Merge branch 'dev' into commandertvis/hermitian-conjugate

# Conflicts:
#	kmath-core/src/commonMain/kotlin/kscience/kmath/linear/VirtualMatrix.kt
#	kmath-core/src/commonMain/kotlin/kscience/kmath/nd/Structure2D.kt

CHANGELOG.md

@@ -32,9 +32,11 @@
 - Use `Point<Double>` instead of specialized type in `kmath-for-real`
 - Optimized dot product for buffer matrices moved to `kmath-for-real`
 - EjmlMatrix context is an object
-- Matrix LUP `inverse` renamed to `inverseWithLUP`
+- Matrix LUP `inverse` renamed to `inverseWithLup`
 - `NumericAlgebra` moved outside of regular algebra chain (`Ring` no longer implements it).
 - Features moved to NDStructure and became transparent.
+- 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
 
 ### Deprecated
 

README.md

@@ -114,7 +114,7 @@ submit a feature request if you want something to be implemented first.
 >
 > **Features:**
 > - [algebras](kmath-core/src/commonMain/kotlin/kscience/kmath/operations/Algebra.kt) : Algebraic structures: contexts and elements
-> - [nd](kmath-core/src/commonMain/kotlin/kscience/kmath/structures/NDStructure.kt) : Many-dimensional structures
+> - [nd](kmath-core/src/commonMain/kotlin/kscience/kmath/nd/NDStructure.kt) : Many-dimensional structures
 > - [buffers](kmath-core/src/commonMain/kotlin/kscience/kmath/structures/Buffers.kt) : One-dimensional structure
 > - [expressions](kmath-core/src/commonMain/kotlin/kscience/kmath/expressions) : Functional Expressions
 > - [domains](kmath-core/src/commonMain/kotlin/kscience/kmath/domains) : Domains

build.gradle.kts

@@ -4,7 +4,7 @@ plugins {
     id("ru.mipt.npm.project")
 }
 
-internal val kmathVersion: String by extra("0.2.0-dev-5")
+internal val kmathVersion: String by extra("0.2.0-dev-6")
 internal val bintrayRepo: String by extra("kscience")
 internal val githubProject: String by extra("kmath")
 

examples/build.gradle.kts

@@ -68,11 +68,12 @@ benchmark {
     targets.register("benchmarks")
     // This one matches sourceSet name above
 
-    configurations.register("fast") {
+    configurations.register("dot") {
         warmups = 1 // number of warmup iterations
         iterations = 3 // number of iterations
         iterationTime = 500 // time in seconds per iteration
         iterationTimeUnit = "ms" // time unity for iterationTime, default is seconds
+        include("DotBenchmark")
     }
 }
 

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

@@ -3,14 +3,12 @@ package kscience.kmath.benchmarks
 import kotlinx.benchmark.Benchmark
 import kscience.kmath.commons.linear.CMMatrixContext
 import kscience.kmath.ejml.EjmlMatrixContext
-
 import kscience.kmath.linear.BufferMatrixContext
+import kscience.kmath.linear.Matrix
 import kscience.kmath.linear.RealMatrixContext
-import kscience.kmath.linear.real
 import kscience.kmath.operations.RealField
 import kscience.kmath.operations.invoke
 import kscience.kmath.structures.Buffer
-import kscience.kmath.structures.Matrix
 import org.openjdk.jmh.annotations.Scope
 import org.openjdk.jmh.annotations.State
 import kotlin.random.Random
@@ -33,38 +31,35 @@ class DotBenchmark {
     }
 
     @Benchmark
-    fun commonsMathMultiplication() {
+    fun cmDot() {
         CMMatrixContext {
             cmMatrix1 dot cmMatrix2
         }
     }
 
     @Benchmark
-    fun ejmlMultiplication() {
+    fun ejmlDot() {
         EjmlMatrixContext {
             ejmlMatrix1 dot ejmlMatrix2
         }
     }
 
     @Benchmark
-    fun ejmlMultiplicationwithConversion() {
+    fun ejmlDotWithConversion() {
         EjmlMatrixContext {
-            val ejmlMatrix1 = matrix1.toEjml()
+            matrix1 dot matrix2
-            val ejmlMatrix2 = matrix2.toEjml()
-
-            ejmlMatrix1 dot ejmlMatrix2
         }
     }
 
     @Benchmark
-    fun bufferedMultiplication() {
+    fun bufferedDot() {
         BufferMatrixContext(RealField, Buffer.Companion::real).invoke {
             matrix1 dot matrix2
         }
     }
 
     @Benchmark
-    fun realMultiplication() {
+    fun realDot() {
         RealMatrixContext {
             matrix1 dot matrix2
         }

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

@@ -26,8 +26,8 @@ class LinearAlgebraBenchmark {
     }
 
     @Benchmark
-    fun kmathLUPInversion() {
+    fun kmathLupInversion() {
-        MatrixContext.real.inverseWithLUP(matrix)
+        MatrixContext.real.inverseWithLup(matrix)
     }
 
     @Benchmark

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

@@ -1,8 +1,9 @@
 package kscience.kmath.benchmarks
 
+import kscience.kmath.nd.*
 import kscience.kmath.operations.RealField
 import kscience.kmath.operations.invoke
-import kscience.kmath.structures.*
+import kscience.kmath.structures.Buffer
 import org.openjdk.jmh.annotations.Benchmark
 import org.openjdk.jmh.annotations.Scope
 import org.openjdk.jmh.annotations.State
@@ -11,22 +12,16 @@ import org.openjdk.jmh.annotations.State
 internal class NDFieldBenchmark {
     @Benchmark
     fun autoFieldAdd() {
-        bufferedField {
+        autoField {
-            var res: NDBuffer<Double> = one
+            var res: NDStructure<Double> = one
             repeat(n) { res += one }
         }
     }
 
-    @Benchmark
-    fun autoElementAdd() {
-        var res = genericField.one
-        repeat(n) { res += 1.0 }
-    }
-
     @Benchmark
     fun specializedFieldAdd() {
         specializedField {
-            var res: NDBuffer<Double> = one
+            var res: NDStructure<Double> = one
             repeat(n) { res += 1.0 }
         }
     }
@@ -35,16 +30,16 @@ internal class NDFieldBenchmark {
     @Benchmark
     fun boxingFieldAdd() {
         genericField {
-            var res: NDBuffer<Double> = one
+            var res: NDStructure<Double> = one
-            repeat(n) { res += one }
+            repeat(n) { res += 1.0 }
         }
     }
 
     companion object {
         const val dim: Int = 1000
         const val n: Int = 100
-        val bufferedField: BufferedNDField<Double, RealField> = NDField.auto(RealField, dim, dim)
+        val autoField = NDAlgebra.auto(RealField, dim, dim)
-        val specializedField: RealNDField = NDField.real(dim, dim)
+        val specializedField: RealNDField = NDAlgebra.real(dim, dim)
-        val genericField: BoxingNDField<Double, RealField> = NDField.boxing(RealField, dim, dim)
+        val genericField = NDAlgebra.field(RealField, Buffer.Companion::boxing, dim, dim)
     }
 }

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

@@ -1,10 +1,8 @@
 package kscience.kmath.benchmarks
 
+import kscience.kmath.nd.*
 import kscience.kmath.operations.RealField
 import kscience.kmath.operations.invoke
-import kscience.kmath.structures.BufferedNDField
-import kscience.kmath.structures.NDField
-import kscience.kmath.structures.RealNDField
 import kscience.kmath.viktor.ViktorNDField
 import org.jetbrains.bio.viktor.F64Array
 import org.openjdk.jmh.annotations.Benchmark
@@ -17,15 +15,23 @@ internal class ViktorBenchmark {
     final val n: Int = 100
 
     // automatically build context most suited for given type.
-    final val autoField: BufferedNDField<Double, RealField> = NDField.auto(RealField, dim, dim)
+    final val autoField: NDField<Double, RealField> = NDAlgebra.auto(RealField, dim, dim)
-    final val realField: RealNDField = NDField.real(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() {
         autoField {
-            var res = one
+            var res: NDStructure<Double> = one
-            repeat(n) { res += one }
+            repeat(n) { res += 1.0 }
+        }
+    }
+
+    @Benchmark
+    fun realFieldAddition() {
+        realField {
+            var res: NDStructure<Double> = one
+            repeat(n) { res += 1.0 }
         }
     }
 
@@ -33,7 +39,7 @@ internal class ViktorBenchmark {
     fun viktorFieldAddition() {
         viktorField {
             var res = one
-            repeat(n) { res += one }
+            repeat(n) { res += 1.0 }
         }
     }
 
@@ -43,22 +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 +1,49 @@
+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: NDField<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 viktorFieldLog() {
+        viktorField {
+            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/operations/ComplexDemo.kt

@@ -1,18 +1,17 @@
 package kscience.kmath.operations
 
-import kscience.kmath.structures.NDElement
+import kscience.kmath.nd.NDAlgebra
-import kscience.kmath.structures.NDField
+import kscience.kmath.nd.complex
-import kscience.kmath.structures.complex
 
 fun main() {
     // 2d element
-    val element = NDElement.complex(2, 2) { (i,j) ->
+    val element = NDAlgebra.complex(2, 2).produce { (i,j) ->
         Complex(i.toDouble() - j.toDouble(), i.toDouble() + j.toDouble())
     }
     println(element)
 
     // 1d element operation
-    val result = with(NDField.complex(8)) {
+    val result = with(NDAlgebra.complex(8)) {
         val a = produce { (it) -> i * it - it.toDouble() }
         val b = 3
         val c = Complex(1.0, 1.0)

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

@@ -1,6 +1,9 @@
+@file:Suppress("unused")
+
 package kscience.kmath.structures
 
 import kscience.kmath.linear.transpose
+import kscience.kmath.nd.*
 import kscience.kmath.operations.Complex
 import kscience.kmath.operations.ComplexField
 import kscience.kmath.operations.invoke
@@ -10,12 +13,12 @@ fun main() {
     val dim = 1000
     val n = 1000
 
-    val realField = NDField.real(dim, dim)
+    val realField = NDAlgebra.real(dim, dim)
-    val complexField: ComplexNDField = NDField.complex(dim, dim)
+    val complexField: ComplexNDField = NDAlgebra.complex(dim, dim)
 
     val realTime = measureTimeMillis {
         realField {
-            var res: NDBuffer<Double> = one
+            var res: NDStructure<Double> = one
             repeat(n) {
                 res += 1.0
             }
@@ -26,8 +29,10 @@ fun main() {
 
     val complexTime = measureTimeMillis {
         complexField {
-            var res: NDBuffer<Complex> = one
+            var res: NDStructure<Complex> = one
-            repeat(n) { res += 1.0 }
+            repeat(n) {
+                res += 1.0
+            }
         }
     }
 

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

@@ -1,9 +1,11 @@
 package kscience.kmath.structures
 
 import kotlinx.coroutines.GlobalScope
+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
@@ -22,42 +24,62 @@ fun main() {
     val n = 1000
 
     // automatically build context most suited for given type.
-    val autoField = NDField.auto(RealField, dim, dim)
+    val autoField = NDAlgebra.auto(RealField, dim, dim)
     // specialized nd-field for Double. It works as generic Double field as well
-    val specializedField = NDField.real(dim, dim)
+    val realField = NDAlgebra.real(dim, dim)
     //A generic boxing field. It should be used for objects, not primitives.
-    val genericField = NDField.boxing(RealField, dim, dim)
+    val boxingField = NDAlgebra.field(RealField, Buffer.Companion::boxing, dim, dim)
     // Nd4j specialized field.
     val nd4jField = Nd4jArrayField.real(dim, dim)
+    //viktor field
+    val viktorField = ViktorNDField(dim,dim)
+    //parallel processing based on Java Streams
+    val parallelField = NDAlgebra.realWithStream(dim,dim)
 
-    measureAndPrint("Automatic field addition") {
+    measureAndPrint("Boxing addition") {
-        autoField {
+        boxingField {
-            var res: NDBuffer<Double> = one
+            var res: NDStructure<Double> = one
             repeat(n) { res += 1.0 }
         }
     }
 
-    measureAndPrint("Element addition") {
-        var res = genericField.one
-        repeat(n) { res += 1.0 }
-    }
-
     measureAndPrint("Specialized addition") {
-        specializedField {
+        realField {
-            var res: NDBuffer<Double> = one
+            var res: NDStructure<Double> = one
             repeat(n) { res += 1.0 }
         }
     }
 
     measureAndPrint("Nd4j specialized addition") {
         nd4jField {
-            var res = one
+            var res: NDStructure<Double> = one
+            repeat(n) { res += 1.0 }
+        }
+    }
+
+    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
@@ -67,14 +89,4 @@ fun main() {
 
         res.elements().forEach { it.second }
     }
-
-    measureAndPrint("Generic addition") {
-        //genericField.run(action)
-        genericField {
-            var res: NDBuffer<Double> = one
-            repeat(n) {
-                res += 1.0 // couldn't avoid using `one` due to resolution ambiguity }
-            }
-        }
-    }
 }

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)
+class StreamRealNDField(
+    override val shape: IntArray,
+) : NDField<Double, RealField>,
+    RingWithNumbers<NDStructure<Double>>,
+    ExtendedField<NDStructure<Double>> {
+
+    private val strides = DefaultStrides(shape)
+    override val elementContext: RealField get() = RealField
+    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 }
+    }
+
+    private 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 NDStructure<Double>.map(
+        transform: RealField.(Double) -> Double,
+    ): NDBuffer<Double> {
+        val array = Arrays.stream(buffer.array).parallel().map { RealField.transform(it) }.toArray()
+        return NDBuffer(strides, array.asBuffer())
+    }
+
+    override fun NDStructure<Double>.mapIndexed(
+        transform: RealField.(index: IntArray, Double) -> Double,
+    ): NDBuffer<Double> {
+        val array = IntStream.range(0, strides.linearSize).parallel().mapToDouble { offset ->
+            RealField.transform(
+                strides.index(offset),
+                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> = arg.map() { power(it, pow) }
+
+    override fun exp(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { exp(it) }
+
+    override fun ln(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { ln(it) }
+
+    override fun sin(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { sin(it) }
+    override fun cos(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { cos(it) }
+    override fun tan(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { tan(it) }
+    override fun asin(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { asin(it) }
+    override fun acos(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { acos(it) }
+    override fun atan(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { atan(it) }
+
+    override fun sinh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { sinh(it) }
+    override fun cosh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { cosh(it) }
+    override fun tanh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { tanh(it) }
+    override fun asinh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { asinh(it) }
+    override fun acosh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { acosh(it) }
+    override fun atanh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map() { atanh(it) }
+}
+
+fun NDAlgebra.Companion.realWithStream(vararg shape: Int): StreamRealNDField = StreamRealNDField(shape)

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

@@ -1,5 +1,7 @@
 package kscience.kmath.structures
 
+import kscience.kmath.nd.DefaultStrides
+import kscience.kmath.nd.NDBuffer
 import kotlin.system.measureTimeMillis
 
 fun main() {
@@ -7,7 +9,7 @@ fun main() {
     val array = DoubleArray(n * n) { 1.0 }
     val buffer = RealBuffer(array)
     val strides = DefaultStrides(intArrayOf(n, n))
-    val structure = BufferNDStructure(strides, buffer)
+    val structure = NDBuffer(strides, buffer)
 
     measureTimeMillis {
         var res = 0.0

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

@@ -1,5 +1,7 @@
 package kscience.kmath.structures
 
+import kscience.kmath.nd.NDStructure
+import kscience.kmath.nd.mapToBuffer
 import kotlin.system.measureTimeMillis
 
 fun main() {

kmath-commons/src/main/kotlin/kscience/kmath/commons/linear/CMMatrix.kt

@@ -1,11 +1,8 @@
 package kscience.kmath.commons.linear
 
-import kscience.kmath.linear.DiagonalFeature
+import kscience.kmath.linear.*
-import kscience.kmath.linear.MatrixContext
-import kscience.kmath.linear.Point
-import kscience.kmath.linear.origin
 import kscience.kmath.misc.UnstableKMathAPI
-import kscience.kmath.structures.Matrix
+import kscience.kmath.structures.RealBuffer
 import org.apache.commons.math3.linear.*
 import kotlin.reflect.KClass
 import kotlin.reflect.cast
@@ -17,8 +14,40 @@ public inline class CMMatrix(public val origin: RealMatrix) : Matrix<Double> {
     @UnstableKMathAPI
     override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
         DiagonalFeature::class -> if (origin is DiagonalMatrix) DiagonalFeature else null
+
+        DeterminantFeature::class, LupDecompositionFeature::class -> object :
+            DeterminantFeature<Double>,
+            LupDecompositionFeature<Double> {
+            private val lup by lazy { LUDecomposition(origin) }
+            override val determinant: Double by lazy { lup.determinant }
+            override val l: Matrix<Double> by lazy { CMMatrix(lup.l) + LFeature }
+            override val u: Matrix<Double> by lazy { CMMatrix(lup.u) + UFeature }
+            override val p: Matrix<Double> by lazy { CMMatrix(lup.p) }
+        }
+
+        CholeskyDecompositionFeature::class -> object : CholeskyDecompositionFeature<Double> {
+            override val l: Matrix<Double> by lazy {
+                val cholesky = CholeskyDecomposition(origin)
+                CMMatrix(cholesky.l) + LFeature
+            }
+        }
+
+        QRDecompositionFeature::class -> object : QRDecompositionFeature<Double> {
+            private val qr by lazy { QRDecomposition(origin) }
+            override val q: Matrix<Double> by lazy { CMMatrix(qr.q) + OrthogonalFeature }
+            override val r: Matrix<Double> by lazy { CMMatrix(qr.r) + UFeature }
+        }
+
+        SingularValueDecompositionFeature::class -> object : SingularValueDecompositionFeature<Double> {
+            private val sv by lazy { SingularValueDecomposition(origin) }
+            override val u: Matrix<Double> by lazy { CMMatrix(sv.u) }
+            override val s: Matrix<Double> by lazy { CMMatrix(sv.s) }
+            override val v: Matrix<Double> by lazy { CMMatrix(sv.v) }
+            override val singularValues: Point<Double> by lazy { RealBuffer(sv.singularValues) }
+        }
+
         else -> null
-    }?.let { type.cast(it) }
+    }?.let(type::cast)
 
     public override operator fun get(i: Int, j: Int): Double = origin.getEntry(i, j)
 }

kmath-commons/src/main/kotlin/kscience/kmath/commons/linear/CMSolver.kt

@@ -1,7 +1,7 @@
 package kscience.kmath.commons.linear
 
+import kscience.kmath.linear.Matrix
 import kscience.kmath.linear.Point
-import kscience.kmath.structures.Matrix
 import org.apache.commons.math3.linear.*
 
 public enum class CMDecomposition {

kmath-core/README.md

@@ -3,7 +3,7 @@
 The core features of KMath:
 
  - [algebras](src/commonMain/kotlin/kscience/kmath/operations/Algebra.kt) : Algebraic structures: contexts and elements
- - [nd](src/commonMain/kotlin/kscience/kmath/structures/NDStructure.kt) : Many-dimensional structures
+ - [nd](src/commonMain/kotlin/kscience/kmath/nd/NDStructure.kt) : Many-dimensional structures
  - [buffers](src/commonMain/kotlin/kscience/kmath/structures/Buffers.kt) : One-dimensional structure
  - [expressions](src/commonMain/kotlin/kscience/kmath/expressions) : Functional Expressions
  - [domains](src/commonMain/kotlin/kscience/kmath/domains) : Domains

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/SymbolIndexer.kt

@@ -1,8 +1,8 @@
 package kscience.kmath.expressions
 
 import kscience.kmath.linear.Point
+import kscience.kmath.nd.Structure2D
 import kscience.kmath.structures.BufferFactory
-import kscience.kmath.structures.Structure2D
 
 /**
  * An environment to easy transform indexed variables to symbols and back.

