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Add multik tensor factories and benchmarks

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This commit is contained in:
Alexander Nozik 2021-10-18 11:35:09 +03:00
parent 827f115a92
commit a81ab474f7
23 changed files with 84 additions and 57 deletions
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12
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt
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@ -9,7 +9,12 @@ import kotlinx.benchmark.Benchmark
import kotlinx.benchmark.Blackhole
import kotlinx.benchmark.Scope
import kotlinx.benchmark.State
import org.jetbrains.kotlinx.multik.api.Multik
import org.jetbrains.kotlinx.multik.api.ones
import org.jetbrains.kotlinx.multik.ndarray.data.DN
import org.jetbrains.kotlinx.multik.ndarray.data.DataType
import space.kscience.kmath.multik.multikND
import space.kscience.kmath.multik.multikTensorAlgebra
import space.kscience.kmath.nd.BufferedFieldOpsND
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.ndAlgebra
@ -73,6 +78,13 @@ internal class NDFieldBenchmark {
blackhole.consume(res)
}
@Benchmark
fun multikInPlaceAdd(blackhole: Blackhole) = with(DoubleField.multikTensorAlgebra) {
val res = Multik.ones<Double, DN>(shape, DataType.DoubleDataType).wrap()
repeat(n) { res += 1.0 }
blackhole.consume(res)
}
// @Benchmark
// fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
// var res: StructureND<Double> = one(dim, dim)

4
benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
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@ -23,7 +23,7 @@ internal class ViktorLogBenchmark {
@Benchmark
fun realFieldLog(blackhole: Blackhole) {
with(realField) {
val fortyTwo = produce(shape) { 42.0 }
val fortyTwo = structureND(shape) { 42.0 }
var res = one(shape)
repeat(n) { res = ln(fortyTwo) }
blackhole.consume(res)
@ -33,7 +33,7 @@ internal class ViktorLogBenchmark {
@Benchmark
fun viktorFieldLog(blackhole: Blackhole) {
with(viktorField) {
val fortyTwo = produce(shape) { 42.0 }
val fortyTwo = structureND(shape) { 42.0 }
var res = one
repeat(n) { res = ln(fortyTwo) }
blackhole.consume(res)

4
examples/src/main/kotlin/space/kscience/kmath/functions/matrixIntegration.kt
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@ -9,7 +9,7 @@ import space.kscience.kmath.integration.gaussIntegrator
import space.kscience.kmath.integration.integrate
import space.kscience.kmath.integration.value
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.produce
import space.kscience.kmath.nd.structureND
import space.kscience.kmath.nd.withNdAlgebra
import space.kscience.kmath.operations.algebra
import space.kscience.kmath.operations.invoke
@ -18,7 +18,7 @@ fun main(): Unit = Double.algebra {
withNdAlgebra(2, 2) {
//Produce a diagonal StructureND
fun diagonal(v: Double) = produce { (i, j) ->
fun diagonal(v: Double) = structureND { (i, j) ->
if (i == j) v else 0.0
}

6
examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt
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@ -11,7 +11,7 @@ import space.kscience.kmath.complex.bufferAlgebra
import space.kscience.kmath.complex.ndAlgebra
import space.kscience.kmath.nd.BufferND
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.produce
import space.kscience.kmath.nd.structureND
fun main() = Complex.algebra {
val complex = 2 + 2 * i
@ -24,14 +24,14 @@ fun main() = Complex.algebra {
println(buffer)
// 2d element
val element: BufferND<Complex> = ndAlgebra.produce(2, 2) { (i, j) ->
val element: BufferND<Complex> = ndAlgebra.structureND(2, 2) { (i, j) ->
Complex(i - j, i + j)
}
println(element)
// 1d element operation
val result: StructureND<Complex> = ndAlgebra{
val a = produce(8) { (it) -> i * it - it.toDouble() }
val a = structureND(8) { (it) -> i * it - it.toDouble() }
val b = 3
val c = Complex(1.0, 1.0)

2
examples/src/main/kotlin/space/kscience/kmath/operations/mixedNDOperations.kt
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@ -10,7 +10,7 @@ import space.kscience.kmath.viktor.ViktorStructureND
import space.kscience.kmath.viktor.viktorAlgebra
fun main() {
val viktorStructure: ViktorStructureND = DoubleField.viktorAlgebra.produce(Shape(2, 2)) { (i, j) ->
val viktorStructure: ViktorStructureND = DoubleField.viktorAlgebra.structureND(Shape(2, 2)) { (i, j) ->
if (i == j) 2.0 else 0.0
}

