asinh()	Inverse hyperbolic sine operation.
FieldUnivariateDerivative2<T>	atan()	Arc tangent operation.
FieldUnivariateDerivative2<T>	atan2(FieldUnivariateDerivative2<T> x)	Two arguments arc tangent operation.
FieldUnivariateDerivative2<T>	atanh()	Inverse hyperbolic tangent operation.
FieldUnivariateDerivative2<T>	cbrt()	Cubic root.
FieldUnivariateDerivative2<T>	compose(T g0, T g1, T g2)	Compute composition of the instance by a function.
FieldUnivariateDerivative2<T>	copySign(double sign)	Returns the instance with the sign of the argument.
FieldUnivariateDerivative2<T>	copySign(FieldUnivariateDerivative2<T> sign)	Returns the instance with the sign of the argument.
FieldUnivariateDerivative2<T>	copySign(T sign)	Returns the instance with the sign of the argument.
FieldUnivariateDerivative2<T>	cos()	Cosine operation.
FieldUnivariateDerivative2<T>	cosh()	Hyperbolic cosine operation.
FieldUnivariateDerivative2<T>	divide(double a)	'÷' operator.
FieldUnivariateDerivative2<T>	divide(FieldUnivariateDerivative2<T> a)	Compute this ÷ a.
FieldUnivariateDerivative2<T>	divide(T a)	'÷' operator.
boolean	equals(Object other)	Test for the equality of two univariate derivatives.
FieldUnivariateDerivative2<T>	exp()	Exponential.
FieldUnivariateDerivative2<T>	expm1()	Exponential minus 1.
FieldUnivariateDerivative2<T>	getAddendum()	Get the addendum to the real value of the number.
T	getDerivative(int n)	Get a derivative from the univariate derivative.
FieldUnivariateDerivative2Field<T>	getField()	Get the Field to which the instance belongs.
T	getFirstDerivative()	Get the first derivative.
int	getOrder()	Get the derivation order.
FieldUnivariateDerivative2<T>	getPi()	Get the Archimedes constant π.
T	getSecondDerivative()	Get the second derivative.
T	getValue()	Get the value part of the univariate derivative.
Field<T>	getValueField()	Get the Field the value and parameters of the function belongs to.
int	hashCode()	Get a hashCode for the univariate derivative.
FieldUnivariateDerivative2<T>	hypot(FieldUnivariateDerivative2<T> y)	Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
FieldUnivariateDerivative2<T>	linearCombination(double[] a, FieldUnivariateDerivative2<T>[] b)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2, double a3, FieldUnivariateDerivative2<T> b3)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2, double a3, FieldUnivariateDerivative2<T> b3, double a4, FieldUnivariateDerivative2<T> b4)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(FieldUnivariateDerivative2<T>[] a, FieldUnivariateDerivative2<T>[] b)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2, FieldUnivariateDerivative2<T> a3, FieldUnivariateDerivative2<T> b3)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2, FieldUnivariateDerivative2<T> a3, FieldUnivariateDerivative2<T> b3, FieldUnivariateDerivative2<T> a4, FieldUnivariateDerivative2<T> b4)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(T[] a, FieldUnivariateDerivative2<T>[] b)	Compute a linear combination.
FieldUnivariateDerivative2<T>	linearCombination(T a1, FieldUnivariateDerivative2<T> b1, T a2, FieldUnivariateDerivative2<T> b2, T a3, FieldUnivariateDerivative2<T> b3)	Compute a linear combination.
FieldUnivariateDerivative2<T>	log()	Natural logarithm.
FieldUnivariateDerivative2<T>	log10()	Base 10 logarithm.
FieldUnivariateDerivative2<T>	log1p()	Shifted natural logarithm.
FieldUnivariateDerivative2<T>	multiply(double a)	'×' operator.
FieldUnivariateDerivative2<T>	multiply(int n)	Compute n × this.
FieldUnivariateDerivative2<T>	multiply(FieldUnivariateDerivative2<T> a)	Compute this × a.
FieldUnivariateDerivative2<T>	multiply(T a)	'×' operator.
FieldUnivariateDerivative2<T>	negate()	Returns the additive inverse of this element.
FieldUnivariateDerivative2<T>	newInstance(double value)	Create an instance corresponding to a constant real value.
FieldUnivariateDerivative2<T>	newInstance(T value)	Create an instance corresponding to a constant Field value.
FieldUnivariateDerivative2<T>	pow(double p)	Power operation.
static <T extends CalculusFieldElement<T>> FieldUnivariateDerivative2<T>	pow(double a, FieldUnivariateDerivative2<T> x)	Compute ax where a is a double and x a FieldUnivariateDerivative2
FieldUnivariateDerivative2<T>	pow(int n)	Integer power operation.
FieldUnivariateDerivative2<T>	reciprocal()	Returns the multiplicative inverse of this element.
FieldUnivariateDerivative2<T>	remainder(double a)	IEEE remainder operator.
FieldUnivariateDerivative2<T>	remainder(FieldUnivariateDerivative2<T> a)	IEEE remainder operator.
FieldUnivariateDerivative2<T>	remainder(T a)	IEEE remainder operator.
FieldUnivariateDerivative2<T>	rootN(int n)	Nth root.
FieldUnivariateDerivative2<T>	scalb(int n)	Multiply the instance by a power of 2.
FieldUnivariateDerivative2<T>	sin()	Sine operation.
FieldSinCos<FieldUnivariateDerivative2<T>>	sinCos()	Combined Sine and Cosine operation.
FieldUnivariateDerivative2<T>	sinh()	Hyperbolic sine operation.
FieldSinhCosh<FieldUnivariateDerivative2<T>>	sinhCosh()	Combined hyperbolic sine and cosine operation.
FieldUnivariateDerivative2<T>	sqrt()	Square root.
FieldUnivariateDerivative2<T>	square()	Compute this × this.
FieldUnivariateDerivative2<T>	subtract(double a)	'-' operator.
FieldUnivariateDerivative2<T>	subtract(FieldUnivariateDerivative2<T> a)	Compute this - a.
FieldUnivariateDerivative2<T>	tan()	Tangent operation.
FieldUnivariateDerivative2<T>	tanh()	Hyperbolic tangent operation.
T	taylor(double delta)	Evaluate Taylor expansion a univariate derivative.
T	taylor(T delta)	Evaluate Taylor expansion a univariate derivative.
FieldUnivariateDerivative2<T>	toDegrees()	Convert radians to degrees, with error of less than 0.5 ULP
FieldDerivativeStructure<T>	toDerivativeStructure()	Convert the instance to a FieldDerivativeStructure.
FieldUnivariateDerivative2<T>	toRadians()	Convert degrees to radians, with error of less than 0.5 ULP
FieldUnivariateDerivative2<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 org.hipparchus.analysis.differentiation.FieldUnivariateDerivative