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

@@ -1,7 +1,19 @@
 package kscience.kmath.linear
 
+import kscience.kmath.nd.NDStructure
+import kscience.kmath.nd.Structure2D
 import kscience.kmath.operations.Ring
-import kscience.kmath.structures.*
+import kscience.kmath.operations.invoke
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.BufferFactory
+import kscience.kmath.structures.asSequence
+
+/**
+ * Alias for [Structure2D] with more familiar name.
+ *
+ * @param T the type of items.
+ */
+public typealias Matrix<T> = Structure2D<T>
 
 /**
  * Basic implementation of Matrix space based on [NDStructure]
@@ -17,6 +29,62 @@ public class BufferMatrixContext<T : Any, R : Ring<T>>(
 
     public override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
 
+    private fun Matrix<T>.toBufferMatrix(): BufferMatrix<T> = if (this is BufferMatrix) this else {
+        produce(rowNum, colNum) { i, j -> get(i, j) }
+    }
+
+    public fun one(rows: Int, columns: Int): Matrix<Double> = VirtualMatrix(rows, columns) { i, j ->
+        if (i == j) 1.0 else 0.0
+    } + DiagonalFeature
+
+    public override infix fun Matrix<T>.dot(other: Matrix<T>): BufferMatrix<T> {
+        require(colNum == other.rowNum) { "Matrix dot operation dimension mismatch: ($rowNum, $colNum) x (${other.rowNum}, ${other.colNum})" }
+        val bufferMatrix = toBufferMatrix()
+        val otherBufferMatrix = other.toBufferMatrix()
+        return elementContext {
+            produce(rowNum, other.colNum) { i, j ->
+                var res = one
+                for (l in 0 until colNum) {
+                    res += bufferMatrix[i, l] * otherBufferMatrix[l, j]
+                }
+                res
+            }
+        }
+    }
+
+    public override infix fun Matrix<T>.dot(vector: Point<T>): Point<T> {
+        require(colNum == vector.size) { "Matrix dot vector operation dimension mismatch: ($rowNum, $colNum) x (${vector.size})" }
+        val bufferMatrix = toBufferMatrix()
+        return elementContext {
+            bufferFactory(rowNum) { i ->
+                var res = one
+                for (j in 0 until colNum) {
+                    res += bufferMatrix[i, j] * vector[j]
+                }
+                res
+            }
+        }
+    }
+
+    override fun add(a: Matrix<T>, b: Matrix<T>): BufferMatrix<T> {
+        require(a.rowNum == b.rowNum) { "Row number mismatch in matrix addition. Left side: ${a.rowNum}, right side: ${b.rowNum}" }
+        require(a.colNum == b.colNum) { "Column number mismatch in matrix addition. Left side: ${a.colNum}, right side: ${b.colNum}" }
+        val aBufferMatrix = a.toBufferMatrix()
+        val bBufferMatrix = b.toBufferMatrix()
+        return elementContext {
+            produce(a.rowNum, a.colNum) { i, j ->
+                aBufferMatrix[i, j] + bBufferMatrix[i, j]
+            }
+        }
+    }
+
+    override fun multiply(a: Matrix<T>, k: Number): BufferMatrix<T> {
+        val aBufferMatrix = a.toBufferMatrix()
+        return elementContext {
+            produce(a.rowNum, a.colNum) { i, j -> aBufferMatrix[i, j] * k.toDouble() }
+        }
+    }
+
     public companion object
 }
 

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

@@ -1,7 +1,6 @@
 package kscience.kmath.linear
 
 import kscience.kmath.structures.Buffer
-import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.VirtualBuffer
 
 public typealias Point<T> = Buffer<T>

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

@@ -1,6 +1,7 @@
 package kscience.kmath.linear
 
 import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.nd.getFeature
 import kscience.kmath.operations.*
 import kscience.kmath.structures.*
 
@@ -151,7 +152,7 @@ public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext
 public fun MatrixContext<Double, Matrix<Double>>.lup(matrix: Matrix<Double>): LupDecomposition<Double> =
     lup(Buffer.Companion::real, RealField, matrix) { it < 1e-11 }
 
-public fun <T : Any> LupDecomposition<T>.solveWithLUP(
+public fun <T : Any> LupDecomposition<T>.solveWithLup(
     factory: MutableBufferFactory<T>,
     matrix: Matrix<T>,
 ): Matrix<T> {
@@ -199,14 +200,14 @@ public fun <T : Any> LupDecomposition<T>.solveWithLUP(
     }
 }
 
-public inline fun <reified T : Any> LupDecomposition<T>.solveWithLUP(matrix: Matrix<T>): Matrix<T> =
+public inline fun <reified T : Any> LupDecomposition<T>.solveWithLup(matrix: Matrix<T>): Matrix<T> =
-    solveWithLUP(MutableBuffer.Companion::auto, matrix)
+    solveWithLup(MutableBuffer.Companion::auto, matrix)
 
 /**
- * Solve a linear equation **a*x = b** using LUP decomposition
+ * Solves a system of linear equations *ax = b** using LUP decomposition.
  */
 @OptIn(UnstableKMathAPI::class)
-public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.solveWithLUP(
+public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.solveWithLup(
     a: Matrix<T>,
     b: Matrix<T>,
     noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
@@ -214,26 +215,26 @@ public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext
 ): Matrix<T> {
     // Use existing decomposition if it is provided by matrix
     val decomposition = a.getFeature() ?: lup(bufferFactory, elementContext, a, checkSingular)
-    return decomposition.solveWithLUP(bufferFactory, b)
+    return decomposition.solveWithLup(bufferFactory, b)
 }
 
-public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.inverseWithLUP(
+public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.inverseWithLup(
     matrix: Matrix<T>,
     noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
     noinline checkSingular: (T) -> Boolean,
-): Matrix<T> = solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
+): Matrix<T> = solveWithLup(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
 
 
 @OptIn(UnstableKMathAPI::class)
-public fun RealMatrixContext.solveWithLUP(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
+public fun RealMatrixContext.solveWithLup(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
     // Use existing decomposition if it is provided by matrix
     val bufferFactory: MutableBufferFactory<Double> = MutableBuffer.Companion::real
     val decomposition: LupDecomposition<Double> = a.getFeature() ?: lup(bufferFactory, RealField, a) { it < 1e-11 }
-    return decomposition.solveWithLUP(bufferFactory, b)
+    return decomposition.solveWithLup(bufferFactory, b)
 }
 
 /**
  * Inverses a square matrix using LUP decomposition. Non square matrix will throw a error.
  */
-public fun RealMatrixContext.inverseWithLUP(matrix: Matrix<Double>): Matrix<Double> =
+public fun RealMatrixContext.inverseWithLup(matrix: Matrix<Double>): Matrix<Double> =
-    solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum))
+    solveWithLup(matrix, one(matrix.rowNum, matrix.colNum))

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

@@ -1,6 +1,9 @@
 package kscience.kmath.linear
 
-import kscience.kmath.structures.*
+import kscience.kmath.nd.Structure2D
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.BufferFactory
+import kscience.kmath.structures.asBuffer
 
 public class MatrixBuilder(public val rows: Int, public val columns: Int) {
     public operator fun <T : Any> invoke(vararg elements: T): Matrix<T> {
@@ -22,7 +25,7 @@ public fun <T : Any> Structure2D.Companion.row(vararg values: T): Matrix<T> {
 public inline fun <reified T : Any> Structure2D.Companion.row(
     size: Int,
     factory: BufferFactory<T> = Buffer.Companion::auto,
-    noinline builder: (Int) -> T
+    noinline builder: (Int) -> T,
 ): Matrix<T> {
     val buffer = factory(size, builder)
     return BufferMatrix(1, size, buffer)
@@ -36,7 +39,7 @@ public fun <T : Any> Structure2D.Companion.column(vararg values: T): Matrix<T> {
 public inline fun <reified T : Any> Structure2D.Companion.column(
     size: Int,
     factory: BufferFactory<T> = Buffer.Companion::auto,
-    noinline builder: (Int) -> T
+    noinline builder: (Int) -> T,
 ): Matrix<T> {
     val buffer = factory(size, builder)
     return BufferMatrix(size, 1, buffer)

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

@@ -6,7 +6,6 @@ import kscience.kmath.operations.invoke
 import kscience.kmath.operations.sum
 import kscience.kmath.structures.Buffer
 import kscience.kmath.structures.BufferFactory
-import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.asSequence
 
 /**

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

@@ -1,7 +1,5 @@
 package kscience.kmath.linear
 
-import kscience.kmath.structures.Matrix
-
 /**
  * A marker interface representing some properties of matrices or additional transformations of them. Features are used
  * to optimize matrix operations performance in some cases or retrieve the APIs.
@@ -11,8 +9,8 @@ public interface MatrixFeature
 /**
  * Matrices with this feature are considered to have only diagonal non-null elements.
  */
-public interface DiagonalFeature : MatrixFeature{
+public interface DiagonalFeature : MatrixFeature {
-    public companion object: DiagonalFeature
+    public companion object : DiagonalFeature
 }
 
 /**
@@ -39,6 +37,8 @@ public interface InverseMatrixFeature<T : Any> : MatrixFeature {
 
 /**
  * Matrices with this feature can compute their determinant.
+ *
+ * @param T the type of matrices' items.
  */
 public interface DeterminantFeature<T : Any> : MatrixFeature {
     /**

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

@@ -1,11 +1,10 @@
 package kscience.kmath.linear
 
 import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.nd.Structure2D
+import kscience.kmath.nd.getFeature
 import kscience.kmath.operations.Ring
-import kscience.kmath.structures.Matrix
-import kscience.kmath.structures.Structure2D
 import kscience.kmath.structures.asBuffer
-import kscience.kmath.structures.getFeature
 import kotlin.math.sqrt
 import kotlin.reflect.KClass
 import kotlin.reflect.safeCast
@@ -39,7 +38,8 @@ public class MatrixWrapper<T : Any> internal  constructor(
  * Origin does not necessary store all features.
  */
 @UnstableKMathAPI
-public val <T : Any> Matrix<T>.origin: Matrix<T> get() = (this as? MatrixWrapper)?.origin ?: this
+public val <T : Any> Matrix<T>.origin: Matrix<T>
+    get() = (this as? MatrixWrapper)?.origin ?: this
 
 /**
  * Add a single feature to a [Matrix]
@@ -60,12 +60,6 @@ public operator fun <T : Any> Matrix<T>.plus(newFeatures: Collection<MatrixFeatu
         MatrixWrapper(this, newFeatures.toSet())
     }
 
-public inline fun Structure2D.Companion.real(
-    rows: Int,
-    columns: Int,
-    initializer: (Int, Int) -> Double,
-): BufferMatrix<Double> = MatrixContext.real.produce(rows, columns, initializer)
-
 /**
  * Build a square matrix from given elements.
  */

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

@@ -1,12 +1,10 @@
 package kscience.kmath.linear
 
-import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.RealBuffer
 
-@Suppress("OVERRIDE_BY_INLINE")
 public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
 
-    public override inline fun produce(
+    public override fun produce(
         rows: Int,
         columns: Int,
         initializer: (i: Int, j: Int) -> Double,
@@ -15,7 +13,7 @@ public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
         return BufferMatrix(rows, columns, buffer)
     }
 
-    private fun Matrix<Double>.wrap(): BufferMatrix<Double> = if (this is BufferMatrix) this else {
+    public fun Matrix<Double>.toBufferMatrix(): BufferMatrix<Double> = if (this is BufferMatrix) this else {
         produce(rowNum, colNum) { i, j -> get(i, j) }
     }
 
@@ -25,10 +23,12 @@ public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
 
     public override infix fun Matrix<Double>.dot(other: Matrix<Double>): BufferMatrix<Double> {
         require(colNum == other.rowNum) { "Matrix dot operation dimension mismatch: ($rowNum, $colNum) x (${other.rowNum}, ${other.colNum})" }
+        val bufferMatrix = toBufferMatrix()
+        val otherBufferMatrix = other.toBufferMatrix()
         return produce(rowNum, other.colNum) { i, j ->
             var res = 0.0
             for (l in 0 until colNum) {
-                res += get(i, l) * other.get(l, j)
+                res += bufferMatrix[i, l] * otherBufferMatrix[l, j]
             }
             res
         }
@@ -36,10 +36,11 @@ public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
 
     public override infix fun Matrix<Double>.dot(vector: Point<Double>): Point<Double> {
         require(colNum == vector.size) { "Matrix dot vector operation dimension mismatch: ($rowNum, $colNum) x (${vector.size})" }
+        val bufferMatrix = toBufferMatrix()
         return RealBuffer(rowNum) { i ->
             var res = 0.0
             for (j in 0 until colNum) {
-                res += get(i, j) * vector[j]
+                res += bufferMatrix[i, j] * vector[j]
             }
             res
         }
@@ -48,17 +49,23 @@ public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
     override fun add(a: Matrix<Double>, b: Matrix<Double>): BufferMatrix<Double> {
         require(a.rowNum == b.rowNum) { "Row number mismatch in matrix addition. Left side: ${a.rowNum}, right side: ${b.rowNum}" }
         require(a.colNum == b.colNum) { "Column number mismatch in matrix addition. Left side: ${a.colNum}, right side: ${b.colNum}" }
+        val aBufferMatrix = a.toBufferMatrix()
+        val bBufferMatrix = b.toBufferMatrix()
         return produce(a.rowNum, a.colNum) { i, j ->
-            a[i, j] + b[i, j]
+            aBufferMatrix[i, j] + bBufferMatrix[i, j]
         }
     }
 
-    override fun Matrix<Double>.times(value: Double): BufferMatrix<Double> =
+    override fun Matrix<Double>.times(value: Double): BufferMatrix<Double> {
-        produce(rowNum, colNum) { i, j -> get(i, j) * value }
+        val bufferMatrix = toBufferMatrix()
+        return produce(rowNum, colNum) { i, j -> bufferMatrix[i, j] * value }
+    }
 
 
-    override fun multiply(a: Matrix<Double>, k: Number): BufferMatrix<Double> =
+    override fun multiply(a: Matrix<Double>, k: Number): BufferMatrix<Double> {
-        produce(a.rowNum, a.colNum) { i, j -> a[i, j] * k.toDouble() }
+        val aBufferMatrix = a.toBufferMatrix()
+        return produce(a.rowNum, a.colNum) { i, j -> aBufferMatrix[i, j] * k.toDouble() }
+    }
 }
 
 

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

@@ -1,7 +1,5 @@
 package kscience.kmath.linear
 
-import kscience.kmath.structures.Matrix
-
 /**
  * The matrix where each element is evaluated each time when is being accessed.
  *

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

@@ -0,0 +1,134 @@
+package kscience.kmath.nd
+
+import kscience.kmath.nd.*
+import kscience.kmath.operations.*
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.BufferFactory
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+
+public interface BufferNDAlgebra<T, C> : NDAlgebra<T, C> {
+    public val strides: Strides
+    public val bufferFactory: BufferFactory<T>
+
+    override fun produce(initializer: C.(IntArray) -> T): NDBuffer<T> = NDBuffer(
+        strides,
+        bufferFactory(strides.linearSize) { offset ->
+            elementContext.initializer(strides.index(offset))
+        }
+    )
+
+    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.buffer
+            else -> bufferFactory(strides.linearSize) { offset -> get(strides.index(offset)) }
+        }
+
+    override fun NDStructure<T>.map(transform: C.(T) -> T): NDBuffer<T> {
+        val buffer = bufferFactory(strides.linearSize) { offset ->
+            elementContext.transform(buffer[offset])
+        }
+        return NDBuffer(strides, buffer)
+    }
+
+    override fun NDStructure<T>.mapIndexed(transform: C.(index: IntArray, T) -> T): NDBuffer<T> {
+        val buffer = bufferFactory(strides.linearSize) { offset ->
+            elementContext.transform(
+                strides.index(offset),
+                buffer[offset]
+            )
+        }
+        return NDBuffer(strides, buffer)
+    }
+
+    override fun combine(a: NDStructure<T>, b: NDStructure<T>, transform: C.(T, T) -> T): NDBuffer<T> {
+        val buffer = bufferFactory(strides.linearSize) { offset ->
+            elementContext.transform(a.buffer[offset], b.buffer[offset])
+        }
+        return NDBuffer(strides, buffer)
+    }
+}
+
+public open class BufferedNDSpace<T, R : Space<T>>(
+    final override val shape: IntArray,
+    final override val elementContext: R,
+    final override val bufferFactory: BufferFactory<T>,
+) : NDSpace<T, R>, BufferNDAlgebra<T, R> {
+    override val strides: Strides = DefaultStrides(shape)
+    override val zero: NDBuffer<T> by lazy { produce { zero } }
+}
+
+public open class BufferedNDRing<T, R : Ring<T>>(
+    shape: IntArray,
+    elementContext: R,
+    bufferFactory: BufferFactory<T>,
+) : BufferedNDSpace<T, R>(shape, elementContext, bufferFactory), NDRing<T, R> {
+    override val one: NDBuffer<T> by lazy { produce { one } }
+}
+
+public open class BufferedNDField<T, R : Field<T>>(
+    shape: IntArray,
+    elementContext: R,
+    bufferFactory: BufferFactory<T>,
+) : BufferedNDRing<T, R>(shape, elementContext, bufferFactory), NDField<T, R>
+
+// space factories
+public fun <T, A : Space<T>> NDAlgebra.Companion.space(
+    space: A,
+    bufferFactory: BufferFactory<T>,
+    vararg shape: Int,
+): BufferedNDSpace<T, A> = BufferedNDSpace(shape, space, bufferFactory)
+
+public inline fun <T, A : Space<T>, R> A.ndSpace(
+    noinline bufferFactory: BufferFactory<T>,
+    vararg shape: Int,
+    action: BufferedNDSpace<T, A>.() -> R,
+): R {
+    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+    return NDAlgebra.space(this, bufferFactory, *shape).run(action)
+}
+
+//ring factories
+public fun <T, A : Ring<T>> NDAlgebra.Companion.ring(
+    ring: A,
+    bufferFactory: BufferFactory<T>,
+    vararg shape: Int,
+): BufferedNDRing<T, A> = BufferedNDRing(shape, ring, bufferFactory)
+
+public inline fun <T, A : Ring<T>, R> A.ndRing(
+    noinline bufferFactory: BufferFactory<T>,
+    vararg shape: Int,
+    action: BufferedNDRing<T, A>.() -> R,
+): R {
+    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+    return NDAlgebra.ring(this, bufferFactory, *shape).run(action)
+}
+
+//field factories
+public fun <T, A : Field<T>> NDAlgebra.Companion.field(
+    field: A,
+    bufferFactory: BufferFactory<T>,
+    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,
+): 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>,
+    vararg shape: Int,
+    action: BufferedNDField<T, A>.() -> R,
+): R {
+    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+    return NDAlgebra.field(this, bufferFactory, *shape).run(action)
+}

