CHANGELOG.md

@@ -18,6 +18,7 @@
 - Some minor utilities to `kmath-for-real`
 - Generic operation result parameter to `MatrixContext`
 - New `MatrixFeature` interfaces for matrix decompositions
+- Basic Quaternion vector support in `kmath-complex`.
 - Integration with GNU Scientific Library with `kmath-gsl` for Kotlin/Native Linux x64 target.
 
 ### Changed
@@ -39,6 +40,7 @@
 - Capitalization of LUP in many names changed to Lup.
 - Refactored `NDStructure` algebra to be more simple, preferring under-the-hood conversion to explicit NDStructure types
 - Refactor histograms. They are marked as prototype
+- `Complex` and related features moved to a separate module `kmath-complex`
 - Refactor AlgebraElement
 
 ### Deprecated

README.md

@@ -104,6 +104,17 @@ KMath is a modular library. Different modules provide different features with di
 > **Maturity**: EXPERIMENTAL
 <hr/>
 
+* ### [kmath-complex](kmath-complex)
+> Complex numbers and quaternions.
+>
+> **Maturity**: PROTOTYPE
+>
+> **Features:**
+> - [complex](kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/Complex.kt) : Complex Numbers
+> - [quaternion](kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/Quaternion.kt) : Quaternions
+
+<hr/>
+
 * ### [kmath-core](kmath-core)
 > Core classes, algebra definitions, basic linear algebra
 >

examples/build.gradle.kts

@@ -29,6 +29,7 @@ dependencies {
     implementation(project(":kmath-core"))
     implementation(project(":kmath-coroutines"))
     implementation(project(":kmath-commons"))
+    implementation(project(":kmath-complex"))
     implementation(project(":kmath-stat"))
     implementation(project(":kmath-viktor"))
     implementation(project(":kmath-dimensions"))

examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/DotBenchmark.kt

@@ -14,7 +14,7 @@ import org.openjdk.jmh.annotations.State
 import kotlin.random.Random
 
 @State(Scope.Benchmark)
-class DotBenchmark {
+internal class DotBenchmark {
     companion object {
         val random = Random(12224)
         val dim = 1000

examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/ExpressionsInterpretersBenchmark.kt

@@ -1,6 +1,8 @@
-package kscience.kmath.ast
+package kscience.kmath.benchmarks
 
 import kscience.kmath.asm.compile
+import kscience.kmath.ast.MstField
+import kscience.kmath.ast.mstInField
 import kscience.kmath.expressions.Expression
 import kscience.kmath.expressions.expressionInField
 import kscience.kmath.expressions.invoke
@@ -37,7 +39,7 @@ internal class ExpressionsInterpretersBenchmark {
     @Benchmark
     fun asmExpression() {
         val expr = algebra.mstInField {
-            symbol("x") * 2.0 + 2.0 / symbol("x") - 16.0
+            MstField.symbol("x") * 2.0 + 2.0 / MstField.symbol("x") - 16.0
         }.compile()
 
         invokeAndSum(expr)

examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt

@@ -1,5 +1,4 @@
-package kscience.kmath.linear
-
+package kscience.kmath.benchmarks
 
 import kotlinx.benchmark.Benchmark
 import kscience.kmath.commons.linear.CMMatrixContext
@@ -7,14 +6,17 @@ import kscience.kmath.commons.linear.CMMatrixContext.dot
 import kscience.kmath.commons.linear.inverse
 import kscience.kmath.ejml.EjmlMatrixContext
 import kscience.kmath.ejml.inverse
+import kscience.kmath.linear.Matrix
+import kscience.kmath.linear.MatrixContext
+import kscience.kmath.linear.inverseWithLup
+import kscience.kmath.linear.real
 import kscience.kmath.operations.invoke
-import kscience.kmath.structures.Matrix
 import org.openjdk.jmh.annotations.Scope
 import org.openjdk.jmh.annotations.State
 import kotlin.random.Random
 
 @State(Scope.Benchmark)
-class LinearAlgebraBenchmark {
+internal class LinearAlgebraBenchmark {
     companion object {
         val random = Random(1224)
         val dim = 100

examples/src/main/kotlin/kscience/kmath/operations/ComplexDemo.kt

@@ -1,11 +1,12 @@
 package kscience.kmath.operations
 
+import kscience.kmath.complex.Complex
+import kscience.kmath.complex.complex
 import kscience.kmath.nd.NDAlgebra
-import kscience.kmath.nd.complex
 
 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)
@@ -18,5 +19,6 @@ fun main() {
 
         (a pow b) + c
     }
+
     println(result)
 }

examples/src/main/kotlin/kscience/kmath/structures/ComplexND.kt

@@ -2,10 +2,12 @@
 
 package kscience.kmath.structures
 
+import kscience.kmath.complex.*
 import kscience.kmath.linear.transpose
-import kscience.kmath.nd.*
-import kscience.kmath.operations.Complex
-import kscience.kmath.operations.ComplexField
+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
 

gradle.properties

@@ -2,7 +2,6 @@ kotlin.code.style=official
 kotlin.mpp.enableGranularSourceSetsMetadata=true
 kotlin.mpp.stability.nowarn=true
 kotlin.native.enableDependencyPropagation=false
-kotlin.native.ignoreDisabledTargets=true
 kotlin.parallel.tasks.in.project=true
 org.gradle.jvmargs=-XX:MaxMetaspaceSize=512m
 org.gradle.parallel=true

kmath-ast/build.gradle.kts

@@ -25,6 +25,12 @@ kotlin.sourceSets {
         }
     }
 
+    commonTest {
+        dependencies {
+            implementation(project(":kmath-complex"))
+        }
+    }
+
     jsMain {
         dependencies {
             implementation(npm("astring", "1.4.3"))

kmath-ast/src/jsTest/kotlin/kscience/kmath/estree/TestESTreeConsistencyWithInterpreter.kt

