Shapeless ND and Buffer algebras

CHANGELOG.md

@@ -42,6 +42,9 @@
 - Use `Symbol` factory function instead of `StringSymbol`
 - New discoverability pattern: `<Type>.algebra.<nd/etc>`
 - Adjusted commons-math API for linear solvers to match conventions.
+- Buffer algebra does not require size anymore
+- Operations -> Ops
+- Default Buffer and ND algebras are now Ops and lack neutral elements (0, 1) as well as algebra-level shapes.
 
 ### Deprecated
 - Specialized `DoubleBufferAlgebra`

benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/NDFieldBenchmark.kt

@@ -9,9 +9,10 @@ import kotlinx.benchmark.Benchmark
 import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
+import space.kscience.kmath.nd.BufferedFieldOpsND
 import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.nd.autoNdAlgebra
 import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.one
 import space.kscience.kmath.nd4j.nd4j
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.Buffer
@@ -23,21 +24,21 @@ import space.kscience.kmath.tensors.core.tensorAlgebra
 internal class NDFieldBenchmark {
     @Benchmark
     fun autoFieldAdd(blackhole: Blackhole) = with(autoField) {
-        var res: StructureND<Double> = one
+        var res: StructureND<Double> = one(shape)
-        repeat(n) { res += one }
+        repeat(n) { res += 1.0 }
         blackhole.consume(res)
     }
 
     @Benchmark
     fun specializedFieldAdd(blackhole: Blackhole) = with(specializedField) {
-        var res: StructureND<Double> = one
+        var res: StructureND<Double> = one(shape)
         repeat(n) { res += 1.0 }
         blackhole.consume(res)
     }
 
     @Benchmark
     fun boxingFieldAdd(blackhole: Blackhole) = with(genericField) {
-        var res: StructureND<Double> = one
+        var res: StructureND<Double> = one(shape)
         repeat(n) { res += 1.0 }
         blackhole.consume(res)
     }
@@ -56,19 +57,20 @@ internal class NDFieldBenchmark {
         blackhole.consume(res)
     }
 
-//    @Benchmark
+    @Benchmark
-//    fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
+    fun nd4jAdd(blackhole: Blackhole) = with(nd4jField) {
-//        var res: StructureND<Double> = one
+        var res: StructureND<Double> = one(dim, dim)
-//        repeat(n) { res += 1.0 }
+        repeat(n) { res += 1.0 }
-//        blackhole.consume(res)
+        blackhole.consume(res)
-//    }
+    }
 
     private companion object {
         private const val dim = 1000
         private const val n = 100
-        private val autoField = DoubleField.autoNdAlgebra(dim, dim)
+        private val shape = intArrayOf(dim, dim)
-        private val specializedField = DoubleField.ndAlgebra(dim, dim)
+        private val autoField = BufferedFieldOpsND(DoubleField, Buffer.Companion::auto)
-        private val genericField = DoubleField.ndAlgebra(Buffer.Companion::boxing, dim, dim)
+        private val specializedField = DoubleField.ndAlgebra
-        private val nd4jField = DoubleField.nd4j(dim, dim)
+        private val genericField = BufferedFieldOpsND(DoubleField, Buffer.Companion::boxing)
+        private val nd4jField = DoubleField.nd4j
     }
 }

benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorBenchmark.kt

@@ -10,18 +10,17 @@ import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
 import org.jetbrains.bio.viktor.F64Array
-import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.nd.*
-import space.kscience.kmath.nd.autoNdAlgebra
-import space.kscience.kmath.nd.ndAlgebra
 import space.kscience.kmath.operations.DoubleField
-import space.kscience.kmath.viktor.ViktorNDField
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.viktor.ViktorFieldND
 
 @State(Scope.Benchmark)
 internal class ViktorBenchmark {
     @Benchmark
     fun automaticFieldAddition(blackhole: Blackhole) {
         with(autoField) {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
             blackhole.consume(res)
         }
@@ -30,7 +29,7 @@ internal class ViktorBenchmark {
     @Benchmark
     fun realFieldAddition(blackhole: Blackhole) {
         with(realField) {
-            var res: StructureND<Double> = one
+            var res: StructureND<Double> = one(shape)
             repeat(n) { res += 1.0 }
             blackhole.consume(res)
         }
@@ -39,7 +38,7 @@ internal class ViktorBenchmark {
     @Benchmark
     fun viktorFieldAddition(blackhole: Blackhole) {
         with(viktorField) {
-            var res = one
+            var res = one(shape)
             repeat(n) { res += 1.0 }
             blackhole.consume(res)
         }
@@ -56,10 +55,11 @@ internal class ViktorBenchmark {
     private companion object {
         private const val dim = 1000
         private const val n = 100
+        private val shape = Shape(dim, dim)
 
         // automatically build context most suited for given type.
-        private val autoField = DoubleField.autoNdAlgebra(dim, dim)
+        private val autoField = BufferedFieldOpsND(DoubleField, Buffer.Companion::auto)
-        private val realField = DoubleField.ndAlgebra(dim, dim)
+        private val realField = DoubleField.ndAlgebra
-        private val viktorField = ViktorNDField(dim, dim)
+        private val viktorField = ViktorFieldND(dim, dim)
     }
 }

benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt

@@ -10,18 +10,21 @@ import kotlinx.benchmark.Blackhole
 import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
 import org.jetbrains.bio.viktor.F64Array
-import space.kscience.kmath.nd.autoNdAlgebra
+import space.kscience.kmath.nd.BufferedFieldOpsND
+import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.one
 import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.viktor.ViktorFieldND
 
 @State(Scope.Benchmark)
 internal class ViktorLogBenchmark {
     @Benchmark
     fun realFieldLog(blackhole: Blackhole) {
-        with(realNdField) {
+        with(realField) {
-            val fortyTwo = produce { 42.0 }
+            val fortyTwo = produce(shape) { 42.0 }
-            var res = one
+            var res = one(shape)
             repeat(n) { res = ln(fortyTwo) }
             blackhole.consume(res)
         }
@@ -30,7 +33,7 @@ internal class ViktorLogBenchmark {
     @Benchmark
     fun viktorFieldLog(blackhole: Blackhole) {
         with(viktorField) {
-            val fortyTwo = produce { 42.0 }
+            val fortyTwo = produce(shape) { 42.0 }
             var res = one
             repeat(n) { res = ln(fortyTwo) }
             blackhole.consume(res)
@@ -48,10 +51,11 @@ internal class ViktorLogBenchmark {
     private companion object {
         private const val dim = 1000
         private const val n = 100
+        private val shape = Shape(dim, dim)
 
         // automatically build context most suited for given type.
-        private val autoField = DoubleField.autoNdAlgebra(dim, dim)
+        private val autoField = BufferedFieldOpsND(DoubleField, Buffer.Companion::auto)
-        private val realNdField = DoubleField.ndAlgebra(dim, dim)
+        private val realField = DoubleField.ndAlgebra
-        private val viktorField = ViktorFieldND(intArrayOf(dim, dim))
+        private val viktorField = ViktorFieldND(dim, dim)
     }
 }

examples/src/main/kotlin/space/kscience/kmath/operations/complexDemo.kt

@@ -11,27 +11,27 @@ import space.kscience.kmath.complex.bufferAlgebra
 import space.kscience.kmath.complex.ndAlgebra
 import space.kscience.kmath.nd.BufferND
 import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.nd.produce
 
 fun main() = Complex.algebra {
     val complex = 2 + 2 * i
     println(complex * 8 - 5 * i)
 
     //flat buffer
-    val buffer = bufferAlgebra(8).run {
+    val buffer = with(bufferAlgebra){
-        buffer { Complex(it, -it) }.map { Complex(it.im, it.re) }
+        buffer(8) { Complex(it, -it) }.map { Complex(it.im, it.re) }
     }
     println(buffer)
 
-
     // 2d element
-    val element: BufferND<Complex> = ndAlgebra(2, 2).produce { (i, j) ->
+    val element: BufferND<Complex> = ndAlgebra.produce(2, 2) { (i, j) ->
         Complex(i - j, i + j)
     }
     println(element)
 
     // 1d element operation
-    val result: StructureND<Complex> = ndAlgebra(8).run {
+    val result: StructureND<Complex> = ndAlgebra{
-        val a = produce { (it) -> i * it - it.toDouble() }
+        val a = produce(8) { (it) -> i * it - it.toDouble() }
         val b = 3
         val c = Complex(1.0, 1.0)
 

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

@@ -14,7 +14,7 @@ import space.kscience.kmath.nd.ndAlgebra
 import space.kscience.kmath.nd4j.Nd4jArrayField
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.viktor.ViktorNDField
+import space.kscience.kmath.viktor.ViktorFieldND
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 import kotlin.system.measureTimeMillis
@@ -41,7 +41,7 @@ fun main() {
     // Nd4j specialized field.
     val nd4jField = Nd4jArrayField.real(dim, dim)
     //viktor field
-    val viktorField = ViktorNDField(dim, dim)
+    val viktorField = ViktorFieldND(dim, dim)
     //parallel processing based on Java Streams
     val parallelField = DoubleField.ndStreaming(dim, dim)
 

examples/src/main/kotlin/space/kscience/kmath/structures/StreamDoubleFieldND.kt

@@ -8,7 +8,7 @@ package space.kscience.kmath.structures
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 import java.util.*
 import java.util.stream.IntStream
 
@@ -17,11 +17,11 @@ import java.util.stream.IntStream
  * execution.
  */
 class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, DoubleField>,
-    NumbersAddOperations<StructureND<Double>>,
+    NumbersAddOps<StructureND<Double>>,
     ExtendedField<StructureND<Double>> {
 
     private val strides = DefaultStrides(shape)
-    override val elementContext: DoubleField get() = DoubleField
+    override val elementAlgebra: DoubleField get() = DoubleField
     override val zero: BufferND<Double> by lazy { produce { zero } }
     override val one: BufferND<Double> by lazy { produce { one } }
 
@@ -36,7 +36,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
                 this@StreamDoubleFieldND.shape,
                 shape
             )
-            this is BufferND && this.strides == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer
+            this is BufferND && this.indexes == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer
             else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
         }
 
@@ -69,7 +69,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
         return BufferND(strides, array.asBuffer())
     }
 
-    override fun combine(
+    override fun zip(
         a: StructureND<Double>,
         b: StructureND<Double>,
         transform: DoubleField.(Double, Double) -> Double,

examples/src/main/kotlin/space/kscience/kmath/structures/buffers.kt

@@ -8,6 +8,7 @@ package space.kscience.kmath.structures
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.buffer
 import space.kscience.kmath.operations.bufferAlgebra
+import space.kscience.kmath.operations.withSize
 
 inline fun <reified R : Any> MutableBuffer.Companion.same(
     n: Int,
@@ -16,7 +17,7 @@ inline fun <reified R : Any> MutableBuffer.Companion.same(
 
 
 fun main() {
-    with(DoubleField.bufferAlgebra(5)) {
+    with(DoubleField.bufferAlgebra.withSize(5)) {
         println(number(2.0) + buffer(1, 2, 3, 4, 5))
     }
 }

gradle/wrapper/gradle-wrapper.properties

@@ -1,5 +1,5 @@
 distributionBase=GRADLE_USER_HOME
 distributionPath=wrapper/dists
-distributionUrl=https\://services.gradle.org/distributions/gradle-7.1.1-bin.zip
+distributionUrl=https\://services.gradle.org/distributions/gradle-7.2-bin.zip
 zipStoreBase=GRADLE_USER_HOME
 zipStorePath=wrapper/dists

kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/parser.kt

@@ -18,10 +18,10 @@ import com.github.h0tk3y.betterParse.parser.ParseResult
 import com.github.h0tk3y.betterParse.parser.Parser
 import space.kscience.kmath.expressions.MST
 import space.kscience.kmath.expressions.Symbol
-import space.kscience.kmath.operations.FieldOperations
+import space.kscience.kmath.operations.FieldOps
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import space.kscience.kmath.operations.PowerOperations
-import space.kscience.kmath.operations.RingOperations
+import space.kscience.kmath.operations.RingOps
 
 /**
  * better-parse implementation of grammar defined in the ArithmeticsEvaluator.g4.
@@ -60,7 +60,7 @@ public object ArithmeticsEvaluator : Grammar<MST>() {
         .or(binaryFunction)
         .or(unaryFunction)
         .or(singular)
-        .or(-minus and parser(ArithmeticsEvaluator::term) map { MST.Unary(GroupOperations.MINUS_OPERATION, it) })
+        .or(-minus and parser(ArithmeticsEvaluator::term) map { MST.Unary(GroupOps.MINUS_OPERATION, it) })
         .or(-lpar and parser(ArithmeticsEvaluator::subSumChain) and -rpar)
 
     private val powChain: Parser<MST> by leftAssociative(term = term, operator = pow) { a, _, b ->
@@ -72,9 +72,9 @@ public object ArithmeticsEvaluator : Grammar<MST>() {
         operator = div or mul use TokenMatch::type
     ) { a, op, b ->
         if (op == div)
-            MST.Binary(FieldOperations.DIV_OPERATION, a, b)
+            MST.Binary(FieldOps.DIV_OPERATION, a, b)
         else
-            MST.Binary(RingOperations.TIMES_OPERATION, a, b)
+            MST.Binary(RingOps.TIMES_OPERATION, a, b)
     }
 
     private val subSumChain: Parser<MST> by leftAssociative(
@@ -82,9 +82,9 @@ public object ArithmeticsEvaluator : Grammar<MST>() {
         operator = plus or minus use TokenMatch::type
     ) { a, op, b ->
         if (op == plus)
-            MST.Binary(GroupOperations.PLUS_OPERATION, a, b)
+            MST.Binary(GroupOps.PLUS_OPERATION, a, b)
         else
-            MST.Binary(GroupOperations.MINUS_OPERATION, a, b)
+            MST.Binary(GroupOps.MINUS_OPERATION, a, b)
     }
 
     override val rootParser: Parser<MST> by subSumChain

kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/features.kt

@@ -39,7 +39,7 @@ public val PrintNumeric: RenderFeature = RenderFeature { _, node ->
 @UnstableKMathAPI
 private fun printSignedNumberString(s: String): MathSyntax = if (s.startsWith('-'))
     UnaryMinusSyntax(
-        operation = GroupOperations.MINUS_OPERATION,
+        operation = GroupOps.MINUS_OPERATION,
         operand = OperandSyntax(
             operand = NumberSyntax(string = s.removePrefix("-")),
             parentheses = true,
@@ -72,7 +72,7 @@ public class PrettyPrintFloats(public val types: Set<KClass<out Number>>) : Rend
             val exponent = afterE.toDouble().toString().removeSuffix(".0")
 
             return MultiplicationSyntax(
-                operation = RingOperations.TIMES_OPERATION,
+                operation = RingOps.TIMES_OPERATION,
                 left = OperandSyntax(operand = NumberSyntax(significand), parentheses = true),
                 right = OperandSyntax(
                     operand = SuperscriptSyntax(
@@ -91,7 +91,7 @@ public class PrettyPrintFloats(public val types: Set<KClass<out Number>>) : Rend
 
             if (toString.startsWith('-'))
                 return UnaryMinusSyntax(
-                    operation = GroupOperations.MINUS_OPERATION,
+                    operation = GroupOps.MINUS_OPERATION,
                     operand = OperandSyntax(operand = infty, parentheses = true),
                 )
 
@@ -211,9 +211,9 @@ public class BinaryPlus(operations: Collection<String>?) : Binary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.PLUS_OPERATION].
+         * The default instance configured with [GroupOps.PLUS_OPERATION].
          */
-        public val Default: BinaryPlus = BinaryPlus(setOf(GroupOperations.PLUS_OPERATION))
+        public val Default: BinaryPlus = BinaryPlus(setOf(GroupOps.PLUS_OPERATION))
     }
 }
 
@@ -233,9 +233,9 @@ public class BinaryMinus(operations: Collection<String>?) : Binary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.MINUS_OPERATION].
+         * The default instance configured with [GroupOps.MINUS_OPERATION].
          */
-        public val Default: BinaryMinus = BinaryMinus(setOf(GroupOperations.MINUS_OPERATION))
+        public val Default: BinaryMinus = BinaryMinus(setOf(GroupOps.MINUS_OPERATION))
     }
 }
 
@@ -253,9 +253,9 @@ public class UnaryPlus(operations: Collection<String>?) : Unary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.PLUS_OPERATION].
+         * The default instance configured with [GroupOps.PLUS_OPERATION].
          */
-        public val Default: UnaryPlus = UnaryPlus(setOf(GroupOperations.PLUS_OPERATION))
+        public val Default: UnaryPlus = UnaryPlus(setOf(GroupOps.PLUS_OPERATION))
     }
 }
 
@@ -273,9 +273,9 @@ public class UnaryMinus(operations: Collection<String>?) : Unary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [GroupOperations.MINUS_OPERATION].
+         * The default instance configured with [GroupOps.MINUS_OPERATION].
          */
-        public val Default: UnaryMinus = UnaryMinus(setOf(GroupOperations.MINUS_OPERATION))
+        public val Default: UnaryMinus = UnaryMinus(setOf(GroupOps.MINUS_OPERATION))
     }
 }
 
@@ -295,9 +295,9 @@ public class Fraction(operations: Collection<String>?) : Binary(operations) {
 
     public companion object {
         /**
-         * The default instance configured with [FieldOperations.DIV_OPERATION].
+         * The default instance configured with [FieldOps.DIV_OPERATION].
          */
-        public val Default: Fraction = Fraction(setOf(FieldOperations.DIV_OPERATION))
+        public val Default: Fraction = Fraction(setOf(FieldOps.DIV_OPERATION))
     }
 }
 
