Global refactor of tensors

CHANGELOG.md

@@ -7,6 +7,7 @@
 - Algebra now has an obligatory `bufferFactory` (#477).
 
 ### Changed
+- Major refactor of tensors (only minor API changes)
 - Kotlin 1.7.20
 - `LazyStructure` `deffered` -> `async` to comply with coroutines code style
 - Default `dot` operation in tensor algebra no longer support broadcasting. Instead `matmul` operation is added to `DoubleTensorAlgebra`.

build.gradle.kts

@@ -1,9 +1,10 @@
+import space.kscience.gradle.isInDevelopment
 import space.kscience.gradle.useApache2Licence
 import space.kscience.gradle.useSPCTeam
 
 plugins {
     id("space.kscience.gradle.project")
-    id("org.jetbrains.kotlinx.kover") version "0.5.0"
+    id("org.jetbrains.kotlinx.kover") version "0.6.0"
 }
 
 allprojects {
@@ -14,7 +15,7 @@ allprojects {
     }
 
     group = "space.kscience"
-    version = "0.3.1-dev-3"
+    version = "0.3.1-dev-4"
 }
 
 subprojects {
@@ -75,8 +76,14 @@ ksciencePublish {
         useApache2Licence()
         useSPCTeam()
     }
-    github("kmath", "SciProgCentre", addToRelease = false)
+    github("kmath", "SciProgCentre")
-    space("https://maven.pkg.jetbrains.space/mipt-npm/p/sci/dev")
+    space(
+        if (isInDevelopment) {
+            "https://maven.pkg.jetbrains.space/mipt-npm/p/sci/dev"
+        } else {
+            "https://maven.pkg.jetbrains.space/mipt-npm/p/sci/release"
+        }
+    )
     sonatype()
 }
 

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

@@ -52,7 +52,7 @@ fun main() {
         // inverse Sigma matrix can be restored from singular values with diagonalEmbedding function
         val sigma = diagonalEmbedding(singValues.map{ if (abs(it) < 1e-3) 0.0 else 1.0/it })
 
-        val alphaOLS = v dot sigma dot u.transpose() dot y
+        val alphaOLS = v dot sigma dot u.transposed() dot y
         println("Estimated alpha:\n" +
                 "$alphaOLS")
 

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

@@ -27,7 +27,7 @@ fun main(): Unit = Double.tensorAlgebra.withBroadcast {  // work in context with
     println("y:\n$y")
 
     // stack them into single dataset
-    val dataset = stack(listOf(x, y)).transpose()
+    val dataset = stack(listOf(x, y)).transposed()
 
     // normalize both x and y
     val xMean = x.mean()

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

@@ -75,7 +75,7 @@ fun main() = Double.tensorAlgebra.withBroadcast {// work in context with linear
 
     // solveLT(l, b) function can be easily adapted for upper triangular matrix by the permutation matrix revMat
     // create it by placing ones on side diagonal
-    val revMat = u.zeroesLike()
+    val revMat = zeroesLike(u)
     val n = revMat.shape[0]
     for (i in 0 until n) {
         revMat[intArrayOf(i, n - 1 - i)] = 1.0

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

@@ -3,16 +3,14 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
  */
 
-@file:OptIn(PerformancePitfall::class)
-
 package space.kscience.kmath.tensors
 
-import space.kscience.kmath.misc.PerformancePitfall
+import space.kscience.kmath.operations.asIterable
 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.copyArray
+import space.kscience.kmath.tensors.core.toDoubleTensor
 import kotlin.math.sqrt
 
 const val seed = 100500L
@@ -82,9 +80,9 @@ class Dense(
     }
 
     override fun backward(input: DoubleTensor, outputError: DoubleTensor): DoubleTensor = DoubleTensorAlgebra {
-        val gradInput = outputError dot weights.transpose()
+        val gradInput = outputError dot weights.transposed()
 
-        val gradW = input.transpose() dot outputError
+        val gradW = input.transposed() dot outputError
         val gradBias = outputError.mean(dim = 0, keepDim = false) * input.shape[0].toDouble()
 
         weights -= learningRate * gradW
@@ -109,12 +107,11 @@ fun accuracy(yPred: DoubleTensor, yTrue: DoubleTensor): Double {
 }
 
 // neural network class
-@OptIn(ExperimentalStdlibApi::class)
 class NeuralNetwork(private val layers: List<Layer>) {
     private fun softMaxLoss(yPred: DoubleTensor, yTrue: DoubleTensor): DoubleTensor = BroadcastDoubleTensorAlgebra {
 
-        val onesForAnswers = yPred.zeroesLike()
+        val onesForAnswers = zeroesLike(yPred)
-        yTrue.copyArray().forEachIndexed { index, labelDouble ->
+        yTrue.source.asIterable().forEachIndexed { index, labelDouble ->
             val label = labelDouble.toInt()
             onesForAnswers[intArrayOf(index, label)] = 1.0
         }
@@ -166,7 +163,7 @@ class NeuralNetwork(private val layers: List<Layer>) {
             for ((xBatch, yBatch) in iterBatch(xTrain, yTrain)) {
                 train(xBatch, yBatch)
             }
-            println("Accuracy:${accuracy(yTrain, predict(xTrain).argMax(1, true).asDouble())}")
+            println("Accuracy:${accuracy(yTrain, predict(xTrain).argMax(1, true).toDoubleTensor())}")
         }
     }
 
@@ -233,7 +230,7 @@ fun main() = BroadcastDoubleTensorAlgebra {
     val prediction = model.predict(xTest)
 
     // process raw prediction via argMax
-    val predictionLabels = prediction.argMax(1, true).asDouble()
+    val predictionLabels = prediction.argMax(1, true).toDoubleTensor()
 
     // find out accuracy
     val acc = accuracy(yTest, predictionLabels)

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

@@ -237,19 +237,4 @@ public interface MutableStructureND<T> : StructureND<T> {
  */
 public operator fun <T> MutableStructureND<T>.set(vararg index: Int, value: T) {
     set(index, value)
-}
+}
-
-/**
- * Transform a structure element-by element in place.
- */
-@OptIn(PerformancePitfall::class)
-public inline fun <T> MutableStructureND<T>.mapInPlace(action: (index: IntArray, t: T) -> T): Unit =
-    elements().forEach { (index, oldValue) -> this[index] = action(index, oldValue) }
-
-public inline fun <reified T : Any> StructureND<T>.zip(
-    struct: StructureND<T>,
-    crossinline block: (T, T) -> T,
-): StructureND<T> {
-    require(shape.contentEquals(struct.shape)) { "Shape mismatch in structure combination" }
-    return StructureND.auto(shape) { block(this[it], struct[it]) }
-}

kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/Buffer.kt

@@ -114,7 +114,6 @@ public interface Buffer<out T> {
          *
          * The [size] is specified, and each element is calculated by calling the specified [initializer] function.
          */
-        @Suppress("UNCHECKED_CAST")
         public inline fun <reified T : Any> auto(size: Int, initializer: (Int) -> T): Buffer<T> =
             auto(T::class, size, initializer)
     }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/DoubleBuffer.kt

@@ -47,11 +47,6 @@ public inline fun DoubleBuffer(size: Int, init: (Int) -> Double): DoubleBuffer =
  */
 public fun DoubleBuffer(vararg doubles: Double): DoubleBuffer = DoubleBuffer(doubles)
 
-/**
- * Simplified [DoubleBuffer] to array comparison
- */
-public fun DoubleBuffer.contentEquals(vararg doubles: Double): Boolean = array.contentEquals(doubles)
-
 /**
  * Returns a new [DoubleArray] containing all the elements of this [Buffer].
  */

kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/IntBuffer.kt

@@ -24,8 +24,7 @@ public value class IntBuffer(public val array: IntArray) : MutableBuffer<Int> {
 
     override operator fun iterator(): IntIterator = array.iterator()
 
-    override fun copy(): MutableBuffer<Int> =
+    override fun copy(): IntBuffer = IntBuffer(array.copyOf())
-        IntBuffer(array.copyOf())
 }
 
 /**

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

@@ -74,7 +74,9 @@ class NumberNDFieldTest {
 
     @Test
     fun combineTest() {
-        val division = array1.zip(array2, Double::div)
+        algebra {
+            val division = zip(array1, array2) { l, r -> l / r }
+        }
     }
 
     object L2Norm : Norm<StructureND<Number>, Double> {

kmath-for-real/build.gradle.kts

@@ -2,13 +2,13 @@ plugins {
     id("space.kscience.gradle.mpp")
 }
 
-kscience{
+kscience {
     native()
-}
-
-kotlin.sourceSets.commonMain {
     dependencies {
-        api(project(":kmath-core"))
+        api(projects.kmathCore)
+    }
+    dependencies("commonTest") {
+        implementation(projects.testUtils)
     }
 }
 
@@ -24,21 +24,21 @@ readme {
     feature(
         id = "DoubleVector",
         ref = "src/commonMain/kotlin/space/kscience/kmath/real/DoubleVector.kt"
-    ){
+    ) {
         "Numpy-like operations for Buffers/Points"
     }
 
     feature(
         id = "DoubleMatrix",
         ref = "src/commonMain/kotlin/space/kscience/kmath/real/DoubleMatrix.kt"
-    ){
+    ) {
         "Numpy-like operations for 2d real structures"
     }
 
     feature(
         id = "grids",
         ref = "src/commonMain/kotlin/space/kscience/kmath/structures/grids.kt"
-    ){
+    ) {
         "Uniform grid generators"
     }
 }

kmath-for-real/src/commonTest/kotlin/space/kscience/kmath/real/DoubleMatrixTest.kt

@@ -11,7 +11,7 @@ import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.algebra
-import space.kscience.kmath.structures.contentEquals
+import space.kscience.kmath.testutils.contentEquals
 import kotlin.test.Test
 import kotlin.test.assertEquals
 import kotlin.test.assertTrue

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

@@ -72,6 +72,20 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
             }
         }
 
+    /**
+     * Transform a structure element-by element in place.
+     */
+    public inline fun <T> MutableStructureND<T>.mapIndexedInPlace(operation: (index: IntArray, t: T) -> T): Unit {
+        if (this is MultikTensor) {
+            array.multiIndices.iterator().forEach {
+                set(it, operation(it, get(it)))
+            }
+        } else {
+            indices.forEach { set(it, operation(it, get(it))) }
+        }
+    }
+
+
     @OptIn(PerformancePitfall::class)
     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
@@ -121,7 +135,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
         if (this is MultikTensor) {
             array.plusAssign(value)
         } else {
-            mapInPlace { _, t -> elementAlgebra.add(t, value) }
+            mapIndexedInPlace { _, t -> elementAlgebra.add(t, value) }
         }
     }
 
@@ -129,7 +143,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
         if (this is MultikTensor) {
             array.plusAssign(arg.asMultik().array)
         } else {
-            mapInPlace { index, t -> elementAlgebra.add(t, arg[index]) }
+            mapIndexedInPlace { index, t -> elementAlgebra.add(t, arg[index]) }
         }
     }
 
@@ -145,7 +159,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
         if (this is MultikTensor) {
             array.minusAssign(value)
         } else {
-            mapInPlace { _, t -> elementAlgebra.run { t - value } }
+            mapIndexedInPlace { _, t -> elementAlgebra.run { t - value } }
         }
     }
 
@@ -153,7 +167,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
         if (this is MultikTensor) {
             array.minusAssign(arg.asMultik().array)
         } else {
-            mapInPlace { index, t -> elementAlgebra.run { t - arg[index] } }
+            mapIndexedInPlace { index, t -> elementAlgebra.run { t - arg[index] } }
         }
     }
 
@@ -170,7 +184,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
         if (this is MultikTensor) {
             array.timesAssign(value)
         } else {
-            mapInPlace { _, t -> elementAlgebra.multiply(t, value) }
+            mapIndexedInPlace { _, t -> elementAlgebra.multiply(t, value) }
         }
     }
 
@@ -178,7 +192,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
         if (this is MultikTensor) {
             array.timesAssign(arg.asMultik().array)
         } else {
-            mapInPlace { index, t -> elementAlgebra.multiply(t, arg[index]) }
+            mapIndexedInPlace { index, t -> elementAlgebra.multiply(t, arg[index]) }
         }
     }
 
@@ -187,7 +201,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
 
     override fun Tensor<T>.getTensor(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 Tensor<T>.transposed(i: Int, j: Int): MultikTensor<T> = asMultik().array.transpose(i, j).wrap()
 
     override fun Tensor<T>.view(shape: IntArray): MultikTensor<T> {
         require(shape.all { it > 0 })
@@ -283,7 +297,7 @@ public abstract class MultikDivisionTensorAlgebra<T, A : Field<T>>(
         if (this is MultikTensor) {
             array.divAssign(value)
         } else {
-            mapInPlace { _, t -> elementAlgebra.divide(t, value) }
+            mapIndexedInPlace { _, t -> elementAlgebra.divide(t, value) }
         }
     }
 
@@ -291,7 +305,7 @@ public abstract class MultikDivisionTensorAlgebra<T, A : Field<T>>(
         if (this is MultikTensor) {
             array.divAssign(arg.asMultik().array)
         } else {
-            mapInPlace { index, t -> elementAlgebra.divide(t, arg[index]) }
+            mapIndexedInPlace { index, t -> elementAlgebra.divide(t, arg[index]) }
         }
     }
 }

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

@@ -96,7 +96,7 @@ public sealed interface Nd4jTensorAlgebra<T : Number, A : Field<T>> : AnalyticTe
 
     override fun StructureND<T>.unaryMinus(): Nd4jArrayStructure<T> = ndArray.neg().wrap()
     override fun Tensor<T>.getTensor(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 Tensor<T>.transposed(i: Int, j: Int): Nd4jArrayStructure<T> = ndArray.swapAxes(i, j).wrap()
     override fun StructureND<T>.dot(other: StructureND<T>): Nd4jArrayStructure<T> = ndArray.mmul(other.ndArray).wrap()
 
     override fun StructureND<T>.min(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =

kmath-tensorflow/src/main/kotlin/space/kscience/kmath/tensorflow/TensorFlowAlgebra.kt

@@ -188,7 +188,7 @@ public abstract class TensorFlowAlgebra<T, TT : TNumber, A : Ring<T>> internal c
         StridedSliceHelper.stridedSlice(ops.scope(), it, Indices.at(i.toLong()))
     }
 
-    override fun Tensor<T>.transpose(i: Int, j: Int): Tensor<T> = operate {
+    override fun Tensor<T>.transposed(i: Int, j: Int): Tensor<T> = operate {
         ops.linalg.transpose(it, ops.constant(intArrayOf(i, j)))
     }
 

kmath-tensors/build.gradle.kts

@@ -25,6 +25,12 @@ kotlin.sourceSets {
             api(project(":kmath-stat"))
         }
     }
+
+    commonTest{
+        dependencies{
+            implementation(projects.testUtils)
+        }
+    }
 }
 
 readme {

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

@@ -180,7 +180,7 @@ 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 Tensor<T>.transposed(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.

