Major tensor refactoring

CHANGELOG.md

@@ -2,11 +2,14 @@
 
 ## [Unreleased]
 ### Added
+- Type-aliases for numbers like `Float64`
 - 2D optimal trajectory computation in a separate module `kmath-trajectory`
 - Autodiff for generic algebra elements in core!
 - Algebra now has an obligatory `bufferFactory` (#477).
 
 ### Changed
+- Tensor operations switched to prefix notation
+- Row-wise and column-wise ND shapes in the core
 - Shape is read-only
 - Major refactor of tensors (only minor API changes)
 - Kotlin 1.7.20

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

@@ -13,6 +13,8 @@ import space.kscience.kmath.linear.linearSpace
 import space.kscience.kmath.linear.matrix
 import space.kscience.kmath.linear.symmetric
 import space.kscience.kmath.operations.DoubleField
+import space.kscience.kmath.tensors.core.symEigJacobi
+import space.kscience.kmath.tensors.core.symEigSvd
 import space.kscience.kmath.tensors.core.tensorAlgebra
 import kotlin.random.Random
 
@@ -27,11 +29,11 @@ internal class TensorAlgebraBenchmark {
 
     @Benchmark
     fun tensorSymEigSvd(blackhole: Blackhole) = with(Double.tensorAlgebra) {
-        blackhole.consume(matrix.symEigSvd(1e-10))
+        blackhole.consume(symEigSvd(matrix, 1e-10))
     }
 
     @Benchmark
     fun tensorSymEigJacobi(blackhole: Blackhole) = with(Double.tensorAlgebra) {
-        blackhole.consume(matrix.symEigJacobi(50, 1e-10))
+        blackhole.consume(symEigJacobi(matrix, 50, 1e-10))
     }
 }

build.gradle.kts

@@ -15,7 +15,7 @@ allprojects {
     }
 
     group = "space.kscience"
-    version = "0.3.1-dev-6"
+    version = "0.3.1-dev-7"
 }
 
 subprojects {

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

@@ -8,17 +8,20 @@ package space.kscience.kmath.structures
 import space.kscience.kmath.nd.BufferND
 import space.kscience.kmath.nd.ShapeND
 import space.kscience.kmath.nd.StructureND
-import space.kscience.kmath.operations.map
+import space.kscience.kmath.operations.mapToBuffer
 import kotlin.system.measureTimeMillis
 
-private inline fun <T, reified R: Any> BufferND<T>.map(block: (T) -> R): BufferND<R> = BufferND(indices, buffer.map(block))
+private inline fun <T, reified R : Any> BufferND<T>.mapToBufferND(
+    bufferFactory: BufferFactory<R> = BufferFactory.auto(),
+    crossinline block: (T) -> R,
+): BufferND<R> = BufferND(indices, buffer.mapToBuffer(bufferFactory, block))
 
 @Suppress("UNUSED_VARIABLE")
 fun main() {
     val n = 6000
     val structure = StructureND.buffered(ShapeND(n, n), Buffer.Companion::auto) { 1.0 }
-    structure.map { it + 1 } // warm-up
+    structure.mapToBufferND { it + 1 } // warm-up
-    val time1 = measureTimeMillis { val res = structure.map { it + 1 } }
+    val time1 = measureTimeMillis { val res = structure.mapToBufferND { it + 1 } }
     println("Structure mapping finished in $time1 millis")
     val array = DoubleArray(n * n) { 1.0 }
 

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

@@ -5,18 +5,17 @@
 
 package space.kscience.kmath.tensors
 
-import space.kscience.kmath.misc.PerformancePitfall
 import space.kscience.kmath.nd.ShapeND
 import space.kscience.kmath.nd.contentEquals
 import space.kscience.kmath.operations.invoke
 import space.kscience.kmath.tensors.core.DoubleTensor
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
-
+import space.kscience.kmath.tensors.core.randomNormal
+import space.kscience.kmath.tensors.core.randomNormalLike
 import kotlin.math.abs
 
 // OLS estimator using SVD
 
-@OptIn(PerformancePitfall::class)
 fun main() {
     //seed for random
     val randSeed = 100500L
@@ -42,10 +41,10 @@ fun main() {
 
         // calculate y and add gaussian noise (N(0, 0.05))
         val y = x dot alpha
-        y += y.randomNormalLike(randSeed) * 0.05
+        y += randomNormalLike(y, randSeed) * 0.05
 
         // now restore the coefficient vector with OSL estimator with SVD
-        val (u, singValues, v) = x.svd()
+        val (u, singValues, v) = svd(x)
 
         // we have to make sure the singular values of the matrix are not close to zero
         println("Singular values:\n$singValues")
@@ -66,7 +65,7 @@ fun main() {
             require(yTrue.shape contentEquals yPred.shape)
 
             val diff = yTrue - yPred
-            return diff.dot(diff).sqrt().value()
+            return sqrt(diff.dot(diff)).value()
         }
 
         println("MSE: ${mse(alpha, alphaOLS)}")

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

@@ -6,8 +6,7 @@
 package space.kscience.kmath.tensors
 
 import space.kscience.kmath.nd.ShapeND
-import space.kscience.kmath.tensors.core.tensorAlgebra
+import space.kscience.kmath.tensors.core.*
-import space.kscience.kmath.tensors.core.withBroadcast
 
