Tensor algebra generified

CHANGELOG.md

@@ -45,6 +45,7 @@
 - Buffer algebra does not require size anymore
 - Operations -> Ops
 - Default Buffer and ND algebras are now Ops and lack neutral elements (0, 1) as well as algebra-level shapes.
+- Tensor algebra takes read-only structures as input and inherits AlgebraND
 
 ### Deprecated
 - Specialized `DoubleBufferAlgebra`

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

@@ -13,8 +13,7 @@ import org.jetbrains.kotlinx.multik.api.Multik
 import org.jetbrains.kotlinx.multik.api.ones
 import org.jetbrains.kotlinx.multik.ndarray.data.DN
 import org.jetbrains.kotlinx.multik.ndarray.data.DataType
-import space.kscience.kmath.multik.multikND
+import space.kscience.kmath.multik.multikAlgebra
-import space.kscience.kmath.multik.multikTensorAlgebra
 import space.kscience.kmath.nd.BufferedFieldOpsND
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.ndAlgebra
@@ -79,7 +78,7 @@ internal class NDFieldBenchmark {
     }
 
     @Benchmark
-    fun multikInPlaceAdd(blackhole: Blackhole) = with(DoubleField.multikTensorAlgebra) {
+    fun multikInPlaceAdd(blackhole: Blackhole) = with(DoubleField.multikAlgebra) {
         val res = Multik.ones<Double, DN>(shape, DataType.DoubleDataType).wrap()
         repeat(n) { res += 1.0 }
         blackhole.consume(res)
@@ -100,7 +99,7 @@ internal class NDFieldBenchmark {
         private val specializedField = DoubleField.ndAlgebra
         private val genericField = BufferedFieldOpsND(DoubleField, Buffer.Companion::boxing)
         private val nd4jField = DoubleField.nd4j
-        private val multikField = DoubleField.multikND
+        private val multikField = DoubleField.multikAlgebra
         private val viktorField = DoubleField.viktorAlgebra
     }
 }

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

@@ -7,12 +7,12 @@ package space.kscience.kmath.tensors
 
 import org.jetbrains.kotlinx.multik.api.Multik
 import org.jetbrains.kotlinx.multik.api.ndarray
-import space.kscience.kmath.multik.multikND
+import space.kscience.kmath.multik.multikAlgebra
 import space.kscience.kmath.nd.one
 import space.kscience.kmath.operations.DoubleField
 
-fun main(): Unit = with(DoubleField.multikND) {
+fun main(): Unit = with(DoubleField.multikAlgebra) {
     val a = Multik.ndarray(intArrayOf(1, 2, 3)).asType<Double>().wrap()
     val b = Multik.ndarray(doubleArrayOf(1.0, 2.0, 3.0)).wrap()
-    one(a.shape) - a + b * 3
+    one(a.shape) - a + b * 3.0
 }

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

@@ -1,137 +0,0 @@
-package space.kscience.kmath.multik
-
-import org.jetbrains.kotlinx.multik.api.math.cos
-import org.jetbrains.kotlinx.multik.api.math.sin
-import org.jetbrains.kotlinx.multik.api.mk
-import org.jetbrains.kotlinx.multik.api.zeros
-import org.jetbrains.kotlinx.multik.ndarray.data.*
-import org.jetbrains.kotlinx.multik.ndarray.operations.*
-import space.kscience.kmath.nd.FieldOpsND
-import space.kscience.kmath.nd.RingOpsND
-import space.kscience.kmath.nd.Shape
-import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.operations.*
-
-/**
- * A ring algebra for Multik operations
- */
-public open class MultikRingOpsND<T, A : Ring<T>> internal constructor(
-    public val type: DataType,
-    override val elementAlgebra: A
-) : RingOpsND<T, A> {
-
-    public fun MutableMultiArray<T, *>.wrap(): MultikTensor<T> = MultikTensor(this.asDNArray())
-
-    override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
-        val res = mk.zeros<T, DN>(shape, type).asDNArray()
-        for (index in res.multiIndices) {
-            res[index] = elementAlgebra.initializer(index)
-        }
-        return res.wrap()
-    }
-
-    public fun StructureND<T>.asMultik(): MultikTensor<T> = if (this is MultikTensor) {
-        this
-    } else {
-        structureND(shape) { get(it) }
-    }
-
-    override fun StructureND<T>.map(transform: A.(T) -> T): MultikTensor<T> {
-        //taken directly from Multik sources
-        val array = asMultik().array
-        val data = initMemoryView<T>(array.size, type)
-        var count = 0
-        for (el in array) data[count++] = elementAlgebra.transform(el)
-        return NDArray(data, shape = array.shape, dim = array.dim).wrap()
-    }
-
-    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): MultikTensor<T> {
-        //taken directly from Multik sources
-        val array = asMultik().array
-        val data = initMemoryView<T>(array.size, type)
-        val indexIter = array.multiIndices.iterator()
-        var index = 0
-        for (item in array) {
-            if (indexIter.hasNext()) {
-                data[index++] = elementAlgebra.transform(indexIter.next(), item)
-            } else {
-                throw ArithmeticException("Index overflow has happened.")
-            }
-        }
-        return NDArray(data, shape = array.shape, dim = array.dim).wrap()
-    }
-
-    override fun zip(left: StructureND<T>, right: StructureND<T>, transform: A.(T, T) -> T): MultikTensor<T> {
-        require(left.shape.contentEquals(right.shape)) { "ND array shape mismatch" } //TODO replace by ShapeMismatchException
-        val leftArray = left.asMultik().array
-        val rightArray = right.asMultik().array
-        val data = initMemoryView<T>(leftArray.size, type)
-        var counter = 0
-        val leftIterator = leftArray.iterator()
-        val rightIterator = rightArray.iterator()
-        //iterating them together
-        while (leftIterator.hasNext()) {
-            data[counter++] = elementAlgebra.transform(leftIterator.next(), rightIterator.next())
-        }
-        return NDArray(data, shape = leftArray.shape, dim = leftArray.dim).wrap()
-    }
-
-    override fun StructureND<T>.unaryMinus(): MultikTensor<T> = asMultik().array.unaryMinus().wrap()
-
-    override fun add(left: StructureND<T>, right: StructureND<T>): MultikTensor<T> =
-        (left.asMultik().array + right.asMultik().array).wrap()
-
-    override fun StructureND<T>.plus(arg: T): MultikTensor<T> =
-        asMultik().array.plus(arg).wrap()
-
-    override fun StructureND<T>.minus(arg: T): MultikTensor<T> = asMultik().array.minus(arg).wrap()
-
-    override fun T.plus(arg: StructureND<T>): MultikTensor<T> = arg + this
-
-    override fun T.minus(arg: StructureND<T>): MultikTensor<T> = arg.map { this@minus - it }
-
-    override fun multiply(left: StructureND<T>, right: StructureND<T>): MultikTensor<T> =
-        left.asMultik().array.times(right.asMultik().array).wrap()
-
-    override fun StructureND<T>.times(arg: T): MultikTensor<T> =
-        asMultik().array.times(arg).wrap()
-
-    override fun T.times(arg: StructureND<T>): MultikTensor<T> = arg * this
-
-    override fun StructureND<T>.unaryPlus(): MultikTensor<T> = asMultik()
-
-    override fun StructureND<T>.plus(other: StructureND<T>): MultikTensor<T> =
-        asMultik().array.plus(other.asMultik().array).wrap()
-
-    override fun StructureND<T>.minus(other: StructureND<T>): MultikTensor<T> =
-        asMultik().array.minus(other.asMultik().array).wrap()
-
-    override fun StructureND<T>.times(other: StructureND<T>): MultikTensor<T> =
-        asMultik().array.times(other.asMultik().array).wrap()
-}
-
-/**
- * A field algebra for multik operations
- */
-public class MultikFieldOpsND<T, A : Field<T>> internal constructor(
-    type: DataType,
-    elementAlgebra: A
-) : MultikRingOpsND<T, A>(type, elementAlgebra), FieldOpsND<T, A> {
-    override fun StructureND<T>.div(other: StructureND<T>): StructureND<T> =
-        asMultik().array.div(other.asMultik().array).wrap()
-}
-
-public val DoubleField.multikND: MultikFieldOpsND<Double, DoubleField>
-    get() = MultikFieldOpsND(DataType.DoubleDataType, DoubleField)
-
-public val FloatField.multikND: MultikFieldOpsND<Float, FloatField>
-    get() = MultikFieldOpsND(DataType.FloatDataType, FloatField)
-
-public val ShortRing.multikND: MultikRingOpsND<Short, ShortRing>
-    get() = MultikRingOpsND(DataType.ShortDataType, ShortRing)
-
-public val IntRing.multikND: MultikRingOpsND<Int, IntRing>
-    get() = MultikRingOpsND(DataType.IntDataType, IntRing)
-
-public val LongRing.multikND: MultikRingOpsND<Long, LongRing>
-    get() = MultikRingOpsND(DataType.LongDataType, LongRing)

