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Prototype of generic complex numbers

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This commit is contained in:
Iaroslav Postovalov 2021-03-16 23:17:54 +07:00
parent c377d6cda8
commit 0e89e783fd
35 changed files with 917 additions and 788 deletions
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22
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
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@ -20,9 +20,9 @@ import java.math.BigInteger
internal class BigIntBenchmark {
val kmNumber = BigIntField.number(Int.MAX_VALUE)
val jvmNumber = JBigIntegerField.number(Int.MAX_VALUE)
val jvmNumber = JBigIntegerRing.number(Int.MAX_VALUE)
val largeKmNumber = BigIntField { number(11).pow(100_000U) }
val largeJvmNumber: BigInteger = JBigIntegerField { number(11).pow(100_000) }
val largeJvmNumber: BigInteger = JBigIntegerRing { number(11).pow(100_000) }
val bigExponent = 50_000
@Benchmark
@ -31,7 +31,7 @@ internal class BigIntBenchmark {
}
@Benchmark
fun jvmAdd(blackhole: Blackhole) = JBigIntegerField {
fun jvmAdd(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume(jvmNumber + jvmNumber + jvmNumber)
}
@ -41,7 +41,7 @@ internal class BigIntBenchmark {
}
@Benchmark
fun jvmAddLarge(blackhole: Blackhole) = JBigIntegerField {
fun jvmAddLarge(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume(largeJvmNumber + largeJvmNumber + largeJvmNumber)
}
@ -56,12 +56,12 @@ internal class BigIntBenchmark {
}
@Benchmark
fun jvmMultiply(blackhole: Blackhole) = JBigIntegerField {
fun jvmMultiply(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume(jvmNumber * jvmNumber * jvmNumber)
}
@Benchmark
fun jvmMultiplyLarge(blackhole: Blackhole) = JBigIntegerField {
fun jvmMultiplyLarge(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume(largeJvmNumber*largeJvmNumber)
}
@ -71,27 +71,27 @@ internal class BigIntBenchmark {
}
@Benchmark
fun jvmPower(blackhole: Blackhole) = JBigIntegerField {
fun jvmPower(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume(jvmNumber.pow(bigExponent))
}
@Benchmark
fun kmParsing16(blackhole: Blackhole) = JBigIntegerField {
fun kmParsing16(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume("0x7f57ed8b89c29a3b9a85c7a5b84ca3929c7b7488593".parseBigInteger())
}
@Benchmark
fun kmParsing10(blackhole: Blackhole) = JBigIntegerField {
fun kmParsing10(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume("236656783929183747565738292847574838922010".parseBigInteger())
}
@Benchmark
fun jvmParsing10(blackhole: Blackhole) = JBigIntegerField {
fun jvmParsing10(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume("236656783929183747565738292847574838922010".toBigInteger(10))
}
@Benchmark
fun jvmParsing16(blackhole: Blackhole) = JBigIntegerField {
fun jvmParsing16(blackhole: Blackhole) = JBigIntegerRing {
blackhole.consume("7f57ed8b89c29a3b9a85c7a5b84ca3929c7b7488593".toBigInteger(16))
}
}

5
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BufferBenchmark.kt
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@ -17,7 +17,7 @@ import space.kscience.kmath.structures.MutableBuffer
internal class BufferBenchmark {
@Benchmark
fun genericDoubleBufferReadWrite() {
val buffer = DoubleBuffer(size) { it.toDouble() }
val buffer = DoubleBuffer(size, Int::toDouble)
(0 until size).forEach {
buffer[it]
@ -26,7 +26,8 @@ internal class BufferBenchmark {
@Benchmark
fun complexBufferReadWrite() {
val buffer = MutableBuffer.complex(size / 2) { Complex(it.toDouble(), -it.toDouble()) }
val buffer =
MutableBuffer.complex(MutableBuffer.Companion::double, size / 2) { Complex(it.toDouble(), -it.toDouble()) }
(0 until size / 2).forEach {
buffer[it]

2
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
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@ -47,7 +47,7 @@ internal class NDFieldBenchmark {
private const val dim = 1000
private const val n = 100
private val autoField = AlgebraND.auto(DoubleField, dim, dim)
private val specializedField = AlgebraND.real(dim, dim)
private val specializedField = AlgebraND.double(dim, dim)
private val genericField = AlgebraND.field(DoubleField, Buffer.Companion::boxing, dim, dim)
}
}

4
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt
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@ -13,7 +13,7 @@ import org.jetbrains.bio.viktor.F64Array
import space.kscience.kmath.nd.AlgebraND
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.auto
import space.kscience.kmath.nd.real
import space.kscience.kmath.nd.double
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.viktor.ViktorNDField
@ -60,7 +60,7 @@ internal class ViktorBenchmark {
// automatically build context most suited for given type.
private val autoField = AlgebraND.auto(DoubleField, dim, dim)
private val realField = AlgebraND.real(dim, dim)
private val realField = AlgebraND.double(dim, dim)
private val viktorField = ViktorNDField(dim, dim)
}
}

4
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
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@ -12,7 +12,7 @@ import kotlinx.benchmark.State
import org.jetbrains.bio.viktor.F64Array
import space.kscience.kmath.nd.AlgebraND
import space.kscience.kmath.nd.auto
import space.kscience.kmath.nd.real
import space.kscience.kmath.nd.double
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.viktor.ViktorFieldND
@ -52,7 +52,7 @@ internal class ViktorLogBenchmark {
// automatically build context most suited for given type.
private val autoField = AlgebraND.auto(DoubleField, dim, dim)
private val realNdField = AlgebraND.real(dim, dim)
private val realNdField = AlgebraND.double(dim, dim)
private val viktorField = ViktorFieldND(intArrayOf(dim, dim))
}
}

5
examples/src/main/kotlin/space/kscience/kmath/operations/ComplexDemo.kt
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@ -8,16 +8,17 @@ package space.kscience.kmath.operations
import space.kscience.kmath.complex.Complex
import space.kscience.kmath.complex.complex
import space.kscience.kmath.nd.AlgebraND
import space.kscience.kmath.nd.double
fun main() {
// 2d element
val element = AlgebraND.complex(2, 2).produce { (i, j) ->
val element = AlgebraND.double(2, 2).complex().produce { (i, j) ->
Complex(i.toDouble() - j.toDouble(), i.toDouble() + j.toDouble())
}
println(element)
// 1d element operation
val result = with(AlgebraND.complex(8)) {
val result = with(AlgebraND.double(8).complex()) {
val a = produce { (it) -> i * it - it.toDouble() }
val b = 3
val c = Complex(1.0, 1.0)

22
examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
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@ -12,19 +12,19 @@ import space.kscience.kmath.linear.transpose
import space.kscience.kmath.nd.AlgebraND
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.as2D
import space.kscience.kmath.nd.real
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.nd.double
import space.kscience.kmath.operations.*
import kotlin.system.measureTimeMillis
fun main() {
val dim = 1000
val n = 1000
val realField = AlgebraND.real(dim, dim)
val complexField: ComplexFieldND = AlgebraND.complex(dim, dim)
val doubleField = AlgebraND.double(dim, dim)
val complexField = doubleField.complex()
val realTime = measureTimeMillis {
realField {
doubleField {
var res: StructureND<Double> = one
repeat(n) {
res += 1.0
@ -36,9 +36,9 @@ fun main() {
val complexTime = measureTimeMillis {
complexField {
var res: StructureND<Complex> = one
var res: StructureND<Complex<Double>> = one
repeat(n) {
res += 1.0
res += Complex(1.0, 0.0)
}
}
}
@ -48,18 +48,16 @@ fun main() {
fun complexExample() {
//Create a context for 2-d structure with complex values
ComplexField {
nd(4, 8) {
AlgebraND.double(4, 8).complex().run {
//a constant real-valued structure
val x = one * 2.5
operator fun Number.plus(other: Complex) = Complex(this.toDouble() + other.re, other.im)
operator fun Number.plus(other: Complex<Double>) = Complex(toDouble() + other.re, other.im)
//a structure generator specific to this context
val matrix = produce { (k, l) -> k + l * i }
//Perform sum
val sum = matrix + x + 1.0
val sum = matrix + x + Complex(1.0,0.0)
//Represent the sum as 2d-structure and transpose
sum.as2D().transpose()
}
}
}

4
examples/src/main/kotlin/space/kscience/kmath/structures/NDField.kt
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@ -32,8 +32,8 @@ fun main() {
// automatically build context most suited for given type.
val autoField = AlgebraND.auto(DoubleField, dim, dim)
// specialized nd-field for Double. It works as generic Double field as well.
val realField = AlgebraND.real(dim, dim)
// specialized nd-field for Double. It works as generic Double field as well
val realField = AlgebraND.double(dim, dim)
//A generic boxing field. It should be used for objects, not primitives.
val boxingField = AlgebraND.field(DoubleField, Buffer.Companion::boxing, dim, dim)
// Nd4j specialized field.