@@ -422,9 +422,9 @@ public class Multiplication(operations: Collection<String>?) : Binary(operations
 
     public companion object {
         /**
-         * The default instance configured with [RingOperations.TIMES_OPERATION].
+         * The default instance configured with [RingOps.TIMES_OPERATION].
          */
-        public val Default: Multiplication = Multiplication(setOf(RingOperations.TIMES_OPERATION))
+        public val Default: Multiplication = Multiplication(setOf(RingOps.TIMES_OPERATION))
     }
 }
 

kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/rendering/phases.kt

@@ -7,10 +7,10 @@ package space.kscience.kmath.ast.rendering
 
 import space.kscience.kmath.ast.rendering.FeaturedMathRendererWithPostProcess.PostProcessPhase
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.FieldOperations
+import space.kscience.kmath.operations.FieldOps
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import space.kscience.kmath.operations.PowerOperations
-import space.kscience.kmath.operations.RingOperations
+import space.kscience.kmath.operations.RingOps
 
 /**
  * Removes unnecessary times (×) symbols from [MultiplicationSyntax].
@@ -306,10 +306,10 @@ public class SimplifyParentheses(public val precedenceFunction: (MathSyntax) ->
 
                 is BinarySyntax -> when (it.operation) {
                     PowerOperations.POW_OPERATION -> 1
-                    RingOperations.TIMES_OPERATION -> 3
+                    RingOps.TIMES_OPERATION -> 3
-                    FieldOperations.DIV_OPERATION -> 3
+                    FieldOps.DIV_OPERATION -> 3
-                    GroupOperations.MINUS_OPERATION -> 4
+                    GroupOps.MINUS_OPERATION -> 4
-                    GroupOperations.PLUS_OPERATION -> 4
+                    GroupOps.PLUS_OPERATION -> 4
                     else -> 0
                 }
 

kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestLatex.kt

@@ -7,7 +7,7 @@ package space.kscience.kmath.ast.rendering
 
 import space.kscience.kmath.ast.rendering.TestUtils.testLatex
 import space.kscience.kmath.expressions.MST
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import kotlin.test.Test
 
 internal class TestLatex {
@@ -36,7 +36,7 @@ internal class TestLatex {
     fun unaryOperator() = testLatex("sin(1)", "\\operatorname{sin}\\,\\left(1\\right)")
 
     @Test
-    fun unaryPlus() = testLatex(MST.Unary(GroupOperations.PLUS_OPERATION, MST.Numeric(1)), "+1")
+    fun unaryPlus() = testLatex(MST.Unary(GroupOps.PLUS_OPERATION, MST.Numeric(1)), "+1")
 
     @Test
     fun unaryMinus() = testLatex("-x", "-x")

kmath-ast/src/commonTest/kotlin/space/kscience/kmath/ast/rendering/TestMathML.kt

@@ -7,7 +7,7 @@ package space.kscience.kmath.ast.rendering
 
 import space.kscience.kmath.ast.rendering.TestUtils.testMathML
 import space.kscience.kmath.expressions.MST
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import kotlin.test.Test
 
 internal class TestMathML {
@@ -47,7 +47,7 @@ internal class TestMathML {
 
     @Test
     fun unaryPlus() =
-        testMathML(MST.Unary(GroupOperations.PLUS_OPERATION, MST.Numeric(1)), "<mo>+</mo><mn>1</mn>")
+        testMathML(MST.Unary(GroupOps.PLUS_OPERATION, MST.Numeric(1)), "<mo>+</mo><mn>1</mn>")
 
     @Test
     fun unaryMinus() = testMathML("-x", "<mo>-</mo><mi>x</mi>")

kmath-ast/src/jsMain/kotlin/space/kscience/kmath/wasm/internal/WasmBuilder.kt

@@ -108,8 +108,8 @@ internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double>(f64, DoubleF
     override fun visitNumeric(mst: Numeric): ExpressionRef = ctx.f64.const(mst.value)
 
     override fun visitUnary(mst: Unary): ExpressionRef = when (mst.operation) {
-        GroupOperations.MINUS_OPERATION -> ctx.f64.neg(visit(mst.value))
+        GroupOps.MINUS_OPERATION -> ctx.f64.neg(visit(mst.value))
-        GroupOperations.PLUS_OPERATION -> visit(mst.value)
+        GroupOps.PLUS_OPERATION -> visit(mst.value)
         PowerOperations.SQRT_OPERATION -> ctx.f64.sqrt(visit(mst.value))
         TrigonometricOperations.SIN_OPERATION -> ctx.call("sin", arrayOf(visit(mst.value)), f64)
         TrigonometricOperations.COS_OPERATION -> ctx.call("cos", arrayOf(visit(mst.value)), f64)
@@ -129,10 +129,10 @@ internal class DoubleWasmBuilder(target: MST) : WasmBuilder<Double>(f64, DoubleF
     }
 
     override fun visitBinary(mst: Binary): ExpressionRef = when (mst.operation) {
-        GroupOperations.PLUS_OPERATION -> ctx.f64.add(visit(mst.left), visit(mst.right))
+        GroupOps.PLUS_OPERATION -> ctx.f64.add(visit(mst.left), visit(mst.right))
-        GroupOperations.MINUS_OPERATION -> ctx.f64.sub(visit(mst.left), visit(mst.right))
+        GroupOps.MINUS_OPERATION -> ctx.f64.sub(visit(mst.left), visit(mst.right))
-        RingOperations.TIMES_OPERATION -> ctx.f64.mul(visit(mst.left), visit(mst.right))
+        RingOps.TIMES_OPERATION -> ctx.f64.mul(visit(mst.left), visit(mst.right))
-        FieldOperations.DIV_OPERATION -> ctx.f64.div(visit(mst.left), visit(mst.right))
+        FieldOps.DIV_OPERATION -> ctx.f64.div(visit(mst.left), visit(mst.right))
         PowerOperations.POW_OPERATION -> ctx.call("pow", arrayOf(visit(mst.left), visit(mst.right)), f64)
         else -> super.visitBinary(mst)
     }
@@ -142,15 +142,15 @@ internal class IntWasmBuilder(target: MST) : WasmBuilder<Int>(i32, IntRing, targ
     override fun visitNumeric(mst: Numeric): ExpressionRef = ctx.i32.const(mst.value)
 
     override fun visitUnary(mst: Unary): ExpressionRef = when (mst.operation) {
-        GroupOperations.MINUS_OPERATION -> ctx.i32.sub(ctx.i32.const(0), visit(mst.value))
+        GroupOps.MINUS_OPERATION -> ctx.i32.sub(ctx.i32.const(0), visit(mst.value))
-        GroupOperations.PLUS_OPERATION -> visit(mst.value)
+        GroupOps.PLUS_OPERATION -> visit(mst.value)
         else -> super.visitUnary(mst)
     }
 
     override fun visitBinary(mst: Binary): ExpressionRef = when (mst.operation) {
-        GroupOperations.PLUS_OPERATION -> ctx.i32.add(visit(mst.left), visit(mst.right))
+        GroupOps.PLUS_OPERATION -> ctx.i32.add(visit(mst.left), visit(mst.right))
-        GroupOperations.MINUS_OPERATION -> ctx.i32.sub(visit(mst.left), visit(mst.right))
+        GroupOps.MINUS_OPERATION -> ctx.i32.sub(visit(mst.left), visit(mst.right))
-        RingOperations.TIMES_OPERATION -> ctx.i32.mul(visit(mst.left), visit(mst.right))
+        RingOps.TIMES_OPERATION -> ctx.i32.mul(visit(mst.left), visit(mst.right))
         else -> super.visitBinary(mst)
     }
 }

kmath-commons/src/main/kotlin/space/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt

@@ -9,7 +9,7 @@ import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 import space.kscience.kmath.expressions.*
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 
 /**
  * A field over commons-math [DerivativeStructure].
@@ -22,7 +22,7 @@ public class DerivativeStructureField(
     public val order: Int,
     bindings: Map<Symbol, Double>,
 ) : ExtendedField<DerivativeStructure>, ExpressionAlgebra<Double, DerivativeStructure>,
-    NumbersAddOperations<DerivativeStructure> {
+    NumbersAddOps<DerivativeStructure> {
     public val numberOfVariables: Int = bindings.size
 
     override val zero: DerivativeStructure by lazy { DerivativeStructure(numberOfVariables, order) }

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

@@ -52,7 +52,7 @@ private val PI_DIV_2 = Complex(PI / 2, 0)
 public object ComplexField :
     ExtendedField<Complex>,
     Norm<Complex, Complex>,
-    NumbersAddOperations<Complex>,
+    NumbersAddOps<Complex>,
     ScaleOperations<Complex> {
 
     override val zero: Complex = 0.0.toComplex()
@@ -216,7 +216,6 @@ public data class Complex(val re: Double, val im: Double) {
 
 public val Complex.Companion.algebra: ComplexField get() = ComplexField
 
-
 /**
  * Creates a complex number with real part equal to this real.
  *

kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/ComplexFieldND.kt

@@ -6,13 +6,8 @@
 package space.kscience.kmath.complex
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.nd.BufferND
+import space.kscience.kmath.nd.*
-import space.kscience.kmath.nd.BufferedFieldND
+import space.kscience.kmath.operations.*
-import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.operations.BufferField
-import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
-import space.kscience.kmath.operations.bufferAlgebra
 import space.kscience.kmath.structures.Buffer
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
@@ -22,100 +17,61 @@ import kotlin.contracts.contract
  * An optimized nd-field for complex numbers
  */
 @OptIn(UnstableKMathAPI::class)
-public class ComplexFieldND(
+public sealed class ComplexFieldOpsND : BufferedFieldOpsND<Complex, ComplexField>(ComplexField.bufferAlgebra),
-    shape: IntArray,
+    ScaleOperations<StructureND<Complex>>, ExtendedFieldOps<StructureND<Complex>> {
-) : BufferedFieldND<Complex, ComplexField>(shape, ComplexField, Buffer.Companion::complex),
-    NumbersAddOperations<StructureND<Complex>>,
-    ExtendedField<StructureND<Complex>> {
 
-    override val zero: BufferND<Complex> by lazy { produce { zero } }
+    override fun StructureND<Complex>.toBufferND(): BufferND<Complex> = when (this) {
-    override val one: BufferND<Complex> by lazy { produce { one } }
+        is BufferND -> this
-
+        else -> {
-    override fun number(value: Number): BufferND<Complex> {
+            val indexer = indexerBuilder(shape)
-        val d = value.toComplex() // minimize conversions
+            BufferND(indexer, Buffer.complex(indexer.linearSize) { offset -> get(indexer.index(offset)) })
-        return produce { d }
+        }
     }
 
-//
+    //TODO do specialization
-//    @Suppress("OVERRIDE_BY_INLINE")
-//    override inline fun map(
-//        arg: AbstractNDBuffer<Double>,
-//        transform: DoubleField.(Double) -> Double,
-//    ): RealNDElement {
-//        check(arg)
-//        val array = RealBuffer(arg.strides.linearSize) { offset -> DoubleField.transform(arg.buffer[offset]) }
-//        return BufferedNDFieldElement(this, array)
-//    }
-//
-//    @Suppress("OVERRIDE_BY_INLINE")
-//    override inline fun produce(initializer: DoubleField.(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: DoubleField.(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: DoubleField.(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: StructureND<Complex>, pow: Number): BufferND<Complex> = arg.map { power(it, pow) }
+    override fun scale(a: StructureND<Complex>, value: Double): BufferND<Complex> =
+        mapInline(a.toBufferND()) { it * value }
 
-    override fun exp(arg: StructureND<Complex>): BufferND<Complex> = arg.map { exp(it) }
+    override fun power(arg: StructureND<Complex>, pow: Number): BufferND<Complex> =
+        mapInline(arg.toBufferND()) { power(it, pow) }
 
-    override fun ln(arg: StructureND<Complex>): BufferND<Complex> = arg.map { ln(it) }
+    override fun exp(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { exp(it) }
+    override fun ln(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { ln(it) }
 
-    override fun sin(arg: StructureND<Complex>): BufferND<Complex> = arg.map { sin(it) }
+    override fun sin(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { sin(it) }
-    override fun cos(arg: StructureND<Complex>): BufferND<Complex> = arg.map { cos(it) }
+    override fun cos(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { cos(it) }
-    override fun tan(arg: StructureND<Complex>): BufferND<Complex> = arg.map { tan(it) }
+    override fun tan(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { tan(it) }
-    override fun asin(arg: StructureND<Complex>): BufferND<Complex> = arg.map { asin(it) }
+    override fun asin(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { asin(it) }
-    override fun acos(arg: StructureND<Complex>): BufferND<Complex> = arg.map { acos(it) }
+    override fun acos(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { acos(it) }
-    override fun atan(arg: StructureND<Complex>): BufferND<Complex> = arg.map { atan(it) }
+    override fun atan(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { atan(it) }
 
-    override fun sinh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { sinh(it) }
+    override fun sinh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { sinh(it) }
-    override fun cosh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { cosh(it) }
+    override fun cosh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { cosh(it) }
-    override fun tanh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { tanh(it) }
+    override fun tanh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { tanh(it) }
-    override fun asinh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { asinh(it) }
+    override fun asinh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { asinh(it) }
-    override fun acosh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { acosh(it) }
+    override fun acosh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { acosh(it) }
-    override fun atanh(arg: StructureND<Complex>): BufferND<Complex> = arg.map { atanh(it) }
+    override fun atanh(arg: StructureND<Complex>): BufferND<Complex> = mapInline(arg.toBufferND()) { atanh(it) }
-}
 
-
+    public companion object : ComplexFieldOpsND()
-/**
- * Fast element production using function inlining
- */
-public inline fun BufferedFieldND<Complex, ComplexField>.produceInline(initializer: ComplexField.(Int) -> Complex): BufferND<Complex> {
-    contract { callsInPlace(initializer, InvocationKind.EXACTLY_ONCE) }
-    val buffer = Buffer.complex(strides.linearSize) { offset -> ComplexField.initializer(offset) }
-    return BufferND(strides, buffer)
 }
 
 @UnstableKMathAPI
-public fun ComplexField.bufferAlgebra(size: Int): BufferField<Complex, ComplexField> =
+public val ComplexField.bufferAlgebra: BufferFieldOps<Complex, ComplexField>
-    bufferAlgebra(Buffer.Companion::complex, size)
+    get() = bufferAlgebra(Buffer.Companion::complex)
+
+
+@OptIn(UnstableKMathAPI::class)
+public class ComplexFieldND(override val shape: Shape) :
+    ComplexFieldOpsND(), FieldND<Complex, ComplexField>, NumbersAddOps<StructureND<Complex>> {
+
+    override fun number(value: Number): BufferND<Complex> {
+        val d = value.toDouble() // minimize conversions
+        return produce(shape) { d.toComplex() }
+    }
+}
+
+public val ComplexField.ndAlgebra: ComplexFieldOpsND get() = ComplexFieldOpsND
 
 public fun ComplexField.ndAlgebra(vararg shape: Int): ComplexFieldND = ComplexFieldND(shape)
 

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

@@ -44,7 +44,7 @@ public val Quaternion.r: Double
  */
 @OptIn(UnstableKMathAPI::class)
 public object QuaternionField : Field<Quaternion>, Norm<Quaternion, Quaternion>, PowerOperations<Quaternion>,
-    ExponentialOperations<Quaternion>, NumbersAddOperations<Quaternion>, ScaleOperations<Quaternion> {
+    ExponentialOperations<Quaternion>, NumbersAddOps<Quaternion>, ScaleOperations<Quaternion> {
     override val zero: Quaternion = 0.toQuaternion()
     override val one: Quaternion = 1.toQuaternion()
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/FunctionalExpressionAlgebra.kt

@@ -52,13 +52,13 @@ public open class FunctionalExpressionGroup<T, out A : Group<T>>(
     override val zero: Expression<T> get() = const(algebra.zero)
 
     override fun Expression<T>.unaryMinus(): Expression<T> =
-        unaryOperation(GroupOperations.MINUS_OPERATION, this)
+        unaryOperation(GroupOps.MINUS_OPERATION, this)
 
     /**
      * Builds an Expression of addition of two another expressions.
      */
     override fun add(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperation(GroupOperations.PLUS_OPERATION, a, b)
+        binaryOperation(GroupOps.PLUS_OPERATION, a, b)
 
 //    /**
 //     * Builds an Expression of multiplication of expression by number.
@@ -89,7 +89,7 @@ public open class FunctionalExpressionRing<T, out A : Ring<T>>(
      * Builds an Expression of multiplication of two expressions.
      */
     override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, b)
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, b)
 
     public operator fun Expression<T>.times(arg: T): Expression<T> = this * const(arg)
     public operator fun T.times(arg: Expression<T>): Expression<T> = arg * this
@@ -108,7 +108,7 @@ public open class FunctionalExpressionField<T, out A : Field<T>>(
      * Builds an Expression of division an expression by another one.
      */
     override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> =
-        binaryOperationFunction(FieldOperations.DIV_OPERATION)(a, b)
+        binaryOperationFunction(FieldOps.DIV_OPERATION)(a, b)
 
     public operator fun Expression<T>.div(arg: T): Expression<T> = this / const(arg)
     public operator fun T.div(arg: Expression<T>): Expression<T> = arg / this