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

@@ -0,0 +1,113 @@
+package kscience.kmath.nd
+
+import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.operations.*
+import kscience.kmath.structures.Buffer
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+
+
+/**
+ * An optimized nd-field for complex numbers
+ */
+@OptIn(UnstableKMathAPI::class)
+public class ComplexNDField(
+    shape: IntArray,
+) : BufferedNDField<Complex, ComplexField>(shape, ComplexField, Buffer.Companion::complex),
+    RingWithNumbers<NDStructure<Complex>>,
+    ExtendedField<NDStructure<Complex>> {
+
+    override val zero: NDBuffer<Complex> by lazy { produce { zero } }
+    override val one: NDBuffer<Complex> by lazy { produce { one } }
+
+    override fun number(value: Number): NDBuffer<Complex> {
+        val d = value.toComplex() // minimize conversions
+        return produce { d }
+    }
+//
+//    @Suppress("OVERRIDE_BY_INLINE")
+//    override inline fun map(
+//        arg: AbstractNDBuffer<Double>,
+//        transform: RealField.(Double) -> Double,
+//    ): RealNDElement {
+//        check(arg)
+//        val array = RealBuffer(arg.strides.linearSize) { offset -> RealField.transform(arg.buffer[offset]) }
+//        return BufferedNDFieldElement(this, array)
+//    }
+//
+//    @Suppress("OVERRIDE_BY_INLINE")
+//    override inline fun produce(initializer: RealField.(IntArray) -> Double): RealNDElement {
+//        val array = RealBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
+//        return BufferedNDFieldElement(this, array)
+//    }
+//
+//    @Suppress("OVERRIDE_BY_INLINE")
+//    override inline fun mapIndexed(
+//        arg: AbstractNDBuffer<Double>,
+//        transform: RealField.(index: IntArray, Double) -> Double,
+//    ): RealNDElement {
+//        check(arg)
+//        return BufferedNDFieldElement(
+//            this,
+//            RealBuffer(arg.strides.linearSize) { offset ->
+//                elementContext.transform(
+//                    arg.strides.index(offset),
+//                    arg.buffer[offset]
+//                )
+//            })
+//    }
+//
+//    @Suppress("OVERRIDE_BY_INLINE")
+//    override inline fun combine(
+//        a: AbstractNDBuffer<Double>,
+//        b: AbstractNDBuffer<Double>,
+//        transform: RealField.(Double, Double) -> Double,
+//    ): RealNDElement {
+//        check(a, b)
+//        val buffer = RealBuffer(strides.linearSize) { offset ->
+//            elementContext.transform(a.buffer[offset], b.buffer[offset])
+//        }
+//        return BufferedNDFieldElement(this, buffer)
+//    }
+
+    override fun power(arg: NDStructure<Complex>, pow: Number): NDBuffer<Complex> = arg.map() { power(it, pow) }
+
+    override fun exp(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { exp(it) }
+
+    override fun ln(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { ln(it) }
+
+    override fun sin(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { sin(it) }
+    override fun cos(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { cos(it) }
+    override fun tan(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { tan(it) }
+    override fun asin(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { asin(it) }
+    override fun acos(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { acos(it) }
+    override fun atan(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { atan(it) }
+
+    override fun sinh(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { sinh(it) }
+    override fun cosh(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { cosh(it) }
+    override fun tanh(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { tanh(it) }
+    override fun asinh(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { asinh(it) }
+    override fun acosh(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { acosh(it) }
+    override fun atanh(arg: NDStructure<Complex>): NDBuffer<Complex> = arg.map() { atanh(it) }
+}
+
+
+/**
+ * Fast element production using function inlining
+ */
+public inline fun BufferedNDField<Complex, ComplexField>.produceInline(initializer: ComplexField.(Int) -> Complex): NDBuffer<Complex> {
+    contract { callsInPlace(initializer, InvocationKind.EXACTLY_ONCE) }
+    val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.initializer(offset) }
+    return NDBuffer(strides, buffer)
+}
+
+
+public fun NDAlgebra.Companion.complex(vararg shape: Int): ComplexNDField = ComplexNDField(shape)
+
+/**
+ * Produce a context for n-dimensional operations inside this real field
+ */
+public inline fun <R> ComplexField.nd(vararg shape: Int, action: ComplexNDField.() -> R): R {
+    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+    return ComplexNDField(shape).action()
+}

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

@@ -0,0 +1,262 @@
+package kscience.kmath.nd
+
+import kscience.kmath.operations.Field
+import kscience.kmath.operations.Ring
+import kscience.kmath.operations.Space
+import kscience.kmath.structures.*
+
+/**
+ * An exception is thrown when the expected ans actual shape of NDArray differs.
+ *
+ * @property expected the expected shape.
+ * @property actual the actual shape.
+ */
+public class ShapeMismatchException(public val expected: IntArray, public val actual: IntArray) :
+    RuntimeException("Shape ${actual.contentToString()} doesn't fit in expected shape ${expected.contentToString()}.")
+
+/**
+ * The base interface for all ND-algebra implementations.
+ *
+ * @param T the type of ND-structure element.
+ * @param C the type of the element context.
+ * @param N the type of the structure.
+ */
+public interface NDAlgebra<T, C> {
+    /**
+     * The shape of ND-structures this algebra operates on.
+     */
+    public val shape: IntArray
+
+    /**
+     * The algebra over elements of ND structure.
+     */
+    public val elementContext: C
+
+    /**
+     * Produces a new [N] structure using given initializer function.
+     */
+    public fun produce(initializer: C.(IntArray) -> T): NDStructure<T>
+
+    /**
+     * Maps elements from one structure to another one by applying [transform] to them.
+     */
+    public fun NDStructure<T>.map(transform: C.(T) -> T): NDStructure<T>
+
+    /**
+     * Maps elements from one structure to another one by applying [transform] to them alongside with their indices.
+     */
+    public fun NDStructure<T>.mapIndexed(transform: C.(index: IntArray, T) -> T): NDStructure<T>
+
+    /**
+     * Combines two structures into one.
+     */
+    public fun combine(a: NDStructure<T>, b: NDStructure<T>, transform: C.(T, T) -> T): NDStructure<T>
+
+    /**
+     * Element-wise invocation of function working on [T] on a [NDStructure].
+     */
+    public operator fun Function1<T, T>.invoke(structure: NDStructure<T>): NDStructure<T> =
+        structure.map() { value -> this@invoke(value) }
+
+    public companion object
+}
+
+/**
+ * Checks if given elements are consistent with this context.
+ *
+ * @param structures the structures to check.
+ * @return the array of valid structures.
+ */
+internal fun <T, C> NDAlgebra<T, C>.checkShape(vararg structures: NDStructure<T>): Array<out NDStructure<T>> = structures
+    .map(NDStructure<T>::shape)
+    .singleOrNull { !shape.contentEquals(it) }
+    ?.let<IntArray, Array<out NDStructure<T>>> { throw ShapeMismatchException(shape, it) }
+    ?: structures
+
+/**
+ * Checks if given element is consistent with this context.
+ *
+ * @param element the structure to check.
+ * @return the valid structure.
+ */
+internal fun <T, C> NDAlgebra<T, C>.checkShape(element: NDStructure<T>): NDStructure<T> {
+    if (!element.shape.contentEquals(shape)) throw ShapeMismatchException(shape, element.shape)
+    return element
+}
+
+/**
+ * Space of [NDStructure].
+ *
+ * @param T the type of the element contained in ND structure.
+ * @param N the type of ND structure.
+ * @param S the type of space of structure elements.
+ */
+public interface NDSpace<T, S : Space<T>> : Space<NDStructure<T>>, NDAlgebra<T, S> {
+    /**
+     * Element-wise addition.
+     *
+     * @param a the addend.
+     * @param b the augend.
+     * @return the sum.
+     */
+    public override fun add(a: NDStructure<T>, b: NDStructure<T>): NDStructure<T> =
+        combine(a, b) { aValue, bValue -> add(aValue, bValue) }
+
+    /**
+     * Element-wise multiplication by scalar.
+     *
+     * @param a the multiplicand.
+     * @param k the multiplier.
+     * @return the product.
+     */
+    public override fun multiply(a: NDStructure<T>, k: Number): NDStructure<T> = a.map() { multiply(it, k) }
+
+    // TODO move to extensions after KEEP-176
+
+    /**
+     * Adds an ND structure to an element of it.
+     *
+     * @receiver the addend.
+     * @param arg the augend.
+     * @return the sum.
+     */
+    public operator fun NDStructure<T>.plus(arg: T): NDStructure<T> = this.map() { value -> add(arg, value) }
+
+    /**
+     * Subtracts an element from ND structure of it.
+     *
+     * @receiver the dividend.
+     * @param arg the divisor.
+     * @return the quotient.
+     */
+    public operator fun NDStructure<T>.minus(arg: T): NDStructure<T> = this.map() { value -> add(arg, -value) }
+
+    /**
+     * Adds an element to ND structure of it.
+     *
+     * @receiver the addend.
+     * @param arg the augend.
+     * @return the sum.
+     */
+    public operator fun T.plus(arg: NDStructure<T>): NDStructure<T> = arg.map() { value -> add(this@plus, value) }
+
+    /**
+     * Subtracts an ND structure from an element of it.
+     *
+     * @receiver the dividend.
+     * @param arg the divisor.
+     * @return the quotient.
+     */
+    public operator fun T.minus(arg: NDStructure<T>): NDStructure<T> = arg.map() { value -> add(-this@minus, value) }
+
+    public companion object
+}
+
+/**
+ * Ring of [NDStructure].
+ *
+ * @param T the type of the element contained in ND structure.
+ * @param N the type of ND structure.
+ * @param R the type of ring of structure elements.
+ */
+public interface NDRing<T, R : Ring<T>> : Ring<NDStructure<T>>, NDSpace<T, R> {
+    /**
+     * Element-wise multiplication.
+     *
+     * @param a the multiplicand.
+     * @param b the multiplier.
+     * @return the product.
+     */
+    public override fun multiply(a: NDStructure<T>, b: NDStructure<T>): NDStructure<T> =
+        combine(a, b) { aValue, bValue -> multiply(aValue, bValue) }
+
+    //TODO move to extensions after KEEP-176
+
+    /**
+     * Multiplies an ND structure by an element of it.
+     *
+     * @receiver the multiplicand.
+     * @param arg the multiplier.
+     * @return the product.
+     */
+    public operator fun NDStructure<T>.times(arg: T): NDStructure<T> = this.map() { value -> multiply(arg, value) }
+
+    /**
+     * Multiplies an element by a ND structure of it.
+     *
+     * @receiver the multiplicand.
+     * @param arg the multiplier.
+     * @return the product.
+     */
+    public operator fun T.times(arg: NDStructure<T>): NDStructure<T> = arg.map() { value -> multiply(this@times, value) }
+
+    public companion object
+}
+
+/**
+ * Field of [NDStructure].
+ *
+ * @param T the type of the element contained in ND structure.
+ * @param N the type of ND structure.
+ * @param F the type field of structure elements.
+ */
+public interface NDField<T, F : Field<T>> : Field<NDStructure<T>>, NDRing<T, F> {
+    /**
+     * Element-wise division.
+     *
+     * @param a the dividend.
+     * @param b the divisor.
+     * @return the quotient.
+     */
+    public override fun divide(a: NDStructure<T>, b: NDStructure<T>): NDStructure<T> =
+        combine(a, b) { aValue, bValue -> divide(aValue, bValue) }
+
+    //TODO move to extensions after KEEP-176
+    /**
+     * Divides an ND structure by an element of it.
+     *
+     * @receiver the dividend.
+     * @param arg the divisor.
+     * @return the quotient.
+     */
+    public operator fun NDStructure<T>.div(arg: T): NDStructure<T> = this.map() { value -> divide(arg, value) }
+
+    /**
+     * Divides an element by an ND structure of it.
+     *
+     * @receiver the dividend.
+     * @param arg the divisor.
+     * @return the quotient.
+     */
+    public operator fun T.div(arg: NDStructure<T>): NDStructure<T> = arg.map() { divide(it, this@div) }
+
+//    @ThreadLocal
+//    public companion object {
+//        private val realNDFieldCache: MutableMap<IntArray, RealNDField> = hashMapOf()
+//
+//        /**
+//         * Create a nd-field for [Double] values or pull it from cache if it was created previously.
+//         */
+//        public fun real(vararg shape: Int): RealNDField = realNDFieldCache.getOrPut(shape) { RealNDField(shape) }
+//
+//        /**
+//         * Create an ND field with boxing generic buffer.
+//         */
+//        public fun <T : Any, F : Field<T>> boxing(
+//            field: F,
+//            vararg shape: Int,
+//            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
+//        ): BufferedNDField<T, F> = BufferedNDField(shape, field, bufferFactory)
+//
+//        /**
+//         * Create a most suitable implementation for nd-field using reified class.
+//         */
+//        @Suppress("UNCHECKED_CAST")
+//        public inline fun <reified T : Any, F : Field<T>> auto(field: F, vararg shape: Int): NDField<T, F> =
+//            when {
+//                T::class == Double::class -> real(*shape) as NDField<T, F>
+//                T::class == Complex::class -> complex(*shape) as BufferedNDField<T, F>
+//                else -> BoxingNDField(shape, field, Buffer.Companion::auto)
+//            }
+//    }
+}

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

@@ -1,6 +1,10 @@
-package kscience.kmath.structures
+package kscience.kmath.nd
 
 import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.BufferFactory
+import kscience.kmath.structures.MutableBuffer
+import kscience.kmath.structures.asSequence
 import kotlin.jvm.JvmName
 import kotlin.native.concurrent.ThreadLocal
 import kotlin.reflect.KClass
@@ -74,8 +78,8 @@ public interface NDStructure<T> {
             strides: Strides,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
             initializer: (IntArray) -> T,
-        ): BufferNDStructure<T> =
+        ): NDBuffer<T> =
-            BufferNDStructure(strides, bufferFactory(strides.linearSize) { i -> initializer(strides.index(i)) })
+            NDBuffer(strides, bufferFactory(strides.linearSize) { i -> initializer(strides.index(i)) })
 
         /**
          * Inline create NDStructure with non-boxing buffer implementation if it is possible
@@ -83,40 +87,40 @@ public interface NDStructure<T> {
         public inline fun <reified T : Any> auto(
             strides: Strides,
             crossinline initializer: (IntArray) -> T,
-        ): BufferNDStructure<T> =
+        ): NDBuffer<T> =
-            BufferNDStructure(strides, Buffer.auto(strides.linearSize) { i -> initializer(strides.index(i)) })
+            NDBuffer(strides, Buffer.auto(strides.linearSize) { i -> initializer(strides.index(i)) })
 
         public inline fun <T : Any> auto(
             type: KClass<T>,
             strides: Strides,
             crossinline initializer: (IntArray) -> T,
-        ): BufferNDStructure<T> =
+        ): NDBuffer<T> =
-            BufferNDStructure(strides, Buffer.auto(type, strides.linearSize) { i -> initializer(strides.index(i)) })
+            NDBuffer(strides, Buffer.auto(type, strides.linearSize) { i -> initializer(strides.index(i)) })
 
         public fun <T> build(
             shape: IntArray,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
             initializer: (IntArray) -> T,
-        ): BufferNDStructure<T> = build(DefaultStrides(shape), bufferFactory, initializer)
+        ): NDBuffer<T> = build(DefaultStrides(shape), bufferFactory, initializer)
 
         public inline fun <reified T : Any> auto(
             shape: IntArray,
             crossinline initializer: (IntArray) -> T,
-        ): BufferNDStructure<T> =
+        ): NDBuffer<T> =
             auto(DefaultStrides(shape), initializer)
 
         @JvmName("autoVarArg")
         public inline fun <reified T : Any> auto(
             vararg shape: Int,
             crossinline initializer: (IntArray) -> T,
-        ): BufferNDStructure<T> =
+        ): NDBuffer<T> =
             auto(DefaultStrides(shape), initializer)
 
         public inline fun <T : Any> auto(
             type: KClass<T>,
             vararg shape: Int,
             crossinline initializer: (IntArray) -> T,
-        ): BufferNDStructure<T> =
+        ): NDBuffer<T> =
             auto(type, DefaultStrides(shape), initializer)
     }
 }
@@ -156,7 +160,7 @@ public inline fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) ->
  */
 public interface Strides {
     /**
-     * Shape of NDstructure
+     * Shape of NDStructure
      */
     public val shape: IntArray
 