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

@@ -15,12 +15,14 @@ import org.jetbrains.kotlinx.multik.api.zeros
 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.DefaultStrides
 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
 import space.kscience.kmath.tensors.api.TensorAlgebra
+import space.kscience.kmath.tensors.api.TensorPartialDivisionAlgebra
 
 @JvmInline
 public value class MultikTensor<T>(public val array: MutableMultiArray<T, DN>) : Tensor<T> {
@@ -50,18 +52,70 @@ private fun <T, D : Dimension> MultiArray<T, D>.asD2Array(): D2Array<T> {
     else throw ClassCastException("Cannot cast MultiArray to NDArray.")
 }
 
-public class MultikTensorAlgebra<T : Number, A: Ring<T>> internal constructor(
+public abstract class MultikTensorAlgebra<T, A : Ring<T>> : TensorAlgebra<T, A> where T : Number, T : Comparable<T> {
-    public val type: DataType,
+
-    override val elementAlgebra: A,
+    public abstract val type: DataType
-    public val comparator: Comparator<T>
+
-) : TensorAlgebra<T, A> {
+    override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
+        val strides = DefaultStrides(shape)
+        val memoryView = initMemoryView<T>(strides.linearSize, type)
+        strides.indices().forEachIndexed { linearIndex, tensorIndex ->
+            memoryView[linearIndex] = elementAlgebra.initializer(tensorIndex)
+        }
+        return MultikTensor(NDArray(memoryView, shape = shape, dim = DN(shape.size)))
+    }
+
+    override fun StructureND<T>.map(transform: A.(T) -> T): MultikTensor<T> = if (this is MultikTensor) {
+        val data = initMemoryView<T>(array.size, type)
+        var count = 0
+        for (el in array) data[count++] = elementAlgebra.transform(el)
+        NDArray(data, shape = shape, dim = array.dim).wrap()
+    } else {
+        structureND(shape) { index ->
+            transform(get(index))
+        }
+    }
+
+    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): MultikTensor<T> =
+        if (this is MultikTensor) {
+            val array = asMultik().array
+            val data = initMemoryView<T>(array.size, type)
+            val indexIter = array.multiIndices.iterator()
+            var index = 0
+            for (item in array) {
+                if (indexIter.hasNext()) {
+                    data[index++] = elementAlgebra.transform(indexIter.next(), item)
+                } else {
+                    throw ArithmeticException("Index overflow has happened.")
+                }
+            }
+            NDArray(data, shape = array.shape, dim = array.dim).wrap()
+        } else {
+            structureND(shape) { index ->
+                transform(index, get(index))
+            }
+        }
+
+    override fun zip(left: StructureND<T>, right: StructureND<T>, transform: A.(T, T) -> T): MultikTensor<T> {
+        require(left.shape.contentEquals(right.shape)) { "ND array shape mismatch" } //TODO replace by ShapeMismatchException
+        val leftArray = left.asMultik().array
+        val rightArray = right.asMultik().array
+        val data = initMemoryView<T>(leftArray.size, type)
+        var counter = 0
+        val leftIterator = leftArray.iterator()
+        val rightIterator = rightArray.iterator()
+        //iterating them together
+        while (leftIterator.hasNext()) {
+            data[counter++] = elementAlgebra.transform(leftIterator.next(), rightIterator.next())
+        }
+        return NDArray(data, shape = leftArray.shape, dim = leftArray.dim).wrap()
+    }
 
     /**
      * 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 StructureND<T>.asMultik(): MultikTensor<T> {
+    public fun StructureND<T>.asMultik(): MultikTensor<T> = if (this is MultikTensor) {
-        return if (this is MultikTensor) {
         this
     } else {
         val res = mk.zeros<T, DN>(shape, type).asDNArray()
@@ -70,9 +124,8 @@ public class MultikTensorAlgebra<T : Number, A: Ring<T>> internal constructor(
         }
         res.wrap()
     }
-    }
 
-    public fun MutableMultiArray<T, DN>.wrap(): MultikTensor<T> = MultikTensor(this)
+    public fun MutableMultiArray<T, *>.wrap(): MultikTensor<T> = MultikTensor(this.asDNArray())
 
     override fun StructureND<T>.valueOrNull(): T? = if (shape contentEquals intArrayOf(1)) {
         get(intArrayOf(0))
@@ -81,8 +134,8 @@ public class MultikTensorAlgebra<T : Number, A: Ring<T>> internal constructor(
     override fun T.plus(other: StructureND<T>): MultikTensor<T> =
         other.plus(this)
 
-    override fun StructureND<T>.plus(value: T): MultikTensor<T> =
+    override fun StructureND<T>.plus(arg: T): MultikTensor<T> =
-        asMultik().array.deepCopy().apply { plusAssign(value) }.wrap()
+        asMultik().array.deepCopy().apply { plusAssign(arg) }.wrap()
 
     override fun StructureND<T>.plus(other: StructureND<T>): MultikTensor<T> =
         asMultik().array.plus(other.asMultik().array).wrap()
@@ -155,11 +208,11 @@ public class MultikTensorAlgebra<T : Number, A: Ring<T>> internal constructor(
     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()
+    override fun StructureND<T>.get(i: Int): MultikTensor<T> = asMultik().array.mutableView(i).wrap()
 
-    override fun Tensor<T>.transpose(i: Int, j: Int): MultikTensor<T> = asMultik().array.transpose(i, j).wrap()
+    override fun StructureND<T>.transpose(i: Int, j: Int): MultikTensor<T> = asMultik().array.transpose(i, j).wrap()
 
-    override fun Tensor<T>.view(shape: IntArray): MultikTensor<T> {
+    override fun StructureND<T>.view(shape: IntArray): MultikTensor<T> {
         require(shape.all { it > 0 })
         require(shape.fold(1, Int::times) == this.shape.size) {
             "Cannot reshape array of size ${this.shape.size} into a new shape ${
@@ -178,9 +231,9 @@ public class MultikTensorAlgebra<T : Number, A: Ring<T>> internal constructor(
         }.wrap()
     }
 
-    override fun Tensor<T>.viewAs(other: Tensor<T>): MultikTensor<T> = view(other.shape)
+    override fun StructureND<T>.viewAs(other: StructureND<T>): MultikTensor<T> = view(other.shape)
 
-    override fun Tensor<T>.dot(other: Tensor<T>): MultikTensor<T> =
+    override fun StructureND<T>.dot(other: StructureND<T>): MultikTensor<T> =
         if (this.shape.size == 1 && other.shape.size == 1) {
             Multik.ndarrayOf(
                 asMultik().array.asD1Array() dot other.asMultik().array.asD1Array()
@@ -197,45 +250,95 @@ public class MultikTensorAlgebra<T : Number, A: Ring<T>> internal constructor(
         TODO("Diagonal embedding not implemented")
     }
 
-    override fun Tensor<T>.sum(): T = asMultik().array.reduceMultiIndexed { _: IntArray, acc: T, t: T ->
+    override fun StructureND<T>.sum(): T = asMultik().array.reduceMultiIndexed { _: IntArray, acc: T, t: T ->
         elementAlgebra.add(acc, t)
     }
 