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

@@ -7,8 +7,8 @@ package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.tensors.api.Tensor
-import space.kscience.kmath.tensors.core.internal.array
 import space.kscience.kmath.tensors.core.internal.broadcastTensors
 import space.kscience.kmath.tensors.core.internal.broadcastTo
 
@@ -22,8 +22,8 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val broadcast = broadcastTensors(asDoubleTensor(), arg.asDoubleTensor())
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
+        val resBuffer = DoubleBuffer(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[i] + newOther.mutableBuffer.array()[i]
+            newThis.source[i] + newOther.source[i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
@@ -31,8 +31,7 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
     override fun Tensor<Double>.plusAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.asDoubleTensor(), asDoubleTensor().shape)
         for (i in 0 until asDoubleTensor().indices.linearSize) {
-            asDoubleTensor().mutableBuffer.array()[asDoubleTensor().bufferStart + i] +=
+            asDoubleTensor().source[i] += newOther.source[i]
-                newOther.mutableBuffer.array()[asDoubleTensor().bufferStart + i]
         }
     }
 
@@ -40,17 +39,16 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val broadcast = broadcastTensors(asDoubleTensor(), arg.asDoubleTensor())
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
+        val resBuffer = DoubleBuffer(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[i] - newOther.mutableBuffer.array()[i]
+            newThis.source[i] - newOther.source[i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
 
     override fun Tensor<Double>.minusAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.asDoubleTensor(), asDoubleTensor().shape)
-        for (i in 0 until asDoubleTensor().indices.linearSize) {
+        for (i in 0 until indices.linearSize) {
-            asDoubleTensor().mutableBuffer.array()[asDoubleTensor().bufferStart + i] -=
+            asDoubleTensor().source[i] -= newOther.source[i]
-                newOther.mutableBuffer.array()[asDoubleTensor().bufferStart + i]
         }
     }
 
@@ -58,18 +56,16 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val broadcast = broadcastTensors(asDoubleTensor(), arg.asDoubleTensor())
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
+        val resBuffer = DoubleBuffer(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[newThis.bufferStart + i] *
+            newThis.source[i] * newOther.source[i]
-                    newOther.mutableBuffer.array()[newOther.bufferStart + i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
 
     override fun Tensor<Double>.timesAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.asDoubleTensor(), asDoubleTensor().shape)
-        for (i in 0 until asDoubleTensor().indices.linearSize) {
+        for (i in 0 until indices.linearSize) {
-            asDoubleTensor().mutableBuffer.array()[asDoubleTensor().bufferStart + i] *=
+            asDoubleTensor().source[+i] *= newOther.source[i]
-                newOther.mutableBuffer.array()[asDoubleTensor().bufferStart + i]
         }
     }
 
@@ -77,18 +73,16 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val broadcast = broadcastTensors(asDoubleTensor(), arg.asDoubleTensor())
         val newThis = broadcast[0]
         val newOther = broadcast[1]
-        val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
+        val resBuffer = DoubleBuffer(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[newOther.bufferStart + i] /
+            newThis.source[i] / newOther.source[i]
-                    newOther.mutableBuffer.array()[newOther.bufferStart + i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
 
     override fun Tensor<Double>.divAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.asDoubleTensor(), asDoubleTensor().shape)
-        for (i in 0 until asDoubleTensor().indices.linearSize) {
+        for (i in 0 until indices.linearSize) {
-            asDoubleTensor().mutableBuffer.array()[asDoubleTensor().bufferStart + i] /=
+            asDoubleTensor().source[i] /= newOther.source[i]
-                newOther.mutableBuffer.array()[asDoubleTensor().bufferStart + i]
         }
     }
 }

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

@@ -13,12 +13,12 @@ import space.kscience.kmath.tensors.api.Tensor
 /**
  * Represents [Tensor] over a [MutableBuffer] intended to be used through [DoubleTensor] and [IntTensor]
  */
-public open class BufferedTensor<T> internal constructor(
+public abstract class BufferedTensor<T>(
     override val shape: IntArray,
-    @PublishedApi internal val mutableBuffer: MutableBuffer<T>,
-    @PublishedApi internal val bufferStart: Int,
 ) : Tensor<T> {
 
+    public abstract val source: MutableBuffer<T>
+
     /**
      * Buffer strides based on [TensorLinearStructure] implementation
      */
@@ -27,14 +27,8 @@ public open class BufferedTensor<T> internal constructor(
     /**
      * Number of elements in tensor
      */
-    public val numElements: Int
+    public val linearSize: Int get() = indices.linearSize
-        get() = indices.linearSize
 
-    override fun get(index: IntArray): T = mutableBuffer[bufferStart + indices.offset(index)]
-
-    override fun set(index: IntArray, value: T) {
-        mutableBuffer[bufferStart + indices.offset(index)] = value
-    }
 
     @PerformancePitfall
     override fun elements(): Sequence<Pair<IntArray, T>> = indices.asSequence().map {

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

@@ -5,16 +5,88 @@
 
 package space.kscience.kmath.tensors.core
 
-import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.*
 import space.kscience.kmath.tensors.core.internal.toPrettyString
 
+public class OffsetDoubleBuffer(
+    private val source: DoubleBuffer,
+    private val offset: Int,
+    override val size: Int,
+) : MutableBuffer<Double> {
+
+    init {
+        require(offset >= 0) { "Offset must be non-negative" }
+        require(size >= 0) { "Size must be non-negative" }
+        require(offset + size <= source.size) { "Maximum index must be inside source dimension" }
+    }
+
+    override fun set(index: Int, value: Double) {
+        require(index in 0 until size) { "Index must be in [0, size)" }
+        source[index + offset] = value
+    }
+
+    override fun get(index: Int): Double = source[index + offset]
+
+    /**
+     * Copy only a part of buffer that belongs to this tensor
+     */
+    override fun copy(): DoubleBuffer = source.array.copyOfRange(offset, offset + size).asBuffer()
+
+    override fun iterator(): Iterator<Double> = iterator {
+        for (i in indices) {
+            yield(get(i))
+        }
+    }
+
+    override fun toString(): String = Buffer.toString(this)
+
+    public fun view(addOffset: Int, newSize: Int = size - addOffset): OffsetDoubleBuffer =
+        OffsetDoubleBuffer(source, offset + addOffset, newSize)
+}
+
+public fun OffsetDoubleBuffer.slice(range: IntRange): OffsetDoubleBuffer = view(range.first, range.last - range.first)
+
+/**
+ * Map only operable content of the offset buffer
+ */
+public inline fun OffsetDoubleBuffer.map(operation: (Double) -> Double): DoubleBuffer =
+    DoubleBuffer(size) { operation(get(it)) }
+
+public inline fun OffsetDoubleBuffer.zip(
+    other: OffsetDoubleBuffer,
+    operation: (l: Double, r: Double) -> Double,
+): DoubleBuffer {
+    require(size == other.size) { "The sizes of zipped buffers must be the same" }
+    return DoubleBuffer(size) { operation(get(it), other[it]) }
+}
+
+/**
+ * map in place
+ */
+public inline fun OffsetDoubleBuffer.mapInPlace(operation: (Double) -> Double) {
+    indices.forEach { set(it, operation(get(it))) }
+}
+
 /**
  * Default [BufferedTensor] implementation for [Double] values
  */
-public class DoubleTensor @PublishedApi internal constructor(
+public class DoubleTensor(
     shape: IntArray,
-    buffer: DoubleArray,
+    override val source: OffsetDoubleBuffer,
-    offset: Int = 0
+) : BufferedTensor<Double>(shape) {
-) : BufferedTensor<Double>(shape, DoubleBuffer(buffer), offset) {
+
+    init {
+        require(linearSize == source.size) { "Source buffer size must be equal tensor size" }
+    }
+
+    public constructor(shape: IntArray, buffer: DoubleBuffer) : this(shape, OffsetDoubleBuffer(buffer, 0, buffer.size))
+
+    override fun get(index: IntArray): Double = this.source[indices.offset(index)]
+
+    override fun set(index: IntArray, value: Double) {
+        source[indices.offset(index)] = value
+    }
+
+
     override fun toString(): String = toPrettyString()
 }

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

@@ -5,17 +5,87 @@
 
 package space.kscience.kmath.tensors.core
 
-import space.kscience.kmath.structures.IntBuffer
+import space.kscience.kmath.structures.*
-import space.kscience.kmath.tensors.core.internal.array
 
 /**
  * Default [BufferedTensor] implementation for [Int] values
  */
-public class IntTensor @PublishedApi internal constructor(
+public class OffsetIntBuffer(
-    shape: IntArray,
+    private val source: IntBuffer,
-    buffer: IntArray,
+    private val offset: Int,
-    offset: Int = 0,
+    override val size: Int,
-) : BufferedTensor<Int>(shape, IntBuffer(buffer), offset) {
+) : MutableBuffer<Int> {
-    public fun asDouble(): DoubleTensor =
+
-        DoubleTensor(shape, mutableBuffer.array().map { it.toDouble() }.toDoubleArray(), bufferStart)
+    init {
+        require(offset >= 0) { "Offset must be non-negative" }
+        require(size >= 0) { "Size must be non-negative" }
+        require(offset + size <= source.size) { "Maximum index must be inside source dimension" }
+    }
+
+    override fun set(index: Int, value: Int) {
+        require(index in 0 until size) { "Index must be in [0, size)" }
+        source[index + offset] = value
+    }
+
+    override fun get(index: Int): Int = source[index + offset]
+
+    /**
+     * Copy only a part of buffer that belongs to this tensor
+     */
+    override fun copy(): IntBuffer = source.array.copyOfRange(offset, offset + size).asBuffer()
+
+    override fun iterator(): Iterator<Int> = iterator {
+        for (i in indices) {
+            yield(get(i))
+        }
+    }
+
+    override fun toString(): String = Buffer.toString(this)
+
+    public fun view(addOffset: Int, newSize: Int = size - addOffset): OffsetIntBuffer =
+        OffsetIntBuffer(source, offset + addOffset, newSize)
+}
+
+public fun OffsetIntBuffer.slice(range: IntRange): OffsetIntBuffer = view(range.first, range.last - range.first)
+
+/**
+ * Map only operable content of the offset buffer
+ */
+public inline fun OffsetIntBuffer.map(operation: (Int) -> Int): IntBuffer =
+    IntBuffer(size) { operation(get(it)) }
+
+public inline fun OffsetIntBuffer.zip(
+    other: OffsetIntBuffer,
+    operation: (l: Int, r: Int) -> Int,
+): IntBuffer {
+    require(size == other.size) { "The sizes of zipped buffers must be the same" }
+    return IntBuffer(size) { operation(get(it), other[it]) }
+}
+
+/**
+ * map in place
+ */
+public inline fun OffsetIntBuffer.mapInPlace(operation: (Int) -> Int) {
+    indices.forEach { set(it, operation(get(it))) }
+}
+
+/**
+ * Default [BufferedTensor] implementation for [Int] values
+ */
+public class IntTensor(
+    shape: IntArray,
+    override val source: OffsetIntBuffer,
+) : BufferedTensor<Int>(shape) {
+
+    init {
+        require(linearSize == source.size) { "Source buffer size must be equal tensor size" }
+    }
+
+    public constructor(shape: IntArray, buffer: IntBuffer) : this(shape, OffsetIntBuffer(buffer, 0, buffer.size))
+
+    override fun get(index: IntArray): Int = this.source[indices.offset(index)]
+
+    override fun set(index: IntArray, value: Int) {
+        source[indices.offset(index)] = value
+    }
 }