@@ -1,11 +1,11 @@
 package kscience.kmath.estree
 
 import kscience.kmath.ast.*
+import kscience.kmath.complex.ComplexField
+import kscience.kmath.complex.toComplex
 import kscience.kmath.expressions.invoke
 import kscience.kmath.operations.ByteRing
-import kscience.kmath.operations.ComplexField
 import kscience.kmath.operations.RealField
-import kscience.kmath.operations.toComplex
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-ast/src/jvmTest/kotlin/kscience/kmath/asm/TestAsmConsistencyWithInterpreter.kt

@@ -1,11 +1,10 @@
 package kscience.kmath.asm
 
 import kscience.kmath.ast.*
+import kscience.kmath.complex.*
 import kscience.kmath.expressions.invoke
 import kscience.kmath.operations.ByteRing
-import kscience.kmath.operations.ComplexField
 import kscience.kmath.operations.RealField
-import kscience.kmath.operations.toComplex
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-ast/src/jvmTest/kotlin/kscience/kmath/ast/ParserTest.kt

@@ -1,9 +1,9 @@
 package kscience.kmath.ast
 
+import kscience.kmath.complex.Complex
+import kscience.kmath.complex.ComplexField
 import kscience.kmath.expressions.invoke
 import kscience.kmath.operations.Algebra
-import kscience.kmath.operations.Complex
-import kscience.kmath.operations.ComplexField
 import kscience.kmath.operations.RealField
 import kotlin.test.Test
 import kotlin.test.assertEquals

kmath-commons/build.gradle.kts

@@ -5,6 +5,7 @@ description = "Commons math binding for kmath"
 
 dependencies {
     api(project(":kmath-core"))
+    api(project(":kmath-complex"))
     api(project(":kmath-coroutines"))
     api(project(":kmath-stat"))
     api(project(":kmath-functions"))

kmath-commons/src/main/kotlin/kscience/kmath/commons/transform/Transformations.kt

@@ -3,7 +3,7 @@ package kscience.kmath.commons.transform
 import kotlinx.coroutines.FlowPreview
 import kotlinx.coroutines.flow.Flow
 import kotlinx.coroutines.flow.map
-import kscience.kmath.operations.Complex
+import kscience.kmath.complex.*
 import kscience.kmath.streaming.chunked
 import kscience.kmath.streaming.spread
 import kscience.kmath.structures.*

kmath-complex/README.md

@@ -0,0 +1,45 @@
+# The Core Module (`kmath-core`)
+
+Complex and hypercomplex number systems in KMath:
+
+ - [complex](src/commonMain/kotlin/kscience/kmath/complex/Complex.kt) : Complex Numbers
+ - [quaternion](src/commonMain/kotlin/kscience/kmath/complex/Quaternion.kt) : Quaternions
+
+
+> #### Artifact:
+>
+> This module artifact: `kscience.kmath:kmath-complex:0.2.0-dev-6`.
+>
+> Bintray release version:        [ ![Download](https://api.bintray.com/packages/mipt-npm/kscience/kmath-complex/images/download.svg) ](https://bintray.com/mipt-npm/kscience/kmath-complex/_latestVersion)
+>
+> Bintray development version:    [ ![Download](https://api.bintray.com/packages/mipt-npm/dev/kmath-complex/images/download.svg) ](https://bintray.com/mipt-npm/dev/kmath-complex/_latestVersion)
+>
+> **Gradle:**
+>
+> ```gradle
+> repositories {
+>     maven { url "https://dl.bintray.com/kotlin/kotlin-eap" }
+>     maven { url 'https://dl.bintray.com/mipt-npm/kscience' }
+>     maven { url 'https://dl.bintray.com/mipt-npm/dev' }
+>     maven { url 'https://dl.bintray.com/hotkeytlt/maven' }
+> 
+> }
+> 
+> dependencies {
+>     implementation 'kscience.kmath:kmath-complex:0.2.0-dev-6'
+> }
+> ```
+> **Gradle Kotlin DSL:**
+>
+> ```kotlin
+> repositories {
+>     maven("https://dl.bintray.com/kotlin/kotlin-eap")
+>     maven("https://dl.bintray.com/mipt-npm/kscience")
+>     maven("https://dl.bintray.com/mipt-npm/dev")
+>     maven("https://dl.bintray.com/hotkeytlt/maven")
+> }
+> 
+> dependencies {
+>     implementation("kscience.kmath:kmath-complex:0.2.0-dev-6")
+> }
+> ```

kmath-complex/build.gradle.kts

@@ -0,0 +1,36 @@
+import ru.mipt.npm.gradle.Maturity
+
+plugins {
+    id("ru.mipt.npm.mpp")
+    id("ru.mipt.npm.native")
+}
+
+kotlin.sourceSets {
+    all {
+        languageSettings.useExperimentalAnnotation("kscience.kmath.misc.UnstableKMathAPI")
+    }
+
+    commonMain {
+        dependencies {
+            api(project(":kmath-core"))
+        }
+    }
+}
+
+readme {
+    description = "Complex numbers and quaternions."
+    maturity = Maturity.PROTOTYPE
+    propertyByTemplate("artifact", rootProject.file("docs/templates/ARTIFACT-TEMPLATE.md"))
+
+    feature(
+        id = "complex",
+        description = "Complex Numbers",
+        ref = "src/commonMain/kotlin/kscience/kmath/complex/Complex.kt"
+    )
+
+    feature(
+        id = "quaternion",
+        description = "Quaternions",
+        ref = "src/commonMain/kotlin/kscience/kmath/complex/Quaternion.kt"
+    )
+}

