Refactor TensorAlgebra to take StructureND and inherit AlgebraND

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

@@ -36,7 +36,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
                 this@StreamDoubleFieldND.shape,
                 shape
             )
-            this is BufferND && this.indexes == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer
+            this is BufferND && this.indices == this@StreamDoubleFieldND.strides -> this.buffer as DoubleBuffer
             else -> DoubleBuffer(strides.linearSize) { offset -> get(strides.index(offset)) }
         }
 

examples/src/main/kotlin/space/kscience/kmath/tensors/neuralNetwork.kt

@@ -9,7 +9,7 @@ import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
 import space.kscience.kmath.tensors.core.DoubleTensor
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
-import space.kscience.kmath.tensors.core.toDoubleArray
+import space.kscience.kmath.tensors.core.copyArray
 import kotlin.math.sqrt
 
 const val seed = 100500L
@@ -111,7 +111,7 @@ class NeuralNetwork(private val layers: List<Layer>) {
     private fun softMaxLoss(yPred: DoubleTensor, yTrue: DoubleTensor): DoubleTensor = BroadcastDoubleTensorAlgebra {
 
         val onesForAnswers = yPred.zeroesLike()
-        yTrue.toDoubleArray().forEachIndexed { index, labelDouble ->
+        yTrue.copyArray().forEachIndexed { index, labelDouble ->
             val label = labelDouble.toInt()
             onesForAnswers[intArrayOf(index, label)] = 1.0
         }

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

@@ -131,19 +131,19 @@ public interface GroupOpsND<T, out A : GroupOps<T>> : GroupOps<StructureND<T>>,
      * Adds an element to ND structure of it.
      *
      * @receiver the augend.
-     * @param arg the addend.
+     * @param other the addend.
      * @return the sum.
      */
-    public operator fun T.plus(arg: StructureND<T>): StructureND<T> = arg + this
+    public operator fun T.plus(other: StructureND<T>): StructureND<T> = other.map { value -> add(this@plus, value) }
 
     /**
      * Subtracts an ND structure from an element of it.
      *
      * @receiver the dividend.
-     * @param arg the divisor.
+     * @param other the divisor.
      * @return the quotient.
      */
-    public operator fun T.minus(arg: StructureND<T>): StructureND<T> = arg.map { value -> add(-this@minus, value) }
+    public operator fun T.minus(other: StructureND<T>): StructureND<T> = other.map { value -> add(-this@minus, value) }
 
     public companion object
 }

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

@@ -51,7 +51,7 @@ public inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.mapInline(
     arg: BufferND<T>,
     crossinline transform: A.(T) -> T
 ): BufferND<T> {
-    val indexes = arg.indexes
+    val indexes = arg.indices
     return BufferND(indexes, bufferAlgebra.mapInline(arg.buffer, transform))
 }
 
@@ -59,7 +59,7 @@ internal inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.mapIndexedInline(
     arg: BufferND<T>,
     crossinline transform: A.(index: IntArray, arg: T) -> T
 ): BufferND<T> {
-    val indexes = arg.indexes
+    val indexes = arg.indices
     return BufferND(
         indexes,
         bufferAlgebra.mapIndexedInline(arg.buffer) { offset, value ->
@@ -73,8 +73,8 @@ internal inline fun <T, A : Algebra<T>> BufferAlgebraND<T, A>.zipInline(
     r: BufferND<T>,
     crossinline block: A.(l: T, r: T) -> T
 ): BufferND<T> {
-    require(l.indexes == r.indexes) { "Zip requires the same shapes, but found ${l.shape} on the left and ${r.shape} on the right" }
+    require(l.indices == r.indices) { "Zip requires the same shapes, but found ${l.shape} on the left and ${r.shape} on the right" }
-    val indexes = l.indexes
+    val indexes = l.indices
     return BufferND(indexes, bufferAlgebra.zipInline(l.buffer, r.buffer, block))
 }
 

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

@@ -15,20 +15,20 @@ import space.kscience.kmath.structures.MutableBufferFactory
  * Represents [StructureND] over [Buffer].
  *
  * @param T the type of items.
- * @param indexes The strides to access elements of [Buffer] by linear indices.
+ * @param indices The strides to access elements of [Buffer] by linear indices.
  * @param buffer The underlying buffer.
  */
 public open class BufferND<out T>(
-    public val indexes: ShapeIndexer,
+    public val indices: ShapeIndexer,
     public open val buffer: Buffer<T>,
 ) : StructureND<T> {
 
-    override operator fun get(index: IntArray): T = buffer[indexes.offset(index)]
+    override operator fun get(index: IntArray): T = buffer[indices.offset(index)]
 
-    override val shape: IntArray get() = indexes.shape
+    override val shape: IntArray get() = indices.shape
 
     @PerformancePitfall
-    override fun elements(): Sequence<Pair<IntArray, T>> = indexes.indices().map {
+    override fun elements(): Sequence<Pair<IntArray, T>> = indices.indices().map {
         it to this[it]
     }
 
@@ -43,7 +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.indexes, factory.invoke(indexes.linearSize) { transform(buffer[it]) })
+        BufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) })
     else {
         val strides = DefaultStrides(shape)
         BufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
@@ -62,7 +62,7 @@ public class MutableBufferND<T>(
     override val buffer: MutableBuffer<T>,
 ) : MutableStructureND<T>, BufferND<T>(strides, buffer) {
     override fun set(index: IntArray, value: T) {
-        buffer[indexes.offset(index)] = value
+        buffer[indices.offset(index)] = value
     }
 }
 
@@ -74,7 +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.indexes, factory.invoke(indexes.linearSize) { transform(buffer[it]) })
+        MutableBufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[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

@@ -33,7 +33,7 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(D
         arg: DoubleBufferND,
         transform: (Double) -> Double
     ): DoubleBufferND {
-        val indexes = arg.indexes
+        val indexes = arg.indices
         val array = arg.buffer.array
         return DoubleBufferND(indexes, DoubleBuffer(indexes.linearSize) { transform(array[it]) })
     }
@@ -43,8 +43,8 @@ public sealed class DoubleFieldOpsND : BufferedFieldOpsND<Double, DoubleField>(D
         r: DoubleBufferND,
         block: (l: Double, r: Double) -> Double
     ): DoubleBufferND {
-        require(l.indexes == r.indexes) { "Zip requires the same shapes, but found ${l.shape} on the left and ${r.shape} on the right" }
+        require(l.indices == r.indices) { "Zip requires the same shapes, but found ${l.shape} on the left and ${r.shape} on the right" }
-        val indexes = l.indexes
+        val indexes = l.indices
         val lArray = l.buffer.array
         val rArray = r.buffer.array
         return DoubleBufferND(indexes, DoubleBuffer(indexes.linearSize) { block(lArray[it], rArray[it]) })

