examples/src/main/kotlin/space/kscience/kmath/fit/chiSquared.kt

@@ -12,8 +12,6 @@ import space.kscience.kmath.commons.optimization.CMOptimizer
 import space.kscience.kmath.distributions.NormalDistribution
 import space.kscience.kmath.expressions.chiSquaredExpression
 import space.kscience.kmath.expressions.symbol
-import space.kscience.kmath.operations.asIterable
-import space.kscience.kmath.operations.toList
 import space.kscience.kmath.optimization.FunctionOptimizationTarget
 import space.kscience.kmath.optimization.optimizeWith
 import space.kscience.kmath.optimization.resultPoint
@@ -22,6 +20,8 @@ import space.kscience.kmath.real.DoubleVector
 import space.kscience.kmath.real.map
 import space.kscience.kmath.real.step
 import space.kscience.kmath.stat.RandomGenerator
+import space.kscience.kmath.structures.asIterable
+import space.kscience.kmath.structures.toList
 import space.kscience.plotly.*
 import space.kscience.plotly.models.ScatterMode
 import space.kscience.plotly.models.TraceValues

examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt

@@ -13,8 +13,6 @@ import space.kscience.kmath.distributions.NormalDistribution
 import space.kscience.kmath.expressions.Symbol
 import space.kscience.kmath.expressions.binding
 import space.kscience.kmath.expressions.symbol
-import space.kscience.kmath.operations.asIterable
-import space.kscience.kmath.operations.toList
 import space.kscience.kmath.optimization.QowOptimizer
 import space.kscience.kmath.optimization.chiSquaredOrNull
 import space.kscience.kmath.optimization.fitWith
@@ -22,6 +20,8 @@ import space.kscience.kmath.optimization.resultPoint
 import space.kscience.kmath.real.map
 import space.kscience.kmath.real.step
 import space.kscience.kmath.stat.RandomGenerator
+import space.kscience.kmath.structures.asIterable
+import space.kscience.kmath.structures.toList
 import space.kscience.plotly.*
 import space.kscience.plotly.models.ScatterMode
 import kotlin.math.abs

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

@@ -1,37 +1,43 @@
 package space.kscience.kmath.series
 
 
-import net.jafama.StrictFastMath.abs
+import kotlinx.html.FlowContent
+import kotlinx.html.h1
 import space.kscience.kmath.operations.algebra
 import space.kscience.kmath.operations.bufferAlgebra
-import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.operations.toList
 import space.kscience.kmath.structures.Buffer
-import space.kscience.plotly.Plotly
+import space.kscience.kmath.structures.toList
-import space.kscience.plotly.makeFile
+import space.kscience.plotly.*
-import space.kscience.plotly.scatter
 import kotlin.math.PI
-import kotlin.math.max
 
-fun main() = Double.algebra.bufferAlgebra.seriesAlgebra(0..100).invoke {
+fun main() = with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
-    fun Buffer<Double>.plot() {
+    fun FlowContent.plotSeries(buffer: Buffer<Double>) {
-        val ls = labels
+        val ls = buffer.labels
-        Plotly.plot {
+        plot {
             scatter {
                 x.numbers = ls
-                y.numbers = toList()
+                y.numbers = buffer.toList()
             }
-        }.makeFile()
+            layout {
+                xaxis {
+                    range(0.0..100.0)
+                }
+            }
+        }
     }
 
 
-    val s1 = series(100) { sin(2 * PI * it / 100) }
+    val s1 = series(100) { sin(2 * PI * it / 100) + 1.0 }
-    val s2 = series(100) { 1.0 }
+    val s2 = s1.slice(20..50).moveTo(40)
 
-    (s1 - s2).plot()
+    val s3: Buffer<Double> = s1.zip(s2) { l, r -> l + r } //s1 + s2
-
+    val s4 = ln(s3)
-    // Kolmogorov-Smirnov test statistic
-    val kst = (s1 - s2).fold(0.0) { sup, arg -> max(sup, abs(arg))}
 
+    Plotly.page {
+        h1 { +"This is my plot" }
+        plotSeries(s1)
+        plotSeries(s2)
+        plotSeries(s4)
+    }.makeFile()
 
 }

kmath-commons/src/main/kotlin/space/kscience/kmath/commons/random/CMRandomGeneratorWrapper.kt

@@ -7,10 +7,11 @@ package space.kscience.kmath.commons.random
 
 import kotlinx.coroutines.runBlocking
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.samplers.GaussianSampler
 import space.kscience.kmath.misc.toIntExact
+import space.kscience.kmath.samplers.GaussianSampler
+import space.kscience.kmath.samplers.next
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.next
+
 
 public class CMRandomGeneratorWrapper(
     public val factory: (IntArray) -> RandomGenerator,

kmath-commons/src/main/kotlin/space/kscience/kmath/commons/transform/Transformations.kt

@@ -10,13 +10,9 @@ import kotlinx.coroutines.flow.Flow
 import kotlinx.coroutines.flow.map
 import org.apache.commons.math3.transform.*
 import space.kscience.kmath.complex.Complex
-import space.kscience.kmath.operations.SuspendBufferTransform
 import space.kscience.kmath.streaming.chunked
 import space.kscience.kmath.streaming.spread
-import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.*
-import space.kscience.kmath.structures.DoubleBuffer
-import space.kscience.kmath.structures.VirtualBuffer
-import space.kscience.kmath.structures.asBuffer
 
 
 /**

kmath-commons/src/test/kotlin/space/kscience/kmath/commons/optimization/OptimizeTest.kt

@@ -13,11 +13,11 @@ import space.kscience.kmath.expressions.Symbol.Companion.x
 import space.kscience.kmath.expressions.Symbol.Companion.y
 import space.kscience.kmath.expressions.chiSquaredExpression
 import space.kscience.kmath.expressions.symbol
-import space.kscience.kmath.operations.map
 import space.kscience.kmath.optimization.*
 import space.kscience.kmath.stat.RandomGenerator
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.structures.map
 import kotlin.math.pow
 import kotlin.test.Test
 

kmath-core/src/commonMain/kotlin/space/kscience/kmath/domains/HyperSquareDomain.kt