getFreeParameters, getPartialDerivative

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.hipparchus.CalculusFieldElement

isFinite, isInfinite, isNaN, norm, round

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

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

Methods inherited from interface org.hipparchus.FieldElement

isZero

Constructor Details

FieldUnivariateDerivative2

public FieldUnivariateDerivative2(T f0,
 T f1,
 T f2)

Build an instance with values and derivative.

Parameters:

f0 - value of the function

f1 - first derivative of the function

f2 - second derivative of the function

FieldUnivariateDerivative2

public FieldUnivariateDerivative2(FieldDerivativeStructure<T> ds)
                           throws MathIllegalArgumentException

Build an instance from a FieldDerivativeStructure.

Parameters:

ds - derivative structure

Throws:

MathIllegalArgumentException - if either ds parameters is not 1 or ds order is not 2

Method Details

newInstance

public FieldUnivariateDerivative2<T> newInstance(double value)

Create an instance corresponding to a constant real value.

Parameters:

value - constant real value

Returns:

instance corresponding to a constant real value

newInstance

public FieldUnivariateDerivative2<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.

Parameters:

value - constant value

Returns:

instance corresponding to a constant Field value

withValue

public FieldUnivariateDerivative2<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.

Parameters:

value - zeroth-order derivative of new represented function

Returns:

new object with changed value

getAddendum

public FieldUnivariateDerivative2<T> getAddendum()

Get the addendum to the real value of the number.

