Package org.hipparchus.util

Class Tuple

java.lang.Object

org.hipparchus.util.Tuple

All Implemented Interfaces:

CalculusFieldElement<Tuple>, FieldElement<Tuple>

public class Tuple
extends Object
implements CalculusFieldElement<Tuple>

This class allows to perform the same computation of all components of a Tuple at once.

Since:

1.2

Constructor Summary

Constructors

Constructor	Description
Tuple(double... x)	Creates a new instance from its components.

Method Summary

Modifier and Type	Method	Description
Tuple	abs()	absolute value.
Tuple	acos()	Arc cosine operation.
Tuple	acosh()	Inverse hyperbolic cosine operation.
Tuple	add(double a)	'+' operator.
Tuple	add(Tuple a)	Compute this + a.
Tuple	asin()	Arc sine operation.
Tuple	asinh()	Inverse hyperbolic sine operation.
Tuple	atan()	Arc tangent operation.
Tuple	atan2(Tuple x)	Two arguments arc tangent operation.
Tuple	atanh()	Inverse hyperbolic tangent operation.
Tuple	cbrt()	Cubic root.
Tuple	ceil()	Get the smallest whole number larger than instance.
Tuple	copySign(double sign)	Returns the instance with the sign of the argument.
Tuple	copySign(Tuple sign)	Returns the instance with the sign of the argument.
Tuple	cos()	Cosine operation.
Tuple	cosh()	Hyperbolic cosine operation.
Tuple	divide(double a)	'÷' operator.
Tuple	divide(Tuple a)	Compute this ÷ a.
boolean	equals(Object obj)
Tuple	exp()	Exponential.
Tuple	expm1()	Exponential minus 1.
Tuple	floor()	Get the largest whole number smaller than instance.
Tuple	getAddendum()	Get the addendum to the real value of the number.
double	getComponent(int index)	Get one component of the tuple.
double[]	getComponents()	Get all components of the tuple.
int	getDimension()	Get the dimension of the tuple.
Field<Tuple>	getField()	Get the Field to which the instance belongs.
Tuple	getPi()	Get the Archimedes constant π.
double	getReal()	Get the real value of the number.
int	hashCode()
Tuple	hypot(Tuple y)	Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
Tuple	linearCombination(double[] a, Tuple[] b)	Compute a linear combination.
Tuple	linearCombination(double a1, Tuple b1, double a2, Tuple b2)	Compute a linear combination.
Tuple	linearCombination(double a1, Tuple b1, double a2, Tuple b2, double a3, Tuple b3)	Compute a linear combination.
Tuple	linearCombination(double a1, Tuple b1, double a2, Tuple b2, double a3, Tuple b3, double a4, Tuple b4)	Compute a linear combination.
Tuple	linearCombination(Tuple[] a, Tuple[] b)	Compute a linear combination.
Tuple	linearCombination(Tuple a1, Tuple b1, Tuple a2, Tuple b2)	Compute a linear combination.
Tuple	linearCombination(Tuple a1, Tuple b1, Tuple a2, Tuple b2, Tuple a3, Tuple b3)	Compute a linear combination.
Tuple	linearCombination(Tuple a1, Tuple b1, Tuple a2, Tuple b2, Tuple a3, Tuple b3, Tuple a4, Tuple b4)	Compute a linear combination.
Tuple	log()	Natural logarithm.
Tuple	log10()	Base 10 logarithm.
Tuple	log1p()	Shifted natural logarithm.
Tuple	multiply(double a)	'×' operator.
Tuple	multiply(int n)	Compute n × this.
Tuple	multiply(Tuple a)	Compute this × a.
Tuple	negate()	Returns the additive inverse of this element.
Tuple	newInstance(double value)	Create an instance corresponding to a constant real value.
Tuple	pow(double p)	Power operation.
Tuple	pow(int n)	Integer power operation.
Tuple	pow(Tuple e)	Power operation.
Tuple	reciprocal()	Returns the multiplicative inverse of this element.
Tuple	remainder(double a)	IEEE remainder operator.
Tuple	remainder(Tuple a)	IEEE remainder operator.
Tuple	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.
Tuple	rootN(int n)	Nth root.
Tuple	scalb(int n)	Multiply the instance by a power of 2.
Tuple	sign()	Compute the sign of the instance.
Tuple	sin()	Sine operation.
FieldSinCos<Tuple>	sinCos()	Combined Sine and Cosine operation.
Tuple	sinh()	Hyperbolic sine operation.
FieldSinhCosh<Tuple>	sinhCosh()	Combined hyperbolic sine and cosine operation.
Tuple	sqrt()	Square root.
Tuple	square()	Compute this × this.
Tuple	subtract(double a)	'-' operator.
Tuple	subtract(Tuple a)	Compute this - a.
Tuple	tan()	Tangent operation.
Tuple	tanh()	Hyperbolic tangent operation.
Tuple	toDegrees()	Convert radians to degrees, with error of less than 0.5 ULP
Tuple	toRadians()	Convert degrees to radians, with error of less than 0.5 ULP
Tuple	ulp()	Compute least significant bit (Unit in Last Position) for a number.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.hipparchus.CalculusFieldElement

