Fix division of Complex, minor reformat and rearrangement of NumberAlgebra, implement hyperbolic functions

kmath-commons/src/main/kotlin/scientifik/kmath/commons/expressions/DiffExpression.kt

@@ -17,7 +17,6 @@ class DerivativeStructureField(
 ) : ExtendedField<DerivativeStructure> {
 
     override val zero: DerivativeStructure by lazy { DerivativeStructure(order, parameters.size) }
-
     override val one: DerivativeStructure by lazy { DerivativeStructure(order, parameters.size, 1.0) }
 
     private val variables: Map<String, DerivativeStructure> = parameters.mapValues { (key, value) ->
@@ -60,10 +59,18 @@ class DerivativeStructureField(
 
     override fun sin(arg: DerivativeStructure): DerivativeStructure = arg.sin()
     override fun cos(arg: DerivativeStructure): DerivativeStructure = arg.cos()
+    override fun tan(arg: DerivativeStructure): DerivativeStructure = arg.tan()
     override fun asin(arg: DerivativeStructure): DerivativeStructure = arg.asin()
     override fun acos(arg: DerivativeStructure): DerivativeStructure = arg.acos()
     override fun atan(arg: DerivativeStructure): DerivativeStructure = arg.atan()
 
+    override fun sinh(arg: DerivativeStructure): DerivativeStructure = arg.sinh()
+    override fun cosh(arg: DerivativeStructure): DerivativeStructure = arg.cosh()
+    override fun tanh(arg: DerivativeStructure): DerivativeStructure = arg.tanh()
+    override fun asinh(arg: DerivativeStructure): DerivativeStructure = arg.asinh()
+    override fun acosh(arg: DerivativeStructure): DerivativeStructure = arg.acosh()
+    override fun atanh(arg: DerivativeStructure): DerivativeStructure = arg.atanh()
+
     override fun power(arg: DerivativeStructure, pow: Number): DerivativeStructure = when (pow) {
         is Double -> arg.pow(pow)
         is Int -> arg.pow(pow)
@@ -71,9 +78,7 @@ class DerivativeStructureField(
     }
 
     fun power(arg: DerivativeStructure, pow: DerivativeStructure): DerivativeStructure = arg.pow(pow)
-
     override fun exp(arg: DerivativeStructure): DerivativeStructure = arg.exp()
-
     override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
 
     override operator fun DerivativeStructure.plus(b: Number): DerivativeStructure = add(b.toDouble())

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt

@@ -8,28 +8,47 @@ import scientifik.memory.MemorySpec
 import scientifik.memory.MemoryWriter
 import kotlin.math.*
 
+/**
+ * A complex conjugate.
+ */
+val Complex.conjugate: Complex
+    get() = Complex(re, -im)
+
+/**
+ * Absolute value of complex number.
+ */
+val Complex.r: Double
+    get() = sqrt(re * re + im * im)
+
+/**
+ * An angle between vector represented by complex number and X axis.
+ */
+val Complex.theta: Double
+    get() = atan(im / re)
+
 private val PI_DIV_2 = Complex(PI / 2, 0)
 
 /**
- * A field for complex numbers
+ * A field for complex numbers.
  */
 object ComplexField : ExtendedField<Complex> {
-    override val zero: Complex = Complex(0.0, 0.0)
+    override val zero: Complex = Complex(0, 0)
+    override val one: Complex = Complex(1, 0)
 
-    override val one: Complex = Complex(1.0, 0.0)
+    /**
-
+     * The imaginary unit constant.
-    val i = Complex(0.0, 1.0)
+     */
+    val i = Complex(0, 1)
 
     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 {
-        val norm = b.re * b.re + b.im * b.im
+        val scale = b.re * b.re + b.im * b.im
-        return Complex((a.re * b.re + a.im * b.im) / norm, (a.re * b.im - a.im * b.re) / norm)
+        return a * Complex(b.re / scale, -b.im / scale)
     }
 
     override fun sin(arg: Complex): Complex = i * (exp(-i * arg) - exp(i * arg)) / 2
@@ -38,42 +57,40 @@ object ComplexField : ExtendedField<Complex> {
     override fun acos(arg: Complex): Complex = PI_DIV_2 + i * ln(sqrt(one - arg pow 2) + i * arg)
     override fun atan(arg: Complex): Complex = i * (ln(one - i * arg) - ln(one + i * arg)) / 2
 
+    override fun sinh(arg: Complex): Complex = (exp(arg) - exp(-arg)) / 2
+    override fun cosh(arg: Complex): Complex = (exp(arg) + exp(-arg)) / 2
+    override fun tanh(arg: Complex): Complex = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))
+    override fun asinh(arg: Complex): Complex = ln(sqrt(arg pow 2) + arg)
+    override fun acosh(arg: Complex): Complex = ln(arg + sqrt((arg - 1) * (arg + 1)))
+    override fun atanh(arg: Complex): Complex = (ln(arg + 1) - ln(1 - arg)) / 2
+
     override fun power(arg: Complex, pow: Number): Complex =
         arg.r.pow(pow.toDouble()) * (cos(pow.toDouble() * arg.theta) + i * sin(pow.toDouble() * arg.theta))
 
     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)
 