kmath-complex/docs/README-TEMPLATE.md

@@ -0,0 +1,7 @@
+# The Core Module (`kmath-core`)
+
+Complex and hypercomplex number systems in KMath:
+
+${features}
+
+${artifact}

kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/Complex.kt

@@ -1,9 +1,12 @@
-package kscience.kmath.operations
+package kscience.kmath.complex
 
 import kscience.kmath.memory.MemoryReader
 import kscience.kmath.memory.MemorySpec
 import kscience.kmath.memory.MemoryWriter
-import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.operations.ExtendedField
+import kscience.kmath.operations.FieldElement
+import kscience.kmath.operations.Norm
+import kscience.kmath.operations.RingWithNumbers
 import kscience.kmath.structures.Buffer
 import kscience.kmath.structures.MemoryBuffer
 import kscience.kmath.structures.MutableBuffer
@@ -42,74 +45,70 @@ 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()
+    public override val zero: Complex = 0.0.toComplex()
+    public override val one: Complex = 1.0.toComplex()
 
     /**
      * The imaginary unit.
      */
-    public val i: Complex = Complex(0.0, 1.0)
+    public val i: Complex by lazy { Complex(0.0, 1.0) }
 
-    override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
+    public override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
+    public override fun multiply(a: Complex, k: Number): Complex = Complex(a.re * k.toDouble(), a.im * k.toDouble())
 
-    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 =
+    public 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) -> {
+    public 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)
-                Complex(Double.NaN, Double.NaN)
+                throw ArithmeticException("Division by zero or infinity")
             else
                 Complex((a.re + a.im * wr) / wd, (a.im - a.re * wr) / wd)
         }
 
-        b.im == 0.0 -> Complex(Double.NaN, Double.NaN)
+        b.im == 0.0 -> throw ArithmeticException("Division by zero")
 
         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)
+                throw ArithmeticException("Division by zero or infinity")
             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
+    public override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2
+    public override fun cos(arg: Complex): Complex = (exp(-i * arg) + exp(i * arg)) / 2
 
-    override fun tan(arg: Complex): Complex {
+    public 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)
+    public override fun asin(arg: Complex): Complex = -i * ln(sqrt(1 - (arg * arg)) + i * arg)
+    public override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(1 - (arg * arg)) + i * arg)
 
-    override fun atan(arg: Complex): Complex {
+    public 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)
+    public 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))
+    public 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)
+    public override fun ln(arg: Complex): Complex = ln(arg.r) + i * atan2(arg.im, arg.re)
 
     /**
      * Adds complex number to real one.
@@ -156,9 +155,9 @@ public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex>, Rin
      */
     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)
+    public 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)
+    public override fun symbol(value: String): Complex = if (value == "i") i else super<ExtendedField>.symbol(value)
 }
 
 /**
@@ -167,29 +166,21 @@ public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex>, Rin
  * @property re The real part.
  * @property im The imaginary part.
  */
-@OptIn(UnstableKMathAPI::class)
-public data class Complex(
-    val re: Double,
-    val im: Double,
-) : FieldElement<Complex, ComplexField>, Comparable<Complex> {
+public data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
     public constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble())
+    public constructor(re: Number) : this(re.toDouble(), 0.0)
 
-    override val context: ComplexField get() = ComplexField
-
-    override fun compareTo(other: Complex): Int = r.compareTo(other.r)
-
-    override fun toString(): String {
-        return "($re + i*$im)"
-    }
+    public override val context: ComplexField get() = ComplexField
 
+    public override fun toString(): String = "($re + i*$im)"
 
     public companion object : MemorySpec<Complex> {
-        override val objectSize: Int
+        public override val objectSize: Int
             get() = 16
 
-        override fun MemoryReader.read(offset: Int): Complex = Complex(readDouble(offset), readDouble(offset + 8))
+        public override fun MemoryReader.read(offset: Int): Complex = Complex(readDouble(offset), readDouble(offset + 8))
 
-        override fun MemoryWriter.write(offset: Int, value: Complex) {
+        public override fun MemoryWriter.write(offset: Int, value: Complex) {
             writeDouble(offset, value.re)
             writeDouble(offset + 8, value.im)
         }
@@ -203,7 +194,7 @@ public data class Complex(
  * @receiver the real part.
  * @return the new complex number.
  */
-public fun Number.toComplex(): Complex = Complex(this, 0.0)
+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

kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/ComplexNDField.kt

@@ -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

kmath-complex/src/commonMain/kotlin/kscience/kmath/complex/Quaternion.kt

@@ -0,0 +1,259 @@
+package kscience.kmath.complex
+
+import kscience.kmath.memory.MemoryReader
+import kscience.kmath.memory.MemorySpec
+import kscience.kmath.memory.MemoryWriter
+import kscience.kmath.operations.*
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.MemoryBuffer
+import kscience.kmath.structures.MutableBuffer
+import 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() {
+        val n = QuaternionField { 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].
+ */
+public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>, PowerOperations<Quaternion>,
+    ExponentialOperations<Quaternion>, RingWithNumbers<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)
+
+    public 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)
+
+    public override fun multiply(a: Quaternion, k: Number): Quaternion {
+        val d = k.toDouble()
+        return Quaternion(a.w * d, a.x * d, a.y * d, a.z * d)
+    }
+
+    public 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,
+    )
+
+    public 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,
+        )
+    }
+
+    public 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)
+    }
+
+    public 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)
+    }
+
+    public 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 { 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)
+    }
+
+    public override operator fun Number.plus(b: Quaternion): Quaternion = Quaternion(toDouble() + b.w, b.x, b.y, b.z)
+
+    public override operator fun Number.minus(b: Quaternion): Quaternion =
+        Quaternion(toDouble() - b.w, -b.x, -b.y, -b.z)
+
+    public override operator fun Quaternion.plus(b: Number): Quaternion = Quaternion(w + b.toDouble(), x, y, z)
+    public override operator fun Quaternion.minus(b: Number): Quaternion = Quaternion(w - b.toDouble(), x, y, z)
+
+    public override operator fun Number.times(b: Quaternion): Quaternion =
+        Quaternion(toDouble() * b.w, toDouble() * b.x, toDouble() * b.y, toDouble() * b.z)
+
+    public override fun Quaternion.unaryMinus(): Quaternion = Quaternion(-w, -x, -y, -z)
+    public override fun norm(arg: Quaternion): Quaternion = sqrt(arg.conjugate * arg)
+
+    public override fun symbol(value: String): Quaternion = when (value) {
+        "i" -> i
+        "j" -> j
+        "k" -> k
+        else -> super<Field>.symbol(value)
+    }
+}
+
+/**
+ * Represents `double`-based quaternion.
+ *
+ * @property w The first component.
+ * @property x The second component.
+ * @property y The third component.
+ * @property z The fourth component.
+ */
+public data class Quaternion(val w: Double, val x: Double, val y: Double, val z: Double) :
+    FieldElement<Quaternion, QuaternionField> {
+    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" }
+    }
+
+    public override val context: QuaternionField
+        get() = QuaternionField
+
+    /**
+     * Returns a string representation of this quaternion.
+     */
+    public override fun toString(): String = "($w + $x * i + $y * j + $z * k)"
+
+    public companion object : MemorySpec<Quaternion> {
+        public override val objectSize: Int
+            get() = 32
+
+        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 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)

kmath-complex/src/commonTest/kotlin/kscience/kmath/complex/ComplexBufferSpecTest.kt

@@ -1,7 +1,6 @@
-package kscience.kmath.structures
+package kscience.kmath.complex
 
-import kscience.kmath.operations.Complex
-import kscience.kmath.operations.complex
+import kscience.kmath.structures.Buffer
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-complex/src/commonTest/kotlin/kscience/kmath/complex/ComplexFieldTest.kt

@@ -1,6 +1,6 @@
-package kscience.kmath.operations
+package kscience.kmath.complex
 
-import kscience.kmath.operations.internal.FieldVerifier
+import kscience.kmath.operations.invoke
 import kotlin.math.PI
 import kotlin.math.abs
 import kotlin.test.Test
@@ -8,8 +8,9 @@ import kotlin.test.assertEquals
 import kotlin.test.assertTrue
 
 internal class ComplexFieldTest {
-    @Test
-    fun verify() = ComplexField { FieldVerifier(this, 42.0 * i, 66.0 + 28 * i, 2.0 + 0 * i, 5).verify() }
+    //    TODO make verifier classes available in this source set
+    //    @Test
+    //    fun verify() = ComplexField { FieldVerifier(this, 42.0 * i, 66.0 + 28 * i, 2.0 + 0 * i, 5).verify() }
 
     @Test
     fun testAddition() {
@@ -37,8 +38,6 @@ internal class ComplexFieldTest {
         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(Double.NaN, Double.NaN), ComplexField { Complex(1, 1) / Complex(Double.NaN, Double.NaN) })
-        assertEquals(Complex(Double.NaN, Double.NaN), ComplexField { Complex(1, 1) / Complex(0, 0) })
     }
 
     @Test

kmath-complex/src/commonTest/kotlin/kscience/kmath/complex/ComplexTest.kt

@@ -0,0 +1,31 @@
+package kscience.kmath.complex
+
+import 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())
+    }
+}

kmath-complex/src/commonTest/kotlin/kscience/kmath/complex/ExpressionFieldForComplexTest.kt

@@ -0,0 +1,26 @@
+package kscience.kmath.complex
+
+import kscience.kmath.expressions.FunctionalExpressionField
+import kscience.kmath.expressions.bind
+import kscience.kmath.expressions.invoke
+import kscience.kmath.expressions.symbol
+import kscience.kmath.operations.invoke
+import kotlin.test.Test
+import kotlin.test.assertEquals
+
+internal class ExpressionFieldForComplexTest {
+    val x by symbol
+
+    @Test
+    fun testComplex() {
+        val context = FunctionalExpressionField(ComplexField)
+
+        val expression = context {
+            val x = bind(x)
+            x * x + 2 * x + one
+        }
+
+        assertEquals(expression(x to Complex(1.0, 0.0)), Complex(4.0, 0.0))
+        //assertEquals(expression(), Complex(9.0, 0.0))
+    }
+}

kmath-complex/src/commonTest/kotlin/kscience/kmath/complex/QuaternionFieldTest.kt

@@ -0,0 +1,45 @@
+package kscience.kmath.complex
+
+import 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) })
+    }
+
+//    @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 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() })
+    }
+}

kmath-core/api/kmath-core.api

@@ -1038,71 +1038,6 @@ public class kscience/kmath/nd/BufferedNDSpace : kscience/kmath/nd/BufferNDAlgeb
 	public fun unaryPlus (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDStructure;
 }
 