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

@@ -11,7 +11,7 @@ package space.kscience.kmath.tensors.core
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.operations.IntRing
-import space.kscience.kmath.structures.MutableBuffer
+import space.kscience.kmath.structures.*
 import space.kscience.kmath.tensors.api.*
 import space.kscience.kmath.tensors.core.internal.*
 import kotlin.math.*
@@ -23,10 +23,6 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
 
     public companion object : IntTensorAlgebra()
 
-    override fun StructureND<Int>.dot(other: StructureND<Int>): Tensor<Int> {
-        TODO("Not yet implemented")
-    }
-
     override val elementAlgebra: IntRing get() = IntRing
 
 
@@ -36,56 +32,64 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      * @param transform the function to be applied to each element of the tensor.
      * @return the resulting tensor after applying the function.
      */
-    @PerformancePitfall
     @Suppress("OVERRIDE_BY_INLINE")
     final override inline fun StructureND<Int>.map(transform: IntRing.(Int) -> Int): IntTensor {
         val tensor = this.asIntTensor()
         //TODO remove additional copy
-        val sourceArray = tensor.copyArray()
+        val array = IntBuffer(tensor.source.size) { IntRing.transform(tensor.source[it]) }
-        val array = IntArray(tensor.numElements) { IntRing.transform(sourceArray[it]) }
         return IntTensor(
             tensor.shape,
             array,
-            tensor.bufferStart
         )
     }
 
-    @PerformancePitfall
+    public inline fun Tensor<Int>.mapInPlace(operation: (Int) -> Int) {
+        if (this is IntTensor) {
+            source.mapInPlace(operation)
+        } else {
+            indices.forEach { set(it, operation(get(it))) }
+        }
+    }
+
+    public inline fun Tensor<Int>.mapIndexedInPlace(operation: (IntArray, Int) -> Int) {
+        indices.forEach { set(it, operation(it, get(it))) }
+    }
+
     @Suppress("OVERRIDE_BY_INLINE")
     final override inline fun StructureND<Int>.mapIndexed(transform: IntRing.(index: IntArray, Int) -> Int): IntTensor {
         val tensor = this.asIntTensor()
         //TODO remove additional copy
-        val sourceArray = tensor.copyArray()
+        val buffer = IntBuffer(tensor.source.size) {
-        val array = IntArray(tensor.numElements) { IntRing.transform(tensor.indices.index(it), sourceArray[it]) }
+            IntRing.transform(tensor.indices.index(it), tensor.source[it])
-        return IntTensor(
+        }
-            tensor.shape,
+        return IntTensor(tensor.shape, buffer)
-            array,
-            tensor.bufferStart
-        )
     }
 
-    @PerformancePitfall
+    @Suppress("OVERRIDE_BY_INLINE")
-    override fun zip(
+    final override inline fun zip(
         left: StructureND<Int>,
         right: StructureND<Int>,
         transform: IntRing.(Int, Int) -> Int,
     ): IntTensor {
-        require(left.shape.contentEquals(right.shape)) {
+        checkShapesCompatible(left, right)
-            "The shapes in zip are not equal: left - ${left.shape}, right - ${right.shape}"
+
-        }
         val leftTensor = left.asIntTensor()
-        val leftArray = leftTensor.copyArray()
         val rightTensor = right.asIntTensor()
-        val rightArray = rightTensor.copyArray()
+        val buffer = IntBuffer(leftTensor.source.size) {
-        val array = IntArray(leftTensor.numElements) { IntRing.transform(leftArray[it], rightArray[it]) }
+            IntRing.transform(leftTensor.source[it], rightTensor.source[it])
-        return IntTensor(
+        }
-            leftTensor.shape,
+        return IntTensor(leftTensor.shape, buffer)
-            array
-        )
     }
 
-    override fun StructureND<Int>.valueOrNull(): Int? = if (asIntTensor().shape contentEquals intArrayOf(1))
+
-        asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart] else null
+    public inline fun StructureND<Int>.reduceElements(transform: (IntBuffer) -> Int): Int =
+        transform(asIntTensor().source.copy())
+    //TODO do we need protective copy?
+
+    override fun StructureND<Int>.valueOrNull(): Int? {
+        val dt = asIntTensor()
+        return if (dt.shape contentEquals intArrayOf(1)) dt.source[0] else null
+    }
 
     override fun StructureND<Int>.value(): Int = valueOrNull()
         ?: throw IllegalArgumentException("The tensor shape is $shape, but value method is allowed only for shape [1]")
@@ -94,16 +98,16 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      * Constructs a tensor with the specified shape and data.
      *
      * @param shape the desired shape for the tensor.
-     * @param buffer one-dimensional data array.
+     * @param array one-dimensional data array.
-     * @return tensor with the [shape] shape and [buffer] data.
+     * @return tensor with the [shape] shape and [array] data.
      */
-    public fun fromArray(shape: IntArray, buffer: IntArray): IntTensor {
+    public fun fromArray(shape: IntArray, array: IntArray): IntTensor {
-        checkEmptyShape(shape)
+        checkNotEmptyShape(shape)
-        check(buffer.isNotEmpty()) { "Illegal empty buffer provided" }
+        check(array.isNotEmpty()) { "Illegal empty buffer provided" }
-        check(buffer.size == shape.reduce(Int::times)) {
+        check(array.size == shape.reduce(Int::times)) {
-            "Inconsistent shape ${shape.toList()} for buffer of size ${buffer.size} provided"
+            "Inconsistent shape ${shape.toList()} for buffer of size ${array.size} provided"
         }
-        return IntTensor(shape, buffer, 0)
+        return IntTensor(shape, array.asBuffer())
     }
 
     /**
@@ -119,10 +123,10 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
     )
 
     override fun Tensor<Int>.getTensor(i: Int): IntTensor {
-        val lastShape = asIntTensor().shape.drop(1).toIntArray()
+        val dt = asIntTensor()
+        val lastShape = shape.drop(1).toIntArray()
         val newShape = if (lastShape.isNotEmpty()) lastShape else intArrayOf(1)
-        val newStart = newShape.reduce(Int::times) * i + asIntTensor().bufferStart
+        return IntTensor(newShape, dt.source.view(newShape.reduce(Int::times) * i))
-        return IntTensor(newShape, asIntTensor().mutableBuffer.array(), newStart)
     }
 
     /**
@@ -133,8 +137,8 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      * @return tensor with the [shape] shape and filled with [value].
      */
     public fun full(value: Int, shape: IntArray): IntTensor {
-        checkEmptyShape(shape)
+        checkNotEmptyShape(shape)
-        val buffer = IntArray(shape.reduce(Int::times)) { value }
+        val buffer = IntBuffer(shape.reduce(Int::times)) { value }
         return IntTensor(shape, buffer)
     }
 
@@ -144,9 +148,9 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      * @param value the value to fill the output tensor with.
      * @return tensor with the `input` tensor shape and filled with [value].
      */
-    public fun Tensor<Int>.fullLike(value: Int): IntTensor {
+    public fun fullLike(structureND: StructureND<*>, value: Int): IntTensor {
-        val shape = asIntTensor().shape
+        val shape = structureND.shape
-        val buffer = IntArray(asIntTensor().numElements) { value }
+        val buffer = IntBuffer(structureND.indices.linearSize) { value }
         return IntTensor(shape, buffer)
     }
 
@@ -163,7 +167,7 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      *
      * @return tensor filled with the scalar value `0`, with the same shape as `input` tensor.
      */
-    public fun StructureND<Int>.zeroesLike(): IntTensor = asIntTensor().fullLike(0)
+    public fun zeroesLike(structureND: StructureND<Int>): IntTensor = fullLike(structureND.asIntTensor(), 0)
 
     /**
      * Returns a tensor filled with the scalar value `1`, with the shape defined by the variable argument [shape].
@@ -178,7 +182,7 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      *
      * @return tensor filled with the scalar value `1`, with the same shape as `input` tensor.
      */
-    public fun Tensor<Int>.onesLike(): IntTensor = asIntTensor().fullLike(1)
+    public fun onesLike(structureND: Tensor<*>): IntTensor = fullLike(structureND, 1)
 
     /**
      * Returns a 2D tensor with shape ([n], [n]), with ones on the diagonal and zeros elsewhere.
@@ -188,7 +192,7 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      */
     public fun eye(n: Int): IntTensor {
         val shape = intArrayOf(n, n)
-        val buffer = IntArray(n * n) { 0 }
+        val buffer = IntBuffer(n * n) { 0 }
         val res = IntTensor(shape, buffer)
         for (i in 0 until n) {
             res[intArrayOf(i, i)] = 1
@@ -196,151 +200,92 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
         return res
     }
 
-    /**
+    override fun Int.plus(arg: StructureND<Int>): IntTensor = arg.map { this@plus + it }
-     * Return a copy of the tensor.
-     *
-     * @return a copy of the `input` tensor with a copied buffer.
-     */
-    public fun StructureND<Int>.copy(): IntTensor =
-        IntTensor(asIntTensor().shape, asIntTensor().mutableBuffer.array().copyOf(), asIntTensor().bufferStart)
 
-    override fun Int.plus(arg: StructureND<Int>): IntTensor {
+    override fun StructureND<Int>.plus(arg: Int): IntTensor = map { it + arg }
-        val resBuffer = IntArray(arg.asIntTensor().numElements) { i ->
-            arg.asIntTensor().mutableBuffer.array()[arg.asIntTensor().bufferStart + i] + this
-        }
-        return IntTensor(arg.shape, resBuffer)
-    }
 
-    override fun StructureND<Int>.plus(arg: Int): IntTensor = arg + asIntTensor()
+    override fun StructureND<Int>.plus(arg: StructureND<Int>): IntTensor = zip(this, arg) { l, r -> l + r }
-
-    override fun StructureND<Int>.plus(arg: StructureND<Int>): IntTensor {
-        checkShapesCompatible(asIntTensor(), arg.asIntTensor())
-        val resBuffer = IntArray(asIntTensor().numElements) { i ->
-            asIntTensor().mutableBuffer.array()[i] + arg.asIntTensor().mutableBuffer.array()[i]
-        }
-        return IntTensor(asIntTensor().shape, resBuffer)
-    }
 
     override fun Tensor<Int>.plusAssign(value: Int) {
-        for (i in 0 until asIntTensor().numElements) {
+        mapInPlace { it + value }
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] += value
-        }
     }
 
     override fun Tensor<Int>.plusAssign(arg: StructureND<Int>) {
         checkShapesCompatible(asIntTensor(), arg.asIntTensor())
-        for (i in 0 until asIntTensor().numElements) {
+        mapIndexedInPlace { index, value ->
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] +=
+            value + arg[index]
-                arg.asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i]
         }
     }
 
-    override fun Int.minus(arg: StructureND<Int>): IntTensor {
+    override fun Int.minus(arg: StructureND<Int>): IntTensor = arg.map { this@minus - it }
-        val resBuffer = IntArray(arg.asIntTensor().numElements) { i ->
-            this - arg.asIntTensor().mutableBuffer.array()[arg.asIntTensor().bufferStart + i]
-        }
-        return IntTensor(arg.shape, resBuffer)
-    }
 
-    override fun StructureND<Int>.minus(arg: Int): IntTensor {
+    override fun StructureND<Int>.minus(arg: Int): IntTensor = map { it - arg }
-        val resBuffer = IntArray(asIntTensor().numElements) { i ->
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] - arg
-        }
-        return IntTensor(asIntTensor().shape, resBuffer)
-    }
 
-    override fun StructureND<Int>.minus(arg: StructureND<Int>): IntTensor {
+    override fun StructureND<Int>.minus(arg: StructureND<Int>): IntTensor = zip(this, arg) { l, r -> l + r }
-        checkShapesCompatible(asIntTensor(), arg)
-        val resBuffer = IntArray(asIntTensor().numElements) { i ->
-            asIntTensor().mutableBuffer.array()[i] - arg.asIntTensor().mutableBuffer.array()[i]
-        }
-        return IntTensor(asIntTensor().shape, resBuffer)
-    }
 
     override fun Tensor<Int>.minusAssign(value: Int) {
-        for (i in 0 until asIntTensor().numElements) {
+        mapInPlace { it - value }
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] -= value
-        }
     }
 
     override fun Tensor<Int>.minusAssign(arg: StructureND<Int>) {
-        checkShapesCompatible(asIntTensor(), arg)
+        checkShapesCompatible(this, arg)
-        for (i in 0 until asIntTensor().numElements) {
+        mapIndexedInPlace { index, value -> value - arg[index] }
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] -=
-                arg.asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i]
-        }
     }
 
-    override fun Int.times(arg: StructureND<Int>): IntTensor {
+    override fun Int.times(arg: StructureND<Int>): IntTensor = arg.map { this@times * it }
-        val resBuffer = IntArray(arg.asIntTensor().numElements) { i ->
-            arg.asIntTensor().mutableBuffer.array()[arg.asIntTensor().bufferStart + i] * this
-        }
-        return IntTensor(arg.shape, resBuffer)
-    }
 
     override fun StructureND<Int>.times(arg: Int): IntTensor = arg * asIntTensor()
 