 
 // simple PCA
@@ -22,7 +21,7 @@ fun main(): Unit = Double.tensorAlgebra.withBroadcast {  // work in context with
     )
 
     // take y dependent on x with noise
-    val y = 2.0 * x + (3.0 + x.randomNormalLike(seed) * 1.5)
+    val y = 2.0 * x + (3.0 + randomNormalLike(x, seed) * 1.5)
 
     println("x:\n$x")
     println("y:\n$y")
@@ -31,14 +30,14 @@ fun main(): Unit = Double.tensorAlgebra.withBroadcast {  // work in context with
     val dataset = stack(listOf(x, y)).transposed()
 
     // normalize both x and y
-    val xMean = x.mean()
+    val xMean = mean(x)
-    val yMean = y.mean()
+    val yMean = mean(y)
 
-    val xStd = x.std()
+    val xStd = std(x)
-    val yStd = y.std()
+    val yStd = std(y)
 
-    val xScaled = (x - xMean) / xStd
+    val xScaled: DoubleTensor = (x - xMean) / xStd
-    val yScaled = (y - yMean) / yStd
+    val yScaled: DoubleTensor = (y - yMean) / yStd
 
     // save means ans standard deviations for further recovery
     val mean = fromArray(
@@ -54,11 +53,11 @@ fun main(): Unit = Double.tensorAlgebra.withBroadcast {  // work in context with
     println("Standard deviations:\n$std")
 
     // calculate the covariance matrix of scaled x and y
-    val covMatrix = cov(listOf(xScaled, yScaled))
+    val covMatrix = covariance(listOf(xScaled.asDoubleTensor1D(), yScaled.asDoubleTensor1D()))
     println("Covariance matrix:\n$covMatrix")
 
     // and find out eigenvector of it
-    val (_, evecs) = covMatrix.symEig()
+    val (_, evecs) = symEig(covMatrix)
     val v = evecs.getTensor(0)
     println("Eigenvector:\n$v")
 

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

@@ -6,6 +6,7 @@
 package space.kscience.kmath.tensors
 
 import space.kscience.kmath.nd.ShapeND
+import space.kscience.kmath.tensors.core.randomNormal
 import space.kscience.kmath.tensors.core.tensorAlgebra
 import space.kscience.kmath.tensors.core.withBroadcast
 
@@ -23,8 +24,8 @@ fun main() = Double.tensorAlgebra.withBroadcast {  // work in context with broad
 
 
     // find out mean and standard deviation of each column
-    val mean = dataset.mean(0, false)
+    val mean = mean(dataset, 0, false)
-    val std = dataset.std(0, false)
+    val std = std(dataset, 0, false)
 
     println("Mean:\n$mean")
     println("Standard deviation:\n$std")
@@ -36,8 +37,8 @@ fun main() = Double.tensorAlgebra.withBroadcast {  // work in context with broad
     // now we can scale dataset with mean normalization
     val datasetScaled = (dataset - mean) / std
 
-    // find out mean and std of scaled dataset
+    // find out mean and standardDiviation of scaled dataset
 
-    println("Mean of scaled:\n${datasetScaled.mean(0, false)}")
+    println("Mean of scaled:\n${mean(datasetScaled, 0, false)}")
-    println("Mean of scaled:\n${datasetScaled.std(0, false)}")
+    println("Mean of scaled:\n${std(datasetScaled, 0, false)}")
 }

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

@@ -41,7 +41,7 @@ fun main() = Double.tensorAlgebra.withBroadcast {// work in context with linear
     // solve `Ax = b` system using LUP decomposition
 
     // get P, L, U such that PA = LU
-    val (p, l, u) = a.lu()
+    val (p, l, u) = lu(a)
 
     // check P is permutation matrix
     println("P:\n$p")

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

@@ -9,10 +9,7 @@ import space.kscience.kmath.nd.ShapeND
 import space.kscience.kmath.nd.contentEquals
 import space.kscience.kmath.operations.asIterable
 import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.*
-import space.kscience.kmath.tensors.core.DoubleTensor
-import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
-import space.kscience.kmath.tensors.core.toDoubleTensor
 import kotlin.math.sqrt
 
 const val seed = 100500L
@@ -51,7 +48,7 @@ fun reluDer(x: DoubleTensor): DoubleTensor = DoubleTensorAlgebra {
 class ReLU : Activation(::relu, ::reluDer)
 
 fun sigmoid(x: DoubleTensor): DoubleTensor = DoubleTensorAlgebra {
-    1.0 / (1.0 + (-x).exp())
+    1.0 / (1.0 + exp((-x)))
 }
 
 fun sigmoidDer(x: DoubleTensor): DoubleTensor = DoubleTensorAlgebra {
@@ -85,7 +82,7 @@ class Dense(
         val gradInput = outputError dot weights.transposed()
 
         val gradW = input.transposed() dot outputError
-        val gradBias = outputError.mean(dim = 0, keepDim = false) * input.shape[0].toDouble()
+        val gradBias = mean(structureND = outputError, dim = 0, keepDim = false) * input.shape[0].toDouble()
 
         weights -= learningRate * gradW
         bias -= learningRate * gradBias
@@ -118,7 +115,7 @@ class NeuralNetwork(private val layers: List<Layer>) {
             onesForAnswers[intArrayOf(index, label)] = 1.0
         }
 