@@ -185,7 +189,9 @@ public interface Strides {
     /**
      * Iterate over ND indices in a natural order
      */
-    public fun indices(): Sequence<IntArray> = (0 until linearSize).asSequence().map { index(it) }
+    public fun indices(): Sequence<IntArray> = (0 until linearSize).asSequence().map {
+        index(it)
+    }
 }
 
 /**
@@ -211,9 +217,7 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
     }
 
     override fun offset(index: IntArray): Int = index.mapIndexed { i, value ->
-        if (value < 0 || value >= this.shape[i])
+        if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})")
-            throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})")
-
         value * strides[i]
     }.sum()
 
@@ -256,23 +260,29 @@ public class DefaultStrides private constructor(override val shape: IntArray) :
  * Represents [NDStructure] over [Buffer].
  *
  * @param T the type of items.
+ * @param strides The strides to access elements of [Buffer] by linear indices.
+ * @param buffer The underlying buffer.
  */
-public abstract class NDBuffer<T> : NDStructure<T> {
+public open class NDBuffer<T>(
-    /**
+    public val strides: Strides,
-     * The underlying buffer.
+    buffer: Buffer<T>,
-     */
+) : NDStructure<T> {
-    public abstract val buffer: Buffer<T>
 
-    /**
+    init {
-     * The strides to access elements of [Buffer] by linear indices.
+        if (strides.linearSize != buffer.size) {
-     */
+            error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
-    public abstract val strides: Strides
+        }
+    }
+
+    public open val buffer: Buffer<T> = buffer
 
     override operator fun get(index: IntArray): T = buffer[strides.offset(index)]
 
     override val shape: IntArray get() = strides.shape
 
-    override fun elements(): Sequence<Pair<IntArray, T>> = strides.indices().map { it to this[it] }
+    override fun elements(): Sequence<Pair<IntArray, T>> = strides.indices().map {
+        it to this[it]
+    }
 
     override fun equals(other: Any?): Boolean {
         return NDStructure.contentEquals(this, other as? NDStructure<*> ?: return false)
@@ -297,46 +307,30 @@ public abstract class NDBuffer<T> : NDStructure<T> {
         }
         return "NDBuffer(shape=${shape.contentToString()}, buffer=$bufferRepr)"
     }
-
-
 }
 
 /**
- * Boxing generic [NDStructure]
+ * Transform structure to a new structure using provided [BufferFactory] and optimizing if argument is [NDBuffer]
- */
-public class BufferNDStructure<T>(
-    override val strides: Strides,
-    override val buffer: Buffer<T>,
-) : NDBuffer<T>() {
-    init {
-        if (strides.linearSize != buffer.size) {
-            error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
-        }
-    }
-}
-
-/**
- * Transform structure to a new structure using provided [BufferFactory] and optimizing if argument is [BufferNDStructure]
  */
 public inline fun <T, reified R : Any> NDStructure<T>.mapToBuffer(
     factory: BufferFactory<R> = Buffer.Companion::auto,
     crossinline transform: (T) -> R,
-): BufferNDStructure<R> {
+): NDBuffer<R> {
-    return if (this is BufferNDStructure<T>)
+    return if (this is NDBuffer<T>)
-        BufferNDStructure(this.strides, factory.invoke(strides.linearSize) { transform(buffer[it]) })
+        NDBuffer(this.strides, factory.invoke(strides.linearSize) { transform(buffer[it]) })
     else {
         val strides = DefaultStrides(shape)
-        BufferNDStructure(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
+        NDBuffer(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
     }
 }
 
 /**
  * Mutable ND buffer based on linear [MutableBuffer].
  */
-public class MutableBufferNDStructure<T>(
+public class MutableNDBuffer<T>(
-    override val strides: Strides,
+    strides: Strides,
-    override val buffer: MutableBuffer<T>,
+    buffer: MutableBuffer<T>,
-) : NDBuffer<T>(), MutableNDStructure<T> {
+) : NDBuffer<T>(strides, buffer), MutableNDStructure<T> {
 
     init {
         require(strides.linearSize == buffer.size) {
@@ -344,6 +338,8 @@ public class MutableBufferNDStructure<T>(
         }
     }
 
+    override val buffer: MutableBuffer<T> = super.buffer as MutableBuffer<T>
+
     override operator fun set(index: IntArray, value: T): Unit = buffer.set(strides.offset(index), value)
 }
 

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

@@ -0,0 +1,107 @@
+package kscience.kmath.nd
+
+import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.operations.ExtendedField
+import kscience.kmath.operations.RealField
+import kscience.kmath.operations.RingWithNumbers
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.RealBuffer
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+
+@OptIn(UnstableKMathAPI::class)
+public class RealNDField(
+    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@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 NDStructure<Double>.map(
+        transform: RealField.(Double) -> Double,
+    ): NDBuffer<Double> {
+        val buffer = RealBuffer(strides.linearSize) { offset -> RealField.transform(buffer.array[offset]) }
+        return NDBuffer(strides, buffer)
+    }
+
+    @Suppress("OVERRIDE_BY_INLINE")
+    override inline fun produce(initializer: RealField.(IntArray) -> Double): NDBuffer<Double> {
+        val array = DoubleArray(strides.linearSize) { offset ->
+            val index = strides.index(offset)
+            RealField.initializer(index)
+        }
+        return NDBuffer(strides, RealBuffer(array))
+    }
+
+    @Suppress("OVERRIDE_BY_INLINE")
+    override inline fun NDStructure<Double>.mapIndexed(
+        transform: RealField.(index: IntArray, Double) -> Double,
+    ): NDBuffer<Double> = NDBuffer(
+        strides,
+        buffer = RealBuffer(strides.linearSize) { offset ->
+            RealField.transform(
+                strides.index(offset),
+                buffer.array[offset]
+            )
+        })
+
+    @Suppress("OVERRIDE_BY_INLINE")
+    override inline fun combine(
+        a: NDStructure<Double>,
+        b: NDStructure<Double>,
+        transform: RealField.(Double, Double) -> Double,
+    ): NDBuffer<Double> {
+        val buffer = RealBuffer(strides.linearSize) { offset ->
+            RealField.transform(a.buffer.array[offset], b.buffer.array[offset])
+        }
+        return NDBuffer(strides, buffer)
+    }
+
+    override fun power(arg: NDStructure<Double>, pow: Number): NDBuffer<Double> = arg.map { power(it, pow) }
+
+    override fun exp(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { exp(it) }
+
+    override fun ln(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { ln(it) }
+
+    override fun sin(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { sin(it) }
+    override fun cos(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { cos(it) }
+    override fun tan(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { tan(it) }
+    override fun asin(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { asin(it) }
+    override fun acos(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { acos(it) }
+    override fun atan(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { atan(it) }
+
+    override fun sinh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { sinh(it) }
+    override fun cosh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { cosh(it) }
+    override fun tanh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { tanh(it) }
+    override fun asinh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { asinh(it) }
+    override fun acosh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { acosh(it) }
+    override fun atanh(arg: NDStructure<Double>): NDBuffer<Double> = arg.map { atanh(it) }
+}
+
+public fun NDAlgebra.Companion.real(vararg shape: Int): RealNDField = RealNDField(shape)
+
+/**
+ * Produce a context for n-dimensional operations inside this real field
+ */
+public inline fun <R> RealField.nd(vararg shape: Int, action: RealNDField.() -> R): R {
+    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+    return RealNDField(shape).run(action)
+}

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

@@ -0,0 +1,36 @@
+package kscience.kmath.nd
+
+import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.operations.RingWithNumbers
+import kscience.kmath.operations.ShortRing
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.ShortBuffer
+import kotlin.contracts.InvocationKind
+import kotlin.contracts.contract
+
+@OptIn(UnstableKMathAPI::class)
+public class ShortNDRing(
+    shape: IntArray,
+) : BufferedNDRing<Short, ShortRing>(shape, ShortRing, Buffer.Companion::auto),
+    RingWithNumbers<NDStructure<Short>> {
+
+    override val zero: NDBuffer<Short> by lazy { produce { zero } }
+    override val one: NDBuffer<Short> by lazy { produce { one } }
+
+    override fun number(value: Number): NDBuffer<Short> {
+        val d = value.toShort() // minimize conversions
+        return produce { d }
+    }
+}
+
+/**
+ * Fast element production using function inlining.
+ */
+public inline fun BufferedNDRing<Short, ShortRing>.produceInline(crossinline initializer: ShortRing.(Int) -> Short): NDBuffer<Short> {
+    return NDBuffer(strides, ShortBuffer(ShortArray(strides.linearSize) { offset -> ShortRing.initializer(offset) }))
+}
+
+public inline fun <R> ShortRing.nd(vararg shape: Int, action: ShortNDRing.() -> R): R {
+    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+    return ShortNDRing(shape).run(action)
+}

kmath-core/src/commonMain/kotlin/kscience/kmath/nd/Structure1D.kt

@@ -1,4 +1,7 @@
-package kscience.kmath.structures
+package kscience.kmath.nd
+
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.asSequence
 
 /**
  * A structure that is guaranteed to be one-dimensional
@@ -34,7 +37,7 @@ private inline class Buffer1DWrapper<T>(val buffer: Buffer<T>) : Structure1D<T>
     override val size: Int get() = buffer.size
 
     override fun elements(): Sequence<Pair<IntArray, T>> =
-        asSequence().mapIndexed { index, value -> intArrayOf(index) to value }
+        buffer.asSequence().mapIndexed { index, value -> intArrayOf(index) to value }
 
     override operator fun get(index: Int): T = buffer[index]
 }

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

@@ -1,4 +1,9 @@
-package kscience.kmath.structures
+package kscience.kmath.nd
+
+import kscience.kmath.linear.BufferMatrix
+import kscience.kmath.linear.RealMatrixContext
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.VirtualBuffer
 
 /**
  * A structure that is guaranteed to be two-dimensional.
@@ -49,7 +54,15 @@ public interface Structure2D<T> : NDStructure<T> {
             for (j in 0 until colNum) yield(intArrayOf(i, j) to get(i, j))
     }
 
-    public companion object
+    public companion object {
+        public inline fun real(
+            rows: Int,
+            columns: Int,
+            crossinline init: (i: Int, j: Int) -> Double,
+        ): BufferMatrix<Double> = RealMatrixContext.produce(rows,columns) { i, j ->
+            init(i, j)
+        }
+    }
 }
 
 /**

kmath-core/src/commonMain/kotlin/kscience/kmath/operations/BigInt.kt

@@ -1,9 +1,12 @@
 package kscience.kmath.operations
 
 import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.nd.BufferedNDRing
+import kscience.kmath.nd.NDAlgebra
 import kscience.kmath.operations.BigInt.Companion.BASE
 import kscience.kmath.operations.BigInt.Companion.BASE_SIZE
-import kscience.kmath.structures.*
+import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.MutableBuffer
 import kotlin.math.log2
 import kotlin.math.max
 import kotlin.math.min
@@ -462,10 +465,5 @@ public inline fun Buffer.Companion.bigInt(size: Int, initializer: (Int) -> BigIn
 public inline fun MutableBuffer.Companion.bigInt(size: Int, initializer: (Int) -> BigInt): MutableBuffer<BigInt> =
     boxing(size, initializer)
 
-public fun NDAlgebra.Companion.bigInt(vararg shape: Int): BoxingNDRing<BigInt, BigIntField> =
+public fun NDAlgebra.Companion.bigInt(vararg shape: Int): BufferedNDRing<BigInt, BigIntField> =
-    BoxingNDRing(shape, BigIntField, Buffer.Companion::bigInt)
+    BufferedNDRing(shape, BigIntField, Buffer.Companion::bigInt)
-
-public fun NDElement.Companion.bigInt(
-    vararg shape: Int,
-    initializer: BigIntField.(IntArray) -> BigInt
-): BufferedNDRingElement<BigInt, BigIntField> = NDAlgebra.bigInt(*shape).produce(initializer)

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

@@ -1,81 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.Field
-import kscience.kmath.operations.FieldElement
-
-public class BoxingNDField<T, F : Field<T>>(
-    public override val shape: IntArray,
-    public override val elementContext: F,
-    public val bufferFactory: BufferFactory<T>
-) : BufferedNDField<T, F> {
-    public override val zero: BufferedNDFieldElement<T, F> by lazy { produce { zero } }
-    public override val one: BufferedNDFieldElement<T, F> by lazy { produce { one } }
-    public override val strides: Strides = DefaultStrides(shape)
-
-    public fun buildBuffer(size: Int, initializer: (Int) -> T): Buffer<T> =
-        bufferFactory(size, initializer)
-
-    public override fun check(vararg elements: NDBuffer<T>): Array<out NDBuffer<T>> {
-        require(elements.all { it.strides == strides }) { "Element strides are not the same as context strides" }
-        return elements
-    }
-
-    public override fun produce(initializer: F.(IntArray) -> T): BufferedNDFieldElement<T, F> =
-        BufferedNDFieldElement(
-            this,
-            buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) })
-
-    public override fun map(arg: NDBuffer<T>, transform: F.(T) -> T): BufferedNDFieldElement<T, F> {
-        check(arg)
-
-        return BufferedNDFieldElement(
-            this,
-            buildBuffer(arg.strides.linearSize) { offset -> elementContext.transform(arg.buffer[offset]) })
-
-//        val buffer = arg.buffer.transform { _, value -> elementContext.transform(value) }
-//        return BufferedNDFieldElement(this, buffer)
-
-    }
-
-    public override fun mapIndexed(
-        arg: NDBuffer<T>,
-        transform: F.(index: IntArray, T) -> T
-    ): BufferedNDFieldElement<T, F> {
-        check(arg)
-        return BufferedNDFieldElement(
-            this,
-            buildBuffer(arg.strides.linearSize) { offset ->
-                elementContext.transform(
-                    arg.strides.index(offset),
-                    arg.buffer[offset]
-                )
-            })
-
-//        val buffer =
-//            arg.buffer.transform { offset, value -> elementContext.transform(arg.strides.index(offset), value) }
-//        return BufferedNDFieldElement(this, buffer)
-    }
-
-    public override fun combine(
-        a: NDBuffer<T>,
-        b: NDBuffer<T>,
-        transform: F.(T, T) -> T
-    ): BufferedNDFieldElement<T, F> {
-        check(a, b)
-        return BufferedNDFieldElement(
-            this,
-            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
-    }
-
-    public override fun NDBuffer<T>.toElement(): FieldElement<NDBuffer<T>, *, out BufferedNDField<T, F>> =
-        BufferedNDFieldElement(this@BoxingNDField, buffer)
-}
-
-public inline fun <T : Any, F : Field<T>, R> F.nd(
-    noinline bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
-    action: NDField<T, F, *>.() -> R
-): R {
-    val ndfield = NDField.boxing(this, *shape, bufferFactory = bufferFactory)
-    return ndfield.action()
-}

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

@@ -1,71 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.Ring
-import kscience.kmath.operations.RingElement
-
-public class BoxingNDRing<T, R : Ring<T>>(
-    override val shape: IntArray,
-    override val elementContext: R,
-    public val bufferFactory: BufferFactory<T>
-) : BufferedNDRing<T, R> {
-    override val strides: Strides = DefaultStrides(shape)
-    override val zero: BufferedNDRingElement<T, R> by lazy { produce { zero } }
-    override val one: BufferedNDRingElement<T, R> by lazy { produce { one } }
-
-    public fun buildBuffer(size: Int, initializer: (Int) -> T): Buffer<T> = bufferFactory(size, initializer)
-
-    override fun check(vararg elements: NDBuffer<T>): Array<out NDBuffer<T>> {
-        if (!elements.all { it.strides == this.strides }) error("Element strides are not the same as context strides")
-        return elements
-    }
-
-    override fun produce(initializer: R.(IntArray) -> T): BufferedNDRingElement<T, R> =
-        BufferedNDRingElement(
-            this,
-            buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) })
-
-    override fun map(arg: NDBuffer<T>, transform: R.(T) -> T): BufferedNDRingElement<T, R> {
-        check(arg)
-        return BufferedNDRingElement(
-            this,
-            buildBuffer(arg.strides.linearSize) { offset -> elementContext.transform(arg.buffer[offset]) })
-
-//        val buffer = arg.buffer.transform { _, value -> elementContext.transform(value) }
-//        return BufferedNDFieldElement(this, buffer)
-
-    }
-
-    override fun mapIndexed(
-        arg: NDBuffer<T>,
-        transform: R.(index: IntArray, T) -> T
-    ): BufferedNDRingElement<T, R> {
-        check(arg)
-        return BufferedNDRingElement(
-            this,
-            buildBuffer(arg.strides.linearSize) { offset ->
-                elementContext.transform(
-                    arg.strides.index(offset),
-                    arg.buffer[offset]
-                )
-            })
-
-//        val buffer =
-//            arg.buffer.transform { offset, value -> elementContext.transform(arg.strides.index(offset), value) }
-//        return BufferedNDFieldElement(this, buffer)
-    }
-
-    override fun combine(
-        a: NDBuffer<T>,
-        b: NDBuffer<T>,
-        transform: R.(T, T) -> T
-    ): BufferedNDRingElement<T, R> {
-        check(a, b)
-
-        return BufferedNDRingElement(
-            this,
-            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
-    }
-
-    override fun NDBuffer<T>.toElement(): RingElement<NDBuffer<T>, *, out BufferedNDRing<T, R>> =
-        BufferedNDRingElement(this@BoxingNDRing, buffer)
-}

kmath-core/src/commonMain/kotlin/kscience/kmath/structures/BufferAccessor2D.kt

@@ -1,5 +1,10 @@
 package kscience.kmath.structures
 
+import kscience.kmath.nd.DefaultStrides
+import kscience.kmath.nd.NDStructure
+import kscience.kmath.nd.Structure2D
+import kscience.kmath.nd.as2D
+
 /**
  * A context that allows to operate on a [MutableBuffer] as on 2d array
  */