-    operator fun Double.plus(c: Complex) = add(this.toComplex(), c)
+    operator fun Double.plus(c: Complex): Complex = add(toComplex(), c)
-
+    operator fun Double.minus(c: Complex): Complex = add(toComplex(), -c)
-    operator fun Double.minus(c: Complex) = add(this.toComplex(), -c)
+    operator fun Complex.plus(d: Double): Complex = d + this
-
+    operator fun Complex.minus(d: Double): Complex = add(this, -d.toComplex())
-    operator fun Complex.plus(d: Double) = d + this
+    operator fun Double.times(c: Complex): Complex = Complex(c.re * this, c.im * this)
-
+    override fun symbol(value: String): Complex = if (value == "i") i else super.symbol(value)
-    operator fun Complex.minus(d: Double) = add(this, -d.toComplex())
-
-    operator fun Double.times(c: Complex) = Complex(c.re * this, c.im * this)
-
-    override fun symbol(value: String): Complex = if (value == "i") {
-        i
-    } else {
-        super.symbol(value)
-    }
 }
 
 /**
- * Complex number class
+ * Complex number class.
+ *
+ * @property re the real part of the number.
+ * @property im the imaginary part of the number.
  */
 data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Complex, ComplexField>, Comparable<Complex> {
     constructor(re: Number, im: Number) : this(re.toDouble(), im.toDouble())
 
-    override fun unwrap(): Complex = this
-
-    override fun Complex.wrap(): Complex = this
-
     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)
 
     companion object : MemorySpec<Complex> {
@@ -90,26 +107,12 @@ data class Complex(val re: Double, val im: Double) : FieldElement<Complex, Compl
 }
 
 /**
- * A complex conjugate
+ * Creates a [Complex] with its real part of this double.
  */
-val Complex.conjugate: Complex get() = Complex(re, -im)
+fun Double.toComplex(): Complex = Complex(this, 0.0)
 
-/**
+inline fun Buffer.Companion.complex(size: Int, crossinline init: (Int) -> Complex): Buffer<Complex> =
- * Absolute value of complex number
+    MemoryBuffer.create(Complex, size, init)
- */
-val Complex.r: Double get() = sqrt(re * re + im * im)
 
-/**
+inline fun MutableBuffer.Companion.complex(size: Int, crossinline init: (Int) -> Complex): Buffer<Complex> =
- * An angle between vector represented by complex number and X axis
+    MemoryBuffer.create(Complex, size, init)
- */
-val Complex.theta: Double get() = atan(im / re)
-
-fun Double.toComplex() = Complex(this, 0.0)
-
-inline fun Buffer.Companion.complex(size: Int, crossinline init: (Int) -> Complex): Buffer<Complex> {
-    return MemoryBuffer.create(Complex, size, init)
-}
-
-inline fun MutableBuffer.Companion.complex(size: Int, crossinline init: (Int) -> Complex): Buffer<Complex> {
-    return MemoryBuffer.create(Complex, size, init)
-}

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/NumberAlgebra.kt

@@ -7,23 +7,31 @@ import kotlin.math.pow as kpow
  * Advanced Number-like field that implements basic operations
  */
 interface ExtendedFieldOperations<T> :
-    InverseTrigonometricOperations<T>,
+    TrigonometricOperations<T>,
+    HyperbolicTrigonometricOperations<T>,
     PowerOperations<T>,
     ExponentialOperations<T> {
 
     override fun tan(arg: T): T = sin(arg) / cos(arg)
+    override fun tanh(arg: T): T = sinh(arg) / cosh(arg)
 
     override fun unaryOperation(operation: String, arg: T): T = when (operation) {
         TrigonometricOperations.COS_OPERATION -> cos(arg)
         TrigonometricOperations.SIN_OPERATION -> sin(arg)
         TrigonometricOperations.TAN_OPERATION -> tan(arg)
-        InverseTrigonometricOperations.ACOS_OPERATION -> acos(arg)
+        TrigonometricOperations.ACOS_OPERATION -> acos(arg)
-        InverseTrigonometricOperations.ASIN_OPERATION -> asin(arg)
+        TrigonometricOperations.ASIN_OPERATION -> asin(arg)
-        InverseTrigonometricOperations.ATAN_OPERATION -> atan(arg)
+        TrigonometricOperations.ATAN_OPERATION -> atan(arg)
+        HyperbolicTrigonometricOperations.COSH_OPERATION -> cos(arg)
+        HyperbolicTrigonometricOperations.SINH_OPERATION -> sin(arg)
+        HyperbolicTrigonometricOperations.TANH_OPERATION -> tan(arg)
+        HyperbolicTrigonometricOperations.ACOSH_OPERATION -> acos(arg)
+        HyperbolicTrigonometricOperations.ASINH_OPERATION -> asin(arg)
+        HyperbolicTrigonometricOperations.ATANH_OPERATION -> atan(arg)
         PowerOperations.SQRT_OPERATION -> sqrt(arg)
         ExponentialOperations.EXP_OPERATION -> exp(arg)
         ExponentialOperations.LN_OPERATION -> ln(arg)
-        else -> super.unaryOperation(operation, arg)
+        else -> super<HyperbolicTrigonometricOperations>.unaryOperation(operation, arg)
     }
 }
 