-public final class kscience/kmath/nd/ComplexNDField : kscience/kmath/nd/BufferedNDField, kscience/kmath/operations/ExtendedField, kscience/kmath/operations/RingWithNumbers {
-	public fun <init> ([I)V
-	public synthetic fun acos (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun acos (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun acosh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun acosh (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun asin (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun asin (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun asinh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun asinh (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun atan (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun atan (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun atanh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun atanh (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun cos (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun cos (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun cosh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun cosh (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun exp (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun exp (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun getOne ()Ljava/lang/Object;
-	public fun getOne ()Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun getZero ()Ljava/lang/Object;
-	public fun getZero ()Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun leftSideNumberOperation (Ljava/lang/String;Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun leftSideNumberOperation (Ljava/lang/String;Ljava/lang/Number;Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDStructure;
-	public fun leftSideNumberOperationFunction (Ljava/lang/String;)Lkotlin/jvm/functions/Function2;
-	public synthetic fun ln (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun ln (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun minus (Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun minus (Ljava/lang/Number;Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDStructure;
-	public synthetic fun minus (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun minus (Lkscience/kmath/nd/NDStructure;Ljava/lang/Number;)Lkscience/kmath/nd/NDStructure;
-	public synthetic fun number (Ljava/lang/Number;)Ljava/lang/Object;
-	public fun number (Ljava/lang/Number;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun plus (Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun plus (Ljava/lang/Number;Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDStructure;
-	public synthetic fun plus (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun plus (Lkscience/kmath/nd/NDStructure;Ljava/lang/Number;)Lkscience/kmath/nd/NDStructure;
-	public synthetic fun pow (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun pow (Lkscience/kmath/nd/NDStructure;Ljava/lang/Number;)Lkscience/kmath/nd/NDStructure;
-	public synthetic fun power (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun power (Lkscience/kmath/nd/NDStructure;Ljava/lang/Number;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun rightSideNumberOperation (Ljava/lang/String;Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun rightSideNumberOperation (Ljava/lang/String;Lkscience/kmath/nd/NDStructure;Ljava/lang/Number;)Lkscience/kmath/nd/NDStructure;
-	public fun rightSideNumberOperationFunction (Ljava/lang/String;)Lkotlin/jvm/functions/Function2;
-	public synthetic fun sin (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun sin (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun sinh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun sinh (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun sqrt (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun sqrt (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDStructure;
-	public synthetic fun tan (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun tan (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public synthetic fun tanh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun tanh (Lkscience/kmath/nd/NDStructure;)Lkscience/kmath/nd/NDBuffer;
-	public fun unaryOperationFunction (Ljava/lang/String;)Lkotlin/jvm/functions/Function1;
-}
-
-public final class kscience/kmath/nd/ComplexNDFieldKt {
-	public static final fun complex (Lkscience/kmath/nd/NDAlgebra$Companion;[I)Lkscience/kmath/nd/ComplexNDField;
-	public static final fun nd (Lkscience/kmath/operations/ComplexField;[ILkotlin/jvm/functions/Function1;)Ljava/lang/Object;
-	public static final fun produceInline (Lkscience/kmath/nd/BufferedNDField;Lkotlin/jvm/functions/Function2;)Lkscience/kmath/nd/NDBuffer;
-}
-
 public final class kscience/kmath/nd/DefaultStrides : kscience/kmath/nd/Strides {
 	public static final field Companion Lkscience/kmath/nd/DefaultStrides$Companion;
 	public synthetic fun <init> ([ILkotlin/jvm/internal/DefaultConstructorMarker;)V
@@ -1682,145 +1617,6 @@ public final class kscience/kmath/operations/ByteRing : kscience/kmath/operation
 	public synthetic fun unaryPlus (Ljava/lang/Object;)Ljava/lang/Object;
 }
 
