Change the default strides and unify strides processing

examples/src/main/kotlin/space/kscience/kmath/series/analyzeDif.kt

@@ -7,6 +7,7 @@ import space.kscience.kmath.operations.DoubleBufferOps
 import space.kscience.kmath.operations.algebra
 import space.kscience.kmath.operations.bufferAlgebra
 import space.kscience.kmath.operations.toList
+import space.kscience.kmath.stat.KMComparisonResult
 import space.kscience.kmath.stat.ksComparisonStatistic
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.slice
@@ -31,12 +32,12 @@ fun main() = with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
 
 
     val s1 = series(100) { sin(2 * PI * it / 100) + 1.0 }
-    val s2 = s1.slice(20U..50U).moveTo(40)
+    val s2 = s1.slice(20..50).moveTo(40)
 
     val s3: Buffer<Double> = s1.zip(s2) { l, r -> l + r } //s1 + s2
     val s4 = DoubleBufferOps.ln(s3)
 
-    val kmTest = ksComparisonStatistic(s1, s2)
+    val kmTest: KMComparisonResult<Double> = ksComparisonStatistic(s1, s2)
 
     Plotly.page {
         h1 { +"This is my plot" }

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

@@ -21,7 +21,7 @@ class StreamDoubleFieldND(override val shape: IntArray) : FieldND<Double, Double
     NumbersAddOps<StructureND<Double>>,
     ExtendedField<StructureND<Double>> {
 
-    private val strides = DefaultStrides(shape)
+    private val strides = ColumnStrides(shape)
     override val elementAlgebra: DoubleField get() = DoubleField
     override val zero: BufferND<Double> by lazy { structureND(shape) { zero } }
     override val one: BufferND<Double> by lazy { structureND(shape) { one } }

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

@@ -6,7 +6,7 @@
 package space.kscience.kmath.structures
 
 import space.kscience.kmath.nd.BufferND
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import kotlin.system.measureTimeMillis
 
 @Suppress("ASSIGNED_BUT_NEVER_ACCESSED_VARIABLE")
@@ -14,7 +14,7 @@ fun main() {
     val n = 6000
     val array = DoubleArray(n * n) { 1.0 }
     val buffer = DoubleBuffer(array)
-    val strides = DefaultStrides(intArrayOf(n, n))
+    val strides = ColumnStrides(intArrayOf(n, n))
     val structure = BufferND(strides, buffer)
 
     measureTimeMillis {

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

@@ -38,7 +38,7 @@ public inline fun <T, R : Any> StructureND<T>.mapToBuffer(
 ): BufferND<R> = if (this is BufferND<T>)
     BufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) })
 else {
-    val strides = DefaultStrides(shape)
+    val strides = ColumnStrides(shape)
     BufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
 }
 
@@ -75,7 +75,7 @@ public inline fun <T, reified R : Any> MutableStructureND<T>.mapToMutableBuffer(
     return if (this is MutableBufferND<T>)
         MutableBufferND(this.indices, factory.invoke(indices.linearSize) { transform(buffer[it]) })
     else {
-        val strides = DefaultStrides(shape)
+        val strides = ColumnStrides(shape)
         MutableBufferND(strides, factory.invoke(strides.linearSize) { transform(get(strides.index(it))) })
     }
 }

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

@@ -24,7 +24,7 @@ public fun Shape(shapeFirst: Int, vararg shapeRest: Int): Shape = intArrayOf(sha
 public interface WithShape {
     public val shape: Shape
 
-    public val indices: ShapeIndexer get() = DefaultStrides(shape)
+    public val indices: ShapeIndexer get() = ColumnStrides(shape)
 }
 
 internal fun requireIndexInShape(index: IntArray, shape: Shape) {

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

@@ -5,6 +5,7 @@
 
 package space.kscience.kmath.nd
 
+import kotlin.math.max
 import kotlin.native.concurrent.ThreadLocal
 
 /**
@@ -61,12 +62,16 @@ public abstract class Strides : ShapeIndexer {
      * Iterate over ND indices in a natural order
      */
     public override fun asSequence(): Sequence<IntArray> = (0 until linearSize).asSequence().map(::index)
+
+    public companion object{
+        public fun linearSizeOf(shape: IntArray): Int = shape.reduce(Int::times)
+    }
 }
 
 /**
- * Simple implementation of [Strides].
+ * Column-first [Strides]. Columns are represented as continuous arrays
  */
-public class DefaultStrides(override val shape: IntArray) : Strides() {
+public class ColumnStrides(override val shape: IntArray) : Strides() {
     override val linearSize: Int get() = strides[shape.size]
 
