CHANGELOG.md

@@ -32,6 +32,8 @@
 - Optimized dot product for buffer matrices moved to `kmath-for-real`
 - EjmlMatrix context is an object
 - Matrix LUP `inverse` renamed to `inverseWithLUP`
+- `NumericAlgebra` moved outside of regular algebra chain (`Ring` no longer implements it).
+- Features moved to NDStructure and became transparent.
 
 ### Deprecated
 

build.gradle.kts

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

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

@@ -0,0 +1,25 @@
+package kscience.kmath.benchmarks
+
+import kscience.kmath.structures.NDField
+import org.openjdk.jmh.annotations.Benchmark
+import org.openjdk.jmh.annotations.Scope
+import org.openjdk.jmh.annotations.State
+import org.openjdk.jmh.infra.Blackhole
+import kotlin.random.Random
+
+@State(Scope.Benchmark)
+class LargeNDBenchmark {
+    val arraySize = 10000
+    val RANDOM = Random(222)
+    val src1 = DoubleArray(arraySize) { RANDOM.nextDouble() }
+    val src2 = DoubleArray(arraySize) { RANDOM.nextDouble() }
+    val field = NDField.real(arraySize)
+    val kmathArray1 = field.produce { (a) -> src1[a] }
+    val kmathArray2 = field.produce { (a) -> src2[a] }
+
+    @Benchmark
+    fun test10000(bh: Blackhole) {
+        bh.consume(field.add(kmathArray1, kmathArray2))
+    }
+
+}

examples/src/main/kotlin/kscience/kmath/stat/DistributionBenchmark.kt

@@ -3,7 +3,6 @@ package kscience.kmath.commons.prob
 import kotlinx.coroutines.Dispatchers
 import kotlinx.coroutines.async
 import kotlinx.coroutines.runBlocking
-import kscience.kmath.chains.BlockingRealChain
 import kscience.kmath.stat.*
 import org.apache.commons.rng.sampling.distribution.ZigguratNormalizedGaussianSampler
 import org.apache.commons.rng.simple.RandomSource
@@ -13,7 +12,7 @@ import java.time.Instant
 private fun runChain(): Duration {
     val generator = RandomGenerator.fromSource(RandomSource.MT, 123L)
     val normal = Distribution.normal(NormalSamplerMethod.Ziggurat)
-    val chain = normal.sample(generator) as BlockingRealChain
+    val chain = normal.sample(generator)
     val startTime = Instant.now()
     var sum = 0.0
 

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

@@ -11,7 +11,7 @@ fun main() {
     val n = 1000
 
     val realField = NDField.real(dim, dim)
-    val complexField = NDField.complex(dim, dim)
+    val complexField: ComplexNDField = NDField.complex(dim, dim)
 
     val realTime = measureTimeMillis {
         realField {

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

@@ -33,7 +33,7 @@ fun main() {
     measureAndPrint("Automatic field addition") {
         autoField {
             var res: NDBuffer<Double> = one
-            repeat(n) { res += number(1.0) }
+            repeat(n) { res += 1.0 }
         }
     }
 
@@ -52,7 +52,7 @@ fun main() {
     measureAndPrint("Nd4j specialized addition") {
         nd4jField {
             var res = one
-            repeat(n) { res += 1.0 as Number }
+            repeat(n) { res += 1.0 }
         }
     }
 
@@ -73,7 +73,7 @@ fun main() {
         genericField {
             var res: NDBuffer<Double> = one
             repeat(n) {
-                res += one // couldn't avoid using `one` due to resolution ambiguity }
+                res += 1.0 // couldn't avoid using `one` due to resolution ambiguity }
             }
         }
     }

kmath-ast/src/commonMain/kotlin/kscience/kmath/ast/MstAlgebra.kt

@@ -1,5 +1,6 @@
 package kscience.kmath.ast
 
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.*
 
 /**
@@ -25,8 +26,11 @@ public object MstSpace : Space<MST>, NumericAlgebra<MST> {
     public override fun number(value: Number): MST.Numeric = MstAlgebra.number(value)
     public override fun symbol(value: String): MST.Symbolic = MstAlgebra.symbol(value)
     public override fun add(a: MST, b: MST): MST.Binary = binaryOperationFunction(SpaceOperations.PLUS_OPERATION)(a, b)
-    public override operator fun MST.unaryPlus(): MST.Unary = unaryOperationFunction(SpaceOperations.PLUS_OPERATION)(this)
+    public override operator fun MST.unaryPlus(): MST.Unary =
-    public override operator fun MST.unaryMinus(): MST.Unary = unaryOperationFunction(SpaceOperations.MINUS_OPERATION)(this)
+        unaryOperationFunction(SpaceOperations.PLUS_OPERATION)(this)
+
+    public override operator fun MST.unaryMinus(): MST.Unary =
+        unaryOperationFunction(SpaceOperations.MINUS_OPERATION)(this)
 
     public override operator fun MST.minus(b: MST): MST.Binary =
         binaryOperationFunction(SpaceOperations.MINUS_OPERATION)(this, b)
@@ -44,7 +48,8 @@ public object MstSpace : Space<MST>, NumericAlgebra<MST> {
 /**
  * [Ring] over [MST] nodes.
  */
-public object MstRing : Ring<MST>, NumericAlgebra<MST> {
+@OptIn(UnstableKMathAPI::class)
+public object MstRing : Ring<MST>, RingWithNumbers<MST> {
     public override val zero: MST.Numeric
         get() = MstSpace.zero
 
@@ -54,7 +59,9 @@ public object MstRing : Ring<MST>, NumericAlgebra<MST> {
     public override fun symbol(value: String): MST.Symbolic = MstSpace.symbol(value)
     public override fun add(a: MST, b: MST): MST.Binary = MstSpace.add(a, b)
     public override fun multiply(a: MST, k: Number): MST.Binary = MstSpace.multiply(a, k)
-    public override fun multiply(a: MST, b: MST): MST.Binary = binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, b)
+    public override fun multiply(a: MST, b: MST): MST.Binary =
+        binaryOperationFunction(RingOperations.TIMES_OPERATION)(a, b)
+
     public override operator fun MST.unaryPlus(): MST.Unary = MstSpace { +this@unaryPlus }
     public override operator fun MST.unaryMinus(): MST.Unary = MstSpace { -this@unaryMinus }
     public override operator fun MST.minus(b: MST): MST.Binary = MstSpace { this@minus - b }
@@ -69,7 +76,8 @@ public object MstRing : Ring<MST>, NumericAlgebra<MST> {
 /**
  * [Field] over [MST] nodes.
  */
-public object MstField : Field<MST> {
+@OptIn(UnstableKMathAPI::class)
+public object MstField : Field<MST>, RingWithNumbers<MST> {
     public override val zero: MST.Numeric
         get() = MstRing.zero
 
@@ -81,7 +89,9 @@ public object MstField : Field<MST> {
     public override fun add(a: MST, b: MST): MST.Binary = MstRing.add(a, b)
     public override fun multiply(a: MST, k: Number): MST.Binary = MstRing.multiply(a, k)
     public override fun multiply(a: MST, b: MST): MST.Binary = MstRing.multiply(a, b)
-    public override fun divide(a: MST, b: MST): MST.Binary = binaryOperationFunction(FieldOperations.DIV_OPERATION)(a, b)
+    public override fun divide(a: MST, b: MST): MST.Binary =
+        binaryOperationFunction(FieldOperations.DIV_OPERATION)(a, b)
+
     public override operator fun MST.unaryPlus(): MST.Unary = MstRing { +this@unaryPlus }
     public override operator fun MST.unaryMinus(): MST.Unary = MstRing { -this@unaryMinus }
     public override operator fun MST.minus(b: MST): MST.Binary = MstRing { this@minus - b }
@@ -89,13 +99,14 @@ public object MstField : Field<MST> {
     public override fun binaryOperationFunction(operation: String): (left: MST, right: MST) -> MST.Binary =
         MstRing.binaryOperationFunction(operation)
 
-    public override fun unaryOperationFunction(operation: String): (arg: MST) -> MST.Unary = MstRing.unaryOperationFunction(operation)
+    public override fun unaryOperationFunction(operation: String): (arg: MST) -> MST.Unary =
+        MstRing.unaryOperationFunction(operation)
 }
 
 /**
  * [ExtendedField] over [MST] nodes.
  */
-public object MstExtendedField : ExtendedField<MST> {
+public object MstExtendedField : ExtendedField<MST>, NumericAlgebra<MST> {
     public override val zero: MST.Numeric
         get() = MstField.zero
 
@@ -103,6 +114,7 @@ public object MstExtendedField : ExtendedField<MST> {
         get() = MstField.one
 
     public override fun symbol(value: String): MST.Symbolic = MstField.symbol(value)
+    public override fun number(value: Number): MST.Numeric = MstRing.number(value)
     public override fun sin(arg: MST): MST.Unary = unaryOperationFunction(TrigonometricOperations.SIN_OPERATION)(arg)
     public override fun cos(arg: MST): MST.Unary = unaryOperationFunction(TrigonometricOperations.COS_OPERATION)(arg)
     public override fun tan(arg: MST): MST.Unary = unaryOperationFunction(TrigonometricOperations.TAN_OPERATION)(arg)
@@ -132,5 +144,6 @@ public object MstExtendedField : ExtendedField<MST> {
     public override fun binaryOperationFunction(operation: String): (left: MST, right: MST) -> MST.Binary =
         MstField.binaryOperationFunction(operation)
 
-    public override fun unaryOperationFunction(operation: String): (arg: MST) -> MST.Unary = MstField.unaryOperationFunction(operation)
+    public override fun unaryOperationFunction(operation: String): (arg: MST) -> MST.Unary =
+        MstField.unaryOperationFunction(operation)
 }

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

@@ -1,7 +1,9 @@
 package kscience.kmath.commons.expressions
 
 import kscience.kmath.expressions.*
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.ExtendedField
+import kscience.kmath.operations.RingWithNumbers
 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 
 /**
@@ -10,15 +12,18 @@ import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
  * @property order The derivation order.
  * @property bindings The map of bindings values. All bindings are considered free parameters
  */
+@OptIn(UnstableKMathAPI::class)
 public class DerivativeStructureField(
     public val order: Int,
     bindings: Map<Symbol, Double>,
-) : ExtendedField<DerivativeStructure>, ExpressionAlgebra<Double, DerivativeStructure> {
+) : ExtendedField<DerivativeStructure>, ExpressionAlgebra<Double, DerivativeStructure>, RingWithNumbers<DerivativeStructure> {
     public val numberOfVariables: Int = bindings.size
 
     public override val zero: DerivativeStructure by lazy { DerivativeStructure(numberOfVariables, order) }
     public override val one: DerivativeStructure by lazy { DerivativeStructure(numberOfVariables, order, 1.0) }
 