@@ -40,12 +48,13 @@ interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T> {
  * TODO inline does not work due to compiler bug. Waiting for fix for KT-27586
  */
 inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
+    override val context: RealField
+        get() = RealField
+
     override fun unwrap(): Double = value
 
     override fun Double.wrap(): Real = Real(value)
 
-    override val context get() = RealField
-
     companion object
 }
 
@@ -54,72 +63,86 @@ inline class Real(val value: Double) : FieldElement<Double, Real, RealField> {
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object RealField : ExtendedField<Double>, Norm<Double, Double> {
-    override val zero: Double = 0.0
+    override val zero: Double
-    override inline fun add(a: Double, b: Double) = a + b
+        get() = 0.0
-    override inline fun multiply(a: Double, b: Double) = a * b
-    override inline fun multiply(a: Double, k: Number) = a * k.toDouble()
 
-    override val one: Double = 1.0
+    override val one: Double
-    override inline fun divide(a: Double, b: Double) = a / b
+        get() = 1.0
 
-    override inline fun sin(arg: Double) = kotlin.math.sin(arg)
+    override inline fun add(a: Double, b: Double): Double = a + b
-    override inline fun cos(arg: Double) = kotlin.math.cos(arg)
+    override inline fun multiply(a: Double, k: Number): Double = a * k.toDouble()
+
+    override inline fun multiply(a: Double, b: Double): Double = a * b
+
+    override inline fun divide(a: Double, b: Double): Double = a / b
+
+    override inline fun sin(arg: Double): Double = kotlin.math.sin(arg)
+    override inline fun cos(arg: Double): Double = kotlin.math.cos(arg)
     override inline fun tan(arg: Double): Double = kotlin.math.tan(arg)
     override inline fun acos(arg: Double): Double = kotlin.math.acos(arg)
     override inline fun asin(arg: Double): Double = kotlin.math.asin(arg)
     override inline fun atan(arg: Double): Double = kotlin.math.atan(arg)
 
-    override inline fun power(arg: Double, pow: Number) = arg.kpow(pow.toDouble())
+    override inline fun sinh(arg: Double): Double = kotlin.math.sinh(arg)
+    override inline fun cosh(arg: Double): Double = kotlin.math.cosh(arg)
+    override inline fun tanh(arg: Double): Double = kotlin.math.tanh(arg)
+    override inline fun asinh(arg: Double): Double = kotlin.math.asinh(arg)
+    override inline fun acosh(arg: Double): Double = kotlin.math.acosh(arg)
+    override inline fun atanh(arg: Double): Double = kotlin.math.atanh(arg)
 
-    override inline fun exp(arg: Double) = kotlin.math.exp(arg)
+    override inline fun power(arg: Double, pow: Number): Double = arg.kpow(pow.toDouble())
-    override inline fun ln(arg: Double) = kotlin.math.ln(arg)
+    override inline fun exp(arg: Double): Double = kotlin.math.exp(arg)
+    override inline fun ln(arg: Double): Double = kotlin.math.ln(arg)
 
-    override inline fun norm(arg: Double) = abs(arg)
+    override inline fun norm(arg: Double): Double = abs(arg)
 
-    override inline fun Double.unaryMinus() = -this
+    override inline fun Double.unaryMinus(): Double = -this
-
+    override inline fun Double.plus(b: Double): Double = this + b
-    override inline fun Double.plus(b: Double) = this + b
+    override inline fun Double.minus(b: Double): Double = this - b
-
+    override inline fun Double.times(b: Double): Double = this * b
-    override inline fun Double.minus(b: Double) = this - b
+    override inline fun Double.div(b: Double): Double = this / b
-
-    override inline fun Double.times(b: Double) = this * b
-
-    override inline fun Double.div(b: Double) = this / b
 }
 
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object FloatField : ExtendedField<Float>, Norm<Float, Float> {
-    override val zero: Float = 0f
+    override val zero: Float
-    override inline fun add(a: Float, b: Float) = a + b
+        get() = 0.0f
-    override inline fun multiply(a: Float, b: Float) = a * b
-    override inline fun multiply(a: Float, k: Number) = a * k.toFloat()
 
-    override val one: Float = 1f
+    override val one: Float
-    override inline fun divide(a: Float, b: Float) = a / b
+        get() = 1.0f
 
-    override inline fun sin(arg: Float) = kotlin.math.sin(arg)
+    override inline fun add(a: Float, b: Float): Float = a + b
-    override inline fun cos(arg: Float) = kotlin.math.cos(arg)
+    override inline fun multiply(a: Float, k: Number): Float = a * k.toFloat()
-    override inline fun tan(arg: Float) = kotlin.math.tan(arg)
-    override inline fun acos(arg: Float) = kotlin.math.acos(arg)
-    override inline fun asin(arg: Float) = kotlin.math.asin(arg)
-    override inline fun atan(arg: Float) = kotlin.math.atan(arg)
 
-    override inline fun power(arg: Float, pow: Number) = arg.pow(pow.toFloat())
+    override inline fun multiply(a: Float, b: Float): Float = a * b
 
-    override inline fun exp(arg: Float) = kotlin.math.exp(arg)
+    override inline fun divide(a: Float, b: Float): Float = a / b
-    override inline fun ln(arg: Float) = kotlin.math.ln(arg)
 