-        val softmaxValue = yPred.exp() / yPred.exp().sum(dim = 1, keepDim = true)
+        val softmaxValue = exp(yPred) / exp(yPred).sum(dim = 1, keepDim = true)
 
         (-onesForAnswers + softmaxValue) / (yPred.shape[0].toDouble())
     }
@@ -176,7 +173,6 @@ class NeuralNetwork(private val layers: List<Layer>) {
 }
 
 
-@OptIn(ExperimentalStdlibApi::class)
 fun main() = BroadcastDoubleTensorAlgebra {
     val features = 5
     val sampleSize = 250

gradle.properties

@@ -11,3 +11,7 @@ org.gradle.configureondemand=true
 org.gradle.jvmargs=-Xmx4096m
 
 toolsVersion=0.13.1-kotlin-1.7.20
+
+
+org.gradle.parallel=true
+org.gradle.workers.max=4

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

@@ -13,12 +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.operations.DoubleBufferOps.Companion.map
 import space.kscience.kmath.optimization.*
 import space.kscience.kmath.random.RandomGenerator
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.asBuffer
-import kotlin.math.pow
 import kotlin.test.Test
 
 internal class OptimizeTest {

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

@@ -268,7 +268,7 @@ public open class DSRing<T, A>(
 
     protected fun DS<T, A>.mapData(block: A.(T) -> T): DS<T, A> {
         require(derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" }
-        val newData: Buffer<T> = data.map(valueBufferFactory) {
+        val newData: Buffer<T> = data.mapToBuffer(valueBufferFactory) {
             algebra.block(it)
         }
         return DS(newData)
@@ -276,7 +276,7 @@ public open class DSRing<T, A>(
 
     protected fun DS<T, A>.mapDataIndexed(block: (Int, T) -> T): DS<T, A> {
         require(derivativeAlgebra == this@DSRing) { "All derivative operations should be done in the same algebra" }
-        val newData: Buffer<T> = data.mapIndexed(valueBufferFactory, block)
+        val newData: Buffer<T> = data.mapIndexedToBuffer(valueBufferFactory, block)
         return DS(newData)
     }
 

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

@@ -11,6 +11,8 @@ import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.indices
 import kotlin.jvm.JvmName
 
+//TODO move to stat
+
 /**
  * Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic
  * differentiation.

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

@@ -5,8 +5,6 @@
 
 package space.kscience.kmath.operations
 
-import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.operations.DoubleField.pow
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.DoubleBuffer
 
@@ -32,9 +30,9 @@ public class DoubleBufferField(public val size: Int) : ExtendedField<Buffer<Doub
     override fun atanh(arg: Buffer<Double>): DoubleBuffer = super<DoubleBufferOps>.atanh(arg)
 
     override fun power(arg: Buffer<Double>, pow: Number): DoubleBuffer = if (pow.isInteger()) {
-        arg.mapInline { it.pow(pow.toInt()) }
+        arg.map { it.pow(pow.toInt()) }
     } else {
-        arg.mapInline {
+        arg.map {
             if(it<0) throw IllegalArgumentException("Negative argument $it could not be raised to the fractional power")
             it.pow(pow.toDouble())
         }
@@ -42,103 +40,4 @@ public class DoubleBufferField(public val size: Int) : ExtendedField<Buffer<Doub
 
     override fun unaryOperationFunction(operation: String): (arg: Buffer<Double>) -> Buffer<Double> =
         super<ExtendedField>.unaryOperationFunction(operation)
-
-    //    override fun number(value: Number): Buffer<Double> = DoubleBuffer(size) { value.toDouble() }
-//
-//    override fun Buffer<Double>.unaryMinus(): Buffer<Double> = DoubleBufferOperations.run {
-//        -this@unaryMinus
-//    }
-//
-//    override fun add(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
-//        require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
-//        return DoubleBufferOperations.add(a, b)
-//    }
-//
-
-//
-//    override fun multiply(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
-//        require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
-//        return DoubleBufferOperations.multiply(a, b)
-//    }
-//
-//    override fun divide(a: Buffer<Double>, b: Buffer<Double>): DoubleBuffer {
-//        require(a.size == size) { "The buffer size ${a.size} does not match context size $size" }
-//        return DoubleBufferOperations.divide(a, b)
-//    }
-//
-//    override fun sin(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.sin(arg)
-//    }
-//
-//    override fun cos(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.cos(arg)
-//    }
-//
-//    override fun tan(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.tan(arg)
-//    }
-//
-//    override fun asin(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.asin(arg)
-//    }
-//
-//    override fun acos(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.acos(arg)
-//    }
-//
-//    override fun atan(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.atan(arg)
-//    }
-//
-//    override fun sinh(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.sinh(arg)
-//    }
-//
-//    override fun cosh(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.cosh(arg)
-//    }
-//
-//    override fun tanh(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.tanh(arg)
-//    }
-//
-//    override fun asinh(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.asinh(arg)
-//    }
-//
-//    override fun acosh(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.acosh(arg)
-//    }
-//
-//    override fun atanh(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.atanh(arg)
-//    }
-//
-//    override fun power(arg: Buffer<Double>, pow: Number): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.power(arg, pow)
-//    }
-//
-//    override fun exp(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.exp(arg)
-//    }
-//
-//    override fun ln(arg: Buffer<Double>): DoubleBuffer {
-//        require(arg.size == size) { "The buffer size ${arg.size} does not match context size $size" }
-//        return DoubleBufferOperations.ln(arg)
-//    }
-
 }

