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dual.go
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// Copyright ©2018 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package dualquat
import (
"fmt"
"strings"
"gonum.org/v1/gonum/num/dual"
"gonum.org/v1/gonum/num/quat"
)
// Number is a float64 precision dual quaternion. A dual quaternion
// is a hypercomplex number composed of two quaternions, q₀+q₂ϵ,
// where ϵ²=0, but ϵ≠0. Here, q₀ is termed the real and q₂ the dual.
type Number struct {
Real, Dual quat.Number
}
var zeroQuat quat.Number
// Format implements fmt.Formatter.
func (d Number) Format(fs fmt.State, c rune) {
prec, pOk := fs.Precision()
if !pOk {
prec = -1
}
width, wOk := fs.Width()
if !wOk {
width = -1
}
switch c {
case 'v':
if fs.Flag('#') {
fmt.Fprintf(fs, "%T{Real:%#v, Dual:%#v}", d, d.Real, d.Dual)
return
}
if fs.Flag('+') {
fmt.Fprintf(fs, "{Real:%+v, Dual:%+v}", d.Real, d.Dual)
return
}
c = 'g'
prec = -1
fallthrough
case 'e', 'E', 'f', 'F', 'g', 'G':
fre := fmtString(fs, c, prec, width, false)
fim := fmtString(fs, c, prec, width, true)
fmt.Fprintf(fs, fmt.Sprintf("(%s+%[2]sϵ)", fre, fim), d.Real, d.Dual)
default:
fmt.Fprintf(fs, "%%!%c(%T=%[2]v)", c, d)
return
}
}
// This is horrible, but it's what we have.
func fmtString(fs fmt.State, c rune, prec, width int, wantPlus bool) string {
var b strings.Builder
b.WriteByte('%')
for _, f := range "0+- " {
if fs.Flag(int(f)) || (f == '+' && wantPlus) {
b.WriteByte(byte(f))
}
}
if width >= 0 {
fmt.Fprint(&b, width)
}
if prec >= 0 {
b.WriteByte('.')
if prec > 0 {
fmt.Fprint(&b, prec)
}
}
b.WriteRune(c)
return b.String()
}
// Add returns the sum of x and y.
func Add(x, y Number) Number {
return Number{
Real: quat.Add(x.Real, y.Real),
Dual: quat.Add(x.Dual, y.Dual),
}
}
// Sub returns the difference of x and y, x-y.
func Sub(x, y Number) Number {
return Number{
Real: quat.Sub(x.Real, y.Real),
Dual: quat.Sub(x.Dual, y.Dual),
}
}
// Mul returns the dual product of x and y.
func Mul(x, y Number) Number {
return Number{
Real: quat.Mul(x.Real, y.Real),
Dual: quat.Add(quat.Mul(x.Real, y.Dual), quat.Mul(x.Dual, y.Real)),
}
}
// Inv returns the dual inverse of d.
func Inv(d Number) Number {
return Number{
Real: quat.Inv(d.Real),
Dual: quat.Scale(-1, quat.Mul(d.Dual, quat.Inv(quat.Mul(d.Real, d.Real)))),
}
}
// Conj returns the dual quaternion conjugate of d₁+d₂ϵ, d̅₁-d̅₂ϵ.
func Conj(d Number) Number {
return Number{
Real: quat.Conj(d.Real),
Dual: quat.Scale(-1, quat.Conj(d.Dual)),
}
}
// ConjDual returns the dual conjugate of d₁+d₂ϵ, d₁-d₂ϵ.
func ConjDual(d Number) Number {
return Number{
Real: d.Real,
Dual: quat.Scale(-1, d.Dual),
}
}
// ConjQuat returns the quaternion conjugate of d₁+d₂ϵ, d̅₁+d̅₂ϵ.
func ConjQuat(d Number) Number {
return Number{
Real: quat.Conj(d.Real),
Dual: quat.Conj(d.Dual),
}
}
// Scale returns d scaled by f.
func Scale(f float64, d Number) Number {
return Number{Real: quat.Scale(f, d.Real), Dual: quat.Scale(f, d.Dual)}
}
// Abs returns the absolute value of d.
func Abs(d Number) dual.Number {
return dual.Number{
Real: quat.Abs(d.Real),
Emag: quat.Abs(d.Dual),
}
}