     /**
@@ -100,22 +105,64 @@ public class DefaultStrides(override val shape: IntArray) : Strides() {
 
     override fun equals(other: Any?): Boolean {
         if (this === other) return true
-        if (other !is DefaultStrides) return false
+        if (other !is ColumnStrides) return false
-        if (!shape.contentEquals(other.shape)) return false
+        return shape.contentEquals(other.shape)
-        return true
     }
 
     override fun hashCode(): Int = shape.contentHashCode()
 
 
-    public companion object {
+    public companion object
-        /**
-         * Cached builder for default strides
-         */
-        @Deprecated("Replace by Strides(shape)")
-        public operator fun invoke(shape: IntArray): Strides =
-            defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
 }
+
+/**
+ * This [Strides] implementation follows the last dimension first convention
+ * For more information: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.strides.html
+ *
+ * @param shape the shape of the tensor.
+ */
+public class RowStrides(override val shape: IntArray) : Strides() {
+
+    override val strides: IntArray by lazy {
+        val nDim = shape.size
+        val res = IntArray(nDim)
+        if (nDim == 0) return@lazy res
+
+        var current = nDim - 1
+        res[current] = 1
+
+        while (current > 0) {
+            res[current - 1] = max(1, shape[current]) * res[current]
+            current--
+        }
+        res
+    }
+
+    override fun index(offset: Int): IntArray {
+        val res = IntArray(shape.size)
+        var current = offset
+        var strideIndex = 0
+
+        while (strideIndex < shape.size) {
+            res[strideIndex] = (current / strides[strideIndex])
+            current %= strides[strideIndex]
+            strideIndex++
+        }
+        return res
+    }
+
+    override val linearSize: Int get() = linearSizeOf(shape)
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other !is RowStrides) return false
+        return shape.contentEquals(other.shape)
+    }
+
+    override fun hashCode(): Int = shape.contentHashCode()
+
+    public companion object
+
 }
 
 @ThreadLocal
@@ -124,4 +171,4 @@ private val defaultStridesCache = HashMap<IntArray, Strides>()
 /**
  * Cached builder for default strides
  */
-public fun Strides(shape: IntArray): Strides = defaultStridesCache.getOrPut(shape) { DefaultStrides(shape) }
+public fun Strides(shape: IntArray): Strides = defaultStridesCache.getOrPut(shape) { RowStrides(shape) }

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt

@@ -7,6 +7,7 @@ package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.MutableBuffer
 import space.kscience.kmath.structures.MutableListBuffer
 import space.kscience.kmath.structures.VirtualBuffer
 import kotlin.jvm.JvmInline
@@ -84,15 +85,15 @@ public interface MutableStructure2D<T> : Structure2D<T>, MutableStructureND<T> {
      * The buffer of rows of this structure. It gets elements from the structure dynamically.
      */
     @PerformancePitfall
-    override val rows: List<MutableStructure1D<T>>
+    override val rows: List<MutableBuffer<T>>
-        get() = List(rowNum) { i -> MutableBuffer1DWrapper(MutableListBuffer(colNum) { j -> get(i, j) }) }
+        get() = List(rowNum) { i -> MutableListBuffer(colNum) { j -> get(i, j) } }
 
     /**
      * The buffer of columns of this structure. It gets elements from the structure dynamically.
      */
     @PerformancePitfall
-    override val columns: List<MutableStructure1D<T>>
+    override val columns: List<MutableBuffer<T>>
-        get() = List(colNum) { j -> MutableBuffer1DWrapper(MutableListBuffer(rowNum) { i -> get(i, j) }) }
+        get() = List(colNum) { j -> MutableListBuffer(rowNum) { i -> get(i, j) } }
 }
 
 /**

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

@@ -148,25 +148,25 @@ public interface StructureND<out T> : Featured<StructureFeature>, WithShape {
             shape: IntArray,
             bufferFactory: BufferFactory<T> = BufferFactory.boxing(),
             initializer: (IntArray) -> T,
-        ): BufferND<T> = buffered(DefaultStrides(shape), bufferFactory, initializer)
+        ): BufferND<T> = buffered(ColumnStrides(shape), bufferFactory, initializer)
 
         public inline fun <reified T : Any> auto(
             shape: IntArray,
             crossinline initializer: (IntArray) -> T,
-        ): BufferND<T> = auto(DefaultStrides(shape), initializer)
+        ): BufferND<T> = auto(ColumnStrides(shape), initializer)
 
         @JvmName("autoVarArg")
         public inline fun <reified T : Any> auto(
             vararg shape: Int,
             crossinline initializer: (IntArray) -> T,
         ): BufferND<T> =
-            auto(DefaultStrides(shape), initializer)
+            auto(ColumnStrides(shape), initializer)
 
         public inline fun <T : Any> auto(
             type: KClass<T>,
             vararg shape: Int,
             crossinline initializer: (IntArray) -> T,
-        ): BufferND<T> = auto(type, DefaultStrides(shape), initializer)
+        ): BufferND<T> = auto(type, ColumnStrides(shape), initializer)
     }
 }
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt

@@ -5,7 +5,7 @@
 
 package space.kscience.kmath.structures
 
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import space.kscience.kmath.nd.Structure2D
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.as2D
@@ -31,7 +31,7 @@ internal class BufferAccessor2D<T>(
 
     //TODO optimize wrapper
     fun MutableBuffer<T>.collect(): Structure2D<T> = StructureND.buffered(
-        DefaultStrides(intArrayOf(rowNum, colNum)),
+        ColumnStrides(intArrayOf(rowNum, colNum)),
         factory
     ) { (i, j) ->
         get(i, j)

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

@@ -15,6 +15,9 @@ public interface BufferView<T> : Buffer<T> {
      */
     @UnstableKMathAPI
     public fun originIndex(index: Int): Int
+
+    @OptIn(UnstableKMathAPI::class)
+    override fun get(index: Int): T = origin[originIndex(index)]
 }
 
 /**
@@ -22,40 +25,40 @@ public interface BufferView<T> : Buffer<T> {
  */
 public class BufferSlice<T>(
     override val origin: Buffer<T>,
-    public val offset: UInt = 0U,
+    public val offset: Int = 0,
     override val size: Int,
 ) : BufferView<T> {
 
     init {
         require(size > 0) { "Size must be positive" }
-        require(offset + size.toUInt() <= origin.size.toUInt()) {
+        require(offset + size <= origin.size) {
-            "End of buffer ${offset + size.toUInt()} is beyond the end of origin buffer size ${origin.size}"
+            "End of buffer ${offset + size} is beyond the end of origin buffer size ${origin.size}"
         }
     }
 
     override fun get(index: Int): T = if (index >= size) {
         throw IndexOutOfBoundsException("$index is out of ${0 until size} rage")
     } else {
-        origin[index.toUInt() + offset]
+        origin[index + offset]
     }
 
     override fun iterator(): Iterator<T> =
-        (offset until (offset + size.toUInt())).asSequence().map { origin[it] }.iterator()
+        (offset until (offset + size)).asSequence().map { origin[it] }.iterator()
 
     @UnstableKMathAPI
-    override fun originIndex(index: Int): Int = if (index >= size) -1 else index - offset.toInt()
+    override fun originIndex(index: Int): Int = if (index >= size) -1 else index - offset
 
-    override fun toString(): String = "$origin[$offset..${offset + size.toUInt()}"
+    override fun toString(): String = "$origin[$offset..${offset + size}"
 }
 
 /**
- * An expanded buffer that could include the whole initial buffer ot its part and fills all space beyond it borders with [defaultValue].
+ * An expanded buffer that could include the whole initial buffer or its part and fills all space beyond it borders with [defaultValue].
  *
  * The [offset] parameter shows the shift of expanded buffer start relative to origin start and could be both positive and negative.
  */
 public class BufferExpanded<T>(
     override val origin: Buffer<T>,
-    public val defaultValue: T,
+    private val defaultValue: T,
     public val offset: Int = 0,
     override val size: Int = origin.size,
 ) : BufferView<T> {
@@ -79,17 +82,17 @@ public class BufferExpanded<T>(
 /**
  * Zero-copy select a slice inside the original buffer
  */
-public fun <T> Buffer<T>.slice(range: UIntRange): BufferView<T> = if (this is BufferSlice) {
+public fun <T> Buffer<T>.slice(range: IntRange): BufferView<T> = if (this is BufferSlice) {
     BufferSlice(
         origin,
         this.offset + range.first,
-        (range.last - range.first).toInt() + 1
+        (range.last - range.first) + 1
     )
 } else {
     BufferSlice(
         this,
         range.first,
-        (range.last - range.first).toInt() + 1
+        (range.last - range.first) + 1
     )
 }
 
