Package org.hipparchus

Interface CalculusFieldElement<T extends FieldElement<T>>

Type Parameters:

T - the type of the field elements

All Superinterfaces:

FieldElement<T>

All Known Subinterfaces:

Derivative<T>, Derivative1<T>, FieldDerivative<S,T>, FieldDerivative1<S,T>

All Known Implementing Classes:

Binary64, Complex, DerivativeStructure, Dfp, DfpDec, FieldComplex, FieldDerivativeStructure, FieldGradient, FieldTuple, FieldUnivariateDerivative, FieldUnivariateDerivative1, FieldUnivariateDerivative2, Gradient, SparseGradient, Tuple, UnivariateDerivative, UnivariateDerivative1, UnivariateDerivative2

public interface CalculusFieldElement<T extends FieldElement<T>>
extends FieldElement<T>

Interface representing a field with calculus capabilities (sin, cos, ...).

Since:

1.7

See Also:

• FieldElement

Method Summary

Modifier and Type	Method	Description
T	abs()	absolute value.
T	acos()	Arc cosine operation.
T	acosh()	Inverse hyperbolic cosine operation.
default T	add(double a)	'+' operator.
T	asin()	Arc sine operation.
T	asinh()	Inverse hyperbolic sine operation.
T	atan()	Arc tangent operation.
T	atan2(T x)	Two arguments arc tangent operation.
T	atanh()	Inverse hyperbolic tangent operation.
default T	cbrt()	Cubic root.
default T	ceil()	Get the smallest whole number larger than instance.
default T	copySign(double sign)	Returns the instance with the sign of the argument.
T	copySign(T sign)	Returns the instance with the sign of the argument.
T	cos()	Cosine operation.
T	cosh()	Hyperbolic cosine operation.
default T	divide(double a)	'÷' operator.
default T	divide(T a)	Compute this ÷ a.
T	exp()	Exponential.
T	expm1()	Exponential minus 1.
default T	floor()	Get the largest whole number smaller than instance.
T	getAddendum()	Get the addendum to the real value of the number.
default int	getExponent()	Return the exponent of the instance, removing the bias.
default T	getPi()	Get the Archimedes constant π.
T	hypot(T y)	Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
default boolean	isFinite()	Check if the instance is finite (neither infinite nor NaN).
default boolean	isInfinite()	Check if the instance is infinite.
default boolean	isNaN()	Check if the instance is Not a Number.
default T	linearCombination(double[] a, T[] b)	Compute a linear combination.
default T	linearCombination(double a1, T b1, double a2, T b2)	Compute a linear combination.
default T	linearCombination(double a1, T b1, double a2, T b2, double a3, T b3)	Compute a linear combination.
default T	linearCombination(double a1, T b1, double a2, T b2, double a3, T b3, double a4, T b4)	Compute a linear combination.
T	linearCombination(T[] a, T[] b)	Compute a linear combination.
T	linearCombination(T a1, T b1, T a2, T b2)	Compute a linear combination.
T	linearCombination(T a1, T b1, T a2, T b2, T a3, T b3)	Compute a linear combination.
T	linearCombination(T a1, T b1, T a2, T b2, T a3, T b3, T a4, T b4)	Compute a linear combination.
T	log()	Natural logarithm.
T	log10()	Base 10 logarithm.
T	log1p()	Shifted natural logarithm.
default T	multiply(double a)	'×' operator.
default T	multiply(int n)	Compute n × this.
T	newInstance(double value)	Create an instance corresponding to a constant real value.
default double	norm()	norm.
default T	pow(double p)	Power operation.
default T	pow(int n)	Integer power operation.
T	pow(T e)	Power operation.
T	remainder(double a)	IEEE remainder operator.
T	remainder(T a)	IEEE remainder operator.
default T	rint()	Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
default T	rootN(int n)	Nth root.
default long	round()	Get the closest long to instance real value.
T	scalb(int n)	Multiply the instance by a power of 2.
default T	sign()	Compute the sign of the instance.
T	sin()	Sine operation.
default FieldSinCos<T>	sinCos()	Combined Sine and Cosine operation.
T	sinh()	Hyperbolic sine operation.
default FieldSinhCosh<T>	sinhCosh()	Combined hyperbolic sine and cosine operation.
default T	sqrt()	Square root.
default T	square()	Compute this × this.
default T	subtract(double a)	'-' operator.
default T	subtract(T a)	Compute this - a.
default T	tan()	Tangent operation.
default T	tanh()	Hyperbolic tangent operation.
default T	toDegrees()	Convert radians to degrees, with error of less than 0.5 ULP
default T	toRadians()	Convert degrees to radians, with error of less than 0.5 ULP
default T	ulp()	Compute least significant bit (Unit in Last Position) for a number.

Methods inherited from interface org.hipparchus.FieldElement

add, getField, getReal, isZero, multiply, negate, reciprocal

Method Details

getAddendum

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

Since:

4.0

getPi

default T getPi()

Get the Archimedes constant π.

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

Returns:

Archimedes constant π

Since:

2.0

newInstance

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

add

default T add(double a)

'+' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this+a

subtract

default T subtract(double a)

'-' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this-a

subtract

default T subtract(T a)

Compute this - a.

Specified by:

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

Parameters:

a - element to subtract

Returns:

a new element representing this - a

multiply

default T multiply(double a)

'×' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this×a

multiply

default T multiply(int n)

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

Specified by:

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

Parameters:

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

Returns:

A new element representing n × this.

divide

default T divide(double a)

'÷' operator.

Parameters:

a - right hand side parameter of the operator

Returns:

this÷a

getExponent

default int getExponent()

Return the exponent of the instance, removing the bias.