-    override fun Tensor<T>.sum(dim: Int, keepDim: Boolean): MultikTensor<T> {
+    override fun StructureND<T>.sum(dim: Int, keepDim: Boolean): MultikTensor<T> {
         TODO("Not yet implemented")
     }
 
-    override fun Tensor<T>.min(): T =
+    override fun StructureND<T>.min(): T? = asMultik().array.min()
-        asMultik().array.minWith(comparator) ?: error("No elements in tensor")
 
-    override fun Tensor<T>.min(dim: Int, keepDim: Boolean): MultikTensor<T> {
+    override fun StructureND<T>.min(dim: Int, keepDim: Boolean): Tensor<T> {
         TODO("Not yet implemented")
     }
 
-    override fun Tensor<T>.max(): T =
+    override fun StructureND<T>.max(): T? = asMultik().array.max()
-        asMultik().array.maxWith(comparator) ?: error("No elements in tensor")
 
-
+    override fun StructureND<T>.max(dim: Int, keepDim: Boolean): Tensor<T> {
-    override fun Tensor<T>.max(dim: Int, keepDim: Boolean): MultikTensor<T> {
         TODO("Not yet implemented")
     }
 
-    override fun Tensor<T>.argMax(dim: Int, keepDim: Boolean): MultikTensor<T> {
+    override fun StructureND<T>.argMax(dim: Int, keepDim: Boolean): Tensor<T> {
         TODO("Not yet implemented")
     }
 }
 
-public val DoubleField.multikTensorAlgebra: MultikTensorAlgebra<Double, DoubleField>
+public abstract class MultikDivisionTensorAlgebra<T, A : Field<T>>
-    get() = MultikTensorAlgebra(DataType.DoubleDataType, DoubleField) { o1, o2 -> o1.compareTo(o2) }
+    : MultikTensorAlgebra<T, A>(), TensorPartialDivisionAlgebra<T, A> where T : Number, T : Comparable<T> {
 
-public val FloatField.multikTensorAlgebra: MultikTensorAlgebra<Float, FloatField>
+    override fun T.div(arg: StructureND<T>): MultikTensor<T> = arg.map { elementAlgebra.divide(this@div, it) }
-    get() = MultikTensorAlgebra(DataType.FloatDataType, FloatField) { o1, o2 -> o1.compareTo(o2) }
 
-public val ShortRing.multikTensorAlgebra: MultikTensorAlgebra<Short, ShortRing>
+    override fun StructureND<T>.div(arg: T): MultikTensor<T> =
-    get() = MultikTensorAlgebra(DataType.ShortDataType, ShortRing) { o1, o2 -> o1.compareTo(o2) }
+        asMultik().array.deepCopy().apply { divAssign(arg) }.wrap()
 
-public val IntRing.multikTensorAlgebra: MultikTensorAlgebra<Int, IntRing>
+    override fun StructureND<T>.div(other: StructureND<T>): MultikTensor<T> =
-    get() = MultikTensorAlgebra(DataType.IntDataType, IntRing) { o1, o2 -> o1.compareTo(o2) }
+        asMultik().array.div(other.asMultik().array).wrap()
 
-public val LongRing.multikTensorAlgebra: MultikTensorAlgebra<Long, LongRing>
+    override fun Tensor<T>.divAssign(value: T) {
-    get() = MultikTensorAlgebra(DataType.LongDataType, LongRing) { o1, o2 -> o1.compareTo(o2) }
+        if (this is MultikTensor) {
+            array.divAssign(value)
+        } else {
+            mapInPlace { _, t -> elementAlgebra.divide(t, value) }
+        }
+    }
+
+    override fun Tensor<T>.divAssign(other: StructureND<T>) {
+        if (this is MultikTensor) {
+            array.divAssign(other.asMultik().array)
+        } else {
+            mapInPlace { index, t -> elementAlgebra.divide(t, other[index]) }
+        }
+    }
+}
+
+public object MultikDoubleAlgebra : MultikDivisionTensorAlgebra<Double, DoubleField>() {
+    override val elementAlgebra: DoubleField get() = DoubleField
+    override val type: DataType get() = DataType.DoubleDataType
+}
+
+public val Double.Companion.multikAlgebra: MultikTensorAlgebra<Double, DoubleField> get() = MultikDoubleAlgebra
+public val DoubleField.multikAlgebra: MultikTensorAlgebra<Double, DoubleField> get() = MultikDoubleAlgebra
+
+public object MultikFloatAlgebra : MultikDivisionTensorAlgebra<Float, FloatField>() {
+    override val elementAlgebra: FloatField get() = FloatField
+    override val type: DataType get() = DataType.FloatDataType
+}
+
+public val Float.Companion.multikAlgebra: MultikTensorAlgebra<Float, FloatField> get() = MultikFloatAlgebra
+public val FloatField.multikAlgebra: MultikTensorAlgebra<Float, FloatField> get() = MultikFloatAlgebra
+
+public object MultikShortAlgebra : MultikTensorAlgebra<Short, ShortRing>() {
+    override val elementAlgebra: ShortRing get() = ShortRing
+    override val type: DataType get() = DataType.ShortDataType
+}
+
+public val Short.Companion.multikAlgebra: MultikTensorAlgebra<Short, ShortRing> get() = MultikShortAlgebra
+public val ShortRing.multikAlgebra: MultikTensorAlgebra<Short, ShortRing> get() = MultikShortAlgebra
+
+public object MultikIntAlgebra : MultikTensorAlgebra<Int, IntRing>() {
+    override val elementAlgebra: IntRing get() = IntRing
+    override val type: DataType get() = DataType.IntDataType
+}
+
+public val Int.Companion.multikAlgebra: MultikTensorAlgebra<Int, IntRing> get() = MultikIntAlgebra
+public val IntRing.multikAlgebra: MultikTensorAlgebra<Int, IntRing> get() = MultikIntAlgebra
+
+public object MultikLongAlgebra : MultikTensorAlgebra<Long, LongRing>() {
+    override val elementAlgebra: LongRing get() = LongRing
+    override val type: DataType get() = DataType.LongDataType
+}
+
+public val Long.Companion.multikAlgebra: MultikTensorAlgebra<Long, LongRing> get() = MultikLongAlgebra
+public val LongRing.multikAlgebra: MultikTensorAlgebra<Long, LongRing> get() = MultikLongAlgebra

kmath-multik/src/test/kotlin/space/kscience/kmath/multik/MultikNDTest.kt

@@ -7,7 +7,7 @@ import space.kscience.kmath.operations.invoke
 
 internal class MultikNDTest {
     @Test
-    fun basicAlgebra(): Unit = DoubleField.multikND{
+    fun basicAlgebra(): Unit = DoubleField.multikAlgebra{
         one(2,2) + 1.0
     }
 }

kmath-nd4j/src/main/kotlin/space/kscience/kmath/nd4j/Nd4jTensorAlgebra.kt

@@ -13,6 +13,7 @@ import org.nd4j.linalg.factory.Nd4j
 import org.nd4j.linalg.factory.ops.NDBase
 import org.nd4j.linalg.ops.transforms.Transforms
 import space.kscience.kmath.misc.PerformancePitfall
+import space.kscience.kmath.nd.DefaultStrides
 import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.DoubleField
@@ -27,22 +28,6 @@ import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
  */
 public sealed interface Nd4jTensorAlgebra<T : Number, A : Field<T>> : AnalyticTensorAlgebra<T, A> {
 
-    override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): Nd4jArrayStructure<T> {
-        val array =
-    }
-
-    override fun StructureND<T>.map(transform: A.(T) -> T): Nd4jArrayStructure<T> {
-        TODO("Not yet implemented")
-    }
-
-    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): Nd4jArrayStructure<T> {
-        TODO("Not yet implemented")
-    }
-
-    override fun zip(left: StructureND<T>, right: StructureND<T>, transform: A.(T, T) -> T): Nd4jArrayStructure<T> {
-        TODO("Not yet implemented")
-    }
-
     /**
      * Wraps [INDArray] to [Nd4jArrayStructure].
      */
@@ -53,8 +38,21 @@ public sealed interface Nd4jTensorAlgebra<T : Number, A : Field<T>> : AnalyticTe
      */
     public val StructureND<T>.ndArray: INDArray
 