@@ -103,7 +106,7 @@ public fun <T> Buffer<T>.expand(
 ): BufferView<T> = if (range.first >= 0 && range.last < size) {
     BufferSlice(
         this,
-        range.first.toUInt(),
+        range.first,
         (range.last - range.first) + 1
     )
 } else {
@@ -118,7 +121,7 @@ public fun <T> Buffer<T>.expand(
 /**
  * A [BufferView] that overrides indexing of the original buffer
  */
-public class PermutatedBuffer<T>(
+public class PermutedBuffer<T>(
     override val origin: Buffer<T>,
     private val permutations: IntArray,
 ) : BufferView<T> {
@@ -145,4 +148,4 @@ public class PermutatedBuffer<T>(
 /**
  * Created a permuted view of given buffer using provided [indices]
  */
-public fun <T> Buffer<T>.permute(indices: IntArray): PermutatedBuffer<T> = PermutatedBuffer(this, indices)
+public fun <T> Buffer<T>.permute(indices: IntArray): PermutedBuffer<T> = PermutedBuffer(this, indices)

kmath-core/src/commonTest/kotlin/space/kscience/kmath/nd/StridesTest.kt

@@ -0,0 +1,38 @@
+/*
+ * 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.nd
+
+import kotlin.test.Test
+
+class StridesTest {
+    @Test
+    fun checkRowBasedStrides() {
+        val strides = RowStrides(intArrayOf(3, 3))
+        var counter = 0
+        for(i in 0..2){
+            for(j in 0..2){
+//                print(strides.offset(intArrayOf(i,j)).toString() + "\t")
+                require(strides.offset(intArrayOf(i,j)) == counter)
+                counter++
+            }
+            println()
+        }
+    }
+
+    @Test
+    fun checkColumnBasedStrides() {
+        val strides = ColumnStrides(intArrayOf(3, 3))
+        var counter = 0
+        for(i in 0..2){
+            for(j in 0..2){
+//                print(strides.offset(intArrayOf(i,j)).toString() + "\t")
+                require(strides.offset(intArrayOf(j,i)) == counter)
+                counter++
+            }
+            println()
+        }
+    }
+}

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

@@ -9,7 +9,7 @@ internal class BufferExpandedTest {
 
     @Test
     fun shrink(){
-        val view = buffer.slice(20U..30U)
+        val view = buffer.slice(20..30)
         assertEquals(20, view[0])
         assertEquals(30, view[10])
         assertFails { view[11] }

kmath-coroutines/src/jvmMain/kotlin/space/kscience/kmath/structures/LazyStructureND.kt

@@ -8,7 +8,7 @@ package space.kscience.kmath.structures
 import kotlinx.coroutines.*
 import space.kscience.kmath.coroutines.Math
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import space.kscience.kmath.nd.StructureND
 
 public class LazyStructureND<out T>(
@@ -27,7 +27,7 @@ public class LazyStructureND<out T>(
 
     @OptIn(PerformancePitfall::class)
     override fun elements(): Sequence<Pair<IntArray, T>> {
-        val strides = DefaultStrides(shape)
+        val strides = ColumnStrides(shape)
         val res = runBlocking { strides.asSequence().toList().map { index -> index to await(index) } }
         return res.asSequence()
     }

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

@@ -7,7 +7,7 @@ package space.kscience.kmath.histogram
 
 import space.kscience.kmath.domains.Domain
 import space.kscience.kmath.linear.Point
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import space.kscience.kmath.nd.FieldOpsND
 import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.StructureND
@@ -32,7 +32,7 @@ public class HistogramND<T : Comparable<T>, D : Domain<T>, V : Any>(
     override val dimension: Int get() = group.shape.size
 
     override val bins: Iterable<DomainBin<T, D, V>>
-        get() = DefaultStrides(group.shape).asSequence().map {
+        get() = ColumnStrides(group.shape).asSequence().map {
             group.produceBin(it, values[it])
         }.asIterable()
 }

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

@@ -8,7 +8,7 @@
 package space.kscience.kmath.histogram
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.real.DoubleVector
 import kotlin.random.Random
@@ -73,7 +73,7 @@ internal class MultivariateHistogramTest {
             }
             val res = histogram1 - histogram2
             assertTrue {
-                DefaultStrides(shape).asSequence().all { index ->
+                ColumnStrides(shape).asSequence().all { index ->
                     res.values[index] <= histogram1.values[index]
                 }
             }

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

@@ -31,7 +31,7 @@ public abstract class MultikTensorAlgebra<T, A : Ring<T>>(
     protected val multikStat: Statistics = multikEngine.getStatistics()
 
     override fun structureND(shape: Shape, initializer: A.(IntArray) -> T): MultikTensor<T> {
-        val strides = DefaultStrides(shape)
+        val strides = ColumnStrides(shape)
         val memoryView = initMemoryView<T>(strides.linearSize, type)
         strides.asSequence().forEachIndexed { linearIndex, tensorIndex ->
             memoryView[linearIndex] = elementAlgebra.initializer(tensorIndex)