-public final class kscience/kmath/operations/Complex : java/lang/Comparable, kscience/kmath/operations/FieldElement {
-	public static final field Companion Lkscience/kmath/operations/Complex$Companion;
-	public fun <init> (DD)V
-	public fun <init> (Ljava/lang/Number;Ljava/lang/Number;)V
-	public synthetic fun compareTo (Ljava/lang/Object;)I
-	public fun compareTo (Lkscience/kmath/operations/Complex;)I
-	public final fun component1 ()D
-	public final fun component2 ()D
-	public final fun copy (DD)Lkscience/kmath/operations/Complex;
-	public static synthetic fun copy$default (Lkscience/kmath/operations/Complex;DDILjava/lang/Object;)Lkscience/kmath/operations/Complex;
-	public fun equals (Ljava/lang/Object;)Z
-	public synthetic fun getContext ()Lkscience/kmath/operations/Algebra;
-	public fun getContext ()Lkscience/kmath/operations/ComplexField;
-	public final fun getIm ()D
-	public final fun getRe ()D
-	public fun hashCode ()I
-	public fun toString ()Ljava/lang/String;
-}
-
-public final class kscience/kmath/operations/Complex$Companion : kscience/kmath/memory/MemorySpec {
-	public fun getObjectSize ()I
-	public synthetic fun read (Lkscience/kmath/memory/MemoryReader;I)Ljava/lang/Object;
-	public fun read (Lkscience/kmath/memory/MemoryReader;I)Lkscience/kmath/operations/Complex;
-	public synthetic fun write (Lkscience/kmath/memory/MemoryWriter;ILjava/lang/Object;)V
-	public fun write (Lkscience/kmath/memory/MemoryWriter;ILkscience/kmath/operations/Complex;)V
-}
-
-public final class kscience/kmath/operations/ComplexField : kscience/kmath/operations/ExtendedField, kscience/kmath/operations/Norm, kscience/kmath/operations/RingWithNumbers {
-	public static final field INSTANCE Lkscience/kmath/operations/ComplexField;
-	public synthetic fun acos (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun acos (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun acosh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun acosh (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun add (Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun add (Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun asin (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun asin (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun asinh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun asinh (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun atan (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun atan (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun atanh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun atanh (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun binaryOperation (Ljava/lang/String;Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun binaryOperation (Ljava/lang/String;Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public fun binaryOperationFunction (Ljava/lang/String;)Lkotlin/jvm/functions/Function2;
-	public synthetic fun cos (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun cos (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun cosh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun cosh (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun div (Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun div (Ljava/lang/Number;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun div (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public synthetic fun div (Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun div (Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public fun div (Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun divide (Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun divide (Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun exp (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun exp (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public final fun getI ()Lkscience/kmath/operations/Complex;
-	public synthetic fun getOne ()Ljava/lang/Object;
-	public fun getOne ()Lkscience/kmath/operations/Complex;
-	public synthetic fun getZero ()Ljava/lang/Object;
-	public fun getZero ()Lkscience/kmath/operations/Complex;
-	public synthetic fun leftSideNumberOperation (Ljava/lang/String;Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun leftSideNumberOperation (Ljava/lang/String;Ljava/lang/Number;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public fun leftSideNumberOperationFunction (Ljava/lang/String;)Lkotlin/jvm/functions/Function2;
-	public synthetic fun ln (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun ln (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public final fun minus (DLkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun minus (Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun minus (Ljava/lang/Number;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun minus (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public synthetic fun minus (Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public final fun minus (Lkscience/kmath/operations/Complex;D)Lkscience/kmath/operations/Complex;
-	public fun minus (Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public fun minus (Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun multiply (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public synthetic fun multiply (Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun multiply (Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public fun multiply (Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun norm (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun norm (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun number (Ljava/lang/Number;)Ljava/lang/Object;
-	public fun number (Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public final fun plus (DLkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun plus (Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun plus (Ljava/lang/Number;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun plus (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public synthetic fun plus (Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public final fun plus (Lkscience/kmath/operations/Complex;D)Lkscience/kmath/operations/Complex;
-	public fun plus (Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public fun plus (Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun pow (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun pow (Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public synthetic fun power (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun power (Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public synthetic fun rightSideNumberOperation (Ljava/lang/String;Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public fun rightSideNumberOperation (Ljava/lang/String;Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public fun rightSideNumberOperationFunction (Ljava/lang/String;)Lkotlin/jvm/functions/Function2;
-	public synthetic fun sin (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun sin (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun sinh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun sinh (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun sqrt (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun sqrt (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun symbol (Ljava/lang/String;)Ljava/lang/Object;
-	public fun symbol (Ljava/lang/String;)Lkscience/kmath/operations/Complex;
-	public synthetic fun tan (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun tan (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun tanh (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun tanh (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public final fun times (DLkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun times (Ljava/lang/Number;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun times (Ljava/lang/Number;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun times (Ljava/lang/Object;Ljava/lang/Number;)Ljava/lang/Object;
-	public synthetic fun times (Ljava/lang/Object;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun times (Lkscience/kmath/operations/Complex;Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-	public fun times (Lkscience/kmath/operations/Complex;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun unaryMinus (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun unaryMinus (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public synthetic fun unaryOperation (Ljava/lang/String;Ljava/lang/Object;)Ljava/lang/Object;
-	public fun unaryOperation (Ljava/lang/String;Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public fun unaryOperationFunction (Ljava/lang/String;)Lkotlin/jvm/functions/Function1;
-	public synthetic fun unaryPlus (Ljava/lang/Object;)Ljava/lang/Object;
-	public fun unaryPlus (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-}
-
-public final class kscience/kmath/operations/ComplexKt {
-	public static final fun complex (Lkscience/kmath/structures/Buffer$Companion;ILkotlin/jvm/functions/Function1;)Lkscience/kmath/structures/Buffer;
-	public static final fun complex (Lkscience/kmath/structures/MutableBuffer$Companion;ILkotlin/jvm/functions/Function1;)Lkscience/kmath/structures/MutableBuffer;
-	public static final fun getConjugate (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public static final fun getR (Lkscience/kmath/operations/Complex;)D
-	public static final fun getReciprocal (Lkscience/kmath/operations/Complex;)Lkscience/kmath/operations/Complex;
-	public static final fun getTheta (Lkscience/kmath/operations/Complex;)D
-	public static final fun toComplex (Ljava/lang/Number;)Lkscience/kmath/operations/Complex;
-}
-
 public abstract interface class kscience/kmath/operations/ExponentialOperations : kscience/kmath/operations/Algebra {
 	public static final field Companion Lkscience/kmath/operations/ExponentialOperations$Companion;
 	public static final field EXP_OPERATION Ljava/lang/String;

kmath-core/build.gradle.kts

@@ -1,17 +1,21 @@
+import ru.mipt.npm.gradle.Maturity
+
 plugins {
     id("ru.mipt.npm.mpp")
     id("ru.mipt.npm.native")
 }
 