+    override fun number(value: Number): DerivativeStructure = const(value.toDouble())
+
     /**
      * A class that implements both [DerivativeStructure] and a [Symbol]
      */

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

@@ -1,42 +1,28 @@
 package kscience.kmath.commons.linear
 
-import kscience.kmath.linear.*
+import kscience.kmath.linear.DiagonalFeature
+import kscience.kmath.linear.MatrixContext
+import kscience.kmath.linear.MatrixWrapper
+import kscience.kmath.linear.Point
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.structures.Matrix
-import kscience.kmath.structures.NDStructure
 import org.apache.commons.math3.linear.*
+import kotlin.reflect.KClass
+import kotlin.reflect.cast
 
-public class CMMatrix(public val origin: RealMatrix, features: Set<MatrixFeature>? = null) : FeaturedMatrix<Double> {
+public inline class CMMatrix(public val origin: RealMatrix) : Matrix<Double> {
     public override val rowNum: Int get() = origin.rowDimension
     public override val colNum: Int get() = origin.columnDimension
 
-    public override val features: Set<MatrixFeature> = features ?: sequence<MatrixFeature> {
+    @UnstableKMathAPI
-        if (origin is DiagonalMatrix) yield(DiagonalFeature)
+    override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
-    }.toHashSet()
+        DiagonalFeature::class -> if (origin is DiagonalMatrix) DiagonalFeature else null
-
+        else -> null
-    public override fun suggestFeature(vararg features: MatrixFeature): CMMatrix =
+    }?.let { type.cast(it) }
-        CMMatrix(origin, this.features + features)
 
     public override operator fun get(i: Int, j: Int): Double = origin.getEntry(i, j)
-
-    public override fun equals(other: Any?): Boolean {
-        return NDStructure.equals(this, other as? NDStructure<*> ?: return false)
-    }
-
-    public override fun hashCode(): Int {
-        var result = origin.hashCode()
-        result = 31 * result + features.hashCode()
-        return result
-    }
 }
 
-//TODO move inside context
-public fun Matrix<Double>.toCM(): CMMatrix = if (this is CMMatrix) {
-    this
-} else {
-    //TODO add feature analysis
-    val array = Array(rowNum) { i -> DoubleArray(colNum) { j -> get(i, j) } }
-    CMMatrix(Array2DRowRealMatrix(array))
-}
 
 public fun RealMatrix.asMatrix(): CMMatrix = CMMatrix(this)
 
@@ -61,6 +47,16 @@ public object CMMatrixContext : MatrixContext<Double, CMMatrix> {
         return CMMatrix(Array2DRowRealMatrix(array))
     }
 
+    public fun Matrix<Double>.toCM(): CMMatrix = when {
+        this is CMMatrix -> this
+        this is MatrixWrapper && matrix is CMMatrix -> matrix as CMMatrix
+        else -> {
+            //TODO add feature analysis
+            val array = Array(rowNum) { i -> DoubleArray(colNum) { j -> get(i, j) } }
+            CMMatrix(Array2DRowRealMatrix(array))
+        }
+    }
+
     public override fun Matrix<Double>.dot(other: Matrix<Double>): CMMatrix =
         CMMatrix(toCM().origin.multiply(other.toCM().origin))
 

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

@@ -7,8 +7,9 @@ import kscience.kmath.operations.*
  *
  * @param algebra The algebra to provide for Expressions built.
  */
-public abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(public val algebra: A) :
+public abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(
-    ExpressionAlgebra<T, Expression<T>> {
+    public val algebra: A,
+) : ExpressionAlgebra<T, Expression<T>> {
     /**
      * Builds an Expression of constant expression which does not depend on arguments.
      */
@@ -42,8 +43,9 @@ public abstract class FunctionalExpressionAlgebra<T, A : Algebra<T>>(public val
 /**
  * A context class for [Expression] construction for [Space] algebras.
  */
-public open class FunctionalExpressionSpace<T, A : Space<T>>(algebra: A) :
+public open class FunctionalExpressionSpace<T, A : Space<T>>(
-    FunctionalExpressionAlgebra<T, A>(algebra), Space<Expression<T>> {
+    algebra: A,
+) : FunctionalExpressionAlgebra<T, A>(algebra), Space<Expression<T>> {
     public override val zero: Expression<T> get() = const(algebra.zero)
 
     /**
@@ -71,8 +73,9 @@ public open class FunctionalExpressionSpace<T, A : Space<T>>(algebra: A) :
         super<FunctionalExpressionAlgebra>.binaryOperationFunction(operation)
 }
 
-public open class FunctionalExpressionRing<T, A>(algebra: A) : FunctionalExpressionSpace<T, A>(algebra),
+public open class FunctionalExpressionRing<T, A : Ring<T>>(
-    Ring<Expression<T>> where  A : Ring<T>, A : NumericAlgebra<T> {
+    algebra: A,
+) : FunctionalExpressionSpace<T, A>(algebra), Ring<Expression<T>> {
     public override val one: Expression<T>
         get() = const(algebra.one)
 
@@ -92,9 +95,8 @@ public open class FunctionalExpressionRing<T, A>(algebra: A) : FunctionalExpress
         super<FunctionalExpressionSpace>.binaryOperationFunction(operation)
 }
 
-public open class FunctionalExpressionField<T, A>(algebra: A) :
+public open class FunctionalExpressionField<T, A : Field<T>>(algebra: A) :
-    FunctionalExpressionRing<T, A>(algebra), Field<Expression<T>>
+    FunctionalExpressionRing<T, A>(algebra), Field<Expression<T>> {
-        where A : Field<T>, A : NumericAlgebra<T> {
     /**
      * Builds an Expression of division an expression by another one.
      */
@@ -111,9 +113,12 @@ public open class FunctionalExpressionField<T, A>(algebra: A) :
         super<FunctionalExpressionRing>.binaryOperationFunction(operation)
 }
 
-public open class FunctionalExpressionExtendedField<T, A>(algebra: A) :
+public open class FunctionalExpressionExtendedField<T, A : ExtendedField<T>>(
-    FunctionalExpressionField<T, A>(algebra),
+    algebra: A,
-    ExtendedField<Expression<T>> where A : ExtendedField<T>, A : NumericAlgebra<T> {
+) : FunctionalExpressionField<T, A>(algebra), ExtendedField<Expression<T>> {
+
+    override fun number(value: Number): Expression<T> = const(algebra.number(value))
+
     public override fun sin(arg: Expression<T>): Expression<T> =
         unaryOperationFunction(TrigonometricOperations.SIN_OPERATION)(arg)
 
@@ -135,7 +140,8 @@ public open class FunctionalExpressionExtendedField<T, A>(algebra: A) :
     public override fun exp(arg: Expression<T>): Expression<T> =
         unaryOperationFunction(ExponentialOperations.EXP_OPERATION)(arg)
 
-    public override fun ln(arg: Expression<T>): Expression<T> = unaryOperationFunction(ExponentialOperations.LN_OPERATION)(arg)
+    public override fun ln(arg: Expression<T>): Expression<T> =
+        unaryOperationFunction(ExponentialOperations.LN_OPERATION)(arg)
 
     public override fun unaryOperationFunction(operation: String): (arg: Expression<T>) -> Expression<T> =
         super<FunctionalExpressionField>.unaryOperationFunction(operation)

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

@@ -1,6 +1,7 @@
 package kscience.kmath.expressions
 
 import kscience.kmath.linear.Point
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.*
 import kscience.kmath.structures.asBuffer
 import kotlin.contracts.InvocationKind
@@ -79,10 +80,11 @@ public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
 /**
  * Represents field in context of which functions can be derived.
  */
+@OptIn(UnstableKMathAPI::class)
 public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
     public val context: F,
     bindings: Map<Symbol, T>,
-) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>> {
+) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>>, RingWithNumbers<AutoDiffValue<T>> {
     public override val zero: AutoDiffValue<T>
         get() = const(context.zero)
 

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

@@ -1,10 +1,7 @@
 package kscience.kmath.linear
 
 import kscience.kmath.operations.Ring
-import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.*
-import kscience.kmath.structures.BufferFactory
-import kscience.kmath.structures.NDStructure
-import kscience.kmath.structures.asSequence
 
 /**
  * Basic implementation of Matrix space based on [NDStructure]
@@ -27,8 +24,7 @@ public class BufferMatrix<T : Any>(
     public override val rowNum: Int,
     public override val colNum: Int,
     public val buffer: Buffer<out T>,
-    public override val features: Set<MatrixFeature> = emptySet(),
+) : Matrix<T> {
-) : FeaturedMatrix<T> {
 
     init {
         require(buffer.size == rowNum * colNum) { "Dimension mismatch for matrix structure" }
@@ -36,9 +32,6 @@ public class BufferMatrix<T : Any>(
 
     override val shape: IntArray get() = intArrayOf(rowNum, colNum)
 
-    public override fun suggestFeature(vararg features: MatrixFeature): BufferMatrix<T> =
-        BufferMatrix(rowNum, colNum, buffer, this.features + features)
-
     public override operator fun get(index: IntArray): T = get(index[0], index[1])
     public override operator fun get(i: Int, j: Int): T = buffer[i * colNum + j]
 
@@ -50,23 +43,26 @@ public class BufferMatrix<T : Any>(
         if (this === other) return true
 
         return when (other) {
-            is NDStructure<*> -> return NDStructure.equals(this, other)
+            is NDStructure<*> -> NDStructure.equals(this, other)
             else -> false
         }
     }
 
-    public override fun hashCode(): Int {
+    override fun hashCode(): Int {
-        var result = buffer.hashCode()
+        var result = rowNum
-        result = 31 * result + features.hashCode()
+        result = 31 * result + colNum
+        result = 31 * result + buffer.hashCode()
         return result
     }
 
     public override fun toString(): String {
         return if (rowNum <= 5 && colNum <= 5)
-            "Matrix(rowsNum = $rowNum, colNum = $colNum, features=$features)\n" +
+            "Matrix(rowsNum = $rowNum, colNum = $colNum)\n" +
                     rows.asSequence().joinToString(prefix = "(", postfix = ")", separator = "\n ") { buffer ->
                         buffer.asSequence().joinToString(separator = "\t") { it.toString() }
                     }
-        else "Matrix(rowsNum = $rowNum, colNum = $colNum, features=$features)"
+        else "Matrix(rowsNum = $rowNum, colNum = $colNum)"
     }
+
+
 }

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

@@ -1,13 +1,14 @@
 package kscience.kmath.linear
 
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.*
 import kscience.kmath.structures.*
 
