la.maths

Class Q

java.lang.Object

la.la.Value

la.la.Value.Structured

la.maths.Vector

la.maths.Vector.Doubles

la.maths.Q

All Implemented Interfaces:

java.lang.Comparable<Value>, Value.Scannable

public abstract class Q
extends Vector.Doubles

Q, the (abstract) class of quaternions. Quaternions generalize Complex numbers and can be used to rotate 3D Vectors.

Nested Class Summary

Nested classes/interfaces inherited from class la.maths.Vector

Vector.Derived, Vector.Doubles, Vector.GP, Vector.Ints, Vector.Slice, Vector.Strings, Vector.Weighted

Nested classes/interfaces inherited from class la.la.Value

Value.Atomic, Value.Bool, Value.Char, Value.Chars, Value.Cts, Value.Defer, Value.Discrete, Value.Enum, Value.Inc_Or, Value.Int, Value.Lambda, Value.List, Value.Maybe, Value.Option, Value.Real, Value.Scannable, Value.Structured, Value.Triv, Value.Tuple

Field Summary

Fields inherited from class la.maths.Vector

empty

Fields inherited from class la.la.Value

C, comparator, CR, E, eight, ffalse, five, fiveR, four, fourR, half, negCR, negOne, negOneR, negTenR, nilVal, nine, None, one, oneR, PI, PIby2, point01, point1, point5, point9, quarter, seven, six, ten, tenR, three, threeR, triv, ttrue, two, twoR, zero, zeroR

Constructor Summary

Constructors

Constructor and Description
Q()

Method Summary

Modifier and Type	Method and Description
Q	asQ() Return 'this' -- also see Vector.asQ().
Vector	asV3() For 'this' Quaternion, (a,b,c,d), return the 3D Vector (b,c,d).
Q	conjugate() Return the conjugate, (a,-b,-c,-d), of 'this' Quaternion (a,b,c,d).
static Q	double1(double a) Return the Quaternion (a + 0i +0j + 0k).
static Q	doubles(double[] abcd) Given an array of doubles {a,b,c,d}, return the Quaternion (a + bi +cj + dk).
static Q	doubles(double a, double b, double c, double d) Return the Quaternion (a + bi +cj + dk).
double	i() The i-part, elt(1).x().
Q	inverse() Return the inverse of 'this' Quaternion, that is, its conjugate divided by its norm2.
double	j() The j-part, elt(2).x().
double	k() The k-part, elt(3).x().
static void	main(java.lang.String[] argv) main() allows Q to be (slightly) tested, in isolation.
int	nElts() Return 4.
Q	times(Q q) Multiply Quaternions 'this' and 'q'.
java.lang.String	toString() Show 'this' Quaternion as "(a±bi±cj±dk)".
double	wt(int i) Error: wt(i) is not a Quaternion operation.
double	wts() Error: wts() is not a Quaternion operation.
double	x() The "real" part, elt(0).x().

Methods inherited from class la.maths.Vector.Doubles

eltType, type

Methods inherited from class la.maths.Vector

addMore, addMore, append, append, as_1xn, as_nx1, asDiagonal, asMatrix, asQrotn, bOp, closes, col, cols, combine, compareTo, constAoM, constNlAoM, constWt, csv, csv, delete, delete, dot, doubles, doubles, drop, drop, dropLast, elt, elt, elts, foldl, foldl, foldr, foldr, fromScannable, ints, ints, isRectangular, isSquare, map, match, merge, nCols, nearlySymmetric, nearlySymmetric, nElts, nlAoM, nlAoM, norm_Cts, norm, normalised, normalised1, normalised2, opens, repeat, rotate, rotate, rowLength, scaled, shape, singleton, slice, sorted, sorted, sorted, strings, sumSq, take, takeLast, times, toSeries, uniqueElts, unzip, unzip, uOp, values, weight, weight, weight, weightLike, weightLike, wtMedian, wtNlAoM, wtNlAoM, wts, zip, zip

Methods inherited from class la.la.Value.Structured

AoM, elts, frth, fst, print, separator, snd, thrd

Methods inherited from class la.la.Value

apply, cons, cts, errMsg, error, force, isTuple, just, n, pair, quad, real, RTE, triple, tuple, UOE

Methods inherited from class java.lang.Object

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

Constructor Detail

Q

public Q()

Method Detail

wt

public double wt(int i)

Error: wt(i) is not a Quaternion operation.

Overrides:

wt in class Vector

wts

public double wts()

Error: wts() is not a Quaternion operation.

Overrides:

wts in class Vector

x

public double x()

The "real" part, elt(0).x().

Overrides:

x in class Value

i

public double i()

The i-part, elt(1).x().

j

public double j()

The j-part, elt(2).x().

k

public double k()

The k-part, elt(3).x().

nElts

public int nElts()

Return 4.

Specified by:

nElts in class Vector

times

public Q times(Q q)

Multiply Quaternions 'this' and 'q'. It generalizes complex multiplication.

conjugate

public Q conjugate()

Return the conjugate, (a,-b,-c,-d), of 'this' Quaternion (a,b,c,d).

inverse

public Q inverse()

Return the inverse of 'this' Quaternion, that is, its conjugate divided by its norm².

asV3

public Vector asV3()

For 'this' Quaternion, (a,b,c,d), return the 3D Vector (b,c,d).

asQ

public Q asQ()

Return 'this' -- also see Vector.asQ().

Overrides:

asQ in class Vector

toString

public java.lang.String toString()

Show 'this' Quaternion as "(a±bi±cj±dk)".

Overrides:

toString in class Value.Structured

doubles

public static Q doubles(double[] abcd)

Given an array of doubles {a,b,c,d}, return the Quaternion (a + bi +cj + dk).

doubles

public static Q doubles(double a,
                        double b,
                        double c,
                        double d)

Return the Quaternion (a + bi +cj + dk).

double1

public static Q double1(double a)

Return the Quaternion (a + 0i +0j + 0k).

main

public static void main(java.lang.String[] argv)

main() allows Q to be (slightly) tested, in isolation.