The addendum is considered to be the part that when added back to the real part recovers the instance. This means that when e.getReal() is finite (i.e. neither infinite nor NaN), then e.getAddendum().add(e.getReal()) is e and e.subtract(e.getReal()) is e.getAddendum(). Beware that for non-finite numbers, these two equalities may not hold. The first equality (with the addition), always holds even for infinity and NaNs if the real part is independent of the addendum (this is the case for all derivatives types, as well as for complex and Dfp, but it is not the case for Tuple and FieldTuple). The second equality (with the subtraction), generally doesn't hold for non-finite numbers, because the subtraction generates NaNs.

Returns:

real value

getValue

public T getValue()

Get the value part of the univariate derivative.

Returns:

value part of the univariate derivative

getDerivative

public T getDerivative(int n)

Get a derivative from the univariate derivative.

Specified by:

getDerivative in class FieldUnivariateDerivative<T extends CalculusFieldElement<T>,FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>>

Parameters:

n - derivation order (must be between 0 and getOrder(), both inclusive)

Returns:

n^th derivative, or NaN if n is either negative or strictly larger than getOrder()

getOrder

public int getOrder()

Get the derivation order.

Returns:

derivation order

getFirstDerivative

public T getFirstDerivative()

Get the first derivative.

Returns:

first derivative

See Also:

• getValue()

getSecondDerivative

public T getSecondDerivative()

Get the second derivative.

Returns:

second derivative

See Also:

• getValue()
• getFirstDerivative()

getValueField

public Field<T> getValueField()

Get the Field the value and parameters of the function belongs to.

Returns:

Field the value and parameters of the function belongs to

toDerivativeStructure

public FieldDerivativeStructure<T> toDerivativeStructure()

Convert the instance to a FieldDerivativeStructure.

Specified by:

toDerivativeStructure in class FieldUnivariateDerivative<T extends CalculusFieldElement<T>,FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>>

Returns:

derivative structure with same value and derivative as the instance

add

public FieldUnivariateDerivative2<T> add(double a)

'+' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this+a

add

public FieldUnivariateDerivative2<T> add(FieldUnivariateDerivative2<T> a)

Compute this + a.

Parameters:

a - element to add

Returns:

a new element representing this + a

subtract

public FieldUnivariateDerivative2<T> subtract(double a)

'-' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this-a

subtract

public FieldUnivariateDerivative2<T> subtract(FieldUnivariateDerivative2<T> a)

Compute this - a.

Parameters:

a - element to subtract

Returns:

a new element representing this - a

multiply

public FieldUnivariateDerivative2<T> multiply(T a)

'×' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this×a

multiply

public FieldUnivariateDerivative2<T> multiply(int n)

Compute n × this. Multiplication by an integer number is defined as the following sum \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]

Parameters:

n - Number of times this must be added to itself.

Returns:

A new element representing n × this.

multiply

public FieldUnivariateDerivative2<T> multiply(double a)

'×' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this×a

multiply

public FieldUnivariateDerivative2<T> multiply(FieldUnivariateDerivative2<T> a)

Compute this × a.

Parameters:

a - element to multiply

Returns:

a new element representing this × a

square

public FieldUnivariateDerivative2<T> square()

Compute this × this.

Returns:

a new element representing this × this

divide

public FieldUnivariateDerivative2<T> divide(T a)

'÷' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this÷a

divide

public FieldUnivariateDerivative2<T> divide(double a)

'÷' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this÷a

divide

public FieldUnivariateDerivative2<T> divide(FieldUnivariateDerivative2<T> a)

Compute this ÷ a.

Parameters:

a - element to divide by

Returns:

a new element representing this ÷ a

remainder

public FieldUnivariateDerivative2<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 FieldUnivariateDerivative2<T> remainder(double 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

remainder

public FieldUnivariateDerivative2<T> remainder(FieldUnivariateDerivative2<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

negate

public FieldUnivariateDerivative2<T> negate()

Returns the additive inverse of this element.

Returns:

the opposite of this.

abs

public FieldUnivariateDerivative2<T> abs()

absolute value.