7
kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/TestParser.kt
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@ -6,6 +6,7 @@
package space.kscience.kmath.ast
import space.kscience.kmath.complex.Complex
import space.kscience.kmath.complex.ComplexDoubleField
import space.kscience.kmath.complex.ComplexField
import space.kscience.kmath.expressions.evaluate
import space.kscience.kmath.operations.Algebra
@ -17,15 +18,15 @@ internal class TestParser {
@Test
fun evaluateParsedMst() {
val mst = "2+2*(2+2)".parseMath()
val res = ComplexField.evaluate(mst)
val res = ComplexDoubleField.evaluate(mst)
assertEquals(Complex(10.0, 0.0), res)
}
@Test
fun evaluateMstSymbol() {
val mst = "i".parseMath()
val res = ComplexField.evaluate(mst)
assertEquals(ComplexField.i, res)
val res = ComplexDoubleField.evaluate(mst)
assertEquals(ComplexDoubleField.i, res)
}

17
kmath-commons/src/main/kotlin/space/kscience/kmath/commons/transform/Transformations.kt
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@ -15,12 +15,11 @@ import space.kscience.kmath.streaming.spread
import space.kscience.kmath.structures.*
/**
* Streaming and buffer transformations
*/
public object Transformations {
private fun Buffer<Complex>.toArray(): Array<org.apache.commons.math3.complex.Complex> =
private fun Buffer<Complex<Double>>.toArray(): Array<org.apache.commons.math3.complex.Complex> =
Array(size) { org.apache.commons.math3.complex.Complex(get(it).re, get(it).im) }
private fun Buffer<Double>.asArray() = if (this is DoubleBuffer) {
@ -40,14 +39,14 @@ public object Transformations {
public fun fourier(
normalization: DftNormalization = DftNormalization.STANDARD,
direction: TransformType = TransformType.FORWARD,
): SuspendBufferTransform<Complex, Complex> = {
): SuspendBufferTransform<Complex<Double>, Complex<Double>> = {
FastFourierTransformer(normalization).transform(it.toArray(), direction).asBuffer()
}
public fun realFourier(
normalization: DftNormalization = DftNormalization.STANDARD,
direction: TransformType = TransformType.FORWARD,
): SuspendBufferTransform<Double, Complex> = {
): SuspendBufferTransform<Double, Complex<Double>> = {
FastFourierTransformer(normalization).transform(it.asArray(), direction).asBuffer()
}
@ -76,10 +75,10 @@ public object Transformations {
* Process given [Flow] with commons-math fft transformation
*/
@FlowPreview
public fun Flow<Buffer<Complex>>.FFT(
public fun Flow<Buffer<Complex<Double>>>.FFT(
normalization: DftNormalization = DftNormalization.STANDARD,
direction: TransformType = TransformType.FORWARD,
): Flow<Buffer<Complex>> {
): Flow<Buffer<Complex<Double>>> {
val transform = Transformations.fourier(normalization, direction)
return map { transform(it) }
}
@ -89,7 +88,7 @@ public fun Flow<Buffer<Complex>>.FFT(
public fun Flow<Buffer<Double>>.FFT(
normalization: DftNormalization = DftNormalization.STANDARD,
direction: TransformType = TransformType.FORWARD,
): Flow<Buffer<Complex>> {
): Flow<Buffer<Complex<Double>>> {
val transform = Transformations.realFourier(normalization, direction)
return map(transform)
}
@ -103,10 +102,10 @@ public fun Flow<Double>.FFT(
bufferSize: Int = Int.MAX_VALUE,
normalization: DftNormalization = DftNormalization.STANDARD,
direction: TransformType = TransformType.FORWARD,
): Flow<Complex> = chunked(bufferSize).FFT(normalization, direction).spread()
): Flow<Complex<Double>> = chunked(bufferSize).FFT(normalization, direction).spread()
/**
* Map a complex flow into real flow by taking real part of each number
*/
@FlowPreview
public fun Flow<Complex>.real(): Flow<Double> = map { it.re }
public fun Flow<Complex<Double>>.real(): Flow<Double> = map { it.re }

365
kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
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@ -5,223 +5,248 @@
package space.kscience.kmath.complex
import space.kscience.kmath.memory.MemoryReader
import space.kscience.kmath.memory.MemorySpec
import space.kscience.kmath.memory.MemoryWriter
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.ExtendedField
import space.kscience.kmath.operations.Norm
import space.kscience.kmath.operations.NumbersAddOperations
import space.kscience.kmath.operations.ScaleOperations
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.MemoryBuffer
import space.kscience.kmath.structures.MutableBuffer
import space.kscience.kmath.structures.MutableMemoryBuffer
import kotlin.math.*
import space.kscience.kmath.operations.*
import kotlin.js.JsName
import kotlin.jvm.JvmName
/**
* Represents generic complex value consisting of real and imaginary part.
*
* @param T the type of components.
* @property re The real component.
* @property im The imaginary component.
*/
public data class Complex<out T : Any>(public val re: T, public val im: T) {
/**
* Converts this complex number to string formatted like `[re] + i * [im]`.
*/
override fun toString(): String = "$re + i * $im"
}
/**
* The algebra of [Complex].
*
* @param T the type of components.
* @property algebra the algebra over [T].
*/
public open class ComplexAlgebra<T : Any>(public open val algebra: NumericAlgebra<T>) : NumericAlgebra<Complex<T>> {
/**
* The imaginary unit.
*/
public open val i: Complex<T> by lazy {
algebra { Complex(number(0), number(1)) }
}
override fun number(value: Number): Complex<T> =
algebra { Complex(algebra.number(value), algebra.number(0)) }
override fun bindSymbol(value: String): Complex<T> = if (value == "i") i else super.bindSymbol(value)
}
/**
* The group of [Complex].
*
* @param T the type of components.
*/
public open class ComplexGroup<T : Any, out A>(override val algebra: A) : ComplexAlgebra<T>(algebra),
Group<Complex<T>> where A : NumericAlgebra<T>, A : Group<T> {
override val zero: Complex<T> by lazy {
algebra { Complex(zero, zero) }
}
/**
* This complex's conjugate.
*/
public val Complex.conjugate: Complex
get() = Complex(re, -im)
public val Complex<T>.conjugate: Complex<T>
get() = Complex(re, algebra { -im })
override fun add(a: Complex<T>, b: Complex<T>): Complex<T> = algebra { Complex(a.re + b.re, a.im + b.im) }
override fun Complex<T>.unaryMinus(): Complex<T> = algebra { Complex(-re, -im) }
@JsName("unaryMinus_T")
public operator fun T.unaryMinus(): Complex<T> = algebra { Complex(-this@unaryMinus, zero) }
@JsName("unaryPlus_T")
public operator fun T.unaryPlus(): Complex<T> = algebra { Complex(this@unaryPlus, zero) }
public operator fun T.plus(b: Complex<T>): Complex<T> = add(+this, b)
public operator fun Complex<T>.plus(b: T): Complex<T> = add(this, +b)
public operator fun T.minus(b: Complex<T>): Complex<T> = add(+this, -b)
public operator fun Complex<T>.minus(b: T): Complex<T> = add(this, -b)
}
/**
* The ring of [Complex].
*
* @param T the type of components.
*/
public open class ComplexRing<T : Any, out A>(override val algebra: A) : ComplexGroup<T, A>(algebra),
Ring<Complex<T>> where A : NumericAlgebra<T>, A : Ring<T> {
override val one: Complex<T> by lazy {
algebra { Complex(one, zero) }
}
override val i: Complex<T> by lazy {
algebra { Complex(zero, one) }
}
override fun multiply(a: Complex<T>, b: Complex<T>): Complex<T> =
algebra { Complex(a.re * b.re - a.im * b.im, a.im * b.re + a.re * b.im) }
public operator fun T.times(b: Complex<T>): Complex<T> = multiply(+this, b)
public operator fun Complex<T>.times(b: T): Complex<T> = multiply(this, +b)
}
/**
* [ComplexRing] instance for [ByteRing].
*/
public val ComplexByteRing: ComplexRing<Byte, ByteRing> = ComplexRing(ByteRing)
/**
* [ComplexRing] instance for [ShortRing].
*/
public val ComplexShortRing: ComplexRing<Short, ShortRing> = ComplexRing(ShortRing)
/**
* [ComplexRing] instance for [IntRing].
*/
public val ComplexIntRing: ComplexRing<Int, IntRing> = ComplexRing(IntRing)
/**
* [ComplexRing] instance for [LongRing].
*/
public val ComplexLongRing: ComplexRing<Long, LongRing> = ComplexRing(LongRing)
/**
* The field of [Complex].
*/
public open class ComplexField<T : Any, out A>(override val algebra: A) : ComplexRing<T, A>(algebra),
Field<Complex<T>> where A : Field<T> {
/**
* This complex's reciprocal.
*/
public val Complex.reciprocal: Complex
get() {
public val Complex<T>.reciprocal: Complex<T>
get() = algebra {
val scale = re * re + im * im
return Complex(re / scale, -im / scale)
Complex(re / scale, -im / scale)
}
/**
* Absolute value of complex number.
*/
public val Complex.r: Double
get() = sqrt(re * re + im * im)
override fun divide(a: Complex<T>, b: Complex<T>): Complex<T> = a * b.reciprocal
/**
* An angle between vector represented by complex number and X axis.
*/
public val Complex.theta: Double
get() = atan(im / re)
override fun number(value: Number): Complex<T> = super<ComplexRing>.number(value)
private val PI_DIV_2 = Complex(PI / 2, 0)
override fun scale(a: Complex<T>, value: Double): Complex<T> =
algebra { Complex(a.re * value, a.im * value) }
/**
* A field of [Complex].
*/
@OptIn(UnstableKMathAPI::class)
public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex>, NumbersAddOperations<Complex>,
ScaleOperations<Complex> {
override val zero: Complex = 0.0.toComplex()
override val one: Complex = 1.0.toComplex()
override operator fun Complex<T>.div(k: Number): Complex<T> =
algebra { Complex(re / k.toDouble(), im / k.toDouble()) }
/**
* The imaginary unit.
*/
public val i: Complex by lazy { Complex(0.0, 1.0) }
public operator fun T.div(b: Complex<T>): Complex<T> = divide(+this, b)
public operator fun Complex<T>.div(b: T): Complex<T> = divide(this, +b)
override fun Complex.unaryMinus(): Complex = Complex(-re, -im)
override fun number(value: Number): Complex = Complex(value.toDouble(), 0.0)
override fun scale(a: Complex, value: Double): Complex = Complex(a.re * value, a.im * value)
override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
// override fun multiply(a: Complex, k: Number): Complex = Complex(a.re * k.toDouble(), a.im * k.toDouble())
override fun multiply(a: Complex, b: Complex): Complex =
Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
override fun divide(a: Complex, b: Complex): Complex = when {
abs(b.im) < abs(b.re) -> {
val wr = b.im / b.re
val wd = b.re + wr * b.im
if (wd.isNaN() || wd == 0.0)
throw ArithmeticException("Division by zero or infinity")
else
Complex((a.re + a.im * wr) / wd, (a.im - a.re * wr) / wd)
@JsName("scale_T")
public fun scale(a: T, value: Double): Complex<T> = scale(+a, value)
}
b.im == 0.0 -> throw ArithmeticException("Division by zero")
else -> {
val wr = b.re / b.im
val wd = b.im + wr * b.re
/**
* [ComplexRing] instance for [BigIntField].
*/
public val ComplexBigIntField: ComplexField<BigInt, BigIntField> = ComplexField(BigIntField)
if (wd.isNaN() || wd == 0.0)
throw ArithmeticException("Division by zero or infinity")
else
Complex((a.re * wr + a.im) / wd, (a.im * wr - a.re) / wd)
}
}
override operator fun Complex.div(k: Number): Complex = Complex(re / k.toDouble(), im / k.toDouble())
/**
* The extended field of Complex.
*/
public open class ComplexExtendedField<T : Any, out A>(override val algebra: A) : ComplexField<T, A>(algebra),
ExtendedField<Complex<T>>, Norm<Complex<T>, T> where A : ExtendedField<T> {
private val two by lazy { one + one }
override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2.0
override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2.0
/**
* The *r* component of the polar form of this number.
*/
public val Complex<T>.r: T
get() = norm(this)
override fun tan(arg: Complex): Complex {
/**
* The *&theta;* component of the polar form of this number.
*/
public val Complex<T>.theta: T
get() = algebra { atan(im / re) }
override fun bindSymbol(value: String): Complex<T> =
if (value == "i") i else super<ExtendedField>.bindSymbol(value)
override fun sin(arg: Complex<T>): Complex<T> = i * (exp(-i * arg) - exp(i * arg)) / two
override fun cos(arg: Complex<T>): Complex<T> = (exp(-i * arg) + exp(i * arg)) / two
override fun tan(arg: Complex<T>): Complex<T> {
val e1 = exp(-i * arg)
val e2 = exp(i * arg)
return i * (e1 - e2) / (e1 + e2)
}
override fun asin(arg: Complex): Complex = -i * ln(sqrt(1 - (arg * arg)) + i * arg)
override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(1 - (arg * arg)) + i * arg)
override fun asin(arg: Complex<T>): Complex<T> = -i * ln(sqrt(one - (arg * arg)) + i * arg)
override fun acos(arg: Complex<T>): Complex<T> =
(pi / two) + i * ln(sqrt(one - (arg * arg)) + i * arg)
override fun atan(arg: Complex): Complex {
override fun atan(arg: Complex<T>): Complex<T> = algebra {
val iArg = i * arg
return i * (ln(1 - iArg) - ln(1 + iArg)) / 2
return i * (ln(this@ComplexExtendedField.one - iArg) - ln(this@ComplexExtendedField.one + iArg)) / 2
}
override fun power(arg: Complex, pow: Number): Complex = if (arg.im == 0.0)
arg.re.pow(pow.toDouble()).toComplex()
override fun power(arg: Complex<T>, pow: Number): Complex<T> = algebra {
if (arg.im == 0.0)
Complex(arg.re.pow(pow.toDouble()), algebra.zero)
else
exp(pow * ln(arg))
}
override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im))
override fun exp(arg: Complex<T>): Complex<T> =
Complex(algebra.exp(arg.re), algebra.zero) * Complex(algebra.cos(arg.im), algebra.sin(arg.im))
override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)
override fun ln(arg: Complex<T>): Complex<T> = algebra { Complex(ln(norm(arg)), atan(arg.im / arg.re)) }
override fun norm(arg: Complex<T>): T = algebra { sqrt(arg.re * arg.re + arg.im * arg.im) }
/**
* Adds complex number to real one.
*
* @receiver the augend.
* @param c the addend.
* @return the sum.
*/
public operator fun Double.plus(c: Complex): Complex = add(this.toComplex(), c)
@JsName("norm_T_3")
@JvmName("norm\$T")
public fun norm(arg: T): T = algebra { sqrt(arg * arg) }
/**
* Subtracts complex number from real one.
*
* @receiver the minuend.
* @param c the subtrahend.
* @return the difference.
*/
public operator fun Double.minus(c: Complex): Complex = add(this.toComplex(), -c)
@JsName("sin_T")
public fun sin(arg: T): Complex<T> = sin(+arg)
/**
* Adds real number to complex one.
*
* @receiver the augend.
* @param d the addend.
* @return the sum.
*/
public operator fun Complex.plus(d: Double): Complex = d + this
@JsName("cos_T")
public fun cos(arg: T): Complex<T> = cos(+arg)
/**
* Subtracts real number from complex one.
*
* @receiver the minuend.
* @param d the subtrahend.
* @return the difference.
*/
public operator fun Complex.minus(d: Double): Complex = add(this, -d.toComplex())
@JsName("tan_T")
public fun tan(arg: T): Complex<T> = tan(+arg)
/**
* Multiplies real number by complex one.
*
* @receiver the multiplier.
* @param c the multiplicand.
* @receiver the product.
*/
public operator fun Double.times(c: Complex): Complex = Complex(c.re * this, c.im * this)
@JsName("asin_T")
public fun asin(arg: T): Complex<T> = asin(+arg)
override fun norm(arg: Complex): Complex = sqrt(arg.conjugate * arg)
@JsName("acos_T")
public fun acos(arg: T): Complex<T> = acos(+arg)
override fun bindSymbolOrNull(value: String): Complex? = if (value == "i") i else null
@JsName("atan_T")
public fun atan(arg: T): Complex<T> = atan(+arg)
@JsName("power_T")
public fun power(arg: T, pow: Number): Complex<T> = power(+arg, pow)
@JsName("exp_T")
public fun exp(arg: T): Complex<T> = exp(+arg)
@JsName("ln_T")
public fun ln(arg: T): Complex<T> = ln(+arg)
}
/**
* Represents `double`-based complex number.
*
* @property re The real part.
* @property im The imaginary part.
* [ComplexRing] instance for [DoubleField].
*/
@OptIn(UnstableKMathAPI::class)
public data class Complex(val re: Double, val im: Double) {
public constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble())
public constructor(re: Number) : this(re.toDouble(), 0.0)
override fun toString(): String = "($re + i * $im)"
public companion object : MemorySpec<Complex> {
override val objectSize: Int
get() = 16
override fun MemoryReader.read(offset: Int): Complex =
Complex(readDouble(offset), readDouble(offset + 8))
override fun MemoryWriter.write(offset: Int, value: Complex) {
writeDouble(offset, value.re)
writeDouble(offset + 8, value.im)
}
}
}
public val ComplexDoubleField: ComplexExtendedField<Double, DoubleField> = ComplexExtendedField(DoubleField)
/**
* Creates a complex number with real part equal to this real.
*
* @receiver the real part.
* @return the new complex number.
* [ComplexRing] instance for [FloatField].
*/
public fun Number.toComplex(): Complex = Complex(this)
/**
* Creates a new buffer of complex numbers with the specified [size], where each element is calculated by calling the
* specified [init] function.
*/
public inline fun Buffer.Companion.complex(size: Int, init: (Int) -> Complex): Buffer<Complex> =
MemoryBuffer.create(Complex, size, init)
/**
* Creates a new buffer of complex numbers with the specified [size], where each element is calculated by calling the
* specified [init] function.
*/
public inline fun MutableBuffer.Companion.complex(size: Int, init: (Int) -> Complex): MutableBuffer<Complex> =
MutableMemoryBuffer.create(Complex, size, init)
public val ComplexFloatField: ComplexExtendedField<Double, DoubleField> = ComplexExtendedField(DoubleField)