@@ -7,6 +7,7 @@ package space.kscience.kmath.domains
 import space.kscience.kmath.linear.Point
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.indices
 
 /**
  *

kmath-core/src/commonMain/kotlin/space/kscience/kmath/expressions/specialExpressions.kt

@@ -6,8 +6,9 @@
 package space.kscience.kmath.expressions
 
 import space.kscience.kmath.operations.ExtendedField
-import space.kscience.kmath.operations.asIterable
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.asIterable
+import space.kscience.kmath.structures.indices
 import kotlin.jvm.JvmName
 
 /**

kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/BufferedLinearSpace.kt

@@ -13,6 +13,7 @@ import space.kscience.kmath.operations.*
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
 import space.kscience.kmath.structures.VirtualBuffer
+import space.kscience.kmath.structures.indices
 
 
 public class BufferedLinearSpace<T, out A : Ring<T>>(

kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt

@@ -6,10 +6,10 @@
 package space.kscience.kmath.nd
 
 import space.kscience.kmath.misc.PerformancePitfall
-import space.kscience.kmath.operations.asSequence
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.MutableBuffer
 import space.kscience.kmath.structures.asMutableBuffer
+import space.kscience.kmath.structures.asSequence
 import kotlin.jvm.JvmInline
 
 /**

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BufferAlgebra.kt

@@ -8,7 +8,6 @@ package space.kscience.kmath.operations
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.BufferFactory
-import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.ShortBuffer
 
 public interface WithSize {
@@ -183,7 +182,7 @@ public class BufferField<T, A : Field<T>>(
 /**
  * Generate full buffer field from given buffer operations
  */
-public fun <T, A : Field<T>> BufferFieldOps<T, A>.withSize(size: Int): BufferField<T, A> =
+public fun <T, A : Field<T>> BufferAlgebra<T, A>.withSize(size: Int): BufferField<T, A> =
     BufferField(elementAlgebra, bufferFactory, size)
 
 //Double buffer specialization
@@ -196,6 +195,4 @@ public fun BufferField<Double, *>.buffer(vararg elements: Number): Buffer<Double
 public fun <T, A : Field<T>> A.bufferAlgebra(bufferFactory: BufferFactory<T>): BufferFieldOps<T, A> =
     BufferFieldOps(this, bufferFactory)
 
-public val DoubleField.bufferAlgebra: BufferFieldOps<Double, DoubleField>
+public val DoubleField.bufferAlgebra: DoubleBufferOps get() =  DoubleBufferOps
-    get() = BufferFieldOps(DoubleField, ::DoubleBuffer)
-

kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/DoubleBufferOps.kt

@@ -7,10 +7,7 @@ package space.kscience.kmath.operations
 
 import space.kscience.kmath.linear.Point
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.*
-import space.kscience.kmath.structures.BufferFactory
-import space.kscience.kmath.structures.DoubleBuffer
-import space.kscience.kmath.structures.asBuffer
 
 import kotlin.math.*
 

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

@@ -5,7 +5,7 @@
 
 package space.kscience.kmath.structures
 
-import space.kscience.kmath.operations.asSequence
+import space.kscience.kmath.operations.WithSize
 import kotlin.jvm.JvmInline
 import kotlin.reflect.KClass
 
@@ -30,11 +30,11 @@ public typealias MutableBufferFactory<T> = (Int, (Int) -> T) -> MutableBuffer<T>
  *
  * @param T the type of elements contained in the buffer.
  */
-public interface Buffer<out T> {
+public interface Buffer<out T> : WithSize {
     /**
      * The size of this buffer.
      */
-    public val size: Int
+    override val size: Int
 
     /**
      * Gets element at given index.
@@ -44,15 +44,10 @@ public interface Buffer<out T> {
     /**
      * Iterates over all elements.
      */
-    public operator fun iterator(): Iterator<T>
+    public operator fun iterator(): Iterator<T> = indices.asSequence().map(::get).iterator()
 
     override fun toString(): String
 
-    /**
-     * Returns an [IntRange] of the valid indices for this [Buffer].
-     */
-    public val indices: IntRange get() = 0 until size
-
     public companion object {
 
         public fun toString(buffer: Buffer<*>): String =
@@ -105,7 +100,12 @@ public interface Buffer<out T> {
     }
 }
 
-public operator fun<T> Buffer<T>.get(index: UInt): T = get(index.toInt())
+/**
+ * Returns an [IntRange] of the valid indices for this [Buffer].
+ */
+public val <T> Buffer<T>.indices: IntRange get() = 0 until size
+
+public operator fun <T> Buffer<T>.get(index: UInt): T = get(index.toInt())
 
 /**
  * if index is in range of buffer, return the value. Otherwise, return null.

