org.jscience.mathematics.algebraic.numbers
Class Quaternion

java.lang.Object
  java.lang.Number
      org.jscience.mathematics.algebraic.numbers.Quaternion

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, Field.Member, Ring.Member, AbelianGroup.Member, Module.Member, VectorSpace.Member, Member

public final class Quaternion
extends java.lang.Number
implements java.lang.Cloneable, java.io.Serializable, Field.Member, CStarAlgebra.Member

The Quaternion class encapsulates quaternions.

See Also:

Serialized Form

Field Summary

static Quaternion	I
static Quaternion	J
static Quaternion	K
static double	MAX_IMAGINARY_VALUE
static double	MAX_REAL_VALUE
static double	MIN_IMAGINARY_VALUE
static double	MIN_REAL_VALUE
static double	NaN
static double	NEGATIVE_IMAGINARY_INFINITY
static double	NEGATIVE_REAL_INFINITY
static Quaternion	ONE
static double	POSITIVE_IMAGINARY_INFINITY
static double	POSITIVE_REAL_INFINITY
static java.lang.Class	TYPE
static Quaternion	ZERO

Constructor Summary

Quaternion(double real, Double3Vector imag)
Constructs a quaternion.

Quaternion(double q0, double q1, double q2, double q3)
Constructs the quaternion q₀+iq₁+jq₂+kq₃.

Quaternion(Quaternion quat)
Constructs a quaternion.

Method Summary

AbelianGroup.Member	add(AbelianGroup.Member x) Returns the addition of this number and another.
Quaternion	add(Quaternion q) Returns the addition of this quaternion and another.
Quaternion	addImag(Double3Vector imag) Returns the addition of this quaternion with an imaginary part.
Quaternion	addReal(double real) Returns the addition of this quaternion with a real part.
java.lang.Object	clone()
Quaternion	conjugate() Returns the conjugate of this quaternion.
Quaternion	divide(double x) Returns the division of this quaternion by a scalar.
Field.Member	divide(Field.Member x) Returns the division of this number and another.
Quaternion	divide(Quaternion q) Returns the division of this quaternion by another.
double	doubleValue()
boolean	equals(java.lang.Object obj) Compares two quaternions for equality.
float	floatValue()
int	hashCode() Returns a hashcode for this quaternion.
Double3Vector	imag() Returns the imaginary part of this quaternion.
int	intValue()
Field.Member	inverse() Returns the inverse of this quaternion.
CStarAlgebra.Member	involution() Returns the involution of this quaternion.
boolean	isInfinite() Returns true if either the real or imaginary part is infinite.
boolean	isNaN() Returns true if either the real or imaginary part is NaN.
long	longValue()
Quaternion	multiply(double x) Returns the multiplication of this quaternion by a scalar.
Quaternion	multiply(Quaternion q) Returns the multiplication of this quaternion and another.
Ring.Member	multiply(Ring.Member x) Returns the multiplication of this number and another.
AbelianGroup.Member	negate() Returns the negative of this quaternion.
double	norm() Returns the l2-norm (magnitude), which is also the C* norm.
double	real() Returns the real part of this quaternion.
VectorSpace.Member	scalarDivide(Field.Member x) Returns the division of this number by a real scalar.
Module.Member	scalarMultiply(Ring.Member x) Returns the multiplication of this number by a real scalar.
AbelianGroup.Member	subtract(AbelianGroup.Member x) Returns the subtraction of this number and another.
Quaternion	subtract(Quaternion q) Returns the subtraction of this quaternion by another.
Quaternion	subtractImag(Double3Vector imag) Returns the subtraction of this quaternion by an imaginary part.
Quaternion	subtractReal(double real) Returns the subtraction of this quaternion by a real part.
double	sumSquares() Returns the sum of the squares of the components.
java.lang.String	toString() Returns a string representing the value of this quaternion.

Methods inherited from class java.lang.Number

byteValue, shortValue

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

ZERO

public static final Quaternion ZERO

ONE

public static final Quaternion ONE

I

public static final Quaternion I

J

public static final Quaternion J

K

public static final Quaternion K

MAX_REAL_VALUE

public static final double MAX_REAL_VALUE

See Also:

Constant Field Values

MIN_REAL_VALUE

public static final double MIN_REAL_VALUE

See Also:

Constant Field Values

MAX_IMAGINARY_VALUE

public static final double MAX_IMAGINARY_VALUE

See Also:

Constant Field Values

MIN_IMAGINARY_VALUE

public static final double MIN_IMAGINARY_VALUE

See Also:

Constant Field Values

NaN

public static final double NaN

See Also:

Constant Field Values

NEGATIVE_REAL_INFINITY

public static final double NEGATIVE_REAL_INFINITY

See Also:

Constant Field Values

POSITIVE_REAL_INFINITY

public static final double POSITIVE_REAL_INFINITY

See Also:

Constant Field Values

NEGATIVE_IMAGINARY_INFINITY

public static final double NEGATIVE_IMAGINARY_INFINITY

See Also:

Constant Field Values

POSITIVE_IMAGINARY_INFINITY

public static final double POSITIVE_IMAGINARY_INFINITY

See Also:

Constant Field Values

TYPE

public static final java.lang.Class TYPE

Constructor Detail

Quaternion

public Quaternion(double real,
                  Double3Vector imag)

Constructs a quaternion.