-    override fun StructureND<Int>.times(arg: StructureND<Int>): IntTensor {
+    override fun StructureND<Int>.times(arg: StructureND<Int>): IntTensor = zip(this, arg) { l, r -> l * r }
-        checkShapesCompatible(asIntTensor(), arg)
-        val resBuffer = IntArray(asIntTensor().numElements) { i ->
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] *
-                    arg.asIntTensor().mutableBuffer.array()[arg.asIntTensor().bufferStart + i]
-        }
-        return IntTensor(asIntTensor().shape, resBuffer)
-    }
 
     override fun Tensor<Int>.timesAssign(value: Int) {
-        for (i in 0 until asIntTensor().numElements) {
+        mapInPlace { it * value }
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] *= value
-        }
     }
 
     override fun Tensor<Int>.timesAssign(arg: StructureND<Int>) {
-        checkShapesCompatible(asIntTensor(), arg)
+        checkShapesCompatible(this, arg)
-        for (i in 0 until asIntTensor().numElements) {
+        mapIndexedInPlace { index, value -> value * arg[index] }
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i] *=
-                arg.asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i]
-        }
     }
 
-    override fun StructureND<Int>.unaryMinus(): IntTensor {
+    override fun StructureND<Int>.unaryMinus(): IntTensor = map { -it }
-        val resBuffer = IntArray(asIntTensor().numElements) { i ->
-            asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + i].unaryMinus()
-        }
-        return IntTensor(asIntTensor().shape, resBuffer)
-    }
 
-    override fun Tensor<Int>.transpose(i: Int, j: Int): IntTensor {
+    override fun Tensor<Int>.transposed(i: Int, j: Int): IntTensor {
-        val ii = asIntTensor().minusIndex(i)
+        // TODO change strides instead of changing content
-        val jj = asIntTensor().minusIndex(j)
+        val dt = asIntTensor()
-        checkTranspose(asIntTensor().dimension, ii, jj)
+        val ii = dt.minusIndex(i)
-        val n = asIntTensor().numElements
+        val jj = dt.minusIndex(j)
+        checkTranspose(dt.dimension, ii, jj)
+        val n = dt.linearSize
         val resBuffer = IntArray(n)
 
-        val resShape = asIntTensor().shape.copyOf()
+        val resShape = dt.shape.copyOf()
         resShape[ii] = resShape[jj].also { resShape[jj] = resShape[ii] }
 
-        val resTensor = IntTensor(resShape, resBuffer)
+        val resTensor = IntTensor(resShape, resBuffer.asBuffer())
 
         for (offset in 0 until n) {
-            val oldMultiIndex = asIntTensor().indices.index(offset)
+            val oldMultiIndex = dt.indices.index(offset)
             val newMultiIndex = oldMultiIndex.copyOf()
             newMultiIndex[ii] = newMultiIndex[jj].also { newMultiIndex[jj] = newMultiIndex[ii] }
 
             val linearIndex = resTensor.indices.offset(newMultiIndex)
-            resTensor.mutableBuffer.array()[linearIndex] =
+            resTensor.source[linearIndex] = dt.source[offset]
-                asIntTensor().mutableBuffer.array()[asIntTensor().bufferStart + offset]
         }
         return resTensor
     }
 
     override fun Tensor<Int>.view(shape: IntArray): IntTensor {
         checkView(asIntTensor(), shape)
-        return IntTensor(shape, asIntTensor().mutableBuffer.array(), asIntTensor().bufferStart)
+        return IntTensor(shape, asIntTensor().source)
     }
 
     override fun Tensor<Int>.viewAs(other: StructureND<Int>): IntTensor =
-        asIntTensor().view(other.shape)
+        view(other.shape)
+
+    override fun StructureND<Int>.dot(other: StructureND<Int>): IntTensor {
+        return if (dimension in 0..2 && other.dimension in 0..2) TODO("not implemented")
+        else error("Only vectors and matrices are allowed in non-broadcasting dot operation")
+    }
 
     override fun diagonalEmbedding(
         diagonalEntries: Tensor<Int>,
@@ -374,7 +319,7 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
                 diagonalEntries.shape.slice(greaterDim - 1 until n - 1).toIntArray()
         val resTensor = zeros(resShape)
 
-        for (i in 0 until diagonalEntries.asIntTensor().numElements) {
+        for (i in 0 until diagonalEntries.asIntTensor().linearSize) {
             val multiIndex = diagonalEntries.asIntTensor().indices.index(i)
 
             var offset1 = 0
@@ -394,16 +339,27 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
         return resTensor.asIntTensor()
     }
 
-    private infix fun Tensor<Int>.eq(
+    /**
+     * Compares element-wise two int tensors
+     *
+     * @param other the tensor to compare with `input` tensor.
+     * @param epsilon permissible error when comparing two Int values.
+     * @return true if two tensors have the same shape and elements, false otherwise.
+     */
+    public fun Tensor<Int>.eq(other: Tensor<Int>): Boolean =
+        asIntTensor().eq(other) { x, y -> x == y }
+
+    private fun Tensor<Int>.eq(
         other: Tensor<Int>,
+        eqFunction: (Int, Int) -> Boolean,
     ): Boolean {
         checkShapesCompatible(asIntTensor(), other)
-        val n = asIntTensor().numElements
+        val n = asIntTensor().linearSize
-        if (n != other.asIntTensor().numElements) {
+        if (n != other.asIntTensor().linearSize) {
             return false
         }
         for (i in 0 until n) {
-            if (asIntTensor().mutableBuffer[asIntTensor().bufferStart + i] != other.asIntTensor().mutableBuffer[other.asIntTensor().bufferStart + i]) {
+            if (!eqFunction(asIntTensor().source[i], other.asIntTensor().source[i])) {
                 return false
             }
         }
@@ -421,10 +377,12 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
         val shape = tensors[0].shape
         check(tensors.all { it.shape contentEquals shape }) { "Tensors must have same shapes" }
         val resShape = intArrayOf(tensors.size) + shape
-        val resBuffer = tensors.flatMap {
+//        val resBuffer: List<Int> = tensors.flatMap {
-            it.asIntTensor().mutableBuffer.array().drop(it.asIntTensor().bufferStart).take(it.asIntTensor().numElements)
+//            it.asIntTensor().source.array.drop(it.asIntTensor().bufferStart)
-        }.toIntArray()
+//                .take(it.asIntTensor().linearSize)
-        return IntTensor(resShape, resBuffer, 0)
+//        }
+        val resBuffer = tensors.map { it.asIntTensor().source }.concat()
+        return IntTensor(resShape, resBuffer)
     }
 
     /**
@@ -435,14 +393,11 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      */
     public fun Tensor<Int>.rowsByIndices(indices: IntArray): IntTensor = stack(indices.map { getTensor(it) })
 
-    private inline fun StructureND<Int>.fold(foldFunction: (IntArray) -> Int): Int =
+    private inline fun StructureND<Int>.foldDimToInt(
-        foldFunction(asIntTensor().copyArray())
-
-    private inline fun <reified R : Any> StructureND<Int>.foldDim(
         dim: Int,
         keepDim: Boolean,
-        foldFunction: (IntArray) -> R,
+        foldFunction: (IntArray) -> Int,
-    ): BufferedTensor<R> {
+    ): IntTensor {
         check(dim < dimension) { "Dimension $dim out of range $dimension" }
         val resShape = if (keepDim) {
             shape.take(dim).toIntArray() + intArrayOf(1) + shape.takeLast(dimension - dim - 1).toIntArray()
@@ -451,9 +406,9 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
         }
         val resNumElements = resShape.reduce(Int::times)
         val init = foldFunction(IntArray(1) { 0 })
-        val resTensor = BufferedTensor(
+        val resTensor = IntTensor(
             resShape,
-            MutableBuffer.auto(resNumElements) { init }, 0
+            IntBuffer(resNumElements) { init }
         )
         for (index in resTensor.indices) {
             val prefix = index.take(dim).toIntArray()
@@ -465,31 +420,33 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
         return resTensor
     }
 
-    override fun StructureND<Int>.sum(): Int = asIntTensor().fold { it.sum() }
+
+    override fun StructureND<Int>.sum(): Int = reduceElements { it.array.sum() }
 
     override fun StructureND<Int>.sum(dim: Int, keepDim: Boolean): IntTensor =
-        foldDim(dim, keepDim) { x -> x.sum() }.asIntTensor()
+        foldDimToInt(dim, keepDim) { x -> x.sum() }
 
-    override fun StructureND<Int>.min(): Int = this.fold { it.minOrNull()!! }
+    override fun StructureND<Int>.min(): Int = reduceElements { it.array.min() }
 
     override fun StructureND<Int>.min(dim: Int, keepDim: Boolean): IntTensor =
-        foldDim(dim, keepDim) { x -> x.minOrNull()!! }.asIntTensor()
+        foldDimToInt(dim, keepDim) { x -> x.minOrNull()!! }
 
-    override fun StructureND<Int>.argMin(dim: Int, keepDim: Boolean): IntTensor =
+    override fun StructureND<Int>.argMin(dim: Int, keepDim: Boolean): Tensor<Int> = foldDimToInt(dim, keepDim) { x ->
-        foldDim(dim, keepDim) { x ->
+        x.withIndex().minBy { it.value }.index
-            x.withIndex().minByOrNull { it.value }?.index!!
+    }
-        }.asIntTensor()
 
-    override fun StructureND<Int>.max(): Int = this.fold { it.maxOrNull()!! }
+    override fun StructureND<Int>.max(): Int = reduceElements { it.array.max() }
 
     override fun StructureND<Int>.max(dim: Int, keepDim: Boolean): IntTensor =
-        foldDim(dim, keepDim) { x -> x.maxOrNull()!! }.asIntTensor()
+        foldDimToInt(dim, keepDim) { x -> x.max() }
 
 
     override fun StructureND<Int>.argMax(dim: Int, keepDim: Boolean): IntTensor =
-        foldDim(dim, keepDim) { x ->
+        foldDimToInt(dim, keepDim) { x ->
-            x.withIndex().maxByOrNull { it.value }?.index!!
+            x.withIndex().maxBy { it.value }.index
-        }.asIntTensor()
+        }
+
+    public fun StructureND<Int>.mean(): Double = sum().toDouble() / indices.linearSize
 }
 
 public val Int.Companion.tensorAlgebra: IntTensorAlgebra get() = IntTensorAlgebra

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

@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.tensors.core.internal
 
+import space.kscience.kmath.structures.asBuffer
 import space.kscience.kmath.tensors.core.DoubleTensor
 import kotlin.math.max
 
@@ -24,8 +25,8 @@ internal fun multiIndexBroadCasting(tensor: DoubleTensor, resTensor: DoubleTenso
         }
 
         val curLinearIndex = tensor.indices.offset(curMultiIndex)
-        resTensor.mutableBuffer.array()[linearIndex] =
+        resTensor.source[linearIndex] =
-            tensor.mutableBuffer.array()[tensor.bufferStart + curLinearIndex]
+            tensor.source[curLinearIndex]
     }
 }
 
@@ -63,7 +64,7 @@ internal fun broadcastTo(tensor: DoubleTensor, newShape: IntArray): DoubleTensor
     }
 
     val n = newShape.reduce { acc, i -> acc * i }
-    val resTensor = DoubleTensor(newShape, DoubleArray(n))
+    val resTensor = DoubleTensor(newShape, DoubleArray(n).asBuffer())
 
     for (i in tensor.shape.indices) {
         val curDim = tensor.shape[i]
@@ -82,7 +83,7 @@ internal fun broadcastTensors(vararg tensors: DoubleTensor): List<DoubleTensor>
     val n = totalShape.reduce { acc, i -> acc * i }
 
     return tensors.map { tensor ->
-        val resTensor = DoubleTensor(totalShape, DoubleArray(n))
+        val resTensor = DoubleTensor(totalShape, DoubleArray(n).asBuffer())
         multiIndexBroadCasting(tensor, resTensor, n)
         resTensor
     }
@@ -106,17 +107,17 @@ internal fun broadcastOuterTensors(vararg tensors: DoubleTensor): List<DoubleTen
         for (tensor in tensors) {
             val matrixShape = tensor.shape.sliceArray(tensor.shape.size - 2 until tensor.shape.size).copyOf()
             val matrixSize = matrixShape[0] * matrixShape[1]
-            val matrix = DoubleTensor(matrixShape, DoubleArray(matrixSize))
+            val matrix = DoubleTensor(matrixShape, DoubleArray(matrixSize).asBuffer())
 
-            val outerTensor = DoubleTensor(totalShape, DoubleArray(n))
+            val outerTensor = DoubleTensor(totalShape, DoubleArray(n).asBuffer())
-            val resTensor = DoubleTensor(totalShape + matrixShape, DoubleArray(n * matrixSize))
+            val resTensor = DoubleTensor(totalShape + matrixShape, DoubleArray(n * matrixSize).asBuffer())
 
             for (linearIndex in 0 until n) {
                 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
 
-                val newTensor = DoubleTensor(curMultiIndex + matrixShape, tensor.mutableBuffer.array())
+                val newTensor = DoubleTensor(curMultiIndex + matrixShape, tensor.source)
 
                 for (i in curMultiIndex.indices) {
                     if (curMultiIndex[i] != 1) {
@@ -136,8 +137,8 @@ internal fun broadcastOuterTensors(vararg tensors: DoubleTensor): List<DoubleTen
                                 matrix.indices.index(i)
                     )
 
-                    resTensor.mutableBuffer.array()[resTensor.bufferStart + newLinearIndex] =
+                    resTensor.source[newLinearIndex] =
-                        newTensor.mutableBuffer.array()[newTensor.bufferStart + curLinearIndex]
+                        newTensor.source[curLinearIndex]
                 }
             }
             add(resTensor)