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

@@ -71,7 +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.indexes == st2.indexes)
+            if (st1 is BufferND && st2 is BufferND && st1.indices == st2.indices)
                 return Buffer.contentEquals(st1.buffer, st2.buffer)
 
             //element by element comparison if it could not be avoided
@@ -87,7 +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.indexes == st2.indexes)
+            if (st1 is BufferND && st2 is BufferND && st1.indices == st2.indices)
                 return Buffer.contentEquals(st1.buffer, st2.buffer)
 
             //element by element comparison if it could not be avoided

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(indexes.linearSize) { offset -> DoubleField.transform(buffer[offset]) }
+    val array = DoubleArray(indices.linearSize) { offset -> DoubleField.transform(buffer[offset]) }
-    return BufferND(indexes, DoubleBuffer(array))
+    return BufferND(indices, DoubleBuffer(array))
 }
 
 /**

kmath-multik/src/main/kotlin/space/kscience/kmath/multik/MultikTensorAlgebra.kt

@@ -16,6 +16,7 @@ import org.jetbrains.kotlinx.multik.ndarray.data.*
 import org.jetbrains.kotlinx.multik.ndarray.operations.*
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.Shape
+import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.mapInPlace
 import space.kscience.kmath.operations.*
 import space.kscience.kmath.tensors.api.Tensor
@@ -49,17 +50,17 @@ private fun <T, D : Dimension> MultiArray<T, D>.asD2Array(): D2Array<T> {
     else throw ClassCastException("Cannot cast MultiArray to NDArray.")
 }
 
-public class MultikTensorAlgebra<T : Number> internal constructor(
+public class MultikTensorAlgebra<T : Number, A: Ring<T>> internal constructor(
     public val type: DataType,
-    public val elementAlgebra: Ring<T>,
+    override val elementAlgebra: A,
     public val comparator: Comparator<T>
-) : TensorAlgebra<T> {
+) : TensorAlgebra<T, A> {
 
     /**
      * Convert a tensor to [MultikTensor] if necessary. If tensor is converted, changes on the resulting tensor
      * are not reflected back onto the source
      */
-    public fun Tensor<T>.asMultik(): MultikTensor<T> {
+    public fun StructureND<T>.asMultik(): MultikTensor<T> {
         return if (this is MultikTensor) {
             this
         } else {
@@ -73,17 +74,17 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
 
     public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
 
-    override fun Tensor<T>.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) {
+    override fun StructureND<T>.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) {
         get(intArrayOf(0))
     } else null
 
-    override fun T.plus(other: Tensor<T>): MultikTensor<T> =
+    override fun T.plus(other: StructureND<T>): MultikTensor<T> =
         other.plus(this)
 
-    override fun Tensor<T>.plus(value: T): MultikTensor<T> =
+    override fun StructureND<T>.plus(value: T): MultikTensor<T> =
         asMultik().array.deepCopy().apply { plusAssign(value) }.wrap()
 
-    override fun Tensor<T>.plus(other: Tensor<T>): MultikTensor<T> =
+    override fun StructureND<T>.plus(other: StructureND<T>): MultikTensor<T> =
         asMultik().array.plus(other.asMultik().array).wrap()
 
     override fun Tensor<T>.plusAssign(value: T) {
@@ -94,7 +95,7 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
         }
     }
 
-    override fun Tensor<T>.plusAssign(other: Tensor<T>) {
+    override fun Tensor<T>.plusAssign(other: StructureND<T>) {
         if (this is MultikTensor) {
             array.plusAssign(other.asMultik().array)
         } else {
@@ -102,12 +103,12 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
         }
     }
 
-    override fun T.minus(other: Tensor<T>): MultikTensor<T> = (-(other.asMultik().array - this)).wrap()
+    override fun T.minus(other: StructureND<T>): MultikTensor<T> = (-(other.asMultik().array - this)).wrap()
 
-    override fun Tensor<T>.minus(value: T): MultikTensor<T> =
+    override fun StructureND<T>.minus(arg: T): MultikTensor<T> =
-        asMultik().array.deepCopy().apply { minusAssign(value) }.wrap()
+        asMultik().array.deepCopy().apply { minusAssign(arg) }.wrap()
 
-    override fun Tensor<T>.minus(other: Tensor<T>): MultikTensor<T> =
+    override fun StructureND<T>.minus(other: StructureND<T>): MultikTensor<T> =
         asMultik().array.minus(other.asMultik().array).wrap()
 
     override fun Tensor<T>.minusAssign(value: T) {
@@ -118,7 +119,7 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
         }
     }
 
-    override fun Tensor<T>.minusAssign(other: Tensor<T>) {
+    override fun Tensor<T>.minusAssign(other: StructureND<T>) {
         if (this is MultikTensor) {
             array.minusAssign(other.asMultik().array)
         } else {
@@ -126,13 +127,13 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
         }
     }
 
-    override fun T.times(other: Tensor<T>): MultikTensor<T> =
+    override fun T.times(arg: StructureND<T>): MultikTensor<T> =
-        other.asMultik().array.deepCopy().apply { timesAssign(this@times) }.wrap()
+        arg.asMultik().array.deepCopy().apply { timesAssign(this@times) }.wrap()
 
-    override fun Tensor<T>.times(value: T): Tensor<T> =
+    override fun StructureND<T>.times(arg: T): Tensor<T> =
-        asMultik().array.deepCopy().apply { timesAssign(value) }.wrap()
+        asMultik().array.deepCopy().apply { timesAssign(arg) }.wrap()
 
-    override fun Tensor<T>.times(other: Tensor<T>): MultikTensor<T> =
+    override fun StructureND<T>.times(other: StructureND<T>): MultikTensor<T> =
         asMultik().array.times(other.asMultik().array).wrap()
 
     override fun Tensor<T>.timesAssign(value: T) {
@@ -143,7 +144,7 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
         }
     }
 
-    override fun Tensor<T>.timesAssign(other: Tensor<T>) {
+    override fun Tensor<T>.timesAssign(other: StructureND<T>) {
         if (this is MultikTensor) {
             array.timesAssign(other.asMultik().array)
         } else {
@@ -151,7 +152,7 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
         }
     }
 