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/MstAlgebra.kt

@@ -31,18 +31,18 @@ public object MstGroup : Group<MST>, NumericAlgebra<MST>, ScaleOperations<MST> {
 
     override fun number(value: Number): MST.Numeric = MstNumericAlgebra.number(value)
     override fun bindSymbolOrNull(value: String): Symbol = MstNumericAlgebra.bindSymbolOrNull(value)
-    override fun add(a: MST, b: MST): MST.Binary = binaryOperationFunction(GroupOperations.PLUS_OPERATION)(a, b)
+    override fun add(a: MST, b: MST): MST.Binary = binaryOperationFunction(GroupOps.PLUS_OPERATION)(a, b)
     override operator fun MST.unaryPlus(): MST.Unary =
-        unaryOperationFunction(GroupOperations.PLUS_OPERATION)(this)
+        unaryOperationFunction(GroupOps.PLUS_OPERATION)(this)
 
     override operator fun MST.unaryMinus(): MST.Unary =
-        unaryOperationFunction(GroupOperations.MINUS_OPERATION)(this)
+        unaryOperationFunction(GroupOps.MINUS_OPERATION)(this)
 
     override operator fun MST.minus(b: MST): MST.Binary =
-        binaryOperationFunction(GroupOperations.MINUS_OPERATION)(this, b)
+        binaryOperationFunction(GroupOps.MINUS_OPERATION)(this, b)
 
     override fun scale(a: MST, value: Double): MST.Binary =
-        binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, number(value))
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, number(value))
 
     override fun binaryOperationFunction(operation: String): (left: MST, right: MST) -> MST.Binary =
         MstNumericAlgebra.binaryOperationFunction(operation)
@@ -56,7 +56,7 @@ public object MstGroup : Group<MST>, NumericAlgebra<MST>, ScaleOperations<MST> {
  */
 @Suppress("OVERRIDE_BY_INLINE")
 @OptIn(UnstableKMathAPI::class)
-public object MstRing : Ring<MST>, NumbersAddOperations<MST>, ScaleOperations<MST> {
+public object MstRing : Ring<MST>, NumbersAddOps<MST>, ScaleOperations<MST> {
     override inline val zero: MST.Numeric get() = MstGroup.zero
     override val one: MST.Numeric = number(1.0)
 
@@ -65,10 +65,10 @@ public object MstRing : Ring<MST>, NumbersAddOperations<MST>, ScaleOperations<MS
     override fun add(a: MST, b: MST): MST.Binary = MstGroup.add(a, b)
 
     override fun scale(a: MST, value: Double): MST.Binary =
-        MstGroup.binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, MstGroup.number(value))
+        MstGroup.binaryOperationFunction(RingOps.TIMES_OPERATION)(a, MstGroup.number(value))
 
     override fun multiply(a: MST, b: MST): MST.Binary =
-        binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, b)
+        binaryOperationFunction(RingOps.TIMES_OPERATION)(a, b)
 
     override operator fun MST.unaryPlus(): MST.Unary = MstGroup { +this@unaryPlus }
     override operator fun MST.unaryMinus(): MST.Unary = MstGroup { -this@unaryMinus }
@@ -86,7 +86,7 @@ public object MstRing : Ring<MST>, NumbersAddOperations<MST>, ScaleOperations<MS
  */
 @Suppress("OVERRIDE_BY_INLINE")
 @OptIn(UnstableKMathAPI::class)
-public object MstField : Field<MST>, NumbersAddOperations<MST>, ScaleOperations<MST> {
+public object MstField : Field<MST>, NumbersAddOps<MST>, ScaleOperations<MST> {
     override inline val zero: MST.Numeric get() = MstRing.zero
     override inline val one: MST.Numeric get() = MstRing.one
 
@@ -95,11 +95,11 @@ public object MstField : Field<MST>, NumbersAddOperations<MST>, ScaleOperations<
     override fun add(a: MST, b: MST): MST.Binary = MstRing.add(a, b)
 
     override fun scale(a: MST, value: Double): MST.Binary =
-        MstGroup.binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, MstGroup.number(value))
+        MstGroup.binaryOperationFunction(RingOps.TIMES_OPERATION)(a, MstGroup.number(value))
 
     override fun multiply(a: MST, b: MST): MST.Binary = MstRing.multiply(a, b)
     override fun divide(a: MST, b: MST): MST.Binary =
-        binaryOperationFunction(FieldOperations.DIV_OPERATION)(a, b)
+        binaryOperationFunction(FieldOps.DIV_OPERATION)(a, b)
 
     override operator fun MST.unaryPlus(): MST.Unary = MstRing { +this@unaryPlus }
     override operator fun MST.unaryMinus(): MST.Unary = MstRing { -this@unaryMinus }
@@ -138,7 +138,7 @@ public object MstExtendedField : ExtendedField<MST>, NumericAlgebra<MST> {
     override fun sqrt(arg: MST): MST = unaryOperationFunction(PowerOperations.SQRT_OPERATION)(arg)
 
     override fun scale(a: MST, value: Double): MST =
-        binaryOperation(GroupOperations.PLUS_OPERATION, a, number(value))
+        binaryOperation(GroupOps.PLUS_OPERATION, a, number(value))
 
     override fun multiply(a: MST, b: MST): MST.Binary = MstField.multiply(a, b)
     override fun divide(a: MST, b: MST): MST.Binary = MstField.divide(a, b)

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/SimpleAutoDiff.kt

@@ -59,7 +59,7 @@ public fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T
 public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
     public val context: F,
     bindings: Map<Symbol, T>,
-) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>>, NumbersAddOperations<AutoDiffValue<T>> {
+) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>>, NumbersAddOps<AutoDiffValue<T>> {
     override val zero: AutoDiffValue<T> get() = const(context.zero)
     override val one: AutoDiffValue<T> get() = const(context.one)
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt

@@ -6,12 +6,10 @@
 package space.kscience.kmath.linear
 
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.BufferedRingND
+import space.kscience.kmath.nd.BufferedRingOpsND
 import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.nd.asND
-import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.operations.*
-import space.kscience.kmath.operations.Ring
-import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import space.kscience.kmath.structures.VirtualBuffer
@@ -19,31 +17,28 @@ import space.kscience.kmath.structures.indices
 
 
 public class BufferedLinearSpace<T, out A : Ring<T>>(
-    override val elementAlgebra: A,
+    private val bufferAlgebra: BufferAlgebra<T, A>
-    private val bufferFactory: BufferFactory<T>,
 ) : LinearSpace<T, A> {
+    override val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
 
-    private fun ndRing(
+    private val ndAlgebra = BufferedRingOpsND(bufferAlgebra)
-        rows: Int,
-        cols: Int,
-    ): BufferedRingND<T, A> = elementAlgebra.ndAlgebra(bufferFactory, rows, cols)
 
     override fun buildMatrix(rows: Int, columns: Int, initializer: A.(i: Int, j: Int) -> T): Matrix<T> =
-        ndRing(rows, columns).produce { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
+        ndAlgebra.produce(intArrayOf(rows, columns)) { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
 
     override fun buildVector(size: Int, initializer: A.(Int) -> T): Point<T> =
-        bufferFactory(size) { elementAlgebra.initializer(it) }
+        bufferAlgebra.buffer(size) { elementAlgebra.initializer(it) }
 
-    override fun Matrix<T>.unaryMinus(): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.unaryMinus(): Matrix<T> = ndAlgebra {
         asND().map { -it }.as2D()
     }
 
-    override fun Matrix<T>.plus(other: Matrix<T>): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.plus(other: Matrix<T>): Matrix<T> = ndAlgebra {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::plus. Expected $shape but found ${other.shape}" }
         asND().plus(other.asND()).as2D()
     }
 
-    override fun Matrix<T>.minus(other: Matrix<T>): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.minus(other: Matrix<T>): Matrix<T> = ndAlgebra {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::minus. Expected $shape but found ${other.shape}" }
         asND().minus(other.asND()).as2D()
     }
@@ -88,11 +83,11 @@ public class BufferedLinearSpace<T, out A : Ring<T>>(
         }
     }
 
-    override fun Matrix<T>.times(value: T): Matrix<T> = ndRing(rowNum, colNum).run {
+    override fun Matrix<T>.times(value: T): Matrix<T> = ndAlgebra {
         asND().map { it * value }.as2D()
     }
 }
 
 
 public fun <T, A : Ring<T>> A.linearSpace(bufferFactory: BufferFactory<T>): BufferedLinearSpace<T, A> =
-    BufferedLinearSpace(this, bufferFactory)
+    BufferedLinearSpace(BufferRingOps(this, bufferFactory))

kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/DoubleLinearSpace.kt

@@ -6,11 +6,12 @@
 package space.kscience.kmath.linear
 
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.DoubleFieldND
+import space.kscience.kmath.nd.DoubleFieldOpsND
 import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.nd.asND
-import space.kscience.kmath.operations.DoubleBufferOperations
+import space.kscience.kmath.operations.DoubleBufferOps
 import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.DoubleBuffer
 
@@ -18,30 +19,27 @@ public object DoubleLinearSpace : LinearSpace<Double, DoubleField> {
 
     override val elementAlgebra: DoubleField get() = DoubleField
 
-    private fun ndRing(
-        rows: Int,
-        cols: Int,
-    ): DoubleFieldND = DoubleFieldND(intArrayOf(rows, cols))
-
     override fun buildMatrix(
         rows: Int,
         columns: Int,
         initializer: DoubleField.(i: Int, j: Int) -> Double
-    ): Matrix<Double> = ndRing(rows, columns).produce { (i, j) -> DoubleField.initializer(i, j) }.as2D()
+    ): Matrix<Double> = DoubleFieldOpsND.produce(intArrayOf(rows, columns)) { (i, j) ->
+        DoubleField.initializer(i, j)
+    }.as2D()
 
     override fun buildVector(size: Int, initializer: DoubleField.(Int) -> Double): DoubleBuffer =
         DoubleBuffer(size) { DoubleField.initializer(it) }
 
-    override fun Matrix<Double>.unaryMinus(): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.unaryMinus(): Matrix<Double> = DoubleFieldOpsND {
         asND().map { -it }.as2D()
     }
 
-    override fun Matrix<Double>.plus(other: Matrix<Double>): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.plus(other: Matrix<Double>): Matrix<Double> = DoubleFieldOpsND {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::plus. Expected $shape but found ${other.shape}" }
         asND().plus(other.asND()).as2D()
     }
 
-    override fun Matrix<Double>.minus(other: Matrix<Double>): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.minus(other: Matrix<Double>): Matrix<Double> = DoubleFieldOpsND {
         require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::minus. Expected $shape but found ${other.shape}" }
         asND().minus(other.asND()).as2D()
     }
@@ -84,23 +82,23 @@ public object DoubleLinearSpace : LinearSpace<Double, DoubleField> {
 
     }
 
-    override fun Matrix<Double>.times(value: Double): Matrix<Double> = ndRing(rowNum, colNum).run {
+    override fun Matrix<Double>.times(value: Double): Matrix<Double> = DoubleFieldOpsND {
         asND().map { it * value }.as2D()
     }
 
-    public override fun Point<Double>.plus(other: Point<Double>): DoubleBuffer = DoubleBufferOperations.run {
+    public override fun Point<Double>.plus(other: Point<Double>): DoubleBuffer = DoubleBufferOps.run {
         this@plus + other
     }
 
-    public override fun Point<Double>.minus(other: Point<Double>): DoubleBuffer = DoubleBufferOperations.run {
+    public override fun Point<Double>.minus(other: Point<Double>): DoubleBuffer = DoubleBufferOps.run {
         this@minus - other
     }
 
-    public override fun Point<Double>.times(value: Double): DoubleBuffer = DoubleBufferOperations.run {
+    public override fun Point<Double>.times(value: Double): DoubleBuffer = DoubleBufferOps.run {
         scale(this@times, value)
     }
 
-    public operator fun Point<Double>.div(value: Double): DoubleBuffer = DoubleBufferOperations.run {
+    public operator fun Point<Double>.div(value: Double): DoubleBuffer = DoubleBufferOps.run {
         scale(this@div, 1.0 / value)
     }
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt

@@ -10,6 +10,7 @@ import space.kscience.kmath.nd.MutableStructure2D
 import space.kscience.kmath.nd.Structure2D
 import space.kscience.kmath.nd.StructureFeature
 import space.kscience.kmath.nd.as1D
+import space.kscience.kmath.operations.BufferRingOps
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.invoke
@@ -188,7 +189,7 @@ public interface LinearSpace<T, out A : Ring<T>> {
         public fun <T : Any, A : Ring<T>> buffered(
             algebra: A,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
-        ): LinearSpace<T, A> = BufferedLinearSpace(algebra, bufferFactory)
+        ): LinearSpace<T, A> = BufferedLinearSpace(BufferRingOps(algebra, bufferFactory))
 
         @Deprecated("use DoubleField.linearSpace")
         public val double: LinearSpace<Double, DoubleField> = buffered(DoubleField, ::DoubleBuffer)

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/AlgebraND.kt

@@ -7,7 +7,6 @@ package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.*
-import space.kscience.kmath.structures.*
 import kotlin.reflect.KClass
 
 /**
@@ -19,6 +18,14 @@ import kotlin.reflect.KClass
 public class ShapeMismatchException(public val expected: IntArray, public val actual: IntArray) :
     RuntimeException("Shape ${actual.contentToString()} doesn't fit in expected shape ${expected.contentToString()}.")
 
+public typealias Shape = IntArray
+
+public fun Shape(shapeFirst: Int, vararg shapeRest: Int): Shape = intArrayOf(shapeFirst, *shapeRest)
+
+public interface WithShape {
+    public val shape: Shape
+}
+
 /**
  * The base interface for all ND-algebra implementations.
  *
@@ -26,20 +33,15 @@ public class ShapeMismatchException(public val expected: IntArray, public val ac
  * @param C the type of the element context.
  */
 public interface AlgebraND<T, out C : Algebra<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
+    public val elementAlgebra: C
 
     /**
      * Produces a new NDStructure using given initializer function.
      */
-    public fun produce(initializer: C.(IntArray) -> T): StructureND<T>
+    public fun produce(shape: Shape, initializer: C.(IntArray) -> T): StructureND<T>
 
     /**
      * Maps elements from one structure to another one by applying [transform] to them.
@@ -54,7 +56,7 @@ public interface AlgebraND<T, out C : Algebra<T>> {
     /**
      * Combines two structures into one.
      */
-    public fun combine(a: StructureND<T>, b: StructureND<T>, transform: C.(T, T) -> T): StructureND<T>
+    public fun zip(left: StructureND<T>, right: StructureND<T>, transform: C.(T, T) -> T): StructureND<T>
 
     /**
      * Element-wise invocation of function working on [T] on a [StructureND].
@@ -77,7 +79,6 @@ public interface AlgebraND<T, out C : Algebra<T>> {
     public companion object
 }
 
-
 /**
  * Get a feature of the structure in this scope. Structure features take precedence other context features.
  *
@@ -89,37 +90,13 @@ public interface AlgebraND<T, out C : Algebra<T>> {
 public inline fun <T : Any, reified F : StructureFeature> AlgebraND<T, *>.getFeature(structure: StructureND<T>): F? =
     getFeature(structure, F::class)
 
-/**
- * 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 : Algebra<T>> AlgebraND<T, C>.checkShape(vararg structures: StructureND<T>): Array<out StructureND<T>> =
-    structures
-        .map(StructureND<T>::shape)
-        .singleOrNull { !shape.contentEquals(it) }
-        ?.let<IntArray, Array<out StructureND<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 : Algebra<T>> AlgebraND<T, C>.checkShape(element: StructureND<T>): StructureND<T> {
-    if (!element.shape.contentEquals(shape)) throw ShapeMismatchException(shape, element.shape)
-    return element
-}
-
 /**
  * Space of [StructureND].
  *
  * @param T the type of the element contained in ND structure.
- * @param S the type of group over structure elements.
+ * @param A the type of group over structure elements.
  */
-public interface GroupND<T, out S : Group<T>> : Group<StructureND<T>>, AlgebraND<T, S> {
+public interface GroupOpsND<T, out A : GroupOps<T>> : GroupOps<StructureND<T>>, AlgebraND<T, A> {
     /**
      * Element-wise addition.
      *
@@ -128,7 +105,7 @@ public interface GroupND<T, out S : Group<T>> : Group<StructureND<T>>, AlgebraND
      * @return the sum.
      */
     override fun add(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        combine(a, b) { aValue, bValue -> add(aValue, bValue) }
+        zip(a, b) { aValue, bValue -> add(aValue, bValue) }
 
     // TODO move to extensions after KEEP-176
 
@@ -171,13 +148,17 @@ public interface GroupND<T, out S : Group<T>> : Group<StructureND<T>>, AlgebraND
     public companion object
 }
 
+public interface GroupND<T, out A : Group<T>> : Group<StructureND<T>>, GroupOpsND<T, A>, WithShape {
+    override val zero: StructureND<T> get() = produce(shape) { elementAlgebra.zero }
+}
+
 /**
  * Ring of [StructureND].
  *
  * @param T the type of the element contained in ND structure.
- * @param R the type of ring over structure elements.
+ * @param A the type of ring over structure elements.
  */
-public interface RingND<T, out R : Ring<T>> : Ring<StructureND<T>>, GroupND<T, R> {
+public interface RingOpsND<T, out A : RingOps<T>> : RingOps<StructureND<T>>, GroupOpsND<T, A> {
     /**
      * Element-wise multiplication.
      *
@@ -186,7 +167,7 @@ public interface RingND<T, out R : Ring<T>> : Ring<StructureND<T>>, GroupND<T, R
      * @return the product.
      */
     override fun multiply(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        combine(a, b) { aValue, bValue -> multiply(aValue, bValue) }
+        zip(a, b) { aValue, bValue -> multiply(aValue, bValue) }
 
     //TODO move to extensions after KEEP-176
 
@@ -211,13 +192,19 @@ public interface RingND<T, out R : Ring<T>> : Ring<StructureND<T>>, GroupND<T, R
     public companion object
 }
 