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

@@ -0,0 +1,140 @@
+package space.kscience.kmath.structures
+
+import space.kscience.kmath.misc.UnstableKMathAPI
+
+/**
+ * A buffer that wraps an original buffer
+ */
+public interface BufferView<T> : Buffer<T> {
+    public val origin: Buffer<T>
+
+    /**
+     * Get the index in [origin] buffer from index in this buffer.
+     * Return -1 if element not present in the original buffer
+     * This method should be used internally to optimize non-boxing access.
+     */
+    @UnstableKMathAPI
+    public fun originIndex(index: Int): Int
+}
+
+/**
+ * A zero-copy buffer that "sees" only part of original buffer. Slice can't go beyond original buffer borders.
+ */
+public class BufferSlice<T>(
+    override val origin: Buffer<T>,
+    public val offset: UInt = 0U,
+    override val size: Int,
+) : BufferView<T> {
+
+    init {
+        require(size > 0) { "Size must be positive" }
+        require(offset + size.toUInt() <= origin.size.toUInt()) {
+            "End of buffer ${offset + size.toUInt()} 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 ${0 until size} rage")
+    } else {
+        origin[index.toUInt() + offset]
+    }
+
+    override fun iterator(): Iterator<T> =
+        (offset until (offset + size.toUInt())).asSequence().map { origin[it] }.iterator()
+
+    @UnstableKMathAPI
+    override fun originIndex(index: Int): Int = if (index >= size) -1 else index - offset.toInt()
+
+    override fun toString(): String = "$origin[$offset..${offset + size.toUInt()}"
+}
+
+/**
+ * An expanded buffer that could include the whole initial buffer ot 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,
+    public val offset: Int = 0,
+    override val size: Int = origin.size,
+) : BufferView<T> {
+
+    init {
+        require(size > 0) { "Size must be positive" }
+    }
+
+    override fun get(index: Int): T = when (index) {
+        !in 0 until size -> throw IndexOutOfBoundsException("Index $index is not in $indices")
+        in -offset until origin.size - offset -> origin[index + offset]
+        else -> defaultValue
+    }
+
+    @UnstableKMathAPI
+    override fun originIndex(index: Int): Int = if (index in -offset until origin.size - offset) index + offset else -1
+
+    override fun toString(): String = "$origin[$offset..${offset + size}]"
+}
+
+/**
+ * Zero-copy select a slice inside the original buffer
+ */
+public fun <T> Buffer<T>.slice(range: UIntRange): BufferView<T> = BufferSlice(
+    this,
+    range.first,
+    (range.last - range.first).toInt() + 1
+)
+
+/**
+ * Resize original buffer to a given range using given [range], filling additional segments with [defaultValue].
+ * Range left border could be negative to designate adding new blank segment to the beginning of the buffer
+ */
+public fun <T> Buffer<T>.expand(
+    range: IntRange,
+    defaultValue: T,
+): BufferView<T> = if (range.first >= 0 && range.last < size) {
+    BufferSlice(
+        this,
+        range.first.toUInt(),
+        (range.last - range.first) + 1
+    )
+} else {
+    BufferExpanded(
+        this,
+        defaultValue,
+        range.first,
+        (range.last - range.first) + 1
+    )
+}
+
+/**
+ * A [BufferView] that overrides indexing of the original buffer
+ */
+public class PermutatedBuffer<T>(
+    override val origin: Buffer<T>,
+    private val permutations: IntArray,
+) : BufferView<T> {
+    init {
+        permutations.forEach { index ->
+            if (index !in origin.indices) {
+                throw IndexOutOfBoundsException("Index $index is not in ${origin.indices}")
+            }
+        }
+    }
+
+    override val size: Int get() = permutations.size
+
+    override fun get(index: Int): T = origin[permutations[index]]
+
+    override fun iterator(): Iterator<T> = permutations.asSequence().map { origin[it] }.iterator()
+
+    @UnstableKMathAPI
+    override fun originIndex(index: Int): Int = if (index in permutations.indices) permutations[index] else -1
+
+    override fun toString(): String = Buffer.toString(this)
+}
+
+/**
+ * Created a permuted view of given buffer using provided [indices]
+ */
+public fun <T> Buffer<T>.view(indices: IntArray): PermutatedBuffer<T> = PermutatedBuffer(this, indices)

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

@@ -13,7 +13,7 @@ import kotlin.jvm.JvmInline
  * @property array the underlying array.
  */
 @JvmInline
-public value class DoubleBuffer(public val array: DoubleArray) : MutableBuffer<Double> {
+public value class DoubleBuffer(public val array: DoubleArray) : PrimitiveBuffer<Double> {
     override val size: Int get() = array.size
 
     override operator fun get(index: Int): Double = array[index]

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

@@ -14,7 +14,7 @@ import kotlin.jvm.JvmInline
  * @author Iaroslav Postovalov
  */
 @JvmInline
-public value class FloatBuffer(public val array: FloatArray) : MutableBuffer<Float> {
+public value class FloatBuffer(public val array: FloatArray) : PrimitiveBuffer<Float> {
     override val size: Int get() = array.size
 
     override operator fun get(index: Int): Float = array[index]

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

@@ -13,7 +13,7 @@ import kotlin.jvm.JvmInline
  * @property array the underlying array.
  */
 @JvmInline
-public value class IntBuffer(public val array: IntArray) : MutableBuffer<Int> {
+public value class IntBuffer(public val array: IntArray) : PrimitiveBuffer<Int> {
     override val size: Int get() = array.size
 
     override operator fun get(index: Int): Int = array[index]

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

@@ -13,7 +13,7 @@ import kotlin.jvm.JvmInline
  * @property array the underlying array.
  */
 @JvmInline
-public value class LongBuffer(public val array: LongArray) : MutableBuffer<Long> {
+public value class LongBuffer(public val array: LongArray) : PrimitiveBuffer<Long> {
     override val size: Int get() = array.size
 
     override operator fun get(index: Int): Long = array[index]

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

@@ -94,4 +94,7 @@ public interface MutableBuffer<T> : Buffer<T> {
         public inline fun <reified T : Any> auto(size: Int, initializer: (Int) -> T): MutableBuffer<T> =
             auto(T::class, size, initializer)
     }
-}
+}
+
+
+public sealed interface PrimitiveBuffer<T>: MutableBuffer<T>

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

@@ -3,10 +3,9 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
-package space.kscience.kmath.operations
+package space.kscience.kmath.structures
 