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

@@ -9,9 +9,10 @@ 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
+import space.kscience.kmath.tensors.core.asDoubleTensor
 
 
-internal fun checkEmptyShape(shape: IntArray) =
+internal fun checkNotEmptyShape(shape: IntArray) =
     check(shape.isNotEmpty()) {
         "Illegal empty shape provided"
     }
@@ -25,7 +26,8 @@ internal fun checkBufferShapeConsistency(shape: IntArray, buffer: DoubleArray) =
         "Inconsistent shape ${shape.toList()} for buffer of size ${buffer.size} provided"
     }
 
-internal fun <T> checkShapesCompatible(a: StructureND<T>, b: StructureND<T>) =
+@PublishedApi
+internal fun <T> checkShapesCompatible(a: StructureND<T>, b: StructureND<T>): Unit =
     check(a.shape contentEquals b.shape) {
         "Incompatible shapes ${a.shape.toList()} and ${b.shape.toList()} "
     }
@@ -50,15 +52,14 @@ internal fun checkSquareMatrix(shape: IntArray) {
 
 internal fun DoubleTensorAlgebra.checkSymmetric(
     tensor: Tensor<Double>, epsilon: Double = 1e-6,
-) =
+) = check(tensor.eq(tensor.transposed(), epsilon)) {
-    check(tensor.eq(tensor.transpose(), epsilon)) {
+    "Tensor is not symmetric about the last 2 dimensions at precision $epsilon"
-        "Tensor is not symmetric about the last 2 dimensions at precision $epsilon"
+}
-    }
 
 internal fun DoubleTensorAlgebra.checkPositiveDefinite(tensor: DoubleTensor, epsilon: Double = 1e-6) {
     checkSymmetric(tensor, epsilon)
     for (mat in tensor.matrixSequence())
-        check(mat.toTensor().detLU().value() > 0.0) {
+        check(mat.asDoubleTensor().detLU().value() > 0.0) {
-            "Tensor contains matrices which are not positive definite ${mat.toTensor().detLU().value()}"
+            "Tensor contains matrices which are not positive definite ${mat.asDoubleTensor().detLU().value()}"
         }
 }

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

@@ -0,0 +1,189 @@
+/*
+ * Copyright 2018-2022 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.tensors.core.internal
+
+import space.kscience.kmath.nd.MutableStructure2D
+import space.kscience.kmath.nd.Structure2D
+import space.kscience.kmath.nd.as2D
+import space.kscience.kmath.nd.get
+import space.kscience.kmath.operations.asSequence
+import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.VirtualBuffer
+import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.structures.indices
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.eye
+import space.kscience.kmath.tensors.core.BufferedTensor
+import space.kscience.kmath.tensors.core.DoubleTensor
+import space.kscience.kmath.tensors.core.OffsetDoubleBuffer
+import space.kscience.kmath.tensors.core.copyToTensor
+import kotlin.math.abs
+import kotlin.math.max
+import kotlin.math.sqrt
+
+
+internal fun MutableStructure2D<Double>.jacobiHelper(
+    maxIteration: Int,
+    epsilon: Double,
+): Pair<DoubleBuffer, Structure2D<Double>> {
+    val n = rowNum
+    val A_ = copyToTensor()
+    val V = eye(n)
+    val D = DoubleBuffer(n) { get(it, it) }
+    val B = DoubleBuffer(n) { get(it, it) }
+    val Z = DoubleBuffer(n) { 0.0 }
+
+    // assume that buffered tensor is square matrix
+    operator fun DoubleTensor.get(i: Int, j: Int): Double {
+        return source[i * shape[0] + j]
+    }
+
+    operator fun BufferedTensor<Double>.set(i: Int, j: Int, value: Double) {
+        source[i * shape[0] + j] = value
+    }
+
+    fun maxOffDiagonal(matrix: BufferedTensor<Double>): Double {
+        var maxOffDiagonalElement = 0.0
+        for (i in 0 until n - 1) {
+            for (j in i + 1 until n) {
+                maxOffDiagonalElement = max(maxOffDiagonalElement, abs(matrix[i, j]))
+            }
+        }
+        return maxOffDiagonalElement
+    }
+
+    fun rotate(a: BufferedTensor<Double>, s: Double, tau: Double, i: Int, j: Int, k: Int, l: Int) {
+        val g = a[i, j]
+        val h = a[k, l]
+        a[i, j] = g - s * (h + g * tau)
+        a[k, l] = h + s * (g - h * tau)
+    }
+
+    fun jacobiIteration(
+        a: BufferedTensor<Double>,
+        v: BufferedTensor<Double>,
+        d: DoubleBuffer,
+        z: DoubleBuffer,
+    ) {
+        for (ip in 0 until n - 1) {
+            for (iq in ip + 1 until n) {
+                val g = 100.0 * abs(a[ip, iq])
+
+                if (g <= epsilon * abs(d[ip]) && g <= epsilon * abs(d[iq])) {
+                    a[ip, iq] = 0.0
+                    continue
+                }
+
+                var h = d[iq] - d[ip]
+                val t = when {
+                    g <= epsilon * abs(h) -> (a[ip, iq]) / h
+                    else -> {
+                        val theta = 0.5 * h / (a[ip, iq])
+                        val denominator = abs(theta) + sqrt(1.0 + theta * theta)
+                        if (theta < 0.0) -1.0 / denominator else 1.0 / denominator
+                    }
+                }
+
+                val c = 1.0 / sqrt(1 + t * t)
+                val s = t * c
+                val tau = s / (1.0 + c)
+                h = t * a[ip, iq]
+                z[ip] -= h
+                z[iq] += h
+                d[ip] -= h
+                d[iq] += h
+                a[ip, iq] = 0.0
+
+                for (j in 0 until ip) {
+                    rotate(a, s, tau, j, ip, j, iq)
+                }
+                for (j in (ip + 1) until iq) {
+                    rotate(a, s, tau, ip, j, j, iq)
+                }
+                for (j in (iq + 1) until n) {
+                    rotate(a, s, tau, ip, j, iq, j)
+                }
+                for (j in 0 until n) {
+                    rotate(v, s, tau, j, ip, j, iq)
+                }
+            }
+        }
+    }
+
+    fun updateDiagonal(
+        d: DoubleBuffer,
+        z: DoubleBuffer,
+        b: DoubleBuffer,
+    ) {
+        for (ip in 0 until d.size) {
+            b[ip] += z[ip]
+            d[ip] = b[ip]
+            z[ip] = 0.0
+        }
+    }
+
+    var sm = maxOffDiagonal(A_)
+    for (iteration in 0 until maxIteration) {
+        if (sm < epsilon) {
+            break
+        }
+
+        jacobiIteration(A_, V, D, Z)
+        updateDiagonal(D, Z, B)
+        sm = maxOffDiagonal(A_)
+    }
+
+    // TODO sort eigenvalues
+    return D to V.as2D()
+}
+
+/**
+ * Concatenate a list of arrays
+ */
+internal fun List<OffsetDoubleBuffer>.concat(): DoubleBuffer {
+    val array = DoubleArray(sumOf { it.size })
+    var pointer = 0
+    while (pointer < array.size) {
+        for (bufferIndex in indices) {
+            val buffer = get(bufferIndex)
+            for (innerIndex in buffer.indices) {
+                array[pointer] = buffer[innerIndex]
+                pointer++
+            }
+        }
+    }
+    return array.asBuffer()
+}
+
+internal val DoubleTensor.vectors: VirtualBuffer<DoubleTensor>
+    get() {
+        val n = shape.size
+        val vectorOffset = shape[n - 1]
+        val vectorShape = intArrayOf(shape.last())
+
+        return VirtualBuffer(linearSize / vectorOffset) { index ->
+            val offset = index * vectorOffset
+            DoubleTensor(vectorShape, source.view(offset))
+        }
+    }
+
+
+internal fun DoubleTensor.vectorSequence(): Sequence<DoubleTensor> = vectors.asSequence()
+
+
+internal val DoubleTensor.matrices: VirtualBuffer<DoubleTensor>
+    get(){
+    val n = shape.size
+    check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" }
+    val matrixOffset = shape[n - 1] * shape[n - 2]
+    val matrixShape = intArrayOf(shape[n - 2], shape[n - 1])
+
+    return VirtualBuffer(linearSize / matrixOffset) { index ->
+        val offset = index * matrixOffset
+        DoubleTensor(matrixShape, source.view(offset))
+    }
+}
+
+internal fun DoubleTensor.matrixSequence(): Sequence<DoubleTensor> = matrices.asSequence()

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

@@ -0,0 +1,64 @@
+/*
+ * Copyright 2018-2022 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.tensors.core.internal
+
+import space.kscience.kmath.operations.asSequence
+import space.kscience.kmath.structures.IntBuffer
+import space.kscience.kmath.structures.VirtualBuffer
+import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.structures.indices
+import space.kscience.kmath.tensors.core.IntTensor
+import space.kscience.kmath.tensors.core.OffsetIntBuffer
+
+/**
+ * Concatenate a list of arrays
+ */
+internal fun List<OffsetIntBuffer>.concat(): IntBuffer {
+    val array = IntArray(sumOf { it.size })
+    var pointer = 0
+    while (pointer < array.size) {
+        for (bufferIndex in indices) {
+            val buffer = get(bufferIndex)
+            for (innerIndex in buffer.indices) {
+                array[pointer] = buffer[innerIndex]
+                pointer++
+            }
+        }
+    }
+    return array.asBuffer()
+}
+
+
+internal val IntTensor.vectors: VirtualBuffer<IntTensor>
+    get() {
+        val n = shape.size
+        val vectorOffset = shape[n - 1]
+        val vectorShape = intArrayOf(shape.last())
+
+        return VirtualBuffer(linearSize / vectorOffset) { index ->
+            val offset = index * vectorOffset
+            IntTensor(vectorShape, source.view(offset))
+        }
+    }
+
+
+internal fun IntTensor.vectorSequence(): Sequence<IntTensor> = vectors.asSequence()
+
+
+internal val IntTensor.matrices: VirtualBuffer<IntTensor>
+    get(){
+        val n = shape.size
+        check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" }
+        val matrixOffset = shape[n - 1] * shape[n - 2]
+        val matrixShape = intArrayOf(shape[n - 2], shape[n - 1])
+
+        return VirtualBuffer(linearSize / matrixOffset) { index ->
+            val offset = index * matrixOffset
+            IntTensor(matrixShape, source.view(offset))
+        }
+    }
+
+internal fun IntTensor.matrixSequence(): Sequence<IntTensor> = matrices.asSequence()

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

@@ -5,75 +5,33 @@
 
 package space.kscience.kmath.tensors.core.internal
 
-import space.kscience.kmath.nd.MutableStructure1D
+import space.kscience.kmath.nd.*
-import space.kscience.kmath.nd.MutableStructure2D
-import space.kscience.kmath.nd.as1D
-import space.kscience.kmath.nd.as2D
-import space.kscience.kmath.operations.asSequence
 import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.structures.VirtualBuffer
+import space.kscience.kmath.structures.IntBuffer
-import space.kscience.kmath.tensors.core.BufferedTensor
+import space.kscience.kmath.structures.asBuffer
-import space.kscience.kmath.tensors.core.DoubleTensor
+import space.kscience.kmath.structures.indices
-import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.*
-import space.kscience.kmath.tensors.core.IntTensor
 import kotlin.math.abs
 import kotlin.math.min
 import kotlin.math.sqrt
 
-internal val <T> BufferedTensor<T>.vectors: VirtualBuffer<BufferedTensor<T>>
-    get() {
-        val n = shape.size
-        val vectorOffset = shape[n - 1]
-        val vectorShape = intArrayOf(shape.last())
-
-        return VirtualBuffer(numElements / vectorOffset) { index ->
-            val offset = index * vectorOffset
-            BufferedTensor(vectorShape, mutableBuffer, bufferStart + offset)
-        }
-    }
-
-
-internal fun <T> BufferedTensor<T>.vectorSequence(): Sequence<BufferedTensor<T>> = vectors.asSequence()
-
-/**
- * A random access alternative to [matrixSequence]
- */
-internal val <T> BufferedTensor<T>.matrices: VirtualBuffer<BufferedTensor<T>>
-    get() {
-        val n = shape.size
-        check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" }
-        val matrixOffset = shape[n - 1] * shape[n - 2]
-        val matrixShape = intArrayOf(shape[n - 2], shape[n - 1])
-
-        return VirtualBuffer(numElements / matrixOffset) { index ->
-            val offset = index * matrixOffset
-            BufferedTensor(matrixShape, mutableBuffer, bufferStart + offset)
-        }
-    }
-
-internal fun <T> BufferedTensor<T>.matrixSequence(): Sequence<BufferedTensor<T>> = matrices.asSequence()
-
 internal fun dotTo(
     a: BufferedTensor<Double>,
     b: BufferedTensor<Double>,
     res: BufferedTensor<Double>,
     l: Int, m: Int, n: Int,
 ) {
-    val aStart = a.bufferStart
+    val aBuffer = a.source
-    val bStart = b.bufferStart
+    val bBuffer = b.source
-    val resStart = res.bufferStart
+    val resBuffer = res.source
-
-    val aBuffer = a.mutableBuffer
-    val bBuffer = b.mutableBuffer
-    val resBuffer = res.mutableBuffer
 
     for (i in 0 until l) {
         for (j in 0 until n) {
             var curr = 0.0
             for (k in 0 until m) {
-                curr += aBuffer[aStart + i * m + k] * bBuffer[bStart + k * n + j]
+                curr += aBuffer[i * m + k] * bBuffer[k * n + j]
             }
-            resBuffer[resStart + i * n + j] = curr
+            resBuffer[i * n + j] = curr
         }
     }
 }
@@ -129,7 +87,7 @@ internal fun luHelper(
     return false
 }
 
