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

@@ -15,9 +15,9 @@ internal class ViktorBenchmark {
     final val n: Int = 100
 
     // automatically build context most suited for given type.
-    final val autoField: BufferedNDField<Double, RealField> = NDAlgebra.auto(RealField, dim, dim)
+    final val autoField: NDField<Double, RealField> = NDAlgebra.auto(RealField, dim, dim)
     final val realField: RealNDField = NDAlgebra.real(dim, dim)
-    final val viktorField: ViktorNDField = ViktorNDField(intArrayOf(dim, dim))
+    final val viktorField: ViktorNDField = ViktorNDField(dim, dim)
 
     @Benchmark
     fun automaticFieldAddition() {
@@ -27,6 +27,14 @@ internal class ViktorBenchmark {
         }
     }
 
+    @Benchmark
+    fun realFieldAddition() {
+        realField {
+            var res: NDStructure<Double> = one
+            repeat(n) { res += one }
+        }
+    }
+
     @Benchmark
     fun viktorFieldAddition() {
         viktorField {
@@ -41,22 +49,4 @@ internal class ViktorBenchmark {
         var res = one
         repeat(n) { res = res + one }
     }
-
-    @Benchmark
-    fun realFieldLog() {
-        realField {
-            val fortyTwo = produce { 42.0 }
-            var res = one
-            repeat(n) { res = ln(fortyTwo) }
-        }
-    }
-
-    @Benchmark
-    fun rawViktorLog() {
-        val fortyTwo = F64Array.full(dim, dim, init = 42.0)
-        var res: F64Array
-        repeat(n) {
-            res = fortyTwo.log()
-        }
-    }
 }

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

@@ -0,0 +1,40 @@
+package kscience.kmath.benchmarks
+
+import kscience.kmath.nd.*
+import kscience.kmath.operations.RealField
+import kscience.kmath.operations.invoke
+import kscience.kmath.viktor.ViktorNDField
+import org.jetbrains.bio.viktor.F64Array
+import org.openjdk.jmh.annotations.Benchmark
+import org.openjdk.jmh.annotations.Scope
+import org.openjdk.jmh.annotations.State
+
+@State(Scope.Benchmark)
+internal class ViktorLogBenchmark {
+    final val dim: Int = 1000
+    final val n: Int = 100
+
+    // automatically build context most suited for given type.
+    final val autoField: BufferedNDField<Double, RealField> = NDAlgebra.auto(RealField, dim, dim)
+    final val realField: RealNDField = NDAlgebra.real(dim, dim)
+    final val viktorField: ViktorNDField = ViktorNDField(intArrayOf(dim, dim))
+
+
+    @Benchmark
+    fun realFieldLog() {
+        realField {
+            val fortyTwo = produce { 42.0 }
+            var res = one
+            repeat(n) { res = ln(fortyTwo) }
+        }
+    }
+
+    @Benchmark
+    fun rawViktorLog() {
+        val fortyTwo = F64Array.full(dim, dim, init = 42.0)
+        var res: F64Array
+        repeat(n) {
+            res = fortyTwo.log()
+        }
+    }
+}

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

@@ -5,6 +5,7 @@ import kscience.kmath.nd.*
 import kscience.kmath.nd4j.Nd4jArrayField
 import kscience.kmath.operations.RealField
 import kscience.kmath.operations.invoke
+import kscience.kmath.viktor.ViktorNDField
 import org.nd4j.linalg.factory.Nd4j
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
@@ -25,18 +26,15 @@ fun main() {
     // automatically build context most suited for given type.
     val autoField = NDAlgebra.auto(RealField, dim, dim)
     // specialized nd-field for Double. It works as generic Double field as well
-    val specializedField = NDAlgebra.real(dim, dim)
+    val realField = NDAlgebra.real(dim, dim)
     //A generic boxing field. It should be used for objects, not primitives.
     val boxingField = NDAlgebra.field(RealField, Buffer.Companion::boxing, dim, dim)
     // Nd4j specialized field.
     val nd4jField = Nd4jArrayField.real(dim, dim)
-
+    //viktor field
-    measureAndPrint("Automatic field addition") {
+    val viktorField = ViktorNDField(dim,dim)
-        autoField {
+    //parallel processing based on Java Streams
-            var res: NDStructure<Double> = one
+    val parallelField = NDAlgebra.realWithStream(dim,dim)
-            repeat(n) { res += 1.0 }
-        }
-    }
 
     measureAndPrint("Boxing addition") {
         boxingField {
@@ -46,7 +44,7 @@ fun main() {
     }
 
     measureAndPrint("Specialized addition") {
-        specializedField {
+        realField {
             var res: NDStructure<Double> = one
             repeat(n) { res += 1.0 }
         }
@@ -59,8 +57,29 @@ fun main() {
         }
     }
 