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/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.nd.AlgebraND
import space.kscience.kmath.nd.BufferND
import space.kscience.kmath.nd.BufferedFieldND
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.operations.ExtendedField
import space.kscience.kmath.operations.NumbersAddOperations
import space.kscience.kmath.structures.Buffer
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
/**
* An optimized nd-field for complex numbers
*/
@OptIn(UnstableKMathAPI::class)
public class ComplexFieldND(
shape: IntArray,
) : BufferedFieldND<Complex, ComplexField>(shape, ComplexField, Buffer.Companion::complex),
NumbersAddOperations<StructureND<Complex>>,
ExtendedField<StructureND<Complex>> {
override val zero: BufferND<Complex> by lazy { produce { zero } }
override val one: BufferND<Complex> by lazy { produce { one } }
override fun number(value: Number): BufferND<Complex> {
val d = value.toComplex() // minimize conversions
return produce { d }
}
//
// @Suppress("OVERRIDE_BY_INLINE")
// override inline fun map(
// arg: AbstractNDBuffer<Double>,
// transform: DoubleField.(Double) -> Double,
// ): RealNDElement {
// check(arg)
// val array = RealBuffer(arg.strides.linearSize) { offset -> DoubleField.transform(arg.buffer[offset]) }
// return BufferedNDFieldElement(this, array)
// }
//
// @Suppress("OVERRIDE_BY_INLINE")
// override inline fun produce(initializer: DoubleField.(IntArray) -> Double): RealNDElement {
// val array = RealBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
// return BufferedNDFieldElement(this, array)
// }
//
// @Suppress("OVERRIDE_BY_INLINE")
// override inline fun mapIndexed(
// arg: AbstractNDBuffer<Double>,
// transform: DoubleField.(index: IntArray, Double) -> Double,
// ): RealNDElement {
// check(arg)
// return BufferedNDFieldElement(
// this,
// RealBuffer(arg.strides.linearSize) { offset ->
// elementContext.transform(
// arg.strides.index(offset),
// arg.buffer[offset]
// )
// })
// }
//
// @Suppress("OVERRIDE_BY_INLINE")
// override inline fun combine(
// a: AbstractNDBuffer<Double>,
// b: AbstractNDBuffer<Double>,
// transform: DoubleField.(Double, Double) -> Double,
// ): RealNDElement {
// check(a, b)
// val buffer = RealBuffer(strides.linearSize) { offset ->
// elementContext.transform(a.buffer[offset], b.buffer[offset])
// }
// return BufferedNDFieldElement(this, buffer)
// }
override fun power(arg: StructureND<Complex>, pow: Number): BufferND<Complex> = arg.map { power(it, pow) }
override fun exp(arg: StructureND<Complex>): BufferND<Complex> = arg.map { exp(it) }
override fun ln(arg: StructureND<Complex>): BufferND<Complex> = arg.map { ln(it) }
override fun sin(arg: StructureND<Complex>): BufferND<Complex> = arg.map { sin(it) }
override fun cos(arg: StructureND<Complex>): BufferND<Complex> = arg.map { cos(it) }
override fun tan(arg: StructureND<Complex>): BufferND<Complex> = arg.map { tan(it) }
override fun asin(arg: StructureND<Complex>): BufferND<Complex> = arg.map { asin(it) }
override fun acos(arg: StructureND<Complex>): BufferND<Complex> = arg.map { acos(it) }
override fun atan(arg: StructureND<Complex>): BufferND<Complex> = arg.map { atan(it) }
override fun sinh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { sinh(it) }
override fun cosh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { cosh(it) }
override fun tanh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { tanh(it) }
override fun asinh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { asinh(it) }
override fun acosh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { acosh(it) }
override fun atanh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { atanh(it) }
}
/**
* Fast element production using function inlining
*/
public inline fun BufferedFieldND<Complex, ComplexField>.produceInline(initializer: ComplexField.(Int) -> Complex): BufferND<Complex> {
contract { callsInPlace(initializer, InvocationKind.EXACTLY_ONCE) }
val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.initializer(offset) }
return BufferND(strides, buffer)
}
public fun AlgebraND.Companion.complex(vararg shape: Int): ComplexFieldND = ComplexFieldND(shape)
/**
* Produce a context for n-dimensional operations inside this real field
*/
public inline fun <R> ComplexField.nd(vararg shape: Int, action: ComplexFieldND.() -> R): R {
contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
return ComplexFieldND(shape).action()
}