-internal fun <T> BufferedTensor<T>.setUpPivots(): IntTensor {
+internal fun <T> StructureND<T>.setUpPivots(): IntTensor {
     val n = this.shape.size
     val m = this.shape.last()
     val pivotsShape = IntArray(n - 1) { i -> this.shape[i] }
@@ -137,17 +95,17 @@ internal fun <T> BufferedTensor<T>.setUpPivots(): IntTensor {
 
     return IntTensor(
         pivotsShape,
-        IntArray(pivotsShape.reduce(Int::times)) { 0 }
+        IntBuffer(pivotsShape.reduce(Int::times)) { 0 }
     )
 }
 
 internal fun DoubleTensorAlgebra.computeLU(
-    tensor: DoubleTensor,
+    tensor: StructureND<Double>,
     epsilon: Double,
 ): Pair<DoubleTensor, IntTensor>? {
 
     checkSquareMatrix(tensor.shape)
-    val luTensor = tensor.copy()
+    val luTensor = tensor.copyToTensor()
     val pivotsTensor = tensor.setUpPivots()
 
     for ((lu, pivots) in luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()))
@@ -253,8 +211,8 @@ internal fun DoubleTensorAlgebra.qrHelper(
     checkSquareMatrix(matrix.shape)
     val n = matrix.shape[0]
     val qM = q.as2D()
-    val matrixT = matrix.transpose(0, 1)
+    val matrixT = matrix.transposed(0, 1)
-    val qT = q.transpose(0, 1)
+    val qT = q.transposed(0, 1)
 
     for (j in 0 until n) {
         val v = matrixT.getTensor(j)
@@ -280,10 +238,10 @@ internal fun DoubleTensorAlgebra.svd1d(a: DoubleTensor, epsilon: Double = 1e-10)
     var v: DoubleTensor
     val b: DoubleTensor
     if (n > m) {
-        b = a.transpose(0, 1).dot(a)
+        b = a.transposed(0, 1).dot(a)
         v = DoubleTensor(intArrayOf(m), getRandomUnitVector(m, 0))
     } else {
-        b = a.dot(a.transpose(0, 1))
+        b = a.dot(a.transposed(0, 1))
         v = DoubleTensor(intArrayOf(n), getRandomUnitVector(n, 0))
     }
 
@@ -308,7 +266,7 @@ internal fun DoubleTensorAlgebra.svdHelper(
     val (matrixU, matrixS, matrixV) = USV
 
     for (k in 0 until min(n, m)) {
-        var a = matrix.copy()
+        var a = matrix.copyToTensor()
         for ((singularValue, u, v) in res.slice(0 until k)) {
             val outerProduct = DoubleArray(u.shape[0] * v.shape[0])
             for (i in 0 until u.shape[0]) {
@@ -316,7 +274,7 @@ internal fun DoubleTensorAlgebra.svdHelper(
                     outerProduct[i * v.shape[0] + j] = u.getTensor(i).value() * v.getTensor(j).value()
                 }
             }
-            a = a - singularValue.times(DoubleTensor(intArrayOf(u.shape[0], v.shape[0]), outerProduct))
+            a = a - singularValue.times(DoubleTensor(intArrayOf(u.shape[0], v.shape[0]), outerProduct.asBuffer()))
         }
         var v: DoubleTensor
         var u: DoubleTensor
@@ -328,7 +286,7 @@ internal fun DoubleTensorAlgebra.svdHelper(
             u = u.times(1.0 / norm)
         } else {
             u = svd1d(a, epsilon)
-            v = matrix.transpose(0, 1).dot(u)
+            v = matrix.transposed(0, 1).dot(u)
             norm = DoubleTensorAlgebra { (v dot v).sqrt().value() }
             v = v.times(1.0 / norm)
         }
@@ -337,15 +295,15 @@ internal fun DoubleTensorAlgebra.svdHelper(
     }
 
     val s = res.map { it.first }.toDoubleArray()
-    val uBuffer = res.map { it.second }.flatMap { it.mutableBuffer.array().toList() }.toDoubleArray()
+    val uBuffer = res.map { it.second.source }.concat()
-    val vBuffer = res.map { it.third }.flatMap { it.mutableBuffer.array().toList() }.toDoubleArray()
+    val vBuffer = res.map { it.third.source }.concat()
     for (i in uBuffer.indices) {
-        matrixU.mutableBuffer.array()[matrixU.bufferStart + i] = uBuffer[i]
+        matrixU.source[i] = uBuffer[i]
     }
     for (i in s.indices) {
-        matrixS.mutableBuffer.array()[matrixS.bufferStart + i] = s[i]
+        matrixS.source[i] = s[i]
     }
     for (i in vBuffer.indices) {
-        matrixV.mutableBuffer.array()[matrixV.bufferStart + i] = vBuffer[i]
+        matrixV.source[i] = vBuffer[i]
     }
 }

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

@@ -1,37 +0,0 @@
-/*
- * Copyright 2018-2022 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
- */
-
-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.core.BufferedTensor
-import space.kscience.kmath.tensors.core.DoubleTensor
-import space.kscience.kmath.tensors.core.IntTensor
-import space.kscience.kmath.tensors.core.TensorLinearStructure
-
-internal fun BufferedTensor<Int>.toTensor(): IntTensor =
-    IntTensor(this.shape, this.mutableBuffer.array(), this.bufferStart)
-
-internal fun BufferedTensor<Double>.toTensor(): DoubleTensor =
-    DoubleTensor(this.shape, this.mutableBuffer.array(), this.bufferStart)
-
-internal fun <T> StructureND<T>.copyToBufferedTensor(): BufferedTensor<T> =
-    BufferedTensor(
-        this.shape,
-        TensorLinearStructure(this.shape).asSequence().map(this::get).toMutableList().asMutableBuffer(),
-        0
-    )
-
-internal fun <T> StructureND<T>.toBufferedTensor(): BufferedTensor<T> = when (this) {
-    is BufferedTensor<T> -> this
-    is MutableBufferND<T> -> if (this.indices == TensorLinearStructure(this.shape)) {
-        BufferedTensor(this.shape, this.buffer, 0)
-    } else {
-        this.copyToBufferedTensor()
-    }
-    else -> this.copyToBufferedTensor()
-}

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

@@ -6,41 +6,25 @@
 package space.kscience.kmath.tensors.core.internal
 
 import space.kscience.kmath.nd.as1D
+import space.kscience.kmath.operations.DoubleBufferOps.Companion.map
 import space.kscience.kmath.operations.toMutableList
 import space.kscience.kmath.samplers.GaussianSampler
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.structures.*
+import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.tensors.core.BufferedTensor
 import space.kscience.kmath.tensors.core.DoubleTensor
 import kotlin.math.*
 
-/**
+internal fun getRandomNormals(n: Int, seed: Long): DoubleBuffer {
- * Returns a reference to [IntArray] containing all the elements of this [Buffer] or copy the data.
- */
-internal fun Buffer<Int>.array(): IntArray = when (this) {
-    is IntBuffer -> array
-    else -> this.toIntArray()
-}
-
-/**
- * Returns a reference to [DoubleArray] containing all the elements of this [Buffer] or copy the data.
- */
-@PublishedApi
-internal fun Buffer<Double>.array(): DoubleArray = when (this) {
-    is DoubleBuffer -> array
-    else -> this.toDoubleArray()
-}
-
-internal fun getRandomNormals(n: Int, seed: Long): DoubleArray {
     val distribution = GaussianSampler(0.0, 1.0)
     val generator = RandomGenerator.default(seed)
-    return distribution.sample(generator).nextBufferBlocking(n).toDoubleArray()
+    return distribution.sample(generator).nextBufferBlocking(n)
 }
 
-internal fun getRandomUnitVector(n: Int, seed: Long): DoubleArray {
+internal fun getRandomUnitVector(n: Int, seed: Long): DoubleBuffer {
-    val unnorm = getRandomNormals(n, seed)
+    val unnorm: DoubleBuffer = getRandomNormals(n, seed)
-    val norm = sqrt(unnorm.sumOf { it * it })
+    val norm = sqrt(unnorm.array.sumOf { it * it })
-    return unnorm.map { it / norm }.toDoubleArray()
+    return unnorm.map { it / norm }
 }
 
 internal fun minusIndexFrom(n: Int, i: Int): Int = if (i >= 0) i else {
@@ -71,6 +55,7 @@ internal fun format(value: Double, digits: Int = 4): String = buildString {
                 append("e+")
                 append(order)
             }
+
             else -> {
                 append('e')
                 append(order)
@@ -116,7 +101,7 @@ internal fun DoubleTensor.toPrettyString(): String = buildString {
         }
 
         offset += vectorSize
-        if (this@toPrettyString.numElements == offset) {
+        if (this@toPrettyString.linearSize == offset) {
             break
         }
 

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

@@ -1,46 +0,0 @@
-/*
- * Copyright 2018-2022 KMath contributors.
- * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
- */
-
-package space.kscience.kmath.tensors.core
-
-import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.tensors.api.Tensor
-import space.kscience.kmath.tensors.core.internal.toBufferedTensor
-import space.kscience.kmath.tensors.core.internal.toTensor
-
-/**
- * Casts [Tensor] of [Double] to [DoubleTensor]
- */
-public fun StructureND<Double>.asDoubleTensor(): DoubleTensor = when (this) {
-    is DoubleTensor -> this
-    else -> this.toBufferedTensor().toTensor()
-}
-
-/**
- * Casts [Tensor] of [Int] to [IntTensor]
- */
-public fun StructureND<Int>.asIntTensor(): IntTensor = when (this) {
-    is IntTensor -> this
-    else -> this.toBufferedTensor().toTensor()
-}
-
-/**
- * Returns a copy-protected [DoubleArray] of tensor elements
- */
-public fun DoubleTensor.copyArray(): DoubleArray {
-    //TODO use ArrayCopy
-    return DoubleArray(numElements) { i ->
-        mutableBuffer[bufferStart + i]
-    }
-}
-
-/**
- * Returns a copy-protected [IntArray] of tensor elements
- */
-public fun IntTensor.copyArray(): IntArray {
-    return IntArray(numElements) { i ->
-        mutableBuffer[bufferStart + i]
-    }
-}

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

@@ -0,0 +1,55 @@
+/*
+ * Copyright 2018-2022 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.tensors.core
+
+import space.kscience.kmath.nd.StructureND
+import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.tensors.api.Tensor
+
+
+public fun StructureND<Double>.copyToTensor(): DoubleTensor = if (this is DoubleTensor) {
+    DoubleTensor(shape, source.copy())
+} else {
+    DoubleTensor(
+        shape,
+        TensorLinearStructure(this.shape).map(this::get).toDoubleArray().asBuffer(),
+    )
+}
+
+public fun StructureND<Int>.toDoubleTensor(): DoubleTensor {
+    return if (this is IntTensor) {
+        DoubleTensor(
+            shape,
+            DoubleBuffer(linearSize) { source[it].toDouble() }
+        )
+    } else {
+        val tensor = DoubleTensorAlgebra.zeroesLike(this)
+        indices.forEach {
+            tensor[it] = get(it).toDouble()
+        }
+        return tensor
+    }
+}
+
+/**
+ * Casts [Tensor] of [Double] to [DoubleTensor]
+ */
+public fun StructureND<Double>.asDoubleTensor(): DoubleTensor = when (this) {
+    is DoubleTensor -> this
+    else -> copyToTensor()
+}
+
+/**
+ * Casts [Tensor] of [Int] to [IntTensor]
+ */
+public fun StructureND<Int>.asIntTensor(): IntTensor = when (this) {
+    is IntTensor -> this
+    else -> IntTensor(
+        this.shape,
+        TensorLinearStructure(this.shape).map(this::get).toIntArray().asBuffer()
+    )
+}

kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestBroadcasting.kt

@@ -6,7 +6,10 @@
 package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.tensors.core.internal.*
+import space.kscience.kmath.tensors.core.internal.broadcastOuterTensors
+import space.kscience.kmath.tensors.core.internal.broadcastShapes
+import space.kscience.kmath.tensors.core.internal.broadcastTensors
+import space.kscience.kmath.tensors.core.internal.broadcastTo
 import kotlin.test.Test
 import kotlin.test.assertTrue
 
@@ -34,7 +37,7 @@ internal class TestBroadcasting {
 
         val res = broadcastTo(tensor2, tensor1.shape)
         assertTrue(res.shape contentEquals intArrayOf(2, 3))
-        assertTrue(res.mutableBuffer.array() contentEquals doubleArrayOf(10.0, 20.0, 30.0, 10.0, 20.0, 30.0))
+        assertTrue(res.source contentEquals doubleArrayOf(10.0, 20.0, 30.0, 10.0, 20.0, 30.0))
     }
 