 /**
  * Common implementation of [LupDecompositionFeature].
  */
-public class LUPDecomposition<T : Any>(
+public class LupDecomposition<T : Any>(
-    public val context: MatrixContext<T, FeaturedMatrix<T>>,
+    public val context: MatrixContext<T, Matrix<T>>,
     public val elementContext: Field<T>,
     public val lu: Matrix<T>,
     public val pivot: IntArray,
@@ -18,13 +19,13 @@ public class LUPDecomposition<T : Any>(
      *
      * L is a lower-triangular matrix with [Ring.one] in diagonal
      */
-    override val l: FeaturedMatrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1], setOf(LFeature)) { i, j ->
+    override val l: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
         when {
             j < i -> lu[i, j]
             j == i -> elementContext.one
             else -> elementContext.zero
         }
-    }
+    } + LFeature
 
 
     /**
@@ -32,9 +33,9 @@ public class LUPDecomposition<T : Any>(
      *
      * U is an upper-triangular matrix including the diagonal
      */
-    override val u: FeaturedMatrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1], setOf(UFeature)) { i, j ->
+    override val u: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
         if (j >= i) lu[i, j] else elementContext.zero
-    }
+    } + UFeature
 
     /**
      * Returns the P rows permutation matrix.
@@ -42,7 +43,7 @@ public class LUPDecomposition<T : Any>(
      * P is a sparse matrix with exactly one element set to [Ring.one] in
      * each row and each column, all other elements being set to [Ring.zero].
      */
-    override val p: FeaturedMatrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
+    override val p: Matrix<T> = VirtualMatrix(lu.shape[0], lu.shape[1]) { i, j ->
         if (j == pivot[i]) elementContext.one else elementContext.zero
     }
 
@@ -63,12 +64,12 @@ internal fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, *>.abs
 /**
  * Create a lup decomposition of generic matrix.
  */
-public fun <T : Comparable<T>> MatrixContext<T, FeaturedMatrix<T>>.lup(
+public fun <T : Comparable<T>> MatrixContext<T, Matrix<T>>.lup(
     factory: MutableBufferFactory<T>,
     elementContext: Field<T>,
     matrix: Matrix<T>,
     checkSingular: (T) -> Boolean,
-): LUPDecomposition<T> {
+): LupDecomposition<T> {
     require(matrix.rowNum == matrix.colNum) { "LU decomposition supports only square matrices" }
     val m = matrix.colNum
     val pivot = IntArray(matrix.rowNum)
@@ -137,23 +138,23 @@ public fun <T : Comparable<T>> MatrixContext<T, FeaturedMatrix<T>>.lup(
                 for (row in col + 1 until m) lu[row, col] /= luDiag
             }
 
-            return LUPDecomposition(this@lup, elementContext, lu.collect(), pivot, even)
+            return LupDecomposition(this@lup, elementContext, lu.collect(), pivot, even)
         }
     }
 }
 
-public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, FeaturedMatrix<T>>.lup(
+public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.lup(
     matrix: Matrix<T>,
     noinline checkSingular: (T) -> Boolean,
-): LUPDecomposition<T> = lup(MutableBuffer.Companion::auto, elementContext, matrix, checkSingular)
+): LupDecomposition<T> = lup(MutableBuffer.Companion::auto, elementContext, matrix, checkSingular)
 
-public fun MatrixContext<Double, FeaturedMatrix<Double>>.lup(matrix: Matrix<Double>): LUPDecomposition<Double> =
+public fun MatrixContext<Double, Matrix<Double>>.lup(matrix: Matrix<Double>): LupDecomposition<Double> =
     lup(Buffer.Companion::real, RealField, matrix) { it < 1e-11 }
 
-public fun <T : Any> LUPDecomposition<T>.solveWithLUP(
+public fun <T : Any> LupDecomposition<T>.solveWithLUP(
     factory: MutableBufferFactory<T>,
-    matrix: Matrix<T>
+    matrix: Matrix<T>,
-): FeaturedMatrix<T> {
+): Matrix<T> {
     require(matrix.rowNum == pivot.size) { "Matrix dimension mismatch. Expected ${pivot.size}, but got ${matrix.colNum}" }
 
     BufferAccessor2D(matrix.rowNum, matrix.colNum, factory).run {
@@ -198,25 +199,40 @@ public fun <T : Any> LUPDecomposition<T>.solveWithLUP(
     }
 }
 
-public inline fun <reified T : Any> LUPDecomposition<T>.solveWithLUP(matrix: Matrix<T>): Matrix<T> =
+public inline fun <reified T : Any> LupDecomposition<T>.solveWithLUP(matrix: Matrix<T>): Matrix<T> =
     solveWithLUP(MutableBuffer.Companion::auto, matrix)
 
 /**
  * Solve a linear equation **a*x = b** using LUP decomposition
  */
-public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, FeaturedMatrix<T>>.solveWithLUP(
+@OptIn(UnstableKMathAPI::class)
+public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.solveWithLUP(
     a: Matrix<T>,
     b: Matrix<T>,
     noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
     noinline checkSingular: (T) -> Boolean,
-): FeaturedMatrix<T> {
+): Matrix<T> {
     // Use existing decomposition if it is provided by matrix
     val decomposition = a.getFeature() ?: lup(bufferFactory, elementContext, a, checkSingular)
     return decomposition.solveWithLUP(bufferFactory, b)
 }
 
-public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, FeaturedMatrix<T>>.inverseWithLUP(
+public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.inverseWithLUP(
     matrix: Matrix<T>,
     noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
     noinline checkSingular: (T) -> Boolean,
-): FeaturedMatrix<T> = solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
+): Matrix<T> = solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
+
+
+public fun RealMatrixContext.solveWithLUP(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
+    // Use existing decomposition if it is provided by matrix
+    val bufferFactory: MutableBufferFactory<Double> = MutableBuffer.Companion::real
+    val decomposition: LupDecomposition<Double> = a.getFeature() ?: lup(bufferFactory, RealField, a) { it < 1e-11 }
+    return decomposition.solveWithLUP(bufferFactory, b)
+}
+
+/**
+ * Inverses a square matrix using LUP decomposition. Non square matrix will throw a error.
+ */
+public fun RealMatrixContext.inverseWithLUP(matrix: Matrix<Double>): Matrix<Double> =
+    solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum))

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

@@ -1,12 +1,9 @@
 package kscience.kmath.linear
 
-import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.*
-import kscience.kmath.structures.BufferFactory
-import kscience.kmath.structures.Structure2D
-import kscience.kmath.structures.asBuffer
 
 public class MatrixBuilder(public val rows: Int, public val columns: Int) {
-    public operator fun <T : Any> invoke(vararg elements: T): FeaturedMatrix<T> {
+    public operator fun <T : Any> invoke(vararg elements: T): Matrix<T> {
         require(rows * columns == elements.size) { "The number of elements ${elements.size} is not equal $rows * $columns" }
         val buffer = elements.asBuffer()
         return BufferMatrix(rows, columns, buffer)
@@ -17,7 +14,7 @@ public class MatrixBuilder(public val rows: Int, public val columns: Int) {
 
 public fun Structure2D.Companion.build(rows: Int, columns: Int): MatrixBuilder = MatrixBuilder(rows, columns)
 
-public fun <T : Any> Structure2D.Companion.row(vararg values: T): FeaturedMatrix<T> {
+public fun <T : Any> Structure2D.Companion.row(vararg values: T): Matrix<T> {
     val buffer = values.asBuffer()
     return BufferMatrix(1, values.size, buffer)
 }
@@ -26,12 +23,12 @@ public inline fun <reified T : Any> Structure2D.Companion.row(
     size: Int,
     factory: BufferFactory<T> = Buffer.Companion::auto,
     noinline builder: (Int) -> T
-): FeaturedMatrix<T> {
+): Matrix<T> {
     val buffer = factory(size, builder)
     return BufferMatrix(1, size, buffer)
 }
 
-public fun <T : Any> Structure2D.Companion.column(vararg values: T): FeaturedMatrix<T> {
+public fun <T : Any> Structure2D.Companion.column(vararg values: T): Matrix<T> {
     val buffer = values.asBuffer()
     return BufferMatrix(values.size, 1, buffer)
 }
@@ -40,7 +37,7 @@ public inline fun <reified T : Any> Structure2D.Companion.column(
     size: Int,
     factory: BufferFactory<T> = Buffer.Companion::auto,
     noinline builder: (Int) -> T
-): FeaturedMatrix<T> {
+): Matrix<T> {
     val buffer = factory(size, builder)
     return BufferMatrix(size, 1, buffer)
 }

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

@@ -133,8 +133,6 @@ public interface GenericMatrixContext<T : Any, R : Ring<T>, out M : Matrix<T>> :
     public override fun multiply(a: Matrix<T>, k: Number): M =
         produce(a.rowNum, a.colNum) { i, j -> elementContext { a[i, j] * k } }
 
-    public operator fun Number.times(matrix: FeaturedMatrix<T>): M = multiply(matrix, this)
-
     public override operator fun Matrix<T>.times(value: T): M =
         produce(rowNum, colNum) { i, j -> elementContext { get(i, j) * value } }
 }

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

@@ -1,5 +1,7 @@
 package kscience.kmath.linear
 
+import kscience.kmath.structures.Matrix
+
 /**
  * A marker interface representing some properties of matrices or additional transformations of them. Features are used
  * to optimize matrix operations performance in some cases or retrieve the APIs.
@@ -9,17 +11,19 @@ public interface MatrixFeature
 /**
  * Matrices with this feature are considered to have only diagonal non-null elements.
  */
-public object DiagonalFeature : MatrixFeature
+public interface DiagonalFeature : MatrixFeature{
+    public companion object: DiagonalFeature
+}
 
 /**
  * Matrices with this feature have all zero elements.
  */
-public object ZeroFeature : MatrixFeature
+public object ZeroFeature : DiagonalFeature
 
 /**
  * Matrices with this feature have unit elements on diagonal and zero elements in all other places.
  */
-public object UnitFeature : MatrixFeature
+public object UnitFeature : DiagonalFeature
 
 /**
  * Matrices with this feature can be inverted: [inverse] = `a`<sup>-1</sup> where `a` is the owning matrix.
@@ -30,7 +34,7 @@ public interface InverseMatrixFeature<T : Any> : MatrixFeature {
     /**
      * The inverse matrix of the matrix that owns this feature.
      */
-    public val inverse: FeaturedMatrix<T>
+    public val inverse: Matrix<T>
 }
 