-    override fun Tensor<T>.unaryMinus(): MultikTensor<T> =
+    override fun StructureND<T>.unaryMinus(): MultikTensor<T> =
         asMultik().array.unaryMinus().wrap()
 
     override fun Tensor<T>.get(i: Int): MultikTensor<T> = asMultik().array.mutableView(i).wrap()
@@ -224,17 +225,17 @@ public class MultikTensorAlgebra<T : Number> internal constructor(
     }
 }
 
-public val DoubleField.multikTensorAlgebra: MultikTensorAlgebra<Double>
+public val DoubleField.multikTensorAlgebra: MultikTensorAlgebra<Double, DoubleField>
     get() = MultikTensorAlgebra(DataType.DoubleDataType, DoubleField) { o1, o2 -> o1.compareTo(o2) }
 
-public val FloatField.multikTensorAlgebra: MultikTensorAlgebra<Float>
+public val FloatField.multikTensorAlgebra: MultikTensorAlgebra<Float, FloatField>
     get() = MultikTensorAlgebra(DataType.FloatDataType, FloatField) { o1, o2 -> o1.compareTo(o2) }
 
-public val ShortRing.multikTensorAlgebra: MultikTensorAlgebra<Short>
+public val ShortRing.multikTensorAlgebra: MultikTensorAlgebra<Short, ShortRing>
     get() = MultikTensorAlgebra(DataType.ShortDataType, ShortRing) { o1, o2 -> o1.compareTo(o2) }
 
-public val IntRing.multikTensorAlgebra: MultikTensorAlgebra<Int>
+public val IntRing.multikTensorAlgebra: MultikTensorAlgebra<Int, IntRing>
     get() = MultikTensorAlgebra(DataType.IntDataType, IntRing) { o1, o2 -> o1.compareTo(o2) }
 
-public val LongRing.multikTensorAlgebra: MultikTensorAlgebra<Long>
+public val LongRing.multikTensorAlgebra: MultikTensorAlgebra<Long, LongRing>
     get() = MultikTensorAlgebra(DataType.LongDataType, LongRing) { o1, o2 -> o1.compareTo(o2) }

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/AnalyticTensorAlgebra.kt

@@ -5,13 +5,15 @@
 
 package space.kscience.kmath.tensors.api
 
+import space.kscience.kmath.operations.Field
+
 
 /**
  * Analytic operations on [Tensor].
  *
  * @param T the type of items closed under analytic functions in the tensors.
  */
-public interface AnalyticTensorAlgebra<T> : TensorPartialDivisionAlgebra<T> {
+public interface AnalyticTensorAlgebra<T, A : Field<T>> : TensorPartialDivisionAlgebra<T, A> {
 
     /**
      * @return the mean of all elements in the input tensor.

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt

@@ -5,12 +5,14 @@
 
 package space.kscience.kmath.tensors.api
 
+import space.kscience.kmath.operations.Field
+
 /**
  * Common linear algebra operations. Operates on [Tensor].
  *
  * @param T the type of items closed under division in the tensors.
  */
-public interface LinearOpsTensorAlgebra<T> : TensorPartialDivisionAlgebra<T> {
+public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivisionAlgebra<T, A> {
 
     /**
      * Computes the determinant of a square matrix input, or of each square matrix in a batched input.

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorAlgebra.kt

@@ -5,7 +5,9 @@
 
 package space.kscience.kmath.tensors.api
 
-import space.kscience.kmath.operations.RingOps
+import space.kscience.kmath.nd.RingOpsND
+import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.operations.Ring
 
 /**
  * Algebra over a ring on [Tensor].
@@ -13,20 +15,20 @@ import space.kscience.kmath.operations.RingOps
  *
  * @param T the type of items in the tensors.
  */
-public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
+public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
     /**
      * Returns a single tensor value of unit dimension if tensor shape equals to [1].
      *
      * @return a nullable value of a potentially scalar tensor.
      */
-    public fun Tensor<T>.valueOrNull(): T?
+    public fun StructureND<T>.valueOrNull(): T?
 
     /**
      * Returns a single tensor value of unit dimension. The tensor shape must be equal to [1].
      *
      * @return the value of a scalar tensor.
      */
-    public fun Tensor<T>.value(): T =
+    public fun StructureND<T>.value(): T =
         valueOrNull() ?: throw IllegalArgumentException("Inconsistent value for tensor of with $shape shape")
 
     /**
@@ -36,7 +38,7 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      * @param other tensor to be added.
      * @return the sum of this value and tensor [other].
      */
-    public operator fun T.plus(other: Tensor<T>): Tensor<T>
+    override operator fun T.plus(other: StructureND<T>): Tensor<T>
 
     /**
      * Adds the scalar [value] to each element of this tensor and returns a new resulting tensor.
@@ -44,7 +46,7 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      * @param value the number to be added to each element of this tensor.
      * @return the sum of this tensor and [value].
      */
-    public operator fun Tensor<T>.plus(value: T): Tensor<T>
+    override operator fun StructureND<T>.plus(value: T): Tensor<T>
 
     /**
      * Each element of the tensor [other] is added to each element of this tensor.
@@ -53,7 +55,7 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      * @param other tensor to be added.
      * @return the sum of this tensor and [other].
      */
-    override fun Tensor<T>.plus(other: Tensor<T>): Tensor<T>
+    override operator fun StructureND<T>.plus(other: StructureND<T>): Tensor<T>
 
     /**
      * Adds the scalar [value] to each element of this tensor.
@@ -67,7 +69,7 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      *
      * @param other tensor to be added.
      */
-    public operator fun Tensor<T>.plusAssign(other: Tensor<T>)
+    public operator fun Tensor<T>.plusAssign(other: StructureND<T>)
 
     /**
      * Each element of the tensor [other] is subtracted from this value.
@@ -76,15 +78,15 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      * @param other tensor to be subtracted.
      * @return the difference between this value and tensor [other].
      */
-    public operator fun T.minus(other: Tensor<T>): Tensor<T>
+    override operator fun T.minus(other: StructureND<T>): Tensor<T>
 
     /**
-     * Subtracts the scalar [value] from each element of this tensor and returns a new resulting tensor.
+     * Subtracts the scalar [arg] from each element of this tensor and returns a new resulting tensor.
      *
-     * @param value the number to be subtracted from each element of this tensor.
+     * @param arg the number to be subtracted from each element of this tensor.
-     * @return the difference between this tensor and [value].
+     * @return the difference between this tensor and [arg].
      */
-    public operator fun Tensor<T>.minus(value: T): Tensor<T>
+    override operator fun StructureND<T>.minus(arg: T): Tensor<T>
 
     /**
      * Each element of the tensor [other] is subtracted from each element of this tensor.
@@ -93,7 +95,7 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      * @param other tensor to be subtracted.
      * @return the difference between this tensor and [other].
      */
-    override fun Tensor<T>.minus(other: Tensor<T>): Tensor<T>
+    override operator fun StructureND<T>.minus(other: StructureND<T>): Tensor<T>
 