     @Test
@@ -49,9 +52,9 @@ internal class TestBroadcasting {
         assertTrue(res[1].shape contentEquals intArrayOf(1, 2, 3))
         assertTrue(res[2].shape contentEquals intArrayOf(1, 2, 3))
 
-        assertTrue(res[0].mutableBuffer.array() contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        assertTrue(res[0].source contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
-        assertTrue(res[1].mutableBuffer.array() contentEquals doubleArrayOf(10.0, 20.0, 30.0, 10.0, 20.0, 30.0))
+        assertTrue(res[1].source contentEquals doubleArrayOf(10.0, 20.0, 30.0, 10.0, 20.0, 30.0))
-        assertTrue(res[2].mutableBuffer.array() contentEquals doubleArrayOf(500.0, 500.0, 500.0, 500.0, 500.0, 500.0))
+        assertTrue(res[2].source contentEquals doubleArrayOf(500.0, 500.0, 500.0, 500.0, 500.0, 500.0))
     }
 
     @Test
@@ -66,15 +69,15 @@ internal class TestBroadcasting {
         assertTrue(res[1].shape contentEquals intArrayOf(1, 1, 3))
         assertTrue(res[2].shape contentEquals intArrayOf(1, 1, 1))
 
-        assertTrue(res[0].mutableBuffer.array() contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        assertTrue(res[0].source contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
-        assertTrue(res[1].mutableBuffer.array() contentEquals doubleArrayOf(10.0, 20.0, 30.0))
+        assertTrue(res[1].source contentEquals doubleArrayOf(10.0, 20.0, 30.0))
-        assertTrue(res[2].mutableBuffer.array() contentEquals doubleArrayOf(500.0))
+        assertTrue(res[2].source contentEquals doubleArrayOf(500.0))
     }
 
     @Test
     fun testBroadcastOuterTensorsShapes() = DoubleTensorAlgebra {
-        val tensor1 = fromArray(intArrayOf(2, 1, 3, 2, 3), DoubleArray(2 * 1 * 3 * 2 * 3) {0.0})
+        val tensor1 = fromArray(intArrayOf(2, 1, 3, 2, 3), DoubleArray(2 * 1 * 3 * 2 * 3) { 0.0 })
-        val tensor2 = fromArray(intArrayOf(4, 2, 5, 1, 3, 3), DoubleArray(4 * 2 * 5 * 1 * 3 * 3) {0.0})
+        val tensor2 = fromArray(intArrayOf(4, 2, 5, 1, 3, 3), DoubleArray(4 * 2 * 5 * 1 * 3 * 3) { 0.0 })
         val tensor3 = fromArray(intArrayOf(1, 1), doubleArrayOf(500.0))
 
         val res = broadcastOuterTensors(tensor1, tensor2, tensor3)
@@ -95,16 +98,16 @@ internal class TestBroadcasting {
         val tensor32 = tensor3 - tensor2
 
         assertTrue(tensor21.shape contentEquals intArrayOf(2, 3))
-        assertTrue(tensor21.mutableBuffer.array() contentEquals doubleArrayOf(9.0, 18.0, 27.0, 6.0, 15.0, 24.0))
+        assertTrue(tensor21.source contentEquals doubleArrayOf(9.0, 18.0, 27.0, 6.0, 15.0, 24.0))
 
         assertTrue(tensor31.shape contentEquals intArrayOf(1, 2, 3))
         assertTrue(
-            tensor31.mutableBuffer.array()
+            tensor31.source
                     contentEquals doubleArrayOf(499.0, 498.0, 497.0, 496.0, 495.0, 494.0)
         )
 
         assertTrue(tensor32.shape contentEquals intArrayOf(1, 1, 3))
-        assertTrue(tensor32.mutableBuffer.array() contentEquals doubleArrayOf(490.0, 480.0, 470.0))
+        assertTrue(tensor32.source contentEquals doubleArrayOf(490.0, 480.0, 470.0))
     }
 
 }

kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleAnalyticTensorAlgebra.kt

@@ -6,6 +6,7 @@
 package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.structures.asBuffer
 import kotlin.math.*
 import kotlin.test.Test
 import kotlin.test.assertTrue
@@ -20,14 +21,14 @@ internal class TestDoubleAnalyticTensorAlgebra {
         3.23, 133.7, 25.3,
         100.3, 11.0, 12.012
     )
-    val tensor = DoubleTensor(shape, buffer)
+    val tensor = DoubleTensor(shape, buffer.asBuffer())
 
     fun DoubleArray.fmap(transform: (Double) -> Double): DoubleArray {
         return this.map(transform).toDoubleArray()
     }
 
     fun expectedTensor(transform: (Double) -> Double): DoubleTensor {
-        return DoubleTensor(shape, buffer.fmap(transform))
+        return DoubleTensor(shape, buffer.fmap(transform).asBuffer())
     }
 
     @Test
@@ -106,58 +107,74 @@ internal class TestDoubleAnalyticTensorAlgebra {
         1.0, 2.0,
         -3.0, 4.0
     )
-    val tensor2 = DoubleTensor(shape2, buffer2)
+    val tensor2 = DoubleTensor(shape2, buffer2.asBuffer())
 
     @Test
     fun testMin() = DoubleTensorAlgebra {
         assertTrue { tensor2.min() == -3.0 }
-        assertTrue { tensor2.min(0, true) eq fromArray(
+        assertTrue {
-            intArrayOf(1, 2),
+            tensor2.min(0, true) eq fromArray(
-            doubleArrayOf(-3.0, 2.0)
+                intArrayOf(1, 2),
-        )}
+                doubleArrayOf(-3.0, 2.0)
-        assertTrue { tensor2.min(1, false) eq fromArray(
+            )
-            intArrayOf(2),
+        }
-            doubleArrayOf(1.0, -3.0)
+        assertTrue {
-        )}
+            tensor2.min(1, false) eq fromArray(
+                intArrayOf(2),
+                doubleArrayOf(1.0, -3.0)
+            )
+        }
     }
 
     @Test
     fun testMax() = DoubleTensorAlgebra {
         assertTrue { tensor2.max() == 4.0 }
-        assertTrue { tensor2.max(0, true) eq fromArray(
+        assertTrue {
-            intArrayOf(1, 2),
+            tensor2.max(0, true) eq fromArray(
-            doubleArrayOf(1.0, 4.0)
+                intArrayOf(1, 2),
-        )}
+                doubleArrayOf(1.0, 4.0)
-        assertTrue { tensor2.max(1, false) eq fromArray(
+            )
-            intArrayOf(2),
+        }
-            doubleArrayOf(2.0, 4.0)
+        assertTrue {
-        )}
+            tensor2.max(1, false) eq fromArray(
+                intArrayOf(2),
+                doubleArrayOf(2.0, 4.0)
+            )
+        }
     }
 
     @Test
     fun testSum() = DoubleTensorAlgebra {
         assertTrue { tensor2.sum() == 4.0 }
-        assertTrue { tensor2.sum(0, true) eq fromArray(
+        assertTrue {
-            intArrayOf(1, 2),
+            tensor2.sum(0, true) eq fromArray(
-            doubleArrayOf(-2.0, 6.0)
+                intArrayOf(1, 2),
-        )}
+                doubleArrayOf(-2.0, 6.0)
-        assertTrue { tensor2.sum(1, false) eq fromArray(
+            )
-            intArrayOf(2),
+        }
-            doubleArrayOf(3.0, 1.0)
+        assertTrue {
-        )}
+            tensor2.sum(1, false) eq fromArray(
+                intArrayOf(2),
+                doubleArrayOf(3.0, 1.0)
+            )
+        }
     }
 
     @Test
     fun testMean() = DoubleTensorAlgebra {
         assertTrue { tensor2.mean() == 1.0 }
-        assertTrue { tensor2.mean(0, true) eq fromArray(
+        assertTrue {
-            intArrayOf(1, 2),
+            tensor2.mean(0, true) eq fromArray(
-            doubleArrayOf(-1.0, 3.0)
+                intArrayOf(1, 2),
-        )}
+                doubleArrayOf(-1.0, 3.0)
-        assertTrue { tensor2.mean(1, false) eq fromArray(
+            )
-            intArrayOf(2),
+        }
-            doubleArrayOf(1.5, 0.5)
+        assertTrue {
-        )}
+            tensor2.mean(1, false) eq fromArray(
+                intArrayOf(2),
+                doubleArrayOf(1.5, 0.5)
+            )
+        }
     }
 
 }

kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt

@@ -6,7 +6,6 @@
 package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.tensors.core.internal.array
 import space.kscience.kmath.tensors.core.internal.svd1d
 import kotlin.math.abs
 import kotlin.test.Test
@@ -142,11 +141,11 @@ internal class TestDoubleLinearOpsTensorAlgebra {
     @Test
     fun testCholesky() = DoubleTensorAlgebra {
         val tensor = randomNormal(intArrayOf(2, 5, 5), 0)
-        val sigma = (tensor matmul tensor.transpose()) + diagonalEmbedding(
+        val sigma = (tensor matmul tensor.transposed()) + diagonalEmbedding(
             fromArray(intArrayOf(2, 5), DoubleArray(10) { 0.1 })
         )
         val low = sigma.cholesky()
-        val sigmChol = low matmul low.transpose()
+        val sigmChol = low matmul low.transposed()
         assertTrue(sigma.eq(sigmChol))
     }
 
@@ -157,12 +156,12 @@ internal class TestDoubleLinearOpsTensorAlgebra {
         val res = svd1d(tensor2)
 
         assertTrue(res.shape contentEquals intArrayOf(2))
-        assertTrue { abs(abs(res.mutableBuffer.array()[res.bufferStart]) - 0.386) < 0.01 }
+        assertTrue { abs(abs(res.source[0]) - 0.386) < 0.01 }
-        assertTrue { abs(abs(res.mutableBuffer.array()[res.bufferStart + 1]) - 0.922) < 0.01 }
+        assertTrue { abs(abs(res.source[1]) - 0.922) < 0.01 }
     }
 
     @Test
-    fun testSVD() = DoubleTensorAlgebra{
+    fun testSVD() = DoubleTensorAlgebra {
         testSVDFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
         testSVDFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
     }
@@ -171,16 +170,16 @@ internal class TestDoubleLinearOpsTensorAlgebra {
     fun testBatchedSVD() = DoubleTensorAlgebra {
         val tensor = randomNormal(intArrayOf(2, 5, 3), 0)
         val (tensorU, tensorS, tensorV) = tensor.svd()
-        val tensorSVD = tensorU matmul (diagonalEmbedding(tensorS) matmul tensorV.transpose())
+        val tensorSVD = tensorU matmul (diagonalEmbedding(tensorS) matmul tensorV.transposed())
         assertTrue(tensor.eq(tensorSVD))
     }
 
     @Test
     fun testBatchedSymEig() = DoubleTensorAlgebra {
         val tensor = randomNormal(shape = intArrayOf(2, 3, 3), 0)
-        val tensorSigma = tensor + tensor.transpose()
+        val tensorSigma = tensor + tensor.transposed()
         val (tensorS, tensorV) = tensorSigma.symEig()
-        val tensorSigmaCalc = tensorV matmul (diagonalEmbedding(tensorS) matmul tensorV.transpose())
+        val tensorSigmaCalc = tensorV matmul (diagonalEmbedding(tensorS) matmul tensorV.transposed())
         assertTrue(tensorSigma.eq(tensorSigmaCalc))
     }
 
@@ -194,7 +193,7 @@ private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor, epsilon: Double
     val tensorSVD = svd.first
         .dot(
             diagonalEmbedding(svd.second)
-                .dot(svd.third.transpose())
+                .dot(svd.third.transposed())
         )
 
     assertTrue(tensor.eq(tensorSVD, epsilon))

kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensor.kt

@@ -13,10 +13,7 @@ import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.toDoubleArray
-import space.kscience.kmath.tensors.core.internal.array
 import space.kscience.kmath.tensors.core.internal.matrixSequence
-import space.kscience.kmath.tensors.core.internal.toBufferedTensor
-import space.kscience.kmath.tensors.core.internal.toTensor
 import kotlin.test.Test
 import kotlin.test.assertEquals
 import kotlin.test.assertTrue
@@ -37,7 +34,7 @@ internal class TestDoubleTensor {
         assertEquals(tensor[intArrayOf(0, 1)], 5.8)
         assertTrue(
             tensor.elements().map { it.second }.toList()
-                .toDoubleArray() contentEquals tensor.mutableBuffer.toDoubleArray()
+                .toDoubleArray() contentEquals tensor.source.toDoubleArray()
         )
     }
 
@@ -57,9 +54,9 @@ internal class TestDoubleTensor {
         assertEquals(tensor[intArrayOf(0, 1, 0)], 109.56)
 
         tensor.matrixSequence().forEach {
-            val a = it.toTensor()
+            val a = it.asDoubleTensor()
             val secondRow = a.getTensor(1).as1D()
-            val secondColumn = a.transpose(0, 1).getTensor(1).as1D()
+            val secondColumn = a.transposed(0, 1).getTensor(1).as1D()
             assertEquals(secondColumn[0], 77.89)
             assertEquals(secondRow[1], secondColumn[1])
         }
@@ -72,16 +69,16 @@ internal class TestDoubleTensor {
         val doubleArray = DoubleBuffer(doubleArrayOf(1.0, 2.0, 3.0))
 