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/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.memory.MemoryReader
import space.kscience.kmath.memory.MemorySpec
import space.kscience.kmath.memory.MemoryWriter
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.*
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.MemoryBuffer
import space.kscience.kmath.structures.MutableBuffer
import space.kscience.kmath.structures.MutableMemoryBuffer
import kotlin.math.*
/**
* This quaternion's conjugate.
*/
@UnstableKMathAPI
public val DoubleQuaternion.conjugate: DoubleQuaternion
get() = DoubleQuaternionField { z - x * i - y * j - z * k }
/**
* This quaternion's reciprocal.
*/
@UnstableKMathAPI
public val DoubleQuaternion.reciprocal: DoubleQuaternion
get() = DoubleQuaternionField {
val n = norm(this@reciprocal)
return conjugate / (n * n)
}
/**
* Absolute value of the quaternion.
*/
@UnstableKMathAPI
public val DoubleQuaternion.r: Double
get() = sqrt(w * w + x * x + y * y + z * z)
/**
* A field of [DoubleQuaternion].
*/
@UnstableKMathAPI
public object DoubleQuaternionField : Field<DoubleQuaternion>, Norm<DoubleQuaternion, DoubleQuaternion>,
PowerOperations<DoubleQuaternion>,
ExponentialOperations<DoubleQuaternion>, NumbersAddOperations<DoubleQuaternion>, ScaleOperations<DoubleQuaternion> {
override val zero: DoubleQuaternion = DoubleQuaternion(0)
override val one: DoubleQuaternion = DoubleQuaternion(1)
/**
* The `i` quaternion unit.
*/
public val i: DoubleQuaternion = DoubleQuaternion(0, 1)
/**
* The `j` quaternion unit.
*/
public val j: DoubleQuaternion = DoubleQuaternion(0, 0, 1)
/**
* The `k` quaternion unit.
*/
public val k: DoubleQuaternion = DoubleQuaternion(0, 0, 0, 1)
override fun add(a: DoubleQuaternion, b: DoubleQuaternion): DoubleQuaternion =
DoubleQuaternion(a.w + b.w, a.x + b.x, a.y + b.y, a.z + b.z)
override fun scale(a: DoubleQuaternion, value: Double): DoubleQuaternion =
DoubleQuaternion(a.w * value, a.x * value, a.y * value, a.z * value)
override fun multiply(a: DoubleQuaternion, b: DoubleQuaternion): DoubleQuaternion = DoubleQuaternion(
a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z,
a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x,
a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w,
)
override fun divide(a: DoubleQuaternion, b: DoubleQuaternion): DoubleQuaternion {
val s = b.w * b.w + b.x * b.x + b.y * b.y + b.z * b.z
return DoubleQuaternion(
(b.w * a.w + b.x * a.x + b.y * a.y + b.z * a.z) / s,
(b.w * a.x - b.x * a.w - b.y * a.z + b.z * a.y) / s,
(b.w * a.y + b.x * a.z - b.y * a.w - b.z * a.x) / s,
(b.w * a.z - b.x * a.y + b.y * a.x - b.z * a.w) / s,
)
}
override fun power(arg: DoubleQuaternion, pow: Number): DoubleQuaternion {
if (pow is Int) return pwr(arg, pow)
if (floor(pow.toDouble()) == pow.toDouble()) return pwr(arg, pow.toInt())
return exp(pow * ln(arg))
}
private fun pwr(x: DoubleQuaternion, a: Int): DoubleQuaternion = when {
a < 0 -> -(pwr(x, -a))
a == 0 -> one
a == 1 -> x
a == 2 -> pwr2(x)
a == 3 -> pwr3(x)
a == 4 -> pwr4(x)
else -> {
val x4 = pwr4(x)
var y = x4
repeat((1 until a / 4).count()) { y *= x4 }
if (a % 4 == 3) y *= pwr3(x)
if (a % 4 == 2) y *= pwr2(x)
if (a % 4 == 1) y *= x
y
}
}
private fun pwr2(x: DoubleQuaternion): DoubleQuaternion {
val aa = 2 * x.w
return DoubleQuaternion(x.w * x.w - (x.x * x.x + x.y * x.y + x.z * x.z), aa * x.x, aa * x.y, aa * x.z)
}
private fun pwr3(x: DoubleQuaternion): DoubleQuaternion {
val a2 = x.w * x.w
val n1 = x.x * x.x + x.y * x.y + x.z * x.z
val n2 = 3.0 * a2 - n1
return DoubleQuaternion(x.w * (a2 - 3 * n1), x.x * n2, x.y * n2, x.z * n2)
}
private fun pwr4(x: DoubleQuaternion): DoubleQuaternion {
val a2 = x.w * x.w
val n1 = x.x * x.x + x.y * x.y + x.z * x.z
val n2 = 4 * x.w * (a2 - n1)
return DoubleQuaternion(a2 * a2 - 6 * a2 * n1 + n1 * n1, x.x * n2, x.y * n2, x.z * n2)
}
override fun exp(arg: DoubleQuaternion): DoubleQuaternion {
val un = arg.x * arg.x + arg.y * arg.y + arg.z * arg.z
if (un == 0.0) return DoubleQuaternion(exp(arg.w))
val n1 = sqrt(un)
val ea = exp(arg.w)
val n2 = ea * sin(n1) / n1
return DoubleQuaternion(ea * cos(n1), n2 * arg.x, n2 * arg.y, n2 * arg.z)
}
override fun ln(arg: DoubleQuaternion): DoubleQuaternion {
val nu2 = arg.x * arg.x + arg.y * arg.y + arg.z * arg.z
if (nu2 == 0.0)
return if (arg.w > 0)
DoubleQuaternion(ln(arg.w), 0, 0, 0)
else {
val l = ComplexDoubleField { ln(arg.w) }
DoubleQuaternion(l.re, l.im, 0, 0)
}
val a = arg.w
check(nu2 > 0)
val n = sqrt(a * a + nu2)
val th = acos(a / n) / sqrt(nu2)
return DoubleQuaternion(ln(n), th * arg.x, th * arg.y, th * arg.z)
}
override operator fun Number.plus(b: DoubleQuaternion): DoubleQuaternion =
DoubleQuaternion(toDouble() + b.w, b.x, b.y, b.z)
override operator fun Number.minus(b: DoubleQuaternion): DoubleQuaternion =
DoubleQuaternion(toDouble() - b.w, -b.x, -b.y, -b.z)
override operator fun DoubleQuaternion.plus(b: Number): DoubleQuaternion =
DoubleQuaternion(w + b.toDouble(), x, y, z)
override operator fun DoubleQuaternion.minus(b: Number): DoubleQuaternion =
DoubleQuaternion(w - b.toDouble(), x, y, z)
override operator fun Number.times(b: DoubleQuaternion): DoubleQuaternion =
DoubleQuaternion(toDouble() * b.w, toDouble() * b.x, toDouble() * b.y, toDouble() * b.z)
override fun DoubleQuaternion.unaryMinus(): DoubleQuaternion = DoubleQuaternion(-w, -x, -y, -z)
override fun norm(arg: DoubleQuaternion): DoubleQuaternion = sqrt(arg.conjugate * arg)
override fun bindSymbolOrNull(value: String): DoubleQuaternion? = when (value) {
"i" -> i
"j" -> j
"k" -> k
else -> null
}
override fun number(value: Number): DoubleQuaternion = DoubleQuaternion(value)
override fun sinh(arg: DoubleQuaternion): DoubleQuaternion = (exp(arg) - exp(-arg)) / 2.0
override fun cosh(arg: DoubleQuaternion): DoubleQuaternion = (exp(arg) + exp(-arg)) / 2.0
override fun tanh(arg: DoubleQuaternion): DoubleQuaternion = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))
override fun asinh(arg: DoubleQuaternion): DoubleQuaternion = ln(sqrt(arg * arg + one) + arg)
override fun acosh(arg: DoubleQuaternion): DoubleQuaternion = ln(arg + sqrt((arg - one) * (arg + one)))
override fun atanh(arg: DoubleQuaternion): DoubleQuaternion = (ln(arg + one) - ln(one - arg)) / 2.0
}
/**
* Represents `double`-based quaternion.
*
* @property w The first component.
* @property x The second component.
* @property y The third component.
* @property z The fourth component.
*/
@UnstableKMathAPI
public data class DoubleQuaternion(
val w: Double, val x: Double, val y: Double, val z: Double,
) {
public constructor(w: Number, x: Number, y: Number, z: Number) : this(
w.toDouble(),
x.toDouble(),
y.toDouble(),
z.toDouble(),
)
public constructor(w: Number, x: Number, y: Number) : this(w.toDouble(), x.toDouble(), y.toDouble(), 0.0)
public constructor(w: Number, x: Number) : this(w.toDouble(), x.toDouble(), 0.0, 0.0)
public constructor(w: Number) : this(w.toDouble(), 0.0, 0.0, 0.0)
public constructor(wx: Complex<Number>, yz: Complex<Number>) : this(wx.re, wx.im, yz.re, yz.im)
public constructor(wx: Complex<Number>) : this(wx.re, wx.im, 0, 0)
init {
require(!w.isNaN()) { "w-component of quaternion is not-a-number" }
require(!x.isNaN()) { "x-component of quaternion is not-a-number" }
require(!y.isNaN()) { "x-component of quaternion is not-a-number" }
require(!z.isNaN()) { "x-component of quaternion is not-a-number" }
}
/**
* Returns a string representation of this quaternion.
*/
override fun toString(): String = "($w + $x * i + $y * j + $z * k)"
public companion object : MemorySpec<DoubleQuaternion> {
override val objectSize: Int
get() = 32
override fun MemoryReader.read(offset: Int): DoubleQuaternion =
DoubleQuaternion(readDouble(offset),
readDouble(offset + 8),
readDouble(offset + 16),
readDouble(offset + 24))
override fun MemoryWriter.write(offset: Int, value: DoubleQuaternion) {
writeDouble(offset, value.w)
writeDouble(offset + 8, value.x)
writeDouble(offset + 16, value.y)
writeDouble(offset + 24, value.z)
}
}
}
/**
* Creates a new buffer of quaternions with the specified [size], where each element is calculated by calling the
* specified [init] function.
*/
@UnstableKMathAPI
public inline fun Buffer.Companion.quaternion(size: Int, init: (Int) -> DoubleQuaternion): Buffer<DoubleQuaternion> =
MemoryBuffer.create(DoubleQuaternion, size, init)
/**
* Creates a new buffer of quaternions with the specified [size], where each element is calculated by calling the
* specified [init] function.
*/
@UnstableKMathAPI
public inline fun MutableBuffer.Companion.quaternion(
size: Int,
init: (Int) -> DoubleQuaternion,
): MutableBuffer<DoubleQuaternion> =
MutableMemoryBuffer.create(DoubleQuaternion, size, init)