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

@@ -6,10 +6,8 @@
 package space.kscience.kmath.operations
 
 import space.kscience.kmath.linear.Point
-import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.misc.UnstableKMathAPI
-import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.structures.*
-import space.kscience.kmath.structures.MutableBufferFactory
-import space.kscience.kmath.structures.asBuffer
 import kotlin.math.*
 
 /**
@@ -19,10 +17,29 @@ public abstract class DoubleBufferOps : BufferAlgebra<Double, DoubleField>, Exte
     Norm<Buffer<Double>, Double> {
 
     override val elementAlgebra: DoubleField get() = DoubleField
+
     override val elementBufferFactory: MutableBufferFactory<Double> get() = elementAlgebra.bufferFactory
 
-    override fun Buffer<Double>.map(block: DoubleField.(Double) -> Double): DoubleBuffer =
+    @Suppress("OVERRIDE_BY_INLINE")
-        mapInline { DoubleField.block(it) }
+    @OptIn(UnstableKMathAPI::class)
+    final override inline fun Buffer<Double>.map(block: DoubleField.(Double) -> Double): DoubleBuffer =
+        DoubleArray(size) { DoubleField.block(getDouble(it)) }.asBuffer()
+
+
+    @OptIn(UnstableKMathAPI::class)
+    @Suppress("OVERRIDE_BY_INLINE")
+    final override inline fun Buffer<Double>.mapIndexed(block: DoubleField.(index: Int, arg: Double) -> Double): DoubleBuffer =
+        DoubleBuffer(size) { DoubleField.block(it, getDouble(it)) }
+
+    @OptIn(UnstableKMathAPI::class)
+    @Suppress("OVERRIDE_BY_INLINE")
+    final override inline fun Buffer<Double>.zip(
+        other: Buffer<Double>,
+        block: DoubleField.(left: Double, right: Double) -> Double,
+    ): DoubleBuffer {
+        require(size == other.size) { "Incompatible buffer sizes. left: ${size}, right: ${other.size}" }
+        return DoubleBuffer(size) { DoubleField.block(getDouble(it), other.getDouble(it)) }
+    }
 
     override fun unaryOperationFunction(operation: String): (arg: Buffer<Double>) -> Buffer<Double> =
         super<ExtendedFieldOps>.unaryOperationFunction(operation)
@@ -30,7 +47,7 @@ public abstract class DoubleBufferOps : BufferAlgebra<Double, DoubleField>, Exte
     override fun binaryOperationFunction(operation: String): (left: Buffer<Double>, right: Buffer<Double>) -> Buffer<Double> =
         super<ExtendedFieldOps>.binaryOperationFunction(operation)
 
-    override fun Buffer<Double>.unaryMinus(): DoubleBuffer = mapInline { -it }
+    override fun Buffer<Double>.unaryMinus(): DoubleBuffer = map { -it }
 
     override fun add(left: Buffer<Double>, right: Buffer<Double>): DoubleBuffer {
         require(right.size == left.size) {
@@ -77,6 +94,7 @@ public abstract class DoubleBufferOps : BufferAlgebra<Double, DoubleField>, Exte
 //        } else RealBuffer(DoubleArray(a.size) { a[it] / kValue })
 //    }
 
+    @UnstableKMathAPI
     override fun multiply(left: Buffer<Double>, right: Buffer<Double>): DoubleBuffer {
         require(right.size == left.size) {
             "The size of the first buffer ${left.size} should be the same as for second one: ${right.size} "
@@ -101,55 +119,83 @@ public abstract class DoubleBufferOps : BufferAlgebra<Double, DoubleField>, Exte
         } else DoubleBuffer(DoubleArray(left.size) { left[it] / right[it] })
     }
 
-    override fun sin(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::sin)
+    override fun sin(arg: Buffer<Double>): DoubleBuffer = arg.map { sin(it) }
 
-    override fun cos(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::cos)
+    override fun cos(arg: Buffer<Double>): DoubleBuffer = arg.map { cos(it) }
 
-    override fun tan(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::tan)
+    override fun tan(arg: Buffer<Double>): DoubleBuffer = arg.map { tan(it) }
 
-    override fun asin(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::asin)
+    override fun asin(arg: Buffer<Double>): DoubleBuffer = arg.map { asin(it) }
 
-    override fun acos(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::acos)
+    override fun acos(arg: Buffer<Double>): DoubleBuffer = arg.map { acos(it) }
 
-    override fun atan(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::atan)
+    override fun atan(arg: Buffer<Double>): DoubleBuffer = arg.map { atan(it) }
 
-    override fun sinh(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::sinh)
+    override fun sinh(arg: Buffer<Double>): DoubleBuffer = arg.map { sinh(it) }
 
-    override fun cosh(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::cosh)
+    override fun cosh(arg: Buffer<Double>): DoubleBuffer = arg.map { cosh(it) }
 
-    override fun tanh(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::tanh)
+    override fun tanh(arg: Buffer<Double>): DoubleBuffer = arg.map { tanh(it) }
 
-    override fun asinh(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::asinh)
+    override fun asinh(arg: Buffer<Double>): DoubleBuffer = arg.map { asinh(it) }
 