-kotlin.sourceSets.commonMain {
-    dependencies {
-        api(project(":kmath-memory"))
+kotlin.sourceSets {
+    commonMain {
+        dependencies {
+            api(project(":kmath-memory"))
+        }
     }
 }
 
 readme {
     description = "Core classes, algebra definitions, basic linear algebra"
-    maturity = ru.mipt.npm.gradle.Maturity.DEVELOPMENT
+    maturity = Maturity.DEVELOPMENT
     propertyByTemplate("artifact", rootProject.file("docs/templates/ARTIFACT-TEMPLATE.md"))
 
     feature(

kmath-core/src/commonMain/kotlin/kscience/kmath/linear/MatrixContext.kt

@@ -83,6 +83,7 @@ public interface MatrixContext<T : Any, out M : Matrix<T>> : SpaceOperations<Mat
     public fun <F : Any> getFeature(m: Matrix<T>, type: KClass<F>): F? = m.getFeature(type)
 
     public companion object {
+
         /**
          * A structured matrix with custom buffer
          */
@@ -123,7 +124,7 @@ public inline fun <T : Any, reified F : Any> MatrixContext<T, *>.getFeature(m: M
  */
 public interface GenericMatrixContext<T : Any, R : Ring<T>, out M : Matrix<T>> : MatrixContext<T, M> {
     /**
-     * The ring instance of [T].
+     * The ring over matrix elements.
      */
     public val elementContext: R
 

kmath-core/src/commonMain/kotlin/kscience/kmath/linear/VirtualMatrix.kt

@@ -1,5 +1,10 @@
 package kscience.kmath.linear
 
+/**
+ * The matrix where each element is evaluated each time when is being accessed.
+ *
+ * @property generator the function that provides elements.
+ */
 public class VirtualMatrix<T : Any>(
     override val rowNum: Int,
     override val colNum: Int,

kmath-core/src/commonMain/kotlin/kscience/kmath/nd/Structure2D.kt

@@ -86,3 +86,10 @@ public fun <T> NDStructure<T>.as2D(): Structure2D<T> = if (shape.size == 2)
     Structure2DWrapper(this)
 else
     error("Can't create 2d-structure from ${shape.size}d-structure")
+
+/**
+ * Alias for [Structure2D] with more familiar name.
+ *
+ * @param T the type of items in the matrix.
+ */
+public typealias Matrix<T> = Structure2D<T>

kmath-core/src/commonMain/kotlin/kscience/kmath/structures/Buffer.kt

@@ -1,7 +1,5 @@
 package kscience.kmath.structures
 
-import kscience.kmath.operations.Complex
-import kscience.kmath.operations.complex
 import kotlin.reflect.KClass
 
 /**
@@ -76,7 +74,6 @@ public interface Buffer<T> {
                 Int::class -> IntBuffer(size) { initializer(it) as Int } as Buffer<T>
                 Long::class -> LongBuffer(size) { initializer(it) as Long } as Buffer<T>
                 Float::class -> FloatBuffer(size) { initializer(it) as Float } as Buffer<T>
-                Complex::class -> complex(size) { initializer(it) as Complex } as Buffer<T>
                 else -> boxing(size, initializer)
             }
 
@@ -149,7 +146,6 @@ public interface MutableBuffer<T> : Buffer<T> {
                 Int::class -> IntBuffer(size) { initializer(it) as Int } as MutableBuffer<T>
                 Float::class -> FloatBuffer(size) { initializer(it) as Float } as MutableBuffer<T>
                 Long::class -> LongBuffer(size) { initializer(it) as Long } as MutableBuffer<T>
-                Complex::class -> complex(size) { initializer(it) as Complex } as MutableBuffer<T>
                 else -> boxing(size, initializer)
             }
 

kmath-core/src/commonMain/kotlin/kscience/kmath/structures/MemoryBuffer.kt

@@ -43,8 +43,8 @@ public class MutableMemoryBuffer<T : Any>(memory: Memory, spec: MemorySpec<T>) :
 
     private val writer: MemoryWriter = memory.writer()
 
-    override operator fun set(index: Int, value: T): Unit = writer.write(spec, spec.objectSize * index, value)
-    override fun copy(): MutableBuffer<T> = MutableMemoryBuffer(memory.copy(), spec)
+    public override operator fun set(index: Int, value: T): Unit = writer.write(spec, spec.objectSize * index, value)
+    public override fun copy(): MutableBuffer<T> = MutableMemoryBuffer(memory.copy(), spec)
 
     public companion object {
         public fun <T : Any> create(spec: MemorySpec<T>, size: Int): MutableMemoryBuffer<T> =

kmath-core/src/commonTest/kotlin/kscience/kmath/expressions/ExpressionFieldTest.kt

@@ -1,7 +1,5 @@
 package kscience.kmath.expressions
 
-import kscience.kmath.operations.Complex
-import kscience.kmath.operations.ComplexField
 import kscience.kmath.operations.RealField
 import kscience.kmath.operations.invoke
 import kotlin.test.Test
@@ -10,6 +8,7 @@ import kotlin.test.assertFails
 
 class ExpressionFieldTest {
     val x by symbol
+
     @Test
     fun testExpression() {
         val context = FunctionalExpressionField(RealField)
@@ -20,20 +19,7 @@ class ExpressionFieldTest {
         }
 
         assertEquals(expression(x to 1.0), 4.0)
-        assertFails {  expression()}
-    }
-
-    @Test
-    fun testComplex() {
-        val context = FunctionalExpressionField(ComplexField)
-
-        val expression = context {
-            val  x = bind(x)
-            x * x + 2 * x + one
-        }
-
-        assertEquals(expression(x to Complex(1.0, 0.0)), Complex(4.0, 0.0))
-        //assertEquals(expression(), Complex(9.0, 0.0))
+        assertFails { expression() }
     }
 