     /**
      * Subtracts the scalar [value] from each element of this tensor.
@@ -107,25 +109,25 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      *
      * @param other tensor to be subtracted.
      */
-    public operator fun Tensor<T>.minusAssign(other: Tensor<T>)
+    public operator fun Tensor<T>.minusAssign(other: StructureND<T>)
 
 
     /**
-     * Each element of the tensor [other] is multiplied by this value.
+     * Each element of the tensor [arg] is multiplied by this value.
      * The resulting tensor is returned.
      *
-     * @param other tensor to be multiplied.
+     * @param arg tensor to be multiplied.
-     * @return the product of this value and tensor [other].
+     * @return the product of this value and tensor [arg].
      */
-    public operator fun T.times(other: Tensor<T>): Tensor<T>
+    override operator fun T.times(arg: StructureND<T>): Tensor<T>
 
     /**
-     * Multiplies the scalar [value] by each element of this tensor and returns a new resulting tensor.
+     * Multiplies the scalar [arg] by each element of this tensor and returns a new resulting tensor.
      *
-     * @param value the number to be multiplied by each element of this tensor.
+     * @param arg the number to be multiplied by each element of this tensor.
-     * @return the product of this tensor and [value].
+     * @return the product of this tensor and [arg].
      */
-    public operator fun Tensor<T>.times(value: T): Tensor<T>
+    override operator fun StructureND<T>.times(arg: T): Tensor<T>
 
     /**
      * Each element of the tensor [other] is multiplied by each element of this tensor.
@@ -134,7 +136,7 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      * @param other tensor to be multiplied.
      * @return the product of this tensor and [other].
      */
-    override fun Tensor<T>.times(other: Tensor<T>): Tensor<T>
+    override operator fun StructureND<T>.times(other: StructureND<T>): Tensor<T>
 
     /**
      * Multiplies the scalar [value] by each element of this tensor.
@@ -148,14 +150,14 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      *
      * @param other tensor to be multiplied.
      */
-    public operator fun Tensor<T>.timesAssign(other: Tensor<T>)
+    public operator fun Tensor<T>.timesAssign(other: StructureND<T>)
 
     /**
      * Numerical negative, element-wise.
      *
      * @return tensor negation of the original tensor.
      */
-    override fun Tensor<T>.unaryMinus(): Tensor<T>
+    override operator fun StructureND<T>.unaryMinus(): Tensor<T>
 
     /**
      * Returns the tensor at index i
@@ -324,7 +326,7 @@ public interface TensorAlgebra<T> : RingOps<Tensor<T>> {
      */
     public fun Tensor<T>.argMax(dim: Int, keepDim: Boolean): Tensor<T>
 
-    override fun add(left: Tensor<T>, right: Tensor<T>): Tensor<T> = left + right
+    override fun add(left: StructureND<T>, right: StructureND<T>): Tensor<T> = left + right
 
-    override fun multiply(left: Tensor<T>, right: Tensor<T>): Tensor<T> = left * right
+    override fun multiply(left: StructureND<T>, right: StructureND<T>): Tensor<T> = left * right
 }

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/TensorPartialDivisionAlgebra.kt

@@ -5,30 +5,34 @@
 
 package space.kscience.kmath.tensors.api
 
+import space.kscience.kmath.nd.FieldOpsND
+import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.operations.Field
+
 /**
  * Algebra over a field with partial division on [Tensor].
  * For more information: https://proofwiki.org/wiki/Definition:Division_Algebra
  *
  * @param T the type of items closed under division in the tensors.
  */
-public interface TensorPartialDivisionAlgebra<T> : TensorAlgebra<T> {
+public interface TensorPartialDivisionAlgebra<T, A : Field<T>> : TensorAlgebra<T, A>, FieldOpsND<T, A> {
 
     /**
-     * Each element of the tensor [other] is divided by this value.
+     * Each element of the tensor [arg] is divided by this value.
      * The resulting tensor is returned.
      *
-     * @param other tensor to divide by.
+     * @param arg tensor to divide by.
-     * @return the division of this value by the tensor [other].
+     * @return the division of this value by the tensor [arg].
      */
-    public operator fun T.div(other: Tensor<T>): Tensor<T>
+    override operator fun T.div(arg: StructureND<T>): Tensor<T>
 
     /**
-     * Divide by the scalar [value] each element of this tensor returns a new resulting tensor.
+     * Divide by the scalar [arg] each element of this tensor returns a new resulting tensor.
      *
-     * @param value the number to divide by each element of this tensor.
+     * @param arg the number to divide by each element of this tensor.
-     * @return the division of this tensor by the [value].
+     * @return the division of this tensor by the [arg].
      */
-    public operator fun Tensor<T>.div(value: T): Tensor<T>
+    override operator fun StructureND<T>.div(arg: T): Tensor<T>
 
     /**
      * Each element of the tensor [other] is divided by each element of this tensor.
@@ -37,7 +41,9 @@ public interface TensorPartialDivisionAlgebra<T> : TensorAlgebra<T> {
      * @param other tensor to be divided by.
      * @return the division of this tensor by [other].
      */
-    public operator fun Tensor<T>.div(other: Tensor<T>): Tensor<T>
+    override operator fun StructureND<T>.div(other: StructureND<T>): Tensor<T>
+
+    override fun divide(left: StructureND<T>, right: StructureND<T>): StructureND<T> = left.div(right)
 
     /**
      * Divides by the scalar [value] each element of this tensor.