+public interface RingND<T, out A : Ring<T>> : Ring<StructureND<T>>, RingOpsND<T, A>, GroupND<T, A>, WithShape {
+    override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
+}
+
+
 /**
  * Field of [StructureND].
  *
  * @param T the type of the element contained in ND structure.
- * @param F the type field over structure elements.
+ * @param A the type field over structure elements.
  */
-public interface FieldND<T, out F : Field<T>> : Field<StructureND<T>>, RingND<T, F> {
+public interface FieldOpsND<T, out A : Field<T>> : FieldOps<StructureND<T>>, RingOpsND<T, A>,
+    ScaleOperations<StructureND<T>> {
     /**
      * Element-wise division.
      *
@@ -226,9 +213,9 @@ public interface FieldND<T, out F : Field<T>> : Field<StructureND<T>>, RingND<T,
      * @return the quotient.
      */
     override fun divide(a: StructureND<T>, b: StructureND<T>): StructureND<T> =
-        combine(a, b) { aValue, bValue -> divide(aValue, bValue) }
+        zip(a, b) { aValue, bValue -> divide(aValue, bValue) }
 
-    //TODO move to extensions after KEEP-176
+    //TODO move to extensions after https://github.com/Kotlin/KEEP/blob/master/proposals/context-receivers.md
     /**
      * Divides an ND structure by an element of it.
      *
@@ -247,42 +234,9 @@ public interface FieldND<T, out F : Field<T>> : Field<StructureND<T>>, RingND<T,
      */
     public operator fun T.div(arg: StructureND<T>): StructureND<T> = arg.map { divide(it, this@div) }
 
-    /**
-     * Element-wise scaling.
-     *
-     * @param a the multiplicand.
-     * @param value the multiplier.
-     * @return the product.
-     */
     override fun scale(a: StructureND<T>, value: Double): StructureND<T> = a.map { scale(it, value) }
-
+}
-//    @ThreadLocal
+
-//    public companion object {
+public interface FieldND<T, out A : Field<T>> : Field<StructureND<T>>, FieldOpsND<T, A>, RingND<T, A>, WithShape {
-//        private val realNDFieldCache: MutableMap<IntArray, RealNDField> = hashMapOf()
+    override val one: StructureND<T> get() = produce(shape) { elementAlgebra.one }
-//
-//        /**
-//         * 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/space/kscience/kmath/nd/BufferAlgebraND.kt

@@ -3,145 +3,173 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
+@file:OptIn(UnstableKMathAPI::class)
+
 package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.*
-import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
-import kotlin.contracts.InvocationKind
-import kotlin.contracts.contract
-import kotlin.jvm.JvmName
 
 public interface BufferAlgebraND<T, out A : Algebra<T>> : AlgebraND<T, A> {
-    public val strides: Strides
+    public val indexerBuilder: (IntArray) -> ShapeIndex
-    public val bufferFactory: BufferFactory<T>
+    public val bufferAlgebra: BufferAlgebra<T, A>
+    override val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
 
-    override fun produce(initializer: A.(IntArray) -> T): BufferND<T> = BufferND(
+    override fun produce(shape: Shape, initializer: A.(IntArray) -> T): BufferND<T> {
-        strides,
+        val indexer = indexerBuilder(shape)
-        bufferFactory(strides.linearSize) { offset ->
+        return BufferND(
-            elementContext.initializer(strides.index(offset))
+            indexer,
+            bufferAlgebra.buffer(indexer.linearSize) { offset ->
+                elementAlgebra.initializer(indexer.index(offset))
             }
         )
-
-    public val StructureND<T>.buffer: Buffer<T>
-        get() = when {
-            !shape.contentEquals(this@BufferAlgebraND.shape) -> throw ShapeMismatchException(
-                this@BufferAlgebraND.shape,
-                shape
-            )
-            this is BufferND && this.strides == this@BufferAlgebraND.strides -> this.buffer
-            else -> bufferFactory(strides.linearSize) { offset -> get(strides.index(offset)) }
     }
 
-    override fun StructureND<T>.map(transform: A.(T) -> T): BufferND<T> {
+    public fun StructureND<T>.toBufferND(): BufferND<T> = when (this) {
-        val buffer = bufferFactory(strides.linearSize) { offset ->
+        is BufferND -> this
-            elementContext.transform(buffer[offset])
+        else -> {
+            val indexer = indexerBuilder(shape)
+            BufferND(indexer, bufferAlgebra.buffer(indexer.linearSize) { offset -> get(indexer.index(offset)) })
         }
-        return BufferND(strides, buffer)
     }
 
-    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): BufferND<T> {
+    override fun StructureND<T>.map(transform: A.(T) -> T): BufferND<T> = mapInline(toBufferND(), transform)
-        val buffer = bufferFactory(strides.linearSize) { offset ->
-            elementContext.transform(
-                strides.index(offset),
-                buffer[offset]
-            )
-        }
-        return BufferND(strides, buffer)
-    }
 
-    override fun combine(a: StructureND<T>, b: StructureND<T>, transform: A.(T, T) -> T): BufferND<T> {
+    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): BufferND<T> =
-        val buffer = bufferFactory(strides.linearSize) { offset ->
+        mapIndexedInline(toBufferND(), transform)
-            elementContext.transform(a.buffer[offset], b.buffer[offset])
+
-        }
+    override fun zip(left: StructureND<T>, right: StructureND<T>, transform: A.(T, T) -> T): BufferND<T> =
-        return BufferND(strides, buffer)
+        zipInline(left.toBufferND(), right.toBufferND(), transform)
+
+    public companion object {
+        public val defaultIndexerBuilder: (IntArray) -> ShapeIndex = DefaultStrides.Companion::invoke
     }
 }
 
-public open class BufferedGroupND<T, out A : Group<T>>(
+public inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.mapInline(
-    final override val shape: IntArray,
+    arg: BufferND<T>,
-    final override val elementContext: A,
+    crossinline transform: A.(T) -> T
-    final override val bufferFactory: BufferFactory<T>,
+): BufferND<T> {
-) : GroupND<T, A>, BufferAlgebraND<T, A> {
+    val indexes = arg.indexes
-    override val strides: Strides = DefaultStrides(shape)
+    return BufferND(indexes, bufferAlgebra.mapInline(arg.buffer, transform))
-    override val zero: BufferND<T> by lazy { produce { zero } }
-    override fun StructureND<T>.unaryMinus(): StructureND<T> = produce { -get(it) }
 }
 
-public open class BufferedRingND<T, out R : Ring<T>>(
+internal inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.mapIndexedInline(
-    shape: IntArray,
+    arg: BufferND<T>,
-    elementContext: R,
+    crossinline transform: A.(index: IntArray, arg: T) -> T
+): BufferND<T> {
+    val indexes = arg.indexes
+    return BufferND(
+        indexes,
+        bufferAlgebra.mapIndexedInline(arg.buffer) { offset, value ->
+            transform(indexes.index(offset), value)
+        }
+    )
+}
+
+internal inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.zipInline(
+    l: BufferND<T>,
+    r: BufferND<T>,
+    crossinline block: A.(l: T, r: T) -> T
+): BufferND<T> {
+    require(l.indexes == r.indexes)
+    val indexes = l.indexes
+    return BufferND(indexes, bufferAlgebra.zipInline(l.buffer, r.buffer, block))
+}
+
+public open class BufferedGroupNDOps<T, out A : Group<T>>(
+    override val bufferAlgebra: BufferAlgebra<T, A>,
+    override val indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
+) : GroupOpsND<T, A>, BufferAlgebraND<T, A> {
+    override fun StructureND<T>.unaryMinus(): StructureND<T> = map { -it }
+}
+
+public open class BufferedRingOpsND<T, out A : Ring<T>>(
+    bufferAlgebra: BufferAlgebra<T, A>,
+    indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
+) : BufferedGroupNDOps<T, A>(bufferAlgebra, indexerBuilder), RingOpsND<T, A>
+
+public open class BufferedFieldOpsND<T, out A : Field<T>>(
+    bufferAlgebra: BufferAlgebra<T, A>,
+    indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
+) : BufferedRingOpsND<T, A>(bufferAlgebra, indexerBuilder), FieldOpsND<T, A> {
+
+    public constructor(
+        elementAlgebra: A,
         bufferFactory: BufferFactory<T>,
-) : BufferedGroupND<T, R>(shape, elementContext, bufferFactory), RingND<T, R> {
+        indexerBuilder: (IntArray) -> ShapeIndex = BufferAlgebraND.defaultIndexerBuilder
-    override val one: BufferND<T> by lazy { produce { one } }
+    ) : this(BufferFieldOps(elementAlgebra, bufferFactory), indexerBuilder)
-}
-
-public open class BufferedFieldND<T, out R : Field<T>>(
-    shape: IntArray,
-    elementContext: R,
-    bufferFactory: BufferFactory<T>,
-) : BufferedRingND<T, R>(shape, elementContext, bufferFactory), FieldND<T, R> {
 
     override fun scale(a: StructureND<T>, value: Double): StructureND<T> = a.map { it * value }
 }
 
-// group factories
+public val <T, A : Group<T>> BufferAlgebra<T, A>.nd: BufferedGroupNDOps<T, A> get() = BufferedGroupNDOps(this)
-public fun <T, A : Group<T>> A.ndAlgebra(
+public val <T, A : Ring<T>> BufferAlgebra<T, A>.nd: BufferedRingOpsND<T, A> get() = BufferedRingOpsND(this)
-    bufferFactory: BufferFactory<T>,
+public val <T, A : Field<T>> BufferAlgebra<T, A>.nd: BufferedFieldOpsND<T, A> get() = BufferedFieldOpsND(this)
-    vararg shape: Int,
-): BufferedGroupND<T, A> = BufferedGroupND(shape, this, bufferFactory)
 
-@JvmName("withNdGroup")
-public inline fun <T, A : Group<T>, R> A.withNdAlgebra(
-    noinline bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
-    action: BufferedGroupND<T, A>.() -> R,
-): R {
-    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
-    return ndAlgebra(bufferFactory, *shape).run(action)
-}
 
-//ring factories
+public fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.produce(
-public fun <T, A : Ring<T>> A.ndAlgebra(
-    bufferFactory: BufferFactory<T>,
     vararg shape: Int,
-): BufferedRingND<T, A> = BufferedRingND(shape, this, bufferFactory)
+    initializer: A.(IntArray) -> T
+): BufferND<T> = produce(shape, initializer)
 
-@JvmName("withNdRing")
+//// group factories
-public inline fun <T, A : Ring<T>, R> A.withNdAlgebra(
+//public fun <T, A : Group<T>> A.ndAlgebra(
-    noinline bufferFactory: BufferFactory<T>,
+//    bufferAlgebra: BufferAlgebra<T, A>,
-    vararg shape: Int,
+//    vararg shape: Int,
-    action: BufferedRingND<T, A>.() -> R,
+//): BufferedGroupNDOps<T, A> = BufferedGroupNDOps(bufferAlgebra)
-): R {
+//
-    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+//@JvmName("withNdGroup")
-    return ndAlgebra(bufferFactory, *shape).run(action)
+//public inline fun <T, A : Group<T>, R> A.withNdAlgebra(
-}
+//    noinline bufferFactory: BufferFactory<T>,
+//    vararg shape: Int,
+//    action: BufferedGroupNDOps<T, A>.() -> R,
+//): R {
+//    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+//    return ndAlgebra(bufferFactory, *shape).run(action)
+//}
 
-//field factories
+////ring factories
-public fun <T, A : Field<T>> A.ndAlgebra(
+//public fun <T, A : Ring<T>> A.ndAlgebra(
-    bufferFactory: BufferFactory<T>,
+//    bufferFactory: BufferFactory<T>,
-    vararg shape: Int,
+//    vararg shape: Int,
-): BufferedFieldND<T, A> = BufferedFieldND(shape, this, bufferFactory)
+//): BufferedRingNDOps<T, A> = BufferedRingNDOps(shape, this, bufferFactory)
-
+//
-/**
+//@JvmName("withNdRing")
- * Create a [FieldND] for this [Field] inferring proper buffer factory from the type
+//public inline fun <T, A : Ring<T>, R> A.withNdAlgebra(
- */
+//    noinline bufferFactory: BufferFactory<T>,
-@UnstableKMathAPI
+//    vararg shape: Int,
-@Suppress("UNCHECKED_CAST")
+//    action: BufferedRingNDOps<T, A>.() -> R,
-public inline fun <reified T : Any, A : Field<T>> A.autoNdAlgebra(
+//): R {
-    vararg shape: Int,
+//    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
-): FieldND<T, A> = when (this) {
+//    return ndAlgebra(bufferFactory, *shape).run(action)
-    DoubleField -> DoubleFieldND(shape) as FieldND<T, A>
+//}
-    else -> BufferedFieldND(shape, this, Buffer.Companion::auto)
+//
-}
+////field factories
-
+//public fun <T, A : Field<T>> A.ndAlgebra(
-@JvmName("withNdField")
+//    bufferFactory: BufferFactory<T>,
-public inline fun <T, A : Field<T>, R> A.withNdAlgebra(
+//    vararg shape: Int,
-    noinline bufferFactory: BufferFactory<T>,
+//): BufferedFieldNDOps<T, A> = BufferedFieldNDOps(shape, this, bufferFactory)
-    vararg shape: Int,
+//
-    action: BufferedFieldND<T, A>.() -> R,
+///**
-): R {
+// * Create a [FieldND] for this [Field] inferring proper buffer factory from the type
-    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+// */
-    return ndAlgebra(bufferFactory, *shape).run(action)
+//@UnstableKMathAPI
-}
+//@Suppress("UNCHECKED_CAST")
+//public inline fun <reified T : Any, A : Field<T>> A.autoNdAlgebra(
+//    vararg shape: Int,
+//): FieldND<T, A> = when (this) {
+//    DoubleField -> DoubleFieldND(shape) as FieldND<T, A>
+//    else -> BufferedFieldNDOps(shape, this, Buffer.Companion::auto)
+//}
+//
+//@JvmName("withNdField")
+//public inline fun <T, A : Field<T>, R> A.withNdAlgebra(
+//    noinline bufferFactory: BufferFactory<T>,
+//    vararg shape: Int,
+//    action: BufferedFieldNDOps<T, A>.() -> R,
+//): R {
+//    contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
+//    return ndAlgebra(bufferFactory, *shape).run(action)
+//}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferND.kt

@@ -15,26 +15,20 @@ import space.kscience.kmath.structures.MutableBufferFactory
  * Represents [StructureND] over [Buffer].
  *
  * @param T the type of items.
- * @param strides The strides to access elements of [Buffer] by linear indices.
+ * @param indexes The strides to access elements of [Buffer] by linear indices.
  * @param buffer The underlying buffer.
  */
 public open class BufferND<out T>(
-    public val strides: Strides,
+    public val indexes: ShapeIndex,
     public val buffer: Buffer<T>,
 ) : StructureND<T> {
 
-    init {
+    override operator fun get(index: IntArray): T = buffer[indexes.offset(index)]
-        if (strides.linearSize != buffer.size) {
-            error("Expected buffer side of ${strides.linearSize}, but found ${buffer.size}")
-        }
-    }
 
-    override operator fun get(index: IntArray): T = buffer[strides.offset(index)]
+    override val shape: IntArray get() = indexes.shape
-
-    override val shape: IntArray get() = strides.shape
 
     @PerformancePitfall
-    override fun elements(): Sequence<Pair<IntArray, T>> = strides.indices().map {
+    override fun elements(): Sequence<Pair<IntArray, T>> = indexes.indices().map {
         it to this[it]
     }
 
@@ -49,7 +43,7 @@ public inline fun <T, reified R : Any> StructureND<T>.mapToBuffer(
     crossinline transform: (T) -> R,
 ): BufferND<R> {
     return if (this is BufferND<T>)
-        BufferND(this.strides, factory.invoke(strides.linearSize) { transform(buffer[it]) })
+        BufferND(this.indexes, factory.invoke(indexes.linearSize) { transform(buffer[it]) })
     else {
         val strides = DefaultStrides(shape)
         BufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
@@ -64,11 +58,11 @@ public inline fun <T, reified R : Any> StructureND<T>.mapToBuffer(
  * @param mutableBuffer The underlying buffer.
  */
 public class MutableBufferND<T>(
-    strides: Strides,
+    strides: ShapeIndex,
     public val mutableBuffer: MutableBuffer<T>,
 ) : MutableStructureND<T>, BufferND<T>(strides, mutableBuffer) {
     override fun set(index: IntArray, value: T) {
-        mutableBuffer[strides.offset(index)] = value
+        mutableBuffer[indexes.offset(index)] = value
     }
 }
 
@@ -80,7 +74,7 @@ public inline fun <T, reified R : Any> MutableStructureND<T>.mapToMutableBuffer(
     crossinline transform: (T) -> R,
 ): MutableBufferND<R> {
     return if (this is MutableBufferND<T>)
-        MutableBufferND(this.strides, factory.invoke(strides.linearSize) { transform(mutableBuffer[it]) })
+        MutableBufferND(this.indexes, factory.invoke(indexes.linearSize) { transform(mutableBuffer[it]) })
     else {
         val strides = DefaultStrides(shape)
         MutableBufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/DoubleFieldND.kt

@@ -6,108 +6,68 @@
 package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.*
-import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
-import space.kscience.kmath.operations.ScaleOperations
 import space.kscience.kmath.structures.DoubleBuffer
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
-@OptIn(UnstableKMathAPI::class)
+public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(DoubleField.bufferAlgebra),
-public class DoubleFieldND(
+    ScaleOperations<StructureND<Double>>, ExtendedFieldOps<StructureND<Double>> {
-    shape: IntArray,
-) : BufferedFieldND<Double, DoubleField>(shape, DoubleField, ::DoubleBuffer),
-    NumbersAddOperations<StructureND<Double>>,
-    ScaleOperations<StructureND<Double>>,
-    ExtendedField<StructureND<Double>> {
 
