Package gnu.math

Class Quaternion

java.lang.Object

java.lang.Number

gnu.math.Numeric

gnu.math.Quantity

gnu.math.Quaternion

All Implemented Interfaces:

Serializable

Direct Known Subclasses:

Complex, CQuaternion, DQuaternion

public abstract class Quaternion
extends Quantity

A quaternion is a hypercomplex number of the form w + xi + yj + zk where w, x, y, and k are real, and i, j, and k are imaginary units which satisfy i^2 = j^2 = k^2 = ijk = -1.

See Also:

• Serialized Form

Field Summary

Fields inherited from class gnu.math.Numeric

CEILING, FLOOR, NONNEG_MOD, ROUND, TRUNCATE

Constructor Summary

Constructors

Constructor	Description
Quaternion()

Method Summary

Modifier and Type	Method	Description
Numeric	abs()
static Quaternion	add(Quaternion x, Quaternion y, int k)
Numeric	add(Object y, int k)	Return this + k * obj.
Numeric	addReversed(Numeric x, int k)	Calculate x+k&this.
RealNum	angle()
int	classifyFinite()	Check if value is finite, infinite, or NaN.
RealNum	colatitude()
static int	compare(Quaternion x, Quaternion y)
int	compare(Object obj)	Return an integer for which of this or obj is larger.
Complex	complexPart()
Quaternion	conjugate()
Quaternion	cos()
Numeric	div(Object y)
static Quaternion	divide(Quaternion x, Quaternion y)
Numeric	divReversed(Numeric x)
double	doubleImagValue()	The value of the imaginary component, as a double.
double	doubleJmagValue()	The value of the "j" component, as a double.
double	doubleKmagValue()	The value of the "k" component, as a double.
final double	doubleRealValue()
double	doubleValue()	The value of the real component, as a double.
static boolean	equals(Quaternion x, Quaternion y)
boolean	equals(Object obj)
Quaternion	exp()
boolean	isExact()
boolean	isZero()
static CQuaternion	jmMinusOne()
static CQuaternion	jmOne()
static CQuaternion	kmMinusOne()
static CQuaternion	kmOne()
Quaternion	log()
RealNum	longitude()
long	longValue()
static Quaternion	make(double re, double im, double jm, double km)
static Quaternion	make(RealNum re, RealNum im, RealNum jm, RealNum km)
Numeric	mul(Object y)
Numeric	mulReversed(Numeric x)
Numeric	neg()
static Quaternion	neg(Quaternion x)
Quaternion	number()
static Quaternion	polar(double r, double t, double u, double v)
static Quaternion	polar(RealNum r, RealNum t, RealNum u, RealNum v)
static Quaternion	power(Quaternion x, Quaternion y)
Quaternion	sin()
Quaternion	sqrt()
Quaternion	tan()
static Quaternion	times(Quaternion x, Quaternion y)
Quaternion	toExact()
Quaternion	toInexact()
String	toString(int radix)
Quaternion	unitQuaternion()
Quaternion	unitVector()
Quaternion	vectorPart()

Methods inherited from class gnu.math.Quantity

add, compare, compareReversed, dimensions, divide, im, imValue, jm, jmValue, km, kmValue, make, make, make, re, reValue, times, unit

Methods inherited from class gnu.math.Numeric

add, asNumericOrNull, div_inv, floatValue, geq, grt, intValue, mul_ident, power, sub, toString

Methods inherited from class java.lang.Number

byteValue, shortValue

Methods inherited from class java.lang.Object

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

Constructor Details

Quaternion

public Quaternion()

Method Details

number

public Quaternion number()

Specified by:

number in class Quantity

isExact

public boolean isExact()

Specified by:

isExact in class Numeric

classifyFinite

public int classifyFinite()

Check if value is finite, infinite, or NaN.

Returns:

1 if finite; 0 if infinite; -1 if NaN.

toExact

public Quaternion toExact()

Overrides:

toExact in class Numeric

toInexact

public Quaternion toInexact()

Overrides:

toInexact in class Numeric

jmOne

public static CQuaternion jmOne()

jmMinusOne

public static CQuaternion jmMinusOne()

kmOne

public static CQuaternion kmOne()

kmMinusOne

public static CQuaternion kmMinusOne()

doubleValue

public double doubleValue()

Description copied from class: Quantity

The value of the real component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleValue in class Quantity

doubleImagValue

public double doubleImagValue()

Description copied from class: Quantity

The value of the imaginary component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleImagValue in class Quantity

doubleJmagValue

public double doubleJmagValue()

Description copied from class: Quantity

The value of the "j" component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleJmagValue in class Quantity

doubleKmagValue

public double doubleKmagValue()

Description copied from class: Quantity

The value of the "k" component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleKmagValue in class Quantity

doubleRealValue

public final double doubleRealValue()

longValue

public long longValue()

Overrides:

longValue in class Numeric

complexPart

public Complex complexPart()

vectorPart

public Quaternion vectorPart()

unitVector

public Quaternion unitVector()

unitQuaternion

public Quaternion unitQuaternion()

make

public static Quaternion make(RealNum re,
 RealNum im,
 RealNum jm,
 RealNum km)

make

public static Quaternion make(double re,
 double im,
 double jm,
 double km)

polar

public static Quaternion polar(double r,
 double t,
 double u,
 double v)

polar

public static Quaternion polar(RealNum r,
 RealNum t,
 RealNum u,
 RealNum v)

power

public static Quaternion power(Quaternion x,
 Quaternion y)

abs

public Numeric abs()

Overrides:

abs in class Quantity

angle

public RealNum angle()

colatitude

public RealNum colatitude()

longitude

public RealNum longitude()

conjugate

public Quaternion conjugate()

equals

public static boolean equals(Quaternion x,
 Quaternion y)

equals

public boolean equals(Object obj)

Overrides:

equals in class Numeric

compare

public static int compare(Quaternion x,
 Quaternion y)

compare

public int compare(Object obj)

Description copied from class: Numeric

Return an integer for which of this or obj is larger. Return 1 if this>obj; 0 if this==obj; -1 if this<obj; -2 if this!=obj otherwise (for example if either is NaN); -3 if not comparable (incompatible types).

Overrides:

compare in class Quantity

isZero

public boolean isZero()

Specified by:

isZero in class Numeric

toString

public String toString(int radix)

Overrides:

toString in class Quantity

neg

public static Quaternion neg(Quaternion x)

neg

public Numeric neg()

Overrides:

neg in class Quantity

add

public static Quaternion add(Quaternion x,
 Quaternion y,
 int k)

add

public Numeric add(Object y,
 int k)

Description copied from class: Numeric

Return this + k * obj.

Overrides:

add in class Quantity

addReversed

public Numeric addReversed(Numeric x,
 int k)

Description copied from class: Numeric

Calculate x+k&this.

Overrides:

addReversed in class Quantity

times

public static Quaternion times(Quaternion x,
 Quaternion y)

mul

public Numeric mul(Object y)

Overrides:

mul in class Quantity

mulReversed

public Numeric mulReversed(Numeric x)

Overrides:

mulReversed in class Quantity

divide

public static Quaternion divide(Quaternion x,
 Quaternion y)

div

public Numeric div(Object y)

Overrides:

div in class Quantity

divReversed

public Numeric divReversed(Numeric x)

Overrides:

divReversed in class Quantity

exp

public Quaternion exp()

log

public Quaternion log()

sqrt

public Quaternion sqrt()

sin

public Quaternion sin()

cos

public Quaternion cos()

tan

public Quaternion tan()