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

@@ -6,6 +6,7 @@
 package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.tensors.api.Tensor
 import space.kscience.kmath.tensors.core.internal.array
 import space.kscience.kmath.tensors.core.internal.broadcastTensors
@@ -18,66 +19,66 @@ import space.kscience.kmath.tensors.core.internal.tensor
  */
 public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
 
-    override fun Tensor<Double>.plus(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.plus(other: StructureND<Double>): DoubleTensor {
         val broadcast = broadcastTensors(tensor, other.tensor)
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.linearStructure.linearSize) { i ->
+        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
             newThis.mutableBuffer.array()[i] + newOther.mutableBuffer.array()[i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.plusAssign(other: Tensor<Double>) {
+    override fun Tensor<Double>.plusAssign(other: StructureND<Double>) {
         val newOther = broadcastTo(other.tensor, tensor.shape)
-        for (i in 0 until tensor.linearStructure.linearSize) {
+        for (i in 0 until tensor.indices.linearSize) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] +=
                 newOther.mutableBuffer.array()[tensor.bufferStart + i]
         }
     }
 
-    override fun Tensor<Double>.minus(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.minus(other: StructureND<Double>): DoubleTensor {
         val broadcast = broadcastTensors(tensor, other.tensor)
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.linearStructure.linearSize) { i ->
+        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
             newThis.mutableBuffer.array()[i] - newOther.mutableBuffer.array()[i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.minusAssign(other: Tensor<Double>) {
+    override fun Tensor<Double>.minusAssign(other: StructureND<Double>) {
         val newOther = broadcastTo(other.tensor, tensor.shape)
-        for (i in 0 until tensor.linearStructure.linearSize) {
+        for (i in 0 until tensor.indices.linearSize) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] -=
                 newOther.mutableBuffer.array()[tensor.bufferStart + i]
         }
     }
 
-    override fun Tensor<Double>.times(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.times(other: StructureND<Double>): DoubleTensor {
         val broadcast = broadcastTensors(tensor, other.tensor)
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.linearStructure.linearSize) { i ->
+        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
             newThis.mutableBuffer.array()[newThis.bufferStart + i] *
                     newOther.mutableBuffer.array()[newOther.bufferStart + i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.timesAssign(other: Tensor<Double>) {
+    override fun Tensor<Double>.timesAssign(other: StructureND<Double>) {
         val newOther = broadcastTo(other.tensor, tensor.shape)
-        for (i in 0 until tensor.linearStructure.linearSize) {
+        for (i in 0 until tensor.indices.linearSize) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] *=
                 newOther.mutableBuffer.array()[tensor.bufferStart + i]
         }
     }
 
-    override fun Tensor<Double>.div(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.div(other: StructureND<Double>): DoubleTensor {
         val broadcast = broadcastTensors(tensor, other.tensor)
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.linearStructure.linearSize) { i ->
+        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
             newThis.mutableBuffer.array()[newOther.bufferStart + i] /
                     newOther.mutableBuffer.array()[newOther.bufferStart + i]
         }
@@ -86,7 +87,7 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
 
     override fun Tensor<Double>.divAssign(other: Tensor<Double>) {
         val newOther = broadcastTo(other.tensor, tensor.shape)
-        for (i in 0 until tensor.linearStructure.linearSize) {
+        for (i in 0 until tensor.indices.linearSize) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] /=
                 newOther.mutableBuffer.array()[tensor.bufferStart + i]
         }

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

@@ -23,23 +23,23 @@ public open class BufferedTensor<T> internal constructor(
     /**
      * Buffer strides based on [TensorLinearStructure] implementation
      */
-    public val linearStructure: Strides
+    public val indices: Strides
         get() = TensorLinearStructure(shape)
 
     /**
      * Number of elements in tensor
      */
     public val numElements: Int
-        get() = linearStructure.linearSize
+        get() = indices.linearSize
 
-    override fun get(index: IntArray): T = mutableBuffer[bufferStart + linearStructure.offset(index)]
+    override fun get(index: IntArray): T = mutableBuffer[bufferStart + indices.offset(index)]
 
     override fun set(index: IntArray, value: T) {
-        mutableBuffer[bufferStart + linearStructure.offset(index)] = value
+        mutableBuffer[bufferStart + indices.offset(index)] = value
     }
 
     @PerformancePitfall
-    override fun elements(): Sequence<Pair<IntArray, T>> = linearStructure.indices().map {
+    override fun elements(): Sequence<Pair<IntArray, T>> = indices.indices().map {
         it to get(it)
     }
 }

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

@@ -6,8 +6,10 @@
 package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.nd.MutableStructure2D
+import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.as1D
 import space.kscience.kmath.nd.as2D
+import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.indices
 import space.kscience.kmath.tensors.api.AnalyticTensorAlgebra
 import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
@@ -20,16 +22,71 @@ import kotlin.math.*
  * Implementation of basic operations over double tensors and basic algebra operations on them.
  */
 public open class DoubleTensorAlgebra :
-    TensorPartialDivisionAlgebra<Double>,
+    TensorPartialDivisionAlgebra<Double, DoubleField>,
-    AnalyticTensorAlgebra<Double>,
+    AnalyticTensorAlgebra<Double, DoubleField>,
-    LinearOpsTensorAlgebra<Double>{
+    LinearOpsTensorAlgebra<Double, DoubleField> {
 
     public companion object : DoubleTensorAlgebra()
 
-    override fun Tensor<Double>.valueOrNull(): Double? = if (tensor.shape contentEquals intArrayOf(1))
+    override val elementAlgebra: DoubleField
+        get() = DoubleField
+
+
+    /**
+     * Applies the [transform] function to each element of the tensor and returns the resulting modified tensor.
+     *
+     * @param transform the function to be applied to each element of the tensor.
+     * @return the resulting tensor after applying the function.
+     */
+    @Suppress("OVERRIDE_BY_INLINE")
+    final override inline fun StructureND<Double>.map(transform: DoubleField.(Double) -> Double): DoubleTensor {
+        val tensor = this.tensor
+        //TODO remove additional copy
+        val sourceArray = tensor.copyArray()
+        val array = DoubleArray(tensor.numElements) { DoubleField.transform(sourceArray[it]) }
+        return DoubleTensor(
+            tensor.shape,
+            array,
+            tensor.bufferStart
+        )
+    }
+
+    @Suppress("OVERRIDE_BY_INLINE")
+    final override inline fun StructureND<Double>.mapIndexed(transform: DoubleField.(index: IntArray, Double) -> Double): DoubleTensor {
+        val tensor = this.tensor
+        //TODO remove additional copy
+        val sourceArray = tensor.copyArray()
+        val array = DoubleArray(tensor.numElements) { DoubleField.transform(tensor.indices.index(it), sourceArray[it]) }
+        return DoubleTensor(
+            tensor.shape,
+            array,
+            tensor.bufferStart
+        )
+    }
+
+    override fun zip(
+        left: StructureND<Double>,
+        right: StructureND<Double>,
+        transform: DoubleField.(Double, Double) -> Double
+    ): DoubleTensor {
+        require(left.shape.contentEquals(right.shape)){
+            "The shapes in zip are not equal: left - ${left.shape}, right - ${right.shape}"
+        }
+        val leftTensor = left.tensor
+        val leftArray = leftTensor.copyArray()
+        val rightTensor = right.tensor
+        val rightArray = rightTensor.copyArray()
+        val array = DoubleArray(leftTensor.numElements) { DoubleField.transform(leftArray[it], rightArray[it]) }
+        return DoubleTensor(
+            leftTensor.shape,
+            array
+        )
+    }
+
+    override fun StructureND<Double>.valueOrNull(): Double? = if (tensor.shape contentEquals intArrayOf(1))
         tensor.mutableBuffer.array()[tensor.bufferStart] else null
 