+    override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): Nd4jArrayStructure<T>
+
+    override fun StructureND<T>.map(transform: A.(T) -> T): Nd4jArrayStructure<T> =
+        structureND(shape) { index -> elementAlgebra.transform(get(index)) }
+
+    override fun StructureND<T>.mapIndexed(transform: A.(index: IntArray, T) -> T): Nd4jArrayStructure<T> =
+        structureND(shape) { index -> elementAlgebra.transform(index, get(index)) }
+
+    override fun zip(left: StructureND<T>, right: StructureND<T>, transform: A.(T, T) -> T): Nd4jArrayStructure<T> {
+        require(left.shape.contentEquals(right.shape))
+        return structureND(left.shape) { index -> elementAlgebra.transform(left[index], right[index]) }
+    }
+
     override fun T.plus(other: StructureND<T>): Nd4jArrayStructure<T> = other.ndArray.add(this).wrap()
-    override fun StructureND<T>.plus(value: T): Nd4jArrayStructure<T> = ndArray.add(value).wrap()
+    override fun StructureND<T>.plus(arg: T): Nd4jArrayStructure<T> = ndArray.add(arg).wrap()
 
     override fun StructureND<T>.plus(other: StructureND<T>): Nd4jArrayStructure<T> = ndArray.add(other.ndArray).wrap()
 
@@ -94,51 +92,52 @@ public sealed interface Nd4jTensorAlgebra<T : Number, A : Field<T>> : AnalyticTe
     }
 
     override fun StructureND<T>.unaryMinus(): Nd4jArrayStructure<T> = ndArray.neg().wrap()
-    override fun Tensor<T>.get(i: Int): Nd4jArrayStructure<T> = ndArray.slice(i.toLong()).wrap()
+    override fun StructureND<T>.get(i: Int): Nd4jArrayStructure<T> = ndArray.slice(i.toLong()).wrap()
-    override fun Tensor<T>.transpose(i: Int, j: Int): Nd4jArrayStructure<T> = ndArray.swapAxes(i, j).wrap()
+    override fun StructureND<T>.transpose(i: Int, j: Int): Nd4jArrayStructure<T> = ndArray.swapAxes(i, j).wrap()
-    override fun Tensor<T>.dot(other: Tensor<T>): Nd4jArrayStructure<T> = ndArray.mmul(other.ndArray).wrap()
+    override fun StructureND<T>.dot(other: StructureND<T>): Nd4jArrayStructure<T> = ndArray.mmul(other.ndArray).wrap()
 
-    override fun Tensor<T>.min(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.min(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
         ndArray.min(keepDim, dim).wrap()
 
-    override fun Tensor<T>.sum(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.sum(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
         ndArray.sum(keepDim, dim).wrap()
 
-    override fun Tensor<T>.max(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.max(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
         ndArray.max(keepDim, dim).wrap()
 
-    override fun Tensor<T>.view(shape: IntArray): Nd4jArrayStructure<T> = ndArray.reshape(shape).wrap()
+    override fun StructureND<T>.view(shape: IntArray): Nd4jArrayStructure<T> = ndArray.reshape(shape).wrap()
-    override fun Tensor<T>.viewAs(other: Tensor<T>): Nd4jArrayStructure<T> = view(other.shape)
+    override fun StructureND<T>.viewAs(other: StructureND<T>): Nd4jArrayStructure<T> = view(other.shape)
 
-    override fun Tensor<T>.argMax(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.argMax(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
         ndBase.get().argmax(ndArray, keepDim, dim).wrap()
 
-    override fun Tensor<T>.mean(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> = ndArray.mean(keepDim, dim).wrap()
+    override fun StructureND<T>.mean(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+        ndArray.mean(keepDim, dim).wrap()
 
-    override fun Tensor<T>.exp(): Nd4jArrayStructure<T> = Transforms.exp(ndArray).wrap()
+    override fun StructureND<T>.exp(): Nd4jArrayStructure<T> = Transforms.exp(ndArray).wrap()
-    override fun Tensor<T>.ln(): Nd4jArrayStructure<T> = Transforms.log(ndArray).wrap()
+    override fun StructureND<T>.ln(): Nd4jArrayStructure<T> = Transforms.log(ndArray).wrap()
-    override fun Tensor<T>.sqrt(): Nd4jArrayStructure<T> = Transforms.sqrt(ndArray).wrap()
+    override fun StructureND<T>.sqrt(): Nd4jArrayStructure<T> = Transforms.sqrt(ndArray).wrap()
-    override fun Tensor<T>.cos(): Nd4jArrayStructure<T> = Transforms.cos(ndArray).wrap()
+    override fun StructureND<T>.cos(): Nd4jArrayStructure<T> = Transforms.cos(ndArray).wrap()
-    override fun Tensor<T>.acos(): Nd4jArrayStructure<T> = Transforms.acos(ndArray).wrap()
+    override fun StructureND<T>.acos(): Nd4jArrayStructure<T> = Transforms.acos(ndArray).wrap()
-    override fun Tensor<T>.cosh(): Nd4jArrayStructure<T> = Transforms.cosh(ndArray).wrap()
+    override fun StructureND<T>.cosh(): Nd4jArrayStructure<T> = Transforms.cosh(ndArray).wrap()
 
-    override fun Tensor<T>.acosh(): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.acosh(): Nd4jArrayStructure<T> =
         Nd4j.getExecutioner().exec(ACosh(ndArray, ndArray.ulike())).wrap()
 
-    override fun Tensor<T>.sin(): Nd4jArrayStructure<T> = Transforms.sin(ndArray).wrap()
+    override fun StructureND<T>.sin(): Nd4jArrayStructure<T> = Transforms.sin(ndArray).wrap()
-    override fun Tensor<T>.asin(): Nd4jArrayStructure<T> = Transforms.asin(ndArray).wrap()
+    override fun StructureND<T>.asin(): Nd4jArrayStructure<T> = Transforms.asin(ndArray).wrap()
-    override fun Tensor<T>.sinh(): Tensor<T> = Transforms.sinh(ndArray).wrap()
+    override fun StructureND<T>.sinh(): Tensor<T> = Transforms.sinh(ndArray).wrap()
 
-    override fun Tensor<T>.asinh(): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.asinh(): Nd4jArrayStructure<T> =
         Nd4j.getExecutioner().exec(ASinh(ndArray, ndArray.ulike())).wrap()
 
-    override fun Tensor<T>.tan(): Nd4jArrayStructure<T> = Transforms.tan(ndArray).wrap()
+    override fun StructureND<T>.tan(): Nd4jArrayStructure<T> = Transforms.tan(ndArray).wrap()
-    override fun Tensor<T>.atan(): Nd4jArrayStructure<T> = Transforms.atan(ndArray).wrap()
+    override fun StructureND<T>.atan(): Nd4jArrayStructure<T> = Transforms.atan(ndArray).wrap()
-    override fun Tensor<T>.tanh(): Nd4jArrayStructure<T> = Transforms.tanh(ndArray).wrap()
+    override fun StructureND<T>.tanh(): Nd4jArrayStructure<T> = Transforms.tanh(ndArray).wrap()
-    override fun Tensor<T>.atanh(): Nd4jArrayStructure<T> = Transforms.atanh(ndArray).wrap()
+    override fun StructureND<T>.atanh(): Nd4jArrayStructure<T> = Transforms.atanh(ndArray).wrap()
-    override fun Tensor<T>.ceil(): Nd4jArrayStructure<T> = Transforms.ceil(ndArray).wrap()
+    override fun StructureND<T>.ceil(): Nd4jArrayStructure<T> = Transforms.ceil(ndArray).wrap()
-    override fun Tensor<T>.floor(): Nd4jArrayStructure<T> = Transforms.floor(ndArray).wrap()
+    override fun StructureND<T>.floor(): Nd4jArrayStructure<T> = Transforms.floor(ndArray).wrap()
-    override fun Tensor<T>.std(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.std(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
         ndArray.std(true, keepDim, dim).wrap()
 
     override fun T.div(arg: StructureND<T>): Nd4jArrayStructure<T> = arg.ndArray.rdiv(this).wrap()
@@ -153,7 +152,7 @@ public sealed interface Nd4jTensorAlgebra<T : Number, A : Field<T>> : AnalyticTe
         ndArray.divi(other.ndArray)
     }
 