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

@@ -13,7 +13,7 @@ import org.nd4j.linalg.factory.Nd4j
 import org.nd4j.linalg.factory.ops.NDBase
 import org.nd4j.linalg.ops.transforms.Transforms
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.DoubleField
@@ -178,7 +178,7 @@ public object DoubleNd4jTensorAlgebra : Nd4jTensorAlgebra<Double, DoubleField> {
 
     override fun structureND(shape: Shape, initializer: DoubleField.(IntArray) -> Double): Nd4jArrayStructure<Double> {
         val array: INDArray = Nd4j.zeros(*shape)
-        val indices = DefaultStrides(shape)
+        val indices = ColumnStrides(shape)
         indices.asSequence().forEach { index ->
             array.putScalar(index, elementAlgebra.initializer(index))
         }

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/SeriesAlgebra.kt

@@ -38,7 +38,7 @@ public val <T> Series<T>.absoluteIndices: IntRange get() = position until positi
 /**
  * A [BufferView] with index offset (both positive and negative) and possible size change
  */
-private class OffsetBufer<T>(
+private class SeriesImpl<T>(
     override val origin: Buffer<T>,
     override val position: Int,
     override val size: Int = origin.size,
@@ -86,9 +86,9 @@ public class SeriesAlgebra<T, out A : Ring<T>, out BA : BufferAlgebra<T, A>, L>(
      * Create an offset series with index starting point at [index]
      */
     public fun Buffer<T>.moveTo(index: Int): Series<T> = if (this is Series) {
-        OffsetBufer(origin, index, size)
+        SeriesImpl(origin, index, size)
     } else {
-        OffsetBufer(this, index, size)
+        SeriesImpl(this, index, size)
     }
 
     public val Buffer<T>.offset: Int get() = if (this is Series) position else 0

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

@@ -13,7 +13,7 @@ import org.tensorflow.types.TFloat64
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.operations.DoubleField
@@ -39,7 +39,7 @@ public class DoubleTensorFlowAlgebra internal constructor(
         initializer: DoubleField.(IntArray) -> Double,
     ): StructureND<Double> {
         val res = TFloat64.tensorOf(org.tensorflow.ndarray.Shape.of(*shape.toLongArray())) { array ->
-            DefaultStrides(shape).forEach { index ->
+            ColumnStrides(shape).forEach { index ->
                 array.setDouble(elementAlgebra.initializer(index), *index.toLongArray())
             }
         }

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

@@ -6,6 +6,7 @@
 package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.misc.PerformancePitfall
+import space.kscience.kmath.nd.RowStrides
 import space.kscience.kmath.nd.Strides
 import space.kscience.kmath.structures.MutableBuffer
 import space.kscience.kmath.tensors.api.Tensor
@@ -20,9 +21,9 @@ public abstract class BufferedTensor<T>(
     public abstract val source: MutableBuffer<T>
 
     /**
-     * Buffer strides based on [TensorLinearStructure] implementation
+     * Buffer strides based on [RowStrides] implementation
      */
-    override val indices: Strides get() = TensorLinearStructure(shape)
+    override val indices: Strides get() = RowStrides(shape)
 
     /**
      * Number of elements in tensor

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

@@ -5,32 +5,38 @@
 
 package space.kscience.kmath.tensors.core
 
+import space.kscience.kmath.misc.PerformancePitfall
+import space.kscience.kmath.misc.UnstableKMathAPI
+import space.kscience.kmath.nd.MutableStructure2D
+import space.kscience.kmath.nd.MutableStructureND
+import space.kscience.kmath.nd.Shape
 import space.kscience.kmath.structures.*
 import space.kscience.kmath.tensors.core.internal.toPrettyString
+import kotlin.jvm.JvmInline
 
 public class OffsetDoubleBuffer(
-    private val source: DoubleBuffer,
+    override val origin: DoubleBuffer,
     private val offset: Int,
     override val size: Int,
-) : MutableBuffer<Double> {
+) : MutableBuffer<Double>, BufferView<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" }
+        require(offset + size <= origin.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
+        origin[index + offset] = value
     }
 
-    override fun get(index: Int): Double = source[index + offset]
+    override fun get(index: Int): Double = origin[index + offset]
 
     /**
      * Copy only a part of buffer that belongs to this [OffsetDoubleBuffer]
      */
-    override fun copy(): DoubleBuffer = source.array.copyOfRange(offset, offset + size).asBuffer()
+    override fun copy(): DoubleBuffer = origin.array.copyOfRange(offset, offset + size).asBuffer()
 
     override fun iterator(): Iterator<Double> = iterator {
         for (i in indices) {
@@ -41,7 +47,14 @@ public class OffsetDoubleBuffer(
     override fun toString(): String = Buffer.toString(this)
 
     public fun view(addOffset: Int, newSize: Int = size - addOffset): OffsetDoubleBuffer =
-        OffsetDoubleBuffer(source, offset + addOffset, newSize)
+        OffsetDoubleBuffer(origin, offset + addOffset, newSize)
+
+    @UnstableKMathAPI
+    override fun originIndex(index: Int): Int = if (index in 0 until size) {
+        index + offset
+    } else {
+        -1
+    }
 }
 