-    override fun Tensor<Double>.value(): Double = valueOrNull()
+    override fun StructureND<Double>.value(): Double = valueOrNull()
         ?: throw IllegalArgumentException("The tensor shape is $shape, but value method is allowed only for shape [1]")
 
     /**
@@ -53,10 +110,9 @@ public open class DoubleTensorAlgebra :
      * @param initializer mapping tensor indices to values.
      * @return tensor with the [shape] shape and data generated by the [initializer].
      */
-    public fun produce(shape: IntArray, initializer: (IntArray) -> Double): DoubleTensor =
+    override fun structureND(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): DoubleTensor = fromArray(
-        fromArray(
         shape,
-            TensorLinearStructure(shape).indices().map(initializer).toMutableList().toDoubleArray()
+        TensorLinearStructure(shape).indices().map { DoubleField.initializer(it) }.toMutableList().toDoubleArray()
     )
 
     override operator fun Tensor<Double>.get(i: Int): DoubleTensor {
@@ -146,16 +202,16 @@ public open class DoubleTensorAlgebra :
         return DoubleTensor(tensor.shape, tensor.mutableBuffer.array().copyOf(), tensor.bufferStart)
     }
 
-    override fun Double.plus(other: Tensor<Double>): DoubleTensor {
+    override fun Double.plus(other: StructureND<Double>): DoubleTensor {
         val resBuffer = DoubleArray(other.tensor.numElements) { i ->
             other.tensor.mutableBuffer.array()[other.tensor.bufferStart + i] + this
         }
         return DoubleTensor(other.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.plus(value: Double): DoubleTensor = value + tensor
+    override fun StructureND<Double>.plus(value: Double): DoubleTensor = value + tensor
 
-    override fun Tensor<Double>.plus(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.plus(other: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, other.tensor)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
             tensor.mutableBuffer.array()[i] + other.tensor.mutableBuffer.array()[i]
@@ -169,7 +225,7 @@ public open class DoubleTensorAlgebra :
         }
     }
 
-    override fun Tensor<Double>.plusAssign(other: Tensor<Double>) {
+    override fun Tensor<Double>.plusAssign(other: StructureND<Double>) {
         checkShapesCompatible(tensor, other.tensor)
         for (i in 0 until tensor.numElements) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] +=
@@ -177,21 +233,21 @@ public open class DoubleTensorAlgebra :
         }
     }
 
-    override fun Double.minus(other: Tensor<Double>): DoubleTensor {
+    override fun Double.minus(other: StructureND<Double>): DoubleTensor {
         val resBuffer = DoubleArray(other.tensor.numElements) { i ->
             this - other.tensor.mutableBuffer.array()[other.tensor.bufferStart + i]
         }
         return DoubleTensor(other.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.minus(value: Double): DoubleTensor {
+    override fun StructureND<Double>.minus(arg: Double): DoubleTensor {
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] - value
+            tensor.mutableBuffer.array()[tensor.bufferStart + i] - arg
         }
         return DoubleTensor(tensor.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.minus(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.minus(other: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, other)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
             tensor.mutableBuffer.array()[i] - other.tensor.mutableBuffer.array()[i]
@@ -205,7 +261,7 @@ public open class DoubleTensorAlgebra :
         }
     }
 
-    override fun Tensor<Double>.minusAssign(other: Tensor<Double>) {
+    override fun Tensor<Double>.minusAssign(other: StructureND<Double>) {
         checkShapesCompatible(tensor, other)
         for (i in 0 until tensor.numElements) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] -=
@@ -213,16 +269,16 @@ public open class DoubleTensorAlgebra :
         }
     }
 
-    override fun Double.times(other: Tensor<Double>): DoubleTensor {
+    override fun Double.times(arg: StructureND<Double>): DoubleTensor {
-        val resBuffer = DoubleArray(other.tensor.numElements) { i ->
+        val resBuffer = DoubleArray(arg.tensor.numElements) { i ->
-            other.tensor.mutableBuffer.array()[other.tensor.bufferStart + i] * this
+            arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i] * this
         }
-        return DoubleTensor(other.shape, resBuffer)
+        return DoubleTensor(arg.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.times(value: Double): DoubleTensor = value * tensor
+    override fun StructureND<Double>.times(arg: Double): DoubleTensor = arg * tensor
 
-    override fun Tensor<Double>.times(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.times(other: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, other)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
             tensor.mutableBuffer.array()[tensor.bufferStart + i] *
@@ -237,7 +293,7 @@ public open class DoubleTensorAlgebra :
         }
     }
 
-    override fun Tensor<Double>.timesAssign(other: Tensor<Double>) {
+    override fun Tensor<Double>.timesAssign(other: StructureND<Double>) {
         checkShapesCompatible(tensor, other)
         for (i in 0 until tensor.numElements) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] *=
@@ -245,21 +301,21 @@ public open class DoubleTensorAlgebra :
         }
     }
 
-    override fun Double.div(other: Tensor<Double>): DoubleTensor {
+    override fun Double.div(arg: StructureND<Double>): DoubleTensor {
-        val resBuffer = DoubleArray(other.tensor.numElements) { i ->
+        val resBuffer = DoubleArray(arg.tensor.numElements) { i ->
-            this / other.tensor.mutableBuffer.array()[other.tensor.bufferStart + i]
+            this / arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i]
         }
-        return DoubleTensor(other.shape, resBuffer)
+        return DoubleTensor(arg.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.div(value: Double): DoubleTensor {
+    override fun StructureND<Double>.div(arg: Double): DoubleTensor {
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] / value
+            tensor.mutableBuffer.array()[tensor.bufferStart + i] / arg
         }
         return DoubleTensor(shape, resBuffer)
     }
 
-    override fun Tensor<Double>.div(other: Tensor<Double>): DoubleTensor {
+    override fun StructureND<Double>.div(other: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, other)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
             tensor.mutableBuffer.array()[other.tensor.bufferStart + i] /
@@ -282,7 +338,7 @@ public open class DoubleTensorAlgebra :
         }
     }
 