-    override fun acosh(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::acosh)
+    override fun acosh(arg: Buffer<Double>): DoubleBuffer = arg.map { acosh(it) }
 
-    override fun atanh(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::atanh)
+    override fun atanh(arg: Buffer<Double>): DoubleBuffer = arg.map { atanh(it) }
 
-    override fun exp(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::exp)
+    override fun exp(arg: Buffer<Double>): DoubleBuffer = arg.map { exp(it) }
 
-    override fun ln(arg: Buffer<Double>): DoubleBuffer = arg.mapInline(::ln)
+    override fun ln(arg: Buffer<Double>): DoubleBuffer = arg.map { ln(it) }
 
     override fun norm(arg: Buffer<Double>): Double = DoubleL2Norm.norm(arg)
 
-    override fun scale(a: Buffer<Double>, value: Double): DoubleBuffer = a.mapInline { it * value }
+    override fun scale(a: Buffer<Double>, value: Double): DoubleBuffer = a.map { it * value }
 
     override fun power(arg: Buffer<Double>, pow: Number): Buffer<Double> = if (pow is Int) {
-        arg.mapInline { it.pow(pow) }
+        arg.map { it.pow(pow) }
     } else {
-        arg.mapInline { it.pow(pow.toDouble()) }
+        arg.map { it.pow(pow.toDouble()) }
     }
 
-    public companion object : DoubleBufferOps() {
+    public companion object : DoubleBufferOps()
-        public inline fun Buffer<Double>.mapInline(block: (Double) -> Double): DoubleBuffer =
-            if (this is DoubleBuffer) {
-                DoubleArray(size) { block(array[it]) }.asBuffer()
-            } else {
-                DoubleArray(size) { block(get(it)) }.asBuffer()
-            }
-    }
 }
 
 public object DoubleL2Norm : Norm<Point<Double>, Double> {
     override fun norm(arg: Point<Double>): Double = sqrt(arg.fold(0.0) { acc: Double, d: Double -> acc + d.pow(2) })
 }
 
+public fun DoubleBufferOps.sum(buffer: Buffer<Double>): Double = buffer.reduce(Double::plus)
+
+/**
+ * Sum of elements using given [conversion]
+ */
+public inline fun <T> DoubleBufferOps.sumOf(buffer: Buffer<T>, conversion: (T) -> Double): Double =
+    buffer.fold(0.0) { acc, value -> acc + conversion(value) }
+
+public fun DoubleBufferOps.average(buffer: Buffer<Double>): Double = sum(buffer) / buffer.size
+
+/**
+ * Average of elements using given [conversion]
+ */
+public inline fun <T> DoubleBufferOps.averageOf(buffer: Buffer<T>, conversion: (T) -> Double): Double =
+    sumOf(buffer, conversion) / buffer.size
+
+public fun DoubleBufferOps.dispersion(buffer: Buffer<Double>): Double {
+    val av = average(buffer)
+    return buffer.fold(0.0) { acc, value -> acc + (value - av).pow(2) } / buffer.size
+}
+
+public fun DoubleBufferOps.std(buffer: Buffer<Double>): Double = sqrt(dispersion(buffer))
+
+public fun DoubleBufferOps.covariance(x: Buffer<Double>, y: Buffer<Double>): Double {
+    require(x.size == y.size) { "Expected buffers of the same size, but x.size == ${x.size} and y.size == ${y.size}" }
+    val xMean = average(x)
+    val yMean = average(y)
+    var sum = 0.0
+    x.indices.forEach {
+        sum += (x[it] - xMean) * (y[it] - yMean)
+    }
+    return sum / (x.size - 1)
+}
+
+

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

@@ -5,6 +5,21 @@
 
 package space.kscience.kmath.operations
 
+import space.kscience.kmath.misc.PerformancePitfall
+import space.kscience.kmath.structures.Buffer
+
+/**
+ * Returns the sum of all elements in the iterable in this [Group].
+ *
+ * @receiver the algebra that provides addition.
+ * @param data the iterable to sum up.
+ * @return the sum.
+ */
+@PerformancePitfall("Potential boxing access to buffer elements")
+public fun <T> Group<T>.sum(data: Buffer<T>): T = data.fold(zero) { left, right ->
+    add(left, right)
+}
+
 /**
  * Returns the sum of all elements in the iterable in this [Group].
  *
@@ -29,6 +44,18 @@ public fun <T> Group<T>.sum(data: Sequence<T>): T = data.fold(zero) { left, righ
     add(left, right)
 }
 
+/**
+ * Returns an average value of elements in the iterable in this [Group].
+ *
+ * @receiver the algebra that provides addition and division.
+ * @param data the iterable to find average.
+ * @return the average value.
+ * @author Iaroslav Postovalov
+ */
+@PerformancePitfall("Potential boxing access to buffer elements")
+public fun <T, S> S.average(data: Buffer<T>): T where S : Group<T>, S : ScaleOperations<T> =
+    sum(data) / data.size
+
 /**
  * Returns an average value of elements in the iterable in this [Group].
  *
@@ -95,4 +122,3 @@ public fun <T, S> Iterable<T>.averageWith(space: S): T where S : Group<T>, S : S
  */
 public fun <T, S> Sequence<T>.averageWith(space: S): T where S : Group<T>, S : ScaleOperations<T> =
     space.average(this)
-