 public fun OffsetDoubleBuffer.slice(range: IntRange): OffsetDoubleBuffer = view(range.first, range.last - range.first)
@@ -90,3 +103,59 @@ public class DoubleTensor(
 
     override fun toString(): String = toPrettyString()
 }
+
+@JvmInline
+public value class DoubleTensor2D(public val tensor: DoubleTensor) : MutableStructureND<Double> by tensor,
+    MutableStructure2D<Double> {
+
+    init {
+        require(tensor.shape.size == 2) { "Only 2D tensors could be cast to 2D" }
+    }
+
+    override val rowNum: Int get() = shape[0]
+    override val colNum: Int get() = shape[1]
+
+    override fun get(i: Int, j: Int): Double = tensor.source[i * colNum + j]
+
+    override fun set(i: Int, j: Int, value: Double) {
+        tensor.source[i * colNum + j] = value
+    }
+
+    @OptIn(PerformancePitfall::class)
+    override val rows: List<OffsetDoubleBuffer>
+        get() = List(rowNum) { i ->
+            tensor.source.view(i * colNum, colNum)
+        }
+
+
+//    @OptIn(PerformancePitfall::class)
+//    override val columns: List<MutableBuffer<Double>> get() = List(colNum) { j ->
+//        object : MutableBuffer<Double>{
+//
+//            override fun get(index: Int): Double {
+//                tensor.source.get()
+//            }
+//
+//            override fun set(index: Int, value: Double) {
+//                TODO("Not yet implemented")
+//            }
+//
+//            override fun copy(): MutableBuffer<Double> {
+//                TODO("Not yet implemented")
+//            }
+//
+//            override val size: Int
+//                get() = TODO("Not yet implemented")
+//
+//            override fun toString(): String {
+//                TODO("Not yet implemented")
+//            }
+//
+//        }
+//    }
+
+    @PerformancePitfall
+    override fun elements(): Sequence<Pair<IntArray, Double>> = tensor.elements()
+    override fun get(index: IntArray): Double = tensor[index]
+    override val shape: Shape get() = tensor.shape
+}

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

@@ -11,6 +11,7 @@ package space.kscience.kmath.tensors.core
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.*
+import space.kscience.kmath.nd.Strides.Companion.linearSizeOf
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.*
 import space.kscience.kmath.tensors.api.AnalyticTensorAlgebra
@@ -121,7 +122,7 @@ public open class DoubleTensorAlgebra :
      */
     override fun structureND(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): DoubleTensor = fromArray(
         shape,
-        TensorLinearStructure(shape).asSequence().map { DoubleField.initializer(it) }.toMutableList().toDoubleArray()
+        RowStrides(shape).asSequence().map { DoubleField.initializer(it) }.toMutableList().toDoubleArray()
     )
 
     override fun Tensor<Double>.getTensor(i: Int): DoubleTensor {
@@ -130,7 +131,7 @@ public open class DoubleTensorAlgebra :
         val newShape = if (lastShape.isNotEmpty()) lastShape else intArrayOf(1)
         return DoubleTensor(
             newShape,
-            dt.source.view(newShape.reduce(Int::times) * i, TensorLinearStructure.linearSizeOf(newShape))
+            dt.source.view(newShape.reduce(Int::times) * i, linearSizeOf(newShape))
         )
     }
 

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

@@ -119,7 +119,7 @@ public open class IntTensorAlgebra : TensorAlgebra<Int, IntRing> {
      */
     override fun structureND(shape: IntArray, initializer: IntRing.(IntArray) -> Int): IntTensor = fromArray(
         shape,
-        TensorLinearStructure(shape).asSequence().map { IntRing.initializer(it) }.toMutableList().toIntArray()
+        RowStrides(shape).asSequence().map { IntRing.initializer(it) }.toMutableList().toIntArray()
     )
 