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

@@ -1,43 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.*
-
-public interface BufferedNDAlgebra<T, C> : NDAlgebra<T, C, NDBuffer<T>> {
-    public val strides: Strides
-
-    public override fun check(vararg elements: NDBuffer<T>): Array<out NDBuffer<T>> {
-        require(elements.all { it.strides == strides }) { "Strides mismatch" }
-        return elements
-    }
-
-    /**
-     * Convert any [NDStructure] to buffered structure using strides from this context.
-     * If the structure is already [NDBuffer], conversion is free. If not, it could be expensive because iteration over
-     * indices.
-     *
-     * If the argument is [NDBuffer] with different strides structure, the new element will be produced.
-     */
-    public fun NDStructure<T>.toBuffer(): NDBuffer<T> =
-        if (this is NDBuffer<T> && this.strides == this@BufferedNDAlgebra.strides)
-            this
-        else
-            produce { index -> this@toBuffer[index] }
-
-    /**
-     * Convert a buffer to element of this algebra
-     */
-    public fun NDBuffer<T>.toElement(): MathElement<out BufferedNDAlgebra<T, C>>
-}
-
-
-public interface BufferedNDSpace<T, S : Space<T>> : NDSpace<T, S, NDBuffer<T>>, BufferedNDAlgebra<T, S> {
-    public override fun NDBuffer<T>.toElement(): SpaceElement<NDBuffer<T>, *, out BufferedNDSpace<T, S>>
-}
-
-public interface BufferedNDRing<T, R : Ring<T>> : NDRing<T, R, NDBuffer<T>>, BufferedNDSpace<T, R> {
-    override fun NDBuffer<T>.toElement(): RingElement<NDBuffer<T>, *, out BufferedNDRing<T, R>>
-}
-
-public interface BufferedNDField<T, F : Field<T>> : NDField<T, F, NDBuffer<T>>, BufferedNDRing<T, F> {
-    override fun NDBuffer<T>.toElement(): FieldElement<NDBuffer<T>, *, out BufferedNDField<T, F>>
-}

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

@@ -1,86 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.*
-
-/**
- * Base class for an element with context, containing strides
- */
-public abstract class BufferedNDElement<T, C> : NDBuffer<T>(), NDElement<T, C, NDBuffer<T>> {
-    abstract override val context: BufferedNDAlgebra<T, C>
-
-    override val strides: Strides get() = context.strides
-
-    override val shape: IntArray get() = context.shape
-}
-
-public class BufferedNDSpaceElement<T, S : Space<T>>(
-    override val context: BufferedNDSpace<T, S>,
-    override val buffer: Buffer<T>
-) : BufferedNDElement<T, S>(), SpaceElement<NDBuffer<T>, BufferedNDSpaceElement<T, S>, BufferedNDSpace<T, S>> {
-
-    override fun unwrap(): NDBuffer<T> = this
-
-    override fun NDBuffer<T>.wrap(): BufferedNDSpaceElement<T, S> {
-        context.check(this)
-        return BufferedNDSpaceElement(context, buffer)
-    }
-}
-
-public class BufferedNDRingElement<T, R : Ring<T>>(
-    override val context: BufferedNDRing<T, R>,
-    override val buffer: Buffer<T>
-) : BufferedNDElement<T, R>(), RingElement<NDBuffer<T>, BufferedNDRingElement<T, R>, BufferedNDRing<T, R>> {
-    override fun unwrap(): NDBuffer<T> = this
-
-    override fun NDBuffer<T>.wrap(): BufferedNDRingElement<T, R> {
-        context.check(this)
-        return BufferedNDRingElement(context, buffer)
-    }
-}
-
-public class BufferedNDFieldElement<T, F : Field<T>>(
-    override val context: BufferedNDField<T, F>,
-    override val buffer: Buffer<T>
-) : BufferedNDElement<T, F>(), FieldElement<NDBuffer<T>, BufferedNDFieldElement<T, F>, BufferedNDField<T, F>> {
-    override fun unwrap(): NDBuffer<T> = this
-
-    override fun NDBuffer<T>.wrap(): BufferedNDFieldElement<T, F> {
-        context.check(this)
-        return BufferedNDFieldElement(context, buffer)
-    }
-}
-
-
-/**
- * Element by element application of any operation on elements to the whole array. Just like in numpy.
- */
-public operator fun <T : Any, F : Field<T>> Function1<T, T>.invoke(ndElement: BufferedNDElement<T, F>): MathElement<out BufferedNDAlgebra<T, F>> =
-    ndElement.context.run { map(ndElement) { invoke(it) }.toElement() }
-
-/* plus and minus */
-
-/**
- * Summation operation for [BufferedNDElement] and single element
- */
-public operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.plus(arg: T): NDElement<T, F, NDBuffer<T>> =
-    context.map(this) { it + arg }.wrap()
-
-/**
- * Subtraction operation between [BufferedNDElement] and single element
- */
-public operator fun <T : Any, F : Space<T>> BufferedNDElement<T, F>.minus(arg: T): NDElement<T, F, NDBuffer<T>> =
-    context.map(this) { it - arg }.wrap()
-
-/* prod and div */
-
-/**
- * Product operation for [BufferedNDElement] and single element
- */
-public operator fun <T : Any, F : Ring<T>> BufferedNDElement<T, F>.times(arg: T): NDElement<T, F, NDBuffer<T>> =
-    context.map(this) { it * arg }.wrap()
-
-/**
- * Division operation between [BufferedNDElement] and single element
- */
-public operator fun <T : Any, F : Field<T>> BufferedNDElement<T, F>.div(arg: T): NDElement<T, F, NDBuffer<T>> =
-    context.map(this) { it / arg }.wrap()

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

@@ -1,158 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.misc.UnstableKMathAPI
-import kscience.kmath.operations.*
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-
-public typealias ComplexNDElement = BufferedNDFieldElement<Complex, ComplexField>
-
-/**
- * An optimized nd-field for complex numbers
- */
-@OptIn(UnstableKMathAPI::class)
-public class ComplexNDField(override val shape: IntArray) :
-    BufferedNDField<Complex, ComplexField>,
-    ExtendedNDField<Complex, ComplexField, NDBuffer<Complex>>,
-    RingWithNumbers<NDBuffer<Complex>>{
-
-    override val strides: Strides = DefaultStrides(shape)
-    override val elementContext: ComplexField get() = ComplexField
-    override val zero: ComplexNDElement by lazy { produce { zero } }
-    override val one: ComplexNDElement by lazy { produce { one } }
-
-    override fun number(value: Number): NDBuffer<Complex> {
-        val c = value.toComplex()
-        return produce { c }
-    }
-
-    public inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Complex): Buffer<Complex> =
-        Buffer.complex(size) { initializer(it) }
-
-    /**
-     * Inline transform an NDStructure to another structure
-     */
-    override fun map(
-        arg: NDBuffer<Complex>,
-        transform: ComplexField.(Complex) -> Complex,
-    ): ComplexNDElement {
-        check(arg)
-        val array = buildBuffer(arg.strides.linearSize) { offset -> ComplexField.transform(arg.buffer[offset]) }
-        return BufferedNDFieldElement(this, array)
-    }
-
-    override fun produce(initializer: ComplexField.(IntArray) -> Complex): ComplexNDElement {
-        val array = buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
-        return BufferedNDFieldElement(this, array)
-    }
-
-    override fun mapIndexed(
-        arg: NDBuffer<Complex>,
-        transform: ComplexField.(index: IntArray, Complex) -> Complex,
-    ): ComplexNDElement {
-        check(arg)
-
-        return BufferedNDFieldElement(
-            this,
-            buildBuffer(arg.strides.linearSize) { offset ->
-                elementContext.transform(
-                    arg.strides.index(offset),
-                    arg.buffer[offset]
-                )
-            })
-    }
-
-    override fun combine(
-        a: NDBuffer<Complex>,
-        b: NDBuffer<Complex>,
-        transform: ComplexField.(Complex, Complex) -> Complex,
-    ): ComplexNDElement {
-        check(a, b)
-
-        return BufferedNDFieldElement(
-            this,
-            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
-    }
-
-    override fun NDBuffer<Complex>.toElement(): FieldElement<NDBuffer<Complex>, *, out BufferedNDField<Complex, ComplexField>> =
-        BufferedNDFieldElement(this@ComplexNDField, buffer)
-
-    override fun power(arg: NDBuffer<Complex>, pow: Number): ComplexNDElement =
-        map(arg) { power(it, pow) }
-
-    override fun exp(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { exp(it) }
-    override fun ln(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { ln(it) }
-
-    override fun sin(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { sin(it) }
-    override fun cos(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { cos(it) }
-    override fun tan(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { tan(it) }
-    override fun asin(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { asin(it) }
-    override fun acos(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { acos(it) }
-    override fun atan(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { atan(it) }
-
-    override fun sinh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { sinh(it) }
-    override fun cosh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { cosh(it) }
-    override fun tanh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { tanh(it) }
-    override fun asinh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { asinh(it) }
-    override fun acosh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { acosh(it) }
-    override fun atanh(arg: NDBuffer<Complex>): ComplexNDElement = map(arg) { atanh(it) }
-}
-
-
-/**
- * Fast element production using function inlining
- */
-public inline fun BufferedNDField<Complex, ComplexField>.produceInline(initializer: ComplexField.(Int) -> Complex): ComplexNDElement {
-    val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.initializer(offset) }
-    return BufferedNDFieldElement(this, buffer)
-}
-
-/**
- * Map one [ComplexNDElement] using function with indices.
- */
-public inline fun ComplexNDElement.mapIndexed(transform: ComplexField.(index: IntArray, Complex) -> Complex): ComplexNDElement =
-    context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
-
-/**
- * Map one [ComplexNDElement] using function without indices.
- */
-public inline fun ComplexNDElement.map(transform: ComplexField.(Complex) -> Complex): ComplexNDElement {
-    val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.transform(buffer[offset]) }
-    return BufferedNDFieldElement(context, buffer)
-}
-
-/**
- * Element by element application of any operation on elements to the whole array. Just like in numpy
- */
-public operator fun Function1<Complex, Complex>.invoke(ndElement: ComplexNDElement): ComplexNDElement =
-    ndElement.map { this@invoke(it) }
-
-/* plus and minus */
-
-/**
- * Summation operation for [BufferedNDElement] and single element
- */
-public operator fun ComplexNDElement.plus(arg: Complex): ComplexNDElement = map { it + arg }
-
-/**
- * Subtraction operation between [BufferedNDElement] and single element
- */
-public operator fun ComplexNDElement.minus(arg: Complex): ComplexNDElement = map { it - arg }
-
-public operator fun ComplexNDElement.plus(arg: Double): ComplexNDElement = map { it + arg }
-public operator fun ComplexNDElement.minus(arg: Double): ComplexNDElement = map { it - arg }
-
-public fun NDField.Companion.complex(vararg shape: Int): ComplexNDField = ComplexNDField(shape)
-
-public fun NDElement.Companion.complex(
-    vararg shape: Int,
-    initializer: ComplexField.(IntArray) -> Complex,
-): ComplexNDElement = NDField.complex(*shape).produce(initializer)
-
-/**
- * Produce a context for n-dimensional operations inside this real field
- */
-public inline fun <R> ComplexField.nd(vararg shape: Int, action: ComplexNDField.() -> R): R {
-    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
-    return NDField.complex(*shape).action()
-}

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

@@ -1,44 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.ExtendedField
-
-/**
- * [ExtendedField] over [NDStructure].
- *
- * @param T the type of the element contained in ND structure.
- * @param N the type of ND structure.
- * @param F the extended field of structure elements.
- */
-public interface ExtendedNDField<T : Any, F : ExtendedField<T>, N : NDStructure<T>> : NDField<T, F, N>, ExtendedField<N>
-
-///**
-// * NDField that supports [ExtendedField] operations on its elements
-// */
-//class ExtendedNDFieldWrapper<T : Any, F : ExtendedField<T>, N : NDStructure<T>>(private val ndField: NDField<T, F, N>) :
-//    ExtendedNDField<T, F, N>, NDField<T, F, N> by ndField {
-//
-//    override val shape: IntArray get() = ndField.shape
-//    override val elementContext: F get() = ndField.elementContext
-//
-//    override fun produce(initializer: F.(IntArray) -> T) = ndField.produce(initializer)
-//
-//    override fun power(arg: N, pow: Double): N {
-//        return produce { with(elementContext) { power(arg[it], pow) } }
-//    }
-//
-//    override fun exp(arg: N): N {
-//        return produce { with(elementContext) { exp(arg[it]) } }
-//    }
-//
-//    override fun ln(arg: N): N {
-//        return produce { with(elementContext) { ln(arg[it]) } }
-//    }
-//
-//    override fun sin(arg: N): N {
-//        return produce { with(elementContext) { sin(arg[it]) } }
-//    }
-//
-//    override fun cos(arg: N): N {
-//        return produce { with(elementContext) { cos(arg[it]) } }
-//    }
-//}

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

@@ -1,259 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.Complex
-import kscience.kmath.operations.Field
-import kscience.kmath.operations.Ring
-import kscience.kmath.operations.Space
-import kotlin.native.concurrent.ThreadLocal
-
-/**
- * An exception is thrown when the expected ans actual shape of NDArray differs.
- *
- * @property expected the expected shape.
- * @property actual the actual shape.
- */
-public class ShapeMismatchException(public val expected: IntArray, public val actual: IntArray) :
-    RuntimeException("Shape ${actual.contentToString()} doesn't fit in expected shape ${expected.contentToString()}.")
-
-/**
- * The base interface for all ND-algebra implementations.
- *
- * @param T the type of ND-structure element.
- * @param C the type of the element context.
- * @param N the type of the structure.
- */
-public interface NDAlgebra<T, C, N : NDStructure<T>> {
-    /**
-     * The shape of ND-structures this algebra operates on.
-     */
-    public val shape: IntArray
-
-    /**
-     * The algebra over elements of ND structure.
-     */
-    public val elementContext: C
-
-    /**
-     * Produces a new [N] structure using given initializer function.
-     */
-    public fun produce(initializer: C.(IntArray) -> T): N
-
-    /**
-     * Maps elements from one structure to another one by applying [transform] to them.
-     */
-    public fun map(arg: N, transform: C.(T) -> T): N
-
-    /**
-     * Maps elements from one structure to another one by applying [transform] to them alongside with their indices.
-     */
-    public fun mapIndexed(arg: N, transform: C.(index: IntArray, T) -> T): N
-
-    /**
-     * Combines two structures into one.
-     */
-    public fun combine(a: N, b: N, transform: C.(T, T) -> T): N
-
-    /**
-     * Checks if given element is consistent with this context.
-     *
-     * @param element the structure to check.
-     * @return the valid structure.
-     */
-    public fun check(element: N): N {
-        if (!element.shape.contentEquals(shape)) throw ShapeMismatchException(shape, element.shape)
-        return element
-    }
-
-    /**
-     * Checks if given elements are consistent with this context.
-     *
-     * @param elements the structures to check.
-     * @return the array of valid structures.
-     */
-    public fun check(vararg elements: N): Array<out N> = elements
-        .map(NDStructure<T>::shape)
-        .singleOrNull { !shape.contentEquals(it) }
-        ?.let<IntArray, Array<out N>> { throw ShapeMismatchException(shape, it) }
-        ?: elements
-
-    /**
-     * Element-wise invocation of function working on [T] on a [NDStructure].
-     */
-    public operator fun Function1<T, T>.invoke(structure: N): N = map(structure) { value -> this@invoke(value) }
-
-    public companion object
-}
-
-/**
- * Space of [NDStructure].
- *
- * @param T the type of the element contained in ND structure.
- * @param N the type of ND structure.
- * @param S the type of space of structure elements.
- */
-public interface NDSpace<T, S : Space<T>, N : NDStructure<T>> : Space<N>, NDAlgebra<T, S, N> {
-    /**
-     * Element-wise addition.
-     *
-     * @param a the addend.
-     * @param b the augend.
-     * @return the sum.
-     */
-    public override fun add(a: N, b: N): N = combine(a, b) { aValue, bValue -> add(aValue, bValue) }
-
-    /**
-     * Element-wise multiplication by scalar.
-     *
-     * @param a the multiplicand.
-     * @param k the multiplier.
-     * @return the product.
-     */
-    public override fun multiply(a: N, k: Number): N = map(a) { multiply(it, k) }
-
-    // TODO move to extensions after KEEP-176
-
-    /**
-     * Adds an ND structure to an element of it.
-     *
-     * @receiver the addend.
-     * @param arg the augend.
-     * @return the sum.
-     */
-    public operator fun N.plus(arg: T): N = map(this) { value -> add(arg, value) }
-
-    /**
-     * Subtracts an element from ND structure of it.
-     *
-     * @receiver the dividend.
-     * @param arg the divisor.
-     * @return the quotient.
-     */
-    public operator fun N.minus(arg: T): N = map(this) { value -> add(arg, -value) }
-
-    /**
-     * Adds an element to ND structure of it.
-     *
-     * @receiver the addend.
-     * @param arg the augend.
-     * @return the sum.
-     */
-    public operator fun T.plus(arg: N): N = map(arg) { value -> add(this@plus, value) }
-
-    /**
-     * Subtracts an ND structure from an element of it.
-     *
-     * @receiver the dividend.
-     * @param arg the divisor.
-     * @return the quotient.
-     */
-    public operator fun T.minus(arg: N): N = map(arg) { value -> add(-this@minus, value) }
-
-    public companion object
-}
-
-/**
- * Ring of [NDStructure].
- *
- * @param T the type of the element contained in ND structure.
- * @param N the type of ND structure.
- * @param R the type of ring of structure elements.
- */
-public interface NDRing<T, R : Ring<T>, N : NDStructure<T>> : Ring<N>, NDSpace<T, R, N> {
-    /**
-     * Element-wise multiplication.
-     *
-     * @param a the multiplicand.
-     * @param b the multiplier.
-     * @return the product.
-     */
-    public override fun multiply(a: N, b: N): N = combine(a, b) { aValue, bValue -> multiply(aValue, bValue) }
-
-    //TODO move to extensions after KEEP-176
-
-    /**
-     * Multiplies an ND structure by an element of it.
-     *
-     * @receiver the multiplicand.
-     * @param arg the multiplier.
-     * @return the product.
-     */
-    public operator fun N.times(arg: T): N = map(this) { value -> multiply(arg, value) }
-
-    /**
-     * Multiplies an element by a ND structure of it.
-     *
-     * @receiver the multiplicand.
-     * @param arg the multiplier.
-     * @return the product.
-     */
-    public operator fun T.times(arg: N): N = map(arg) { value -> multiply(this@times, value) }
-
-    public companion object
-}
-
-/**
- * Field of [NDStructure].
- *
- * @param T the type of the element contained in ND structure.
- * @param N the type of ND structure.
- * @param F the type field of structure elements.
- */
-public interface NDField<T, F : Field<T>, N : NDStructure<T>> : Field<N>, NDRing<T, F, N> {
-    /**
-     * Element-wise division.
-     *
-     * @param a the dividend.
-     * @param b the divisor.
-     * @return the quotient.
-     */
-    public override fun divide(a: N, b: N): N = combine(a, b) { aValue, bValue -> divide(aValue, bValue) }
-
-    //TODO move to extensions after KEEP-176
-    /**
-     * Divides an ND structure by an element of it.
-     *
-     * @receiver the dividend.
-     * @param arg the divisor.
-     * @return the quotient.
-     */
-    public operator fun N.div(arg: T): N = map(this) { value -> divide(arg, value) }
-
-    /**
-     * Divides an element by an ND structure of it.
-     *
-     * @receiver the dividend.
-     * @param arg the divisor.
-     * @return the quotient.
-     */
-    public operator fun T.div(arg: N): N = map(arg) { divide(it, this@div) }
-
-    @ThreadLocal
-    public companion object {
-        private val realNDFieldCache: MutableMap<IntArray, RealNDField> = hashMapOf()
-
-        /**
-         * Create a nd-field for [Double] values or pull it from cache if it was created previously.
-         */
-        public fun real(vararg shape: Int): RealNDField = realNDFieldCache.getOrPut(shape) { RealNDField(shape) }
-
-        /**
-         * Create an ND field with boxing generic buffer.
-         */
-        public fun <T : Any, F : Field<T>> boxing(
-            field: F,
-            vararg shape: Int,
-            bufferFactory: BufferFactory<T> = Buffer.Companion::boxing
-        ): BoxingNDField<T, F> = BoxingNDField(shape, field, bufferFactory)
-
-        /**
-         * Create a most suitable implementation for nd-field using reified class.
-         */
-        @Suppress("UNCHECKED_CAST")
-        public inline fun <reified T : Any, F : Field<T>> auto(field: F, vararg shape: Int): BufferedNDField<T, F> =
-            when {
-                T::class == Double::class -> real(*shape) as BufferedNDField<T, F>
-                T::class == Complex::class -> complex(*shape) as BufferedNDField<T, F>
-                else -> BoxingNDField(shape, field, Buffer.Companion::auto)
-            }
-    }
-}