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.structures.*
 
 /**
  * Typealias for buffer transformations.
@@ -103,4 +102,40 @@ public inline fun <T1, T2, reified R : Any> Buffer<T1>.zip(
 ): Buffer<R> {
     require(size == other.size) { "Buffer size mismatch in zip: expected $size but found ${other.size}" }
     return bufferFactory(size) { transform(get(it), other[it]) }
+}
+
+/**
+ * Simular to https://kotlinlang.org/api/latest/jvm/stdlib/kotlin.collections/binary-search.html.
+ * The implementation is copied from Kotlin stdlib
+ */
+public fun <T : Comparable<T>> Buffer<T>.binarySearch(element: T, fromIndex: Int = 0, toIndex: Int = size): Int {
+    var low = fromIndex
+    var high = toIndex - 1
+
+    while (low <= high) {
+        val mid = (low + high).ushr(1) // safe from overflows
+        val midVal = get(mid)
+        val cmp = compareValues(midVal, element)
+
+        when {
+            cmp < 0 -> low = mid + 1
+            cmp > 0 -> high = mid - 1
+            else -> return mid // key found
+        }
+    }
+    return -(low + 1)  // key not found
+}
+
+/**
+ * Create a buffer containing sorted elements of this buffer.
+ */
+@Suppress("CAST_NEVER_SUCCEEDS")
+public fun <T : Comparable<T>> Buffer<T>.sorted(): Buffer<T> = when (this) {
+    is PrimitiveBuffer -> when (this) {
+        is LongBuffer -> toLongArray().apply { sort() }  as Buffer<T>
+        is FloatBuffer -> toFloatArray().apply { sort() }  as Buffer<T>
+        is IntBuffer -> toIntArray().apply { sort() }  as Buffer<T>
+        is DoubleBuffer -> toDoubleArray().apply { sort() }  as Buffer<T>
+    }
+    else -> asIterable().sorted().asBuffer()
 }

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

@@ -0,0 +1,27 @@
+package space.kscience.kmath.structures
+
+import kotlin.test.Test
+import kotlin.test.assertEquals
+import kotlin.test.assertFails
+
+internal class BufferExpandedTest {
+    private val buffer = (0..100).toList().asBuffer()
+
+    @Test
+    fun shrink(){
+        val view = buffer.slice(20U..30U)
+        assertEquals(20, view[0])
+        assertEquals(30, view[10])
+        assertFails { view[11] }
+    }
+
+    @Test
+    fun expandNegative(){
+        val view: BufferView<Int> = buffer.expand(-20..113,0)
+        assertEquals(0,view[4])
+        assertEquals(0,view[123])
+        assertEquals(100, view[120])
+        assertFails { view[-2] }
+        assertFails { view[134] }
+    }
+}

kmath-coroutines/src/jvmTest/kotlin/space/kscience/kmath/streaming/RingBufferTest.kt

@@ -7,7 +7,7 @@ package space.kscience.kmath.streaming
 
 import kotlinx.coroutines.flow.*
 import kotlinx.coroutines.runBlocking
-import space.kscience.kmath.operations.asSequence
+import space.kscience.kmath.structures.asSequence
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

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

@@ -13,9 +13,9 @@ import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.operations.algebra
-import space.kscience.kmath.operations.asIterable
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.asIterable
 import kotlin.math.pow
 
 /*

kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/RealVector.kt

@@ -11,6 +11,7 @@ import space.kscience.kmath.operations.DoubleL2Norm
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.MutableBuffer.Companion.double
 import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.structures.indices
 import kotlin.math.pow
 
 public typealias DoubleVector = Point<Double>

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegrator.kt

@@ -8,6 +8,7 @@ import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.operations.Field
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.structures.indices
 
 /**
  * A simple one-pass integrator based on Gauss rule

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/GaussIntegratorRuleFactory.kt

@@ -5,10 +5,10 @@
 
 package space.kscience.kmath.integration
 
-import space.kscience.kmath.operations.map
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.asBuffer
+import space.kscience.kmath.structures.map
 import kotlin.jvm.Synchronized
 import kotlin.math.ulp
 import kotlin.native.concurrent.ThreadLocal

kmath-functions/src/commonMain/kotlin/space/kscience/kmath/integration/SplineIntegrator.kt

@@ -12,10 +12,14 @@ import space.kscience.kmath.interpolation.SplineInterpolator
 import space.kscience.kmath.interpolation.interpolatePolynomials
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.*
+import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.operations.Field
+import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.operations.sum
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.MutableBufferFactory
+import space.kscience.kmath.structures.map
 
 /**
  * Compute analytical indefinite integral of this [PiecewisePolynomial], keeping all intervals intact

kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/Vector2DTest.kt

@@ -1,6 +1,7 @@
 package space.kscience.kmath.geometry
 
-import space.kscience.kmath.operations.toList
+
+import space.kscience.kmath.structures.toList
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/Vector3DTest.kt

@@ -1,6 +1,6 @@
 package space.kscience.kmath.geometry
 
-import space.kscience.kmath.operations.toList
+import space.kscience.kmath.structures.toList
 import kotlin.test.Test
 import kotlin.test.assertEquals
 

kmath-histograms/src/jvmMain/kotlin/space/kscience/kmath/histogram/UnivariateHistogram.kt

@@ -7,8 +7,8 @@ package space.kscience.kmath.histogram
 
 import space.kscience.kmath.domains.UnivariateDomain
 import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.asSequence
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.asSequence
 
 
 @UnstableKMathAPI

kmath-jupyter/src/main/kotlin/space/kscience/kmath/jupyter/KMathJupyter.kt

@@ -21,9 +21,9 @@ import space.kscience.kmath.expressions.MST
 import space.kscience.kmath.expressions.MstRing
 import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.Structure2D
-import space.kscience.kmath.operations.asSequence
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.asSequence
 
 /**
  * A function for conversion of number to MST for pretty print

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/Distribution.kt

@@ -6,8 +6,8 @@
 package space.kscience.kmath.distributions
 
 import space.kscience.kmath.chains.Chain
+import space.kscience.kmath.samplers.Sampler
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.Sampler
 
 /**
  * A distribution of typed objects.

