forked from kscience/kmath
Implement fast quaternion implementation, minor changes to complex
This commit is contained in:
Iaroslav Postovalov
parent
457931dd86
commit
76717c49b1
@ -8,6 +8,7 @@
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- Automatic README generation for features (#139)
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- Native support for `memory`, `core` and `dimensions`
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- `kmath-ejml` to supply EJML SimpleMatrix wrapper.
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- Basic Quaternion vector support.
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### Changed
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- Package changed from `scientifik` to `kscience.kmath`.
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@ -42,22 +42,21 @@ private val PI_DIV_2 = Complex(PI / 2, 0)
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* A field of [Complex].
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*/
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public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
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override val zero: Complex = 0.0.toComplex()
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override val one: Complex = 1.0.toComplex()
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override val zero: Complex by lazy { 0.toComplex() }
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override val one: Complex by lazy { 1.toComplex() }
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/**
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* The imaginary unit.
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*/
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public val i: Complex = Complex(0.0, 1.0)
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public val i: Complex by lazy { Complex(0, 1) }
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override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
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public override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
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public override fun multiply(a: Complex, k: Number): Complex = Complex(a.re * k.toDouble(), a.im * k.toDouble())
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override fun multiply(a: Complex, k: Number): Complex = Complex(a.re * k.toDouble(), a.im * k.toDouble())
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override fun multiply(a: Complex, b: Complex): Complex =
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public override fun multiply(a: Complex, b: Complex): Complex =
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Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
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override fun divide(a: Complex, b: Complex): Complex = when {
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public override fun divide(a: Complex, b: Complex): Complex = when {
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b.re.isNaN() || b.im.isNaN() -> Complex(Double.NaN, Double.NaN)
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(if (b.im < 0) -b.im else +b.im) < (if (b.re < 0) -b.re else +b.re) -> {
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@ -83,31 +82,31 @@ public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
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}
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}
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override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2
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override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2
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public override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2
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public override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2
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override fun tan(arg: Complex): Complex {
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public override fun tan(arg: Complex): Complex {
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val e1 = exp(-i * arg)
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val e2 = exp(i * arg)
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return i * (e1 - e2) / (e1 + e2)
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}
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override fun asin(arg: Complex): Complex = -i * ln(sqrt(1 - (arg * arg)) + i * arg)
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override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(1 - (arg * arg)) + i * arg)
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public override fun asin(arg: Complex): Complex = -i * ln(sqrt(1 - (arg * arg)) + i * arg)
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public override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(1 - (arg * arg)) + i * arg)
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override fun atan(arg: Complex): Complex {
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public override fun atan(arg: Complex): Complex {
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val iArg = i * arg
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return i * (ln(1 - iArg) - ln(1 + iArg)) / 2
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}
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override fun power(arg: Complex, pow: Number): Complex = if (arg.im == 0.0)
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public override fun power(arg: Complex, pow: Number): Complex = if (arg.im == 0.0)
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arg.re.pow(pow.toDouble()).toComplex()
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else
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exp(pow * ln(arg))
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override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im))
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public override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im))
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override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)
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public override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)
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/**
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* Adds complex number to real one.
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@ -116,7 +115,7 @@ public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
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* @param c the augend.
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* @return the sum.
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*/
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public operator fun Double.plus(c: Complex): Complex = add(this.toComplex(), c)
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public operator fun Double.plus(c: Complex): Complex = add(toComplex(), c)
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/**
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* Subtracts complex number from real one.
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@ -125,7 +124,7 @@ public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
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* @param c the subtrahend.
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* @return the difference.
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*/
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public operator fun Double.minus(c: Complex): Complex = add(this.toComplex(), -c)
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public operator fun Double.minus(c: Complex): Complex = add(toComplex(), -c)
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/**
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* Adds real number to complex one.