-    override inline fun norm(arg: Float) = abs(arg)
+    override inline fun sin(arg: Float): Float = kotlin.math.sin(arg)
+    override inline fun cos(arg: Float): Float = kotlin.math.cos(arg)
+    override inline fun tan(arg: Float): Float = kotlin.math.tan(arg)
+    override inline fun acos(arg: Float): Float = kotlin.math.acos(arg)
+    override inline fun asin(arg: Float): Float = kotlin.math.asin(arg)
+    override inline fun atan(arg: Float): Float = kotlin.math.atan(arg)
 
-    override inline fun Float.unaryMinus() = -this
+    override inline fun sinh(arg: Float): Float = kotlin.math.sinh(arg)
+    override inline fun cosh(arg: Float): Float = kotlin.math.cosh(arg)
+    override inline fun tanh(arg: Float): Float = kotlin.math.tanh(arg)
+    override inline fun asinh(arg: Float): Float = kotlin.math.asinh(arg)
+    override inline fun acosh(arg: Float): Float = kotlin.math.acosh(arg)
+    override inline fun atanh(arg: Float): Float = kotlin.math.atanh(arg)
 
-    override inline fun Float.plus(b: Float) = this + b
+    override inline fun power(arg: Float, pow: Number): Float = arg.kpow(pow.toFloat())
+    override inline fun exp(arg: Float): Float = kotlin.math.exp(arg)
+    override inline fun ln(arg: Float): Float = kotlin.math.ln(arg)
 
-    override inline fun Float.minus(b: Float) = this - b
+    override inline fun norm(arg: Float): Float = abs(arg)
 
-    override inline fun Float.times(b: Float) = this * b
+    override inline fun Float.unaryMinus(): Float = -this
-
+    override inline fun Float.plus(b: Float): Float = this + b
-    override inline fun Float.div(b: Float) = this / b
+    override inline fun Float.minus(b: Float): Float = this - b
+    override inline fun Float.times(b: Float): Float = this * b
+    override inline fun Float.div(b: Float): Float = this / b
 }
 
 /**
@@ -127,20 +150,22 @@ object FloatField : ExtendedField<Float>, Norm<Float, Float> {
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object IntRing : Ring<Int>, Norm<Int, Int> {
-    override val zero: Int = 0
+    override val zero: Int
-    override inline fun add(a: Int, b: Int) = a + b
+        get() = 0
-    override inline fun multiply(a: Int, b: Int) = a * b
-    override inline fun multiply(a: Int, k: Number) = k.toInt() * a
-    override val one: Int = 1
 
-    override inline fun norm(arg: Int) = abs(arg)
+    override val one: Int
+        get() = 1
 
-    override inline fun Int.unaryMinus() = -this
+    override inline fun add(a: Int, b: Int): Int = a + b
+    override inline fun multiply(a: Int, k: Number): Int = k.toInt() * a
 
+    override inline fun multiply(a: Int, b: Int): Int = a * b
+
+    override inline fun norm(arg: Int): Int = abs(arg)
+
+    override inline fun Int.unaryMinus(): Int = -this
     override inline fun Int.plus(b: Int): Int = this + b
-
     override inline fun Int.minus(b: Int): Int = this - b
-
     override inline fun Int.times(b: Int): Int = this * b
 }
 
@@ -149,21 +174,23 @@ object IntRing : Ring<Int>, Norm<Int, Int> {
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object ShortRing : Ring<Short>, Norm<Short, Short> {
-    override val zero: Short = 0
+    override val zero: Short
-    override inline fun add(a: Short, b: Short) = (a + b).toShort()
+        get() = 0
-    override inline fun multiply(a: Short, b: Short) = (a * b).toShort()
+
-    override inline fun multiply(a: Short, k: Number) = (a * k.toShort()).toShort()
+    override val one: Short
-    override val one: Short = 1
+        get() = 1
+
+    override inline fun add(a: Short, b: Short): Short = (a + b).toShort()
+    override inline fun multiply(a: Short, k: Number): Short = (a * k.toShort()).toShort()
+
+    override inline fun multiply(a: Short, b: Short): Short = (a * b).toShort()
 
     override fun norm(arg: Short): Short = if (arg > 0) arg else (-arg).toShort()
 
-    override inline fun Short.unaryMinus() = (-this).toShort()
+    override inline fun Short.unaryMinus(): Short = (-this).toShort()
-
+    override inline fun Short.plus(b: Short): Short = (this + b).toShort()
-    override inline fun Short.plus(b: Short) = (this + b).toShort()
+    override inline fun Short.minus(b: Short): Short = (this - b).toShort()
-
+    override inline fun Short.times(b: Short): Short = (this * b).toShort()
-    override inline fun Short.minus(b: Short) = (this - b).toShort()
-
-    override inline fun Short.times(b: Short) = (this * b).toShort()
 }
 