-    override fun Tensor<T>.variance(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun StructureND<T>.variance(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
         Nd4j.getExecutioner().exec(Variance(ndArray, true, true, dim)).wrap()
 
     private companion object {
@@ -170,6 +169,16 @@ public object DoubleNd4jTensorAlgebra : Nd4jTensorAlgebra<Double, DoubleField> {
 
     override fun INDArray.wrap(): Nd4jArrayStructure<Double> = asDoubleStructure()
 
+    override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): Nd4jArrayStructure<Double> {
+        val array: INDArray = Nd4j.zeros(*shape)
+        val indices = DefaultStrides(shape)
+        indices.indices().forEach { index ->
+            array.putScalar(index, elementAlgebra.initializer(index))
+        }
+        return array.wrap()
+    }
+
+
     @OptIn(PerformancePitfall::class)
     override val StructureND<Double>.ndArray: INDArray
         get() = when (this) {
@@ -190,10 +199,10 @@ public object DoubleNd4jTensorAlgebra : Nd4jTensorAlgebra<Double, DoubleField> {
         dim2: Int,
     ): Tensor<Double> = DoubleTensorAlgebra.diagonalEmbedding(diagonalEntries, offset, dim1, dim2)
 
-    override fun Tensor<Double>.sum(): Double = ndArray.sumNumber().toDouble()
+    override fun StructureND<Double>.sum(): Double = ndArray.sumNumber().toDouble()
-    override fun Tensor<Double>.min(): Double = ndArray.minNumber().toDouble()
+    override fun StructureND<Double>.min(): Double = ndArray.minNumber().toDouble()
-    override fun Tensor<Double>.max(): Double = ndArray.maxNumber().toDouble()
+    override fun StructureND<Double>.max(): Double = ndArray.maxNumber().toDouble()
-    override fun Tensor<Double>.mean(): Double = ndArray.meanNumber().toDouble()
+    override fun StructureND<Double>.mean(): Double = ndArray.meanNumber().toDouble()
-    override fun Tensor<Double>.std(): Double = ndArray.stdNumber().toDouble()
+    override fun StructureND<Double>.std(): Double = ndArray.stdNumber().toDouble()
-    override fun Tensor<Double>.variance(): Double = ndArray.varNumber().toDouble()
+    override fun StructureND<Double>.variance(): Double = ndArray.varNumber().toDouble()
 }

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

@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.tensors.api
 
+import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.Field
 
 
@@ -18,7 +19,7 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> : TensorPartialDivisionA
     /**
      * @return the mean of all elements in the input tensor.
      */
-    public fun Tensor<T>.mean(): T
+    public fun StructureND<T>.mean(): T
 
     /**
      * Returns the mean of each row of the input tensor in the given dimension [dim].
@@ -31,12 +32,12 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> : TensorPartialDivisionA
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the mean of each row of the input tensor in the given dimension [dim].
      */
-    public fun Tensor<T>.mean(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun StructureND<T>.mean(dim: Int, keepDim: Boolean): Tensor<T>
 
     /**
      * @return the standard deviation of all elements in the input tensor.
      */
-    public fun Tensor<T>.std(): T
+    public fun StructureND<T>.std(): T
 
     /**
      * Returns the standard deviation of each row of the input tensor in the given dimension [dim].
@@ -49,12 +50,12 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> : TensorPartialDivisionA
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the standard deviation of each row of the input tensor in the given dimension [dim].
      */
-    public fun Tensor<T>.std(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun StructureND<T>.std(dim: Int, keepDim: Boolean): Tensor<T>
 
     /**
      * @return the variance of all elements in the input tensor.
      */
-    public fun Tensor<T>.variance(): T
+    public fun StructureND<T>.variance(): T
 
     /**
      * Returns the variance of each row of the input tensor in the given dimension [dim].
@@ -67,57 +68,57 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> : TensorPartialDivisionA
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the variance of each row of the input tensor in the given dimension [dim].
      */
-    public fun Tensor<T>.variance(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun StructureND<T>.variance(dim: Int, keepDim: Boolean): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.exp.html
-    public fun Tensor<T>.exp(): Tensor<T>
+    public fun StructureND<T>.exp(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.log.html
-    public fun Tensor<T>.ln(): Tensor<T>
+    public fun StructureND<T>.ln(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.sqrt.html
-    public fun Tensor<T>.sqrt(): Tensor<T>
+    public fun StructureND<T>.sqrt(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.cos
-    public fun Tensor<T>.cos(): Tensor<T>
+    public fun StructureND<T>.cos(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.acos
-    public fun Tensor<T>.acos(): Tensor<T>
+    public fun StructureND<T>.acos(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.cosh
-    public fun Tensor<T>.cosh(): Tensor<T>
+    public fun StructureND<T>.cosh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.acosh
-    public fun Tensor<T>.acosh(): Tensor<T>
+    public fun StructureND<T>.acosh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sin
-    public fun Tensor<T>.sin(): Tensor<T>
+    public fun StructureND<T>.sin(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asin
-    public fun Tensor<T>.asin(): Tensor<T>
+    public fun StructureND<T>.asin(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sinh
-    public fun Tensor<T>.sinh(): Tensor<T>
+    public fun StructureND<T>.sinh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asinh
-    public fun Tensor<T>.asinh(): Tensor<T>
+    public fun StructureND<T>.asinh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.atan.html#torch.tan
-    public fun Tensor<T>.tan(): Tensor<T>
+    public fun StructureND<T>.tan(): Tensor<T>
 
     //https://pytorch.org/docs/stable/generated/torch.atan.html#torch.atan
-    public fun Tensor<T>.atan(): Tensor<T>
+    public fun StructureND<T>.atan(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.tanh
-    public fun Tensor<T>.tanh(): Tensor<T>
+    public fun StructureND<T>.tanh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.atanh
-    public fun Tensor<T>.atanh(): Tensor<T>
+    public fun StructureND<T>.atanh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.ceil.html#torch.ceil
-    public fun Tensor<T>.ceil(): Tensor<T>
+    public fun StructureND<T>.ceil(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.floor.html#torch.floor
-    public fun Tensor<T>.floor(): Tensor<T>
+    public fun StructureND<T>.floor(): Tensor<T>
 
 }

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

@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.tensors.api
 
+import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.Field
 
 /**
@@ -20,7 +21,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      *
      * @return the determinant.
      */
-    public fun Tensor<T>.det(): Tensor<T>
+    public fun StructureND<T>.det(): Tensor<T>
 
     /**
      * Computes the multiplicative inverse matrix of a square matrix input, or of each square matrix in a batched input.
@@ -30,7 +31,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      *
      * @return the multiplicative inverse of a matrix.
      */
-    public fun Tensor<T>.inv(): Tensor<T>
+    public fun StructureND<T>.inv(): Tensor<T>
 
     /**
      * Cholesky decomposition.
@@ -46,7 +47,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return the batch of `L` matrices.
      */
-    public fun Tensor<T>.cholesky(): Tensor<T>
+    public fun StructureND<T>.cholesky(): Tensor<T>
 
     /**
      * QR decomposition.
@@ -60,7 +61,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return pair of `Q` and `R` tensors.
      */
-    public fun Tensor<T>.qr(): Pair<Tensor<T>, Tensor<T>>
+    public fun StructureND<T>.qr(): Pair<Tensor<T>, Tensor<T>>
 
     /**
      * LUP decomposition
@@ -74,7 +75,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return triple of P, L and U tensors
      */
-    public fun Tensor<T>.lu(): Triple<Tensor<T>, Tensor<T>, Tensor<T>>
+    public fun StructureND<T>.lu(): Triple<Tensor<T>, Tensor<T>, Tensor<T>>
 