4
examples/src/main/kotlin/space/kscience/kmath/structures/ComplexND.kt
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@ -12,7 +12,7 @@ import space.kscience.kmath.linear.transpose
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.as2D
import space.kscience.kmath.nd.ndAlgebra
import space.kscience.kmath.nd.produce
import space.kscience.kmath.nd.structureND
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.invoke
import kotlin.system.measureTimeMillis
@ -55,7 +55,7 @@ fun complexExample() {
val x = one * 2.5
operator fun Number.plus(other: Complex) = Complex(this.toDouble() + other.re, other.im)
//a structure generator specific to this context
val matrix = produce { (k, l) -> k + l * i }
val matrix = structureND { (k, l) -> k + l * i }
//Perform sum
val sum = matrix + x + 1.0

8
examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt
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@ -22,12 +22,12 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
private val strides = DefaultStrides(shape)
override val elementAlgebra: DoubleField get() = DoubleField
override val zero: BufferND<Double> by lazy { produce(shape) { zero } }
override val one: BufferND<Double> by lazy { produce(shape) { one } }
override val zero: BufferND<Double> by lazy { structureND(shape) { zero } }
override val one: BufferND<Double> by lazy { structureND(shape) { one } }
override fun number(value: Number): BufferND<Double> {
val d = value.toDouble() // minimize conversions
return produce(shape) { d }
return structureND(shape) { d }
}
private val StructureND<Double>.buffer: DoubleBuffer
@ -40,7 +40,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
}
override fun produce(shape: Shape, initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
val index = strides.index(offset)
DoubleField.initializer(index)

2
kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt
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@ -67,7 +67,7 @@ public class ComplexFieldND(override val shape: Shape) :
override fun number(value: Number): BufferND<Complex> {
val d = value.toDouble() // minimize conversions
return produce(shape) { d.toComplex() }
return structureND(shape) { d.toComplex() }
}
}

2
kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt
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@ -24,7 +24,7 @@ public class BufferedLinearSpace<T, out A : Ring<T>>(
private val ndAlgebra = BufferedRingOpsND(bufferAlgebra)
override fun buildMatrix(rows: Int, columns: Int, initializer: A.(i: Int, j: Int) -> T): Matrix<T> =
ndAlgebra.produce(intArrayOf(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
ndAlgebra.structureND(intArrayOf(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
override fun buildVector(size: Int, initializer: A.(Int) -> T): Point<T> =
bufferAlgebra.buffer(size) { elementAlgebra.initializer(it) }

2
kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt
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@ -23,7 +23,7 @@ public object DoubleLinearSpace : LinearSpace<Double, DoubleField> {
rows: Int,
columns: Int,
initializer: DoubleField.(i: Int, j: Int) -> Double
): Matrix<Double> = DoubleFieldOpsND.produce(intArrayOf(rows, columns)) { (i, j) ->
): Matrix<Double> = DoubleFieldOpsND.structureND(intArrayOf(rows, columns)) { (i, j) ->
DoubleField.initializer(i, j)
}.as2D()

10
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt
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@ -39,9 +39,9 @@ public interface AlgebraND<T, out C : Algebra<T>> {
public val elementAlgebra: C
/**
* Produces a new NDStructure using given initializer function.
* Produces a new [StructureND] using given initializer function.
*/
public fun produce(shape: Shape, initializer: C.(IntArray) -> T): StructureND<T>
public fun structureND(shape: Shape, initializer: C.(IntArray) -> T): StructureND<T>
/**
* Maps elements from one structure to another one by applying [transform] to them.
@ -149,7 +149,7 @@ public interface GroupOpsND<T, out A : GroupOps<T>> : GroupOps<StructureND<T>>,
}
public interface GroupND<T, out A : Group<T>> : Group<StructureND<T>>, GroupOpsND<T, A>, WithShape {
override val zero: StructureND<T> get() = produce(shape) { elementAlgebra.zero }
override val zero: StructureND<T> get() = structureND(shape) { elementAlgebra.zero }
}
/**
@ -193,7 +193,7 @@ public interface RingOpsND<T, out A : RingOps<T>> : RingOps<StructureND<T>>, Gro
}
public interface RingND<T, out A : Ring<T>> : Ring<StructureND<T>>, RingOpsND<T, A>, GroupND<T, A>, WithShape {
override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
override val one: StructureND<T> get() = structureND(shape) { elementAlgebra.one }
}
@ -240,5 +240,5 @@ public interface FieldOpsND<T, out A : Field<T>> :
}
public interface FieldND<T, out A : Field<T>> : Field<StructureND<T>>, FieldOpsND<T, A>, RingND<T, A>, WithShape {
override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
override val one: StructureND<T> get() = structureND(shape) { elementAlgebra.one }
}