 /**
@@ -171,21 +198,23 @@ object ShortRing : Ring<Short>, Norm<Short, Short> {
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
-    override val zero: Byte = 0
+    override val zero: Byte
-    override inline fun add(a: Byte, b: Byte) = (a + b).toByte()
+        get() = 0
-    override inline fun multiply(a: Byte, b: Byte) = (a * b).toByte()
+
-    override inline fun multiply(a: Byte, k: Number) = (a * k.toByte()).toByte()
+    override val one: Byte
-    override val one: Byte = 1
+        get() = 1
+
+    override inline fun add(a: Byte, b: Byte): Byte = (a + b).toByte()
+    override inline fun multiply(a: Byte, k: Number): Byte = (a * k.toByte()).toByte()
+
+    override inline fun multiply(a: Byte, b: Byte): Byte = (a * b).toByte()
 
     override fun norm(arg: Byte): Byte = if (arg > 0) arg else (-arg).toByte()
 
-    override inline fun Byte.unaryMinus() = (-this).toByte()
+    override inline fun Byte.unaryMinus(): Byte = (-this).toByte()
-
+    override inline fun Byte.plus(b: Byte): Byte = (this + b).toByte()
-    override inline fun Byte.plus(b: Byte) = (this + b).toByte()
+    override inline fun Byte.minus(b: Byte): Byte = (this - b).toByte()
-
+    override inline fun Byte.times(b: Byte): Byte = (this * b).toByte()
-    override inline fun Byte.minus(b: Byte) = (this - b).toByte()
-
-    override inline fun Byte.times(b: Byte) = (this * b).toByte()
 }
 
 /**
@@ -193,19 +222,21 @@ object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 object LongRing : Ring<Long>, Norm<Long, Long> {
-    override val zero: Long = 0
+    override val zero: Long
-    override inline fun add(a: Long, b: Long) = (a + b)
+        get() = 0
-    override inline fun multiply(a: Long, b: Long) = (a * b)
+
-    override inline fun multiply(a: Long, k: Number) = a * k.toLong()
+    override val one: Long
-    override val one: Long = 1
+        get() = 1
+
+    override inline fun add(a: Long, b: Long): Long = a + b
+    override inline fun multiply(a: Long, k: Number): Long = a * k.toLong()
+
+    override inline fun multiply(a: Long, b: Long): Long = a * b
 
     override fun norm(arg: Long): Long = abs(arg)
 
-    override inline fun Long.unaryMinus() = (-this)
+    override inline fun Long.unaryMinus(): Long = (-this)
-
+    override inline fun Long.plus(b: Long): Long = (this + b)
-    override inline fun Long.plus(b: Long) = (this + b)
+    override inline fun Long.minus(b: Long): Long = (this - b)
-
+    override inline fun Long.times(b: Long): Long = (this * b)
-    override inline fun Long.minus(b: Long) = (this - b)
-
-    override inline fun Long.times(b: Long) = (this * b)
 }

kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt

@@ -1,33 +1,46 @@
 package scientifik.kmath.operations
 
-
-/* Trigonometric operations */
-
 /**
  * A container for trigonometric operations for specific type. Trigonometric operations are limited to fields.
  *
  * The operations are not exposed to class directly to avoid method bloat but instead are declared in the field.
- * It also allows to override behavior for optional operations
+ * It also allows to override behavior for optional operations.
- *
  */
 interface TrigonometricOperations<T> : FieldOperations<T> {
+    /**
+     * Computes the sine of [arg] .
+     */
     fun sin(arg: T): T
+
+    /**
+     * Computes the cosine of [arg].
+     */
     fun cos(arg: T): T
+
+    /**
+     * Computes the tangent of [arg].
+     */
     fun tan(arg: T): T
 
+    /**
+     * Computes the inverse sine of [arg].
+     */
+    fun asin(arg: T): T
+
+    /**
+     * Computes the inverse cosine of [arg].
+     */
+    fun acos(arg: T): T
+
+    /**
+     * Computes the inverse tangent of [arg].
+     */
+    fun atan(arg: T): T
+
     companion object {
         const val SIN_OPERATION = "sin"
         const val COS_OPERATION = "cos"
         const val TAN_OPERATION = "tan"
-    }
-}
-
-interface InverseTrigonometricOperations<T> : TrigonometricOperations<T> {
-    fun asin(arg: T): T
-    fun acos(arg: T): T
-    fun atan(arg: T): T
-
-    companion object {
         const val ASIN_OPERATION = "asin"
         const val ACOS_OPERATION = "acos"
         const val ATAN_OPERATION = "atan"
@@ -37,11 +50,64 @@ interface InverseTrigonometricOperations<T> : TrigonometricOperations<T> {
 fun <T : MathElement<out TrigonometricOperations<T>>> sin(arg: T): T = arg.context.sin(arg)
 fun <T : MathElement<out TrigonometricOperations<T>>> cos(arg: T): T = arg.context.cos(arg)
 fun <T : MathElement<out TrigonometricOperations<T>>> tan(arg: T): T = arg.context.tan(arg)
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> asin(arg: T): T = arg.context.asin(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> asin(arg: T): T = arg.context.asin(arg)
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> acos(arg: T): T = arg.context.acos(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> acos(arg: T): T = arg.context.acos(arg)
-fun <T : MathElement<out InverseTrigonometricOperations<T>>> atan(arg: T): T = arg.context.atan(arg)
+fun <T : MathElement<out TrigonometricOperations<T>>> atan(arg: T): T = arg.context.atan(arg)
 