For double numbers of the form 2^x, the unbiased exponent is exactly x.

Returns:

exponent for the instance, without bias

scalb

T scalb(int n)

Multiply the instance by a power of 2.

Parameters:

n - power of 2

Returns:

this × 2ⁿ

ulp

default T ulp()

Compute least significant bit (Unit in Last Position) for a number.

Returns:

ulp(this)

Since:

2.0

hypot

T hypot(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.

Parameters:

y - a value

Returns:

sqrt(this² +y²)

Throws:

MathIllegalArgumentException - if number of free parameters or orders are inconsistent

divide

default T divide(T a)

Compute this ÷ a.

Specified by:

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

Parameters:

a - element to divide by

Returns:

a new element representing this ÷ a

sqrt

default T sqrt()

Square root.

Returns:

square root of the instance

cbrt

default T cbrt()

Cubic root.

Returns:

cubic root of the instance

rootN

default T rootN(int n)

N^th root.

Parameters:

n - order of the root

Returns:

n^th root of the instance

square

default T square()

Compute this × this.

Returns:

a new element representing this × this

Since:

3.1

pow

default T pow(double p)

Power operation.

Parameters:

p - power to apply

Returns:

this^p

pow

default T pow(int n)

Integer power operation.

Parameters:

n - power to apply

Returns:

thisⁿ

pow

T pow(T e)
throws MathIllegalArgumentException

Power operation.

Parameters:

e - exponent

Returns:

this^e

Throws:

MathIllegalArgumentException - if number of free parameters or orders are inconsistent

exp

T exp()

Exponential.

Returns:

exponential of the instance

expm1

T expm1()

Exponential minus 1.

Returns:

exponential minus one of the instance

log

T log()

Natural logarithm.

Returns:

logarithm of the instance

log1p

T log1p()

Shifted natural logarithm.

Returns:

logarithm of one plus the instance

log10

T log10()

Base 10 logarithm.

Returns:

base 10 logarithm of the instance

cos

T cos()

Cosine operation.

Returns:

cos(this)

sin

T sin()

Sine operation.

Returns:

sin(this)

sinCos

default FieldSinCos<T> sinCos()

Combined Sine and Cosine operation.

Returns:

[sin(this), cos(this)]

Since:

1.4

tan

default T tan()

Tangent operation.

Returns:

tan(this)

acos

T acos()

Arc cosine operation.

Returns:

acos(this)

asin

T asin()

Arc sine operation.

Returns:

asin(this)

atan

T atan()

Arc tangent operation.

Returns:

atan(this)

atan2

T atan2(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.

Parameters:

x - second argument of the arc tangent

Returns:

atan2(this, x)

Throws:

MathIllegalArgumentException - if number of free parameters or orders are inconsistent

cosh

T cosh()

Hyperbolic cosine operation.

Returns:

cosh(this)

sinh

T sinh()

Hyperbolic sine operation.

Returns:

sinh(this)

sinhCosh

default FieldSinhCosh<T> sinhCosh()

Combined hyperbolic sine and cosine operation.

Returns:

[sinh(this), cosh(this)]

Since:

2.0

tanh

default T tanh()

Hyperbolic tangent operation.

Returns:

tanh(this)

acosh

T acosh()

Inverse hyperbolic cosine operation.

Returns:

acosh(this)

asinh

T asinh()

Inverse hyperbolic sine operation.

Returns:

asin(this)

atanh

T atanh()

Inverse hyperbolic tangent operation.

Returns:

atanh(this)

toDegrees

default T toDegrees()

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

Returns:

instance converted into degrees

toRadians

default T toRadians()

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

Returns:

instance converted into radians

linearCombination

T linearCombination(T[] a,
 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

default T linearCombination(double[] a,
 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

T linearCombination(T a1,
 T b1,
 T a2,
 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:

• linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
• linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

default T linearCombination(double a1,
 T b1,
 double a2,
 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:

• linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
• linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

linearCombination

T linearCombination(T a1,
 T b1,
 T a2,
 T b2,
 T a3,
 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:

• linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

default T linearCombination(double a1,
 T b1,
 double a2,
 T b2,
 double a3,
 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:

• linearCombination(double, FieldElement, double, FieldElement)
• linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

linearCombination

T linearCombination(T a1,
 T b1,
 T a2,
 T b2,
 T a3,
 T b3,
 T a4,
 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:

• linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

default T linearCombination(double a1,
 T b1,
 double a2,
 T b2,
 double a3,
 T b3,
 double a4,
 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:

• linearCombination(double, FieldElement, double, FieldElement)
• linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)

ceil

default T ceil()

Get the smallest whole number larger than instance.

Returns:

ceil(this)

floor

default T floor()

Get the largest whole number smaller than instance.

Returns:

floor(this)

rint

default T rint()

Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.

Returns:

a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5

remainder

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

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

sign

default T sign()

Compute the sign of the instance. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)

Returns:

-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

copySign

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

default 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

isInfinite

default boolean isInfinite()

Check if the instance is infinite.

Returns:

true if the instance is infinite

isFinite

default boolean isFinite()

Check if the instance is finite (neither infinite nor NaN).

Returns:

true if the instance is finite (neither infinite nor NaN)

Since:

2.0

isNaN

default boolean isNaN()

Check if the instance is Not a Number.

Returns:

true if the instance is Not a Number

norm

default double norm()

norm.

Returns:

norm(this)

Since:

2.0

abs

T abs()

absolute value.

Returns:

abs(this)

round

default long round()

Get the closest long to instance real value.

Returns:

closest long to FieldElement.getReal()