 /**
@@ -74,17 +78,17 @@ public interface LupDecompositionFeature<T : Any> : MatrixFeature {
     /**
      * The lower triangular matrix in this decomposition. It may have [LFeature].
      */
-    public val l: FeaturedMatrix<T>
+    public val l: Matrix<T>
 
     /**
      * The upper triangular matrix in this decomposition. It may have [UFeature].
      */
-    public val u: FeaturedMatrix<T>
+    public val u: Matrix<T>
 
     /**
      * The permutation matrix in this decomposition.
      */
-    public val p: FeaturedMatrix<T>
+    public val p: Matrix<T>
 }
 
 /**
@@ -102,12 +106,12 @@ public interface QRDecompositionFeature<T : Any> : MatrixFeature {
     /**
      * The orthogonal matrix in this decomposition. It may have [OrthogonalFeature].
      */
-    public val q: FeaturedMatrix<T>
+    public val q: Matrix<T>
 
     /**
      * The upper triangular matrix in this decomposition. It may have [UFeature].
      */
-    public val r: FeaturedMatrix<T>
+    public val r: Matrix<T>
 }
 
 /**
@@ -120,7 +124,7 @@ public interface CholeskyDecompositionFeature<T : Any> : MatrixFeature {
     /**
      * The triangular matrix in this decomposition. It may have either [UFeature] or [LFeature].
      */
-    public val l: FeaturedMatrix<T>
+    public val l: Matrix<T>
 }
 
 /**
@@ -133,17 +137,17 @@ public interface SingularValueDecompositionFeature<T : Any> : MatrixFeature {
     /**
      * The matrix in this decomposition. It is unitary, and it consists from left singular vectors.
      */
-    public val u: FeaturedMatrix<T>
+    public val u: Matrix<T>
 
     /**
      * The matrix in this decomposition. Its main diagonal elements are singular values.
      */
-    public val s: FeaturedMatrix<T>
+    public val s: Matrix<T>
 
     /**
      * The matrix in this decomposition. It is unitary, and it consists from right singular vectors.
      */
-    public val v: FeaturedMatrix<T>
+    public val v: Matrix<T>
 
     /**
      * The buffer of singular values of this SVD.

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

@@ -1,35 +1,57 @@
 package kscience.kmath.linear
 
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.Ring
 import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.Structure2D
 import kscience.kmath.structures.asBuffer
+import kscience.kmath.structures.getFeature
 import kotlin.math.sqrt
+import kotlin.reflect.KClass
+import kotlin.reflect.safeCast
 
 /**
  * A [Matrix] that holds [MatrixFeature] objects.
  *
  * @param T the type of items.
  */
-public interface FeaturedMatrix<T : Any> : Matrix<T> {
+public class MatrixWrapper<T : Any>(
-    public override val shape: IntArray get() = intArrayOf(rowNum, colNum)
+    public val matrix: Matrix<T>,
+    public val features: Set<MatrixFeature>,
+) : Matrix<T> by matrix {
 
     /**
-     * The set of features this matrix possesses.
+     * Get the first feature matching given class. Does not guarantee that matrix has only one feature matching the criteria
      */
-    public val features: Set<MatrixFeature>
+    @UnstableKMathAPI
+    override fun <T : Any> getFeature(type: KClass<T>): T? = type.safeCast(features.find { type.isInstance(it) })
 
-    /**
+    override fun equals(other: Any?): Boolean = matrix == other
-     * Suggest new feature for this matrix. The result is the new matrix that may or may not reuse existing data structure.
+    override fun hashCode(): Int = matrix.hashCode()
-     *
+    override fun toString(): String {
-     * The implementation does not guarantee to check that matrix actually have the feature, so one should be careful to
+        return "MatrixWrapper(matrix=$matrix, features=$features)"
-     * add only those features that are valid.
+    }
-     */
-    public fun suggestFeature(vararg features: MatrixFeature): FeaturedMatrix<T>
-
-    public companion object
 }
 
+/**
+ * Add a single feature to a [Matrix]
+ */
+public operator fun <T : Any> Matrix<T>.plus(newFeature: MatrixFeature): MatrixWrapper<T> = if (this is MatrixWrapper) {
+    MatrixWrapper(matrix, features + newFeature)
+} else {
+    MatrixWrapper(this, setOf(newFeature))
+}
+
+/**
+ * Add a collection of features to a [Matrix]
+ */
+public operator fun <T : Any> Matrix<T>.plus(newFeatures: Collection<MatrixFeature>): MatrixWrapper<T> =
+    if (this is MatrixWrapper) {
+        MatrixWrapper(matrix, features + newFeatures)
+    } else {
+        MatrixWrapper(this, newFeatures.toSet())
+    }
+
 public inline fun Structure2D.Companion.real(
     rows: Int,
     columns: Int,
@@ -39,51 +61,37 @@ public inline fun Structure2D.Companion.real(
 /**
  * Build a square matrix from given elements.
  */
-public fun <T : Any> Structure2D.Companion.square(vararg elements: T): FeaturedMatrix<T> {
+public fun <T : Any> Structure2D.Companion.square(vararg elements: T): Matrix<T> {
     val size: Int = sqrt(elements.size.toDouble()).toInt()
     require(size * size == elements.size) { "The number of elements ${elements.size} is not a full square" }
     val buffer = elements.asBuffer()
     return BufferMatrix(size, size, buffer)
 }
 
-public val Matrix<*>.features: Set<MatrixFeature> get() = (this as? FeaturedMatrix)?.features ?: emptySet()
-
-/**
- * Check if matrix has the given feature class
- */
-public inline fun <reified T : Any> Matrix<*>.hasFeature(): Boolean =
-    features.find { it is T } != null
-
-/**
- * Get the first feature matching given class. Does not guarantee that matrix has only one feature matching the criteria
- */
-public inline fun <reified T : Any> Matrix<*>.getFeature(): T? =
-    features.filterIsInstance<T>().firstOrNull()
-
 /**
  * Diagonal matrix of ones. The matrix is virtual no actual matrix is created
  */
-public fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R, *>.one(rows: Int, columns: Int): FeaturedMatrix<T> =
+public fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R, *>.one(rows: Int, columns: Int): Matrix<T> =
-    VirtualMatrix(rows, columns, DiagonalFeature) { i, j ->
+    VirtualMatrix(rows, columns) { i, j ->
         if (i == j) elementContext.one else elementContext.zero
-    }
+    } + UnitFeature
 
 
 /**
  * A virtual matrix of zeroes
  */
-public fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R, *>.zero(rows: Int, columns: Int): FeaturedMatrix<T> =
+public fun <T : Any, R : Ring<T>> GenericMatrixContext<T, R, *>.zero(rows: Int, columns: Int): Matrix<T> =
-    VirtualMatrix(rows, columns) { _, _ -> elementContext.zero }
+    VirtualMatrix(rows, columns) { _, _ -> elementContext.zero } + ZeroFeature
 
 public class TransposedFeature<T : Any>(public val original: Matrix<T>) : MatrixFeature
 
 /**
  * Create a virtual transposed matrix without copying anything. `A.transpose().transpose() === A`
  */
+@OptIn(UnstableKMathAPI::class)
 public fun <T : Any> Matrix<T>.transpose(): Matrix<T> {
     return getFeature<TransposedFeature<T>>()?.original ?: VirtualMatrix(
         colNum,
         rowNum,
-        setOf(TransposedFeature(this))
+    ) { i, j -> get(j, i) } + TransposedFeature(this)
-    ) { i, j -> get(j, i) }
 }

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

@@ -1,9 +1,6 @@
 package kscience.kmath.linear
 
-import kscience.kmath.operations.RealField
 import kscience.kmath.structures.Matrix
-import kscience.kmath.structures.MutableBuffer
-import kscience.kmath.structures.MutableBufferFactory
 import kscience.kmath.structures.RealBuffer
 
 @Suppress("OVERRIDE_BY_INLINE")
@@ -22,9 +19,9 @@ public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
         produce(rowNum, colNum) { i, j -> get(i, j) }
     }
 
-    public fun one(rows: Int, columns: Int): FeaturedMatrix<Double> = VirtualMatrix(rows, columns, DiagonalFeature) { i, j ->
+    public fun one(rows: Int, columns: Int): Matrix<Double> = VirtualMatrix(rows, columns) { i, j ->
         if (i == j) 1.0 else 0.0
-    }
+    } + DiagonalFeature
 
     public override infix fun Matrix<Double>.dot(other: Matrix<Double>): BufferMatrix<Double> {
         require(colNum == other.rowNum) { "Matrix dot operation dimension mismatch: ($rowNum, $colNum) x (${other.rowNum}, ${other.colNum})" }
@@ -61,7 +58,7 @@ public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
 
 
     override fun multiply(a: Matrix<Double>, k: Number): BufferMatrix<Double> =
-        produce(a.rowNum, a.colNum) { i, j -> a.get(i, j) * k.toDouble() }
+        produce(a.rowNum, a.colNum) { i, j -> a[i, j] * k.toDouble() }
 }
 
 
@@ -69,16 +66,3 @@ public object RealMatrixContext : MatrixContext<Double, BufferMatrix<Double>> {
  * Partially optimized real-valued matrix
  */
 public val MatrixContext.Companion.real: RealMatrixContext get() = RealMatrixContext
-
-public fun RealMatrixContext.solveWithLUP(a: Matrix<Double>, b: Matrix<Double>): FeaturedMatrix<Double> {
-    // Use existing decomposition if it is provided by matrix
-    val bufferFactory: MutableBufferFactory<Double> = MutableBuffer.Companion::real
-    val decomposition = a.getFeature() ?: lup(bufferFactory, RealField, a) { it < 1e-11 }
-    return decomposition.solveWithLUP(bufferFactory, b)
-}
-
-/**
- * Inverses a square matrix using LUP decomposition. Non square matrix will throw a error.
- */
-public fun RealMatrixContext.inverseWithLUP(matrix: Matrix<Double>): FeaturedMatrix<Double> =
-    solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum))

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

@@ -5,31 +5,16 @@ import kscience.kmath.structures.Matrix
 public class VirtualMatrix<T : Any>(
     override val rowNum: Int,
     override val colNum: Int,
-    override val features: Set<MatrixFeature> = emptySet(),
     public val generator: (i: Int, j: Int) -> T
-) : FeaturedMatrix<T> {
+) : Matrix<T> {
-    public constructor(
-        rowNum: Int,
-        colNum: Int,
-        vararg features: MatrixFeature,
-        generator: (i: Int, j: Int) -> T
-    ) : this(
-        rowNum,
-        colNum,
-        setOf(*features),
-        generator
-    )
 
     override val shape: IntArray get() = intArrayOf(rowNum, colNum)
 
     override operator fun get(i: Int, j: Int): T = generator(i, j)
 