-    override val zero: BufferND<Double> by lazy { produce { zero } }
+    override fun StructureND<Double>.toBufferND(): BufferND<Double> = when (this) {
-    override val one: BufferND<Double> by lazy { produce { one } }
+        is BufferND -> this
+        else -> {
+            val indexer = indexerBuilder(shape)
+            BufferND(indexer, DoubleBuffer(indexer.linearSize) { offset -> get(indexer.index(offset)) })
+        }
+    }
+
+    //TODO do specialization
+
+    override fun scale(a: StructureND<Double>, value: Double): BufferND<Double> =
+        mapInline(a.toBufferND()) { it * value }
+
+    override fun power(arg: StructureND<Double>, pow: Number): BufferND<Double> =
+        mapInline(arg.toBufferND()) { power(it, pow) }
+
+    override fun exp(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { exp(it) }
+    override fun ln(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { ln(it) }
+
+    override fun sin(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { sin(it) }
+    override fun cos(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { cos(it) }
+    override fun tan(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { tan(it) }
+    override fun asin(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { asin(it) }
+    override fun acos(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { acos(it) }
+    override fun atan(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { atan(it) }
+
+    override fun sinh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { sinh(it) }
+    override fun cosh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { cosh(it) }
+    override fun tanh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { tanh(it) }
+    override fun asinh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { asinh(it) }
+    override fun acosh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { acosh(it) }
+    override fun atanh(arg: StructureND<Double>): BufferND<Double> = mapInline(arg.toBufferND()) { atanh(it) }
+
+    public companion object : DoubleFieldOpsND()
+}
+
+@OptIn(UnstableKMathAPI::class)
+public class DoubleFieldND(override val shape: Shape) :
+    DoubleFieldOpsND(), FieldND<Double, DoubleField>, NumbersAddOps<StructureND<Double>> {
 
     override fun number(value: Number): BufferND<Double> {
         val d = value.toDouble() // minimize conversions
-        return produce { d }
+        return produce(shape) { d }
     }
-
-    override val StructureND<Double>.buffer: DoubleBuffer
-        get() = when {
-            !shape.contentEquals(this@DoubleFieldND.shape) -> throw ShapeMismatchException(
-                this@DoubleFieldND.shape,
-                shape
-            )
-            this is BufferND && this.strides == this@DoubleFieldND.strides -> this.buffer as DoubleBuffer
-            else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
-        }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun StructureND<Double>.map(
-        transform: DoubleField.(Double) -> Double,
-    ): BufferND<Double> {
-        val buffer = DoubleBuffer(strides.linearSize) { offset -> DoubleField.transform(buffer.array[offset]) }
-        return BufferND(strides, buffer)
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun produce(initializer: DoubleField.(IntArray) -> Double): BufferND<Double> {
-        val array = DoubleArray(strides.linearSize) { offset ->
-            val index = strides.index(offset)
-            DoubleField.initializer(index)
-        }
-        return BufferND(strides, DoubleBuffer(array))
-    }
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun StructureND<Double>.mapIndexed(
-        transform: DoubleField.(index: IntArray, Double) -> Double,
-    ): BufferND<Double> = BufferND(
-        strides,
-        buffer = DoubleBuffer(strides.linearSize) { offset ->
-            DoubleField.transform(
-                strides.index(offset),
-                buffer.array[offset]
-            )
-        })
-
-    @Suppress("OVERRIDE_BY_INLINE")
-    override inline fun combine(
-        a: StructureND<Double>,
-        b: StructureND<Double>,
-        transform: DoubleField.(Double, Double) -> Double,
-    ): BufferND<Double> {
-        val buffer = DoubleBuffer(strides.linearSize) { offset ->
-            DoubleField.transform(a.buffer.array[offset], b.buffer.array[offset])
-        }
-        return BufferND(strides, buffer)
-    }
-
-    override fun scale(a: StructureND<Double>, value: Double): StructureND<Double> = a.map { it * value }
-
-    override fun power(arg: StructureND<Double>, pow: Number): BufferND<Double> = arg.map { power(it, pow) }
-
-    override fun exp(arg: StructureND<Double>): BufferND<Double> = arg.map { exp(it) }
-    override fun ln(arg: StructureND<Double>): BufferND<Double> = arg.map { ln(it) }
-
-    override fun sin(arg: StructureND<Double>): BufferND<Double> = arg.map { sin(it) }
-    override fun cos(arg: StructureND<Double>): BufferND<Double> = arg.map { cos(it) }
-    override fun tan(arg: StructureND<Double>): BufferND<Double> = arg.map { tan(it) }
-    override fun asin(arg: StructureND<Double>): BufferND<Double> = arg.map { asin(it) }
-    override fun acos(arg: StructureND<Double>): BufferND<Double> = arg.map { acos(it) }
-    override fun atan(arg: StructureND<Double>): BufferND<Double> = arg.map { atan(it) }
-
-    override fun sinh(arg: StructureND<Double>): BufferND<Double> = arg.map { sinh(it) }
-    override fun cosh(arg: StructureND<Double>): BufferND<Double> = arg.map { cosh(it) }
-    override fun tanh(arg: StructureND<Double>): BufferND<Double> = arg.map { tanh(it) }
-    override fun asinh(arg: StructureND<Double>): BufferND<Double> = arg.map { asinh(it) }
-    override fun acosh(arg: StructureND<Double>): BufferND<Double> = arg.map { acosh(it) }
-    override fun atanh(arg: StructureND<Double>): BufferND<Double> = arg.map { atanh(it) }
 }
 
+public val DoubleField.ndAlgebra: DoubleFieldOpsND get() = DoubleFieldOpsND
+
 public fun DoubleField.ndAlgebra(vararg shape: Int): DoubleFieldND = DoubleFieldND(shape)
 
 /**
  * Produce a context for n-dimensional operations inside this real field
  */
+@UnstableKMathAPI
 public inline fun <R> DoubleField.withNdAlgebra(vararg shape: Int, action: DoubleFieldND.() -> R): R {
     contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
     return DoubleFieldND(shape).run(action)

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShapeIndex.kt

@@ -0,0 +1,120 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
+ */
+
+package space.kscience.kmath.nd
+
+import kotlin.native.concurrent.ThreadLocal
+
+/**
+ * A converter from linear index to multivariate index
+ */
+public interface ShapeIndex{
+    public val shape: Shape
+
+    /**
+     * Get linear index from multidimensional index
+     */
+    public fun offset(index: IntArray): Int
+
+    /**
+     * Get multidimensional from linear
+     */
+    public fun index(offset: Int): IntArray
+
+    /**
+     * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides
+     */
+    public val linearSize: Int
+
+    // TODO introduce a fast way to calculate index of the next element?
+
+    /**
+     * Iterate over ND indices in a natural order
+     */
+    public fun indices(): Sequence<IntArray>
+
+    override fun equals(other: Any?): Boolean
+    override fun hashCode(): Int
+}
+
+/**
+ * Linear transformation of indexes
+ */
+public abstract class Strides: ShapeIndex {
+    /**
+     * Array strides
+     */
+    public abstract val strides: IntArray
+
+    public override fun offset(index: IntArray): Int = index.mapIndexed { i, value ->
+        if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})")
+        value * strides[i]
+    }.sum()
+
+    // TODO introduce a fast way to calculate index of the next element?
+
+    /**
+     * Iterate over ND indices in a natural order
+     */
+    public override fun indices(): Sequence<IntArray> = (0 until linearSize).asSequence().map(::index)
+}
+
+/**
+ * Simple implementation of [Strides].
+ */
+public class DefaultStrides private constructor(override val shape: IntArray) : Strides() {
+    override val linearSize: Int get() = strides[shape.size]
+
+    /**
+     * Strides for memory access
+     */
+    override val strides: IntArray by lazy {
+        sequence {
+            var current = 1
+            yield(1)
+
+            shape.forEach {
+                current *= it
+                yield(current)
+            }
+        }.toList().toIntArray()
+    }
+
+    override fun index(offset: Int): IntArray {
+        val res = IntArray(shape.size)
+        var current = offset
+        var strideIndex = strides.size - 2
+
+        while (strideIndex >= 0) {
+            res[strideIndex] = (current / strides[strideIndex])
+            current %= strides[strideIndex]
+            strideIndex--
+        }
+
+        return res
+    }
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other !is DefaultStrides) return false
+        if (!shape.contentEquals(other.shape)) return false
+        return true
+    }
+
+    override fun hashCode(): Int = shape.contentHashCode()
+
+    @ThreadLocal
+    public companion object {
+        //private val defaultStridesCache = HashMap<IntArray, Strides>()
+
+        /**
+         * Cached builder for default strides
+         */
+        public operator fun invoke(shape: IntArray): Strides = DefaultStrides(shape)
+            //defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
+
+        //TODO fix cache
+    }
+}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/ShortRingND.kt

@@ -6,34 +6,27 @@
 package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 import space.kscience.kmath.operations.ShortRing
-import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.operations.bufferAlgebra
-import space.kscience.kmath.structures.ShortBuffer
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
+public sealed class ShortRingOpsND : BufferedRingOpsND<Short, ShortRing>(ShortRing.bufferAlgebra) {
+    public companion object : ShortRingOpsND()
+}
+
 @OptIn(UnstableKMathAPI::class)
 public class ShortRingND(
-    shape: IntArray,
+    override val shape: Shape
-) : BufferedRingND<Short, ShortRing>(shape, ShortRing, Buffer.Companion::auto),
+) : ShortRingOpsND(), RingND<Short, ShortRing>, NumbersAddOps<StructureND<Short>> {
-    NumbersAddOperations<StructureND<Short>> {
-
-    override val zero: BufferND<Short> by lazy { produce { zero } }
-    override val one: BufferND<Short> by lazy { produce { one } }
 
     override fun number(value: Number): BufferND<Short> {
         val d = value.toShort() // minimize conversions
-        return produce { d }
+        return produce(shape) { d }
     }
 }
 
-/**
- * Fast element production using function inlining.
- */
-public inline fun BufferedRingND<Short, ShortRing>.produceInline(crossinline initializer: ShortRing.(Int) -> Short): BufferND<Short> =
-    BufferND(strides, ShortBuffer(ShortArray(strides.linearSize) { offset -> ShortRing.initializer(offset) }))
-
 public inline fun <R> ShortRing.withNdAlgebra(vararg shape: Int, action: ShortRingND.() -> R): R {
     contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
     return ShortRingND(shape).run(action)

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/StructureND.kt

@@ -15,7 +15,6 @@ import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import kotlin.jvm.JvmName
 import kotlin.math.abs
-import kotlin.native.concurrent.ThreadLocal
 import kotlin.reflect.KClass
 
 public interface StructureFeature : Feature<StructureFeature>
@@ -72,7 +71,7 @@ public interface StructureND<out T> : Featured<StructureFeature> {
             if (st1 === st2) return true
 
             // fast comparison of buffers if possible
-            if (st1 is BufferND && st2 is BufferND && st1.strides == st2.strides)
+            if (st1 is BufferND && st2 is BufferND && st1.indexes == st2.indexes)
                 return Buffer.contentEquals(st1.buffer, st2.buffer)
 
             //element by element comparison if it could not be avoided
@@ -88,7 +87,7 @@ public interface StructureND<out T> : Featured<StructureFeature> {
             if (st1 === st2) return true
 
             // fast comparison of buffers if possible
-            if (st1 is BufferND && st2 is BufferND && st1.strides == st2.strides)
+            if (st1 is BufferND && st2 is BufferND && st1.indexes == st2.indexes)
                 return Buffer.contentEquals(st1.buffer, st2.buffer)
 
             //element by element comparison if it could not be avoided
@@ -187,11 +186,11 @@ public fun <T : Comparable<T>> LinearSpace<T, Ring<T>>.contentEquals(
  * Indicates whether some [StructureND] is equal to another one with [absoluteTolerance].
  */
 @PerformancePitfall
-public fun <T : Comparable<T>> GroupND<T, Ring<T>>.contentEquals(
+public fun <T : Comparable<T>> GroupOpsND<T, Ring<T>>.contentEquals(
     st1: StructureND<T>,
     st2: StructureND<T>,
     absoluteTolerance: T,
-): Boolean = st1.elements().all { (index, value) -> elementContext { (value - st2[index]) } < absoluteTolerance }
+): Boolean = st1.elements().all { (index, value) -> elementAlgebra { (value - st2[index]) } < absoluteTolerance }
 
 /**
  * Indicates whether some [StructureND] is equal to another one with [absoluteTolerance].
@@ -231,107 +230,10 @@ public interface MutableStructureND<T> : StructureND<T> {
  * Transform a structure element-by element in place.
  */
 @OptIn(PerformancePitfall::class)
-public inline fun <T> MutableStructureND<T>.mapInPlace(action: (IntArray, T) -> T): Unit =
+public inline fun <T> MutableStructureND<T>.mapInPlace(action: (index: IntArray, t: T) -> T): Unit =
     elements().forEach { (index, oldValue) -> this[index] = action(index, oldValue) }
 
-/**
+public inline fun <reified T : Any> StructureND<T>.zip(
- * A way to convert ND indices to linear one and back.
- */
-public interface Strides {
-    /**
-     * Shape of NDStructure
-     */
-    public val shape: IntArray
-
-    /**
-     * Array strides
-     */
-    public val strides: IntArray
-
-    /**
-     * Get linear index from multidimensional index
-     */
-    public fun offset(index: IntArray): Int = index.mapIndexed { i, value ->
-        if (value < 0 || value >= shape[i]) throw IndexOutOfBoundsException("Index $value out of shape bounds: (0,${this.shape[i]})")
-        value * strides[i]
-    }.sum()
-
-    /**
-     * Get multidimensional from linear
-     */
-    public fun index(offset: Int): IntArray
-
-    /**
-     * The size of linear buffer to accommodate all elements of ND-structure corresponding to strides
-     */
-    public val linearSize: Int
-
-    // TODO introduce a fast way to calculate index of the next element?
-
-    /**
-     * Iterate over ND indices in a natural order
-     */
-    public fun indices(): Sequence<IntArray> = (0 until linearSize).asSequence().map(::index)
-}
-
-/**
- * Simple implementation of [Strides].
- */
-public class DefaultStrides private constructor(override val shape: IntArray) : Strides {
-    override val linearSize: Int
-        get() = strides[shape.size]
-
-    /**
-     * Strides for memory access
-     */
-    override val strides: IntArray by lazy {
-        sequence {
-            var current = 1
-            yield(1)
-
-            shape.forEach {
-                current *= it
-                yield(current)
-            }
-        }.toList().toIntArray()
-    }
-
-    override fun index(offset: Int): IntArray {
-        val res = IntArray(shape.size)
-        var current = offset
-        var strideIndex = strides.size - 2
-
-        while (strideIndex >= 0) {
-            res[strideIndex] = (current / strides[strideIndex])
-            current %= strides[strideIndex]
-            strideIndex--
-        }
-
-        return res
-    }
-
-    override fun equals(other: Any?): Boolean {
-        if (this === other) return true
-        if (other !is DefaultStrides) return false
-        if (!shape.contentEquals(other.shape)) return false
-        return true
-    }
-
-    override fun hashCode(): Int = shape.contentHashCode()
-
-    @ThreadLocal
-    public companion object {
-        private val defaultStridesCache = HashMap<IntArray, Strides>()
-
-        /**
-         * Cached builder for default strides
-         */
-        public operator fun invoke(shape: IntArray): Strides =
-            defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
-    }
-}
-
-public inline fun <reified T : Any> StructureND<T>.combine(
     struct: StructureND<T>,
     crossinline block: (T, T) -> T,
 ): StructureND<T> {

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/algebraNDExtentions.kt

@@ -0,0 +1,34 @@
+/*
+ * Copyright 2018-2021 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
+ */
+
+package space.kscience.kmath.nd
+
+import space.kscience.kmath.operations.Algebra
+import space.kscience.kmath.operations.Group
+import space.kscience.kmath.operations.Ring
+import kotlin.jvm.JvmName
+
+
+public fun <T, A : Algebra<T>> AlgebraND<T, A>.produce(
+    shapeFirst: Int,
+    vararg shapeRest: Int,
+    initializer: A.(IntArray) -> T
+): StructureND<T> = produce(Shape(shapeFirst, *shapeRest), initializer)
+
+public fun <T, A : Group<T>> AlgebraND<T, A>.zero(shape: Shape): StructureND<T> = produce(shape) { zero }
+
+@JvmName("zeroVarArg")
+public fun <T, A : Group<T>> AlgebraND<T, A>.zero(
+    shapeFirst: Int,
+    vararg shapeRest: Int,
+): StructureND<T> = produce(shapeFirst, *shapeRest) { zero }
+
+public fun <T, A : Ring<T>> AlgebraND<T, A>.one(shape: Shape): StructureND<T> = produce(shape) { one }
+
+@JvmName("oneVarArg")
+public fun <T, A : Ring<T>> AlgebraND<T, A>.one(
+    shapeFirst: Int,
+    vararg shapeRest: Int,
+): StructureND<T> = produce(shapeFirst, *shapeRest) { one }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt

@@ -117,7 +117,7 @@ public inline operator fun <A : Algebra<*>, R> A.invoke(block: A.() -> R): R = r
  *
  * @param T the type of element of this semispace.
  */
-public interface GroupOperations<T> : Algebra<T> {
+public interface GroupOps<T> : Algebra<T> {
     /**
      * Addition of two elements.
      *
@@ -162,7 +162,7 @@ public interface GroupOperations<T> : Algebra<T> {
      * @return the difference.
      */
     public operator fun T.minus(b: T): T = add(this, -b)
-
+    // Dynamic dispatch of operations
     override fun unaryOperationFunction(operation: String): (arg: T) -> T = when (operation) {
         PLUS_OPERATION -> { arg -> +arg }
         MINUS_OPERATION -> { arg -> -arg }
@@ -193,7 +193,7 @@ public interface GroupOperations<T> : Algebra<T> {
  *
  * @param T the type of element of this semispace.
  */
-public interface Group<T> : GroupOperations<T> {
+public interface Group<T> : GroupOps<T> {
     /**
      * The neutral element of addition.
      */
@@ -206,7 +206,7 @@ public interface Group<T> : GroupOperations<T> {
  *
  * @param T the type of element of this semiring.
  */
-public interface RingOperations<T> : GroupOperations<T> {
+public interface RingOps<T> : GroupOps<T> {
     /**
      * Multiplies two elements.
      *
@@ -242,7 +242,7 @@ public interface RingOperations<T> : GroupOperations<T> {
  *
  * @param T the type of element of this ring.
  */
-public interface Ring<T> : Group<T>, RingOperations<T> {
+public interface Ring<T> : Group<T>, RingOps<T> {
     /**
      * The neutral element of multiplication
      */
@@ -256,7 +256,7 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
  *
  * @param T the type of element of this semifield.
  */
-public interface FieldOperations<T> : RingOperations<T> {
+public interface FieldOps<T> : RingOps<T> {
     /**
      * Division of two elements.
      *
@@ -295,6 +295,6 @@ public interface FieldOperations<T> : RingOperations<T> {
  *
  * @param T the type of element of this field.
  */
-public interface Field<T> : Ring<T>, FieldOperations<T>, ScaleOperations<T>, NumericAlgebra<T> {
+public interface Field<T> : Ring<T>, FieldOps<T>, ScaleOperations<T>, NumericAlgebra<T> {
     override fun number(value: Number): T = scale(one, value.toDouble())
 }

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

@@ -6,7 +6,7 @@
 package space.kscience.kmath.operations
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.nd.BufferedRingND
+import space.kscience.kmath.nd.BufferedRingOpsND
 import space.kscience.kmath.operations.BigInt.Companion.BASE
 import space.kscience.kmath.operations.BigInt.Companion.BASE_SIZE
 import space.kscience.kmath.structures.Buffer
@@ -26,7 +26,7 @@ private typealias TBase = ULong
  * @author Peter Klimai
  */
 @OptIn(UnstableKMathAPI::class)
-public object BigIntField : Field<BigInt>, NumbersAddOperations<BigInt>, ScaleOperations<BigInt> {
+public object BigIntField : Field<BigInt>, NumbersAddOps<BigInt>, ScaleOperations<BigInt> {
     override val zero: BigInt = BigInt.ZERO
     override val one: BigInt = BigInt.ONE
 
@@ -542,5 +542,5 @@ public inline fun MutableBuffer.Companion.bigInt(size: Int, initializer: (Int) -
 public inline fun BigInt.mutableBuffer(size: Int, initializer: (Int) -> BigInt): Buffer<BigInt> =
     Buffer.boxing(size, initializer)
 
-public fun BigIntField.nd(vararg shape: Int): BufferedRingND<BigInt, BigIntField> =
+public val BigIntField.nd: BufferedRingOpsND<BigInt, BigIntField>
-    BufferedRingND(shape, BigIntField, BigInt::buffer)
+    get() = BufferedRingOpsND(BufferRingOps(BigIntField, BigInt::buffer))

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt

@@ -5,32 +5,34 @@
 
 package space.kscience.kmath.operations
 
-import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.ShortBuffer
+
+public interface WithSize {
+    public val size: Int
+}
 
 /**
  * An algebra over [Buffer]
  */
-@UnstableKMathAPI
+public interface BufferAlgebra<T, out A : Algebra<T>> : Algebra<Buffer<T>> {
-public interface BufferAlgebra<T, A : Algebra<T>> : Algebra<Buffer<T>> {
-    public val bufferFactory: BufferFactory<T>
     public val elementAlgebra: A
-    public val size: Int
+    public val bufferFactory: BufferFactory<T>
 
-    public fun buffer(vararg elements: T): Buffer<T> {
+    public fun buffer(size: Int, vararg elements: T): Buffer<T> {
         require(elements.size == size) { "Expected $size elements but found ${elements.size}" }
         return bufferFactory(size) { elements[it] }
     }
 
     //TODO move to multi-receiver inline extension
-    public fun Buffer<T>.map(block: (T) -> T): Buffer<T> = bufferFactory(size) { block(get(it)) }
+    public fun Buffer<T>.map(block: A.(T) -> T): Buffer<T> = mapInline(this, block)
 
-    public fun Buffer<T>.zip(other: Buffer<T>, block: (left: T, right: T) -> T): Buffer<T> {
+    public fun Buffer<T>.mapIndexed(block: A.(index: Int, arg: T) -> T): Buffer<T> = mapIndexedInline(this, block)
-        require(size == other.size) { "Incompatible buffer sizes. left: $size, right: ${other.size}" }
+
-        return bufferFactory(size) { block(this[it], other[it]) }
+    public fun Buffer<T>.zip(other: Buffer<T>, block: A.(left: T, right: T) -> T): Buffer<T> =
-    }
+        zipInline(this, other, block)
 
     override fun unaryOperationFunction(operation: String): (arg: Buffer<T>) -> Buffer<T> {
         val operationFunction = elementAlgebra.unaryOperationFunction(operation)
@@ -45,112 +47,149 @@ public interface BufferAlgebra<T, A : Algebra<T>> : Algebra<Buffer<T>> {
     }
 }
 
-@UnstableKMathAPI
+/**
-public fun <T> BufferField<T, *>.buffer(initializer: (Int) -> T): Buffer<T> {
+ * Inline map
+ */
+public inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapInline(
+    buffer: Buffer<T>,
+    crossinline block: A.(T) -> T
+): Buffer<T> = bufferFactory(buffer.size) { elementAlgebra.block(buffer[it]) }
+
+/**
+ * Inline map
+ */
+public inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.mapIndexedInline(
+    buffer: Buffer<T>,
+    crossinline block: A.(index: Int, arg: T) -> T
+): Buffer<T> = bufferFactory(buffer.size) { elementAlgebra.block(it, buffer[it]) }
+
+/**
+ * Inline zip
+ */
+public inline fun <T, A : Algebra<T>> BufferAlgebra<T, A>.zipInline(
+    l: Buffer<T>,
+    r: Buffer<T>,
+    crossinline block: A.(l: T, r: T) -> T
+): Buffer<T> {
+    require(l.size == r.size) { "Incompatible buffer sizes. left: ${l.size}, right: ${r.size}" }
+    return bufferFactory(l.size) { elementAlgebra.block(l[it], r[it]) }
+}
+
+public fun <T> BufferAlgebra<T, *>.buffer(size: Int, initializer: (Int) -> T): Buffer<T> {
+    return bufferFactory(size, initializer)
+}
+
+public fun <T, A> A.buffer(initializer: (Int) -> T): Buffer<T> where A : BufferAlgebra<T, *>, A : WithSize {
     return bufferFactory(size, initializer)
 }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.sin(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::sin)
+    mapInline(arg) { sin(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.cos(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::cos)
+    mapInline(arg) { cos(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.tan(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::tan)
+    mapInline(arg) { tan(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.asin(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::asin)
+    mapInline(arg) { asin(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.acos(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::acos)
+    mapInline(arg) { acos(it) }
 
-@UnstableKMathAPI
 public fun <T, A : TrigonometricOperations<T>> BufferAlgebra<T, A>.atan(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::atan)
+    mapInline(arg) { atan(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.exp(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::exp)
+    mapInline(arg) { exp(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.ln(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::ln)
+    mapInline(arg) { ln(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.sinh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::sinh)
+    mapInline(arg) { sinh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.cosh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::cosh)
+    mapInline(arg) { cosh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.tanh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::tanh)
+    mapInline(arg) { tanh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.asinh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::asinh)
+    mapInline(arg) { asinh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.acosh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::acosh)
+    mapInline(arg) { acosh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : ExponentialOperations<T>> BufferAlgebra<T, A>.atanh(arg: Buffer<T>): Buffer<T> =
-    arg.map(elementAlgebra::atanh)
+    mapInline(arg) { atanh(it) }
 
-@UnstableKMathAPI
 public fun <T, A : PowerOperations<T>> BufferAlgebra<T, A>.pow(arg: Buffer<T>, pow: Number): Buffer<T> =
-    with(elementAlgebra) { arg.map { power(it, pow) } }
+    mapInline(arg) { power(it, pow) }
 
 
-@UnstableKMathAPI
+public open class BufferRingOps<T, A: Ring<T>>(
-public class BufferField<T, A : Field<T>>(
-    override val bufferFactory: BufferFactory<T>,
     override val elementAlgebra: A,
+    override val bufferFactory: BufferFactory<T>,
+) : BufferAlgebra<T, A>, RingOps<Buffer<T>>{
+
+    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l + r }
+    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l * r }
+    override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
+
+    override fun unaryOperationFunction(operation: String): (arg: Buffer<T>) -> Buffer<T> =
+        super<BufferAlgebra>.unaryOperationFunction(operation)
+
+    override fun binaryOperationFunction(operation: String): (left: Buffer<T>, right: Buffer<T>) -> Buffer<T> =
+        super<BufferAlgebra>.binaryOperationFunction(operation)
+}
+
+public val ShortRing.bufferAlgebra: BufferRingOps<Short, ShortRing>
+    get() = BufferRingOps(ShortRing, ::ShortBuffer)
+
+public open class BufferFieldOps<T, A : Field<T>>(
+    elementAlgebra: A,
+    bufferFactory: BufferFactory<T>,
+) : BufferRingOps<T, A>(elementAlgebra, bufferFactory), BufferAlgebra<T, A>, FieldOps<Buffer<T>>, ScaleOperations<Buffer<T>> {
+
+    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l + r }
+    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l * r }
+    override fun divide(a: Buffer<T>, b: Buffer<T>): Buffer<T> = zipInline(a, b) { l, r -> l / r }
+
+    override fun scale(a: Buffer<T>, value: Double): Buffer<T> = a.map { scale(it, value) }
+    override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
+
+    override fun binaryOperationFunction(operation: String): (left: Buffer<T>, right: Buffer<T>) -> Buffer<T> =
+        super<BufferRingOps>.binaryOperationFunction(operation)
+}
+
+public class BufferField<T, A : Field<T>>(
+    elementAlgebra: A,
+    bufferFactory: BufferFactory<T>,
     override val size: Int
-) : BufferAlgebra<T, A>, Field<Buffer<T>> {
+) : BufferFieldOps<T, A>(elementAlgebra, bufferFactory), Field<Buffer<T>>, WithSize {
 
     override val zero: Buffer<T> = bufferFactory(size) { elementAlgebra.zero }
     override val one: Buffer<T> = bufferFactory(size) { elementAlgebra.one }
-
-
-    override fun add(a: Buffer<T>, b: Buffer<T>): Buffer<T> = a.zip(b, elementAlgebra::add)
-    override fun multiply(a: Buffer<T>, b: Buffer<T>): Buffer<T> = a.zip(b, elementAlgebra::multiply)
-    override fun divide(a: Buffer<T>, b: Buffer<T>): Buffer<T> = a.zip(b, elementAlgebra::divide)
-
-    override fun scale(a: Buffer<T>, value: Double): Buffer<T> = with(elementAlgebra) { a.map { scale(it, value) } }
-    override fun Buffer<T>.unaryMinus(): Buffer<T> = with(elementAlgebra) { map { -it } }
-
-    override fun unaryOperationFunction(operation: String): (arg: Buffer<T>) -> Buffer<T> {
-        return super<BufferAlgebra>.unaryOperationFunction(operation)
-    }
-
-    override fun binaryOperationFunction(operation: String): (left: Buffer<T>, right: Buffer<T>) -> Buffer<T> {
-        return super<BufferAlgebra>.binaryOperationFunction(operation)
-    }
 }
 
+/**
+ * Generate full buffer field from given buffer operations
+ */
+public fun <T, A : Field<T>> BufferFieldOps<T, A>.withSize(size: Int): BufferField<T, A> =
+    BufferField(elementAlgebra, bufferFactory, size)
+
 //Double buffer specialization
 
-@UnstableKMathAPI
 public fun BufferField<Double, *>.buffer(vararg elements: Number): Buffer<Double> {
     require(elements.size == size) { "Expected $size elements but found ${elements.size}" }
     return bufferFactory(size) { elements[it].toDouble() }
 }
 
-@UnstableKMathAPI
+public fun <T, A : Field<T>> A.bufferAlgebra(bufferFactory: BufferFactory<T>): BufferFieldOps<T, A> =
-public fun <T, A : Field<T>> A.bufferAlgebra(bufferFactory: BufferFactory<T>, size: Int): BufferField<T, A> =
+    BufferFieldOps(this, bufferFactory)
-    BufferField(bufferFactory, this, size)
 
-@UnstableKMathAPI
+public val DoubleField.bufferAlgebra: BufferFieldOps<Double, DoubleField>
-public fun DoubleField.bufferAlgebra(size: Int): BufferField<Double, DoubleField> =
+    get() = BufferFieldOps(DoubleField, ::DoubleBuffer)
-    BufferField(::DoubleBuffer, DoubleField, size)
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferField.kt

@@ -13,21 +13,21 @@ import space.kscience.kmath.structures.DoubleBuffer
  *
  * @property size the size of buffers to operate on.
  */
-public class DoubleBufferField(public val size: Int) : ExtendedField<Buffer<Double>>, DoubleBufferOperations() {
+public class DoubleBufferField(public val size: Int) : ExtendedField<Buffer<Double>>, DoubleBufferOps() {
     override val zero: Buffer<Double> by lazy { DoubleBuffer(size) { 0.0 } }
     override val one: Buffer<Double> by lazy { DoubleBuffer(size) { 1.0 } }
 
-    override fun sinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.sinh(arg)
+    override fun sinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.sinh(arg)
 
-    override fun cosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.cosh(arg)
+    override fun cosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.cosh(arg)
 
-    override fun tanh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.tanh(arg)
+    override fun tanh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.tanh(arg)
 
-    override fun asinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.asinh(arg)
+    override fun asinh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.asinh(arg)
 
-    override fun acosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOperations>.acosh(arg)
+    override fun acosh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.acosh(arg)
 
-    override fun atanh(arg: Buffer<Double>): DoubleBuffer= super<DoubleBufferOperations>.atanh(arg)
+    override fun atanh(arg: Buffer<Double>): DoubleBuffer= super<DoubleBufferOps>.atanh(arg)
 
     //    override fun number(value: Number): Buffer<Double> = DoubleBuffer(size) { value.toDouble() }
 //

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt

@@ -12,9 +12,9 @@ import space.kscience.kmath.structures.DoubleBuffer
 import kotlin.math.*
 
 /**
- * [ExtendedFieldOperations] over [DoubleBuffer].
+ * [ExtendedFieldOps] over [DoubleBuffer].
  */
-public abstract class DoubleBufferOperations : ExtendedFieldOperations<Buffer<Double>>, Norm<Buffer<Double>, Double> {
+public abstract class DoubleBufferOps : ExtendedFieldOps<Buffer<Double>>, Norm<Buffer<Double>, Double> {
     override fun Buffer<Double>.unaryMinus(): DoubleBuffer = if (this is DoubleBuffer) {
         DoubleBuffer(size) { -array[it] }
     } else {
@@ -185,7 +185,7 @@ public abstract class DoubleBufferOperations : ExtendedFieldOperations<Buffer<Do
         DoubleBuffer(DoubleArray(a.size) { aArray[it] * value })
     } else DoubleBuffer(DoubleArray(a.size) { a[it] * value })
 
-    public companion object : DoubleBufferOperations()
+    public companion object : DoubleBufferOps()
 }
 
 public object DoubleL2Norm : Norm<Point<Double>, Double> {

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/NumericAlgebra.kt

@@ -150,7 +150,7 @@ public interface ScaleOperations<T> : Algebra<T> {
  * TODO to be removed and replaced by extensions after multiple receivers are there
  */
 @UnstableKMathAPI
-public interface NumbersAddOperations<T> : Ring<T>, NumericAlgebra<T> {
+public interface NumbersAddOps<T> : Ring<T>, NumericAlgebra<T> {
     /**
      * Addition of element and scalar.
      *

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/numbers.kt

@@ -10,8 +10,8 @@ import kotlin.math.pow as kpow
 /**
  * Advanced Number-like semifield that implements basic operations.
  */
-public interface ExtendedFieldOperations<T> :
+public interface ExtendedFieldOps<T> :
-    FieldOperations<T>,
+    FieldOps<T>,
     TrigonometricOperations<T>,
     PowerOperations<T>,
     ExponentialOperations<T>,
@@ -35,14 +35,14 @@ public interface ExtendedFieldOperations<T> :
         ExponentialOperations.ACOSH_OPERATION -> ::acosh
         ExponentialOperations.ASINH_OPERATION -> ::asinh
         ExponentialOperations.ATANH_OPERATION -> ::atanh
-        else -> super<FieldOperations>.unaryOperationFunction(operation)
+        else -> super<FieldOps>.unaryOperationFunction(operation)
     }
 }
 
 /**
  * Advanced Number-like field that implements basic operations.
  */
-public interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T>, NumericAlgebra<T>{
+public interface ExtendedField<T> : ExtendedFieldOps<T>, Field<T>, NumericAlgebra<T>{
     override fun sinh(arg: T): T = (exp(arg) - exp(-arg)) / 2.0
     override fun cosh(arg: T): T = (exp(arg) + exp(-arg)) / 2.0
     override fun tanh(arg: T): T = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))

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

@@ -7,6 +7,7 @@ package space.kscience.kmath.structures
 
 import space.kscience.kmath.nd.get
 import space.kscience.kmath.nd.ndAlgebra
+import space.kscience.kmath.nd.produce
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.testutils.FieldVerifier
@@ -21,7 +22,7 @@ internal class NDFieldTest {
 
     @Test
     fun testStrides() {
-        val ndArray = DoubleField.ndAlgebra(10, 10).produce { (it[0] + it[1]).toDouble() }
+        val ndArray = DoubleField.ndAlgebra.produce(10, 10) { (it[0] + it[1]).toDouble() }
         assertEquals(ndArray[5, 5], 10.0)
     }
 }