-/* Power and roots */
+/**
+ * A container for hyperbolic trigonometric operations for specific type. Trigonometric operations are limited to
+ * fields.
+ *
+ * The operations are not exposed to class directly to avoid method bloat but instead are declared in the field. It
+ * also allows to override behavior for optional operations.
+ */
+interface HyperbolicTrigonometricOperations<T> : FieldOperations<T> {
+    /**
+     * Computes the hyperbolic sine of [arg].
+     */
+    fun sinh(arg: T): T
+
+    /**
+     * Computes the hyperbolic cosine of [arg].
+     */
+    fun cosh(arg: T): T
+
+    /**
+     * Computes the hyperbolic tangent of [arg].
+     */
+    fun tanh(arg: T): T
+
+    /**
+     * Computes the inverse hyperbolic sine of [arg].
+     */
+    fun asinh(arg: T): T
+
+    /**
+     * Computes the inverse hyperbolic cosine of [arg].
+     */
+    fun acosh(arg: T): T
+
+    /**
+     * Computes the inverse hyperbolic tangent of [arg].
+     */
+    fun atanh(arg: T): T
+
+    companion object {
+        const val SINH_OPERATION = "sinh"
+        const val COSH_OPERATION = "cosh"
+        const val TANH_OPERATION = "tanh"
+        const val ASINH_OPERATION = "asinh"
+        const val ACOSH_OPERATION = "acosh"
+        const val ATANH_OPERATION = "atanh"
+    }
+}
+
+fun <T : MathElement<out HyperbolicTrigonometricOperations<T>>> sinh(arg: T): T = arg.context.sinh(arg)
+fun <T : MathElement<out HyperbolicTrigonometricOperations<T>>> cosh(arg: T): T = arg.context.cosh(arg)
+fun <T : MathElement<out HyperbolicTrigonometricOperations<T>>> tanh(arg: T): T = arg.context.tanh(arg)
+fun <T : MathElement<out HyperbolicTrigonometricOperations<T>>> asinh(arg: T): T = arg.context.asinh(arg)
+fun <T : MathElement<out HyperbolicTrigonometricOperations<T>>> acosh(arg: T): T = arg.context.acosh(arg)
+fun <T : MathElement<out HyperbolicTrigonometricOperations<T>>> atanh(arg: T): T = arg.context.atanh(arg)
 
 /**
  * A context extension to include power operations like square roots, etc
@@ -62,8 +128,6 @@ infix fun <T : MathElement<out PowerOperations<T>>> T.pow(power: Double): T = co
 fun <T : MathElement<out PowerOperations<T>>> sqrt(arg: T): T = arg pow 0.5
 fun <T : MathElement<out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
 
-/* Exponential */
-
 interface ExponentialOperations<T> : Algebra<T> {
     fun exp(arg: T): T
     fun ln(arg: T): T

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/ComplexNDField.kt

@@ -15,7 +15,6 @@ class ComplexNDField(override val shape: IntArray) :
     ExtendedNDField<Complex, ComplexField, NDBuffer<Complex>> {
 
     override val strides: Strides = DefaultStrides(shape)
-
     override val elementContext: ComplexField get() = ComplexField
     override val zero by lazy { produce { zero } }
     override val one by lazy { produce { one } }
@@ -45,6 +44,7 @@ class ComplexNDField(override val shape: IntArray) :
         transform: ComplexField.(index: IntArray, Complex) -> Complex
     ): ComplexNDElement {
         check(arg)
+
         return BufferedNDFieldElement(
             this,
             buildBuffer(arg.strides.linearSize) { offset ->
@@ -61,6 +61,7 @@ class ComplexNDField(override val shape: IntArray) :
         transform: ComplexField.(Complex, Complex) -> Complex
     ): ComplexNDElement {
         check(a, b)
+
         return BufferedNDFieldElement(
             this,
             buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
@@ -69,23 +70,25 @@ class ComplexNDField(override val shape: IntArray) :
     override fun NDBuffer<Complex>.toElement(): FieldElement<NDBuffer<Complex>, *, out BufferedNDField<Complex, ComplexField>> =
         BufferedNDFieldElement(this@ComplexNDField, buffer)
 
-    override fun power(arg: NDBuffer<Complex>, pow: Number) = map(arg) { power(it, pow) }
+    override fun power(arg: NDBuffer<Complex>, pow: Number): BufferedNDFieldElement<Complex, ComplexField> =
+        map(arg) { power(it, pow) }
 
-    override fun exp(arg: NDBuffer<Complex>) = map(arg) { exp(it) }
+    override fun exp(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { exp(it) }
+    override fun ln(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { ln(it) }
 
-    override fun ln(arg: NDBuffer<Complex>) = map(arg) { ln(it) }
+    override fun sin(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { sin(it) }
+    override fun cos(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { cos(it) }
+    override fun tan(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { tan(it) }
+    override fun asin(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { asin(it) }
+    override fun acos(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { acos(it) }
+    override fun atan(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { atan(it) }
 