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@ -154,9 +153,9 @@ public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
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*/
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public operator fun Double.times(c: Complex): Complex = Complex(c.re * this, c.im * this)
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override fun norm(arg: Complex): Complex = sqrt(arg.conjugate * arg)
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override fun symbol(value: String): Complex = if (value == "i") i else super.symbol(value)
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public override fun Complex.unaryMinus(): Complex = Complex(-re, -im)
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public override fun norm(arg: Complex): Complex = sqrt(arg.conjugate * arg)
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public override fun symbol(value: String): Complex = if (value == "i") i else super.symbol(value)
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}
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/**
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@ -169,26 +168,23 @@ public data class Complex(val re: Double, val im: Double) : FieldElement<Complex
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Comparable<Complex> {
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public constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble())
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override val context: ComplexField get() = ComplexField
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override fun unwrap(): Complex = this
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override fun Complex.wrap(): Complex = this
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override fun compareTo(other: Complex): Int = r.compareTo(other.r)
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override fun toString(): String {
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return "($re + i*$im)"
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}
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public override val context: ComplexField
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get() = ComplexField
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public override fun unwrap(): Complex = this
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public override fun Complex.wrap(): Complex = this
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public override fun compareTo(other: Complex): Int = r.compareTo(other.r)
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public override fun toString(): String = "($re + $im * i)"
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public override fun minus(b: Complex): Complex = Complex(re - b.re, im - b.im)
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public companion object : MemorySpec<Complex> {
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override val objectSize: Int
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public override val objectSize: Int
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get() = 16
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override fun MemoryReader.read(offset: Int): Complex = Complex(readDouble(offset), readDouble(offset + 8))
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public override fun MemoryReader.read(offset: Int): Complex =
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Complex(readDouble(offset), readDouble(offset + 8))
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override fun MemoryWriter.write(offset: Int, value: Complex) {
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public override fun MemoryWriter.write(offset: Int, value: Complex) {
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writeDouble(offset, value.re)
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writeDouble(offset + 8, value.im)
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}
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@ -201,7 +197,7 @@ public data class Complex(val re: Double, val im: Double) : FieldElement<Complex
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* @receiver the real part.
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* @return the new complex number.
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*/
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public fun Number.toComplex(): Complex = Complex(this, 0.0)
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public fun Number.toComplex(): Complex = Complex(this, 0)
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/**
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* Creates a new buffer of complex numbers with the specified [size], where each element is calculated by calling the
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@ -0,0 +1,294 @@
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package kscience.kmath.operations
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import kscience.kmath.memory.MemoryReader
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import kscience.kmath.memory.MemorySpec
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import kscience.kmath.memory.MemoryWriter
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import kscience.kmath.structures.Buffer
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import kscience.kmath.structures.MemoryBuffer
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import kscience.kmath.structures.MutableBuffer
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import kscience.kmath.structures.MutableMemoryBuffer
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import kotlin.math.*
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/**
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* This quaternion's conjugate.
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*/
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public val Quaternion.conjugate: Quaternion
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get() = QuaternionField { z - x * i - y * j - z * k }
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/**
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* This quaternion's reciprocal.
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*/
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public val Quaternion.reciprocal: Quaternion
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get() {
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val n = QuaternionField { norm(this@reciprocal) }
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return conjugate / (n * n)
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}
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/**
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* Absolute value of the quaternion.
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*/
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public val Quaternion.r: Double
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get() = sqrt(w * w + x * x + y * y + z * z)
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/**
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* A field of [Quaternion].
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*/
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public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>, PowerOperations<Quaternion>,
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ExponentialOperations<Quaternion> {
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override val zero: Quaternion by lazy { 0.toQuaternion() }
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override val one: Quaternion by lazy { 1.toQuaternion() }
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/**
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* The `i` quaternion unit.
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*/
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public val i: Quaternion by lazy { Quaternion(0, 1, 0, 0) }
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/**
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* The `j` quaternion unit.
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*/
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public val j: Quaternion by lazy { Quaternion(0, 0, 1, 0) }
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/**
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* The `k` quaternion unit.