     override fun Tensor<Int>.getTensor(i: Int): IntTensor {

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

@@ -1,74 +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.Strides
-import kotlin.math.max
-
-/**
- * This [Strides] implementation follows the last dimension first convention
- * For more information: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.strides.html
- *
- * @param shape the shape of the tensor.
- */
-public class TensorLinearStructure(override val shape: IntArray) : Strides() {
-    override val strides: IntArray get() = stridesFromShape(shape)
-
-    override fun index(offset: Int): IntArray =
-        indexFromOffset(offset, strides, shape.size)
-
-    override val linearSize: Int get() = linearSizeOf(shape)
-
-    override fun equals(other: Any?): Boolean {
-        if (this === other) return true
-        if (other == null || this::class != other::class) return false
-
-        other as TensorLinearStructure
-
-        if (!shape.contentEquals(other.shape)) return false
-
-        return true
-    }
-
-    override fun hashCode(): Int {
-        return shape.contentHashCode()
-    }
-
-    public companion object {
-
-        public fun linearSizeOf(shape: IntArray): Int = shape.reduce(Int::times)
-
-        public fun stridesFromShape(shape: IntArray): IntArray {
-            val nDim = shape.size
-            val res = IntArray(nDim)
-            if (nDim == 0)
-                return res
-
-            var current = nDim - 1
-            res[current] = 1
-
-            while (current > 0) {
-                res[current - 1] = max(1, shape[current]) * res[current]
-                current--
-            }
-            return res
-        }
-
-        public fun indexFromOffset(offset: Int, strides: IntArray, nDim: Int): IntArray {
-            val res = IntArray(nDim)
-            var current = offset
-            var strideIndex = 0
-
-            while (strideIndex < nDim) {
-                res[strideIndex] = (current / strides[strideIndex])
-                current %= strides[strideIndex]
-                strideIndex++
-            }
-            return res
-        }
-    }
-
-}

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

@@ -5,17 +5,18 @@
 
 package space.kscience.kmath.tensors.core.internal
 
-import space.kscience.kmath.nd.MutableStructure2D
+import space.kscience.kmath.nd.*
-import space.kscience.kmath.nd.Structure2D
+import space.kscience.kmath.nd.Strides.Companion.linearSizeOf
-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.*
 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
@@ -177,7 +178,7 @@ internal val DoubleTensor.matrices: VirtualBuffer<DoubleTensor>
         val matrixOffset = shape[n - 1] * shape[n - 2]
         val matrixShape = intArrayOf(shape[n - 2], shape[n - 1])
 
-        val size = TensorLinearStructure.linearSizeOf(matrixShape)
+        val size = linearSizeOf(matrixShape)
 
         return VirtualBuffer(linearSize / matrixOffset) { index ->
             val offset = index * matrixOffset

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

@@ -32,8 +32,7 @@ internal fun List<OffsetIntBuffer>.concat(): IntBuffer {
 }
 
 
-internal val IntTensor.vectors: VirtualBuffer<IntTensor>
+internal fun IntTensor.vectors(): VirtualBuffer<IntTensor> {
-    get() {
     val n = shape.size
     val vectorOffset = shape[n - 1]
     val vectorShape = intArrayOf(shape.last())
@@ -45,7 +44,7 @@ internal val IntTensor.vectors: VirtualBuffer<IntTensor>
 }
 
 
-internal fun IntTensor.vectorSequence(): Sequence<IntTensor> = vectors.asSequence()
+internal fun IntTensor.vectorSequence(): Sequence<IntTensor> = vectors().asSequence()
 
 
 internal val IntTensor.matrices: VirtualBuffer<IntTensor>

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

@@ -5,9 +5,8 @@
 
 package space.kscience.kmath.tensors.core.internal
 
-import space.kscience.kmath.nd.as1D
+import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.operations.DoubleBufferOps.Companion.map
-import space.kscience.kmath.operations.toMutableList
 import space.kscience.kmath.random.RandomGenerator
 import space.kscience.kmath.samplers.GaussianSampler
 import space.kscience.kmath.structures.DoubleBuffer
@@ -67,6 +66,7 @@ internal fun format(value: Double, digits: Int = 4): String = buildString {
     repeat(fLength - res.length) { append(' ') }
 }
 
+@OptIn(PerformancePitfall::class)
 internal fun DoubleTensor.toPrettyString(): String = buildString {
     var offset = 0
     val shape = this@toPrettyString.shape
@@ -85,7 +85,7 @@ internal fun DoubleTensor.toPrettyString(): String = buildString {
             charOffset += 1
         }
 
-        val values = vector.as1D().toMutableList().map(::format)
+        val values = vector.elements().map { format(it.second) }
 
         values.joinTo(this, separator = ", ")
 
@@ -101,7 +101,7 @@ internal fun DoubleTensor.toPrettyString(): String = buildString {
         }
 
         offset += vectorSize
-        if (this@toPrettyString.linearSize == offset) {
+        if (this@toPrettyString.indices.linearSize == offset) {
             break
         }
 