+    measureAndPrint("Viktor addition") {
+        viktorField {
+            var res: NDStructure<Double> = one
+            repeat(n) { res += 1.0 }
+        }
+    }
+
+    measureAndPrint("Parallel stream addition") {
+        parallelField {
+            var res: NDStructure<Double> = one
+            repeat(n) { res += 1.0 }
+        }
+    }
+
+    measureAndPrint("Automatic field addition") {
+        autoField {
+            var res: NDStructure<Double> = one
+            repeat(n) { res += 1.0 }
+        }
+    }
+
     measureAndPrint("Lazy addition") {
-        val res = specializedField.one.mapAsync(GlobalScope) {
+        val res = realField.one.mapAsync(GlobalScope) {
             var c = 0.0
             repeat(n) {
                 c += 1.0

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

@@ -0,0 +1,103 @@
+package kscience.kmath.structures
+
+import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.nd.*
+import kscience.kmath.operations.ExtendedField
+import kscience.kmath.operations.RealField
+import kscience.kmath.operations.RingWithNumbers
+import java.util.*
+import java.util.stream.IntStream
+
+/**
+ * A demonstration implementation of NDField over Real using Java [DoubleStream] for parallel execution
+ */
+@OptIn(UnstableKMathAPI::class)
+public class StreamRealNDField(
+    shape: IntArray,
+) : BufferedNDField<Double, RealField>(shape, RealField, Buffer.Companion::real),
+    RingWithNumbers<NDStructure<Double>>,
+    ExtendedField<NDStructure<Double>> {
+
+    override val zero: NDBuffer<Double> by lazy { produce { zero } }
+    override val one: NDBuffer<Double> by lazy { produce { one } }
+
+    override fun number(value: Number): NDBuffer<Double> {
+        val d = value.toDouble() // minimize conversions
+        return produce { d }
+    }
+
+    override val NDStructure<Double>.buffer: RealBuffer
+        get() = when {
+            !shape.contentEquals(this@StreamRealNDField.shape) -> throw ShapeMismatchException(
+                this@StreamRealNDField.shape,
+                shape
+            )
+            this is NDBuffer && this.strides == this@StreamRealNDField.strides -> this.buffer as RealBuffer
+            else -> RealBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
+        }
+
+
+    override fun produce(initializer: RealField.(IntArray) -> Double): NDBuffer<Double> {
+        val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
+            val index = strides.index(offset)
+            RealField.initializer(index)
+        }.toArray()
+
+        return NDBuffer(strides, array.asBuffer())
+    }
+
+    override fun map(
+        arg: NDStructure<Double>,
+        transform: RealField.(Double) -> Double,
+    ): NDBuffer<Double> {
+        val array = Arrays.stream(arg.buffer.array).parallel().map { RealField.transform(it) }.toArray()
+        return NDBuffer(strides, array.asBuffer())
+    }
+
+    override fun mapIndexed(
+        arg: NDStructure<Double>,
+        transform: RealField.(index: IntArray, Double) -> Double,
+    ): NDBuffer<Double> {
+        val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
+            RealField.transform(
+                strides.index(offset),
+                arg.buffer.array[offset]
+            )
+        }.toArray()
+
+        return NDBuffer(strides, array.asBuffer())
+    }
+
+    override fun combine(
+        a: NDStructure<Double>,
+        b: NDStructure<Double>,
+        transform: RealField.(Double, Double) -> Double,
+    ): NDBuffer<Double> {
+        val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
+            RealField.transform(a.buffer.array[offset], b.buffer.array[offset])
+        }.toArray()
+        return NDBuffer(strides, array.asBuffer())
+    }
+
+    override fun power(arg: NDStructure<Double>, pow: Number): NDBuffer<Double> = map(arg) { power(it, pow) }
+
+    override fun exp(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { exp(it) }
+
+    override fun ln(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { ln(it) }
+
+    override fun sin(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { sin(it) }
+    override fun cos(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { cos(it) }
+    override fun tan(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { tan(it) }
+    override fun asin(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { asin(it) }
+    override fun acos(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { acos(it) }
+    override fun atan(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { atan(it) }
+
+    override fun sinh(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { sinh(it) }
+    override fun cosh(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { cosh(it) }
+    override fun tanh(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { tanh(it) }
+    override fun asinh(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { asinh(it) }
+    override fun acosh(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { acosh(it) }
+    override fun atanh(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { atanh(it) }
+}
+
+fun NDAlgebra.Companion.realWithStream(vararg shape: Int): StreamRealNDField = StreamRealNDField(shape)