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/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.memory.MemoryReader
import space.kscience.kmath.memory.MemorySpec
import space.kscience.kmath.memory.MemoryWriter
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.*
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.MemoryBuffer
import space.kscience.kmath.structures.MutableBuffer
import space.kscience.kmath.structures.MutableMemoryBuffer
import kotlin.math.*
/**
* This quaternion's conjugate.
*/
public val Quaternion.conjugate: Quaternion
get() = QuaternionField { z - x * i - y * j - z * k }
/**
* This quaternion's reciprocal.
*/
public val Quaternion.reciprocal: Quaternion
get() {
QuaternionField {
val n = norm(this@reciprocal)
return conjugate / (n * n)
}
}
/**
* Absolute value of the quaternion.
*/
public val Quaternion.r: Double
get() = sqrt(w * w + x * x + y * y + z * z)
/**
* A field of [Quaternion].
*/
@OptIn(UnstableKMathAPI::class)
public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>, PowerOperations<Quaternion>,
ExponentialOperations<Quaternion>, NumbersAddOperations<Quaternion>, ScaleOperations<Quaternion> {
override val zero: Quaternion = 0.toQuaternion()
override val one: Quaternion = 1.toQuaternion()
/**
* The `i` quaternion unit.
*/
public val i: Quaternion = Quaternion(0, 1)
/**
* The `j` quaternion unit.
*/
public val j: Quaternion = Quaternion(0, 0, 1)
/**
* The `k` quaternion unit.
*/
public val k: Quaternion = Quaternion(0, 0, 0, 1)
override fun add(a: Quaternion, b: Quaternion): Quaternion =
Quaternion(a.w + b.w, a.x + b.x, a.y + b.y, a.z + b.z)
override fun scale(a: Quaternion, value: Double): Quaternion =
Quaternion(a.w * value, a.x * value, a.y * value, a.z * value)
override fun multiply(a: Quaternion, b: Quaternion): Quaternion = Quaternion(
a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z,
a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x,
a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w,
)
override fun divide(a: Quaternion, b: Quaternion): Quaternion {
val s = b.w * b.w + b.x * b.x + b.y * b.y + b.z * b.z
return Quaternion(
(b.w * a.w + b.x * a.x + b.y * a.y + b.z * a.z) / s,
(b.w * a.x - b.x * a.w - b.y * a.z + b.z * a.y) / s,
(b.w * a.y + b.x * a.z - b.y * a.w - b.z * a.x) / s,
(b.w * a.z - b.x * a.y + b.y * a.x - b.z * a.w) / s,
)
}
override fun power(arg: Quaternion, pow: Number): Quaternion {
if (pow is Int) return pwr(arg, pow)
if (floor(pow.toDouble()) == pow.toDouble()) return pwr(arg, pow.toInt())
return exp(pow * ln(arg))
}
private fun pwr(x: Quaternion, a: Int): Quaternion = when {
a < 0 -> -(pwr(x, -a))
a == 0 -> one
a == 1 -> x
a == 2 -> pwr2(x)
a == 3 -> pwr3(x)
a == 4 -> pwr4(x)
else -> {
val x4 = pwr4(x)
var y = x4
repeat((1 until a / 4).count()) { y *= x4 }
if (a % 4 == 3) y *= pwr3(x)
if (a % 4 == 2) y *= pwr2(x)
if (a % 4 == 1) y *= x
y
}
}
private fun pwr2(x: Quaternion): Quaternion {
val aa = 2 * x.w
return Quaternion(x.w * x.w - (x.x * x.x + x.y * x.y + x.z * x.z), aa * x.x, aa * x.y, aa * x.z)
}
private fun pwr3(x: Quaternion): Quaternion {
val a2 = x.w * x.w
val n1 = x.x * x.x + x.y * x.y + x.z * x.z
val n2 = 3.0 * a2 - n1
return Quaternion(x.w * (a2 - 3 * n1), x.x * n2, x.y * n2, x.z * n2)
}
private fun pwr4(x: Quaternion): Quaternion {
val a2 = x.w * x.w
val n1 = x.x * x.x + x.y * x.y + x.z * x.z
val n2 = 4 * x.w * (a2 - n1)
return Quaternion(a2 * a2 - 6 * a2 * n1 + n1 * n1, x.x * n2, x.y * n2, x.z * n2)
}
override fun exp(arg: Quaternion): Quaternion {
val un = arg.x * arg.x + arg.y * arg.y + arg.z * arg.z
if (un == 0.0) return exp(arg.w).toQuaternion()
val n1 = sqrt(un)
val ea = exp(arg.w)
val n2 = ea * sin(n1) / n1
return Quaternion(ea * cos(n1), n2 * arg.x, n2 * arg.y, n2 * arg.z)
}
override fun ln(arg: Quaternion): Quaternion {
val nu2 = arg.x * arg.x + arg.y * arg.y + arg.z * arg.z
if (nu2 == 0.0)
return if (arg.w > 0)
Quaternion(ln(arg.w), 0, 0, 0)
else {
val l = ComplexField { ln(arg.w.toComplex()) }
Quaternion(l.re, l.im, 0, 0)
}
val a = arg.w
check(nu2 > 0)
val n = sqrt(a * a + nu2)
val th = acos(a / n) / sqrt(nu2)
return Quaternion(ln(n), th * arg.x, th * arg.y, th * arg.z)
}
override operator fun Number.plus(b: Quaternion): Quaternion = Quaternion(toDouble() + b.w, b.x, b.y, b.z)
override operator fun Number.minus(b: Quaternion): Quaternion =
Quaternion(toDouble() - b.w, -b.x, -b.y, -b.z)
override operator fun Quaternion.plus(b: Number): Quaternion = Quaternion(w + b.toDouble(), x, y, z)
override operator fun Quaternion.minus(b: Number): Quaternion = Quaternion(w - b.toDouble(), x, y, z)
override operator fun Number.times(b: Quaternion): Quaternion =
Quaternion(toDouble() * b.w, toDouble() * b.x, toDouble() * b.y, toDouble() * b.z)
override fun Quaternion.unaryMinus(): Quaternion = Quaternion(-w, -x, -y, -z)
override fun norm(arg: Quaternion): Quaternion = sqrt(arg.conjugate * arg)
override fun bindSymbolOrNull(value: String): Quaternion? = when (value) {
"i" -> i
"j" -> j
"k" -> k
else -> null
}
override fun number(value: Number): Quaternion = value.toQuaternion()
override fun sinh(arg: Quaternion): Quaternion = (exp(arg) - exp(-arg)) / 2.0
override fun cosh(arg: Quaternion): Quaternion = (exp(arg) + exp(-arg)) / 2.0
override fun tanh(arg: Quaternion): Quaternion = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))
override fun asinh(arg: Quaternion): Quaternion = ln(sqrt(arg * arg + one) + arg)
override fun acosh(arg: Quaternion): Quaternion = ln(arg + sqrt((arg - one) * (arg + one)))
override fun atanh(arg: Quaternion): Quaternion = (ln(arg + one) - ln(one - arg)) / 2.0
}
/**
* Represents `double`-based quaternion.
*
* @property w The first component.
* @property x The second component.
* @property y The third component.
* @property z The fourth component.
*/
@OptIn(UnstableKMathAPI::class)
public data class Quaternion(
val w: Double, val x: Double, val y: Double, val z: Double,
) {
public constructor(w: Number, x: Number, y: Number, z: Number) : this(
w.toDouble(),
x.toDouble(),
y.toDouble(),
z.toDouble(),
)
public constructor(w: Number, x: Number, y: Number) : this(w.toDouble(), x.toDouble(), y.toDouble(), 0.0)
public constructor(w: Number, x: Number) : this(w.toDouble(), x.toDouble(), 0.0, 0.0)
public constructor(w: Number) : this(w.toDouble(), 0.0, 0.0, 0.0)
public constructor(wx: Complex, yz: Complex) : this(wx.re, wx.im, yz.re, yz.im)
public constructor(wx: Complex) : this(wx.re, wx.im, 0, 0)
init {
require(!w.isNaN()) { "w-component of quaternion is not-a-number" }
require(!x.isNaN()) { "x-component of quaternion is not-a-number" }
require(!y.isNaN()) { "x-component of quaternion is not-a-number" }
require(!z.isNaN()) { "x-component of quaternion is not-a-number" }
}
/**
* Returns a string representation of this quaternion.
*/
override fun toString(): String = "($w + $x * i + $y * j + $z * k)"
public companion object : MemorySpec<Quaternion> {
override val objectSize: Int
get() = 32
override fun MemoryReader.read(offset: Int): Quaternion =
Quaternion(readDouble(offset), readDouble(offset + 8), readDouble(offset + 16), readDouble(offset + 24))
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 a new quaternion.
*/
public fun Number.toQuaternion(): Quaternion = Quaternion(this)
/**
* Creates a quaternion with `w`-component equal to `re`-component of given complex and `x`-component equal to
* `im`-component of given complex.
*
* @receiver the complex number.
* @return a new quaternion.
*/
public fun Complex.toQuaternion(): Quaternion = Quaternion(this)
/**
* 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)