Returns:

abs(this)

copySign

public FieldUnivariateDerivative2<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 FieldUnivariateDerivative2<T> copySign(FieldUnivariateDerivative2<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 FieldUnivariateDerivative2<T> copySign(double 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

scalb

public FieldUnivariateDerivative2<T> scalb(int n)

Multiply the instance by a power of 2.

Parameters:

n - power of 2

Returns:

this × 2ⁿ

hypot

public FieldUnivariateDerivative2<T> hypot(FieldUnivariateDerivative2<T> y)

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.

Parameters:

y - a value

Returns:

sqrt(this² +y²)

reciprocal

public FieldUnivariateDerivative2<T> reciprocal()

Returns the multiplicative inverse of this element.

Returns:

the inverse of this.

compose

public FieldUnivariateDerivative2<T> compose(T g0,
 T g1,
 T g2)

Compute composition of the instance by a function.

Parameters:

g0 - value of the function at the current point (i.e. at g(getValue()))

g1 - first derivative of the function at the current point (i.e. at g'(getValue()))

g2 - second derivative of the function at the current point (i.e. at g''(getValue()))

Returns:

g(this)

sqrt

public FieldUnivariateDerivative2<T> sqrt()

Square root.

Returns:

square root of the instance

cbrt

public FieldUnivariateDerivative2<T> cbrt()

Cubic root.

Returns:

cubic root of the instance

rootN

public FieldUnivariateDerivative2<T> rootN(int n)

N^th root.

Parameters:

n - order of the root

Returns:

n^th root of the instance

getField

public FieldUnivariateDerivative2Field<T> getField()

Get the Field to which the instance belongs.

Returns:

Field to which the instance belongs

pow

public static <T extends CalculusFieldElement<T>>
FieldUnivariateDerivative2<T> pow(double a,
 FieldUnivariateDerivative2<T> x)

Compute a^x where a is a double and x a FieldUnivariateDerivative2

Type Parameters:

T - the type of the function parameters and value

Parameters:

a - number to exponentiate

x - power to apply

Returns:

a^x

pow

public FieldUnivariateDerivative2<T> pow(double p)

Power operation.

Parameters:

p - power to apply

Returns:

this^p

pow

public FieldUnivariateDerivative2<T> pow(int n)

Integer power operation.

Parameters:

n - power to apply

Returns:

thisⁿ

exp

public FieldUnivariateDerivative2<T> exp()

Exponential.

Returns:

exponential of the instance

expm1

public FieldUnivariateDerivative2<T> expm1()

Exponential minus 1.

Returns:

exponential minus one of the instance

log

public FieldUnivariateDerivative2<T> log()

Natural logarithm.

Returns:

logarithm of the instance

log1p

public FieldUnivariateDerivative2<T> log1p()

Shifted natural logarithm.

Returns:

logarithm of one plus the instance

log10

public FieldUnivariateDerivative2<T> log10()

Base 10 logarithm.

Returns:

base 10 logarithm of the instance

cos

public FieldUnivariateDerivative2<T> cos()

Cosine operation.

Returns:

cos(this)

sin

public FieldUnivariateDerivative2<T> sin()

Sine operation.

Returns:

sin(this)

sinCos

public FieldSinCos<FieldUnivariateDerivative2<T>> sinCos()

Combined Sine and Cosine operation.

Returns:

[sin(this), cos(this)]

tan

public FieldUnivariateDerivative2<T> tan()

Tangent operation.

Returns:

tan(this)

acos

public FieldUnivariateDerivative2<T> acos()

Arc cosine operation.

Returns:

acos(this)

asin

public FieldUnivariateDerivative2<T> asin()

Arc sine operation.

Returns:

asin(this)

atan

public FieldUnivariateDerivative2<T> atan()

Arc tangent operation.

Returns:

atan(this)

atan2

public FieldUnivariateDerivative2<T> atan2(FieldUnivariateDerivative2<T> x)

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.

Parameters:

x - second argument of the arc tangent

Returns:

atan2(this, x)

cosh

public FieldUnivariateDerivative2<T> cosh()

Hyperbolic cosine operation.

Returns:

cosh(this)

sinh

public FieldUnivariateDerivative2<T> sinh()

Hyperbolic sine operation.