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

@@ -1,134 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.Field
-import kscience.kmath.operations.RealField
-import kscience.kmath.operations.Ring
-import kscience.kmath.operations.Space
-
-/**
- * The root for all [NDStructure] based algebra elements. Does not implement algebra element root because of problems with recursive self-types
- * @param T  the type of the element of the structure
- * @param C the type of the context for the element
- * @param N the type of the underlying [NDStructure]
- */
-public interface NDElement<T, C, N : NDStructure<T>> : NDStructure<T> {
-    public val context: NDAlgebra<T, C, N>
-
-    public fun unwrap(): N
-
-    public fun N.wrap(): NDElement<T, C, N>
-
-    public companion object {
-        /**
-         * Create a optimized NDArray of doubles
-         */
-        public fun real(shape: IntArray, initializer: RealField.(IntArray) -> Double = { 0.0 }): RealNDElement =
-            NDField.real(*shape).produce(initializer)
-
-        public inline fun real1D(dim: Int, crossinline initializer: (Int) -> Double = { _ -> 0.0 }): RealNDElement =
-            real(intArrayOf(dim)) { initializer(it[0]) }
-
-        public inline fun real2D(
-            dim1: Int,
-            dim2: Int,
-            crossinline initializer: (Int, Int) -> Double = { _, _ -> 0.0 }
-        ): RealNDElement = real(intArrayOf(dim1, dim2)) { initializer(it[0], it[1]) }
-
-        public inline fun real3D(
-            dim1: Int,
-            dim2: Int,
-            dim3: Int,
-            crossinline initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }
-        ): RealNDElement = real(intArrayOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
-
-
-        /**
-         * Simple boxing NDArray
-         */
-        public fun <T : Any, F : Field<T>> boxing(
-            shape: IntArray,
-            field: F,
-            initializer: F.(IntArray) -> T
-        ): BufferedNDElement<T, F> {
-            val ndField = BoxingNDField(shape, field, Buffer.Companion::boxing)
-            return ndField.produce(initializer)
-        }
-
-        public inline fun <reified T : Any, F : Field<T>> auto(
-            shape: IntArray,
-            field: F,
-            noinline initializer: F.(IntArray) -> T
-        ): BufferedNDFieldElement<T, F> {
-            val ndField = NDField.auto(field, *shape)
-            return BufferedNDFieldElement(ndField, ndField.produce(initializer).buffer)
-        }
-    }
-}
-
-public fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.mapIndexed(transform: C.(index: IntArray, T) -> T): NDElement<T, C, N> =
-    context.mapIndexed(unwrap(), transform).wrap()
-
-public fun <T, C, N : NDStructure<T>> NDElement<T, C, N>.map(transform: C.(T) -> T): NDElement<T, C, N> =
-    context.map(unwrap(), transform).wrap()
-
-/**
- * Element by element application of any operation on elements to the whole [NDElement]
- */
-public operator fun <T, C, N : NDStructure<T>> Function1<T, T>.invoke(ndElement: NDElement<T, C, N>): NDElement<T, C, N> =
-    ndElement.map { value -> this@invoke(value) }
-
-/* plus and minus */
-
-/**
- * Summation operation for [NDElement] and single element
- */
-public operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.plus(arg: T): NDElement<T, S, N> =
-    map { value -> arg + value }
-
-/**
- * Subtraction operation between [NDElement] and single element
- */
-public operator fun <T, S : Space<T>, N : NDStructure<T>> NDElement<T, S, N>.minus(arg: T): NDElement<T, S, N> =
-    map { value -> arg - value }
-
-/* prod and div */
-
-/**
- * Product operation for [NDElement] and single element
- */
-public operator fun <T, R : Ring<T>, N : NDStructure<T>> NDElement<T, R, N>.times(arg: T): NDElement<T, R, N> =
-    map { value -> arg * value }
-
-/**
- * Division operation between [NDElement] and single element
- */
-public operator fun <T, F : Field<T>, N : NDStructure<T>> NDElement<T, F, N>.div(arg: T): NDElement<T, F, N> =
-    map { value -> arg / value }
-
-//    /**
-//     * Reverse sum operation
-//     */
-//    operator fun T.plus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@plus + arg[index] }
-//    }
-//
-//    /**
-//     * Reverse minus operation
-//     */
-//    operator fun T.minus(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@minus - arg[index] }
-//    }
-//
-//    /**
-//     * Reverse product operation
-//     */
-//    operator fun T.times(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@times * arg[index] }
-//    }
-//
-//    /**
-//     * Reverse division operation
-//     */
-//    operator fun T.div(arg: NDStructure<T>): NDElement<T, F> = produce { index ->
-//        field.run { this@div / arg[index] }
-//    }

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

@@ -1,140 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.misc.UnstableKMathAPI
-import kscience.kmath.operations.FieldElement
-import kscience.kmath.operations.RealField
-import kscience.kmath.operations.RingWithNumbers
-
-public typealias RealNDElement = BufferedNDFieldElement<Double, RealField>
-
-@OptIn(UnstableKMathAPI::class)
-public class RealNDField(override val shape: IntArray) :
-    BufferedNDField<Double, RealField>,
-    ExtendedNDField<Double, RealField, NDBuffer<Double>>,
-    RingWithNumbers<NDBuffer<Double>> {
-
-    override val strides: Strides = DefaultStrides(shape)
-
-    override val elementContext: RealField get() = RealField
-    override val zero: RealNDElement by lazy { produce { zero } }
-    override val one: RealNDElement by lazy { produce { one } }
-
-    override fun number(value: Number): NDBuffer<Double> {
-        val d = value.toDouble()
-        return produce { d }
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun map(
-        arg: NDBuffer<Double>,
-        transform: RealField.(Double) -> Double,
-    ): RealNDElement {
-        check(arg)
-        val array = RealBuffer(arg.strides.linearSize) { offset -> RealField.transform(arg.buffer[offset]) }
-        return BufferedNDFieldElement(this, array)
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun produce(initializer: RealField.(IntArray) -> Double): RealNDElement {
-        val array = RealBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
-        return BufferedNDFieldElement(this, array)
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun mapIndexed(
-        arg: NDBuffer<Double>,
-        transform: RealField.(index: IntArray, Double) -> Double,
-    ): RealNDElement {
-        check(arg)
-        return BufferedNDFieldElement(
-            this,
-            RealBuffer(arg.strides.linearSize) { offset ->
-                elementContext.transform(
-                    arg.strides.index(offset),
-                    arg.buffer[offset]
-                )
-            })
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun combine(
-        a: NDBuffer<Double>,
-        b: NDBuffer<Double>,
-        transform: RealField.(Double, Double) -> Double,
-    ): RealNDElement {
-        check(a, b)
-        val buffer = RealBuffer(strides.linearSize) { offset ->
-            elementContext.transform(a.buffer[offset], b.buffer[offset])
-        }
-        return BufferedNDFieldElement(this, buffer)
-    }
-
-    override fun NDBuffer<Double>.toElement(): FieldElement<NDBuffer<Double>, *, out BufferedNDField<Double, RealField>> =
-        BufferedNDFieldElement(this@RealNDField, buffer)
-
-    override fun power(arg: NDBuffer<Double>, pow: Number): RealNDElement = map(arg) { power(it, pow) }
-
-    override fun exp(arg: NDBuffer<Double>): RealNDElement = map(arg) { exp(it) }
-
-    override fun ln(arg: NDBuffer<Double>): RealNDElement = map(arg) { ln(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 sinh(arg: NDBuffer<Double>): RealNDElement = map(arg) { sinh(it) }
-    override fun cosh(arg: NDBuffer<Double>): RealNDElement = map(arg) { cosh(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 acosh(arg: NDBuffer<Double>): RealNDElement = map(arg) { acosh(it) }
-    override fun atanh(arg: NDBuffer<Double>): RealNDElement = map(arg) { atanh(it) }
-}
-
-
-/**
- * Fast element production using function inlining
- */
-public inline fun BufferedNDField<Double, RealField>.produceInline(crossinline initializer: RealField.(Int) -> Double): RealNDElement {
-    val array = DoubleArray(strides.linearSize) { offset -> RealField.initializer(offset) }
-    return BufferedNDFieldElement(this, RealBuffer(array))
-}
-
-/**
- * Map one [RealNDElement] using function with indices.
- */
-public inline fun RealNDElement.mapIndexed(crossinline transform: RealField.(index: IntArray, Double) -> Double): RealNDElement =
-    context.produceInline { offset -> transform(strides.index(offset), buffer[offset]) }
-
-/**
- * Map one [RealNDElement] using function without indices.
- */
-public inline fun RealNDElement.map(crossinline transform: RealField.(Double) -> Double): RealNDElement {
-    val array = DoubleArray(strides.linearSize) { offset -> RealField.transform(buffer[offset]) }
-    return BufferedNDFieldElement(context, RealBuffer(array))
-}
-
-/**
- * Element by element application of any operation on elements to the whole array. Just like in numpy.
- */
-public operator fun Function1<Double, Double>.invoke(ndElement: RealNDElement): RealNDElement =
-    ndElement.map { this@invoke(it) }
-
-/* plus and minus */
-
-/**
- * Summation operation for [BufferedNDElement] and single element
- */
-public operator fun RealNDElement.plus(arg: Double): RealNDElement = map { it + arg }
-
-/**
- * Subtraction operation between [BufferedNDElement] and single element
- */
-public operator fun RealNDElement.minus(arg: Double): RealNDElement = map { it - arg }
-
-/**
- * Produce a context for n-dimensional operations inside this real field
- */
-public inline fun <R> RealField.nd(vararg shape: Int, action: RealNDField.() -> R): R = NDField.real(*shape).run(action)

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

@@ -1,93 +0,0 @@
-package kscience.kmath.structures
-
-import kscience.kmath.operations.RingElement
-import kscience.kmath.operations.ShortRing
-
-public typealias ShortNDElement = BufferedNDRingElement<Short, ShortRing>
-
-public class ShortNDRing(override val shape: IntArray) :
-    BufferedNDRing<Short, ShortRing> {
-
-    override val strides: Strides = DefaultStrides(shape)
-    override val elementContext: ShortRing get() = ShortRing
-    override val zero: ShortNDElement by lazy { produce { zero } }
-    override val one: ShortNDElement by lazy { produce { one } }
-
-    public inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Short): Buffer<Short> =
-        ShortBuffer(ShortArray(size) { initializer(it) })
-
-    /**
-     * Inline transform an NDStructure to
-     */
-    override fun map(
-        arg: NDBuffer<Short>,
-        transform: ShortRing.(Short) -> Short
-    ): ShortNDElement {
-        check(arg)
-        val array = buildBuffer(arg.strides.linearSize) { offset -> ShortRing.transform(arg.buffer[offset]) }
-        return BufferedNDRingElement(this, array)
-    }
-
-    override fun produce(initializer: ShortRing.(IntArray) -> Short): ShortNDElement {
-        val array = buildBuffer(strides.linearSize) { offset -> elementContext.initializer(strides.index(offset)) }
-        return BufferedNDRingElement(this, array)
-    }
-
-    override fun mapIndexed(
-        arg: NDBuffer<Short>,
-        transform: ShortRing.(index: IntArray, Short) -> Short
-    ): ShortNDElement {
-        check(arg)
-
-        return BufferedNDRingElement(
-            this,
-            buildBuffer(arg.strides.linearSize) { offset ->
-                elementContext.transform(
-                    arg.strides.index(offset),
-                    arg.buffer[offset]
-                )
-            })
-    }
-
-    override fun combine(
-        a: NDBuffer<Short>,
-        b: NDBuffer<Short>,
-        transform: ShortRing.(Short, Short) -> Short
-    ): ShortNDElement {
-        check(a, b)
-        return BufferedNDRingElement(
-            this,
-            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
-    }
-
-    override fun NDBuffer<Short>.toElement(): RingElement<NDBuffer<Short>, *, out BufferedNDRing<Short, ShortRing>> =
-        BufferedNDRingElement(this@ShortNDRing, buffer)
-}
-
-
-/**
- * Fast element production using function inlining.
- */
-public inline fun BufferedNDRing<Short, ShortRing>.produceInline(crossinline initializer: ShortRing.(Int) -> Short): ShortNDElement =
-    BufferedNDRingElement(this, ShortBuffer(ShortArray(strides.linearSize) { offset -> ShortRing.initializer(offset) }))
-
-/**
- * Element by element application of any operation on elements to the whole array.
- */
-public operator fun Function1<Short, Short>.invoke(ndElement: ShortNDElement): ShortNDElement =
-    ndElement.context.produceInline { i -> invoke(ndElement.buffer[i]) }
-
-
-/* plus and minus */
-
-/**
- * Summation operation for [ShortNDElement] and single element.
- */
-public operator fun ShortNDElement.plus(arg: Short): ShortNDElement =
-    context.produceInline { i -> (buffer[i] + arg).toShort() }
-
-/**
- * Subtraction operation between [ShortNDElement] and single element.
- */
-public operator fun ShortNDElement.minus(arg: Short): ShortNDElement =
-    context.produceInline { i -> (buffer[i] - arg).toShort() }

kmath-core/src/commonTest/kotlin/kscience/kmath/linear/MatrixTest.kt

@@ -1,9 +1,8 @@
 package kscience.kmath.linear
 
+import kscience.kmath.nd.NDStructure
+import kscience.kmath.nd.as2D
 import kscience.kmath.operations.invoke
-import kscience.kmath.structures.Matrix
-import kscience.kmath.structures.NDStructure
-import kscience.kmath.structures.as2D
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-core/src/commonTest/kotlin/kscience/kmath/linear/RealLUSolverTest.kt

@@ -1,6 +1,5 @@
 package kscience.kmath.linear
 
-import kscience.kmath.structures.Matrix
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
@@ -9,7 +8,7 @@ class RealLUSolverTest {
     @Test
     fun testInvertOne() {
         val matrix = MatrixContext.real.one(2, 2)
-        val inverted = MatrixContext.real.inverseWithLUP(matrix)
+        val inverted = MatrixContext.real.inverseWithLup(matrix)
         assertEquals(matrix, inverted)
     }
 
@@ -37,7 +36,7 @@ class RealLUSolverTest {
             1.0, 3.0
         )
 
-        val inverted = MatrixContext.real.inverseWithLUP(matrix)
+        val inverted = MatrixContext.real.inverseWithLup(matrix)
 
         val expected = Matrix.square(
             0.375, -0.125,

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

@@ -1,5 +1,8 @@
 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 kotlin.test.Test
 import kotlin.test.assertEquals
@@ -7,12 +10,12 @@ import kotlin.test.assertEquals
 internal class NDFieldTest {
     @Test
     fun verify() {
-        NDField.real(12, 32).run { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
+        NDAlgebra.real(12, 32).run { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
     }
 
     @Test
     fun testStrides() {
-        val ndArray = NDElement.real(intArrayOf(10, 10)) { (it[0] + it[1]).toDouble() }
+        val ndArray = NDAlgebra.real(10, 10).produce { (it[0] + it[1]).toDouble() }
         assertEquals(ndArray[5, 5], 10.0)
     }
 }

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

@@ -1,8 +1,8 @@
 package kscience.kmath.structures
 
+import kscience.kmath.nd.*
 import kscience.kmath.operations.Norm
 import kscience.kmath.operations.invoke
-import kscience.kmath.structures.NDElement.Companion.real2D
 import kotlin.math.abs
 import kotlin.math.pow
 import kotlin.test.Test
@@ -10,25 +10,30 @@ import kotlin.test.assertEquals
 
 @Suppress("UNUSED_VARIABLE")
 class NumberNDFieldTest {
-    val array1: RealNDElement = real2D(3, 3) { i, j -> (i + j).toDouble() }
+    val algebra = NDAlgebra.real(3,3)
-    val array2: RealNDElement = real2D(3, 3) { i, j -> (i - j).toDouble() }
+    val array1 = algebra.produce { (i, j) -> (i + j).toDouble() }
+    val array2 = algebra.produce { (i, j) -> (i - j).toDouble() }
 