94
kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/complexBuffers.kt Normal file
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@ -0,0 +1,94 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.BufferFactory
import space.kscience.kmath.structures.MutableBuffer
import space.kscience.kmath.structures.MutableBufferFactory
private class ComplexBuffer<out T : Any>(factory: BufferFactory<T>, override val size: Int, init: (Int) -> Complex<T>) :
Buffer<Complex<T>> {
private val re: Buffer<T>
private val im: Buffer<T>
init {
val tmp = Array(size, init)
re = factory(size) { tmp[it].re }
im = factory(size) { tmp[it].im }
}
override fun get(index: Int): Complex<T> = Complex(re[index], im[index])
override fun iterator(): Iterator<Complex<T>> = object : AbstractIterator<Complex<T>>() {
private val a = re.iterator()
private val b = im.iterator()
override fun computeNext() = if (a.hasNext() && b.hasNext())
setNext(Complex(a.next(), b.next()))
else
done()
}
}
/**
* Creates a new buffer of complex elements with the specified [size], where each element is calculated by calling the
* specified [init] function.
*/
public fun <T : Any> Buffer.Companion.complex(
factory: BufferFactory<T>,
size: Int,
init: (Int) -> Complex<T>,
): Buffer<Complex<T>> = ComplexBuffer(factory, size, init)
private class MutableComplexBuffer<T : Any> private constructor(
override val size: Int,
private val re: MutableBuffer<T>,
private val im: MutableBuffer<T>,
) : MutableBuffer<Complex<T>> {
private constructor(
factory: MutableBufferFactory<T>,
size: Int,
tmp: Array<Complex<T>>,
) : this(size, factory(size) { tmp[it].re }, factory(size) { tmp[it].im })
constructor(
factory: MutableBufferFactory<T>,
size: Int,
init: (Int) -> Complex<T>,
) : this(factory, size, Array(size, init))
override fun get(index: Int): Complex<T> = Complex(re[index], im[index])
override fun set(index: Int, value: Complex<T>) {
re[index] = value.re
im[index] = value.im
}
override fun iterator(): Iterator<Complex<T>> = object : AbstractIterator<Complex<T>>() {
private val a = re.iterator()
private val b = im.iterator()
override fun computeNext() = if (a.hasNext() && b.hasNext())
setNext(Complex(a.next(), b.next()))
else
done()
}
override fun copy(): MutableBuffer<Complex<T>> = MutableComplexBuffer(size, re.copy(), im.copy())
}
/**
* Creates a new buffer of complex elements with the specified [size], where each element is calculated by calling the
* specified [init] function.
*/
public fun <T : Any> MutableBuffer.Companion.complex(
factory: MutableBufferFactory<T>,
size: Int,
init: (Int) -> Complex<T>,
): MutableBuffer<Complex<T>> = MutableComplexBuffer(factory, size, init)

24
kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/complexLinearSpace.kt Normal file
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@ -0,0 +1,24 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.linear.BufferedLinearSpace
import space.kscience.kmath.operations.ExtendedField
import space.kscience.kmath.operations.NumericAlgebra
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.BufferFactory
public class ComplexLinearSpace<T : Any, out A>(
elementContext: A,
bufferFactory: BufferFactory<T>,
) : BufferedLinearSpace<Complex<T>, ComplexRing<T, A>>(
ComplexRing(elementContext),
{ size, init -> Buffer.complex(bufferFactory, size, init) },
) where A : Ring<T>, A : NumericAlgebra<T>
public fun <T : Any, A> BufferedLinearSpace<T, A>.complex(): ComplexLinearSpace<T, A> where A : ExtendedField<T>, A : NumericAlgebra<T> =
ComplexLinearSpace(elementAlgebra, bufferFactory)

68
kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/complexNDAlgebra.kt Normal file
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@ -0,0 +1,68 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.nd.BufferedExtendedFieldND
import space.kscience.kmath.nd.BufferedFieldND
import space.kscience.kmath.nd.BufferedGroupND
import space.kscience.kmath.nd.BufferedRingND
import space.kscience.kmath.operations.*
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.BufferFactory
public open class ComplexGroupND<T : Any, out A>(
shape: IntArray,
elementContext: A,
bufferFactory: BufferFactory<T>,
) : BufferedGroupND<Complex<T>, ComplexGroup<T, A>>(
shape,
ComplexGroup(elementContext),
{ size, init -> Buffer.complex(bufferFactory, size, init) },
) where A : Group<T>, A : NumericAlgebra<T>
public fun <T : Any, A> BufferedGroupND<T, A>.complex(): ComplexGroupND<T, A> where A : Group<T>, A : NumericAlgebra<T> =
ComplexGroupND(shape, elementContext, bufferFactory)
public open class ComplexRingND<T : Any, out A>(
shape: IntArray,
elementContext: A,
bufferFactory: BufferFactory<T>,
) : BufferedRingND<Complex<T>, ComplexRing<T, A>>(
shape,
ComplexRing(elementContext),
{ size, init -> Buffer.complex(bufferFactory, size, init) },
) where A : Ring<T>, A : NumericAlgebra<T>
public fun <T : Any, A> BufferedRingND<T, A>.complex(): ComplexRingND<T, A> where A : Ring<T>, A : NumericAlgebra<T> =
ComplexRingND(shape, elementContext, bufferFactory)
public open class ComplexFieldND<T : Any, out A>(
shape: IntArray,
elementContext: A,
bufferFactory: BufferFactory<T>,
) : BufferedFieldND<Complex<T>, ComplexField<T, A>>(
shape,
ComplexField(elementContext),
{ size, init -> Buffer.complex(bufferFactory, size, init) },
) where A : Field<T>, A : NumericAlgebra<T>
public fun <T : Any, A> BufferedFieldND<T, A>.complex(): ComplexFieldND<T, A> where A : Field<T>, A : NumericAlgebra<T> =
ComplexFieldND(shape, elementContext, bufferFactory)
public open class ComplexExtendedFieldND<T : Any, out A>(
shape: IntArray,
elementContext: A,
bufferFactory: BufferFactory<T>,
) : BufferedExtendedFieldND<Complex<T>, ComplexExtendedField<T, A>>(
shape,
ComplexExtendedField(elementContext),
{ size, init -> Buffer.complex(bufferFactory, size, init) },
) where A : ExtendedField<T>, A : NumericAlgebra<T>
public fun <T : Any, A> BufferedExtendedFieldND<T, A>.complex(): ComplexExtendedFieldND<T, A> where A : ExtendedField<T>, A : NumericAlgebra<T> =
ComplexExtendedFieldND(shape, elementContext, bufferFactory)

3
kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ComplexBufferSpecTest.kt
View File

@ -6,13 +6,14 @@
package space.kscience.kmath.complex
import space.kscience.kmath.structures.Buffer
import space.kscience.kmath.structures.MutableBuffer
import kotlin.test.Test
import kotlin.test.assertEquals
class ComplexBufferSpecTest {
@Test
fun testComplexBuffer() {
val buffer = Buffer.complex(20) { Complex(it.toDouble(), -it.toDouble()) }
val buffer = Buffer.complex(MutableBuffer.Companion::double, 20) { Complex(it.toDouble(), -it.toDouble()) }
assertEquals(Complex(5.0, -5.0), buffer[5])
}
}

76
kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ComplexFieldTest.kt
View File

@ -5,12 +5,11 @@
package space.kscience.kmath.complex
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.invoke
import kotlin.math.PI
import kotlin.math.abs
import space.kscience.kmath.operations.pi
import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.assertTrue
internal class ComplexFieldTest {
// TODO make verifier classes available in this source set
@ -19,63 +18,84 @@ internal class ComplexFieldTest {
@Test
fun testAddition() {
assertEquals(Complex(42, 42), ComplexField { Complex(16, 16) + Complex(26, 26) })
assertEquals(Complex(42, 16), ComplexField { Complex(16, 16) + 26 })
assertEquals(Complex(42, 16), ComplexField { 26 + Complex(16, 16) })
assertEquals(Complex(42, 42), ComplexIntRing { Complex(16, 16) + Complex(26, 26) })
assertEquals(Complex(42, 16), ComplexIntRing { Complex(16, 16) + 26 })
assertEquals(Complex(42, 16), ComplexIntRing { 26 + Complex(16, 16) })
}
@Test
fun testSubtraction() {
assertEquals(Complex(42, 42), ComplexField { Complex(86, 55) - Complex(44, 13) })
assertEquals(Complex(42, 56), ComplexField { Complex(86, 56) - 44 })
assertEquals(Complex(42, 56), ComplexField { 86 - Complex(44, -56) })
assertEquals(Complex(42, 42), ComplexIntRing { Complex(86, 55) - Complex(44, 13) })
assertEquals(Complex(42, 56), ComplexIntRing { Complex(86, 56) - 44 })
assertEquals(Complex(42, 56), ComplexIntRing { 86 - Complex(44, -56) })
}
@Test
fun testMultiplication() {
assertEquals(Complex(42, 42), ComplexField { Complex(4.2, 0) * Complex(10, 10) })
assertEquals(Complex(42, 21), ComplexField { Complex(4.2, 2.1) * 10 })
assertEquals(Complex(42, 21), ComplexField { 10 * Complex(4.2, 2.1) })
assertEquals(Complex(42.0, 42.0), ComplexDoubleField { Complex(4.2, 0.0) * Complex(10.0, 10.0) })
assertEquals(Complex(42.0, 21.0), ComplexDoubleField { Complex(4.2, 2.1) * 10 })
assertEquals(Complex(42.0, 21.0), ComplexDoubleField { 10 * Complex(4.2, 2.1) })
}
@Test
fun testDivision() {
assertEquals(Complex(42, 42), ComplexField { Complex(0, 168) / Complex(2, 2) })
assertEquals(Complex(42, 56), ComplexField { Complex(86, 56) - 44 })
assertEquals(Complex(42, 56), ComplexField { 86 - Complex(44, -56) })
assertEquals(Complex(42.0, 42.0), ComplexDoubleField { Complex(0.0, 168.0) / Complex(2.0, 2.0) })
assertEquals(Complex(42.0, 56.0), ComplexDoubleField { Complex(86.0, 56.0) - 44.0 })
assertEquals(Complex(42.0, 56.0), ComplexDoubleField { 86.0 - Complex(44.0, -56.0) })
}
@Test
fun testSine() {
assertEquals(ComplexField { i * sinh(one) }, ComplexField { sin(i) })
assertEquals(ComplexField { i * sinh(PI.toComplex()) }, ComplexField { sin(i * PI.toComplex()) })
assertEquals(ComplexDoubleField { i * sinh(one) }, ComplexDoubleField { sin(i) })
assertEquals(ComplexDoubleField { i * sinh(pi) }, ComplexDoubleField { sin(i * pi) })
}
@Test
fun testInverseSine() {
assertEquals(Complex(0, -0.0), ComplexField { asin(zero) })
assertTrue(abs(ComplexField { i * asinh(one) }.r - ComplexField { asin(i) }.r) < 0.000000000000001)
fun testInverseSine() = ComplexDoubleField {
assertEquals(norm(zero), norm(asin(zero)), 1e-10)
assertEquals(norm(i * asinh(one)), norm(i * asinh(one)), 1e-10)
}
@Test
fun testInverseHyperbolicSine() {
assertEquals(
ComplexField { i * PI.toComplex() / 2 },
ComplexField { asinh(i) })
assertEquals(ComplexDoubleField { i * pi / 2 }, ComplexDoubleField { asinh(i) })
}
@Test
fun testPower() {
assertEquals(ComplexField.zero, ComplexField { zero pow 2 })
assertEquals(ComplexField.zero, ComplexField { zero pow 2 })
assertEquals(ComplexDoubleField.zero, ComplexDoubleField { zero pow 2 })
assertEquals(ComplexDoubleField.zero, ComplexDoubleField { zero pow 2 })
assertEquals(
ComplexField { i * 8 }.let { it.im.toInt() to it.re.toInt() },
ComplexField { Complex(2, 2) pow 2 }.let { it.im.toInt() to it.re.toInt() })
ComplexDoubleField { i * 8 }.let { it.im.toInt() to it.re.toInt() },
ComplexDoubleField { Complex(2.0, 2.0) pow 2 }.let { it.im.toInt() to it.re.toInt() },
)
}
@Test
fun testNorm() {
assertEquals(2.toComplex(), ComplexField { norm(2 * i) })
assertEquals(2.0, ComplexDoubleField { norm(number(2.0) * i) })
}
@Test
fun conjugate() = ComplexDoubleField {
assertEquals(Complex(0.0, 42.0), Complex(0.0, -42.0).conjugate)
}
@Test
fun reciprocal() = ComplexDoubleField {
assertEquals(norm(Complex(0.5, 0.0)), norm(Complex(2.0, 0.0).reciprocal), 1e-10)
}
@Test
fun polar() {
val num = Complex(0.5, 2.5)
val theta = ComplexDoubleField { num.theta }
val r = ComplexDoubleField { num.r }
DoubleField {
assertEquals(cos(theta), num.re / r, 1e-10)
assertEquals(sin(theta), num.im / r, 1e-10)
}
}
}