getExponent, isFinite, isInfinite, isNaN, norm, round

Methods inherited from interface org.hipparchus.FieldElement

isZero

Constructor Detail

Tuple

public Tuple(double... x)

Creates a new instance from its components.

Parameters:

x - components of the tuple

Method Detail

newInstance

public Tuple newInstance(double value)

Create an instance corresponding to a constant real value.

Specified by:

newInstance in interface CalculusFieldElement<Tuple>

Parameters:

value - constant real value

Returns:

instance corresponding to a constant real value

getDimension

public int getDimension()

Get the dimension of the tuple.

Returns:

dimension of the tuple

getComponent

public double getComponent(int index)

Get one component of the tuple.

Parameters:

index - index of the component, between 0 and getDimension() - 1

Returns:

value of the component

getComponents

public double[] getComponents()

Get all components of the tuple.

Returns:

all components

getField

public Field<Tuple> getField()

Get the Field to which the instance belongs.

Specified by:

getField in interface FieldElement<Tuple>

Returns:

Field to which the instance belongs

add

public Tuple add(Tuple a)

Compute this + a.

Specified by:

add in interface FieldElement<Tuple>

Parameters:

a - element to add

Returns:

a new element representing this + a

subtract

public Tuple subtract(Tuple a)

Compute this - a.

Specified by:

subtract in interface CalculusFieldElement<Tuple>

Specified by:

subtract in interface FieldElement<Tuple>

Parameters:

a - element to subtract

Returns:

a new element representing this - a

negate

public Tuple negate()

Returns the additive inverse of this element.

Specified by:

negate in interface FieldElement<Tuple>

Returns:

the opposite of this.

multiply

public Tuple multiply(Tuple a)

Compute this × a.

Specified by:

multiply in interface FieldElement<Tuple>

Parameters:

a - element to multiply

Returns:

a new element representing this × a

multiply

public Tuple 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 CalculusFieldElement<Tuple>

Specified by:

multiply in interface FieldElement<Tuple>

Parameters:

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

Returns:

A new element representing n × this.

square

public Tuple square()

Compute this × this.

Specified by:

square in interface CalculusFieldElement<Tuple>

Returns:

a new element representing this × this

divide

public Tuple divide(Tuple a)

Compute this ÷ a.

Specified by:

divide in interface CalculusFieldElement<Tuple>

Specified by:

divide in interface FieldElement<Tuple>

Parameters:

a - element to divide by

Returns:

a new element representing this ÷ a

reciprocal

public Tuple reciprocal()

Returns the multiplicative inverse of this element.

Specified by:

reciprocal in interface FieldElement<Tuple>

Returns:

the inverse of this.

equals

public boolean equals(Object obj)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

getReal

public double getReal()

Get the real value of the number.

Specified by:

getReal in interface FieldElement<Tuple>

Returns:

real value

getAddendum

public Tuple 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.

Specified by:

getAddendum in interface CalculusFieldElement<Tuple>

Returns:

real value

add

public Tuple add(double a)

'+' operator.

Specified by:

add in interface CalculusFieldElement<Tuple>

Parameters:

a - right hand side parameter of the operator

Returns:

this+a

subtract

public Tuple subtract(double a)

'-' operator.

Specified by:

subtract in interface CalculusFieldElement<Tuple>

Parameters:

a - right hand side parameter of the operator

Returns:

this-a

multiply

public Tuple multiply(double a)

'×' operator.