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

@@ -7,10 +7,7 @@ package space.kscience.kmath.structures
 
 import space.kscience.kmath.linear.linearSpace
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.nd.*
-import space.kscience.kmath.nd.combine
-import space.kscience.kmath.nd.get
-import space.kscience.kmath.nd.ndAlgebra
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.Norm
 import space.kscience.kmath.operations.algebra
@@ -22,9 +19,9 @@ import kotlin.test.assertEquals
 
 @Suppress("UNUSED_VARIABLE")
 class NumberNDFieldTest {
-    val algebra = DoubleField.ndAlgebra(3, 3)
+    val algebra = DoubleField.ndAlgebra
-    val array1 = algebra.produce { (i, j) -> (i + j).toDouble() }
+    val array1 = algebra.produce(3, 3) { (i, j) -> (i + j).toDouble() }
-    val array2 = algebra.produce { (i, j) -> (i - j).toDouble() }
+    val array2 = algebra.produce(3, 3) { (i, j) -> (i - j).toDouble() }
 
     @Test
     fun testSum() {
@@ -77,7 +74,7 @@ class NumberNDFieldTest {
 
     @Test
     fun combineTest() {
-        val division = array1.combine(array2, Double::div)
+        val division = array1.zip(array2, Double::div)
     }
 
     object L2Norm : Norm<StructureND<Number>, Double> {

kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/chains/flowExtra.kt

@@ -10,12 +10,12 @@ import kotlinx.coroutines.flow.Flow
 import kotlinx.coroutines.flow.map
 import kotlinx.coroutines.flow.runningReduce
 import kotlinx.coroutines.flow.scan
-import space.kscience.kmath.operations.GroupOperations
+import space.kscience.kmath.operations.GroupOps
 import space.kscience.kmath.operations.Ring
 import space.kscience.kmath.operations.ScaleOperations
 import space.kscience.kmath.operations.invoke
 
-public fun <T> Flow<T>.cumulativeSum(group: GroupOperations<T>): Flow<T> =
+public fun <T> Flow<T>.cumulativeSum(group: GroupOps<T>): Flow<T> =
     group { runningReduce { sum, element -> sum + element } }
 
 @ExperimentalCoroutinesApi

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

@@ -13,8 +13,8 @@ import space.kscience.kmath.structures.DoubleBuffer
  * Map one [BufferND] using function without indices.
  */
 public inline fun BufferND<Double>.mapInline(crossinline transform: DoubleField.(Double) -> Double): BufferND<Double> {
-    val array = DoubleArray(strides.linearSize) { offset -> DoubleField.transform(buffer[offset]) }
+    val array = DoubleArray(indexes.linearSize) { offset -> DoubleField.transform(buffer[offset]) }
-    return BufferND(strides, DoubleBuffer(array))
+    return BufferND(indexes, DoubleBuffer(array))
 }
 
 /**

kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/DoubleHistogramSpace.kt

@@ -28,10 +28,9 @@ public class DoubleHistogramSpace(
 
     public val dimension: Int get() = lower.size
 
-    private val shape = IntArray(binNums.size) { binNums[it] + 2 }
+    override val shape: IntArray = IntArray(binNums.size) { binNums[it] + 2 }
     override val histogramValueSpace: DoubleFieldND = DoubleField.ndAlgebra(*shape)
 
-    override val strides: Strides get() = histogramValueSpace.strides
     private val binSize = DoubleBuffer(dimension) { (upper[it] - lower[it]) / binNums[it] }
 
     /**
@@ -52,7 +51,7 @@ public class DoubleHistogramSpace(
         val lowerBoundary = index.mapIndexed { axis, i ->
             when (i) {
                 0 -> Double.NEGATIVE_INFINITY
-                strides.shape[axis] - 1 -> upper[axis]
+                shape[axis] - 1 -> upper[axis]
                 else -> lower[axis] + (i.toDouble()) * binSize[axis]
             }
         }.asBuffer()
@@ -60,7 +59,7 @@ public class DoubleHistogramSpace(
         val upperBoundary = index.mapIndexed { axis, i ->
             when (i) {
                 0 -> lower[axis]
-                strides.shape[axis] - 1 -> Double.POSITIVE_INFINITY
+                shape[axis] - 1 -> Double.POSITIVE_INFINITY
                 else -> lower[axis] + (i.toDouble() + 1) * binSize[axis]
             }
         }.asBuffer()
@@ -75,7 +74,7 @@ public class DoubleHistogramSpace(
     }
 
     override fun produce(builder: HistogramBuilder<Double>.() -> Unit): IndexedHistogram<Double, Double> {
-        val ndCounter = StructureND.auto(strides) { Counter.real() }
+        val ndCounter = StructureND.auto(shape) { Counter.real() }
         val hBuilder = HistogramBuilder<Double> { point, value ->
             val index = getIndex(point)
             ndCounter[index].add(value.toDouble())

kmath-histograms/src/commonMain/kotlin/space/kscience/kmath/histogram/IndexedHistogramSpace.kt

@@ -8,8 +8,9 @@ package space.kscience.kmath.histogram
 import space.kscience.kmath.domains.Domain
 import space.kscience.kmath.linear.Point
 import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.nd.DefaultStrides
 import space.kscience.kmath.nd.FieldND
-import space.kscience.kmath.nd.Strides
+import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.Group
 import space.kscience.kmath.operations.ScaleOperations
@@ -34,10 +35,10 @@ public class IndexedHistogram<T : Comparable<T>, V : Any>(
         return context.produceBin(index, values[index])
     }
 
-    override val dimension: Int get() = context.strides.shape.size
+    override val dimension: Int get() = context.shape.size
 
     override val bins: Iterable<Bin<T>>
-        get() = context.strides.indices().map {
+        get() = DefaultStrides(context.shape).indices().map {
             context.produceBin(it, values[it])
         }.asIterable()
 
@@ -49,7 +50,7 @@ public class IndexedHistogram<T : Comparable<T>, V : Any>(
 public interface IndexedHistogramSpace<T : Comparable<T>, V : Any>
     : Group<IndexedHistogram<T, V>>, ScaleOperations<IndexedHistogram<T, V>> {
     //public val valueSpace: Space<V>
-    public val strides: Strides
+    public val shape: Shape
     public val histogramValueSpace: FieldND<V, *> //= NDAlgebra.space(valueSpace, Buffer.Companion::boxing, *shape),
 
     /**

kmath-histograms/src/commonTest/kotlin/space/kscience/kmath/histogram/MultivariateHistogramTest.kt

@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.histogram
 
+import space.kscience.kmath.nd.DefaultStrides
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.real.DoubleVector
 import kotlin.random.Random
@@ -69,7 +70,7 @@ internal class MultivariateHistogramTest {
             }
             val res = histogram1 - histogram2
             assertTrue {
-                strides.indices().all { index ->
+                DefaultStrides(shape).indices().all { index ->
                     res.values[index] <= histogram1.values[index]
                 }
             }

kmath-kotlingrad/src/main/kotlin/space/kscience/kmath/kotlingrad/scalarsAdapters.kt

@@ -106,8 +106,8 @@ public fun <X : SFun<X>> MST.toSFun(): SFun<X> = when (this) {
     is Symbol -> toSVar()
 
     is MST.Unary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> +value.toSFun<X>()
+        GroupOps.PLUS_OPERATION -> +value.toSFun<X>()
-        GroupOperations.MINUS_OPERATION -> -value.toSFun<X>()
+        GroupOps.MINUS_OPERATION -> -value.toSFun<X>()
         TrigonometricOperations.SIN_OPERATION -> sin(value.toSFun())
         TrigonometricOperations.COS_OPERATION -> cos(value.toSFun())
         TrigonometricOperations.TAN_OPERATION -> tan(value.toSFun())
@@ -124,10 +124,10 @@ public fun <X : SFun<X>> MST.toSFun(): SFun<X> = when (this) {
     }
 
     is MST.Binary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> left.toSFun<X>() + right.toSFun()
+        GroupOps.PLUS_OPERATION -> left.toSFun<X>() + right.toSFun()
-        GroupOperations.MINUS_OPERATION -> left.toSFun<X>() - right.toSFun()
+        GroupOps.MINUS_OPERATION -> left.toSFun<X>() - right.toSFun()
-        RingOperations.TIMES_OPERATION -> left.toSFun<X>() * right.toSFun()
+        RingOps.TIMES_OPERATION -> left.toSFun<X>() * right.toSFun()
-        FieldOperations.DIV_OPERATION -> left.toSFun<X>() / right.toSFun()
+        FieldOps.DIV_OPERATION -> left.toSFun<X>() / right.toSFun()
         PowerOperations.POW_OPERATION -> left.toSFun<X>() pow (right as MST.Numeric).toSConst()
         else -> error("Binary operation $operation not defined in $this")
     }

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

@@ -15,13 +15,6 @@ import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.*
 
-internal fun AlgebraND<*, *>.checkShape(array: INDArray): INDArray {
-    val arrayShape = array.shape().toIntArray()
-    if (!shape.contentEquals(arrayShape)) throw ShapeMismatchException(shape, arrayShape)
-    return array
-}
-
-
 /**
  * Represents [AlgebraND] over [Nd4jArrayAlgebra].
  *
@@ -39,33 +32,34 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
      */
     public val StructureND<T>.ndArray: INDArray
 
-    override fun produce(initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
+    override fun produce(shape: Shape, initializer: C.(IntArray) -> T): Nd4jArrayStructure<T> {
         val struct = Nd4j.create(*shape)!!.wrap()
-        struct.indicesIterator().forEach { struct[it] = elementContext.initializer(it) }
+        struct.indicesIterator().forEach { struct[it] = elementAlgebra.initializer(it) }
         return struct
     }
 
     override fun StructureND<T>.map(transform: C.(T) -> T): Nd4jArrayStructure<T> {
         val newStruct = ndArray.dup().wrap()
-        newStruct.elements().forEach { (idx, value) -> newStruct[idx] = elementContext.transform(value) }
+        newStruct.elements().forEach { (idx, value) -> newStruct[idx] = elementAlgebra.transform(value) }
         return newStruct
     }
 
     override fun StructureND<T>.mapIndexed(
         transform: C.(index: IntArray, T) -> T,
     ): Nd4jArrayStructure<T> {
-        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] = elementAlgebra.transform(idx, this[idx]) }
         return new
     }
 
-    override fun combine(
+    override fun zip(
-        a: StructureND<T>,
+        left: StructureND<T>,
-        b: StructureND<T>,
+        right: StructureND<T>,
         transform: C.(T, T) -> T,
     ): Nd4jArrayStructure<T> {
-        val new = Nd4j.create(*shape).wrap()
+        require(left.shape.contentEquals(right.shape)) { "Can't zip tow structures of shape ${left.shape} and ${right.shape}" }
-        new.indicesIterator().forEach { idx -> new[idx] = elementContext.transform(a[idx], b[idx]) }
+        val new = Nd4j.create(*left.shape).wrap()
+        new.indicesIterator().forEach { idx -> new[idx] = elementAlgebra.transform(left[idx], right[idx]) }
         return new
     }
 }
@@ -76,10 +70,7 @@ public sealed interface Nd4jArrayAlgebra<T, out C : Algebra<T>> : AlgebraND<T, C
  * @param T the type of the element contained in ND structure.
  * @param S the type of space of structure elements.
  */
-public sealed interface Nd4jArrayGroup<T, out S : Ring<T>> : GroupND<T, S>, Nd4jArrayAlgebra<T, S> {
+public sealed interface Nd4jArrayGroupOps<T, out S : Ring<T>> : GroupOpsND<T, S>, Nd4jArrayAlgebra<T, S> {
-
-    override val zero: Nd4jArrayStructure<T>
-        get() = Nd4j.zeros(*shape).wrap()
 
     override fun add(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
         a.ndArray.add(b.ndArray).wrap()
@@ -101,10 +92,7 @@ public sealed interface Nd4jArrayGroup<T, out S : Ring<T>> : GroupND<T, S>, Nd4j
  * @param R the type of ring of structure elements.
  */
 @OptIn(UnstableKMathAPI::class)
-public sealed interface Nd4jArrayRing<T, out R : Ring<T>> : RingND<T, R>, Nd4jArrayGroup<T, R> {
+public sealed interface Nd4jArrayRingOps<T, out R : Ring<T>> : RingOpsND<T, R>, Nd4jArrayGroupOps<T, R> {
-
-    override val one: Nd4jArrayStructure<T>
-        get() = Nd4j.ones(*shape).wrap()
 
     override fun multiply(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
         a.ndArray.mul(b.ndArray).wrap()
@@ -125,21 +113,12 @@ public sealed interface Nd4jArrayRing<T, out R : Ring<T>> : RingND<T, R>, Nd4jAr
 //    }
 
     public companion object {
-        private val intNd4jArrayRingCache: ThreadLocal<MutableMap<IntArray, IntNd4jArrayRing>> =
-            ThreadLocal.withInitial(::HashMap)
-
-        /**
-         * Creates an [RingND] for [Int] values or pull it from cache if it was created previously.
-         */
-        public fun int(vararg shape: Int): Nd4jArrayRing<Int, IntRing> =
-            intNd4jArrayRingCache.get().getOrPut(shape) { IntNd4jArrayRing(shape) }
-
         /**
          * Creates a most suitable implementation of [RingND] using reified class.
          */
         @Suppress("UNCHECKED_CAST")
-        public inline fun <reified T : Number> auto(vararg shape: Int): Nd4jArrayRing<T, Ring<T>> = when {
+        public inline fun <reified T : Number> auto(vararg shape: Int): Nd4jArrayRingOps<T, Ring<T>> = when {
-            T::class == Int::class -> int(*shape) as Nd4jArrayRing<T, Ring<T>>
+            T::class == Int::class -> IntRing.nd4j as Nd4jArrayRingOps<T, Ring<T>>
             else -> throw UnsupportedOperationException("This factory method only supports Long type.")
         }
     }
@@ -151,38 +130,21 @@ public sealed interface Nd4jArrayRing<T, out R : Ring<T>> : RingND<T, R>, Nd4jAr
  * @param T the type of the element contained in ND structure.
  * @param F the type field of structure elements.
  */
-public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldND<T, F>, Nd4jArrayRing<T, F> {
+public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldOpsND<T, F>, Nd4jArrayRingOps<T, F> {
+
     override fun divide(a: StructureND<T>, b: StructureND<T>): Nd4jArrayStructure<T> =
         a.ndArray.div(b.ndArray).wrap()
 
     public operator fun Number.div(b: StructureND<T>): Nd4jArrayStructure<T> = b.ndArray.rdiv(this).wrap()
 
     public companion object {
-        private val floatNd4jArrayFieldCache: ThreadLocal<MutableMap<IntArray, FloatNd4jArrayField>> =
-            ThreadLocal.withInitial(::HashMap)
-
-        private val doubleNd4JArrayFieldCache: ThreadLocal<MutableMap<IntArray, DoubleNd4jArrayField>> =
-            ThreadLocal.withInitial(::HashMap)
-
-        /**
-         * Creates an [FieldND] for [Float] values or pull it from cache if it was created previously.
-         */
-        public fun float(vararg shape: Int): Nd4jArrayRing<Float, FloatField> =
-            floatNd4jArrayFieldCache.get().getOrPut(shape) { FloatNd4jArrayField(shape) }
-
-        /**
-         * Creates an [FieldND] for [Double] values or pull it from cache if it was created previously.
-         */
-        public fun real(vararg shape: Int): Nd4jArrayRing<Double, DoubleField> =
-            doubleNd4JArrayFieldCache.get().getOrPut(shape) { DoubleNd4jArrayField(shape) }
-
         /**
          * Creates a most suitable implementation of [FieldND] using reified class.
          */
         @Suppress("UNCHECKED_CAST")
         public inline fun <reified T : Any> auto(vararg shape: Int): Nd4jArrayField<T, Field<T>> = when {
-            T::class == Float::class -> float(*shape) as Nd4jArrayField<T, Field<T>>
+            T::class == Float::class -> FloatField.nd4j as Nd4jArrayField<T, Field<T>>
-            T::class == Double::class -> real(*shape) as Nd4jArrayField<T, Field<T>>
+            T::class == Double::class -> DoubleField.nd4j as Nd4jArrayField<T, Field<T>>
             else -> throw UnsupportedOperationException("This factory method only supports Float and Double types.")
         }
     }
@@ -191,8 +153,9 @@ public sealed interface Nd4jArrayField<T, out F : Field<T>> : FieldND<T, F>, Nd4
 /**
  * Represents intersection of [ExtendedField] and [Field] over [Nd4jArrayStructure].
  */
-public sealed interface Nd4jArrayExtendedField<T, out F : ExtendedField<T>> : ExtendedField<StructureND<T>>,
+public sealed interface Nd4jArrayExtendedFieldOps<T, out F : ExtendedField<T>> :
-    Nd4jArrayField<T, F> {
+    ExtendedFieldOps<StructureND<T>>, Nd4jArrayField<T, F> {
+
     override fun sin(arg: StructureND<T>): StructureND<T> = Transforms.sin(arg.ndArray).wrap()
     override fun cos(arg: StructureND<T>): StructureND<T> = Transforms.cos(arg.ndArray).wrap()
     override fun asin(arg: StructureND<T>): StructureND<T> = Transforms.asin(arg.ndArray).wrap()
@@ -221,63 +184,59 @@ public sealed interface Nd4jArrayExtendedField<T, out F : ExtendedField<T>> : Ex
 /**
  * Represents [FieldND] over [Nd4jArrayDoubleStructure].
  */
-public class DoubleNd4jArrayField(override val shape: IntArray) : Nd4jArrayExtendedField<Double, DoubleField> {
+public open class DoubleNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps<Double, DoubleField> {
-    override val elementContext: DoubleField get() = DoubleField
+    override val elementAlgebra: DoubleField get() = DoubleField
 