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

@@ -18,40 +18,36 @@ public interface BufferNDAlgebra<T, C> : NDAlgebra<T, C> {
         }
     )
 
-    public val NDStructure<T>.ndBuffer: NDBuffer<T>
+    public val NDStructure<T>.buffer: Buffer<T>
         get() = when {
             !shape.contentEquals(this@BufferNDAlgebra.shape) -> throw ShapeMismatchException(
                 this@BufferNDAlgebra.shape,
                 shape
             )
-            this is NDBuffer && this.strides == this@BufferNDAlgebra.strides -> this
+            this is NDBuffer && this.strides == this@BufferNDAlgebra.strides -> this.buffer
-            else -> produce { this@ndBuffer[it] }
+            else -> bufferFactory(strides.linearSize) { offset -> get(strides.index(offset)) }
         }
 
     override fun map(arg: NDStructure<T>, transform: C.(T) -> T): NDBuffer<T> {
-        val argAsBuffer = arg.ndBuffer
         val buffer = bufferFactory(strides.linearSize) { offset ->
-            elementContext.transform(argAsBuffer.buffer[offset])
+            elementContext.transform(arg.buffer[offset])
         }
         return NDBuffer(strides, buffer)
     }
 
     override fun mapIndexed(arg: NDStructure<T>, transform: C.(index: IntArray, T) -> T): NDStructure<T> {
-        val argAsBuffer = arg.ndBuffer
         val buffer = bufferFactory(strides.linearSize) { offset ->
             elementContext.transform(
                 strides.index(offset),
-                argAsBuffer[offset]
+                arg.buffer[offset]
             )
         }
         return NDBuffer(strides, buffer)
     }
 
     override fun combine(a: NDStructure<T>, b: NDStructure<T>, transform: C.(T, T) -> T): NDStructure<T> {
-        val aBuffer = a.ndBuffer
-        val bBuffer = b.ndBuffer
         val buffer = bufferFactory(strides.linearSize) { offset ->
-            elementContext.transform(aBuffer.buffer[offset], bBuffer.buffer[offset])
+            elementContext.transform(a.buffer[offset], b.buffer[offset])
         }
         return NDBuffer(strides, buffer)
     }
@@ -119,10 +115,14 @@ public fun <T, A : Field<T>> NDAlgebra.Companion.field(
     vararg shape: Int,
 ): BufferedNDField<T, A> = BufferedNDField(shape, field, bufferFactory)
 
+@Suppress("UNCHECKED_CAST")
 public inline fun <reified T : Any, A : Field<T>> NDAlgebra.Companion.auto(
     field: A,
     vararg shape: Int,
-): BufferedNDField<T, A> = BufferedNDField(shape, field, Buffer.Companion::auto)
+): NDField<T, A> = when (field) {
+    RealField -> RealNDField(shape) as NDField<T, A>
+    else -> BufferedNDField(shape, field, Buffer.Companion::auto)
+}
 
 public inline fun <T, A : Field<T>, R> A.ndField(
     noinline bufferFactory: BufferFactory<T>,

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

@@ -11,7 +11,7 @@ import kotlin.contracts.contract
  * An optimized nd-field for complex numbers
  */
 @OptIn(UnstableKMathAPI::class)
-public open class ComplexNDField(
+public class ComplexNDField(
     shape: IntArray,
 ) : BufferedNDField<Complex, ComplexField>(shape, ComplexField, Buffer.Companion::complex),
     RingWithNumbers<NDStructure<Complex>>,

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

@@ -24,37 +24,46 @@ public class RealNDField(
         return produce { d }
     }
 
+    override val NDStructure<Double>.buffer: RealBuffer
+        get() = when {
+            !shape.contentEquals(this@RealNDField.shape) -> throw ShapeMismatchException(
+                this@RealNDField.shape,
+                shape
+            )
+            this is NDBuffer && this.strides == this@RealNDField.strides -> this.buffer as RealBuffer
+            else -> RealBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
+        }
+
     @Suppress("OVERRIDE_BY_INLINE")
     override inline fun map(
         arg: NDStructure<Double>,
         transform: RealField.(Double) -> Double,
     ): NDBuffer<Double> {
-        val argAsBuffer = arg.ndBuffer
+        val buffer = RealBuffer(strides.linearSize) { offset -> RealField.transform(arg.buffer.array[offset]) }
-        val buffer = RealBuffer(strides.linearSize) { offset -> RealField.transform(argAsBuffer.buffer[offset]) }
         return NDBuffer(strides, buffer)
     }
 