     @Test
     fun testSum() {
+        algebra {
             val sum = array1 + array2
             assertEquals(4.0, sum[2, 2])
         }
+    }
 
     @Test
     fun testProduct() {
+        algebra {
             val product = array1 * array2
             assertEquals(0.0, product[2, 2])
         }
+    }
 
     @Test
     fun testGeneration() {
 
-        val array = real2D(3, 3) { i, j -> (i * 10 + j).toDouble() }
+        val array = Structure2D.real(3, 3) { i, j -> (i * 10 + j).toDouble() }
 
         for (i in 0..2) {
             for (j in 0..2) {
@@ -40,17 +45,21 @@ class NumberNDFieldTest {
 
     @Test
     fun testExternalFunction() {
+        algebra {
             val function: (Double) -> Double = { x -> x.pow(2) + 2 * x + 1 }
             val result = function(array1) + 1.0
             assertEquals(10.0, result[1, 1])
         }
+    }
 
     @Test
     fun testLibraryFunction() {
+        algebra {
             val abs: (Double) -> Double = ::abs
             val result = abs(array2)
             assertEquals(2.0, result[0, 2])
         }
+    }
 
     @Test
     fun combineTest() {
@@ -64,6 +73,8 @@ class NumberNDFieldTest {
 
     @Test
     fun testInternalContext() {
-        (NDField.real(*array1.shape)) { with(L2Norm) { 1 + norm(array1) + exp(array2) } }
+        algebra {
+            (NDAlgebra.real(*array1.shape)) { with(L2Norm) { 1 + norm(array1) + exp(array2) } }
+        }
     }
 }

kmath-coroutines/src/jvmMain/kotlin/kscience/kmath/structures/LazyNDStructure.kt

@@ -2,6 +2,8 @@ package kscience.kmath.structures
 
 import kotlinx.coroutines.*
 import kscience.kmath.coroutines.Math
+import kscience.kmath.nd.DefaultStrides
+import kscience.kmath.nd.NDStructure
 
 public class LazyNDStructure<T>(
     public val scope: CoroutineScope,

kmath-dimensions/src/commonMain/kotlin/kscience/kmath/dimensions/Wrappers.kt

@@ -1,9 +1,8 @@
 package kscience.kmath.dimensions
 
 import kscience.kmath.linear.*
+import kscience.kmath.nd.Structure2D
 import kscience.kmath.operations.invoke
-import kscience.kmath.structures.Matrix
-import kscience.kmath.structures.Structure2D
 
 /**
  * A matrix with compile-time controlled dimension

kmath-ejml/src/main/kotlin/kscience/kmath/ejml/EjmlMatrix.kt

@@ -2,8 +2,7 @@ package kscience.kmath.ejml
 
 import kscience.kmath.linear.*
 import kscience.kmath.misc.UnstableKMathAPI
-import kscience.kmath.structures.Matrix
+import kscience.kmath.nd.NDStructure
-import kscience.kmath.structures.NDStructure
 import kscience.kmath.structures.RealBuffer
 import org.ejml.dense.row.factory.DecompositionFactory_DDRM
 import org.ejml.simple.SimpleMatrix
@@ -16,21 +15,20 @@ import kotlin.reflect.cast
  * @property origin the underlying [SimpleMatrix].
  * @author Iaroslav Postovalov
  */
-public class EjmlMatrix(
+public class EjmlMatrix(public val origin: SimpleMatrix) : Matrix<Double> {
-    public val origin: SimpleMatrix,
-) : Matrix<Double> {
     public override val rowNum: Int get() = origin.numRows()
-
     public override val colNum: Int get() = origin.numCols()
 
     @UnstableKMathAPI
-    override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
+    public override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
         InverseMatrixFeature::class -> object : InverseMatrixFeature<Double> {
             override val inverse: Matrix<Double> by lazy { EjmlMatrix(origin.invert()) }
         }
+
         DeterminantFeature::class -> object : DeterminantFeature<Double> {
             override val determinant: Double by lazy(origin::determinant)
         }
+
         SingularValueDecompositionFeature::class -> object : SingularValueDecompositionFeature<Double> {
             private val svd by lazy {
                 DecompositionFactory_DDRM.svd(origin.numRows(), origin.numCols(), true, true, false)
@@ -42,14 +40,19 @@ public class EjmlMatrix(
             override val v: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getV(null, false))) }
             override val singularValues: Point<Double> by lazy { RealBuffer(svd.singularValues) }
         }
+
         QRDecompositionFeature::class -> object : QRDecompositionFeature<Double> {
             private val qr by lazy {
                 DecompositionFactory_DDRM.qr().apply { decompose(origin.ddrm.copy()) }
             }
 
-            override val q: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getQ(null, false))) }
+            override val q: Matrix<Double> by lazy {
-            override val r: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getR(null, false))) }
+                EjmlMatrix(SimpleMatrix(qr.getQ(null, false))) + OrthogonalFeature
             }
+
+            override val r: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getR(null, false))) + UFeature }
+        }
+
         CholeskyDecompositionFeature::class -> object : CholeskyDecompositionFeature<Double> {
             override val l: Matrix<Double> by lazy {
                 val cholesky =
@@ -58,6 +61,7 @@ public class EjmlMatrix(
                 EjmlMatrix(SimpleMatrix(cholesky.getT(null))) + LFeature
             }
         }
+
         LupDecompositionFeature::class -> object : LupDecompositionFeature<Double> {
             private val lup by lazy {
                 DecompositionFactory_DDRM.lu(origin.numRows(), origin.numCols()).apply { decompose(origin.ddrm.copy()) }
@@ -73,8 +77,9 @@ public class EjmlMatrix(
 
             override val p: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(lup.getRowPivot(null))) }
         }
+
         else -> null
-    }?.let { type.cast(it) }
+    }?.let(type::cast)
 
     public override operator fun get(i: Int, j: Int): Double = origin[i, j]
 

kmath-ejml/src/main/kotlin/kscience/kmath/ejml/EjmlMatrixContext.kt

@@ -1,12 +1,8 @@
 package kscience.kmath.ejml
 
-import kscience.kmath.linear.InverseMatrixFeature
+import kscience.kmath.linear.*
-import kscience.kmath.linear.MatrixContext
-import kscience.kmath.linear.Point
-import kscience.kmath.linear.origin
 import kscience.kmath.misc.UnstableKMathAPI
-import kscience.kmath.structures.Matrix
+import kscience.kmath.nd.getFeature
-import kscience.kmath.structures.getFeature
 import org.ejml.simple.SimpleMatrix
 
 /**

kmath-ejml/src/test/kotlin/kscience/kmath/ejml/EjmlMatrixTest.kt

@@ -5,7 +5,7 @@ import kscience.kmath.linear.LupDecompositionFeature
 import kscience.kmath.linear.MatrixFeature
 import kscience.kmath.linear.plus
 import kscience.kmath.misc.UnstableKMathAPI
-import kscience.kmath.structures.getFeature
+import kscience.kmath.nd.getFeature
 import org.ejml.dense.row.factory.DecompositionFactory_DDRM
 import org.ejml.simple.SimpleMatrix
 import kotlin.random.Random

kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealMatrix.kt

@@ -1,12 +1,8 @@
 package kscience.kmath.real
 
-import kscience.kmath.linear.MatrixContext
+import kscience.kmath.linear.*
-import kscience.kmath.linear.VirtualMatrix
-import kscience.kmath.linear.inverseWithLUP
-import kscience.kmath.linear.real
 import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.structures.Buffer
-import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.RealBuffer
 import kscience.kmath.structures.asIterable
 import kotlin.math.pow
@@ -144,7 +140,7 @@ public fun RealMatrix.min(): Double? = elements().map { (_, value) -> value }.mi
 public fun RealMatrix.max(): Double? = elements().map { (_, value) -> value }.maxOrNull()
 public fun RealMatrix.average(): Double = elements().map { (_, value) -> value }.average()
 
-public inline fun RealMatrix.map(transform: (Double) -> Double): RealMatrix =
+public inline fun RealMatrix.map(crossinline transform: (Double) -> Double): RealMatrix =
     MatrixContext.real.produce(rowNum, colNum) { i, j ->
         transform(get(i, j))
     }
@@ -152,7 +148,7 @@ public inline fun RealMatrix.map(transform: (Double) -> Double): RealMatrix =
 /**
  * Inverse a square real matrix using LUP decomposition
  */
-public fun RealMatrix.inverseWithLUP(): RealMatrix = MatrixContext.real.inverseWithLUP(this)
+public fun RealMatrix.inverseWithLup(): RealMatrix = MatrixContext.real.inverseWithLup(this)
 
 //extended operations
 

kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/realND.kt

@@ -0,0 +1,31 @@
+package kscience.kmath.real
+
+import kscience.kmath.nd.NDBuffer
+import kscience.kmath.operations.RealField
+import kscience.kmath.structures.RealBuffer
+
+/**
+ * Map one [NDBuffer] using function without indices.
+ */
+public inline fun NDBuffer<Double>.mapInline(crossinline transform: RealField.(Double) -> Double): NDBuffer<Double> {
+    val array = DoubleArray(strides.linearSize) { offset -> RealField.transform(buffer[offset]) }
+    return NDBuffer(strides, RealBuffer(array))
+}
+
+/**
+ * Element by element application of any operation on elements to the whole array. Just like in numpy.
+ */
+public operator fun Function1<Double, Double>.invoke(ndElement: NDBuffer<Double>): NDBuffer<Double> =
+    ndElement.mapInline { this@invoke(it) }
+
+/* plus and minus */
+
+/**
+ * Summation operation for [NDBuffer] and single element
+ */
+public operator fun NDBuffer<Double>.plus(arg: Double): NDBuffer<Double> = mapInline { it + arg }
+
+/**
+ * Subtraction operation between [NDBuffer] and single element
+ */
+public operator fun NDBuffer<Double>.minus(arg: Double): NDBuffer<Double> = mapInline { it - arg }

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

@@ -1,8 +1,8 @@
 package kaceince.kmath.real
 
+import kscience.kmath.linear.Matrix
 import kscience.kmath.linear.build
 import kscience.kmath.real.*
-import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.contentEquals
 import kotlin.test.Test
 import kotlin.test.assertEquals

kmath-functions/src/commonMain/kotlin/kscience/kmath/interpolation/XYPointSet.kt

@@ -1,7 +1,7 @@
 package kscience.kmath.interpolation
 
+import kscience.kmath.nd.Structure2D
 import kscience.kmath.structures.Buffer
-import kscience.kmath.structures.Structure2D
 
 public interface XYPointSet<X, Y> {
     public val size: Int

kmath-histograms/build.gradle.kts

@@ -1,8 +1,18 @@
 plugins { id("ru.mipt.npm.mpp") }
 
-kotlin.sourceSets.commonMain {
+kotlin.sourceSets {
+    commonMain {
         dependencies {
             api(project(":kmath-core"))
-        api(project(":kmath-for-real"))
+        }
+    }
+    commonTest{
+        dependencies{
+            implementation(project(":kmath-for-real"))
+        }
     }
 }
+
+readme {
+    this.maturity = ru.mipt.npm.gradle.Maturity.PROTOTYPE
+}

kmath-histograms/src/commonMain/kotlin/kscience/kmath/histogram/RealHistogram.kt

@@ -1,6 +1,8 @@
 package kscience.kmath.histogram
 
 import kscience.kmath.linear.Point
+import kscience.kmath.nd.DefaultStrides
+import kscience.kmath.nd.NDStructure
 import kscience.kmath.operations.SpaceOperations
 import kscience.kmath.operations.invoke
 import kscience.kmath.structures.*

kmath-histograms/src/commonTest/kotlin/scietifik/kmath/histogram/MultivariateHistogramTest.kt

@@ -5,7 +5,6 @@ import kscience.kmath.histogram.fill
 import kscience.kmath.histogram.put
 import kscience.kmath.real.RealVector
 import kscience.kmath.real.invoke
-import kscience.kmath.structures.Buffer
 import kotlin.random.Random
 import kotlin.test.*
 

kmath-histograms/src/jvmMain/kotlin/kscience/kmath/histogram/UnivariateHistogram.kt

@@ -1,6 +1,6 @@
 package kscience.kmath.histogram
 
-import kscience.kmath.real.RealVector
+import kscience.kmath.linear.Point
 import kscience.kmath.structures.Buffer
 import kscience.kmath.structures.asBuffer
 import java.util.*
@@ -11,12 +11,12 @@ import kotlin.math.floor
 public class UnivariateBin(
     public val position: Double,
     public val size: Double,
-    public val counter: LongCounter = LongCounter()
+    public val counter: LongCounter = LongCounter(),
 ) : Bin<Double> {
     //TODO add weighting
     public override val value: Number get() = counter.sum()
 
-    public override val center: RealVector get() = doubleArrayOf(position).asBuffer()
+    public override val center: Point<Double> get() = doubleArrayOf(position).asBuffer()
     public override val dimension: Int get() = 1
 
     public operator fun contains(value: Double): Boolean = value in (position - size / 2)..(position + size / 2)
@@ -27,8 +27,9 @@ public class UnivariateBin(
 /**
  * Univariate histogram with log(n) bin search speed
  */
-public class UnivariateHistogram private constructor(private val factory: (Double) -> UnivariateBin) :
+public class UnivariateHistogram private constructor(
-    MutableHistogram<Double, UnivariateBin> {
+    private val factory: (Double) -> UnivariateBin,
+) : MutableHistogram<Double, UnivariateBin> {
 
     private val bins: TreeMap<Double, UnivariateBin> = TreeMap()
 

kmath-nd4j/src/main/kotlin/kscience.kmath.nd4j/Nd4jArrayAlgebra.kt

@@ -1,55 +1,68 @@
 package kscience.kmath.nd4j
 
 import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.nd.*
 import kscience.kmath.operations.*
-import kscience.kmath.structures.NDAlgebra
+import kscience.kmath.structures.*
-import kscience.kmath.structures.NDField
-import kscience.kmath.structures.NDRing
-import kscience.kmath.structures.NDSpace
 import org.nd4j.linalg.api.ndarray.INDArray
 import org.nd4j.linalg.factory.Nd4j
 
+internal fun NDAlgebra<*, *>.checkShape(array: INDArray): INDArray {
+    val arrayShape = array.shape().toIntArray()
+    if (!shape.contentEquals(arrayShape)) throw ShapeMismatchException(shape, arrayShape)
+    return array
+}
+
+
 /**
  * Represents [NDAlgebra] over [Nd4jArrayAlgebra].
  *
  * @param T the type of ND-structure element.
  * @param C the type of the element context.
  */
-public interface Nd4jArrayAlgebra<T, C> : NDAlgebra<T, C, Nd4jArrayStructure<T>> {
+public interface Nd4jArrayAlgebra<T, C> : NDAlgebra<T, C> {
     /**
      * Wraps [INDArray] to [N].
      */
     public fun INDArray.wrap(): Nd4jArrayStructure<T>
 
+    public val NDStructure<T>.ndArray: INDArray
+        get() = when {
+            !shape.contentEquals(this@Nd4jArrayAlgebra.shape) -> throw ShapeMismatchException(
+                this@Nd4jArrayAlgebra.shape,
+                shape
+            )
+            this is Nd4jArrayStructure -> ndArray //TODO check strides
+            else -> {
+                TODO()
+            }
+        }
+
     public override fun produce(initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
         val struct = Nd4j.create(*shape)!!.wrap()
         struct.indicesIterator().forEach { struct[it] = elementContext.initializer(it) }
         return struct
     }
 
-    public override fun map(arg: Nd4jArrayStructure<T>, transform: C.(T) -> T): Nd4jArrayStructure<T> {
+    public override fun NDStructure<T>.map(transform: C.(T) -> T): Nd4jArrayStructure<T> {
-        check(arg)
+        val newStruct = ndArray.dup().wrap()
-        val newStruct = arg.ndArray.dup().wrap()
         newStruct.elements().forEach { (idx, value) -> newStruct[idx] = elementContext.transform(value) }
         return newStruct
     }
 
-    public override fun mapIndexed(
+    public override fun NDStructure<T>.mapIndexed(
-        arg: Nd4jArrayStructure<T>,
         transform: C.(index: IntArray, T) -> T,
     ): Nd4jArrayStructure<T> {
-        check(arg)
+        val new = Nd4j.create(*this@Nd4jArrayAlgebra.shape).wrap()
-        val new = Nd4j.create(*shape).wrap()
+        new.indicesIterator().forEach { idx -> new[idx] = elementContext.transform(idx, this[idx]) }
-        new.indicesIterator().forEach { idx -> new[idx] = elementContext.transform(idx, arg[idx]) }
         return new
     }
 
     public override fun combine(
-        a: Nd4jArrayStructure<T>,
+        a: NDStructure<T>,
-        b: Nd4jArrayStructure<T>,
+        b: NDStructure<T>,
         transform: C.(T, T) -> T,
     ): Nd4jArrayStructure<T> {
-        check(a, b)
         val new = Nd4j.create(*shape).wrap()
         new.indicesIterator().forEach { idx -> new[idx] = elementContext.transform(a[idx], b[idx]) }
         return new
@@ -62,38 +75,32 @@ public interface Nd4jArrayAlgebra<T, C> : NDAlgebra<T, C, Nd4jArrayStructure<T>>
  * @param T the type of the element contained in ND structure.
  * @param S the type of space of structure elements.
  */
-public interface Nd4jArraySpace<T, S : Space<T>> : NDSpace<T, S, Nd4jArrayStructure<T>>, Nd4jArrayAlgebra<T, S> {
+public interface Nd4jArraySpace<T, S : Space<T>> : NDSpace<T, S>, Nd4jArrayAlgebra<T, S> {
 
     public override val zero: Nd4jArrayStructure<T>
         get() = Nd4j.zeros(*shape).wrap()
 
-    public override fun add(a: Nd4jArrayStructure<T>, b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
+    public override fun add(a: NDStructure<T>, b: NDStructure<T>): Nd4jArrayStructure<T> {
-        check(a, b)
         return a.ndArray.add(b.ndArray).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<T>.minus(b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
+    public override operator fun NDStructure<T>.minus(b: NDStructure<T>): Nd4jArrayStructure<T> {
-        check(this, b)
         return ndArray.sub(b.ndArray).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<T>.unaryMinus(): Nd4jArrayStructure<T> {
+    public override operator fun NDStructure<T>.unaryMinus(): Nd4jArrayStructure<T> {
-        check(this)
         return ndArray.neg().wrap()
     }
 