-    override fun suggestFeature(vararg features: MatrixFeature): VirtualMatrix<T> =
-        VirtualMatrix(rowNum, colNum, this.features + features, generator)
-
     override fun equals(other: Any?): Boolean {
         if (this === other) return true
-        if (other !is FeaturedMatrix<*>) return false
+        if (other !is Matrix<*>) return false
 
         if (rowNum != other.rowNum) return false
         if (colNum != other.colNum) return false
@@ -40,21 +25,9 @@ public class VirtualMatrix<T : Any>(
     override fun hashCode(): Int {
         var result = rowNum
         result = 31 * result + colNum
-        result = 31 * result + features.hashCode()
         result = 31 * result + generator.hashCode()
         return result
     }
 
 
-    public companion object {
-        /**
-         * Wrap a matrix adding additional features to it
-         */
-        public fun <T : Any> wrap(matrix: Matrix<T>, vararg features: MatrixFeature): FeaturedMatrix<T> {
-            return if (matrix is VirtualMatrix)
-                VirtualMatrix(matrix.rowNum, matrix.colNum, matrix.features + features, matrix.generator)
-            else
-                VirtualMatrix(matrix.rowNum, matrix.colNum, matrix.features + features) { i, j -> matrix[i, j] }
-        }
-    }
 }

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

@@ -88,85 +88,6 @@ public interface Algebra<T> {
     public fun binaryOperation(operation: String, left: T, right: T): T = binaryOperationFunction(operation)(left, right)
 }
 
-/**
- * An algebraic structure where elements can have numeric representation.
- *
- * @param T the type of element of this structure.
- */
-public interface NumericAlgebra<T> : Algebra<T> {
-    /**
-     * Wraps a number to [T] object.
-     *
-     * @param value the number to wrap.
-     * @return an object.
-     */
-    public fun number(value: Number): T
-
-    /**
-     * Dynamically dispatches a binary operation with the certain name with numeric first argument.
-     *
-     * This function must follow two properties:
-     *
-     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
-     * 2. This function is symmetric with the other [leftSideNumberOperation] overload:
-     * i.e. `leftSideNumberOperationFunction(a)(b, c) == leftSideNumberOperation(a, b)`.
-     *
-     * @param operation the name of operation.
-     * @return an operation.
-     */
-    public fun leftSideNumberOperationFunction(operation: String): (left: Number, right: T) -> T =
-        { l, r -> binaryOperationFunction(operation)(number(l), r) }
-
-    /**
-     * Dynamically invokes a binary operation with the certain name with numeric first argument.
-     *
-     * This function must follow two properties:
-     *
-     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
-     * 2. This function is symmetric with second [leftSideNumberOperation] overload:
-     * i.e. `leftSideNumberOperationFunction(a)(b, c) == leftSideNumberOperation(a, b, c)`.
-     *
-     * @param operation the name of operation.
-     * @param left the first argument of operation.
-     * @param right the second argument of operation.
-     * @return a result of operation.
-     */
-    public fun leftSideNumberOperation(operation: String, left: Number, right: T): T =
-        leftSideNumberOperationFunction(operation)(left, right)
-
-    /**
-     * Dynamically dispatches a binary operation with the certain name with numeric first argument.
-     *
-     * This function must follow two properties:
-     *
-     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
-     * 2. This function is symmetric with the other [rightSideNumberOperationFunction] overload:
-     * i.e. `rightSideNumberOperationFunction(a)(b, c) == leftSideNumberOperation(a, b, c)`.
-     *
-     * @param operation the name of operation.
-     * @return an operation.
-     */
-    public fun rightSideNumberOperationFunction(operation: String): (left: T, right: Number) -> T =
-        { l, r -> binaryOperationFunction(operation)(l, number(r)) }
-
-    /**
-     * Dynamically invokes a binary operation with the certain name with numeric second argument.
-     *
-     * This function must follow two properties:
-     *
-     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
-     * 2. This function is symmetric with the other [rightSideNumberOperationFunction] overload:
-     * i.e. `rightSideNumberOperationFunction(a)(b, c) == rightSideNumberOperation(a, b, c)`.
-     *
-     * @param operation the name of operation.
-     * @param left the first argument of operation.
-     * @param right the second argument of operation.
-     * @return a result of operation.
-     */
-    public fun rightSideNumberOperation(operation: String, left: T, right: Number): T =
-        rightSideNumberOperationFunction(operation)(left, right)
-}
-
 /**
  * Call a block with an [Algebra] as receiver.
  */
@@ -341,47 +262,11 @@ public interface RingOperations<T> : SpaceOperations<T> {
  *
  * @param T the type of element of this ring.
  */
-public interface Ring<T> : Space<T>, RingOperations<T>, NumericAlgebra<T> {
+public interface Ring<T> : Space<T>, RingOperations<T> {
     /**
      * neutral operation for multiplication
      */
     public val one: T
-
-    public override fun number(value: Number): T = one * value.toDouble()
-
-    /**
-     * Addition of element and scalar.
-     *
-     * @receiver the addend.
-     * @param b the augend.
-     */
-    public operator fun T.plus(b: Number): T = this + number(b)
-
-    /**
-     * Addition of scalar and element.
-     *
-     * @receiver the addend.
-     * @param b the augend.
-     */
-    public operator fun Number.plus(b: T): T = b + this
-
-    /**
-     * Subtraction of element from number.
-     *
-     * @receiver the minuend.
-     * @param b the subtrahend.
-     * @receiver the difference.
-     */
-    public operator fun T.minus(b: Number): T = this - number(b)
-
-    /**
-     * Subtraction of number from element.
-     *
-     * @receiver the minuend.
-     * @param b the subtrahend.
-     * @receiver the difference.
-     */
-    public operator fun Number.minus(b: T): T = -b + this
 }
 
 /**

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

@@ -1,5 +1,6 @@
 package kscience.kmath.operations
 
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.BigInt.Companion.BASE
 import kscience.kmath.operations.BigInt.Companion.BASE_SIZE
 import kscience.kmath.structures.*
@@ -16,7 +17,8 @@ public typealias TBase = ULong
  *
  * @author Robert Drynkin (https://github.com/robdrynkin) and Peter Klimai (https://github.com/pklimai)
  */
-public object BigIntField : Field<BigInt> {
+@OptIn(UnstableKMathAPI::class)
+public object BigIntField : Field<BigInt>, RingWithNumbers<BigInt> {
     override val zero: BigInt = BigInt.ZERO
     override val one: BigInt = BigInt.ONE
 

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

@@ -41,7 +41,7 @@ private val PI_DIV_2 = Complex(PI / 2, 0)
 /**
  * A field of [Complex].
  */
-public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
+public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex>, RingWithNumbers<Complex> {
     override val zero: Complex = 0.0.toComplex()
     override val one: Complex = 1.0.toComplex()
 
@@ -156,7 +156,7 @@ public object ComplexField : ExtendedField<Complex>, Norm<Complex, Complex> {
 
     override fun norm(arg: Complex): Complex = sqrt(arg.conjugate * arg)
 
-    override fun symbol(value: String): Complex = if (value == "i") i else super.symbol(value)
+    override fun symbol(value: String): Complex = if (value == "i") i else super<ExtendedField>.symbol(value)
 }
 
 /**

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

@@ -0,0 +1,125 @@
+package kscience.kmath.operations
+
+import kscience.kmath.misc.UnstableKMathAPI
+
+/**
+ * An algebraic structure where elements can have numeric representation.
+ *
+ * @param T the type of element of this structure.
+ */
+public interface NumericAlgebra<T> : Algebra<T> {
+    /**
+     * Wraps a number to [T] object.
+     *
+     * @param value the number to wrap.
+     * @return an object.
+     */
+    public fun number(value: Number): T
+
+    /**
+     * Dynamically dispatches a binary operation with the certain name with numeric first argument.
+     *
+     * This function must follow two properties:
+     *
+     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
+     * 2. This function is symmetric with the other [leftSideNumberOperation] overload:
+     * i.e. `leftSideNumberOperationFunction(a)(b, c) == leftSideNumberOperation(a, b)`.
+     *
+     * @param operation the name of operation.
+     * @return an operation.
+     */
+    public fun leftSideNumberOperationFunction(operation: String): (left: Number, right: T) -> T =
+        { l, r -> binaryOperationFunction(operation)(number(l), r) }
+
+    /**
+     * Dynamically invokes a binary operation with the certain name with numeric first argument.
+     *
+     * This function must follow two properties:
+     *
+     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
+     * 2. This function is symmetric with second [leftSideNumberOperation] overload:
+     * i.e. `leftSideNumberOperationFunction(a)(b, c) == leftSideNumberOperation(a, b, c)`.
+     *
+     * @param operation the name of operation.
+     * @param left the first argument of operation.
+     * @param right the second argument of operation.
+     * @return a result of operation.
+     */
+    public fun leftSideNumberOperation(operation: String, left: Number, right: T): T =
+        leftSideNumberOperationFunction(operation)(left, right)
+
+    /**
+     * Dynamically dispatches a binary operation with the certain name with numeric first argument.
+     *
+     * This function must follow two properties:
+     *
+     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
+     * 2. This function is symmetric with the other [rightSideNumberOperationFunction] overload:
+     * i.e. `rightSideNumberOperationFunction(a)(b, c) == leftSideNumberOperation(a, b, c)`.
+     *
+     * @param operation the name of operation.
+     * @return an operation.
+     */
+    public fun rightSideNumberOperationFunction(operation: String): (left: T, right: Number) -> T =
+        { l, r -> binaryOperationFunction(operation)(l, number(r)) }
+
+    /**
+     * Dynamically invokes a binary operation with the certain name with numeric second argument.
+     *
+     * This function must follow two properties:
+     *
+     * 1. In case if operation is not defined in the structure, the function throws [kotlin.IllegalStateException].
+     * 2. This function is symmetric with the other [rightSideNumberOperationFunction] overload:
+     * i.e. `rightSideNumberOperationFunction(a)(b, c) == rightSideNumberOperation(a, b, c)`.
+     *
+     * @param operation the name of operation.
+     * @param left the first argument of operation.
+     * @param right the second argument of operation.
+     * @return a result of operation.
+     */
+    public fun rightSideNumberOperation(operation: String, left: T, right: Number): T =
+        rightSideNumberOperationFunction(operation)(left, right)
+}
+
+/**
+ * A combination of [NumericAlgebra] and [Ring] that adds intrinsic simple operations on numbers like `T+1`
+ * TODO to be removed and replaced by extensions after multiple receivers are there
+ */
+@UnstableKMathAPI
+public interface RingWithNumbers<T>: Ring<T>, NumericAlgebra<T>{
+    public override fun number(value: Number): T = one * value
+
+    /**
+     * Addition of element and scalar.
+     *
+     * @receiver the addend.
+     * @param b the augend.
+     */
+    public operator fun T.plus(b: Number): T = this + number(b)
+
+    /**
+     * Addition of scalar and element.
+     *
+     * @receiver the addend.
+     * @param b the augend.
+     */
+    public operator fun Number.plus(b: T): T = b + this
+
+    /**
+     * Subtraction of element from number.
+     *
+     * @receiver the minuend.
+     * @param b the subtrahend.
+     * @receiver the difference.
+     */
+    public operator fun T.minus(b: Number): T = this - number(b)
+
+    /**
+     * Subtraction of number from element.
+     *
+     * @receiver the minuend.
+     * @param b the subtrahend.
+     * @receiver the difference.
+     */
+    public operator fun Number.minus(b: T): T = -b + this
+}