     @Suppress("OVERRIDE_BY_INLINE")
     override inline fun produce(initializer: RealField.(IntArray) -> Double): NDBuffer<Double>  {
-        val buffer = RealBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
+        val array = DoubleArray(strides.linearSize) { offset ->
-        return  NDBuffer(strides, buffer)
+            val index = strides.index(offset)
+            RealField.initializer(index)
+        }
+        return NDBuffer(strides, RealBuffer(array))
     }
 
     @Suppress("OVERRIDE_BY_INLINE")
     override inline fun mapIndexed(
         arg: NDStructure<Double>,
         transform: RealField.(index: IntArray, Double) -> Double,
-    ): NDBuffer<Double>  {
+    ): NDBuffer<Double> = NDBuffer(
-        val argAsBuffer = arg.ndBuffer
-        return NDBuffer(
         strides,
-            RealBuffer(strides.linearSize) { offset ->
+        buffer = RealBuffer(strides.linearSize) { offset ->
-                elementContext.transform(
+            RealField.transform(
                 strides.index(offset),
-                    argAsBuffer.buffer[offset]
+                arg.buffer.array[offset]
             )
         })
-    }
 
     @Suppress("OVERRIDE_BY_INLINE")
     override inline fun combine(
@@ -62,10 +71,8 @@ public class RealNDField(
         b: NDStructure<Double>,
         transform: RealField.(Double, Double) -> Double,
     ): NDBuffer<Double>  {
-        val aBuffer = a.ndBuffer
-        val bBuffer = b.ndBuffer
         val buffer = RealBuffer(strides.linearSize) { offset ->
-            elementContext.transform(aBuffer.buffer[offset], bBuffer.buffer[offset])
+            RealField.transform(a.buffer.array[offset], b.buffer.array[offset])
         }
         return  NDBuffer(strides, buffer)
     }
@@ -91,19 +98,6 @@ public class RealNDField(
     override fun atanh(arg: NDStructure<Double>): NDBuffer<Double> = map(arg) { atanh(it) }
 }
 
-
-/**
- * Fast element production using function inlining
- */
-public inline fun BufferedNDField<Double, RealField>.produceInline(crossinline initializer: RealField.(IntArray) -> Double): NDBuffer<Double> {
-    contract { callsInPlace(initializer, InvocationKind.EXACTLY_ONCE) }
-    val array = DoubleArray(strides.linearSize) { offset ->
-        val index = strides.index(offset)
-        RealField.initializer(index)
-    }
-    return NDBuffer(strides, RealBuffer(array))
-}
-
 public fun NDAlgebra.Companion.real(vararg shape: Int): RealNDField = RealNDField(shape)
 
 /**

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

@@ -9,7 +9,7 @@ import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
 @OptIn(UnstableKMathAPI::class)
-public open class ShortNDRing(
+public class ShortNDRing(
     shape: IntArray,
 ) : BufferedNDRing<Short, ShortRing>(shape, ShortRing, Buffer.Companion::auto),
     RingWithNumbers<NDStructure<Short>> {

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

@@ -58,7 +58,7 @@ public interface Structure2D<T> : NDStructure<T> {
             rows: Int,
             columns: Int,
             crossinline init: (i: Int, j: Int) -> Double,
-        ): Matrix<Double> = NDAlgebra.real(rows, columns).produceInline { (i, j) ->
+        ): Matrix<Double> = NDAlgebra.real(rows, columns).produce { (i, j) ->
             init(i, j)
         }.as2D()
     }

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

@@ -11,8 +11,8 @@ import kotlin.test.assertEquals
 @Suppress("UNUSED_VARIABLE")
 class NumberNDFieldTest {
     val algebra = NDAlgebra.real(3,3)
-    val array1 = algebra.produceInline { (i, j) -> (i + j).toDouble() }
+    val array1 = algebra.produce { (i, j) -> (i + j).toDouble() }
-    val array2 = algebra.produceInline { (i, j) -> (i - j).toDouble() }
+    val array2 = algebra.produce { (i, j) -> (i - j).toDouble() }
 
     @Test
     fun testSum() {

kmath-viktor/src/main/kotlin/kscience/kmath/viktor/ViktorNDStructure.kt

@@ -94,3 +94,5 @@ public class ViktorNDField(public override val shape: IntArray) : NDField<Double
     public override inline fun NDStructure<Double>.plus(arg: Double): ViktorNDStructure =
         (f64Buffer.plus(arg)).asStructure()
 }
+
+public fun ViktorNDField(vararg shape: Int): ViktorNDField = ViktorNDField(shape)