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

@@ -6,6 +6,7 @@
 package space.kscience.kmath.tensors.core
 
 import space.kscience.kmath.nd.DoubleBufferND
+import space.kscience.kmath.nd.RowStrides
 import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.asBuffer
@@ -17,12 +18,12 @@ import space.kscience.kmath.tensors.api.Tensor
  */
 public fun StructureND<Double>.copyToTensor(): DoubleTensor = if (this is DoubleTensor) {
     DoubleTensor(shape, source.copy())
-} else if (this is DoubleBufferND && indices is TensorLinearStructure) {
+} else if (this is DoubleBufferND && indices is RowStrides) {
     DoubleTensor(shape, buffer.copy())
 } else {
     DoubleTensor(
         shape,
-        TensorLinearStructure(this.shape).map(this::get).toDoubleArray().asBuffer(),
+        RowStrides(this.shape).map(this::get).toDoubleArray().asBuffer(),
     )
 }
 
@@ -46,7 +47,7 @@ public fun StructureND<Int>.toDoubleTensor(): DoubleTensor {
  */
 public fun StructureND<Double>.asDoubleTensor(): DoubleTensor = if (this is DoubleTensor) {
     this
-} else if (this is DoubleBufferND && indices is TensorLinearStructure) {
+} else if (this is DoubleBufferND && indices is RowStrides) {
     DoubleTensor(shape, buffer)
 } else {
     copyToTensor()
@@ -59,6 +60,6 @@ public fun StructureND<Int>.asIntTensor(): IntTensor = when (this) {
     is IntTensor -> this
     else -> IntTensor(
         this.shape,
-        TensorLinearStructure(this.shape).map(this::get).toIntArray().asBuffer()
+        RowStrides(this.shape).map(this::get).toIntArray().asBuffer()
     )
 }

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

@@ -66,7 +66,7 @@ internal class TestDoubleTensor {
         val doubleArray = DoubleBuffer(1.0, 2.0, 3.0)
 
         // create ND buffers, no data is copied
-        val ndArray: MutableBufferND<Double> = DoubleBufferND(DefaultStrides(intArrayOf(3)), doubleArray)
+        val ndArray: MutableBufferND<Double> = DoubleBufferND(ColumnStrides(intArrayOf(3)), doubleArray)
 
         // map to tensors
         val tensorArray = ndArray.asDoubleTensor() // Data is copied because of strides change.

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

@@ -33,7 +33,7 @@ public open class ViktorFieldOpsND :
 
     override fun structureND(shape: IntArray, initializer: DoubleField.(IntArray) -> Double): ViktorStructureND =
         F64Array(*shape).apply {
-            DefaultStrides(shape).asSequence().forEach { index ->
+            ColumnStrides(shape).asSequence().forEach { index ->
                 set(value = DoubleField.initializer(index), indices = index)
             }
         }.asStructure()
@@ -43,7 +43,7 @@ public open class ViktorFieldOpsND :
     @PerformancePitfall
     override fun StructureND<Double>.map(transform: DoubleField.(Double) -> Double): ViktorStructureND =
         F64Array(*shape).apply {
-            DefaultStrides(shape).asSequence().forEach { index ->
+            ColumnStrides(shape).asSequence().forEach { index ->
                 set(value = DoubleField.transform(this@map[index]), indices = index)
             }
         }.asStructure()
@@ -52,7 +52,7 @@ public open class ViktorFieldOpsND :
     override fun StructureND<Double>.mapIndexed(
         transform: DoubleField.(index: IntArray, Double) -> Double,
     ): ViktorStructureND = F64Array(*shape).apply {
-        DefaultStrides(shape).asSequence().forEach { index ->
+        ColumnStrides(shape).asSequence().forEach { index ->
             set(value = DoubleField.transform(index, this@mapIndexed[index]), indices = index)
         }
     }.asStructure()
@@ -65,7 +65,7 @@ public open class ViktorFieldOpsND :
     ): ViktorStructureND {
         require(left.shape.contentEquals(right.shape))
         return F64Array(*left.shape).apply {
-            DefaultStrides(left.shape).asSequence().forEach { index ->
+            ColumnStrides(left.shape).asSequence().forEach { index ->
                 set(value = DoubleField.transform(left[index], right[index]), indices = index)
             }
         }.asStructure()

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

@@ -7,7 +7,7 @@ package space.kscience.kmath.viktor
 
 import org.jetbrains.bio.viktor.F64Array
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.nd.DefaultStrides
+import space.kscience.kmath.nd.ColumnStrides
 import space.kscience.kmath.nd.MutableStructureND
 
 @Suppress("OVERRIDE_BY_INLINE", "NOTHING_TO_INLINE")
@@ -22,7 +22,7 @@ public class ViktorStructureND(public val f64Buffer: F64Array) : MutableStructur
 
     @PerformancePitfall
     override fun elements(): Sequence<Pair<IntArray, Double>> =
-        DefaultStrides(shape).asSequence().map { it to get(it) }
+        ColumnStrides(shape).asSequence().map { it to get(it) }
 }
 
 public fun F64Array.asStructure(): ViktorStructureND = ViktorStructureND(this)