     /**
      * Singular Value Decomposition.
@@ -90,7 +91,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return triple `Triple(U, S, V)`.
      */
-    public fun Tensor<T>.svd(): Triple<Tensor<T>, Tensor<T>, Tensor<T>>
+    public fun StructureND<T>.svd(): Triple<Tensor<T>, Tensor<T>, Tensor<T>>
 
     /**
      * Returns eigenvalues and eigenvectors of a real symmetric matrix `input` or a batch of real symmetric matrices,
@@ -100,6 +101,6 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return a pair `eigenvalues to eigenvectors`
      */
-    public fun Tensor<T>.symEig(): Pair<Tensor<T>, Tensor<T>>
+    public fun StructureND<T>.symEig(): Pair<Tensor<T>, Tensor<T>>
 
 }

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

@@ -41,12 +41,12 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
     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.
+     * Adds the scalar [arg] to each element of this tensor and returns a new resulting tensor.
      *
-     * @param value the number to be added to each element of this tensor.
+     * @param arg the number to be added to each element of this tensor.
-     * @return the sum of this tensor and [value].
+     * @return the sum of this tensor and [arg].
      */
-    override operator fun StructureND<T>.plus(value: T): Tensor<T>
+    override operator fun StructureND<T>.plus(arg: T): Tensor<T>
 
     /**
      * Each element of the tensor [other] is added to each element of this tensor.
@@ -166,7 +166,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param i index of the extractable tensor
      * @return subtensor of the original tensor with index [i]
      */
-    public operator fun Tensor<T>.get(i: Int): Tensor<T>
+    public operator fun StructureND<T>.get(i: Int): Tensor<T>
 
     /**
      * Returns a tensor that is a transposed version of this tensor. The given dimensions [i] and [j] are swapped.
@@ -176,7 +176,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param j the second dimension to be transposed
      * @return transposed tensor
      */
-    public fun Tensor<T>.transpose(i: Int = -2, j: Int = -1): Tensor<T>
+    public fun StructureND<T>.transpose(i: Int = -2, j: Int = -1): Tensor<T>
 
     /**
      * Returns a new tensor with the same data as the self tensor but of a different shape.
@@ -186,7 +186,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param shape the desired size
      * @return tensor with new shape
      */
-    public fun Tensor<T>.view(shape: IntArray): Tensor<T>
+    public fun StructureND<T>.view(shape: IntArray): Tensor<T>
 
     /**
      * View this tensor as the same size as [other].
@@ -196,7 +196,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param other the result tensor has the same size as other.
      * @return the result tensor with the same size as other.
      */
-    public fun Tensor<T>.viewAs(other: Tensor<T>): Tensor<T>
+    public fun StructureND<T>.viewAs(other: StructureND<T>): Tensor<T>
 
     /**
      * Matrix product of two tensors.
@@ -227,7 +227,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param other tensor to be multiplied.
      * @return a mathematical product of two tensors.
      */
-    public infix fun Tensor<T>.dot(other: Tensor<T>): Tensor<T>
+    public infix fun StructureND<T>.dot(other: StructureND<T>): Tensor<T>
 
     /**
      * Creates a tensor whose diagonals of certain 2D planes (specified by [dim1] and [dim2])
@@ -262,7 +262,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
     /**
      * @return the sum of all elements in the input tensor.
      */
-    public fun Tensor<T>.sum(): T
+    public fun StructureND<T>.sum(): T
 
     /**
      * Returns the sum of each row of the input tensor in the given dimension [dim].
@@ -275,12 +275,12 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the sum of each row of the input tensor in the given dimension [dim].
      */
-    public fun Tensor<T>.sum(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun StructureND<T>.sum(dim: Int, keepDim: Boolean): Tensor<T>
 
     /**
-     * @return the minimum value of all elements in the input tensor.
+     * @return the minimum value of all elements in the input tensor or null if there are no values
      */
-    public fun Tensor<T>.min(): T
+    public fun StructureND<T>.min(): T?
 
     /**
      * Returns the minimum value of each row of the input tensor in the given dimension [dim].
@@ -293,12 +293,12 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the minimum value of each row of the input tensor in the given dimension [dim].
      */
-    public fun Tensor<T>.min(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun StructureND<T>.min(dim: Int, keepDim: Boolean): Tensor<T>
 
     /**
-     * Returns the maximum value of all elements in the input tensor.
+     * Returns the maximum value of all elements in the input tensor or null if there are no values
      */
-    public fun Tensor<T>.max(): T
+    public fun StructureND<T>.max(): T?
 
     /**
      * Returns the maximum value of each row of the input tensor in the given dimension [dim].
@@ -311,7 +311,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the maximum value of each row of the input tensor in the given dimension [dim].
      */
-    public fun Tensor<T>.max(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun StructureND<T>.max(dim: Int, keepDim: Boolean): Tensor<T>
 
     /**
      * Returns the index of maximum value of each row of the input tensor in the given dimension [dim].
@@ -324,7 +324,7 @@ public interface TensorAlgebra<T, A : Ring<T>> : RingOpsND<T, A> {
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the index of maximum value of each row of the input tensor in the given dimension [dim].
      */
-    public fun Tensor<T>.argMax(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun StructureND<T>.argMax(dim: Int, keepDim: Boolean): Tensor<T>
 
     override fun add(left: StructureND<T>, right: StructureND<T>): Tensor<T> = left + right
 

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

@@ -85,7 +85,7 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         return DoubleTensor(newThis.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.divAssign(other: Tensor<Double>) {
+    override fun Tensor<Double>.divAssign(other: StructureND<Double>) {
         val newOther = broadcastTo(other.tensor, tensor.shape)
         for (i in 0 until tensor.indices.linearSize) {
             tensor.mutableBuffer.array()[tensor.bufferStart + i] /=

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

@@ -115,7 +115,7 @@ public open class DoubleTensorAlgebra :
         TensorLinearStructure(shape).indices().map { DoubleField.initializer(it) }.toMutableList().toDoubleArray()
     )
 
-    override operator fun Tensor<Double>.get(i: Int): DoubleTensor {
+    override operator fun StructureND<Double>.get(i: Int): DoubleTensor {
         val lastShape = tensor.shape.drop(1).toIntArray()
         val newShape = if (lastShape.isNotEmpty()) lastShape else intArrayOf(1)
         val newStart = newShape.reduce(Int::times) * i + tensor.bufferStart
@@ -160,7 +160,7 @@ public open class DoubleTensorAlgebra :
      *
      * @return tensor filled with the scalar value `0.0`, with the same shape as `input` tensor.
      */
-    public fun Tensor<Double>.zeroesLike(): DoubleTensor = tensor.fullLike(0.0)
+    public fun StructureND<Double>.zeroesLike(): DoubleTensor = tensor.fullLike(0.0)
 
     /**
      * Returns a tensor filled with the scalar value `1.0`, with the shape defined by the variable argument [shape].
@@ -198,9 +198,8 @@ public open class DoubleTensorAlgebra :
      *
      * @return a copy of the `input` tensor with a copied buffer.
      */
-    public fun Tensor<Double>.copy(): DoubleTensor {
+    public fun StructureND<Double>.copy(): DoubleTensor =
-        return DoubleTensor(tensor.shape, tensor.mutableBuffer.array().copyOf(), tensor.bufferStart)
+        DoubleTensor(tensor.shape, tensor.mutableBuffer.array().copyOf(), tensor.bufferStart)
-    }
 
     override fun Double.plus(other: StructureND<Double>): DoubleTensor {
         val resBuffer = DoubleArray(other.tensor.numElements) { i ->
@@ -209,7 +208,7 @@ public open class DoubleTensorAlgebra :
         return DoubleTensor(other.shape, resBuffer)
     }
 
-    override fun StructureND<Double>.plus(value: Double): DoubleTensor = value + tensor
+    override fun StructureND<Double>.plus(arg: Double): DoubleTensor = arg + tensor
 
     override fun StructureND<Double>.plus(other: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, other.tensor)
@@ -345,7 +344,7 @@ public open class DoubleTensorAlgebra :
         return DoubleTensor(tensor.shape, resBuffer)
     }
 