36
kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ComplexTest.kt
View File

@ -1,36 +0,0 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.operations.invoke
import kotlin.math.sqrt
import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.assertTrue
internal class ComplexTest {
@Test
fun conjugate() = ComplexField { assertEquals(Complex(0, 42), Complex(0, -42).conjugate) }
@Test
fun reciprocal() = ComplexField { assertTrue((Complex(0.5, -0.0) - 2.toComplex().reciprocal).r < 1e-10) }
@Test
fun r() = ComplexField { assertEquals(sqrt(2.0), (i + 1.0.toComplex()).r) }
@Test
fun theta() = assertEquals(0.0, 1.toComplex().theta)
@Test
fun toComplex() {
assertEquals(Complex(42), 42.toComplex())
assertEquals(Complex(42.0), 42.0.toComplex())
assertEquals(Complex(42f), 42f.toComplex())
assertEquals(Complex(42.0), 42.0.toComplex())
assertEquals(Complex(42.toByte()), 42.toByte().toComplex())
assertEquals(Complex(42.toShort()), 42.toShort().toComplex())
}
}

4
kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ExpressionFieldForComplexTest.kt
View File

@ -17,11 +17,11 @@ internal class ExpressionFieldForComplexTest {
@Test
fun testComplex() {
val expression = FunctionalExpressionField(ComplexField).run {
val expression = FunctionalExpressionField(ComplexDoubleField).run {
val x = bindSymbol(x)
x * x + 2 * x + one
}
assertEquals(expression(x to Complex(1.0, 0.0)), Complex(4.0, 0.0))
assertEquals(Complex(4.0, 0.0), expression(x to Complex(1.0, 0.0)))
}
}

80
kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/QuaternionFieldTest.kt
View File

@ -4,47 +4,47 @@
*/
package space.kscience.kmath.complex
import space.kscience.kmath.operations.invoke
import kotlin.test.Test
import kotlin.test.assertEquals
internal class QuaternionFieldTest {
@Test
fun testAddition() {
assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(16, 16) + Quaternion(26, 26) })
assertEquals(Quaternion(42, 16), QuaternionField { Quaternion(16, 16) + 26 })
assertEquals(Quaternion(42, 16), QuaternionField { 26 + Quaternion(16, 16) })
}
//
//import space.kscience.kmath.operations.invoke
//import kotlin.test.Test
//import kotlin.test.assertEquals
//
//internal class QuaternionFieldTest {
// @Test
// fun testSubtraction() {
// assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(86, 55) - Quaternion(44, 13) })
// assertEquals(Quaternion(42, 56), QuaternionField { Quaternion(86, 56) - 44 })
// assertEquals(Quaternion(42, 56), QuaternionField { 86 - Quaternion(44, -56) })
// fun testAddition() {
// assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(16, 16) + Quaternion(26, 26) })
// assertEquals(Quaternion(42, 16), QuaternionField { Quaternion(16, 16) + 26 })
// assertEquals(Quaternion(42, 16), QuaternionField { 26 + Quaternion(16, 16) })
// }
@Test
fun testMultiplication() {
assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(4.2, 0) * Quaternion(10, 10) })
assertEquals(Quaternion(42, 21), QuaternionField { Quaternion(4.2, 2.1) * 10 })
assertEquals(Quaternion(42, 21), QuaternionField { 10 * Quaternion(4.2, 2.1) })
}
//
//// @Test
//// fun testSubtraction() {
//// assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(86, 55) - Quaternion(44, 13) })
//// assertEquals(Quaternion(42, 56), QuaternionField { Quaternion(86, 56) - 44 })
//// assertEquals(Quaternion(42, 56), QuaternionField { 86 - Quaternion(44, -56) })
//// }
//
// @Test
// fun testDivision() {
// assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(0, 168) / Quaternion(2, 2) })
// assertEquals(Quaternion(42, 56), QuaternionField { Quaternion(86, 56) - 44 })
// assertEquals(Quaternion(42, 56) , QuaternionField { 86 - Quaternion(44, -56) })
// fun testMultiplication() {
// assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(4.2, 0) * Quaternion(10, 10) })
// assertEquals(Quaternion(42, 21), QuaternionField { Quaternion(4.2, 2.1) * 10 })
// assertEquals(Quaternion(42, 21), QuaternionField { 10 * Quaternion(4.2, 2.1) })
// }
//
//// @Test
//// fun testDivision() {
//// assertEquals(Quaternion(42, 42), QuaternionField { Quaternion(0, 168) / Quaternion(2, 2) })
//// assertEquals(Quaternion(42, 56), QuaternionField { Quaternion(86, 56) - 44 })
//// assertEquals(Quaternion(42, 56) , QuaternionField { 86 - Quaternion(44, -56) })
//// }
//
// @Test
// fun testPower() {
// assertEquals(QuaternionField.zero, QuaternionField { zero pow 2 })
// assertEquals(QuaternionField.zero, QuaternionField { zero pow 2 })
//
// assertEquals(
// QuaternionField { i * 8 }.let { it.x.toInt() to it.w.toInt() },
// QuaternionField { Quaternion(2, 2) pow 2 }.let { it.x.toInt() to it.w.toInt() })
// }
//}
@Test
fun testPower() {
assertEquals(QuaternionField.zero, QuaternionField { zero pow 2 })
assertEquals(QuaternionField.zero, QuaternionField { zero pow 2 })
assertEquals(
QuaternionField { i * 8 }.let { it.x.toInt() to it.w.toInt() },
QuaternionField { Quaternion(2, 2) pow 2 }.let { it.x.toInt() to it.w.toInt() })
}
}

22
kmath-complex/src/jvmMain/kotlin/space/kscience/kmath/complex/bigNumbers.kt Normal file
View File

@ -0,0 +1,22 @@
/*
* Copyright 2018-2021 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.complex
import space.kscience.kmath.operations.JBigDecimalField
import space.kscience.kmath.operations.JBigIntegerRing
import java.math.BigDecimal
import java.math.BigInteger
/**
* [ComplexRing] instance for [JBigIntegerRing].
*/
public val ComplexJBigIntegerRing: ComplexRing<BigInteger, JBigIntegerRing> = ComplexRing(JBigIntegerRing)
/**
* [ComplexRing] instance for [JBigDecimalField].
*/
public val ComplexJBigDecimalField: ComplexField<BigDecimal, JBigDecimalField.Companion> =
ComplexField(JBigDecimalField)

4
kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
View File

@ -15,9 +15,9 @@ import space.kscience.kmath.structures.VirtualBuffer
import space.kscience.kmath.structures.indices
public class BufferedLinearSpace<T : Any, out A : Ring<T>>(
public open class BufferedLinearSpace<T : Any, out A : Ring<T>>(
override val elementAlgebra: A,
private val bufferFactory: BufferFactory<T>,
public val bufferFactory: BufferFactory<T>,
) : LinearSpace<T, A> {
private fun ndRing(

8
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
View File

@ -286,3 +286,11 @@ public interface FieldND<T, out F : Field<T>> : Field<StructureND<T>>, RingND<T,
// }
// }
}
/**
* Extended field of [StructureND].
*
* @param T the type of the element contained in ND structure.
* @param F the type of extended field of structure elements.
*/
public interface ExtendedFieldND<T, out F : ExtendedField<T>> : ExtendedField<StructureND<T>>, FieldND<T, F>