Specified by:

multiply in interface CalculusFieldElement<Tuple>

Parameters:

a - right hand side parameter of the operator

Returns:

this×a

divide

public Tuple divide(double a)

'÷' operator.

Specified by:

divide in interface CalculusFieldElement<Tuple>

Parameters:

a - right hand side parameter of the operator

Returns:

this÷a

remainder

public Tuple remainder(double a)

IEEE remainder operator.

Specified by:

remainder in interface CalculusFieldElement<Tuple>

Parameters:

a - right hand side parameter of the operator

Returns:

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

remainder

public Tuple remainder(Tuple a)

IEEE remainder operator.

Specified by:

remainder in interface CalculusFieldElement<Tuple>

Parameters:

a - right hand side parameter of the operator

Returns:

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

abs

public Tuple abs()

absolute value.

Specified by:

abs in interface CalculusFieldElement<Tuple>

Returns:

abs(this)

ceil

public Tuple ceil()

Get the smallest whole number larger than instance.

Specified by:

ceil in interface CalculusFieldElement<Tuple>

Returns:

ceil(this)

floor

public Tuple floor()

Get the largest whole number smaller than instance.

Specified by:

floor in interface CalculusFieldElement<Tuple>

Returns:

floor(this)

rint

public Tuple 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.

Specified by:

rint in interface CalculusFieldElement<Tuple>

Returns:

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

sign

public Tuple 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)

Specified by:

sign in interface CalculusFieldElement<Tuple>

Returns:

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

copySign

public Tuple copySign(Tuple sign)

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

Specified by:

copySign in interface CalculusFieldElement<Tuple>

Parameters:

sign - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

copySign

public Tuple 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<Tuple>

Parameters:

sign - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

scalb

public Tuple scalb(int n)

Multiply the instance by a power of 2.

Specified by:

scalb in interface CalculusFieldElement<Tuple>

Parameters:

n - power of 2

Returns:

this × 2ⁿ

ulp

public Tuple ulp()

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

Specified by:

ulp in interface CalculusFieldElement<Tuple>

Returns:

ulp(this)

hypot

public Tuple hypot(Tuple 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.

Specified by:

hypot in interface CalculusFieldElement<Tuple>

Parameters:

y - a value

Returns:

sqrt(this² +y²)

sqrt

public Tuple sqrt()

Square root.

Specified by:

sqrt in interface CalculusFieldElement<Tuple>

Returns:

square root of the instance

cbrt

public Tuple cbrt()

Cubic root.

Specified by:

cbrt in interface CalculusFieldElement<Tuple>

Returns:

cubic root of the instance

rootN

public Tuple rootN(int n)

N^th root.

Specified by:

rootN in interface CalculusFieldElement<Tuple>

Parameters:

n - order of the root

Returns:

n^th root of the instance

pow

public Tuple pow(double p)

Power operation.

Specified by:

pow in interface CalculusFieldElement<Tuple>

Parameters:

p - power to apply

Returns:

this^p

pow

public Tuple pow(int n)

Integer power operation.

Specified by:

pow in interface CalculusFieldElement<Tuple>

Parameters:

n - power to apply

Returns:

thisⁿ

pow

public Tuple pow(Tuple e)

Power operation.

Specified by:

pow in interface CalculusFieldElement<Tuple>

Parameters:

e - exponent

Returns:

this^e

exp

public Tuple exp()

Exponential.

Specified by:

exp in interface CalculusFieldElement<Tuple>

Returns:

exponential of the instance

expm1

public Tuple expm1()

Exponential minus 1.

Specified by:

expm1 in interface CalculusFieldElement<Tuple>

Returns:

exponential minus one of the instance

log

public Tuple log()

Natural logarithm.

Specified by:

log in interface CalculusFieldElement<Tuple>

Returns:

logarithm of the instance

log1p

public Tuple log1p()

Shifted natural logarithm.

Specified by:

log1p in interface CalculusFieldElement<Tuple>

Returns:

logarithm of one plus the instance

log10

public Tuple log10()

Base 10 logarithm.

Specified by:

log10 in interface CalculusFieldElement<Tuple>

Returns:

base 10 logarithm of the instance

cos

public Tuple cos()

Cosine operation.