     @Test

kmath-core/src/commonTest/kotlin/kscience/kmath/operations/BigIntAlgebraTest.kt

@@ -1,6 +1,6 @@
 package kscience.kmath.operations
 
-import kscience.kmath.operations.internal.RingVerifier
+import kscience.kmath.testutils.RingVerifier
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-core/src/commonTest/kotlin/kscience/kmath/operations/ComplexTest.kt

@@ -1,39 +0,0 @@
-package kscience.kmath.operations
-
-import kotlin.test.Test
-import kotlin.test.assertEquals
-import kotlin.test.assertTrue
-
-internal class ComplexTest {
-    @Test
-    fun conjugate() {
-        assertEquals(
-            Complex(0, -42), (ComplexField.i * 42).conjugate
-        )
-    }
-
-    @Test
-    fun reciprocal() {
-        assertTrue { (Complex(0.5, -0.0) - 2.toComplex().reciprocal).r < 1e-10}
-    }
-
-    @Test
-    fun r() {
-        assertEquals(kotlin.math.sqrt(2.0), (ComplexField.i + 1.0.toComplex()).r)
-    }
-
-    @Test
-    fun theta() {
-        assertEquals(0.0, 1.toComplex().theta)
-    }
-
-    @Test
-    fun toComplex() {
-        assertEquals(Complex(42, 0), 42.toComplex())
-        assertEquals(Complex(42.0, 0), 42.0.toComplex())
-        assertEquals(Complex(42f, 0), 42f.toComplex())
-        assertEquals(Complex(42.0, 0), 42.0.toComplex())
-        assertEquals(Complex(42.toByte(), 0), 42.toByte().toComplex())
-        assertEquals(Complex(42.toShort(), 0), 42.toShort().toComplex())
-    }
-}

kmath-core/src/commonTest/kotlin/kscience/kmath/operations/RealFieldTest.kt

@@ -1,6 +1,6 @@
 package kscience.kmath.operations
 
-import kscience.kmath.operations.internal.FieldVerifier
+import kscience.kmath.testutils.FieldVerifier
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-core/src/commonTest/kotlin/kscience/kmath/structures/NDFieldTest.kt

@@ -3,14 +3,15 @@ package kscience.kmath.structures
 import kscience.kmath.nd.NDAlgebra
 import kscience.kmath.nd.get
 import kscience.kmath.nd.real
-import kscience.kmath.operations.internal.FieldVerifier
+import kscience.kmath.testutils.FieldVerifier
 import kotlin.test.Test
 import kotlin.test.assertEquals
+import kscience.kmath.operations.invoke
 
 internal class NDFieldTest {
     @Test
     fun verify() {
-        NDAlgebra.real(12, 32).run { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
+        (NDAlgebra.real(12, 32)) { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
     }
 
     @Test

kmath-core/src/commonTest/kotlin/kscience/kmath/testutils/AlgebraicVerifier.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.operations.internal
+package kscience.kmath.testutils
 
 import kscience.kmath.operations.Algebra
 

kmath-core/src/commonTest/kotlin/kscience/kmath/testutils/FieldVerifier.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.operations.internal
+package kscience.kmath.testutils
 
 import kscience.kmath.operations.Field
 import kscience.kmath.operations.invoke

kmath-core/src/commonTest/kotlin/kscience/kmath/testutils/RingVerifier.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.operations.internal
+package kscience.kmath.testutils
 
 import kscience.kmath.operations.Ring
 import kscience.kmath.operations.invoke

kmath-core/src/commonTest/kotlin/kscience/kmath/testutils/SpaceVerifier.kt

@@ -1,4 +1,4 @@
-package kscience.kmath.operations.internal
+package kscience.kmath.testutils
 
 import kscience.kmath.operations.Space
 import kscience.kmath.operations.invoke

kmath-coroutines/build.gradle.kts

@@ -12,6 +12,7 @@ kotlin.sourceSets {
     commonMain {
         dependencies {
             api(project(":kmath-core"))
+            api(project(":kmath-complex"))
             api("org.jetbrains.kotlinx:kotlinx-coroutines-core:${ru.mipt.npm.gradle.KScienceVersions.coroutinesVersion}")
         }
     }

kmath-for-real/src/commonTest/kotlin/kaceince/kmath/real/RealMatrixTest.kt

@@ -2,6 +2,7 @@ package kaceince.kmath.real
 
 import kscience.kmath.linear.Matrix
 import kscience.kmath.linear.build
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.real.*
 import kscience.kmath.structures.contentEquals
 import kotlin.test.Test
@@ -91,6 +92,7 @@ internal class RealMatrixTest {
         assertEquals(matrix1.pow(3), matrix3)
     }
 
+    @OptIn(UnstableKMathAPI::class)
     @Test
     fun testTwoMatrixOperations() {
         val matrix1 = Matrix.build(2, 3)(

kmath-stat/build.gradle.kts

@@ -4,7 +4,7 @@ plugins {
 
 kotlin.sourceSets {
     all {
-        with(languageSettings) {
+        languageSettings.apply {
             useExperimentalAnnotation("kotlinx.coroutines.FlowPreview")
             useExperimentalAnnotation("kotlinx.coroutines.ExperimentalCoroutinesApi")
             useExperimentalAnnotation("kotlinx.coroutines.ObsoleteCoroutinesApi")

settings.gradle.kts

@@ -26,9 +26,10 @@ rootProject.name = "kmath"
 
 include(
     ":kmath-memory",
+    ":kmath-complex",
     ":kmath-core",
-    ":kmath-functions",
     ":kmath-coroutines",
+    ":kmath-functions",
     ":kmath-histograms",
     ":kmath-commons",
     ":kmath-viktor",