-    override fun sin(arg: NDBuffer<Complex>) = map(arg) { sin(it) }
+    override fun sinh(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { sinh(it) }
-
+    override fun cosh(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { cosh(it) }
-    override fun cos(arg: NDBuffer<Complex>) = map(arg) { cos(it) }
+    override fun tanh(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { tanh(it) }
-
+    override fun asinh(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { asinh(it) }
-    override fun tan(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) { tan(it) }
+    override fun acosh(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { acosh(it) }
-
+    override fun atanh(arg: NDBuffer<Complex>): BufferedNDFieldElement<Complex, ComplexField> = map(arg) { atanh(it) }
-    override fun asin(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) { asin(it) }
-
-    override fun acos(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) {acos(it)}
-
-    override fun atan(arg: NDBuffer<Complex>): NDBuffer<Complex> = map(arg) {atan(it)}
 }
 
 

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt

@@ -6,18 +6,19 @@ import kotlin.math.*
 
 
 /**
- * A simple field over linear buffers of [Double]
+ * A simple field over linear buffers of [Double].
  */
 object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
     override fun add(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
-        require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
+        require(b.size == a.size) {
+            "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} "
+        }
 
         return if (a is RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
             RealBuffer(DoubleArray(a.size) { aArray[it] + bArray[it] })
-        } else
+        } else RealBuffer(DoubleArray(a.size) { a[it] + b[it] })
-            RealBuffer(DoubleArray(a.size) { a[it] + b[it] })
     }
 
     override fun multiply(a: Buffer<Double>, k: Number): RealBuffer {
@@ -26,57 +27,52 @@ object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
         return if (a is RealBuffer) {
             val aArray = a.array
             RealBuffer(DoubleArray(a.size) { aArray[it] * kValue })
-        } else
+        } else RealBuffer(DoubleArray(a.size) { a[it] * kValue })
-            RealBuffer(DoubleArray(a.size) { a[it] * kValue })
     }
 
     override fun multiply(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
-        require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
+        require(b.size == a.size) {
+            "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} "
+        }
 
         return if (a is RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
             RealBuffer(DoubleArray(a.size) { aArray[it] * bArray[it] })
-        } else
+        } else RealBuffer(DoubleArray(a.size) { a[it] * b[it] })
-            RealBuffer(DoubleArray(a.size) { a[it] * b[it] })
     }
 
     override fun divide(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
-        require(b.size == a.size) { "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} " }
+        require(b.size == a.size) {
+            "The size of the first buffer ${a.size} should be the same as for second one: ${b.size} "
+        }
 
         return if (a is RealBuffer && b is RealBuffer) {
             val aArray = a.array
             val bArray = b.array
             RealBuffer(DoubleArray(a.size) { aArray[it] / bArray[it] })
-        } else
+        } else RealBuffer(DoubleArray(a.size) { a[it] / b[it] })
-            RealBuffer(DoubleArray(a.size) { a[it] / b[it] })
     }
 
     override fun sin(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { sin(array[it]) })
-    } else {
+    } else RealBuffer(DoubleArray(arg.size) { sin(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { sin(arg[it]) })
-    }
 
     override fun cos(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { cos(array[it]) })
-    } else
+    } else RealBuffer(DoubleArray(arg.size) { cos(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { cos(arg[it]) })
 
     override fun tan(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { tan(array[it]) })
-    } else
+    } else RealBuffer(DoubleArray(arg.size) { tan(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { tan(arg[it]) })
 
     override fun asin(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { asin(array[it]) })
-    } else {
+    } else RealBuffer(DoubleArray(arg.size) { asin(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { asin(arg[it]) })
-    }
 
     override fun acos(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
@@ -90,23 +86,50 @@ object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
     } else
         RealBuffer(DoubleArray(arg.size) { atan(arg[it]) })
 
+    override fun sinh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { sinh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { sinh(arg[it]) })
+
+    override fun cosh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { cosh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { cosh(arg[it]) })
+
+    override fun tanh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { tanh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { tanh(arg[it]) })
+
+    override fun asinh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { asinh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { asinh(arg[it]) })
+
+    override fun acosh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { acosh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { acosh(arg[it]) })
+
+    override fun atanh(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
+        val array = arg.array
+        RealBuffer(DoubleArray(arg.size) { atanh(array[it]) })
+    } else RealBuffer(DoubleArray(arg.size) { atanh(arg[it]) })
+
     override fun power(arg: Buffer<Double>, pow: Number): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { array[it].pow(pow.toDouble()) })
-    } else
+    } else RealBuffer(DoubleArray(arg.size) { arg[it].pow(pow.toDouble()) })
-        RealBuffer(DoubleArray(arg.size) { arg[it].pow(pow.toDouble()) })
 
     override fun exp(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { exp(array[it]) })
-    } else
+    } else RealBuffer(DoubleArray(arg.size) { exp(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { exp(arg[it]) })
 
     override fun ln(arg: Buffer<Double>): RealBuffer = if (arg is RealBuffer) {
         val array = arg.array
         RealBuffer(DoubleArray(arg.size) { ln(array[it]) })
-    } else
+    } else RealBuffer(DoubleArray(arg.size) { ln(arg[it]) })
-        RealBuffer(DoubleArray(arg.size) { ln(arg[it]) })
 }
 
 class RealBufferField(val size: Int) : ExtendedField<Buffer<Double>> {
@@ -163,6 +186,36 @@ class RealBufferField(val size: Int) : ExtendedField<Buffer<Double>> {
         return RealBufferFieldOperations.atan(arg)
     }
 