-    override fun Tensor<Double>.unaryMinus(): DoubleTensor {
+    override fun StructureND<Double>.unaryMinus(): DoubleTensor {
         val resBuffer = DoubleArray(tensor.numElements) { i ->
             tensor.mutableBuffer.array()[tensor.bufferStart + i].unaryMinus()
         }
@@ -302,11 +358,11 @@ public open class DoubleTensorAlgebra :
         val resTensor = DoubleTensor(resShape, resBuffer)
 
         for (offset in 0 until n) {
-            val oldMultiIndex = tensor.linearStructure.index(offset)
+            val oldMultiIndex = tensor.indices.index(offset)
             val newMultiIndex = oldMultiIndex.copyOf()
             newMultiIndex[ii] = newMultiIndex[jj].also { newMultiIndex[jj] = newMultiIndex[ii] }
 
-            val linearIndex = resTensor.linearStructure.offset(newMultiIndex)
+            val linearIndex = resTensor.indices.offset(newMultiIndex)
             resTensor.mutableBuffer.array()[linearIndex] =
                 tensor.mutableBuffer.array()[tensor.bufferStart + offset]
         }
@@ -406,7 +462,7 @@ public open class DoubleTensorAlgebra :
         val resTensor = zeros(resShape)
 
         for (i in 0 until diagonalEntries.tensor.numElements) {
-            val multiIndex = diagonalEntries.tensor.linearStructure.index(i)
+            val multiIndex = diagonalEntries.tensor.indices.index(i)
 
             var offset1 = 0
             var offset2 = abs(realOffset)
@@ -425,18 +481,6 @@ public open class DoubleTensorAlgebra :
         return resTensor.tensor
     }
 
-    /**
-     * Applies the [transform] function to each element of the tensor and returns the resulting modified tensor.
-     *
-     * @param transform the function to be applied to each element of the tensor.
-     * @return the resulting tensor after applying the function.
-     */
-    public inline fun Tensor<Double>.map(transform: (Double) -> Double): DoubleTensor = DoubleTensor(
-        tensor.shape,
-        tensor.mutableBuffer.array().map { transform(it) }.toDoubleArray(),
-        tensor.bufferStart
-    )
-
     /**
      * Compares element-wise two tensors with a specified precision.
      *
@@ -526,7 +570,7 @@ public open class DoubleTensorAlgebra :
     public fun Tensor<Double>.rowsByIndices(indices: IntArray): DoubleTensor = stack(indices.map { this[it] })
 
     internal inline fun Tensor<Double>.fold(foldFunction: (DoubleArray) -> Double): Double =
-        foldFunction(tensor.toDoubleArray())
+        foldFunction(tensor.copyArray())
 
     internal inline fun Tensor<Double>.foldDim(
         foldFunction: (DoubleArray) -> Double,
@@ -541,7 +585,7 @@ public open class DoubleTensorAlgebra :
         }
         val resNumElements = resShape.reduce(Int::times)
         val resTensor = DoubleTensor(resShape, DoubleArray(resNumElements) { 0.0 }, 0)
-        for (index in resTensor.linearStructure.indices()) {
+        for (index in resTensor.indices.indices()) {
             val prefix = index.take(dim).toIntArray()
             val suffix = index.takeLast(dimension - dim - 1).toIntArray()
             resTensor[index] = foldFunction(DoubleArray(shape[dim]) { i ->
@@ -645,39 +689,39 @@ public open class DoubleTensorAlgebra :
         return resTensor
     }
 
-    override fun Tensor<Double>.exp(): DoubleTensor = tensor.map(::exp)
+    override fun Tensor<Double>.exp(): DoubleTensor = tensor.map { exp(it) }
 
-    override fun Tensor<Double>.ln(): DoubleTensor = tensor.map(::ln)
+    override fun Tensor<Double>.ln(): DoubleTensor = tensor.map { ln(it) }
 
-    override fun Tensor<Double>.sqrt(): DoubleTensor = tensor.map(::sqrt)
+    override fun Tensor<Double>.sqrt(): DoubleTensor = tensor.map { sqrt(it) }
 
-    override fun Tensor<Double>.cos(): DoubleTensor = tensor.map(::cos)
+    override fun Tensor<Double>.cos(): DoubleTensor = tensor.map { cos(it) }
 
-    override fun Tensor<Double>.acos(): DoubleTensor = tensor.map(::acos)
+    override fun Tensor<Double>.acos(): DoubleTensor = tensor.map { acos(it) }
 
-    override fun Tensor<Double>.cosh(): DoubleTensor = tensor.map(::cosh)
+    override fun Tensor<Double>.cosh(): DoubleTensor = tensor.map { cosh(it) }
 
-    override fun Tensor<Double>.acosh(): DoubleTensor = tensor.map(::acosh)
+    override fun Tensor<Double>.acosh(): DoubleTensor = tensor.map { acosh(it) }
 
-    override fun Tensor<Double>.sin(): DoubleTensor = tensor.map(::sin)
+    override fun Tensor<Double>.sin(): DoubleTensor = tensor.map { sin(it) }
 
-    override fun Tensor<Double>.asin(): DoubleTensor = tensor.map(::asin)
+    override fun Tensor<Double>.asin(): DoubleTensor = tensor.map { asin(it) }
 
-    override fun Tensor<Double>.sinh(): DoubleTensor = tensor.map(::sinh)
+    override fun Tensor<Double>.sinh(): DoubleTensor = tensor.map { sinh(it) }
 
-    override fun Tensor<Double>.asinh(): DoubleTensor = tensor.map(::asinh)
+    override fun Tensor<Double>.asinh(): DoubleTensor = tensor.map { asinh(it) }
 
-    override fun Tensor<Double>.tan(): DoubleTensor = tensor.map(::tan)
+    override fun Tensor<Double>.tan(): DoubleTensor = tensor.map { tan(it) }
 
-    override fun Tensor<Double>.atan(): DoubleTensor = tensor.map(::atan)
+    override fun Tensor<Double>.atan(): DoubleTensor = tensor.map { atan(it) }
 
-    override fun Tensor<Double>.tanh(): DoubleTensor = tensor.map(::tanh)
+    override fun Tensor<Double>.tanh(): DoubleTensor = tensor.map { tanh(it) }
 
-    override fun Tensor<Double>.atanh(): DoubleTensor = tensor.map(::atanh)
+    override fun Tensor<Double>.atanh(): DoubleTensor = tensor.map { atanh(it) }
 
-    override fun Tensor<Double>.ceil(): DoubleTensor = tensor.map(::ceil)
+    override fun Tensor<Double>.ceil(): DoubleTensor = tensor.map { ceil(it) }
 
-    override fun Tensor<Double>.floor(): DoubleTensor = tensor.map(::floor)
+    override fun Tensor<Double>.floor(): DoubleTensor = tensor.map { floor(it) }
 
     override fun Tensor<Double>.inv(): DoubleTensor = invLU(1e-9)
 

