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v0.2.0 #206

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altavir merged 210 commits from dev into master 2021-02-21 16:33:25 +03:00
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9
examples/src/main/kotlin/kscience/kmath/operations/ComplexDemo.kt
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@ -1,23 +1,24 @@
package kscience.kmath.operations
import kscience.kmath.nd.NDAlgebra
import kscience.kmath.complex.Complex
import kscience.kmath.complex.complex
import kscience.kmath.nd.NDAlgebra
fun main() {
// 2d element
val element = NDAlgebra.complex(2, 2).produce { (i,j) ->
val element = NDAlgebra.complex(2, 2).produce { (i, j) ->
Complex(i.toDouble() - j.toDouble(), i.toDouble() + j.toDouble())
}
println(element)
// 1d element operation
val result = with(NDAlgebra.complex(8)) {
val element = NDAlgebra.complex(2, 2).produce { (i,j) ->
val result = (NDAlgebra.complex(8)) {
val a = produce { (it) -> i * it - it.toDouble() }
val b = 3
val c = Complex(1.0, 1.0)
(a pow b) + c
}
println(result)
}

8
examples/src/main/kotlin/kscience/kmath/structures/ComplexND.kt
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@ -2,9 +2,13 @@
package kscience.kmath.structures
import kscience.kmath.linear.transpose
import kscience.kmath.nd.*
import kscience.kmath.complex.*
import kscience.kmath.linear.transpose
import kscience.kmath.nd.NDAlgebra
import kscience.kmath.nd.NDStructure
import kscience.kmath.nd.as2D
import kscience.kmath.nd.real
import kscience.kmath.operations.invoke
import kotlin.system.measureTimeMillis
fun main() {

6
kmath-core/src/commonMain/kotlin/kscience/kmath/nd/ComplexNDField.kt → kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/ComplexNDField.kt
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@ -1,6 +1,10 @@
package kscience.kmath.nd
package kscience.kmath.complex
import kscience.kmath.misc.UnstableKMathAPI
import kscience.kmath.nd.BufferedNDField
import kscience.kmath.nd.NDAlgebra
import kscience.kmath.nd.NDBuffer
import kscience.kmath.nd.NDStructure
import kscience.kmath.operations.*
import kscience.kmath.structures.Buffer
import kotlin.contracts.InvocationKind

221
kmath-core/src/commonMain/kotlin/kscience/kmath/operations/Complex.kt
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@ -1,221 +0,0 @@
package kscience.kmath.operations
import kscience.kmath.memory.MemoryReader
import kscience.kmath.memory.MemorySpec
import kscience.kmath.memory.MemoryWriter
import kscience.kmath.misc.UnstableKMathAPI
import kscience.kmath.structures.Buffer
import kscience.kmath.structures.MemoryBuffer
import kscience.kmath.structures.MutableBuffer
import kscience.kmath.structures.MutableMemoryBuffer
import kotlin.math.*
/**
* This complex's conjugate.
*/
public val Complex.conjugate: Complex
get() = Complex(re, -im)
/**
* This complex's reciprocal.
*/
public val Complex.reciprocal: Complex
get() {
val scale = re * re + im * im
return Complex(re / scale, -im / scale)
}
/**
* Absolute value of complex number.
*/
public val Complex.r: Double
get() = sqrt(re * re + im * im)
/**
* An angle between vector represented by complex number and X axis.
*/
public val Complex.theta: Double
get() = atan(im / re)
private val PI_DIV_2 = Complex(PI / 2, 0)
/**
* A field of [Complex].
*/
@OptIn(UnstableKMathAPI::class)
public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex>, RingWithNumbers<Complex> {
override val zero: Complex = 0.0.toComplex()
override val one: Complex = 1.0.toComplex()
/**
* The imaginary unit.
*/
public val i: Complex = Complex(0.0, 1.0)
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 {
b.re.isNaN() || b.im.isNaN() -> Complex(Double.NaN, Double.NaN)
(if (b.im < 0) -b.im else +b.im) < (if (b.re < 0) -b.re else +b.re) -> {
val wr = b.im / b.re
val wd = b.re + wr * b.im
if (wd.isNaN() || wd == 0.0)
Complex(Double.NaN, Double.NaN)
else
Complex((a.re + a.im * wr) / wd, (a.im - a.re * wr) / wd)
}
b.im == 0.0 -> Complex(Double.NaN, Double.NaN)
else -> {
val wr = b.re / b.im
val wd = b.im + wr * b.re
if (wd.isNaN() || wd == 0.0)
Complex(Double.NaN, Double.NaN)
else
Complex((a.re * wr + a.im) / wd, (a.im * wr - a.re) / wd)
}
}
override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2
override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2
override fun tan(arg: Complex): Complex {
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 atan(arg: Complex): Complex {
val iArg = i * arg
return i * (ln(1 - iArg) - ln(1 + iArg)) / 2
}
override fun power(arg: Complex, pow: Number): Complex = if (arg.im == 0.0)
arg.re.pow(pow.toDouble()).toComplex()
else
exp(pow * ln(arg))
override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im))
override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)
/**
* Adds complex number to real one.
*
* @receiver the addend.
* @param c the augend.
* @return the sum.
*/
public operator fun Double.plus(c: Complex): Complex = add(this.toComplex(), c)
/**
* 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)
/**
* Adds real number to complex one.
*
* @receiver the addend.
* @param d the augend.
* @return the sum.
*/
public operator fun Complex.plus(d: Double): Complex = d + this
/**
* 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())
/**
* 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)
override fun norm(arg: Complex): Complex = sqrt(arg.conjugate * arg)
override fun symbol(value: String): Complex = if (value == "i") i else super<ExtendedField>.symbol(value)
}
/**
* Represents `double`-based complex number.
*
* @property re The real part.
* @property im The imaginary part.
*/
public data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Complex, ComplexField>,
Comparable<Complex> {
public constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble())
override val context: ComplexField get() = ComplexField
override fun unwrap(): Complex = this
override fun Complex.wrap(): Complex = this
override fun compareTo(other: Complex): Int = r.compareTo(other.r)
override fun toString(): String {
return "($re + i*$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)
}
}
}
/**
* Creates a complex number with real part equal to this real.
*
* @receiver the real part.
* @return the new complex number.
*/
public fun Number.toComplex(): Complex = Complex(this, 0.0)
/**
* 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)