Quaternion

public Quaternion(double q0,
                  double q1,
                  double q2,
                  double q3)

Constructs the quaternion q₀+iq₁+jq₂+kq₃.

Quaternion

public Quaternion(Quaternion quat)

Constructs a quaternion.

Method Detail

equals

public boolean equals(java.lang.Object obj)

Compares two quaternions for equality.

Overrides:

equals in class java.lang.Object

Parameters:

obj - a quaternion

toString

public java.lang.String toString()

Returns a string representing the value of this quaternion.

Overrides:

toString in class java.lang.Object

hashCode

public int hashCode()

Returns a hashcode for this quaternion.

Overrides:

hashCode in class java.lang.Object

isNaN

public boolean isNaN()

Returns true if either the real or imaginary part is NaN.

isInfinite

public boolean isInfinite()

Returns true if either the real or imaginary part is infinite.

real

public double real()

Returns the real part of this quaternion.

imag

public Double3Vector imag()

Returns the imaginary part of this quaternion.

norm

public double norm()

Returns the l²-norm (magnitude), which is also the C^* norm.

Specified by:

norm in interface BanachSpace.Member

Returns:

DOCUMENT ME!

sumSquares

public double sumSquares()

Returns the sum of the squares of the components.

intValue

public int intValue()

Specified by:

intValue in class java.lang.Number

longValue

public long longValue()

Specified by:

longValue in class java.lang.Number

floatValue

public float floatValue()

Specified by:

floatValue in class java.lang.Number

doubleValue

public double doubleValue()

Specified by:

doubleValue in class java.lang.Number

negate

public AbelianGroup.Member negate()

Returns the negative of this quaternion.

Specified by:

negate in interface AbelianGroup.Member

Returns:

DOCUMENT ME!

inverse

public Field.Member inverse()

Returns the inverse of this quaternion.

Specified by:

inverse in interface Field.Member

Returns:

DOCUMENT ME!

involution

public CStarAlgebra.Member involution()

Returns the involution of this quaternion.

Specified by:

involution in interface CStarAlgebra.Member

Returns:

DOCUMENT ME!

conjugate

public Quaternion conjugate()

Returns the conjugate of this quaternion.

add

public AbelianGroup.Member add(AbelianGroup.Member x)

Returns the addition of this number and another.

Specified by:

add in interface AbelianGroup.Member

Parameters:

x - a group member

Returns:

DOCUMENT ME!

add

public Quaternion add(Quaternion q)

Returns the addition of this quaternion and another.

Parameters:

q - a quaternion

addReal

public Quaternion addReal(double real)

Returns the addition of this quaternion with a real part.

Parameters:

real - a real part

addImag

public Quaternion addImag(Double3Vector imag)

Returns the addition of this quaternion with an imaginary part.

Parameters:

imag - an imaginary part

subtract

public AbelianGroup.Member subtract(AbelianGroup.Member x)

Returns the subtraction of this number and another.

Specified by:

subtract in interface AbelianGroup.Member

Parameters:

x - a group member

Returns:

DOCUMENT ME!

subtract

public Quaternion subtract(Quaternion q)

Returns the subtraction of this quaternion by another.

Parameters:

q - a quaternion

subtractReal

public Quaternion subtractReal(double real)

Returns the subtraction of this quaternion by a real part.

Parameters:

real - a real part

subtractImag

public Quaternion subtractImag(Double3Vector imag)

Returns the subtraction of this quaternion by an imaginary part.

Parameters:

imag - an imaginary part

scalarMultiply

public Module.Member scalarMultiply(Ring.Member x)

Returns the multiplication of this number by a real scalar.

Specified by:

scalarMultiply in interface Module.Member

Parameters:

x - a ring member

Returns:

DOCUMENT ME!

multiply

public Ring.Member multiply(Ring.Member x)

Returns the multiplication of this number and another.

Specified by:

multiply in interface Ring.Member

Parameters:

x - a ring member

Returns:

DOCUMENT ME!

multiply

public Quaternion multiply(Quaternion q)

Returns the multiplication of this quaternion and another.

Parameters:

q - a quaternion

multiply

public Quaternion multiply(double x)

Returns the multiplication of this quaternion by a scalar.

Parameters:

x - a real number

scalarDivide

public VectorSpace.Member scalarDivide(Field.Member x)

Returns the division of this number by a real scalar.

Specified by:

scalarDivide in interface VectorSpace.Member

Parameters:

x - a field member

Returns:

DOCUMENT ME!

divide

public Field.Member divide(Field.Member x)

Returns the division of this number and another.

Specified by:

divide in interface Field.Member

Parameters:

x - a field member

Returns:

DOCUMENT ME!

divide

public Quaternion divide(Quaternion q)

Returns the division of this quaternion by another.

Parameters:

q - a quaternion

Throws:

java.lang.ArithmeticException - If divide by zero.

divide

public Quaternion divide(double x)

Returns the division of this quaternion by a scalar.

Parameters:

x - a real number

Throws:

java.lang.ArithmeticException - If divide by zero.

clone

public java.lang.Object clone()

Overrides:

clone in class java.lang.Object