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/NormalDistribution.kt

@@ -6,8 +6,8 @@
 package space.kscience.kmath.distributions
 
 import space.kscience.kmath.chains.Chain
-import space.kscience.kmath.internal.InternalErf
 import space.kscience.kmath.samplers.GaussianSampler
+import space.kscience.kmath.samplers.InternalErf
 import space.kscience.kmath.samplers.NormalizedGaussianSampler
 import space.kscience.kmath.samplers.ZigguratNormalizedGaussianSampler
 import space.kscience.kmath.stat.RandomGenerator

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/UniformDistribution.kt

@@ -3,12 +3,11 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
-package space.kscience.kmath.stat
+package space.kscience.kmath.distributions
 
 import space.kscience.kmath.chains.Chain
 import space.kscience.kmath.chains.SimpleChain
-import space.kscience.kmath.distributions.Distribution
+import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.distributions.UnivariateDistribution
 
 public class UniformDistribution(public val range: ClosedFloatingPointRange<Double>) : UnivariateDistribution<Double> {
     private val length: Double = range.endInclusive - range.start

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterExponentialSampler.kt

@@ -7,7 +7,6 @@ package space.kscience.kmath.samplers
 
 import space.kscience.kmath.chains.BlockingDoubleChain
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.Sampler
 import space.kscience.kmath.structures.DoubleBuffer
 import kotlin.math.ln
 import kotlin.math.pow
@@ -67,7 +66,7 @@ public class AhrensDieterExponentialSampler(public val mean: Double) : Sampler<D
             var qi = 0.0
 
             DoubleArray(16) { i ->
-                qi += ln2.pow(i + 1.0) / space.kscience.kmath.internal.InternalUtils.factorial(i + 1)
+                qi += ln2.pow(i + 1.0) / InternalUtils.factorial(i + 1)
                 qi
             }
         }

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AhrensDieterMarsagliaTsangGammaSampler.kt

@@ -7,9 +7,7 @@ package space.kscience.kmath.samplers
 
 import space.kscience.kmath.chains.Chain
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.Sampler
 import space.kscience.kmath.stat.chain
-import space.kscience.kmath.stat.next
 import kotlin.math.*
 
 /**

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/AliasMethodDiscreteSampler.kt

@@ -6,9 +6,7 @@
 package space.kscience.kmath.samplers
 
 import space.kscience.kmath.chains.Chain
-import space.kscience.kmath.internal.InternalUtils
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.Sampler
 import space.kscience.kmath.stat.chain
 import kotlin.math.ceil
 import kotlin.math.max

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalErf.kt

@@ -3,7 +3,7 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
-package space.kscience.kmath.internal
+package space.kscience.kmath.samplers
 
 import kotlin.math.abs
 

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalGamma.kt

@@ -3,7 +3,7 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
-package space.kscience.kmath.internal
+package space.kscience.kmath.samplers
 
 import kotlin.math.*
 

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/InternalUtils.kt

@@ -3,7 +3,7 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
-package space.kscience.kmath.internal
+package space.kscience.kmath.samplers
 
 import kotlin.math.ln
 import kotlin.math.min

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/KempSmallMeanPoissonSampler.kt

@@ -7,7 +7,6 @@ package space.kscience.kmath.samplers
 
 import space.kscience.kmath.chains.BlockingIntChain
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.Sampler
 import space.kscience.kmath.structures.IntBuffer
 import kotlin.math.exp
 

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/NormalizedGaussianSampler.kt

@@ -7,7 +7,6 @@ package space.kscience.kmath.samplers
 
 import space.kscience.kmath.chains.BlockingDoubleChain
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.Sampler
 
 public interface BlockingDoubleSampler: Sampler<Double>{
     override fun sample(generator: RandomGenerator): BlockingDoubleChain

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/PoissonSampler.kt

@@ -6,10 +6,8 @@
 package space.kscience.kmath.samplers
 
 import space.kscience.kmath.chains.BlockingIntChain
-import space.kscience.kmath.internal.InternalUtils
 import space.kscience.kmath.misc.toIntExact
 import space.kscience.kmath.stat.RandomGenerator
-import space.kscience.kmath.stat.Sampler
 import space.kscience.kmath.structures.IntBuffer
 import kotlin.math.*
 

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/Sampler.kt

@@ -3,12 +3,16 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
-package space.kscience.kmath.stat
+package space.kscience.kmath.samplers
 
 import kotlinx.coroutines.flow.first
 import space.kscience.kmath.chains.Chain
 import space.kscience.kmath.chains.collect
-import space.kscience.kmath.structures.*
+import space.kscience.kmath.stat.RandomGenerator
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.BufferFactory
+import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.IntBuffer
 import kotlin.jvm.JvmName
 
 /**

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/samplers/SamplerAlgebra.kt

@@ -3,7 +3,7 @@
  * Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file.
  */
 
-package space.kscience.kmath.stat
+package space.kscience.kmath.samplers
 
 import space.kscience.kmath.chains.Chain
 import space.kscience.kmath.chains.ConstantChain
@@ -12,6 +12,7 @@ import space.kscience.kmath.chains.zip
 import space.kscience.kmath.operations.Group
 import space.kscience.kmath.operations.ScaleOperations
 import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.stat.RandomGenerator
 
 /**
  * Implements [Sampler] by sampling only certain [value].