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

@@ -57,6 +57,9 @@ public fun Buffer<Double>.toDoubleArray(): DoubleArray = when (this) {
     else -> DoubleArray(size, ::get)
 }
 
+/**
+ * Represent this buffer as [DoubleBuffer]. Does not guarantee that changes in the original buffer are reflected on this buffer.
+ */
 public fun Buffer<Double>.toDoubleBuffer(): DoubleBuffer = when (this) {
     is DoubleBuffer -> this
     else -> DoubleArray(size, ::get).asBuffer()

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

@@ -61,18 +61,18 @@ public fun <T> Buffer<T>.toMutableList(): MutableList<T> = when (this) {
  */
 @UnstableKMathAPI
 public inline fun <reified T> Buffer<T>.toTypedArray(): Array<T> = Array(size, ::get)
-
+//
-/**
+///**
- * Create a new buffer from this one with the given mapping function and using [Buffer.Companion.auto] buffer factory.
+// * Create a new buffer from this one with the given mapping function and using [Buffer.Companion.auto] buffer factory.
- */
+// */
-public inline fun <T, reified R : Any> Buffer<T>.map(block: (T) -> R): Buffer<R> =
+//public inline fun <T, reified R : Any> Buffer<T>.map(block: (T) -> R): Buffer<R> =
-    Buffer.auto(size) { block(get(it)) }
+//    Buffer.auto(size) { block(get(it)) }
 
 /**
  * Create a new buffer from this one with the given mapping function.
  * Provided [bufferFactory] is used to construct the new buffer.
  */
-public inline fun <T, R> Buffer<T>.map(
+public inline fun <T, R> Buffer<T>.mapToBuffer(
     bufferFactory: BufferFactory<R>,
     crossinline block: (T) -> R,
 ): Buffer<R> = bufferFactory(size) { block(get(it)) }
@@ -81,23 +81,24 @@ public inline fun <T, R> Buffer<T>.map(
  * Create a new buffer from this one with the given mapping (indexed) function.
  * Provided [bufferFactory] is used to construct the new buffer.
  */
-public inline fun <T, R> Buffer<T>.mapIndexed(
+public inline fun <T, R> Buffer<T>.mapIndexedToBuffer(
     bufferFactory: BufferFactory<R>,
     crossinline block: (index: Int, value: T) -> R,
 ): Buffer<R> = bufferFactory(size) { block(it, get(it)) }
-
+//
-/**
+///**
- * Create a new buffer from this one with the given indexed mapping function.
+// * Create a new buffer from this one with the given indexed mapping function.
- * Provided [BufferFactory] is used to construct the new buffer.
+// * Provided [BufferFactory] is used to construct the new buffer.
- */
+// */
-public inline fun <T, reified R : Any> Buffer<T>.mapIndexed(
+//public inline fun <T, reified R : Any> Buffer<T>.mapIndexed(
-    crossinline block: (index: Int, value: T) -> R,
+//    crossinline block: (index: Int, value: T) -> R,
-): Buffer<R> = Buffer.auto(size) { block(it, get(it)) }
+//): Buffer<R> = Buffer.auto(size) { block(it, get(it)) }
 
 /**
  * Fold given buffer according to [operation]
  */
 public inline fun <T, R> Buffer<T>.fold(initial: R, operation: (acc: R, T) -> R): R {
+    if (size == 0) return initial
     var accumulator = initial
     for (index in this.indices) accumulator = operation(accumulator, get(index))
     return accumulator
@@ -107,18 +108,31 @@ public inline fun <T, R> Buffer<T>.fold(initial: R, operation: (acc: R, T) -> R)
  * Fold given buffer according to indexed [operation]
  */
 public inline fun <T : Any, R> Buffer<T>.foldIndexed(initial: R, operation: (index: Int, acc: R, T) -> R): R {
+    if (size == 0) return initial
     var accumulator = initial
     for (index in this.indices) accumulator = operation(index, accumulator, get(index))
     return accumulator
 }
 
+/**
+ * Reduce a buffer from left to right according to [operation]
+ */
+public inline fun <T> Buffer<T>.reduce(operation: (left: T, value: T) -> T): T {
+    require(size > 0) { "Buffer must have elements" }
+    var current = get(0)
+    for (i in 1 until size) {
+        current = operation(current, get(i))
+    }
+    return current
+}
+
 /**
  * Zip two buffers using given [transform].
  */
 @UnstableKMathAPI
-public inline fun <T1, T2 : Any, reified R : Any> Buffer<T1>.zip(
+public inline fun <T1, T2, R> Buffer<T1>.combineToBuffer(
     other: Buffer<T2>,
-    bufferFactory: BufferFactory<R> = BufferFactory.auto(),
+    bufferFactory: BufferFactory<R>,
     crossinline transform: (T1, T2) -> R,
 ): Buffer<R> {
     require(size == other.size) { "Buffer size mismatch in zip: expected $size but found ${other.size}" }

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

@@ -0,0 +1,20 @@
+/*
+ * Copyright 2018-2022 KMath contributors.
+ * Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
+ */
+
+package space.kscience.kmath.structures
+
+
+public typealias Float32 = Float
+public typealias Float64 = Double
+
+public typealias Int8 = Byte
+public typealias Int16 = Short
+public typealias Int32 = Int
+public typealias Int64 = Long
+
+public typealias UInt8 = UByte
+public typealias UInt16 = UShort
+public typealias UInt32 = UInt
+public typealias UInt64 = ULong

kmath-coroutines/src/commonMain/kotlin/space/kscience/kmath/coroutines/coroutinesExtra.kt