10
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferAlgebraND.kt
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@ -16,7 +16,7 @@ public interface BufferAlgebraND<T, out A : Algebra<T>> : AlgebraND<T, A> {
public val bufferAlgebra: BufferAlgebra<T, A>
override val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
override fun produce(shape: Shape, initializer: A.(IntArray) -> T): BufferND<T> {
override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): BufferND<T> {
val indexer = indexerBuilder(shape)
return BufferND(
indexer,
@ -109,14 +109,14 @@ public val <T, A : Ring<T>> BufferAlgebra<T, A>.nd: BufferedRingOpsND<T, A> get(
public val <T, A : Field<T>> BufferAlgebra<T, A>.nd: BufferedFieldOpsND<T, A> get() = BufferedFieldOpsND(this)
public fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.produce(
public fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.structureND(
vararg shape: Int,
initializer: A.(IntArray) -> T
): BufferND<T> = produce(shape, initializer)
): BufferND<T> = structureND(shape, initializer)
public fun <T, EA : Algebra<T>, A> A.produce(
public fun <T, EA : Algebra<T>, A> A.structureND(
initializer: EA.(IntArray) -> T
): BufferND<T> where A : BufferAlgebraND<T, EA>, A : WithShape = produce(shape, initializer)
): BufferND<T> where A : BufferAlgebraND<T, EA>, A : WithShape = structureND(shape, initializer)
//// group factories
//public fun <T, A : Group<T>> A.ndAlgebra(

4
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt
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@ -60,7 +60,7 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(D
transform: DoubleField.(Double, Double) -> Double
): BufferND<Double> = zipInline(left.toBufferND(), right.toBufferND()) { l, r -> DoubleField.transform(l, r) }
override fun produce(shape: Shape, initializer: DoubleField.(IntArray) -> Double): DoubleBufferND {
override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): DoubleBufferND {
val indexer = indexerBuilder(shape)
return DoubleBufferND(
indexer,
@ -174,7 +174,7 @@ public class DoubleFieldND(override val shape: Shape) :
override fun number(value: Number): DoubleBufferND {
val d = value.toDouble() // minimize conversions
return produce(shape) { d }
return structureND(shape) { d }
}
}

2
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt
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@ -23,7 +23,7 @@ public class ShortRingND(
override fun number(value: Number): BufferND<Short> {
val d = value.toShort() // minimize conversions
return produce(shape) { d }
return structureND(shape) { d }
}
}

12
kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt
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@ -11,24 +11,24 @@ import space.kscience.kmath.operations.Ring
import kotlin.jvm.JvmName
public fun <T, A : Algebra<T>> AlgebraND<T, A>.produce(
public fun <T, A : Algebra<T>> AlgebraND<T, A>.structureND(
shapeFirst: Int,
vararg shapeRest: Int,
initializer: A.(IntArray) -> T
): StructureND<T> = produce(Shape(shapeFirst, *shapeRest), initializer)
): StructureND<T> = structureND(Shape(shapeFirst, *shapeRest), initializer)
public fun <T, A : Group<T>> AlgebraND<T, A>.zero(shape: Shape): StructureND<T> = produce(shape) { zero }
public fun <T, A : Group<T>> AlgebraND<T, A>.zero(shape: Shape): StructureND<T> = structureND(shape) { zero }
@JvmName("zeroVarArg")
public fun <T, A : Group<T>> AlgebraND<T, A>.zero(
shapeFirst: Int,
vararg shapeRest: Int,
): StructureND<T> = produce(shapeFirst, *shapeRest) { zero }
): StructureND<T> = structureND(shapeFirst, *shapeRest) { zero }
public fun <T, A : Ring<T>> AlgebraND<T, A>.one(shape: Shape): StructureND<T> = produce(shape) { one }
public fun <T, A : Ring<T>> AlgebraND<T, A>.one(shape: Shape): StructureND<T> = structureND(shape) { one }
@JvmName("oneVarArg")
public fun <T, A : Ring<T>> AlgebraND<T, A>.one(
shapeFirst: Int,
vararg shapeRest: Int,
): StructureND<T> = produce(shapeFirst, *shapeRest) { one }
): StructureND<T> = structureND(shapeFirst, *shapeRest) { one }