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

@@ -1,80 +1,125 @@
 package space.kscience.kmath.series
 
-import space.kscience.kmath.operations.*
+import space.kscience.kmath.operations.BufferAlgebra
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.RingOps
+import space.kscience.kmath.stat.StatisticalAlgebra
 import space.kscience.kmath.structures.Buffer
-import space.kscience.kmath.structures.BufferFactory
+import space.kscience.kmath.structures.BufferView
-import space.kscience.kmath.structures.getOrNull
 import kotlin.math.max
 import kotlin.math.min
 
-private fun IntRange.intersect(other: IntRange): IntRange =
+@PublishedApi
+internal fun IntRange.intersect(other: IntRange): IntRange =
     max(first, other.first)..min(last, other.last)
 
-private val IntRange.size get() = last - first + 1
+@PublishedApi
+internal val IntRange.size
+    get() = last - first + 1
+
+@PublishedApi
+internal operator fun IntRange.contains(other: IntRange): Boolean = (other.first in this) && (other.last in this)
+
+//TODO add permutated buffer
+//TODO add rank function
+
+
+public interface Series<T> : Buffer<T> {
+    public val origin: Buffer<T>
+    /**
+     * Absolute position of start of this [Series] in [SeriesAlgebra]
+     */
+    public val position: Int
+}
+
+public val <T> Series<T>.absoluteIndices: IntRange get() = position until position + size
+
+/**
+ * A [BufferView] with index offset (both positive and negative) and possible size change
+ */
+private class OffsetBufer<T>(
+    override val origin: Buffer<T>,
+    override val position: Int,
+    override val size: Int = origin.size,
+) : Series<T>, Buffer<T> by origin {
 
-private class BufferView<T>(val buffer: Buffer<T>, val offset: Int, override val size: Int) : Buffer<T> {
     init {
-        require(offset >= 0) { " Range offset must be positive" }
-        require(offset < buffer.size) { "Range offset is beyond the buffer size" }
         require(size > 0) { "Size must be positive" }
-        require(size < buffer.size) { "Slice size is larger than the buffer" }
+        require(size <= origin.size) { "Slice size is larger than the original buffer" }
     }
 
-    override fun get(index: Int): T = buffer[index - offset]
+    override fun toString(): String = "$origin-->${position}"
-
-    override fun iterator(): Iterator<T> = buffer.asSequence().drop(offset).take(size).iterator()
-
-    override fun toString(): String = "$buffer[${offset}:${offset + size - 1}]"
-
-    override val indices: IntRange = offset until offset + size
 }
 
 /**
  * A scope to operation on series
  */
-public class SeriesAlgebra<T, A : Ring<T>, L>(
+public class SeriesAlgebra<T, out A : Ring<T>, out BA : BufferAlgebra<T, A>, L>(
-    public val bufferAlgebra: BufferRingOps<T, A>,
+    override val bufferAlgebra: BA,
     private val labelResolver: (Int) -> L,
-) : RingOps<Buffer<T>> {
+) : RingOps<Buffer<T>>, StatisticalAlgebra<T, A, BA> {
 
-    public val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
+    public val Buffer<T>.indices: IntRange
-    public val bufferFactory: BufferFactory<T> get() = bufferAlgebra.bufferFactory
+        get() = if (this is Series) {
+            absoluteIndices
+        } else {
+            0 until size
+        }
 
-    public val Buffer<T>.offset: UInt get() = indices.first.toUInt()
+    /**
+     * Get the value by absolute index in the series algebra or return null if index is out of range
+     */
+    public fun Buffer<T>.getAbsoluteOrNull(index: Int): T? = when {
+        index !in indices -> null
+        this is Series -> origin[index - position]
+        else -> get(index)
+    }
+
+    /**
+     * Get the value by absolute index in the series algebra or throw [IndexOutOfBoundsException] if index is out of range
+     */
+    public fun Buffer<T>.getAbsolute(index: Int): T =
+        getAbsoluteOrNull(index) ?: throw IndexOutOfBoundsException("Index $index is not in $indices")
+
+    /**
+     * 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)
+    } else {
+        OffsetBufer(this, index, size)
+    }
+
+    /**
+     * Create a buffer view using given absolute range
+     */
+    public fun Buffer<T>.slice(range: IntRange): Series<T> {
+        val size = range.size
+        return if (this is Series) {
+            OffsetBufer(this, indices.first + range.first, size)
+        } else {
+            OffsetBufer(this, range.first, size)
+        }
+    }
+
+    public fun Buffer<T>.expand(range: IntRange, defaultValue: T): Series<T> = if (range in indices) {
+        slice(range)
+    } else {
+        TODO()
+    }
+
+    public val Buffer<T>.offset: Int get() = if (this is Series) position else 0
 
     /**
      * Build a new series
      */
-    public fun series(size: Int, fromIndex: Int = 0, block: A.(label: L) -> T): Buffer<T> {
+    public fun series(size: Int, fromIndex: Int = 0, block: A.(label: L) -> T): Series<T> {
         return bufferFactory(size) {
             val index = it + fromIndex
             elementAlgebra.block(labelResolver(index))
         }.moveTo(fromIndex)
     }
 
-    /**
-     * Move a series starting to start at a given index
-     */
-    public fun Buffer<T>.moveTo(index: Int): Buffer<T> = if (index == 0) {
-        this
-    } else if (this is BufferView) {
-        BufferView(buffer, index.toInt(), size)
-    } else {
-        BufferView(this, index.toInt(), size)
-    }
-
-    /**
-     * Create a buffer view using given range
-     */
-    public fun Buffer<T>.get(range: IntRange): Buffer<T> {
-        val size = range.size
-        return if (this is BufferView) {
-            BufferView(this, indices.first + range.first, size)
-        } else {
-            BufferView(this, range.first, size)
-        }
-    }
-
     /**
      * Get a label buffer for given buffer.
      */
@@ -87,34 +132,15 @@ public class SeriesAlgebra<T, A : Ring<T>, L>(
     public operator fun Buffer<T>.get(label: L): T? {
         val index = labels.indexOf(label)
         if (index == -1) return null
-        return get(index + offset.toInt())
+        return getAbsolute(index + offset.toInt())
-    }
-
-    override fun add(left: Buffer<T>, right: Buffer<T>): Buffer<T> = elementAlgebra.invoke {
-        val newRange = left.indices.intersect(right.indices)
-        //TODO optimize copy at BufferAlgebra level
-        bufferFactory(newRange.size) {
-            val offset = it + newRange.first
-            left[offset] + right[offset]
-        }.moveTo(newRange.first)
-    }
-
-    override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
-
-    override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = elementAlgebra.invoke {
-        val newRange = left.indices.intersect(right.indices)
-        bufferFactory(newRange.size) {
-            val offset = it + newRange.first
-            left[offset] * right[offset]
-        }
     }
 