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

@@ -37,7 +37,7 @@ public interface ExtendedFieldOperations<T> :
 /**
  * Advanced Number-like field that implements basic operations.
  */
-public interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T> {
+public interface ExtendedField<T> : ExtendedFieldOperations<T>, Field<T>, NumericAlgebra<T> {
     public override fun sinh(arg: T): T = (exp(arg) - exp(-arg)) / 2
     public override fun cosh(arg: T): T = (exp(arg) + exp(-arg)) / 2
     public override fun tanh(arg: T): T = (exp(arg) - exp(-arg)) / (exp(-arg) + exp(arg))
@@ -80,6 +80,8 @@ public object RealField : ExtendedField<Double>, Norm<Double, Double> {
     public override val one: Double
         get() = 1.0
 
+    override fun number(value: Number): Double = value.toDouble()
+
     public override fun binaryOperationFunction(operation: String): (left: Double, right: Double) -> Double =
         when (operation) {
             PowerOperations.POW_OPERATION -> ::power
@@ -131,10 +133,13 @@ public object FloatField : ExtendedField<Float>, Norm<Float, Float> {
     public override val one: Float
         get() = 1.0f
 
-    public override fun binaryOperationFunction(operation: String): (left: Float, right: Float) -> Float = when (operation) {
+    override fun number(value: Number): Float = value.toFloat()
-        PowerOperations.POW_OPERATION -> ::power
+
-        else -> super.binaryOperationFunction(operation)
+    public override fun binaryOperationFunction(operation: String): (left: Float, right: Float) -> Float =
-    }
+        when (operation) {
+            PowerOperations.POW_OPERATION -> ::power
+            else -> super.binaryOperationFunction(operation)
+        }
 
     public override inline fun add(a: Float, b: Float): Float = a + b
     public override inline fun multiply(a: Float, k: Number): Float = a * k.toFloat()
@@ -174,13 +179,15 @@ public object FloatField : ExtendedField<Float>, Norm<Float, Float> {
  * A field for [Int] without boxing. Does not produce corresponding ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-public object IntRing : Ring<Int>, Norm<Int, Int> {
+public object IntRing : Ring<Int>, Norm<Int, Int>, NumericAlgebra<Int> {
     public override val zero: Int
         get() = 0
 
     public override val one: Int
         get() = 1
 
+    override fun number(value: Number): Int = value.toInt()
+
     public override inline fun add(a: Int, b: Int): Int = a + b
     public override inline fun multiply(a: Int, k: Number): Int = k.toInt() * a
 
@@ -198,13 +205,15 @@ public object IntRing : Ring<Int>, Norm<Int, Int> {
  * A field for [Short] without boxing. Does not produce appropriate ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-public object ShortRing : Ring<Short>, Norm<Short, Short> {
+public object ShortRing : Ring<Short>, Norm<Short, Short>, NumericAlgebra<Short> {
     public override val zero: Short
         get() = 0
 
     public override val one: Short
         get() = 1
 
+    override fun number(value: Number): Short = value.toShort()
+
     public override inline fun add(a: Short, b: Short): Short = (a + b).toShort()
     public override inline fun multiply(a: Short, k: Number): Short = (a * k.toShort()).toShort()
 
@@ -222,13 +231,15 @@ public object ShortRing : Ring<Short>, Norm<Short, Short> {
  * A field for [Byte] without boxing. Does not produce appropriate ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-public object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
+public object ByteRing : Ring<Byte>, Norm<Byte, Byte>, NumericAlgebra<Byte> {
     public override val zero: Byte
         get() = 0
 
     public override val one: Byte
         get() = 1
 
+    override fun number(value: Number): Byte = value.toByte()
+
     public override inline fun add(a: Byte, b: Byte): Byte = (a + b).toByte()
     public override inline fun multiply(a: Byte, k: Number): Byte = (a * k.toByte()).toByte()
 
@@ -246,13 +257,15 @@ public object ByteRing : Ring<Byte>, Norm<Byte, Byte> {
  * A field for [Double] without boxing. Does not produce appropriate ring element.
  */
 @Suppress("EXTENSION_SHADOWED_BY_MEMBER", "OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
-public object LongRing : Ring<Long>, Norm<Long, Long> {
+public object LongRing : Ring<Long>, Norm<Long, Long>, NumericAlgebra<Long> {
     public override val zero: Long
         get() = 0L
 
     public override val one: Long
         get() = 1L
 
+    override fun number(value: Number): Long = value.toLong()
+
     public override inline fun add(a: Long, b: Long): Long = a + b
     public override inline fun multiply(a: Long, k: Number): Long = a * k.toLong()
 

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

@@ -1,9 +1,7 @@
 package kscience.kmath.structures
 
-import kscience.kmath.operations.Complex
+import kscience.kmath.misc.UnstableKMathAPI
-import kscience.kmath.operations.ComplexField
+import kscience.kmath.operations.*
-import kscience.kmath.operations.FieldElement
-import kscience.kmath.operations.complex
 import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
@@ -12,15 +10,22 @@ public typealias ComplexNDElement = BufferedNDFieldElement<Complex, ComplexField
 /**
  * An optimized nd-field for complex numbers
  */
+@OptIn(UnstableKMathAPI::class)
 public class ComplexNDField(override val shape: IntArray) :
     BufferedNDField<Complex, ComplexField>,
-    ExtendedNDField<Complex, ComplexField, NDBuffer<Complex>> {
+    ExtendedNDField<Complex, ComplexField, NDBuffer<Complex>>,
+    RingWithNumbers<NDBuffer<Complex>>{
 
     override val strides: Strides = DefaultStrides(shape)
     override val elementContext: ComplexField get() = ComplexField
     override val zero: ComplexNDElement by lazy { produce { zero } }
     override val one: ComplexNDElement by lazy { produce { one } }
 
+    override fun number(value: Number): NDBuffer<Complex> {
+        val c = value.toComplex()
+        return produce { c }
+    }
+
     public inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Complex): Buffer<Complex> =
         Buffer.complex(size) { initializer(it) }
 
@@ -29,7 +34,7 @@ public class ComplexNDField(override val shape: IntArray) :
      */
     override fun map(
         arg: NDBuffer<Complex>,
-        transform: ComplexField.(Complex) -> Complex
+        transform: ComplexField.(Complex) -> Complex,
     ): ComplexNDElement {
         check(arg)
         val array = buildBuffer(arg.strides.linearSize) { offset -> ComplexField.transform(arg.buffer[offset]) }
@@ -43,7 +48,7 @@ public class ComplexNDField(override val shape: IntArray) :
 
     override fun mapIndexed(
         arg: NDBuffer<Complex>,
-        transform: ComplexField.(index: IntArray, Complex) -> Complex
+        transform: ComplexField.(index: IntArray, Complex) -> Complex,
     ): ComplexNDElement {
         check(arg)
 
@@ -60,7 +65,7 @@ public class ComplexNDField(override val shape: IntArray) :
     override fun combine(
         a: NDBuffer<Complex>,
         b: NDBuffer<Complex>,
-        transform: ComplexField.(Complex, Complex) -> Complex
+        transform: ComplexField.(Complex, Complex) -> Complex,
     ): ComplexNDElement {
         check(a, b)
 
@@ -141,7 +146,7 @@ public fun NDField.Companion.complex(vararg shape: Int): ComplexNDField = Comple
 
 public fun NDElement.Companion.complex(
     vararg shape: Int,
-    initializer: ComplexField.(IntArray) -> Complex
+    initializer: ComplexField.(IntArray) -> Complex,
 ): ComplexNDElement = NDField.complex(*shape).produce(initializer)
 
 /**

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

@@ -1,5 +1,6 @@
 package kscience.kmath.structures
 
+import kscience.kmath.misc.UnstableKMathAPI
 import kotlin.jvm.JvmName
 import kotlin.native.concurrent.ThreadLocal
 import kotlin.reflect.KClass
@@ -38,9 +39,17 @@ public interface NDStructure<T> {
      */
     public fun elements(): Sequence<Pair<IntArray, T>>
 
+    //force override equality and hash code
     public override fun equals(other: Any?): Boolean
     public override fun hashCode(): Int
 
+    /**
+     * Feature is additional property or hint that does not directly affect the structure, but could in some cases help
+     * optimize operations and performance. If the feature is not present, null is defined.
+     */
+    @UnstableKMathAPI
+    public fun <T : Any> getFeature(type: KClass<T>): T? = null
+
     public companion object {
         /**
          * Indicates whether some [NDStructure] is equal to another one.
@@ -120,6 +129,9 @@ public interface NDStructure<T> {
  */
 public operator fun <T> NDStructure<T>.get(vararg index: Int): T = get(index)
 
+@UnstableKMathAPI
+public inline fun <reified T : Any> NDStructure<*>.getFeature(): T? = getFeature(T::class)
+
 /**
  * Represents mutable [NDStructure].
  */
@@ -133,6 +145,9 @@ public interface MutableNDStructure<T> : NDStructure<T> {
     public operator fun set(index: IntArray, value: T)
 }
 
+/**
+ * Transform a structure element-by element in place.
+ */
 public inline fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) -> T): Unit =
     elements().forEach { (index, oldValue) -> this[index] = action(index, oldValue) }
 

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

@@ -150,6 +150,8 @@ public class RealBufferField(public val size: Int) : ExtendedField<Buffer<Double
     public override val zero: Buffer<Double> by lazy { RealBuffer(size) { 0.0 } }
     public override val one: Buffer<Double> by lazy { RealBuffer(size) { 1.0 } }
 
+    override fun number(value: Number): Buffer<Double> = RealBuffer(size) { value.toDouble() }
+
     public override fun add(a: Buffer<Double>, b: Buffer<Double>): RealBuffer {
         require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
         return RealBufferFieldOperations.add(a, b)

