Quaternion

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Method

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gnu.math

Class Quaternion

java.lang.Object
- java.lang.Number
- - gnu.math.Numeric
  - - gnu.math.Quantity
    - - gnu.math.Quaternion

All Implemented Interfaces:

java.io.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 and Description

Quaternion ()

Constructors
Constructor and Description
`Quaternion ()`

Method Summary

All Methods
Modifier and Type	Method and Description
`Numeric`	`abs ()`
`Numeric`	`add (java.lang.Object y, int k)` Return this + k * obj.
`static Quaternion`	`add (Quaternion x, Quaternion y, int k)`
`Numeric`	`addReversed (Numeric x, int k)` Calculate `x+k&this`.
`RealNum`	`angle ()`
`int`	`classifyFinite ()` Check if value is finite, infinite, or NaN.
`RealNum`	`colatitude ()`
`int`	`compare (java.lang.Object obj)` Return an integer for which of `this` or `obj` is larger.
`static int`	`compare (Quaternion x, Quaternion y)`
`Complex`	`complexPart ()`
`Quaternion`	`conjugate ()`
`Quaternion`	`cos ()`
`Numeric`	`div (java.lang.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.
`double`	`doubleRealValue ()`
`double`	`doubleValue ()` The value of the real component, as a double.
`boolean`	`equals (java.lang.Object obj)`
`static boolean`	`equals (Quaternion x, Quaternion y)`
`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 (java.lang.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 ()`
`java.lang.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 Detail
  - Quaternion
```
public Quaternion()
```
- Method Detail
  - 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(java.lang.Object obj)
```
    Overrides:
    
    equals in class Numeric
  - compare
```
public static int compare(Quaternion x,
 Quaternion y)
```
  - compare
```
public int compare(java.lang.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 java.lang.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(java.lang.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(java.lang.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(java.lang.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()
```

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Summary:
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Field |
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Method

Detail:
Field |
Constr |
Method

Class Quaternion

Field Summary

Fields inherited from class gnu.math.Numeric

Constructor Summary

Method Summary

Methods inherited from class gnu.math.Quantity

Methods inherited from class gnu.math.Numeric

Methods inherited from class java.lang.Number

Methods inherited from class java.lang.Object

Constructor Detail

Quaternion

Method Detail

number

isExact

classifyFinite

toExact

toInexact

jmOne

jmMinusOne

kmOne

kmMinusOne

doubleValue

doubleImagValue

doubleJmagValue

doubleKmagValue

doubleRealValue

longValue

complexPart

vectorPart

unitVector

unitQuaternion

make

make

polar

polar

power

abs

angle

colatitude

longitude

conjugate

equals

equals

compare

compare

isZero

toString

neg

neg

add

add

addReversed

times

mul

mulReversed

divide

div

divReversed

exp

log

sqrt

sin

cos

tan