@@ -81,9 +81,7 @@ public suspend fun <T> AsyncFlow<T>.collect(concurrency: Int, collector: FlowCol
 public suspend inline fun <T> AsyncFlow<T>.collect(
     concurrency: Int,
     crossinline action: suspend (value: T) -> Unit,
-): Unit = collect(concurrency, object : FlowCollector<T> {
+): Unit = collect(concurrency, FlowCollector<T> { value -> action(value) })
-    override suspend fun emit(value: T): Unit = action(value)
-})
 
 public inline fun <T, R> Flow<T>.mapParallel(
     dispatcher: CoroutineDispatcher = Dispatchers.Default,

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

@@ -5,7 +5,7 @@
 
 package space.kscience.kmath.integration
 
-import space.kscience.kmath.operations.map
+import space.kscience.kmath.operations.mapToBuffer
 import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.DoubleBuffer
 import space.kscience.kmath.structures.asBuffer
@@ -33,11 +33,11 @@ public fun GaussIntegratorRuleFactory.build(
     val normalized: Pair<Buffer<Double>, Buffer<Double>> = build(numPoints)
     val length = range.endInclusive - range.start
 
-    val points = normalized.first.map(::DoubleBuffer) {
+    val points = normalized.first.mapToBuffer(::DoubleBuffer) {
         range.start + length / 2 + length / 2 * it
     }
 
-    val weights = normalized.second.map(::DoubleBuffer) {
+    val weights = normalized.second.mapToBuffer(::DoubleBuffer) {
         it * length / 2
     }
 

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

@@ -65,9 +65,9 @@ public class SplineIntegrator<T : Comparable<T>>(
             DoubleBuffer(numPoints) { i -> range.start + i * step }
         }
 
-        val values = nodes.map(bufferFactory) { integrand.function(it) }
+        val values = nodes.mapToBuffer(bufferFactory) { integrand.function(it) }
         val polynomials = interpolator.interpolatePolynomials(
-            nodes.map(bufferFactory) { number(it) },
+            nodes.mapToBuffer(bufferFactory) { number(it) },
             values
         )
         val res = polynomials.integrate(algebra, number(range.start)..number(range.endInclusive))
@@ -93,7 +93,7 @@ public object DoubleSplineIntegrator : UnivariateIntegrator<Double> {
             DoubleBuffer(numPoints) { i -> range.start + i * step }
         }
 
-        val values = nodes.map { integrand.function(it) }
+        val values = nodes.mapToBuffer(::DoubleBuffer) { integrand.function(it) }
         val polynomials = interpolator.interpolatePolynomials(nodes, values)
         val res = polynomials.integrate(DoubleField, range)
         return integrand + IntegrandValue(res) + IntegrandCallsPerformed(integrand.calls + nodes.size)

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

@@ -97,7 +97,7 @@ public class UniformHistogramGroupND<V : Any, A : Field<V>>(
             }
         }
         hBuilder.apply(builder)
-        val values: BufferND<V> = BufferND(ndCounter.indices, ndCounter.buffer.map(valueBufferFactory) { it.value })
+        val values: BufferND<V> = BufferND(ndCounter.indices, ndCounter.buffer.mapToBuffer(valueBufferFactory) { it.value })
 
         return HistogramND(this, values)
     }

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

@@ -12,6 +12,7 @@ import space.kscience.kmath.nd.StructureND
 import space.kscience.kmath.nd.one
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.randomNormal
 import space.kscience.kmath.tensors.core.tensorAlgebra
 import kotlin.test.Test
 import kotlin.test.assertTrue

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

@@ -118,35 +118,35 @@ public sealed interface Nd4jTensorAlgebra<T : Number, A : Field<T>> : AnalyticTe
     override fun StructureND<T>.argMax(dim: Int, keepDim: Boolean): Tensor<Int> =
         ndBase.get().argmax(ndArray, keepDim, dim).asIntStructure()
 
-    override fun StructureND<T>.mean(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun mean(structureND: StructureND<T>, dim: Int, keepDim: Boolean): Tensor<T> =
-        ndArray.mean(keepDim, dim).wrap()
+        structureND.ndArray.mean(keepDim, dim).wrap()
 
-    override fun StructureND<T>.exp(): Nd4jArrayStructure<T> = Transforms.exp(ndArray).wrap()
+    override fun exp(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.exp(arg.ndArray).wrap()
-    override fun StructureND<T>.ln(): Nd4jArrayStructure<T> = Transforms.log(ndArray).wrap()
+    override fun ln(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.log(arg.ndArray).wrap()
-    override fun StructureND<T>.sqrt(): Nd4jArrayStructure<T> = Transforms.sqrt(ndArray).wrap()
+    override fun sqrt(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.sqrt(arg.ndArray).wrap()
-    override fun StructureND<T>.cos(): Nd4jArrayStructure<T> = Transforms.cos(ndArray).wrap()
+    override fun cos(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.cos(arg.ndArray).wrap()
-    override fun StructureND<T>.acos(): Nd4jArrayStructure<T> = Transforms.acos(ndArray).wrap()
+    override fun acos(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.acos(arg.ndArray).wrap()
-    override fun StructureND<T>.cosh(): Nd4jArrayStructure<T> = Transforms.cosh(ndArray).wrap()
+    override fun cosh(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.cosh(arg.ndArray).wrap()
 