Returns:

sinh(this)

sinhCosh

public FieldSinhCosh<FieldUnivariateDerivative2<T>> sinhCosh()

Combined hyperbolic sine and cosine operation.

Returns:

[sinh(this), cosh(this)]

tanh

public FieldUnivariateDerivative2<T> tanh()

Hyperbolic tangent operation.

Returns:

tanh(this)

acosh

public FieldUnivariateDerivative2<T> acosh()

Inverse hyperbolic cosine operation.

Returns:

acosh(this)

asinh

public FieldUnivariateDerivative2<T> asinh()

Inverse hyperbolic sine operation.

Returns:

asin(this)

atanh

public FieldUnivariateDerivative2<T> atanh()

Inverse hyperbolic tangent operation.

Returns:

atanh(this)

toDegrees

public FieldUnivariateDerivative2<T> toDegrees()

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

Returns:

instance converted into degrees

toRadians

public FieldUnivariateDerivative2<T> toRadians()

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

Returns:

instance converted into radians

taylor

public T taylor(double delta)

Evaluate Taylor expansion a univariate derivative.

Parameters:

delta - parameter offset Δx

Returns:

value of the Taylor expansion at x + Δx

taylor

public T taylor(T delta)

Evaluate Taylor expansion a univariate derivative.

Parameters:

delta - parameter offset Δx

Returns:

value of the Taylor expansion at x + Δx

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(T[] a,
 FieldUnivariateDerivative2<T>[] b)

Compute a linear combination.

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T>[] a,
 FieldUnivariateDerivative2<T>[] b)

Compute a linear combination.

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(double[] a,
 FieldUnivariateDerivative2<T>[] b)

Compute a linear combination.

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1,
 FieldUnivariateDerivative2<T> b1,
 FieldUnivariateDerivative2<T> a2,
 FieldUnivariateDerivative2<T> b2)

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

See Also:

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

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(double a1,
 FieldUnivariateDerivative2<T> b1,
 double a2,
 FieldUnivariateDerivative2<T> b2)

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

See Also:

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

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1,
 FieldUnivariateDerivative2<T> b1,
 FieldUnivariateDerivative2<T> a2,
 FieldUnivariateDerivative2<T> b2,
 FieldUnivariateDerivative2<T> a3,
 FieldUnivariateDerivative2<T> b3)

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

See Also:

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

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(T a1,
 FieldUnivariateDerivative2<T> b1,
 T a2,
 FieldUnivariateDerivative2<T> b2,
 T a3,
 FieldUnivariateDerivative2<T> b3)

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, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2)
• linearCombination(double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2)

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(double a1,
 FieldUnivariateDerivative2<T> b1,
 double a2,
 FieldUnivariateDerivative2<T> b2,
 double a3,
 FieldUnivariateDerivative2<T> b3)

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

See Also:

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

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1,
 FieldUnivariateDerivative2<T> b1,
 FieldUnivariateDerivative2<T> a2,
 FieldUnivariateDerivative2<T> b2,
 FieldUnivariateDerivative2<T> a3,
 FieldUnivariateDerivative2<T> b3,
 FieldUnivariateDerivative2<T> a4,
 FieldUnivariateDerivative2<T> b4)

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 fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

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

linearCombination

public FieldUnivariateDerivative2<T> linearCombination(double a1,
 FieldUnivariateDerivative2<T> b1,
 double a2,
 FieldUnivariateDerivative2<T> b2,
 double a3,
 FieldUnivariateDerivative2<T> b3,
 double a4,
 FieldUnivariateDerivative2<T> b4)

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 fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

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

getPi

public FieldUnivariateDerivative2<T> getPi()

Get the Archimedes constant π.

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

Returns:

Archimedes constant π

equals

public boolean equals(Object other)

Test for the equality of two univariate derivatives.

univariate derivatives are considered equal if they have the same derivatives.

Overrides:

equals in class Object

Parameters:

other - Object to test for equality to this

Returns:

true if two univariate derivatives are equal

hashCode

public int hashCode()

Get a hashCode for the univariate derivative.

Overrides:

hashCode in class Object

Returns:

a hash code value for this object