     /**
      * Map a series to another series of the same size
      */
-    public inline fun Buffer<T>.map(crossinline transform: A.(T) -> T): Buffer<T> {
+    public inline fun Buffer<T>.map(crossinline transform: A.(T) -> T): Series<T> {
         val buf = bufferFactory(size) {
-            elementAlgebra.transform(get(it))
+            elementAlgebra.transform(getAbsolute(it))
         }
         return buf.moveTo(indices.first)
     }
@@ -122,49 +148,63 @@ public class SeriesAlgebra<T, A : Ring<T>, L>(
     /**
      * Map series to another series of the same size with label
      */
-    public inline fun Buffer<T>.mapWithLabel(crossinline transform: A.(arg: T, label: L) -> T): Buffer<T> {
+    public inline fun Buffer<T>.mapWithLabel(crossinline transform: A.(arg: T, label: L) -> T): Series<T> {
         val labels = labels
         val buf = bufferFactory(size) {
-            elementAlgebra.transform(get(it), labels[it])
+            elementAlgebra.transform(getAbsolute(it), labels[it])
         }
         return buf.moveTo(indices.first)
     }
 
     public inline fun <R> Buffer<T>.fold(initial: R, operation: A.(acc: R, T) -> R): R {
         var accumulator = initial
-        for (index in this.indices) accumulator = elementAlgebra.operation(accumulator, get(index))
+        for (index in this.indices) accumulator = elementAlgebra.operation(accumulator, getAbsolute(index))
         return accumulator
     }
 
     public inline fun <R> Buffer<T>.foldWithLabel(initial: R, operation: A.(acc: R, arg: T, label: L) -> R): R {
         val labels = labels
         var accumulator = initial
-        for (index in this.indices) accumulator = elementAlgebra.operation(accumulator, get(index), labels[index])
+        for (index in this.indices) accumulator =
+            elementAlgebra.operation(accumulator, getAbsolute(index), labels[index])
         return accumulator
     }
 
     /**
-     * Zip two buffers replacing missing values with [defaultValue]
+     * Zip two buffers in the range whe they overlap
      */
     public inline fun Buffer<T>.zip(
         other: Buffer<T>,
-        defaultValue: T,
+        crossinline operation: A.(left: T, right: T) -> T,
-        crossinline operation: A.(left: T?, right: T?) -> T?,
+    ): Series<T> {
-    ): Buffer<T> {
+        val newRange = indices.intersect(other.indices)
-        val start = min(indices.first, other.indices.first)
+        return bufferFactory(newRange.size) {
-        val size = max(indices.last, other.indices.last) - start
-        return bufferFactory(size) {
             elementAlgebra.operation(
-                getOrNull(it) ?: defaultValue,
+                getAbsolute(it),
-                other.getOrNull(it) ?: defaultValue
+                other.getAbsolute(it)
-            ) ?: defaultValue
+            )
-        }
+        }.moveTo(newRange.first)
     }
+
+    override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
+
+    override fun add(left: Buffer<T>, right: Buffer<T>): Series<T> = left.zip(right) { l, r -> l + r }
+
+    override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = left.zip(right) { l, r -> l * r }
 }
 
-public fun <T, A : Ring<T>, L> BufferRingOps<T, A>.seriesAlgebra(labels: Iterable<L>): SeriesAlgebra<T, A, L> {
+public fun <T, A : Ring<T>, BA : BufferAlgebra<T, A>, L> BA.seriesAlgebra(labels: Iterable<L>): SeriesAlgebra<T, A, BA, L> {
     val l = labels.toList()
     return SeriesAlgebra(this) {
         if (it in l.indices) l[it] else error("Index $it is outside of labels range ${l.indices}")
     }
-}
+}
+
+public fun <T, A : Ring<T>, BA : BufferAlgebra<T, A>, L> BA.seriesAlgebra(labelGenerator: (Int) -> L): SeriesAlgebra<T, A, BA, L> =
+    SeriesAlgebra(this, labelGenerator)
+
+/**
+ * Create a series algebra using offset as a label
+ */
+public fun <T, A : Ring<T>, BA : BufferAlgebra<T, A>> BA.seriesAlgebra(): SeriesAlgebra<T, A, BA, Int> =
+    SeriesAlgebra(this) { it }

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

@@ -0,0 +1,97 @@
+package space.kscience.kmath.series
+
+import space.kscience.kmath.operations.BufferAlgebra
+import space.kscience.kmath.operations.ExponentialOperations
+import space.kscience.kmath.operations.PowerOperations
+import space.kscience.kmath.operations.TrigonometricOperations
+import space.kscience.kmath.structures.Buffer
+
+
+//trigonometric
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.sin(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : TrigonometricOperations<Buffer<T>> =
+    bufferAlgebra.sin(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.cos(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : TrigonometricOperations<Buffer<T>> =
+    bufferAlgebra.cos(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.tan(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : TrigonometricOperations<Buffer<T>> =
+    bufferAlgebra.tan(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.asin(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : TrigonometricOperations<Buffer<T>> =
+    bufferAlgebra.asin(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.acos(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : TrigonometricOperations<Buffer<T>> =
+    bufferAlgebra.acos(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.atan(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : TrigonometricOperations<Buffer<T>> =
+    bufferAlgebra.atan(arg).moveTo(arg.offset)
+
+
+//exponential
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.exp(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.exp(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.ln(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.ln(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.sinh(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.sinh(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.cosh(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.cosh(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.tanh(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.tanh(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.asinh(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.asinh(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.acosh(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.acosh(arg).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.atanh(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : ExponentialOperations<Buffer<T>> =
+    bufferAlgebra.atanh(arg).moveTo(arg.offset)
+
+
+//power
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.power(
+    arg: Buffer<T>,
+    pow: Number,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : PowerOperations<Buffer<T>> =
+    bufferAlgebra.power(arg, pow).moveTo(arg.offset)
+
+public fun <T, BA> SeriesAlgebra<T, *, BA, *>.sqrt(
+    arg: Buffer<T>,
+): Series<T> where BA : BufferAlgebra<T, *>, BA : PowerOperations<Buffer<T>> =
+    bufferAlgebra.sqrt(arg).moveTo(arg.offset)