53
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
View File

@ -57,11 +57,11 @@ public interface BufferAlgebraND<T, out A : Algebra<T>> : AlgebraND<T, A> {
}
}
public open class BufferedGroupND<T, out A : Group<T>>(
public open class BufferedGroupND<T, out G : Group<T>>(
final override val shape: IntArray,
final override val elementContext: A,
final override val elementContext: G,
final override val bufferFactory: BufferFactory<T>,
) : GroupND<T, A>, BufferAlgebraND<T, A> {
) : GroupND<T, G>, BufferAlgebraND<T, G> {
override val strides: Strides = DefaultStrides(shape)
override val zero: BufferND<T> by lazy { produce { zero } }
override fun StructureND<T>.unaryMinus(): StructureND<T> = produce { -get(it) }
@ -75,15 +75,32 @@ public open class BufferedRingND<T, out R : Ring<T>>(
override val one: BufferND<T> by lazy { produce { one } }
}
public open class BufferedFieldND<T, out R : Field<T>>(
public open class BufferedFieldND<T, out F : Field<T>>(
shape: IntArray,
elementContext: R,
elementContext: F,
bufferFactory: BufferFactory<T>,
) : BufferedRingND<T, R>(shape, elementContext, bufferFactory), FieldND<T, R> {
) : BufferedRingND<T, F>(shape, elementContext, bufferFactory), FieldND<T, F> {
override fun scale(a: StructureND<T>, value: Double): StructureND<T> = a.map { it * value }
}
public open class BufferedExtendedFieldND<T, out F : ExtendedField<T>>(
shape: IntArray,
elementContext: F,
bufferFactory: BufferFactory<T>,
) : BufferedFieldND<T, F>(shape, elementContext, bufferFactory), ExtendedFieldND<T, F> {
public override fun sin(arg: StructureND<T>): StructureND<T> = arg.map { elementContext.sin(it) }
public override fun cos(arg: StructureND<T>): StructureND<T> = arg.map { elementContext.cos(it) }
public override fun asin(arg: StructureND<T>): StructureND<T> = arg.map { elementContext.asin(it) }
public override fun acos(arg: StructureND<T>): StructureND<T> = arg.map { elementContext.acos(it) }
public override fun atan(arg: StructureND<T>): StructureND<T> = arg.map { elementContext.atan(it) }
public override fun power(arg: StructureND<T>, pow: Number): StructureND<T> =
arg.map { elementContext.power(it, pow) }
public override fun exp(arg: StructureND<T>): StructureND<T> = arg.map { elementContext.exp(it) }
public override fun ln(arg: StructureND<T>): StructureND<T> = arg.map { elementContext.ln(it) }
}
// group factories
public fun <T, A : Ring<T>> AlgebraND.Companion.group(
space: A,
@ -140,3 +157,27 @@ public inline fun <T, A : Field<T>, R> A.ndField(
contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
return AlgebraND.field(this, bufferFactory, *shape).run(action)
}
public fun <T, A : ExtendedField<T>> AlgebraND.Companion.extendedField(
field: A,
bufferFactory: BufferFactory<T>,
vararg shape: Int,
): BufferedExtendedFieldND<T, A> = BufferedExtendedFieldND(shape, field, bufferFactory)
@Suppress("UNCHECKED_CAST")
public inline fun <reified T : Any, A : ExtendedField<T>> AlgebraND.Companion.auto(
field: A,
vararg shape: Int,
): FieldND<T, A> = when (field) {
DoubleField -> DoubleFieldND(shape) as FieldND<T, A>
else -> BufferedFieldND(shape, field, Buffer.Companion::auto)
}
public inline fun <T, A : ExtendedField<T>, R> A.ndExtendedField(
noinline bufferFactory: BufferFactory<T>,
vararg shape: Int,
action: BufferedExtendedFieldND<T, A>.() -> R,
): R {
contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
return AlgebraND.extendedField(this, bufferFactory, *shape).run(action)
}

10
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
View File

@ -7,9 +7,7 @@ package space.kscience.kmath.nd
import space.kscience.kmath.misc.UnstableKMathAPI
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.ExtendedField
import space.kscience.kmath.operations.NumbersAddOperations
import space.kscience.kmath.operations.ScaleOperations
import space.kscience.kmath.structures.DoubleBuffer
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
@ -17,10 +15,8 @@ import kotlin.contracts.contract
@OptIn(UnstableKMathAPI::class)
public class DoubleFieldND(
shape: IntArray,
) : BufferedFieldND<Double, DoubleField>(shape, DoubleField, ::DoubleBuffer),
NumbersAddOperations<StructureND<Double>>,
ScaleOperations<StructureND<Double>>,
ExtendedField<StructureND<Double>> {
) : BufferedExtendedFieldND<Double, DoubleField>(shape, DoubleField, ::DoubleBuffer),
NumbersAddOperations<StructureND<Double>> {
override val zero: BufferND<Double> by lazy { produce { zero } }
override val one: BufferND<Double> by lazy { produce { one } }
@ -103,7 +99,7 @@ public class DoubleFieldND(
override fun atanh(arg: StructureND<Double>): BufferND<Double> = arg.map { atanh(it) }
}
public fun AlgebraND.Companion.real(vararg shape: Int): DoubleFieldND = DoubleFieldND(shape)
public fun AlgebraND.Companion.double(vararg shape: Int): DoubleFieldND = DoubleFieldND(shape)
/**
* Produce a context for n-dimensional operations inside this real field

6
kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
View File

@ -7,7 +7,7 @@ package space.kscience.kmath.structures
import space.kscience.kmath.nd.AlgebraND
import space.kscience.kmath.nd.get
import space.kscience.kmath.nd.real
import space.kscience.kmath.nd.double
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.testutils.FieldVerifier
import kotlin.test.Test
@ -16,12 +16,12 @@ import kotlin.test.assertEquals
internal class NDFieldTest {
@Test
fun verify() {
(AlgebraND.real(12, 32)) { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
(AlgebraND.double(12, 32)) { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
}
@Test
fun testStrides() {
val ndArray = AlgebraND.real(10, 10).produce { (it[0] + it[1]).toDouble() }
val ndArray = AlgebraND.double(10, 10).produce { (it[0] + it[1]).toDouble() }
assertEquals(ndArray[5, 5], 10.0)
}
}

4
kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
View File

@ -17,7 +17,7 @@ import kotlin.test.assertEquals
@Suppress("UNUSED_VARIABLE")
class NumberNDFieldTest {
val algebra = AlgebraND.real(3, 3)
val algebra = AlgebraND.double(3, 3)
val array1 = algebra.produce { (i, j) -> (i + j).toDouble() }
val array2 = algebra.produce { (i, j) -> (i - j).toDouble() }
@ -83,7 +83,7 @@ class NumberNDFieldTest {
@Test
fun testInternalContext() {
algebra {
(AlgebraND.real(*array1.shape)) { with(L2Norm) { 1 + norm(array1) + exp(array2) } }
(AlgebraND.double(*array1.shape)) { with(L2Norm) { 1 + norm(array1) + exp(array2) } }
}
}
}

4
kmath-core/src/jvmMain/kotlin/space/kscience/kmath/operations/BigNumbers.kt → kmath-core/src/jvmMain/kotlin/space/kscience/kmath/operations/bigNumbers.kt
View File

@ -10,9 +10,9 @@ import java.math.BigInteger
import java.math.MathContext
/**
* A field over [BigInteger].
* A ring over [BigInteger].
*/
public object JBigIntegerField : Ring<BigInteger>, NumericAlgebra<BigInteger> {
public object JBigIntegerRing : Ring<BigInteger>, NumericAlgebra<BigInteger> {
override val zero: BigInteger get() = BigInteger.ZERO
override val one: BigInteger get() = BigInteger.ONE

2
kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/DoubleHistogramSpace.kt
View File

@ -28,7 +28,7 @@ public class DoubleHistogramSpace(
public val dimension: Int get() = lower.size
private val shape = IntArray(binNums.size) { binNums[it] + 2 }
override val histogramValueSpace: DoubleFieldND = AlgebraND.real(*shape)
override val histogramValueSpace: DoubleFieldND = AlgebraND.double(*shape)
override val strides: Strides get() = histogramValueSpace.strides
private val binSize = DoubleBuffer(dimension) { (upper[it] - lower[it]) / binNums[it] }

3
kmath-jafama/build.gradle.kts
View File

@ -1,5 +1,6 @@
plugins {
id("ru.mipt.npm.gradle.jvm")
kotlin("jvm")
id("ru.mipt.npm.gradle.common")
}
description = "Jafama integration module"

12
kmath-jupyter/build.gradle.kts
View File

@ -1,6 +1,7 @@
plugins {
id("ru.mipt.npm.gradle.jvm")
kotlin("jvm")
kotlin("jupyter.api")
id("ru.mipt.npm.gradle.common")
}
dependencies {
@ -9,13 +10,8 @@ dependencies {
api(project(":kmath-for-real"))
}
kscience{
useHtml()
}
readme {
maturity = ru.mipt.npm.gradle.Maturity.PROTOTYPE
}
kscience.useHtml()
readme.maturity = ru.mipt.npm.gradle.Maturity.PROTOTYPE
kotlin.sourceSets.all {
languageSettings.useExperimentalAnnotation("space.kscience.kmath.misc.UnstableKMathAPI")

14
kmath-jupyter/src/main/kotlin/space/kscience/kmath/jupyter/KMathJupyter.kt
View File

@ -12,7 +12,7 @@ import space.kscience.kmath.ast.rendering.FeaturedMathRendererWithPostProcess
import space.kscience.kmath.ast.rendering.MathMLSyntaxRenderer
import space.kscience.kmath.ast.rendering.renderWithStringBuilder
import space.kscience.kmath.complex.Complex
import space.kscience.kmath.complex.Quaternion
import space.kscience.kmath.complex.DoubleQuaternion
import space.kscience.kmath.expressions.MST
import space.kscience.kmath.expressions.MstRing
import space.kscience.kmath.misc.PerformancePitfall
@ -121,18 +121,16 @@ internal class KMathJupyter : JupyterIntegration() {
})
}
render<Complex> {
MstRing {
number(it.re) + number(it.im) * bindSymbol("i")
}.toDisplayResult()
render<Complex<Number>> {
MstRing { number(it.re) + number(it.im) * bindSymbol("i") }.toDisplayResult()
}
render<Quaternion> {
render<DoubleQuaternion> {
MstRing {
number(it.w) +
number(it.x) * bindSymbol("i") +
number(it.x) * bindSymbol("j") +
number(it.x) * bindSymbol("k")
number(it.y) * bindSymbol("j") +
number(it.z) * bindSymbol("k")
}.toDisplayResult()
}
}

8
settings.gradle.kts
View File

@ -5,18 +5,14 @@ pluginManagement {
gradlePluginPortal()
}
val toolsVersion = "0.10.2"
val kotlinVersion = "1.5.21"
plugins {
id("ru.mipt.npm.gradle.project") version toolsVersion
id("ru.mipt.npm.gradle.mpp") version toolsVersion
id("ru.mipt.npm.gradle.jvm") version toolsVersion
id("ru.mipt.npm.gradle.project") version "0.10.2"
kotlin("multiplatform") version kotlinVersion
kotlin("jvm") version kotlinVersion
kotlin("plugin.allopen") version kotlinVersion
id("org.jetbrains.kotlinx.benchmark") version "0.3.1"
kotlin("jupyter.api") version "0.10.0-131-1"
kotlin("jupyter.api") version "0.10.0-174"
}
}