-    public override fun multiply(a: Nd4jArrayStructure<T>, k: Number): Nd4jArrayStructure<T> {
+    public override fun multiply(a: NDStructure<T>, k: Number): Nd4jArrayStructure<T> {
-        check(a)
         return a.ndArray.mul(k).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<T>.div(k: Number): Nd4jArrayStructure<T> {
+    public override operator fun NDStructure<T>.div(k: Number): Nd4jArrayStructure<T> {
-        check(this)
         return ndArray.div(k).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<T>.times(k: Number): Nd4jArrayStructure<T> {
+    public override operator fun NDStructure<T>.times(k: Number): Nd4jArrayStructure<T> {
-        check(this)
         return ndArray.mul(k).wrap()
     }
 }
@@ -105,13 +112,12 @@ public interface Nd4jArraySpace<T, S : Space<T>> : NDSpace<T, S, Nd4jArrayStruct
  * @param R the type of ring of structure elements.
  */
 @OptIn(UnstableKMathAPI::class)
-public interface Nd4jArrayRing<T, R : Ring<T>> : NDRing<T, R, Nd4jArrayStructure<T>>, Nd4jArraySpace<T, R> {
+public interface Nd4jArrayRing<T, R : Ring<T>> : NDRing<T, R>, Nd4jArraySpace<T, R> {
 
     public override val one: Nd4jArrayStructure<T>
         get() = Nd4j.ones(*shape).wrap()
 
-    public override fun multiply(a: Nd4jArrayStructure<T>, b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
+    public override fun multiply(a: NDStructure<T>, b: NDStructure<T>): Nd4jArrayStructure<T> {
-        check(a, b)
         return a.ndArray.mul(b.ndArray).wrap()
     }
 //
@@ -168,17 +174,12 @@ public interface Nd4jArrayRing<T, R : Ring<T>> : NDRing<T, R, Nd4jArrayStructure
  * @param N the type of ND structure.
  * @param F the type field of structure elements.
  */
-public interface Nd4jArrayField<T, F : Field<T>> : NDField<T, F, Nd4jArrayStructure<T>>, Nd4jArrayRing<T, F> {
+public interface Nd4jArrayField<T, F : Field<T>> : NDField<T, F>, Nd4jArrayRing<T, F> {
 
-    public override fun divide(a: Nd4jArrayStructure<T>, b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
+    public override fun divide(a: NDStructure<T>, b: NDStructure<T>): Nd4jArrayStructure<T> =
-        check(a, b)
+        a.ndArray.div(b.ndArray).wrap()
-        return a.ndArray.div(b.ndArray).wrap()
-    }
 
-    public override operator fun Number.div(b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
+    public override operator fun Number.div(b: NDStructure<T>): Nd4jArrayStructure<T> = b.ndArray.rdiv(this).wrap()
-        check(b)
-        return b.ndArray.rdiv(this).wrap()
-    }
 
 
     public companion object {
@@ -219,35 +220,29 @@ public class RealNd4jArrayField(public override val shape: IntArray) : Nd4jArray
     public override val elementContext: RealField
         get() = RealField
 
-    public override fun INDArray.wrap(): Nd4jArrayStructure<Double> = check(asRealStructure())
+    public override fun INDArray.wrap(): Nd4jArrayStructure<Double> = checkShape(this).asRealStructure()
 
-    public override operator fun Nd4jArrayStructure<Double>.div(arg: Double): Nd4jArrayStructure<Double> {
+    public override operator fun NDStructure<Double>.div(arg: Double): Nd4jArrayStructure<Double> {
-        check(this)
         return ndArray.div(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Double>.plus(arg: Double): Nd4jArrayStructure<Double> {
+    public override operator fun NDStructure<Double>.plus(arg: Double): Nd4jArrayStructure<Double> {
-        check(this)
         return ndArray.add(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Double>.minus(arg: Double): Nd4jArrayStructure<Double> {
+    public override operator fun NDStructure<Double>.minus(arg: Double): Nd4jArrayStructure<Double> {
-        check(this)
         return ndArray.sub(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Double>.times(arg: Double): Nd4jArrayStructure<Double> {
+    public override operator fun NDStructure<Double>.times(arg: Double): Nd4jArrayStructure<Double> {
-        check(this)
         return ndArray.mul(arg).wrap()
     }
 
-    public override operator fun Double.div(arg: Nd4jArrayStructure<Double>): Nd4jArrayStructure<Double> {
+    public override operator fun Double.div(arg: NDStructure<Double>): Nd4jArrayStructure<Double> {
-        check(arg)
         return arg.ndArray.rdiv(this).wrap()
     }
 
-    public override operator fun Double.minus(arg: Nd4jArrayStructure<Double>): Nd4jArrayStructure<Double> {
+    public override operator fun Double.minus(arg: NDStructure<Double>): Nd4jArrayStructure<Double> {
-        check(arg)
         return arg.ndArray.rsub(this).wrap()
     }
 }
@@ -259,35 +254,29 @@ public class FloatNd4jArrayField(public override val shape: IntArray) : Nd4jArra
     public override val elementContext: FloatField
         get() = FloatField
 
-    public override fun INDArray.wrap(): Nd4jArrayStructure<Float> = check(asFloatStructure())
+    public override fun INDArray.wrap(): Nd4jArrayStructure<Float> = checkShape(this).asFloatStructure()
 
-    public override operator fun Nd4jArrayStructure<Float>.div(arg: Float): Nd4jArrayStructure<Float> {
+    public override operator fun NDStructure<Float>.div(arg: Float): Nd4jArrayStructure<Float> {
-        check(this)
         return ndArray.div(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Float>.plus(arg: Float): Nd4jArrayStructure<Float> {
+    public override operator fun NDStructure<Float>.plus(arg: Float): Nd4jArrayStructure<Float> {
-        check(this)
         return ndArray.add(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Float>.minus(arg: Float): Nd4jArrayStructure<Float> {
+    public override operator fun NDStructure<Float>.minus(arg: Float): Nd4jArrayStructure<Float> {
-        check(this)
         return ndArray.sub(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Float>.times(arg: Float): Nd4jArrayStructure<Float> {
+    public override operator fun NDStructure<Float>.times(arg: Float): Nd4jArrayStructure<Float> {
-        check(this)
         return ndArray.mul(arg).wrap()
     }
 
-    public override operator fun Float.div(arg: Nd4jArrayStructure<Float>): Nd4jArrayStructure<Float> {
+    public override operator fun Float.div(arg: NDStructure<Float>): Nd4jArrayStructure<Float> {
-        check(arg)
         return arg.ndArray.rdiv(this).wrap()
     }
 
-    public override operator fun Float.minus(arg: Nd4jArrayStructure<Float>): Nd4jArrayStructure<Float> {
+    public override operator fun Float.minus(arg: NDStructure<Float>): Nd4jArrayStructure<Float> {
-        check(arg)
         return arg.ndArray.rsub(this).wrap()
     }
 }
@@ -299,25 +288,21 @@ public class IntNd4jArrayRing(public override val shape: IntArray) : Nd4jArrayRi
     public override val elementContext: IntRing
         get() = IntRing
 
-    public override fun INDArray.wrap(): Nd4jArrayStructure<Int> = check(asIntStructure())
+    public override fun INDArray.wrap(): Nd4jArrayStructure<Int> = checkShape(this).asIntStructure()
 
-    public override operator fun Nd4jArrayStructure<Int>.plus(arg: Int): Nd4jArrayStructure<Int> {
+    public override operator fun NDStructure<Int>.plus(arg: Int): Nd4jArrayStructure<Int> {
-        check(this)
         return ndArray.add(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Int>.minus(arg: Int): Nd4jArrayStructure<Int> {
+    public override operator fun NDStructure<Int>.minus(arg: Int): Nd4jArrayStructure<Int> {
-        check(this)
         return ndArray.sub(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Int>.times(arg: Int): Nd4jArrayStructure<Int> {
+    public override operator fun NDStructure<Int>.times(arg: Int): Nd4jArrayStructure<Int> {
-        check(this)
         return ndArray.mul(arg).wrap()
     }
 
-    public override operator fun Int.minus(arg: Nd4jArrayStructure<Int>): Nd4jArrayStructure<Int> {
+    public override operator fun Int.minus(arg: NDStructure<Int>): Nd4jArrayStructure<Int> {
-        check(arg)
         return arg.ndArray.rsub(this).wrap()
     }
 }
@@ -329,25 +314,21 @@ public class LongNd4jArrayRing(public override val shape: IntArray) : Nd4jArrayR
     public override val elementContext: LongRing
         get() = LongRing
 
-    public override fun INDArray.wrap(): Nd4jArrayStructure<Long> = check(asLongStructure())
+    public override fun INDArray.wrap(): Nd4jArrayStructure<Long> = checkShape(this).asLongStructure()
 
-    public override operator fun Nd4jArrayStructure<Long>.plus(arg: Long): Nd4jArrayStructure<Long> {
+    public override operator fun NDStructure<Long>.plus(arg: Long): Nd4jArrayStructure<Long> {
-        check(this)
         return ndArray.add(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Long>.minus(arg: Long): Nd4jArrayStructure<Long> {
+    public override operator fun NDStructure<Long>.minus(arg: Long): Nd4jArrayStructure<Long> {
-        check(this)
         return ndArray.sub(arg).wrap()
     }
 
-    public override operator fun Nd4jArrayStructure<Long>.times(arg: Long): Nd4jArrayStructure<Long> {
+    public override operator fun NDStructure<Long>.times(arg: Long): Nd4jArrayStructure<Long> {
-        check(this)
         return ndArray.mul(arg).wrap()
     }
 
-    public override operator fun Long.minus(arg: Nd4jArrayStructure<Long>): Nd4jArrayStructure<Long> {
+    public override operator fun Long.minus(arg: NDStructure<Long>): Nd4jArrayStructure<Long> {
-        check(arg)
         return arg.ndArray.rsub(this).wrap()
     }
 }

kmath-nd4j/src/main/kotlin/kscience.kmath.nd4j/Nd4jArrayStructure.kt

@@ -1,7 +1,7 @@
 package kscience.kmath.nd4j
 
-import kscience.kmath.structures.MutableNDStructure
+import kscience.kmath.nd.MutableNDStructure
-import kscience.kmath.structures.NDStructure
+import kscience.kmath.nd.NDStructure
 import org.nd4j.linalg.api.ndarray.INDArray
 
 /**

kmath-nd4j/src/test/kotlin/kscience/kmath/nd4j/Nd4jArrayAlgebraTest.kt

@@ -1,7 +1,7 @@
 package kscience.kmath.nd4j
 
-import org.nd4j.linalg.factory.Nd4j
 import kscience.kmath.operations.invoke
+import org.nd4j.linalg.factory.Nd4j
 import kotlin.test.Test
 import kotlin.test.assertEquals
 import kotlin.test.fail
@@ -20,7 +20,7 @@ internal class Nd4jArrayAlgebraTest {
 
     @Test
     fun testMap() {
-        val res = (IntNd4jArrayRing(intArrayOf(2, 2))) { map(one) { it + it * 2 } }
+        val res = (IntNd4jArrayRing(intArrayOf(2, 2))) { one.map() { it + it * 2 } }
         val expected = (Nd4j.create(2, 2) ?: fail()).asIntStructure()
         expected[intArrayOf(0, 0)] = 3
         expected[intArrayOf(0, 1)] = 3

kmath-nd4j/src/test/kotlin/kscience/kmath/nd4j/Nd4jArrayStructureTest.kt

@@ -1,6 +1,6 @@
 package kscience.kmath.nd4j
 
-import kscience.kmath.structures.get
+import kscience.kmath.nd.get
 import org.nd4j.linalg.factory.Nd4j
 import kotlin.test.Test
 import kotlin.test.assertEquals

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

@@ -1,10 +1,10 @@
 package kscience.kmath.viktor
 
+import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.nd.*
+import kscience.kmath.operations.ExtendedField
 import kscience.kmath.operations.RealField
-import kscience.kmath.structures.DefaultStrides
+import kscience.kmath.operations.RingWithNumbers
-import kscience.kmath.structures.MutableNDStructure
-import kscience.kmath.structures.NDField
-import kscience.kmath.structures.Strides
 import org.jetbrains.bio.viktor.F64Array
 
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
@@ -23,15 +23,28 @@ public inline class ViktorNDStructure(public val f64Buffer: F64Array) : MutableN
 
 public fun F64Array.asStructure(): ViktorNDStructure = ViktorNDStructure(this)
 
+@OptIn(UnstableKMathAPI::class)
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-public class ViktorNDField(public override val shape: IntArray) : NDField<Double, RealField, ViktorNDStructure> {
+public class ViktorNDField(public override val shape: IntArray) : NDField<Double, RealField>,
+    RingWithNumbers<NDStructure<Double>>, ExtendedField<NDStructure<Double>> {
+
+    public val NDStructure<Double>.f64Buffer: F64Array
+        get() = when {
+            !shape.contentEquals(this@ViktorNDField.shape) -> throw ShapeMismatchException(
+                this@ViktorNDField.shape,
+                shape
+            )
+            this is ViktorNDStructure && this.f64Buffer.shape.contentEquals(this@ViktorNDField.shape) -> this.f64Buffer
+            else -> produce { this@f64Buffer[it] }.f64Buffer
+        }
+
     public override val zero: ViktorNDStructure
         get() = F64Array.full(init = 0.0, shape = shape).asStructure()
 
     public override val one: ViktorNDStructure
         get() = F64Array.full(init = 1.0, shape = shape).asStructure()
 
-    public val strides: Strides = DefaultStrides(shape)
+    private val strides: Strides = DefaultStrides(shape)
 
     public override val elementContext: RealField get() = RealField
 
@@ -42,47 +55,67 @@ public class ViktorNDField(public override val shape: IntArray) : NDField<Double
             }
         }.asStructure()
 
-    public override fun map(arg: ViktorNDStructure, transform: RealField.(Double) -> Double): ViktorNDStructure =
+    public override fun NDStructure<Double>.map(transform: RealField.(Double) -> Double): ViktorNDStructure =
-        F64Array(*shape).apply {
+        F64Array(*this@ViktorNDField.shape).apply {
             this@ViktorNDField.strides.indices().forEach { index ->
-                set(value = RealField.transform(arg[index]), indices = index)
+                set(value = RealField.transform(this@map[index]), indices = index)
             }
         }.asStructure()
 
-    public override fun mapIndexed(
+    public override fun NDStructure<Double>.mapIndexed(
-        arg: ViktorNDStructure,
+        transform: RealField.(index: IntArray, Double) -> Double,
-        transform: RealField.(index: IntArray, Double) -> Double
+    ): ViktorNDStructure = F64Array(*this@ViktorNDField.shape).apply {
-    ): ViktorNDStructure = F64Array(*shape).apply {
         this@ViktorNDField.strides.indices().forEach { index ->
-            set(value = RealField.transform(index, arg[index]), indices = index)
+            set(value = RealField.transform(index, this@mapIndexed[index]), indices = index)
         }
     }.asStructure()
 
     public override fun combine(
-        a: ViktorNDStructure,
+        a: NDStructure<Double>,
-        b: ViktorNDStructure,
+        b: NDStructure<Double>,
-        transform: RealField.(Double, Double) -> Double
+        transform: RealField.(Double, Double) -> Double,
     ): ViktorNDStructure = F64Array(*shape).apply {
         this@ViktorNDField.strides.indices().forEach { index ->
             set(value = RealField.transform(a[index], b[index]), indices = index)
         }
     }.asStructure()
 
-    public override fun add(a: ViktorNDStructure, b: ViktorNDStructure): ViktorNDStructure =
+    public override fun add(a: NDStructure<Double>, b: NDStructure<Double>): ViktorNDStructure =
         (a.f64Buffer + b.f64Buffer).asStructure()
 
-    public override fun multiply(a: ViktorNDStructure, k: Number): ViktorNDStructure =
+    public override fun multiply(a: NDStructure<Double>, k: Number): ViktorNDStructure =
         (a.f64Buffer * k.toDouble()).asStructure()
 
-    public override inline fun ViktorNDStructure.plus(b: ViktorNDStructure): ViktorNDStructure =
+    public override inline fun NDStructure<Double>.plus(b: NDStructure<Double>): ViktorNDStructure =
         (f64Buffer + b.f64Buffer).asStructure()
 
-    public override inline fun ViktorNDStructure.minus(b: ViktorNDStructure): ViktorNDStructure =
+    public override inline fun NDStructure<Double>.minus(b: NDStructure<Double>): ViktorNDStructure =
         (f64Buffer - b.f64Buffer).asStructure()
 
-    public override inline fun ViktorNDStructure.times(k: Number): ViktorNDStructure =
+    public override inline fun NDStructure<Double>.times(k: Number): ViktorNDStructure =
         (f64Buffer * k.toDouble()).asStructure()
 
-    public override inline fun ViktorNDStructure.plus(arg: Double): ViktorNDStructure =
+    public override inline fun NDStructure<Double>.plus(arg: Double): ViktorNDStructure =
         (f64Buffer.plus(arg)).asStructure()
+
+    override fun number(value: Number): ViktorNDStructure =
+        F64Array.full(init = value.toDouble(), shape = shape).asStructure()
+
+    override fun sin(arg: NDStructure<Double>): ViktorNDStructure = arg.map { sin(it) }
+
+    override fun cos(arg: NDStructure<Double>): ViktorNDStructure = arg.map { cos(it) }
+
+    override fun asin(arg: NDStructure<Double>): ViktorNDStructure = arg.map { asin(it) }
+
+    override fun acos(arg: NDStructure<Double>): ViktorNDStructure = arg.map { acos(it) }
+
+    override fun atan(arg: NDStructure<Double>): ViktorNDStructure = arg.map { atan(it) }
+
+    override fun power(arg: NDStructure<Double>, pow: Number): ViktorNDStructure = arg.map { it.pow(pow) }
+
+    override fun exp(arg: NDStructure<Double>): ViktorNDStructure = arg.f64Buffer.exp().asStructure()
+
+    override fun ln(arg: NDStructure<Double>): ViktorNDStructure = arg.f64Buffer.log().asStructure()
 }
+
+public fun ViktorNDField(vararg shape: Int): ViktorNDField = ViktorNDField(shape)