-    override fun Tensor<Double>.transpose(i: Int, j: Int): DoubleTensor {
+    override fun StructureND<Double>.transpose(i: Int, j: Int): DoubleTensor {
         val ii = tensor.minusIndex(i)
         val jj = tensor.minusIndex(j)
         checkTranspose(tensor.dimension, ii, jj)
@@ -369,15 +368,15 @@ public open class DoubleTensorAlgebra :
         return resTensor
     }
 
-    override fun Tensor<Double>.view(shape: IntArray): DoubleTensor {
+    override fun StructureND<Double>.view(shape: IntArray): DoubleTensor {
         checkView(tensor, shape)
         return DoubleTensor(shape, tensor.mutableBuffer.array(), tensor.bufferStart)
     }
 
-    override fun Tensor<Double>.viewAs(other: Tensor<Double>): DoubleTensor =
+    override fun StructureND<Double>.viewAs(other: StructureND<Double>): DoubleTensor =
         tensor.view(other.shape)
 
-    override infix fun Tensor<Double>.dot(other: Tensor<Double>): DoubleTensor {
+    override infix fun StructureND<Double>.dot(other: StructureND<Double>): DoubleTensor {
         if (tensor.shape.size == 1 && other.shape.size == 1) {
             return DoubleTensor(intArrayOf(1), doubleArrayOf(tensor.times(other).tensor.mutableBuffer.array().sum()))
         }
@@ -569,10 +568,10 @@ 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 =
+    internal inline fun StructureND<Double>.fold(foldFunction: (DoubleArray) -> Double): Double =
         foldFunction(tensor.copyArray())
 
-    internal inline fun Tensor<Double>.foldDim(
+    internal inline fun StructureND<Double>.foldDim(
         foldFunction: (DoubleArray) -> Double,
         dim: Int,
         keepDim: Boolean,
@@ -596,30 +595,30 @@ public open class DoubleTensorAlgebra :
         return resTensor
     }
 
-    override fun Tensor<Double>.sum(): Double = tensor.fold { it.sum() }
+    override fun StructureND<Double>.sum(): Double = tensor.fold { it.sum() }
 
-    override fun Tensor<Double>.sum(dim: Int, keepDim: Boolean): DoubleTensor =
+    override fun StructureND<Double>.sum(dim: Int, keepDim: Boolean): DoubleTensor =
         foldDim({ x -> x.sum() }, dim, keepDim)
 
-    override fun Tensor<Double>.min(): Double = this.fold { it.minOrNull()!! }
+    override fun StructureND<Double>.min(): Double = this.fold { it.minOrNull()!! }
 
-    override fun Tensor<Double>.min(dim: Int, keepDim: Boolean): DoubleTensor =
+    override fun StructureND<Double>.min(dim: Int, keepDim: Boolean): DoubleTensor =
         foldDim({ x -> x.minOrNull()!! }, dim, keepDim)
 
-    override fun Tensor<Double>.max(): Double = this.fold { it.maxOrNull()!! }
+    override fun StructureND<Double>.max(): Double = this.fold { it.maxOrNull()!! }
 
-    override fun Tensor<Double>.max(dim: Int, keepDim: Boolean): DoubleTensor =
+    override fun StructureND<Double>.max(dim: Int, keepDim: Boolean): DoubleTensor =
         foldDim({ x -> x.maxOrNull()!! }, dim, keepDim)
 
-    override fun Tensor<Double>.argMax(dim: Int, keepDim: Boolean): DoubleTensor =
+    override fun StructureND<Double>.argMax(dim: Int, keepDim: Boolean): DoubleTensor =
         foldDim({ x ->
             x.withIndex().maxByOrNull { it.value }?.index!!.toDouble()
         }, dim, keepDim)
 
 
-    override fun Tensor<Double>.mean(): Double = this.fold { it.sum() / tensor.numElements }
+    override fun StructureND<Double>.mean(): Double = this.fold { it.sum() / tensor.numElements }
 
-    override fun Tensor<Double>.mean(dim: Int, keepDim: Boolean): DoubleTensor =
+    override fun StructureND<Double>.mean(dim: Int, keepDim: Boolean): DoubleTensor =
         foldDim(
             { arr ->
                 check(dim < dimension) { "Dimension $dim out of range $dimension" }
@@ -629,12 +628,12 @@ public open class DoubleTensorAlgebra :
             keepDim
         )
 
-    override fun Tensor<Double>.std(): Double = this.fold { arr ->
+    override fun StructureND<Double>.std(): Double = this.fold { arr ->
         val mean = arr.sum() / tensor.numElements
         sqrt(arr.sumOf { (it - mean) * (it - mean) } / (tensor.numElements - 1))
     }
 
-    override fun Tensor<Double>.std(dim: Int, keepDim: Boolean): DoubleTensor = foldDim(
+    override fun StructureND<Double>.std(dim: Int, keepDim: Boolean): DoubleTensor = foldDim(
         { arr ->
             check(dim < dimension) { "Dimension $dim out of range $dimension" }
             val mean = arr.sum() / shape[dim]
@@ -644,12 +643,12 @@ public open class DoubleTensorAlgebra :
         keepDim
     )
 
-    override fun Tensor<Double>.variance(): Double = this.fold { arr ->
+    override fun StructureND<Double>.variance(): Double = this.fold { arr ->
         val mean = arr.sum() / tensor.numElements
         arr.sumOf { (it - mean) * (it - mean) } / (tensor.numElements - 1)
     }
 
-    override fun Tensor<Double>.variance(dim: Int, keepDim: Boolean): DoubleTensor = foldDim(
+    override fun StructureND<Double>.variance(dim: Int, keepDim: Boolean): DoubleTensor = foldDim(
         { arr ->
             check(dim < dimension) { "Dimension $dim out of range $dimension" }
             val mean = arr.sum() / shape[dim]
@@ -672,7 +671,7 @@ public open class DoubleTensorAlgebra :
      * @param tensors the [List] of 1-dimensional tensors with same shape
      * @return `M`.
      */
-    public fun cov(tensors: List<Tensor<Double>>): DoubleTensor {
+    public fun cov(tensors: List<StructureND<Double>>): DoubleTensor {
         check(tensors.isNotEmpty()) { "List must have at least 1 element" }
         val n = tensors.size
         val m = tensors[0].shape[0]
@@ -689,43 +688,43 @@ public open class DoubleTensorAlgebra :
         return resTensor
     }
 
-    override fun Tensor<Double>.exp(): DoubleTensor = tensor.map { exp(it) }
+    override fun StructureND<Double>.exp(): DoubleTensor = tensor.map { exp(it) }
 
-    override fun Tensor<Double>.ln(): DoubleTensor = tensor.map { ln(it) }
+    override fun StructureND<Double>.ln(): DoubleTensor = tensor.map { ln(it) }
 
-    override fun Tensor<Double>.sqrt(): DoubleTensor = tensor.map { sqrt(it) }
+    override fun StructureND<Double>.sqrt(): DoubleTensor = tensor.map { sqrt(it) }
 
-    override fun Tensor<Double>.cos(): DoubleTensor = tensor.map { cos(it) }
+    override fun StructureND<Double>.cos(): DoubleTensor = tensor.map { cos(it) }
 
-    override fun Tensor<Double>.acos(): DoubleTensor = tensor.map { acos(it) }
+    override fun StructureND<Double>.acos(): DoubleTensor = tensor.map { acos(it) }
 
-    override fun Tensor<Double>.cosh(): DoubleTensor = tensor.map { cosh(it) }
+    override fun StructureND<Double>.cosh(): DoubleTensor = tensor.map { cosh(it) }
 
-    override fun Tensor<Double>.acosh(): DoubleTensor = tensor.map { acosh(it) }
+    override fun StructureND<Double>.acosh(): DoubleTensor = tensor.map { acosh(it) }
 
-    override fun Tensor<Double>.sin(): DoubleTensor = tensor.map { sin(it) }
+    override fun StructureND<Double>.sin(): DoubleTensor = tensor.map { sin(it) }
 