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*/
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public val k: Quaternion by lazy { Quaternion(0, 0, 0, 1) }
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public override fun add(a: Quaternion, b: Quaternion): Quaternion =
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Quaternion(a.w + b.w, a.x + b.x, a.y + b.y, a.z + b.z)
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public override fun multiply(a: Quaternion, k: Number): Quaternion {
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val d = k.toDouble()
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return Quaternion(a.w * d, a.x * d, a.y * d, a.z * d)
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}
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public override fun multiply(a: Quaternion, b: Quaternion): Quaternion = Quaternion(
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a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z,
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a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
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a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x,
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a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w,
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)
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override fun divide(a: Quaternion, b: Quaternion): Quaternion {
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val s = b.w * b.w + b.x * b.x + b.y * b.y + b.z * b.z
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return Quaternion(
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(b.w * a.w + b.x * a.x + b.y * a.y + b.z * a.z) / s,
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(b.w * a.x - b.x * a.w - b.y * a.z + b.z * a.y) / s,
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(b.w * a.y + b.x * a.z - b.y * a.w - b.z * a.x) / s,
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(b.w * a.z - b.x * a.y + b.y * a.x - b.z * a.w) / s,
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)
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}
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public override fun power(arg: Quaternion, pow: Number): Quaternion {
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if (pow is Int) return pwr(arg, pow)
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if (floor(pow.toDouble()) == pow.toDouble()) return pwr(arg, pow.toInt())
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return exp(pow * ln(arg))
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}
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private fun pwr(x: Quaternion, a: Int): Quaternion {
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if (a < 0) return -(pwr(x, -a))
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if (a == 0) return one
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if (a == 1) return x
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if (a == 2) return pwr2(x)
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if (a == 3) return pwr3(x)
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if (a == 4) return pwr4(x)
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val x4 = pwr4(x)
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var y = x4
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repeat((1 until a / 4).count()) { y *= x4 }
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if (a % 4 == 3) y *= pwr3(x)
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if (a % 4 == 2) y *= pwr2(x)
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if (a % 4 == 1) y *= x
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return y
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}
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private inline fun pwr2(x: Quaternion): Quaternion {
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val aa = 2 * x.w
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return Quaternion(
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x.w * x.w - (x.x * x.x + x.y * x.y + x.z * x.z),
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aa * x.x,
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aa * x.y,
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aa * x.z
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)
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}
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private inline fun pwr3(x: Quaternion): Quaternion {
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val a2 = x.w * x.w
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val n1 = x.x * x.x + x.y * x.y + x.z * x.z
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val n2 = 3.0 * a2 - n1
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return Quaternion(
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x.w * (a2 - 3 * n1),
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x.x * n2,
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x.y * n2,
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x.z * n2
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)
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}
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private inline fun pwr4(x: Quaternion): Quaternion {
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val a2 = x.w * x.w
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val n1 = x.x * x.x + x.y * x.y + x.z * x.z
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val n2 = 4 * x.w * (a2 - n1)
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return Quaternion(
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a2 * a2 - 6 * a2 * n1 + n1 * n1,
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x.x * n2,
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x.y * n2,
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x.z * n2
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)
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}
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public override fun exp(arg: Quaternion): Quaternion {
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val un = arg.x * arg.x + arg.y * arg.y + arg.z * arg.z
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if (un == 0.0) return exp(arg.w).toQuaternion()
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val n1 = sqrt(un)
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val ea = exp(arg.w)
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val n2 = ea * sin(n1) / n1
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return Quaternion(ea * cos(n1), n2 * arg.x, n2 * arg.y, n2 * arg.z)
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}
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public override fun ln(arg: Quaternion): Quaternion {
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val nu2 = arg.x * arg.x + arg.y * arg.y + arg.z * arg.z
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if (nu2 == 0.0)
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return if (arg.w > 0)
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Quaternion(ln(arg.w), 0, 0, 0)
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else {
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val l = ComplexField { ln(arg.w.toComplex()) }
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Quaternion(l.re, l.im, 0, 0)
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}
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val a = arg.w
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check(nu2 > 0)
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val n = sqrt(a * a + nu2)
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val th = acos(a / n) / sqrt(nu2)
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return Quaternion(ln(n), th * arg.x, th * arg.y, th * arg.z)
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}
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/**
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* Adds quaternion to real one.
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*
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* @receiver the addend.
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* @param c the augend.
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* @return the sum.
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*/
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public operator fun Double.plus(c: Quaternion): Quaternion = Quaternion(this + c.w, c.x, c.y, c.z)
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/**
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* Subtracts quaternion from real one.
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*
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* @receiver the minuend.
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* @param c the subtrahend.
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* @return the difference.