         // create ND buffers, no data is copied
-        val ndArray = MutableBufferND(DefaultStrides(intArrayOf(3)), doubleArray)
+        val ndArray: MutableBufferND<Double> = MutableBufferND(DefaultStrides(intArrayOf(3)), doubleArray)
 
         // map to tensors
-        val bufferedTensorArray = ndArray.toBufferedTensor() // strides are flipped so data copied
+        val bufferedTensorArray = ndArray.asDoubleTensor() // strides are flipped so data copied
-        val tensorArray = bufferedTensorArray.toTensor() // data not contiguous so copied again
+        val tensorArray = bufferedTensorArray.asDoubleTensor() // data not contiguous so copied again
 
         val tensorArrayPublic = ndArray.asDoubleTensor() // public API, data copied twice
         val sharedTensorArray = tensorArrayPublic.asDoubleTensor() // no data copied by matching type
 
-        assertTrue(tensorArray.mutableBuffer.array() contentEquals sharedTensorArray.mutableBuffer.array())
+        assertTrue(tensorArray.source contentEquals sharedTensorArray.source)
 
         tensorArray[intArrayOf(0)] = 55.9
         assertEquals(tensorArrayPublic[intArrayOf(0)], 1.0)

kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleTensorAlgebra.kt

@@ -6,9 +6,10 @@
 package space.kscience.kmath.tensors.core
 
 
+import space.kscience.kmath.nd.get
 import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.tensors.core.internal.array
 import kotlin.test.Test
+import kotlin.test.assertEquals
 import kotlin.test.assertFalse
 import kotlin.test.assertTrue
 
@@ -18,55 +19,55 @@ internal class TestDoubleTensorAlgebra {
     fun testDoublePlus() = DoubleTensorAlgebra {
         val tensor = fromArray(intArrayOf(2), doubleArrayOf(1.0, 2.0))
         val res = 10.0 + tensor
-        assertTrue(res.mutableBuffer.array() contentEquals doubleArrayOf(11.0, 12.0))
+        assertTrue(res.source contentEquals doubleArrayOf(11.0, 12.0))
     }
 
     @Test
     fun testDoubleDiv() = DoubleTensorAlgebra {
         val tensor = fromArray(intArrayOf(2), doubleArrayOf(2.0, 4.0))
-        val res = 2.0/tensor
+        val res = 2.0 / tensor
-        assertTrue(res.mutableBuffer.array() contentEquals doubleArrayOf(1.0, 0.5))
+        assertTrue(res.source contentEquals doubleArrayOf(1.0, 0.5))
     }
 
     @Test
     fun testDivDouble() = DoubleTensorAlgebra {
         val tensor = fromArray(intArrayOf(2), doubleArrayOf(10.0, 5.0))
         val res = tensor / 2.5
-        assertTrue(res.mutableBuffer.array() contentEquals doubleArrayOf(4.0, 2.0))
+        assertTrue(res.source contentEquals doubleArrayOf(4.0, 2.0))
     }
 
     @Test
     fun testTranspose1x1() = DoubleTensorAlgebra {
         val tensor = fromArray(intArrayOf(1), doubleArrayOf(0.0))
-        val res = tensor.transpose(0, 0)
+        val res = tensor.transposed(0, 0)
 
-        assertTrue(res.mutableBuffer.array() contentEquals doubleArrayOf(0.0))
+        assertTrue(res.source contentEquals doubleArrayOf(0.0))
         assertTrue(res.shape contentEquals intArrayOf(1))
     }
 
     @Test
     fun testTranspose3x2() = DoubleTensorAlgebra {
         val tensor = fromArray(intArrayOf(3, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
-        val res = tensor.transpose(1, 0)
+        val res = tensor.transposed(1, 0)
 
-        assertTrue(res.mutableBuffer.array() contentEquals doubleArrayOf(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))
+        assertTrue(res.source contentEquals doubleArrayOf(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))
         assertTrue(res.shape contentEquals intArrayOf(2, 3))
     }
 
     @Test
     fun testTranspose1x2x3() = DoubleTensorAlgebra {
         val tensor = fromArray(intArrayOf(1, 2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
-        val res01 = tensor.transpose(0, 1)
+        val res01 = tensor.transposed(0, 1)
-        val res02 = tensor.transpose(-3, 2)
+        val res02 = tensor.transposed(-3, 2)
-        val res12 = tensor.transpose()
+        val res12 = tensor.transposed()
 
         assertTrue(res01.shape contentEquals intArrayOf(2, 1, 3))
         assertTrue(res02.shape contentEquals intArrayOf(3, 2, 1))
         assertTrue(res12.shape contentEquals intArrayOf(1, 3, 2))
 
-        assertTrue(res01.mutableBuffer.array() contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
+        assertTrue(res01.source contentEquals doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
-        assertTrue(res02.mutableBuffer.array() contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
+        assertTrue(res02.source contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
-        assertTrue(res12.mutableBuffer.array() contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
+        assertTrue(res12.source contentEquals doubleArrayOf(1.0, 4.0, 2.0, 5.0, 3.0, 6.0))
     }
 
     @Test
@@ -97,8 +98,8 @@ internal class TestDoubleTensorAlgebra {
         assignResult += tensorC
         assignResult += -39.4
 
-        assertTrue(expected.mutableBuffer.array() contentEquals result.mutableBuffer.array())
+        assertTrue(expected.source contentEquals result.source)
-        assertTrue(expected.mutableBuffer.array() contentEquals assignResult.mutableBuffer.array())
+        assertTrue(expected.source contentEquals assignResult.source)
     }
 
     @Test
@@ -111,26 +112,28 @@ internal class TestDoubleTensorAlgebra {
         val tensor5 = fromArray(intArrayOf(2, 3, 3), (1..18).map { 1 + it.toDouble() }.toDoubleArray())
 
         val res12 = tensor1.dot(tensor2)
-        assertTrue(res12.mutableBuffer.array() contentEquals doubleArrayOf(140.0, 320.0))
+        assertTrue(res12.source contentEquals doubleArrayOf(140.0, 320.0))
         assertTrue(res12.shape contentEquals intArrayOf(2))
 
         val res32 = tensor3.matmul(tensor2)
-        assertTrue(res32.mutableBuffer.array() contentEquals doubleArrayOf(-140.0))
+        assertTrue(res32.source contentEquals doubleArrayOf(-140.0))
         assertTrue(res32.shape contentEquals intArrayOf(1, 1))
 
         val res22 = tensor2.dot(tensor2)
-        assertTrue(res22.mutableBuffer.array() contentEquals doubleArrayOf(1400.0))
+        assertTrue(res22.source contentEquals doubleArrayOf(1400.0))
         assertTrue(res22.shape contentEquals intArrayOf(1))
 
         val res11 = tensor1.dot(tensor11)
-        assertTrue(res11.mutableBuffer.array() contentEquals doubleArrayOf(22.0, 28.0, 49.0, 64.0))
+        assertTrue(res11.source contentEquals doubleArrayOf(22.0, 28.0, 49.0, 64.0))
         assertTrue(res11.shape contentEquals intArrayOf(2, 2))
 
         val res45 = tensor4.matmul(tensor5)
-        assertTrue(res45.mutableBuffer.array() contentEquals doubleArrayOf(
+        assertTrue(
-            36.0, 42.0, 48.0, 81.0, 96.0, 111.0, 126.0, 150.0, 174.0,
+            res45.source contentEquals doubleArrayOf(
-            468.0, 501.0, 534.0, 594.0, 636.0, 678.0, 720.0, 771.0, 822.0
+                36.0, 42.0, 48.0, 81.0, 96.0, 111.0, 126.0, 150.0, 174.0,
-        ))
+                468.0, 501.0, 534.0, 594.0, 636.0, 678.0, 720.0, 771.0, 822.0
+            )
+        )
         assertTrue(res45.shape contentEquals intArrayOf(2, 3, 3))
     }
 
@@ -140,31 +143,44 @@ internal class TestDoubleTensorAlgebra {
         val tensor2 = fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0))
         val tensor3 = zeros(intArrayOf(2, 3, 4, 5))
 
-        assertTrue(diagonalEmbedding(tensor3, 0, 3, 4).shape contentEquals
+        assertTrue(
-                intArrayOf(2, 3, 4, 5, 5))
+            diagonalEmbedding(tensor3, 0, 3, 4).shape contentEquals
-        assertTrue(diagonalEmbedding(tensor3, 1, 3, 4).shape contentEquals
+                    intArrayOf(2, 3, 4, 5, 5)
-                intArrayOf(2, 3, 4, 6, 6))
+        )
-        assertTrue(diagonalEmbedding(tensor3, 2, 0, 3).shape contentEquals
+        assertTrue(
-                intArrayOf(7, 2, 3, 7, 4))
+            diagonalEmbedding(tensor3, 1, 3, 4).shape contentEquals
+                    intArrayOf(2, 3, 4, 6, 6)
+        )
+        assertTrue(
+            diagonalEmbedding(tensor3, 2, 0, 3).shape contentEquals
+                    intArrayOf(7, 2, 3, 7, 4)
+        )
 
         val diagonal1 = diagonalEmbedding(tensor1, 0, 1, 0)
         assertTrue(diagonal1.shape contentEquals intArrayOf(3, 3))
-        assertTrue(diagonal1.mutableBuffer.array() contentEquals
+        assertTrue(
-                doubleArrayOf(10.0, 0.0, 0.0, 0.0, 20.0, 0.0, 0.0, 0.0, 30.0))
+            diagonal1.source contentEquals
+                    doubleArrayOf(10.0, 0.0, 0.0, 0.0, 20.0, 0.0, 0.0, 0.0, 30.0)
+        )
 
         val diagonal1Offset = diagonalEmbedding(tensor1, 1, 1, 0)
         assertTrue(diagonal1Offset.shape contentEquals intArrayOf(4, 4))
-        assertTrue(diagonal1Offset.mutableBuffer.array() contentEquals
+        assertTrue(
-                doubleArrayOf(0.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 0.0, 20.0, 0.0, 0.0, 0.0, 0.0, 30.0, 0.0))
+            diagonal1Offset.source contentEquals
+                    doubleArrayOf(0.0, 0.0, 0.0, 0.0, 10.0, 0.0, 0.0, 0.0, 0.0, 20.0, 0.0, 0.0, 0.0, 0.0, 30.0, 0.0)
+        )
 
         val diagonal2 = diagonalEmbedding(tensor2, 1, 0, 2)
         assertTrue(diagonal2.shape contentEquals intArrayOf(4, 2, 4))
-        assertTrue(diagonal2.mutableBuffer.array() contentEquals
+        assertTrue(
-                doubleArrayOf(
+            diagonal2.source contentEquals
-                    0.0, 1.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0,
+                    doubleArrayOf(
-                    0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 5.0, 0.0,
+                        0.0, 1.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0,
-                    0.0, 0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 6.0,
+                        0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 5.0, 0.0,
-                    0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0))
+                        0.0, 0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 6.0,
+                        0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
+                    )
+        )
     }
 
     @Test
@@ -178,4 +194,14 @@ internal class TestDoubleTensorAlgebra {
         assertFalse(tensor1.eq(tensor3))
 
     }
+
+    @Test
+    fun testMap() = DoubleTensorAlgebra {
+        val tensor = one(5, 5, 5)
+        val l = tensor.getTensor(0).map { it + 1.0 }
+        val r = tensor.getTensor(1).map { it - 1.0 }
+        val res = l + r
+        assertTrue { intArrayOf(5, 5) contentEquals res.shape }
+        assertEquals(1.0, res[4, 4])
+    }
 }

kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/offsetBufferEquality.kt

@@ -0,0 +1,24 @@
+/*
+ * Copyright 2018-2022 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.tensors.core
+
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.indices
+import kotlin.jvm.JvmName
+
+
+/**
+ * Simplified [DoubleBuffer] to array comparison
+ */
+public fun OffsetDoubleBuffer.contentEquals(vararg doubles: Double): Boolean = indices.all { get(it) == doubles[it] }
+
+@JvmName("contentEqualsArray")
+public infix fun OffsetDoubleBuffer.contentEquals(otherArray: DoubleArray): Boolean = contentEquals(*otherArray)
+
+@JvmName("contentEqualsBuffer")
+public infix fun OffsetDoubleBuffer.contentEquals(otherBuffer: Buffer<Double>): Boolean =
+    indices.all { get(it) == otherBuffer[it] }

test-utils/src/commonMain/kotlin/bufferEquality.kt

@@ -0,0 +1,20 @@
+/*
+ * Copyright 2018-2022 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.testutils
+
+import space.kscience.kmath.structures.DoubleBuffer
+import kotlin.jvm.JvmName
+
+/**
+ * Simplified [DoubleBuffer] to array comparison
+ */
+public fun DoubleBuffer.contentEquals(vararg doubles: Double): Boolean = array.contentEquals(doubles)
+
+@JvmName("contentEqualsArray")
+public infix fun DoubleBuffer.contentEquals(otherArray: DoubleArray): Boolean = array.contentEquals(otherArray)
+
+@JvmName("contentEqualsBuffer")
+public infix fun DoubleBuffer.contentEquals(otherBuffer: DoubleBuffer): Boolean = array.contentEquals(otherBuffer.array)