-    override fun Tensor<Double>.asin(): DoubleTensor = tensor.map { asin(it) }
+    override fun StructureND<Double>.asin(): DoubleTensor = tensor.map { asin(it) }
 
-    override fun Tensor<Double>.sinh(): DoubleTensor = tensor.map { sinh(it) }
+    override fun StructureND<Double>.sinh(): DoubleTensor = tensor.map { sinh(it) }
 
-    override fun Tensor<Double>.asinh(): DoubleTensor = tensor.map { asinh(it) }
+    override fun StructureND<Double>.asinh(): DoubleTensor = tensor.map { asinh(it) }
 
-    override fun Tensor<Double>.tan(): DoubleTensor = tensor.map { tan(it) }
+    override fun StructureND<Double>.tan(): DoubleTensor = tensor.map { tan(it) }
 
-    override fun Tensor<Double>.atan(): DoubleTensor = tensor.map { atan(it) }
+    override fun StructureND<Double>.atan(): DoubleTensor = tensor.map { atan(it) }
 
-    override fun Tensor<Double>.tanh(): DoubleTensor = tensor.map { tanh(it) }
+    override fun StructureND<Double>.tanh(): DoubleTensor = tensor.map { tanh(it) }
 
-    override fun Tensor<Double>.atanh(): DoubleTensor = tensor.map { atanh(it) }
+    override fun StructureND<Double>.atanh(): DoubleTensor = tensor.map { atanh(it) }
 
-    override fun Tensor<Double>.ceil(): DoubleTensor = tensor.map { ceil(it) }
+    override fun StructureND<Double>.ceil(): DoubleTensor = tensor.map { ceil(it) }
 
-    override fun Tensor<Double>.floor(): DoubleTensor = tensor.map { floor(it) }
+    override fun StructureND<Double>.floor(): DoubleTensor = tensor.map { floor(it) }
 
-    override fun Tensor<Double>.inv(): DoubleTensor = invLU(1e-9)
+    override fun StructureND<Double>.inv(): DoubleTensor = invLU(1e-9)
 
-    override fun Tensor<Double>.det(): DoubleTensor = detLU(1e-9)
+    override fun StructureND<Double>.det(): DoubleTensor = detLU(1e-9)
 
     /**
      * Computes the LU factorization of a matrix or batches of matrices `input`.
@@ -736,7 +735,7 @@ public open class DoubleTensorAlgebra :
      * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor.
      * The `pivots`  has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows.
      */
-    public fun Tensor<Double>.luFactor(epsilon: Double): Pair<DoubleTensor, IntTensor> =
+    public fun StructureND<Double>.luFactor(epsilon: Double): Pair<DoubleTensor, IntTensor> =
         computeLU(tensor, epsilon)
             ?: throw IllegalArgumentException("Tensor contains matrices which are singular at precision $epsilon")
 
@@ -749,7 +748,7 @@ public open class DoubleTensorAlgebra :
      * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor.
      * The `pivots`  has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows.
      */
-    public fun Tensor<Double>.luFactor(): Pair<DoubleTensor, IntTensor> = luFactor(1e-9)
+    public fun StructureND<Double>.luFactor(): Pair<DoubleTensor, IntTensor> = luFactor(1e-9)
 
     /**
      * Unpacks the data and pivots from a LU factorization of a tensor.
@@ -763,7 +762,7 @@ public open class DoubleTensorAlgebra :
      * @return triple of `P`, `L` and `U` tensors
      */
     public fun luPivot(
-        luTensor: Tensor<Double>,
+        luTensor: StructureND<Double>,
         pivotsTensor: Tensor<Int>,
     ): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
         checkSquareMatrix(luTensor.shape)
@@ -806,7 +805,7 @@ public open class DoubleTensorAlgebra :
      * Used when checking the positive definiteness of the input matrix or matrices.
      * @return a pair of `Q` and `R` tensors.
      */
-    public fun Tensor<Double>.cholesky(epsilon: Double): DoubleTensor {
+    public fun StructureND<Double>.cholesky(epsilon: Double): DoubleTensor {
         checkSquareMatrix(shape)
         checkPositiveDefinite(tensor, epsilon)
 
@@ -819,9 +818,9 @@ public open class DoubleTensorAlgebra :
         return lTensor
     }
 
-    override fun Tensor<Double>.cholesky(): DoubleTensor = cholesky(1e-6)
+    override fun StructureND<Double>.cholesky(): DoubleTensor = cholesky(1e-6)
 
-    override fun Tensor<Double>.qr(): Pair<DoubleTensor, DoubleTensor> {
+    override fun StructureND<Double>.qr(): Pair<DoubleTensor, DoubleTensor> {
         checkSquareMatrix(shape)
         val qTensor = zeroesLike()
         val rTensor = zeroesLike()
@@ -837,7 +836,7 @@ public open class DoubleTensorAlgebra :
         return qTensor to rTensor
     }
 
-    override fun Tensor<Double>.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> =
+    override fun StructureND<Double>.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> =
         svd(epsilon = 1e-10)
 
     /**
@@ -853,7 +852,7 @@ public open class DoubleTensorAlgebra :
      * i.e., the precision with which the cosine approaches 1 in an iterative algorithm.
      * @return a triple `Triple(U, S, V)`.
      */
-    public fun Tensor<Double>.svd(epsilon: Double): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
+    public fun StructureND<Double>.svd(epsilon: Double): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
         val size = tensor.dimension
         val commonShape = tensor.shape.sliceArray(0 until size - 2)
         val (n, m) = tensor.shape.sliceArray(size - 2 until size)
@@ -886,7 +885,7 @@ public open class DoubleTensorAlgebra :
         return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
     }
 
-    override fun Tensor<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEig(epsilon = 1e-15)
+    override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEig(epsilon = 1e-15)
 
     /**
      * Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
@@ -896,7 +895,7 @@ public open class DoubleTensorAlgebra :
      * and when the cosine approaches 1 in the SVD algorithm.
      * @return a pair `eigenvalues to eigenvectors`.
      */
-    public fun Tensor<Double>.symEig(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
+    public fun StructureND<Double>.symEig(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
         checkSymmetric(tensor, epsilon)
 
         fun MutableStructure2D<Double>.cleanSym(n: Int) {
@@ -931,7 +930,7 @@ public open class DoubleTensorAlgebra :
      * with zero.
      * @return the determinant.
      */
-    public fun Tensor<Double>.detLU(epsilon: Double = 1e-9): DoubleTensor {
+    public fun StructureND<Double>.detLU(epsilon: Double = 1e-9): DoubleTensor {
         checkSquareMatrix(tensor.shape)
         val luTensor = tensor.copy()
         val pivotsTensor = tensor.setUpPivots()
@@ -964,7 +963,7 @@ public open class DoubleTensorAlgebra :
      * @param epsilon error in the LU algorithm&mdash;permissible error when comparing the determinant of a matrix with zero
      * @return the multiplicative inverse of a matrix.
      */
-    public fun Tensor<Double>.invLU(epsilon: Double = 1e-9): DoubleTensor {
+    public fun StructureND<Double>.invLU(epsilon: Double = 1e-9): DoubleTensor {
         val (luTensor, pivotsTensor) = luFactor(epsilon)
         val invTensor = luTensor.zeroesLike()
 
@@ -989,12 +988,12 @@ public open class DoubleTensorAlgebra :
      * @param epsilon permissible error when comparing the determinant of a matrix with zero.
      * @return triple of `P`, `L` and `U` tensors.
      */
-    public fun Tensor<Double>.lu(epsilon: Double = 1e-9): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
+    public fun StructureND<Double>.lu(epsilon: Double = 1e-9): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
         val (lu, pivots) = tensor.luFactor(epsilon)
         return luPivot(lu, pivots)
     }
 
-    override fun Tensor<Double>.lu(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> = lu(1e-9)
+    override fun StructureND<Double>.lu(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> = lu(1e-9)
 }
 
 public val Double.Companion.tensorAlgebra: DoubleTensorAlgebra.Companion get() = DoubleTensorAlgebra