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*/
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public operator fun Double.minus(c: Quaternion): Quaternion = Quaternion(this - c.w, -c.x, -c.y, -c.z)
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/**
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* Adds real number to quaternion.
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*
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* @receiver the addend.
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* @param d the augend.
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* @return the sum.
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*/
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public operator fun Quaternion.plus(d: Double): Quaternion = Quaternion(w + d, x, y, z)
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/**
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* Subtracts real number from quaternion.
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*
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* @receiver the minuend.
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* @param d the subtrahend.
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* @return the difference.
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*/
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public operator fun Quaternion.minus(d: Double): Quaternion = Quaternion(w - d, x, y, z)
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/**
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* Multiplies real number by quaternion.
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*
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* @receiver the multiplier.
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* @param c the multiplicand.
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* @receiver the product.
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*/
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public operator fun Double.times(c: Quaternion): Quaternion =
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Quaternion(this * c.w, this * c.x, this * c.y, this * c.z)
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public override fun Quaternion.unaryMinus(): Quaternion = Quaternion(-w, -x, -y, -z)
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public override fun norm(arg: Quaternion): Quaternion = sqrt(arg.conjugate * arg)
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public override fun symbol(value: String): Quaternion = when (value) {
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"i" -> i
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"j" -> j
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"k" -> k
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else -> super<Field>.symbol(value)
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}
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}
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/**
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* Represents `double`-based quaternion.
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*
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* @property w The first component.
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* @property x The second component.
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* @property y The third component.
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* @property z The fourth component.
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*/
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public data class Quaternion(val w: Double, val x: Double, val y: Double, val z: Double) :
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FieldElement<Quaternion, Quaternion, QuaternionField>,
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Comparable<Quaternion> {
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public constructor(w: Number, x: Number, y: Number, z: Number) : this(
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w.toDouble(),
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x.toDouble(),
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y.toDouble(),
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z.toDouble()
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)
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public constructor(wx: Complex, yz: Complex) : this(wx.re, wx.im, yz.re, yz.im)
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public override val context: QuaternionField
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get() = QuaternionField
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public override fun div(k: Number): Quaternion {
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val d = k.toDouble()
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return Quaternion(w / d, x / d, y / d, z / d)
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}
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public override fun unwrap(): Quaternion = this
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public override fun Quaternion.wrap(): Quaternion = this
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public override fun compareTo(other: Quaternion): Int = r.compareTo(other.r)
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public override fun toString(): String = "($w + $x * i + $y * j + $z * k)"
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public companion object : MemorySpec<Quaternion> {
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public override val objectSize: Int
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get() = 32
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public override fun MemoryReader.read(offset: Int): Quaternion =
|
||||
Quaternion(readDouble(offset), readDouble(offset + 8), readDouble(offset + 16), readDouble(offset + 24))
|
||||
|
||||
public override fun MemoryWriter.write(offset: Int, value: Quaternion) {
|
||||
writeDouble(offset, value.w)
|
||||
writeDouble(offset + 8, value.x)
|
||||
writeDouble(offset + 16, value.y)
|
||||
writeDouble(offset + 24, value.z)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Creates a quaternion with real part equal to this real.
|
||||
*
|
||||
* @receiver the real part.
|
||||
* @return the new quaternion.
|
||||
*/
|
||||
public fun Number.toQuaternion(): Quaternion = Quaternion(this, 0, 0, 0)
|
||||
|
||||
/**
|
||||
* Creates a new buffer of quaternions with the specified [size], where each element is calculated by calling the
|
||||
* specified [init] function.
|
||||
*/
|
||||
public inline fun Buffer.Companion.quaternion(size: Int, init: (Int) -> Quaternion): Buffer<Quaternion> =
|
||||
MemoryBuffer.create(Quaternion, size, init)
|
||||
|
||||
/**
|
||||
* Creates a new buffer of quaternions with the specified [size], where each element is calculated by calling the
|
||||
* specified [init] function.
|
||||
*/
|
||||
public inline fun MutableBuffer.Companion.quaternion(size: Int, init: (Int) -> Quaternion): MutableBuffer<Quaternion> =
|
||||
MutableMemoryBuffer.create(Quaternion, size, init)
|
||||
Loading…
Reference in New Issue
Block a user