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

@@ -1,13 +1,17 @@
 package kscience.kmath.structures
 
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.FieldElement
 import kscience.kmath.operations.RealField
+import kscience.kmath.operations.RingWithNumbers
 
 public typealias RealNDElement = BufferedNDFieldElement<Double, RealField>
 
+@OptIn(UnstableKMathAPI::class)
 public class RealNDField(override val shape: IntArray) :
     BufferedNDField<Double, RealField>,
-    ExtendedNDField<Double, RealField, NDBuffer<Double>> {
+    ExtendedNDField<Double, RealField, NDBuffer<Double>>,
+    RingWithNumbers<NDBuffer<Double>>{
 
     override val strides: Strides = DefaultStrides(shape)
 
@@ -15,7 +19,12 @@ public class RealNDField(override val shape: IntArray) :
     override val zero: RealNDElement by lazy { produce { zero } }
     override val one: RealNDElement by lazy { produce { one } }
 
-    public inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Double): Buffer<Double> =
+    override fun number(value: Number): NDBuffer<Double> {
+        val d = value.toDouble()
+        return produce { d }
+    }
+
+    private inline fun buildBuffer(size: Int, crossinline initializer: (Int) -> Double): Buffer<Double> =
         RealBuffer(DoubleArray(size) { initializer(it) })
 
     /**
@@ -59,7 +68,8 @@ public class RealNDField(override val shape: IntArray) :
         check(a, b)
         return BufferedNDFieldElement(
             this,
-            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) })
+            buildBuffer(strides.linearSize) { offset -> elementContext.transform(a.buffer[offset], b.buffer[offset]) }
+        )
     }
 
     override fun NDBuffer<Double>.toElement(): FieldElement<NDBuffer<Double>, *, out BufferedNDField<Double, RealField>> =

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

@@ -9,12 +9,14 @@ public interface Structure2D<T> : NDStructure<T> {
     /**
      * The number of rows in this structure.
      */
-    public val rowNum: Int get() = shape[0]
+    public val rowNum: Int
 
     /**
      * The number of columns in this structure.
      */
-    public val colNum: Int get() = shape[1]
+    public val colNum: Int
+
+    public override val shape: IntArray get() = intArrayOf(rowNum, colNum)
 
     /**
      * The buffer of rows of this structure. It gets elements from the structure dynamically.
@@ -56,6 +58,9 @@ public interface Structure2D<T> : NDStructure<T> {
 private inline class Structure2DWrapper<T>(val structure: NDStructure<T>) : Structure2D<T> {
     override val shape: IntArray get() = structure.shape
 
+    override val rowNum: Int get() = shape[0]
+    override val colNum: Int get() = shape[1]
+
     override operator fun get(i: Int, j: Int): T = structure[i, j]
 
     override fun elements(): Sequence<Pair<IntArray, T>> = structure.elements()

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

@@ -1,14 +1,13 @@
 package kscience.kmath.structures
 
 import kscience.kmath.operations.internal.FieldVerifier
-import kscience.kmath.operations.invoke
 import kotlin.test.Test
 import kotlin.test.assertEquals
 
 internal class NDFieldTest {
     @Test
     fun verify() {
-        (NDField.real(12, 32)) { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
+        NDField.real(12, 32).run { FieldVerifier(this, one + 3, one - 23, one * 12, 6.66) }
     }
 
     @Test

kmath-core/src/jvmMain/kotlin/kscience/kmath/operations/BigNumbers.kt

@@ -7,7 +7,7 @@ import java.math.MathContext
 /**
  * A field over [BigInteger].
  */
-public object JBigIntegerField : Field<BigInteger> {
+public object JBigIntegerField : Field<BigInteger>, NumericAlgebra<BigInteger> {
     public override val zero: BigInteger
         get() = BigInteger.ZERO
 
@@ -28,9 +28,9 @@ public object JBigIntegerField : Field<BigInteger> {
  *
  * @property mathContext the [MathContext] to use.
  */
-public abstract class JBigDecimalFieldBase internal constructor(public val mathContext: MathContext = MathContext.DECIMAL64) :
+public abstract class JBigDecimalFieldBase internal constructor(
-    Field<BigDecimal>,
+    private val mathContext: MathContext = MathContext.DECIMAL64,
-    PowerOperations<BigDecimal> {
+) : Field<BigDecimal>, PowerOperations<BigDecimal>, NumericAlgebra<BigDecimal> {
     public override val zero: BigDecimal
         get() = BigDecimal.ZERO
 

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

@@ -40,6 +40,8 @@ public inline class DMatrixWrapper<T, R : Dimension, C : Dimension>(
     private val structure: Structure2D<T>,
 ) : DMatrix<T, R, C> {
     override val shape: IntArray get() = structure.shape
+    override val rowNum: Int get() = shape[0]
+    override val colNum: Int get() = shape[1]
     override operator fun get(i: Int, j: Int): T = structure[i, j]
 }
 
@@ -147,6 +149,7 @@ public inline fun <reified D : Dimension> DMatrixContext<Double>.one(): DMatrix<
     if (i == j) 1.0 else 0.0
 }
 
-public inline fun <reified R : Dimension, reified C : Dimension> DMatrixContext<Double>.zero(): DMatrix<Double, R, C> = produce { _, _ ->
+public inline fun <reified R : Dimension, reified C : Dimension> DMatrixContext<Double>.zero(): DMatrix<Double, R, C> =
-    0.0
+    produce { _, _ ->
-}
+        0.0
+    }

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

@@ -1,10 +1,13 @@
 package kscience.kmath.ejml
 
 import kscience.kmath.linear.*
-import kscience.kmath.structures.NDStructure
+import kscience.kmath.misc.UnstableKMathAPI
+import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.RealBuffer
 import org.ejml.dense.row.factory.DecompositionFactory_DDRM
 import org.ejml.simple.SimpleMatrix
+import kotlin.reflect.KClass
+import kotlin.reflect.cast
 
 /**
  * Represents featured matrix over EJML [SimpleMatrix].
@@ -12,87 +15,65 @@ import org.ejml.simple.SimpleMatrix
  * @property origin the underlying [SimpleMatrix].
  * @author Iaroslav Postovalov
  */
-public class EjmlMatrix(public val origin: SimpleMatrix, features: Set<MatrixFeature> = emptySet()) :
+public inline class EjmlMatrix(
-    FeaturedMatrix<Double> {
+    public val origin: SimpleMatrix,
-    public override val rowNum: Int
+) : Matrix<Double> {
-        get() = origin.numRows()
+    public override val rowNum: Int get() = origin.numRows()
 
-    public override val colNum: Int
+    public override val colNum: Int get() = origin.numCols()
-        get() = origin.numCols()
 
-    public override val shape: IntArray by lazy { intArrayOf(rowNum, colNum) }
+    @UnstableKMathAPI
-
+    override fun <T : Any> getFeature(type: KClass<T>): T? = when (type) {
-    public override val features: Set<MatrixFeature> = hashSetOf(
+        InverseMatrixFeature::class -> object : InverseMatrixFeature<Double> {
-        object : InverseMatrixFeature<Double> {
+            override val inverse: Matrix<Double> by lazy { EjmlMatrix(origin.invert()) }
-            override val inverse: FeaturedMatrix<Double> by lazy { EjmlMatrix(origin.invert()) }
+        }
-        },
+        DeterminantFeature::class -> object : DeterminantFeature<Double> {
-
-        object : DeterminantFeature<Double> {
             override val determinant: Double by lazy(origin::determinant)
-        },
+        }
-
+        SingularValueDecompositionFeature::class -> object : SingularValueDecompositionFeature<Double> {
-        object : SingularValueDecompositionFeature<Double> {
             private val svd by lazy {
                 DecompositionFactory_DDRM.svd(origin.numRows(), origin.numCols(), true, true, false)
                     .apply { decompose(origin.ddrm.copy()) }
             }
 
-            override val u: FeaturedMatrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getU(null, false))) }
+            override val u: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getU(null, false))) }
-            override val s: FeaturedMatrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getW(null))) }
+            override val s: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getW(null))) }
-            override val v: FeaturedMatrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getV(null, false))) }
+            override val v: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(svd.getV(null, false))) }
             override val singularValues: Point<Double> by lazy { RealBuffer(svd.singularValues) }
-        },
+        }
-
+        QRDecompositionFeature::class -> object : QRDecompositionFeature<Double> {
-        object : QRDecompositionFeature<Double> {
             private val qr by lazy {
                 DecompositionFactory_DDRM.qr().apply { decompose(origin.ddrm.copy()) }
             }
 
-            override val q: FeaturedMatrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getQ(null, false))) }
+            override val q: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getQ(null, false))) }
-            override val r: FeaturedMatrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getR(null, false))) }
+            override val r: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(qr.getR(null, false))) }
-        },
+        }
-
+        CholeskyDecompositionFeature::class ->         object : CholeskyDecompositionFeature<Double> {
-        object : CholeskyDecompositionFeature<Double> {
+            override val l: Matrix<Double> by lazy {
-            override val l: FeaturedMatrix<Double> by lazy {
                 val cholesky =
                     DecompositionFactory_DDRM.chol(rowNum, true).apply { decompose(origin.ddrm.copy()) }
 
-                EjmlMatrix(SimpleMatrix(cholesky.getT(null)), setOf(LFeature))
+                EjmlMatrix(SimpleMatrix(cholesky.getT(null))) + LFeature
             }
-        },
+        }
-
+        LupDecompositionFeature::class ->         object : LupDecompositionFeature<Double> {
-        object : LupDecompositionFeature<Double> {
             private val lup by lazy {
                 DecompositionFactory_DDRM.lu(origin.numRows(), origin.numCols()).apply { decompose(origin.ddrm.copy()) }
             }
 
-            override val l: FeaturedMatrix<Double> by lazy {
+            override val l: Matrix<Double> by lazy {
-                EjmlMatrix(SimpleMatrix(lup.getLower(null)), setOf(LFeature))
+                EjmlMatrix(SimpleMatrix(lup.getLower(null))) + LFeature
             }
 
-            override val u: FeaturedMatrix<Double> by lazy {
+            override val u: Matrix<Double> by lazy {
-                EjmlMatrix(SimpleMatrix(lup.getUpper(null)), setOf(UFeature))
+                EjmlMatrix(SimpleMatrix(lup.getUpper(null))) + UFeature
             }
 