-    override fun INDArray.wrap(): Nd4jArrayStructure<Double> = checkShape(this).asDoubleStructure()
+    override fun INDArray.wrap(): Nd4jArrayStructure<Double> = asDoubleStructure()
 
     @OptIn(PerformancePitfall::class)
     override val StructureND<Double>.ndArray: INDArray
         get() = when (this) {
-            is Nd4jArrayStructure<Double> -> checkShape(ndArray)
+            is Nd4jArrayStructure<Double> -> ndArray
             else -> Nd4j.zeros(*shape).also {
                 elements().forEach { (idx, value) -> it.putScalar(idx, value) }
             }
         }
 
-    override fun scale(a: StructureND<Double>, value: Double): Nd4jArrayStructure<Double> {
+    override fun scale(a: StructureND<Double>, value: Double): Nd4jArrayStructure<Double> = a.ndArray.mul(value).wrap()
-        return a.ndArray.mul(value).wrap()
-    }
 
-    override operator fun StructureND<Double>.div(arg: Double): Nd4jArrayStructure<Double> {
+    override operator fun StructureND<Double>.div(arg: Double): Nd4jArrayStructure<Double> = ndArray.div(arg).wrap()
-        return ndArray.div(arg).wrap()
-    }
 
-    override operator fun StructureND<Double>.plus(arg: Double): Nd4jArrayStructure<Double> {
+    override operator fun StructureND<Double>.plus(arg: Double): Nd4jArrayStructure<Double> = ndArray.add(arg).wrap()
-        return ndArray.add(arg).wrap()
-    }
 
-    override operator fun StructureND<Double>.minus(arg: Double): Nd4jArrayStructure<Double> {
+    override operator fun StructureND<Double>.minus(arg: Double): Nd4jArrayStructure<Double> = ndArray.sub(arg).wrap()
-        return ndArray.sub(arg).wrap()
-    }
 
-    override operator fun StructureND<Double>.times(arg: Double): Nd4jArrayStructure<Double> {
+    override operator fun StructureND<Double>.times(arg: Double): Nd4jArrayStructure<Double> = ndArray.mul(arg).wrap()
-        return ndArray.mul(arg).wrap()
-    }
 
-    override operator fun Double.div(arg: StructureND<Double>): Nd4jArrayStructure<Double> {
+    override operator fun Double.div(arg: StructureND<Double>): Nd4jArrayStructure<Double> =
-        return arg.ndArray.rdiv(this).wrap()
+        arg.ndArray.rdiv(this).wrap()
-    }
 
-    override operator fun Double.minus(arg: StructureND<Double>): Nd4jArrayStructure<Double> {
+    override operator fun Double.minus(arg: StructureND<Double>): Nd4jArrayStructure<Double> =
-        return arg.ndArray.rsub(this).wrap()
+        arg.ndArray.rsub(this).wrap()
-    }
+
+    public companion object : DoubleNd4jArrayFieldOps()
 }
 
-public fun DoubleField.nd4j(vararg shape: Int): DoubleNd4jArrayField = DoubleNd4jArrayField(intArrayOf(*shape))
+public val DoubleField.nd4j: DoubleNd4jArrayFieldOps get() = DoubleNd4jArrayFieldOps
+
+public class DoubleNd4jArrayField(override val shape: Shape) : DoubleNd4jArrayFieldOps(), FieldND<Double, DoubleField>
+
+public fun DoubleField.nd4j(shapeFirst: Int, vararg shapeRest: Int): DoubleNd4jArrayField =
+    DoubleNd4jArrayField(intArrayOf(shapeFirst, * shapeRest))
+
 
 /**
  * Represents [FieldND] over [Nd4jArrayStructure] of [Float].
  */
-public class FloatNd4jArrayField(override val shape: IntArray) : Nd4jArrayExtendedField<Float, FloatField> {
+public open class FloatNd4jArrayFieldOps : Nd4jArrayExtendedFieldOps<Float, FloatField> {
-    override val elementContext: FloatField get() = FloatField
+    override val elementAlgebra: FloatField get() = FloatField
 
-    override fun INDArray.wrap(): Nd4jArrayStructure<Float> = checkShape(this).asFloatStructure()
+    override fun INDArray.wrap(): Nd4jArrayStructure<Float> = asFloatStructure()
 
     @OptIn(PerformancePitfall::class)
     override val StructureND<Float>.ndArray: INDArray
         get() = when (this) {
-            is Nd4jArrayStructure<Float> -> checkShape(ndArray)
+            is Nd4jArrayStructure<Float> -> ndArray
             else -> Nd4j.zeros(*shape).also {
                 elements().forEach { (idx, value) -> it.putScalar(idx, value) }
             }
@@ -303,21 +262,29 @@ public class FloatNd4jArrayField(override val shape: IntArray) : Nd4jArrayExtend
 
     override operator fun Float.minus(arg: StructureND<Float>): Nd4jArrayStructure<Float> =
         arg.ndArray.rsub(this).wrap()
+
+    public companion object : FloatNd4jArrayFieldOps()
 }
 
+public class FloatNd4jArrayField(override val shape: Shape) : FloatNd4jArrayFieldOps(), RingND<Float, FloatField>
+
+public val FloatField.nd4j: FloatNd4jArrayFieldOps get() = FloatNd4jArrayFieldOps
+
+public fun FloatField.nd4j(shapeFirst: Int, vararg shapeRest: Int): FloatNd4jArrayField =
+    FloatNd4jArrayField(intArrayOf(shapeFirst, * shapeRest))
+
 /**
  * Represents [RingND] over [Nd4jArrayIntStructure].
  */
-public class IntNd4jArrayRing(override val shape: IntArray) : Nd4jArrayRing<Int, IntRing> {
+public open class IntNd4jArrayRingOps : Nd4jArrayRingOps<Int, IntRing> {
-    override val elementContext: IntRing
+    override val elementAlgebra: IntRing get() = IntRing
-        get() = IntRing
 
-    override fun INDArray.wrap(): Nd4jArrayStructure<Int> = checkShape(this).asIntStructure()
+    override fun INDArray.wrap(): Nd4jArrayStructure<Int> = asIntStructure()
 
     @OptIn(PerformancePitfall::class)
     override val StructureND<Int>.ndArray: INDArray
         get() = when (this) {
-            is Nd4jArrayStructure<Int> -> checkShape(ndArray)
+            is Nd4jArrayStructure<Int> -> ndArray
             else -> Nd4j.zeros(*shape).also {
                 elements().forEach { (idx, value) -> it.putScalar(idx, value) }
             }
@@ -334,4 +301,13 @@ public class IntNd4jArrayRing(override val shape: IntArray) : Nd4jArrayRing<Int,
 
     override operator fun Int.minus(arg: StructureND<Int>): Nd4jArrayStructure<Int> =
         arg.ndArray.rsub(this).wrap()
+
+    public companion object : IntNd4jArrayRingOps()
 }
+
+public val IntRing.nd4j: IntNd4jArrayRingOps get() = IntNd4jArrayRingOps
+
+public class IntNd4jArrayRing(override val shape: Shape) : IntNd4jArrayRingOps(), RingND<Int, IntRing>
+
+public fun IntRing.nd4j(shapeFirst: Int, vararg shapeRest: Int): IntNd4jArrayRing =
+    IntNd4jArrayRing(intArrayOf(shapeFirst, * shapeRest))

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

@@ -8,6 +8,10 @@ package space.kscience.kmath.nd4j
 import org.nd4j.linalg.factory.Nd4j
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.nd.one
+import space.kscience.kmath.nd.produce
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.IntRing
 import space.kscience.kmath.operations.invoke
 import kotlin.math.PI
 import kotlin.test.Test
@@ -19,7 +23,7 @@ import kotlin.test.fail
 internal class Nd4jArrayAlgebraTest {
     @Test
     fun testProduce() {
-        val res = with(DoubleNd4jArrayField(intArrayOf(2, 2))) { produce { it.sum().toDouble() } }
+        val res = DoubleField.nd4j.produce(2, 2) { it.sum().toDouble() }
         val expected = (Nd4j.create(2, 2) ?: fail()).asDoubleStructure()
         expected[intArrayOf(0, 0)] = 0.0
         expected[intArrayOf(0, 1)] = 1.0
@@ -30,7 +34,9 @@ internal class Nd4jArrayAlgebraTest {
 
     @Test
     fun testMap() {
-        val res = with(IntNd4jArrayRing(intArrayOf(2, 2))) { one.map { it + it * 2 } }
+        val res = IntRing.nd4j {
+            one(2, 2).map { it + it * 2 }
+        }
         val expected = (Nd4j.create(2, 2) ?: fail()).asIntStructure()
         expected[intArrayOf(0, 0)] = 3
         expected[intArrayOf(0, 1)] = 3
@@ -41,7 +47,7 @@ internal class Nd4jArrayAlgebraTest {
 
     @Test
     fun testAdd() {
-        val res = with(IntNd4jArrayRing(intArrayOf(2, 2))) { one + 25 }
+        val res = IntRing.nd4j { one(2, 2) + 25 }
         val expected = (Nd4j.create(2, 2) ?: fail()).asIntStructure()
         expected[intArrayOf(0, 0)] = 26
         expected[intArrayOf(0, 1)] = 26
@@ -51,10 +57,10 @@ internal class Nd4jArrayAlgebraTest {
     }
 
     @Test
-    fun testSin() = DoubleNd4jArrayField(intArrayOf(2, 2)).invoke {
+    fun testSin() = DoubleField.nd4j{
-        val initial = produce { (i, j) -> if (i == j) PI / 2 else 0.0 }
+        val initial = produce(2, 2) { (i, j) -> if (i == j) PI / 2 else 0.0 }
         val transformed = sin(initial)
-        val expected = produce { (i, j) -> if (i == j) 1.0 else 0.0 }
+        val expected = produce(2, 2) { (i, j) -> if (i == j) 1.0 else 0.0 }
 
         println(transformed)
         assertTrue { StructureND.contentEquals(transformed, expected) }

kmath-symja/src/main/kotlin/space/kscience/kmath/symja/adapters.kt

@@ -64,8 +64,8 @@ public fun MST.toIExpr(): IExpr = when (this) {
     }
 
     is MST.Unary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> value.toIExpr()
+        GroupOps.PLUS_OPERATION -> value.toIExpr()
-        GroupOperations.MINUS_OPERATION -> F.Negate(value.toIExpr())
+        GroupOps.MINUS_OPERATION -> F.Negate(value.toIExpr())
         TrigonometricOperations.SIN_OPERATION -> F.Sin(value.toIExpr())
         TrigonometricOperations.COS_OPERATION -> F.Cos(value.toIExpr())
         TrigonometricOperations.TAN_OPERATION -> F.Tan(value.toIExpr())
@@ -85,10 +85,10 @@ public fun MST.toIExpr(): IExpr = when (this) {
     }
 
     is MST.Binary -> when (operation) {
-        GroupOperations.PLUS_OPERATION -> left.toIExpr() + right.toIExpr()
+        GroupOps.PLUS_OPERATION -> left.toIExpr() + right.toIExpr()
-        GroupOperations.MINUS_OPERATION -> left.toIExpr() - right.toIExpr()
+        GroupOps.MINUS_OPERATION -> left.toIExpr() - right.toIExpr()
-        RingOperations.TIMES_OPERATION -> left.toIExpr() * right.toIExpr()
+        RingOps.TIMES_OPERATION -> left.toIExpr() * right.toIExpr()
-        FieldOperations.DIV_OPERATION -> F.Divide(left.toIExpr(), right.toIExpr())
+        FieldOps.DIV_OPERATION -> F.Divide(left.toIExpr(), right.toIExpr())
         PowerOperations.POW_OPERATION -> F.Power(left.toIExpr(), F.symjify((right as MST.Numeric).value))
         else -> error("Binary operation $operation not defined in $this")
     }

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensorAlgebra.kt

@@ -373,8 +373,12 @@ public open class DoubleTensorAlgebra :
         return resTensor
     }
 
-    override fun diagonalEmbedding(diagonalEntries: Tensor<Double>, offset: Int, dim1: Int, dim2: Int):
+    override fun diagonalEmbedding(
-            DoubleTensor {
+        diagonalEntries: Tensor<Double>,
+        offset: Int,
+        dim1: Int,
+        dim2: Int
+    ): DoubleTensor {
         val n = diagonalEntries.shape.size
         val d1 = minusIndexFrom(n + 1, dim1)
         val d2 = minusIndexFrom(n + 1, dim2)

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/TensorLinearStructure.kt

@@ -44,7 +44,7 @@ internal fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArra
  *
  * @param shape the shape of the tensor.
  */
-internal class TensorLinearStructure(override val shape: IntArray) : Strides {
+internal class TensorLinearStructure(override val shape: IntArray) : Strides() {
     override val strides: IntArray
         get() = stridesFromShape(shape)
 
@@ -54,4 +54,18 @@ internal class TensorLinearStructure(override val shape: IntArray) : Strides {
     override val linearSize: Int
         get() = shape.reduce(Int::times)
 
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other == null || this::class != other::class) return false
+
+        other as TensorLinearStructure
+
+        if (!shape.contentEquals(other.shape)) return false
+
+        return true
+    }
+
+    override fun hashCode(): Int {
+        return shape.contentHashCode()
+    }
 }

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/internal/tensorCastsUtils.kt

@@ -26,8 +26,11 @@ internal fun <T> Tensor<T>.copyToBufferedTensor(): BufferedTensor<T> =
 
 internal fun <T> Tensor<T>.toBufferedTensor(): BufferedTensor<T> = when (this) {
     is BufferedTensor<T> -> this
-    is MutableBufferND<T> -> if (this.strides.strides contentEquals TensorLinearStructure(this.shape).strides)
+    is MutableBufferND<T> -> if (this.indexes == TensorLinearStructure(this.shape)) {
-        BufferedTensor(this.shape, this.mutableBuffer, 0) else this.copyToBufferedTensor()
+        BufferedTensor(this.shape, this.mutableBuffer, 0)
+    } else {
+        this.copyToBufferedTensor()
+    }
     else -> this.copyToBufferedTensor()
 }
 

kmath-viktor/src/main/kotlin/space/kscience/kmath/viktor/ViktorStructureND.kt

@@ -11,7 +11,7 @@ import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.NumbersAddOperations
+import space.kscience.kmath.operations.NumbersAddOps
 import space.kscience.kmath.operations.ScaleOperations
 
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
@@ -34,7 +34,7 @@ public fun F64Array.asStructure(): ViktorStructureND = ViktorStructureND(this)
 @OptIn(UnstableKMathAPI::class)
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
 public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, DoubleField>,
-    NumbersAddOperations<StructureND<Double>>, ExtendedField<StructureND<Double>>,
+    NumbersAddOps<StructureND<Double>>, ExtendedField<StructureND<Double>>,
     ScaleOperations<StructureND<Double>> {
 
     public val StructureND<Double>.f64Buffer: F64Array
@@ -44,7 +44,7 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
                 shape
             )
             this is ViktorStructureND && this.f64Buffer.shape.contentEquals(this@ViktorFieldND.shape) -> this.f64Buffer
-            else -> produce { this@f64Buffer[it] }.f64Buffer
+            else -> produce(shape) { this@f64Buffer[it] }.f64Buffer
         }
 
     override val zero: ViktorStructureND by lazy { F64Array.full(init = 0.0, shape = shape).asStructure() }
@@ -52,9 +52,9 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
 
     private val strides: Strides = DefaultStrides(shape)
 
-    override val elementContext: DoubleField get() = DoubleField
+    override val elementAlgebra: DoubleField get() = DoubleField
 
-    override fun produce(initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
+    override fun produce(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
         F64Array(*shape).apply {
             this@ViktorFieldND.strides.indices().forEach { index ->
                 set(value = DoubleField.initializer(index), indices = index)
@@ -78,13 +78,13 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
         }
     }.asStructure()
 
-    override fun combine(
+    override fun zip(
-        a: StructureND<Double>,
+        left: StructureND<Double>,
-        b: StructureND<Double>,
+        right: StructureND<Double>,
         transform: DoubleField.(Double, Double) -> Double,
     ): ViktorStructureND = F64Array(*shape).apply {
         this@ViktorFieldND.strides.indices().forEach { index ->
-            set(value = DoubleField.transform(a[index], b[index]), indices = index)
+            set(value = DoubleField.transform(left[index], right[index]), indices = index)
         }
     }.asStructure()
 
@@ -123,4 +123,4 @@ public class ViktorFieldND(override val shape: IntArray) : FieldND<Double, Doubl
     override fun ln(arg: StructureND<Double>): ViktorStructureND = arg.f64Buffer.log().asStructure()
 }
 
-public fun ViktorNDField(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape)
+public fun ViktorFieldND(vararg shape: Int): ViktorFieldND = ViktorFieldND(shape)

settings.gradle.kts

@@ -1,16 +1,18 @@
 pluginManagement {
     repositories {
-        mavenLocal()
         maven("https://repo.kotlin.link")
         mavenCentral()
         gradlePluginPortal()
     }
 
-    val kotlinVersion = "1.6.0-M1"
+    val kotlinVersion = "1.6.0-RC"
+    val toolsVersion = "0.10.5"
 
     plugins {
         id("org.jetbrains.kotlinx.benchmark") version "0.3.1"
-        id("ru.mipt.npm.gradle.project") version "0.10.5"
+        id("ru.mipt.npm.gradle.project") version toolsVersion
+        id("ru.mipt.npm.gradle.jvm") version toolsVersion
+        id("ru.mipt.npm.gradle.mpp") version toolsVersion
         kotlin("multiplatform") version kotlinVersion
         kotlin("plugin.allopen") version kotlinVersion
     }