4
kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NDFieldTest.kt
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@ -7,7 +7,7 @@ package space.kscience.kmath.structures
import space.kscience.kmath.nd.get
import space.kscience.kmath.nd.ndAlgebra
import space.kscience.kmath.nd.produce
import space.kscience.kmath.nd.structureND
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.invoke
import space.kscience.kmath.testutils.FieldVerifier
@ -22,7 +22,7 @@ internal class NDFieldTest {
@Test
fun testStrides() {
val ndArray = DoubleField.ndAlgebra.produce(10, 10) { (it[0] + it[1]).toDouble() }
val ndArray = DoubleField.ndAlgebra.structureND(10, 10) { (it[0] + it[1]).toDouble() }
assertEquals(ndArray[5, 5], 10.0)
}
}

4
kmath-core/src/commonTest/kotlin/space/kscience/kmath/structures/NumberNDFieldTest.kt
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@ -20,8 +20,8 @@ import kotlin.test.assertEquals
@Suppress("UNUSED_VARIABLE")
class NumberNDFieldTest {
val algebra = DoubleField.ndAlgebra
val array1 = algebra.produce(3, 3) { (i, j) -> (i + j).toDouble() }
val array2 = algebra.produce(3, 3) { (i, j) -> (i - j).toDouble() }
val array1 = algebra.structureND(3, 3) { (i, j) -> (i + j).toDouble() }
val array2 = algebra.structureND(3, 3) { (i, j) -> (i - j).toDouble() }
@Test
fun testSum() {

8
kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikOpsND.kt
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@ -18,9 +18,9 @@ public open class MultikRingOpsND<T, A : Ring<T>> internal constructor(
override val elementAlgebra: A
) : RingOpsND<T, A> {
protected fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
override fun produce(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
val res = mk.zeros<T, DN>(shape, type).asDNArray()
for (index in res.multiIndices) {
res[index] = elementAlgebra.initializer(index)
@ -28,10 +28,10 @@ public open class MultikRingOpsND<T, A : Ring<T>> internal constructor(
return res.wrap()
}
protected fun StructureND<T>.asMultik(): MultikTensor<T> = if (this is MultikTensor) {
public fun StructureND<T>.asMultik(): MultikTensor<T> = if (this is MultikTensor) {
this
} else {
produce(shape) { get(it) }
structureND(shape) { get(it) }
}
override fun StructureND<T>.map(transform: A.(T) -> T): MultikTensor<T> {