Specified by:

cos in interface CalculusFieldElement<Tuple>

Returns:

cos(this)

sin

public Tuple sin()

Sine operation.

Specified by:

sin in interface CalculusFieldElement<Tuple>

Returns:

sin(this)

sinCos

public FieldSinCos<Tuple> sinCos()

Combined Sine and Cosine operation.

Specified by:

sinCos in interface CalculusFieldElement<Tuple>

Returns:

[sin(this), cos(this)]

tan

public Tuple tan()

Tangent operation.

Specified by:

tan in interface CalculusFieldElement<Tuple>

Returns:

tan(this)

acos

public Tuple acos()

Arc cosine operation.

Specified by:

acos in interface CalculusFieldElement<Tuple>

Returns:

acos(this)

asin

public Tuple asin()

Arc sine operation.

Specified by:

asin in interface CalculusFieldElement<Tuple>

Returns:

asin(this)

atan

public Tuple atan()

Arc tangent operation.

Specified by:

atan in interface CalculusFieldElement<Tuple>

Returns:

atan(this)

atan2

public Tuple atan2(Tuple 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.

Specified by:

atan2 in interface CalculusFieldElement<Tuple>

Parameters:

x - second argument of the arc tangent

Returns:

atan2(this, x)

cosh

public Tuple cosh()

Hyperbolic cosine operation.

Specified by:

cosh in interface CalculusFieldElement<Tuple>

Returns:

cosh(this)

sinh

public Tuple sinh()

Hyperbolic sine operation.

Specified by:

sinh in interface CalculusFieldElement<Tuple>

Returns:

sinh(this)

sinhCosh

public FieldSinhCosh<Tuple> sinhCosh()

Combined hyperbolic sine and cosine operation.

Specified by:

sinhCosh in interface CalculusFieldElement<Tuple>

Returns:

[sinh(this), cosh(this)]

tanh

public Tuple tanh()

Hyperbolic tangent operation.

Specified by:

tanh in interface CalculusFieldElement<Tuple>

Returns:

tanh(this)

acosh

public Tuple acosh()

Inverse hyperbolic cosine operation.

Specified by:

acosh in interface CalculusFieldElement<Tuple>

Returns:

acosh(this)

asinh

public Tuple asinh()

Inverse hyperbolic sine operation.

Specified by:

asinh in interface CalculusFieldElement<Tuple>

Returns:

asin(this)

atanh

public Tuple atanh()

Inverse hyperbolic tangent operation.

Specified by:

atanh in interface CalculusFieldElement<Tuple>

Returns:

atanh(this)

toDegrees

public Tuple toDegrees()

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

Specified by:

toDegrees in interface CalculusFieldElement<Tuple>

Returns:

instance converted into degrees

toRadians

public Tuple toRadians()

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

Specified by:

toRadians in interface CalculusFieldElement<Tuple>

Returns:

instance converted into radians

linearCombination

public Tuple linearCombination(Tuple[] a,
                               Tuple[] b)
                        throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

public Tuple linearCombination(double[] a,
                               Tuple[] b)
                        throws MathIllegalArgumentException

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

public Tuple linearCombination(Tuple a1,
                               Tuple b1,
                               Tuple a2,
                               Tuple b2)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

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 Tuple linearCombination(double a1,
                               Tuple b1,
                               double a2,
                               Tuple b2)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

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 Tuple linearCombination(Tuple a1,
                               Tuple b1,
                               Tuple a2,
                               Tuple b2,
                               Tuple a3,
                               Tuple b3)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

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 Tuple linearCombination(double a1,
                               Tuple b1,
                               double a2,
                               Tuple b2,
                               double a3,
                               Tuple b3)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

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 Tuple linearCombination(Tuple a1,
                               Tuple b1,
                               Tuple a2,
                               Tuple b2,
                               Tuple a3,
                               Tuple b3,
                               Tuple a4,
                               Tuple b4)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

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 Tuple linearCombination(double a1,
                               Tuple b1,
                               double a2,
                               Tuple b2,
                               double a3,
                               Tuple b3,
                               double a4,
                               Tuple b4)

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<Tuple>

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 Tuple 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<Tuple>

Returns:

Archimedes constant π