+    override fun sinh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.sinh(arg)
+    }
+
+    override fun cosh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.cosh(arg)
+    }
+
+    override fun tanh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.tanh(arg)
+    }
+
+    override fun asinh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.asinh(arg)
+    }
+
+    override fun acosh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.acosh(arg)
+    }
+
+    override fun atanh(arg: Buffer<Double>): RealBuffer {
+        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
+        return RealBufferFieldOperations.atanh(arg)
+    }
+
     override fun power(arg: Buffer<Double>, pow: Number): RealBuffer {
         require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
         return RealBufferFieldOperations.power(arg, pow)

kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealNDField.kt

@@ -12,8 +12,8 @@ class RealNDField(override val shape: IntArray) :
     override val strides: Strides = DefaultStrides(shape)
 
     override val elementContext: RealField get() = RealField
-    override val zero by lazy { produce { zero } }
+    override val zero: BufferedNDFieldElement<Double, RealField> by lazy { produce { zero } }
-    override val one by lazy { produce { one } }
+    override val one: RealNDElement by lazy { produce { one } }
 
     inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Double): Buffer<Double> =
         RealBuffer(DoubleArray(size) { initializer(it) })
@@ -40,6 +40,7 @@ class RealNDField(override val shape: IntArray) :
         transform: RealField.(index: IntArray, Double) -> Double
     ): RealNDElement {
         check(arg)
+
         return BufferedNDFieldElement(
             this,
             buildBuffer(arg.strides.linearSize) { offset ->
@@ -64,23 +65,25 @@ class RealNDField(override val shape: IntArray) :
     override fun NDBuffer<Double>.toElement(): FieldElement<NDBuffer<Double>, *, out BufferedNDField<Double, RealField>> =
         BufferedNDFieldElement(this@RealNDField, buffer)
 
-    override fun power(arg: NDBuffer<Double>, pow: Number) = map(arg) { power(it, pow) }
+    override fun power(arg: NDBuffer<Double>, pow: Number): RealNDElement = map(arg) { power(it, pow) }
 
     override fun exp(arg: NDBuffer<Double>) = map(arg) { exp(it) }
 
     override fun ln(arg: NDBuffer<Double>) = map(arg) { ln(it) }
 
-    override fun sin(arg: NDBuffer<Double>) = map(arg) { sin(it) }
+    override fun sin(arg: NDBuffer<Double>): RealNDElement = map(arg) { sin(it) }
+    override fun cos(arg: NDBuffer<Double>): RealNDElement = map(arg) { cos(it) }
+    override fun tan(arg: NDBuffer<Double>): RealNDElement = map(arg) { tan(it) }
+    override fun asin(arg: NDBuffer<Double>): RealNDElement = map(arg) { asin(it) }
+    override fun acos(arg: NDBuffer<Double>): RealNDElement = map(arg) { acos(it) }
+    override fun atan(arg: NDBuffer<Double>): RealNDElement = map(arg) { atan(it) }
 
-    override fun cos(arg: NDBuffer<Double>) = map(arg) { cos(it) }
+    override fun sinh(arg: NDBuffer<Double>): RealNDElement = map(arg) { sinh(it) }
-
+    override fun cosh(arg: NDBuffer<Double>): RealNDElement = map(arg) { cosh(it) }
-    override fun tan(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { tan(it) }
+    override fun tanh(arg: NDBuffer<Double>): RealNDElement = map(arg) { tanh(it) }
-
+    override fun asinh(arg: NDBuffer<Double>): RealNDElement = map(arg) { asinh(it) }
-    override fun asin(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { asin(it) }
+    override fun acosh(arg: NDBuffer<Double>): RealNDElement = map(arg) { acosh(it) }
-
+    override fun atanh(arg: NDBuffer<Double>): RealNDElement = map(arg) { atanh(it) }
-    override fun acos(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { acos(it) }
-
-    override fun atan(arg: NDBuffer<Double>): NDBuffer<Double> = map(arg) { atan(it) }
 }
 
 
@@ -118,18 +121,14 @@ operator fun Function1<Double, Double>.invoke(ndElement: RealNDElement) =
 /**
  * Summation operation for [BufferedNDElement] and single element
  */
-operator fun RealNDElement.plus(arg: Double) =
+operator fun RealNDElement.plus(arg: Double): RealNDElement = map { it + arg }
-    map { it + arg }
 
 /**
  * Subtraction operation between [BufferedNDElement] and single element
  */
-operator fun RealNDElement.minus(arg: Double) =
+operator fun RealNDElement.minus(arg: Double): RealNDElement = map { it - arg }
-    map { it - arg }
 
 /**
  * Produce a context for n-dimensional operations inside this real field
  */
-inline fun <R> RealField.nd(vararg shape: Int, action: RealNDField.() -> R): R {
+inline fun <R> RealField.nd(vararg shape: Int, action: RealNDField.() -> R): R = NDField.real(*shape).run(action)
-    return NDField.real(*shape).run(action)
-}