23
kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt
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@ -11,7 +11,7 @@ import org.jetbrains.kotlinx.multik.ndarray.data.*
import org.jetbrains.kotlinx.multik.ndarray.operations.*
import space.kscience.kmath.misc.PerformancePitfall
import space.kscience.kmath.nd.mapInPlace
import space.kscience.kmath.operations.Ring
import space.kscience.kmath.operations.*
import space.kscience.kmath.tensors.api.Tensor
import space.kscience.kmath.tensors.api.TensorAlgebra
@ -31,7 +31,7 @@ public value class MultikTensor<T>(public val array: MutableMultiArray<T, DN>) :
}
public abstract class MultikTensorAlgebra<T>(
public class MultikTensorAlgebra<T> internal constructor(
public val type: DataType,
public val elementAlgebra: Ring<T>,
public val comparator: Comparator<T>
@ -41,7 +41,7 @@ public abstract class MultikTensorAlgebra<T>(
* Convert a tensor to [MultikTensor] if necessary. If tensor is converted, changes on the resulting tensor
* are not reflected back onto the source
*/
private fun Tensor<T>.asMultik(): MultikTensor<T> {
public fun Tensor<T>.asMultik(): MultikTensor<T> {
return if (this is MultikTensor) {
this
} else {
@ -53,7 +53,7 @@ public abstract class MultikTensorAlgebra<T>(
}
}
private fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
override fun Tensor<T>.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) {
get(intArrayOf(0))
@ -197,3 +197,18 @@ public abstract class MultikTensorAlgebra<T>(
TODO("Not yet implemented")
}
}
public val DoubleField.multikTensorAlgebra: MultikTensorAlgebra<Double>
get() = MultikTensorAlgebra(DataType.DoubleDataType, DoubleField) { o1, o2 -> o1.compareTo(o2) }
public val FloatField.multikTensorAlgebra: MultikTensorAlgebra<Float>
get() = MultikTensorAlgebra(DataType.FloatDataType, FloatField) { o1, o2 -> o1.compareTo(o2) }
public val ShortRing.multikTensorAlgebra: MultikTensorAlgebra<Short>
get() = MultikTensorAlgebra(DataType.ShortDataType, ShortRing) { o1, o2 -> o1.compareTo(o2) }
public val IntRing.multikTensorAlgebra: MultikTensorAlgebra<Int>
get() = MultikTensorAlgebra(DataType.IntDataType, IntRing) { o1, o2 -> o1.compareTo(o2) }
public val LongRing.multikTensorAlgebra: MultikTensorAlgebra<Long>
get() = MultikTensorAlgebra(DataType.LongDataType, LongRing) { o1, o2 -> o1.compareTo(o2) }

2
kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebra.kt
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@ -32,7 +32,7 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
*/
public val StructureND<T>.ndArray: INDArray
override fun produce(shape: Shape, initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
override fun structureND(shape: Shape, initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
val struct = Nd4j.create(*shape)!!.wrap()
struct.indicesIterator().forEach { struct[it] = elementAlgebra.initializer(it) }
return struct

8
kmath-nd4j/src/test/kotlin/space/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt
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@ -9,7 +9,7 @@ import org.nd4j.linalg.factory.Nd4j
import space.kscience.kmath.misc.PerformancePitfall
import space.kscience.kmath.nd.StructureND
import space.kscience.kmath.nd.one
import space.kscience.kmath.nd.produce
import space.kscience.kmath.nd.structureND
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.IntRing
import space.kscience.kmath.operations.invoke
@ -23,7 +23,7 @@ import kotlin.test.fail
internal class Nd4jArrayAlgebraTest {
@Test
fun testProduce() {
val res = DoubleField.nd4j.produce(2, 2) { it.sum().toDouble() }
val res = DoubleField.nd4j.structureND(2, 2) { it.sum().toDouble() }
val expected = (Nd4j.create(2, 2) ?: fail()).asDoubleStructure()
expected[intArrayOf(0, 0)] = 0.0
expected[intArrayOf(0, 1)] = 1.0
@ -58,9 +58,9 @@ internal class Nd4jArrayAlgebraTest {
@Test
fun testSin() = DoubleField.nd4j{
val initial = produce(2, 2) { (i, j) -> if (i == j) PI / 2 else 0.0 }
val initial = structureND(2, 2) { (i, j) -> if (i == j) PI / 2 else 0.0 }
val transformed = sin(initial)
val expected = produce(2, 2) { (i, j) -> if (i == j) 1.0 else 0.0 }
val expected = structureND(2, 2) { (i, j) -> if (i == j) 1.0 else 0.0 }
println(transformed)
assertTrue { StructureND.contentEquals(transformed, expected) }

4
kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorFieldOpsND.kt
View File

@ -21,12 +21,12 @@ public open class ViktorFieldOpsND :
public val StructureND<Double>.f64Buffer: F64Array
get() = when (this) {
is ViktorStructureND -> this.f64Buffer
else -> produce(shape) { this@f64Buffer[it] }.f64Buffer
else -> structureND(shape) { this@f64Buffer[it] }.f64Buffer
}
override val elementAlgebra: DoubleField get() = DoubleField
override fun produce(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
override fun structureND(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
F64Array(*shape).apply {
DefaultStrides(shape).indices().forEach { index ->
set(value = DoubleField.initializer(index), indices = index)