-            override val p: FeaturedMatrix<Double> by lazy { EjmlMatrix(SimpleMatrix(lup.getRowPivot(null))) }
+            override val p: Matrix<Double> by lazy { EjmlMatrix(SimpleMatrix(lup.getRowPivot(null))) }
-        },
+        }
-    ) union features
+        else -> null
-
+    }?.let{type.cast(it)}
-    public override fun suggestFeature(vararg features: MatrixFeature): EjmlMatrix =
-        EjmlMatrix(origin, this.features + features)
 
     public override operator fun get(i: Int, j: Int): Double = origin[i, j]
-
-    public override fun equals(other: Any?): Boolean {
-        if (other is EjmlMatrix) return origin.isIdentical(other.origin, 0.0)
-        return NDStructure.equals(this, other as? NDStructure<*> ?: return false)
-    }
-
-    public override fun hashCode(): Int {
-        var result = origin.hashCode()
-        result = 31 * result + features.hashCode()
-        return result
-    }
-
-    public override fun toString(): String = "EjmlMatrix(origin=$origin, features=$features)"
 }

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

@@ -1,22 +1,30 @@
 package kscience.kmath.ejml
 
+import kscience.kmath.linear.InverseMatrixFeature
 import kscience.kmath.linear.MatrixContext
+import kscience.kmath.linear.MatrixWrapper
 import kscience.kmath.linear.Point
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.structures.Matrix
+import kscience.kmath.structures.getFeature
 import org.ejml.simple.SimpleMatrix
 
-/**
- * Converts this matrix to EJML one.
- */
-public fun Matrix<Double>.toEjml(): EjmlMatrix =
-    if (this is EjmlMatrix) this else EjmlMatrixContext.produce(rowNum, colNum) { i, j -> get(i, j) }
-
 /**
  * Represents context of basic operations operating with [EjmlMatrix].
  *
  * @author Iaroslav Postovalov
  */
 public object EjmlMatrixContext : MatrixContext<Double, EjmlMatrix> {
+
+    /**
+     * Converts this matrix to EJML one.
+     */
+    public fun Matrix<Double>.toEjml(): EjmlMatrix = when {
+        this is EjmlMatrix -> this
+        this is MatrixWrapper && matrix is EjmlMatrix -> matrix as EjmlMatrix
+        else -> produce(rowNum, colNum) { i, j -> get(i, j) }
+    }
+
     /**
      * Converts this vector to EJML one.
      */
@@ -77,3 +85,8 @@ public fun EjmlMatrixContext.solve(a: Matrix<Double>, b: Matrix<Double>): EjmlMa
  */
 public fun EjmlMatrixContext.solve(a: Matrix<Double>, b: Point<Double>): EjmlVector =
     EjmlVector(a.toEjml().origin.solve(b.toEjml().origin))
+
+@OptIn(UnstableKMathAPI::class)
+public fun EjmlMatrix.inverted(): EjmlMatrix = getFeature<InverseMatrixFeature<Double>>()!!.inverse as EjmlMatrix
+
+public fun EjmlMatrixContext.inverse(matrix: Matrix<Double>): Matrix<Double> = matrix.toEjml().inverted()

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

@@ -3,7 +3,8 @@ package kscience.kmath.ejml
 import kscience.kmath.linear.DeterminantFeature
 import kscience.kmath.linear.LupDecompositionFeature
 import kscience.kmath.linear.MatrixFeature
-import kscience.kmath.linear.getFeature
+import kscience.kmath.linear.plus
+import kscience.kmath.structures.getFeature
 import org.ejml.dense.row.factory.DecompositionFactory_DDRM
 import org.ejml.simple.SimpleMatrix
 import kotlin.random.Random
@@ -58,7 +59,7 @@ internal class EjmlMatrixTest {
 
     @Test
     fun suggestFeature() {
-        assertNotNull(EjmlMatrix(randomMatrix).suggestFeature(SomeFeature).getFeature<SomeFeature>())
+        assertNotNull((EjmlMatrix(randomMatrix) + SomeFeature).getFeature<SomeFeature>())
     }
 
     @Test

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

@@ -1,8 +1,12 @@
 package kscience.kmath.real
 
-import kscience.kmath.linear.*
+import kscience.kmath.linear.MatrixContext
+import kscience.kmath.linear.VirtualMatrix
+import kscience.kmath.linear.inverseWithLUP
+import kscience.kmath.linear.real
 import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.structures.Buffer
+import kscience.kmath.structures.Matrix
 import kscience.kmath.structures.RealBuffer
 import kscience.kmath.structures.asIterable
 import kotlin.math.pow
@@ -19,7 +23,7 @@ import kotlin.math.pow
  *  Functions that help create a real (Double) matrix
  */
 
-public typealias RealMatrix = FeaturedMatrix<Double>
+public typealias RealMatrix = Matrix<Double>
 
 public fun realMatrix(rowNum: Int, colNum: Int, initializer: (i: Int, j: Int) -> Double): RealMatrix =
     MatrixContext.real.produce(rowNum, colNum, initializer)

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

@@ -1,6 +1,5 @@
 package kaceince.kmath.real
 
-import kscience.kmath.linear.VirtualMatrix
 import kscience.kmath.linear.build
 import kscience.kmath.real.*
 import kscience.kmath.structures.Matrix
@@ -42,7 +41,7 @@ internal class RealMatrixTest {
             1.0, 0.0, 0.0,
             0.0, 1.0, 2.0
         )
-        assertEquals(VirtualMatrix.wrap(matrix2), matrix1.repeatStackVertical(3))
+        assertEquals(matrix2, matrix1.repeatStackVertical(3))
     }
 
     @Test

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

@@ -1,5 +1,6 @@
 package kscience.kmath.nd4j
 
+import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.operations.*
 import kscience.kmath.structures.NDAlgebra
 import kscience.kmath.structures.NDField
@@ -35,7 +36,7 @@ public interface Nd4jArrayAlgebra<T, C> : NDAlgebra<T, C, Nd4jArrayStructure<T>>
 
     public override fun mapIndexed(
         arg: Nd4jArrayStructure<T>,
-        transform: C.(index: IntArray, T) -> T
+        transform: C.(index: IntArray, T) -> T,
     ): Nd4jArrayStructure<T> {
         check(arg)
         val new = Nd4j.create(*shape).wrap()
@@ -46,7 +47,7 @@ public interface Nd4jArrayAlgebra<T, C> : NDAlgebra<T, C, Nd4jArrayStructure<T>>
     public override fun combine(
         a: Nd4jArrayStructure<T>,
         b: Nd4jArrayStructure<T>,
-        transform: C.(T, T) -> T
+        transform: C.(T, T) -> T,
     ): Nd4jArrayStructure<T> {
         check(a, b)
         val new = Nd4j.create(*shape).wrap()
@@ -61,8 +62,8 @@ public interface Nd4jArrayAlgebra<T, C> : NDAlgebra<T, C, Nd4jArrayStructure<T>>
  * @param T the type of the element contained in ND structure.
  * @param S the type of space of structure elements.
  */
-public interface Nd4jArraySpace<T, S> : NDSpace<T, S, Nd4jArrayStructure<T>>,
+public interface Nd4jArraySpace<T, S : Space<T>> : NDSpace<T, S, Nd4jArrayStructure<T>>, Nd4jArrayAlgebra<T, S> {
-    Nd4jArrayAlgebra<T, S> where S : Space<T> {
+
     public override val zero: Nd4jArrayStructure<T>
         get() = Nd4j.zeros(*shape).wrap()
 
@@ -103,7 +104,9 @@ public interface Nd4jArraySpace<T, S> : NDSpace<T, S, Nd4jArrayStructure<T>>,
  * @param T the type of the element contained in ND structure.
  * @param R the type of ring of structure elements.
  */
-public interface Nd4jArrayRing<T, R> : NDRing<T, R, Nd4jArrayStructure<T>>, Nd4jArraySpace<T, R> where R : Ring<T> {
+@OptIn(UnstableKMathAPI::class)
+public interface Nd4jArrayRing<T, R : Ring<T>> : NDRing<T, R, Nd4jArrayStructure<T>>, Nd4jArraySpace<T, R> {
+
     public override val one: Nd4jArrayStructure<T>
         get() = Nd4j.ones(*shape).wrap()
 
@@ -111,21 +114,21 @@ public interface Nd4jArrayRing<T, R> : NDRing<T, R, Nd4jArrayStructure<T>>, Nd4j
         check(a, b)
         return a.ndArray.mul(b.ndArray).wrap()
     }
-
+//
-    public override operator fun Nd4jArrayStructure<T>.minus(b: Number): Nd4jArrayStructure<T> {
+//    public override operator fun Nd4jArrayStructure<T>.minus(b: Number): Nd4jArrayStructure<T> {
-        check(this)
+//        check(this)
-        return ndArray.sub(b).wrap()
+//        return ndArray.sub(b).wrap()
-    }
+//    }
-
+//
-    public override operator fun Nd4jArrayStructure<T>.plus(b: Number): Nd4jArrayStructure<T> {
+//    public override operator fun Nd4jArrayStructure<T>.plus(b: Number): Nd4jArrayStructure<T> {
-        check(this)
+//        check(this)
-        return ndArray.add(b).wrap()
+//        return ndArray.add(b).wrap()
-    }
+//    }
-
+//
-    public override operator fun Number.minus(b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
+//    public override operator fun Number.minus(b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
-        check(b)
+//        check(b)
-        return b.ndArray.rsub(this).wrap()
+//        return b.ndArray.rsub(this).wrap()
-    }
+//    }
 
     public companion object {
         private val intNd4jArrayRingCache: ThreadLocal<MutableMap<IntArray, IntNd4jArrayRing>> =
@@ -165,7 +168,8 @@ public interface Nd4jArrayRing<T, R> : NDRing<T, R, Nd4jArrayStructure<T>>, Nd4j
  * @param N the type of ND structure.
  * @param F the type field of structure elements.
  */
-public interface Nd4jArrayField<T, F> : NDField<T, F, Nd4jArrayStructure<T>>, Nd4jArrayRing<T, F> where F : Field<T> {
+public interface Nd4jArrayField<T, F : Field<T>> : NDField<T, F, Nd4jArrayStructure<T>>, Nd4jArrayRing<T, F> {
+
     public override fun divide(a: Nd4jArrayStructure<T>, b: Nd4jArrayStructure<T>): Nd4jArrayStructure<T> {
         check(a, b)
         return a.ndArray.div(b.ndArray).wrap()

settings.gradle.kts

@@ -8,8 +8,8 @@ pluginManagement {
         maven("https://dl.bintray.com/kotlin/kotlinx")
     }
 
-    val toolsVersion = "0.7.1"
+    val toolsVersion = "0.7.3-1.4.30-RC"
-    val kotlinVersion = "1.4.21"
+    val kotlinVersion = "1.4.30-RC"
 
     plugins {
         id("kotlinx.benchmark") version "0.2.0-dev-20"