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Mean.kt

@@ -7,6 +7,7 @@ package space.kscience.kmath.stat
 
 import space.kscience.kmath.operations.*
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.indices
 
 /**
  * Arithmetic mean

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Median.kt

@@ -5,8 +5,8 @@
 
 package space.kscience.kmath.stat
 
-import space.kscience.kmath.operations.asSequence
 import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.asSequence
 
 /**
  * Non-composable median

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/Rank.kt

@@ -0,0 +1,28 @@
+package space.kscience.kmath.stat
+
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.asIterable
+
+public class Rank<T: Comparable<T>>: BlockingStatistic<T, IntArray> {
+    override fun evaluateBlocking(data: Buffer<T>): IntArray {
+        // https://www.geeksforgeeks.org/rank-elements-array/
+        val permutations = ArrayList<Pair<T, Int>>(data.size)
+        data.asIterable().mapIndexedTo(permutations) { i, v -> v to i }
+        permutations.sortBy { it.first }
+        var rank = 1
+        var i = 0
+        val r = IntArray(data.size) { 0 }
+        while (i < data.size) {
+            var j = i
+            while (j < data.size - 1 && permutations[j].first == permutations[j + 1]) ++j
+            val n = j - i + 1
+            (0 until n).map { k ->
+                val idx = permutations[i + k].second
+                r[idx] = rank + ((n - 1) * 0.5f).toInt()
+            }
+            rank += n
+            i += n
+        }
+        return r
+    }
+}

kmath-stat/src/commonMain/kotlin/space/kscience/kmath/stat/StatisticalAlgebra.kt

@@ -0,0 +1,59 @@
+package space.kscience.kmath.stat
+
+import space.kscience.kmath.operations.*
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.BufferFactory
+import space.kscience.kmath.structures.asIterable
+import space.kscience.kmath.structures.sorted
+
+public interface StatisticalAlgebra<T, out A : Algebra<T>, out BA : BufferAlgebra<T, A>> : Algebra<Buffer<T>> {
+    public val bufferAlgebra: BA
+    public val elementAlgebra: A get() = bufferAlgebra.elementAlgebra
+    public val bufferFactory: BufferFactory<T> get() = bufferAlgebra.bufferFactory
+}
+
+/**
+ * Compute [empirical CDF function](https://en.wikipedia.org/wiki/Empirical_distribution_function)
+ */
+public fun <T : Comparable<T>> StatisticalAlgebra<T, *, *>.ecdf(buffer: Buffer<T>): (T) -> Double = { arg ->
+    buffer.asIterable().count { it < arg }.toDouble() / buffer.size
+}
+
+/**
+ * Implementation copied from https://commons.apache.org/proper/commons-math/javadocs/api-3.6.1/index.html?org/apache/commons/math3/stat/inference/KolmogorovSmirnovTest.html
+ */
+public fun <T : Comparable<T>, A, BA : BufferAlgebra<T, A>> StatisticalAlgebra<T, A, BA>.kolmogorovSmirnovTest(
+    x: Buffer<T>,
+    y: Buffer<T>,
+): T where A : Group<T>, A : NumericAlgebra<T> = elementAlgebra.invoke {
+    // Copy and sort the sample arrays
+    val sx = x.sorted()
+    val sy = y.sorted()
+    val n = sx.size
+    val m = sy.size
+
+    var rankX = 0
+    var rankY = 0
+    var curD: T = zero
+
+    // Find the max difference between cdf_x and cdf_y
+    var supD: T = zero
+    do {
+        val z = if (sx[rankX] <= sy[rankY]) sx[rankX] else sy[rankY]
+        while (rankX < n && sx[rankX].compareTo(z) == 0) {
+            rankX += 1;
+            curD += number(m);
+        }
+
+        while (rankY < m && sy[rankY].compareTo(z) == 0) {
+            rankY += 1;
+            curD -= number(n);
+        }
+
+        when {
+            curD > supD -> supD = curD
+            -curD > supD -> supD = -curD
+        }
+    } while (rankX < n && rankY < m);
+    return supD;
+}

kmath-stat/src/jvmTest/kotlin/space/kscience/kmath/stat/SamplerTest.kt

@@ -6,6 +6,8 @@
 package space.kscience.kmath.stat
 
 import kotlinx.coroutines.runBlocking
+import space.kscience.kmath.samplers.Sampler
+import space.kscience.kmath.samplers.sampleBuffer
 import kotlin.test.Test
 
 class SamplerTest {

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

@@ -15,6 +15,7 @@ import space.kscience.kmath.nd.as1D
 import space.kscience.kmath.nd.as2D
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.MutableBuffer
+import space.kscience.kmath.structures.indices
 import space.kscience.kmath.tensors.api.AnalyticTensorAlgebra
 import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
 import space.kscience.kmath.tensors.api.Tensor

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

@@ -12,9 +12,9 @@ import space.kscience.kmath.nd.MutableStructure1D
 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.asSequence
 import space.kscience.kmath.tensors.core.BufferedTensor
 import space.kscience.kmath.tensors.core.DoubleTensor
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra

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

@@ -6,7 +6,6 @@
 package space.kscience.kmath.tensors.core.internal
 
 import space.kscience.kmath.nd.as1D
-import space.kscience.kmath.operations.toMutableList
 import space.kscience.kmath.samplers.GaussianSampler
 import space.kscience.kmath.stat.RandomGenerator
 import space.kscience.kmath.structures.*