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

@@ -10,7 +10,7 @@ import kotlin.math.max
 
 internal fun multiIndexBroadCasting(tensor: DoubleTensor, resTensor: DoubleTensor, linearSize: Int) {
     for (linearIndex in 0 until linearSize) {
-        val totalMultiIndex = resTensor.linearStructure.index(linearIndex)
+        val totalMultiIndex = resTensor.indices.index(linearIndex)
         val curMultiIndex = tensor.shape.copyOf()
 
         val offset = totalMultiIndex.size - curMultiIndex.size
@@ -23,7 +23,7 @@ internal fun multiIndexBroadCasting(tensor: DoubleTensor, resTensor: DoubleTenso
             }
         }
 
-        val curLinearIndex = tensor.linearStructure.offset(curMultiIndex)
+        val curLinearIndex = tensor.indices.offset(curMultiIndex)
         resTensor.mutableBuffer.array()[linearIndex] =
             tensor.mutableBuffer.array()[tensor.bufferStart + curLinearIndex]
     }
@@ -112,7 +112,7 @@ internal fun broadcastOuterTensors(vararg tensors: DoubleTensor): List<DoubleTen
             val resTensor = DoubleTensor(totalShape + matrixShape, DoubleArray(n * matrixSize))
 
             for (linearIndex in 0 until n) {
-                val totalMultiIndex = outerTensor.linearStructure.index(linearIndex)
+                val totalMultiIndex = outerTensor.indices.index(linearIndex)
                 var curMultiIndex = tensor.shape.sliceArray(0..tensor.shape.size - 3).copyOf()
                 curMultiIndex = IntArray(totalMultiIndex.size - curMultiIndex.size) { 1 } + curMultiIndex
 
@@ -127,13 +127,13 @@ internal fun broadcastOuterTensors(vararg tensors: DoubleTensor): List<DoubleTen
                 }
 
                 for (i in 0 until matrixSize) {
-                    val curLinearIndex = newTensor.linearStructure.offset(
+                    val curLinearIndex = newTensor.indices.offset(
                         curMultiIndex +
-                                matrix.linearStructure.index(i)
+                                matrix.indices.index(i)
                     )
-                    val newLinearIndex = resTensor.linearStructure.offset(
+                    val newLinearIndex = resTensor.indices.offset(
                         totalMultiIndex +
-                                matrix.linearStructure.index(i)
+                                matrix.indices.index(i)
                     )
 
                     resTensor.mutableBuffer.array()[resTensor.bufferStart + newLinearIndex] =

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

@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.tensors.core.internal
 
+import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.tensors.api.Tensor
 import space.kscience.kmath.tensors.core.DoubleTensor
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
@@ -25,7 +26,7 @@ internal fun checkBufferShapeConsistency(shape: IntArray, buffer: DoubleArray) =
         "Inconsistent shape ${shape.toList()} for buffer of size ${buffer.size} provided"
     }
 
-internal fun <T> checkShapesCompatible(a: Tensor<T>, b: Tensor<T>) =
+internal fun <T> checkShapesCompatible(a: StructureND<T>, b: StructureND<T>) =
     check(a.shape contentEquals b.shape) {
         "Incompatible shapes ${a.shape.toList()} and ${b.shape.toList()} "
     }

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

@@ -6,6 +6,7 @@
 package space.kscience.kmath.tensors.core.internal
 
 import space.kscience.kmath.nd.MutableBufferND
+import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.structures.asMutableBuffer
 import space.kscience.kmath.tensors.api.Tensor
 import space.kscience.kmath.tensors.core.BufferedTensor
@@ -18,15 +19,15 @@ internal fun BufferedTensor<Int>.asTensor(): IntTensor =
 internal fun BufferedTensor<Double>.asTensor(): DoubleTensor =
     DoubleTensor(this.shape, this.mutableBuffer.array(), this.bufferStart)
 
-internal fun <T> Tensor<T>.copyToBufferedTensor(): BufferedTensor<T> =
+internal fun <T> StructureND<T>.copyToBufferedTensor(): BufferedTensor<T> =
     BufferedTensor(
         this.shape,
         TensorLinearStructure(this.shape).indices().map(this::get).toMutableList().asMutableBuffer(), 0
     )
 
-internal fun <T> Tensor<T>.toBufferedTensor(): BufferedTensor<T> = when (this) {
+internal fun <T> StructureND<T>.toBufferedTensor(): BufferedTensor<T> = when (this) {
     is BufferedTensor<T> -> this
-    is MutableBufferND<T> -> if (this.indexes == TensorLinearStructure(this.shape)) {
+    is MutableBufferND<T> -> if (this.indices == TensorLinearStructure(this.shape)) {
         BufferedTensor(this.shape, this.buffer, 0)
     } else {
         this.copyToBufferedTensor()
@@ -35,7 +36,7 @@ internal fun <T> Tensor<T>.toBufferedTensor(): BufferedTensor<T> = when (this) {
 }
 
 @PublishedApi
-internal val Tensor<Double>.tensor: DoubleTensor
+internal val StructureND<Double>.tensor: DoubleTensor
     get() = when (this) {
         is DoubleTensor -> this
         else -> this.toBufferedTensor().asTensor()

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

@@ -85,7 +85,7 @@ internal fun format(value: Double, digits: Int = 4): String = buildString {
 internal fun DoubleTensor.toPrettyString(): String = buildString {
     var offset = 0
     val shape = this@toPrettyString.shape
-    val linearStructure = this@toPrettyString.linearStructure
+    val linearStructure = this@toPrettyString.indices
     val vectorSize = shape.last()
     append("DoubleTensor(\n")
     var charOffset = 3

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

@@ -19,18 +19,19 @@ public fun Tensor<Double>.toDoubleTensor(): DoubleTensor = this.tensor
 public fun Tensor<Int>.toIntTensor(): IntTensor = this.tensor
 
 /**
- * Returns [DoubleArray] of tensor elements
+ * Returns a copy-protected [DoubleArray] of tensor elements
  */
-public fun DoubleTensor.toDoubleArray(): DoubleArray {
+public fun DoubleTensor.copyArray(): DoubleArray {
+    //TODO use ArrayCopy
     return DoubleArray(numElements) { i ->
         mutableBuffer[bufferStart + i]
     }
 }
 
 /**
- * Returns [IntArray] of tensor elements
+ * Returns a copy-protected [IntArray] of tensor elements
  */
-public fun IntTensor.toIntArray(): IntArray {
+public fun IntTensor.copyArray(): IntArray {
     return IntArray(numElements) { i ->
         mutableBuffer[bufferStart + i]
     }