-    override fun StructureND<T>.acosh(): Nd4jArrayStructure<T> =
+    override fun acosh(arg: StructureND<T>): Nd4jArrayStructure<T> =
-        Nd4j.getExecutioner().exec(ACosh(ndArray, ndArray.ulike())).wrap()
+        Nd4j.getExecutioner().exec(ACosh(arg.ndArray, arg.ndArray.ulike())).wrap()
 
-    override fun StructureND<T>.sin(): Nd4jArrayStructure<T> = Transforms.sin(ndArray).wrap()
+    override fun sin(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.sin(arg.ndArray).wrap()
-    override fun StructureND<T>.asin(): Nd4jArrayStructure<T> = Transforms.asin(ndArray).wrap()
+    override fun asin(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.asin(arg.ndArray).wrap()
-    override fun StructureND<T>.sinh(): Tensor<T> = Transforms.sinh(ndArray).wrap()
+    override fun sinh(arg: StructureND<T>): Tensor<T> = Transforms.sinh(arg.ndArray).wrap()
 
-    override fun StructureND<T>.asinh(): Nd4jArrayStructure<T> =
+    override fun asinh(arg: StructureND<T>): Nd4jArrayStructure<T> =
-        Nd4j.getExecutioner().exec(ASinh(ndArray, ndArray.ulike())).wrap()
+        Nd4j.getExecutioner().exec(ASinh(arg.ndArray, arg.ndArray.ulike())).wrap()
 
-    override fun StructureND<T>.tan(): Nd4jArrayStructure<T> = Transforms.tan(ndArray).wrap()
+    override fun tan(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.tan(arg.ndArray).wrap()
-    override fun StructureND<T>.atan(): Nd4jArrayStructure<T> = Transforms.atan(ndArray).wrap()
+    override fun atan(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.atan(arg.ndArray).wrap()
-    override fun StructureND<T>.tanh(): Nd4jArrayStructure<T> = Transforms.tanh(ndArray).wrap()
+    override fun tanh(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.tanh(arg.ndArray).wrap()
-    override fun StructureND<T>.atanh(): Nd4jArrayStructure<T> = Transforms.atanh(ndArray).wrap()
+    override fun atanh(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.atanh(arg.ndArray).wrap()
     override fun power(arg: StructureND<T>, pow: Number): StructureND<T> = Transforms.pow(arg.ndArray, pow).wrap()
-    override fun StructureND<T>.ceil(): Nd4jArrayStructure<T> = Transforms.ceil(ndArray).wrap()
+    override fun ceil(arg: StructureND<T>): Nd4jArrayStructure<T> = Transforms.ceil(arg.ndArray).wrap()
-    override fun StructureND<T>.floor(): Nd4jArrayStructure<T> = Transforms.floor(ndArray).wrap()
+    override fun floor(structureND: StructureND<T>): Nd4jArrayStructure<T> = Transforms.floor(structureND.ndArray).wrap()
-    override fun StructureND<T>.std(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun std(structureND: StructureND<T>, dim: Int, keepDim: Boolean): Tensor<T> =
-        ndArray.std(true, keepDim, dim).wrap()
+        structureND.ndArray.std(true, keepDim, dim).wrap()
 
     override fun T.div(arg: StructureND<T>): Nd4jArrayStructure<T> = arg.ndArray.rdiv(this).wrap()
     override fun StructureND<T>.div(arg: T): Nd4jArrayStructure<T> = ndArray.div(arg).wrap()
@@ -160,8 +160,8 @@ public sealed interface Nd4jTensorAlgebra<T : Number, A : Field<T>> : AnalyticTe
         ndArray.divi(arg.ndArray)
     }
 
-    override fun StructureND<T>.variance(dim: Int, keepDim: Boolean): Nd4jArrayStructure<T> =
+    override fun variance(structureND: StructureND<T>, dim: Int, keepDim: Boolean): Tensor<T> =
-        Nd4j.getExecutioner().exec(Variance(ndArray, true, true, dim)).wrap()
+        Nd4j.getExecutioner().exec(Variance(structureND.ndArray, true, true, dim)).wrap()
 
     private companion object {
         private val ndBase: ThreadLocal<NDBase> = ThreadLocal.withInitial(::NDBase)
@@ -211,7 +211,7 @@ public object DoubleNd4jTensorAlgebra : Nd4jTensorAlgebra<Double, DoubleField> {
     override fun StructureND<Double>.sum(): Double = ndArray.sumNumber().toDouble()
     override fun StructureND<Double>.min(): Double = ndArray.minNumber().toDouble()
     override fun StructureND<Double>.max(): Double = ndArray.maxNumber().toDouble()
-    override fun StructureND<Double>.mean(): Double = ndArray.meanNumber().toDouble()
+    override fun mean(structureND: StructureND<Double>): Double = structureND.ndArray.meanNumber().toDouble()
-    override fun StructureND<Double>.std(): Double = ndArray.stdNumber().toDouble()
+    override fun std(structureND: StructureND<Double>): Double = structureND.ndArray.stdNumber().toDouble()
-    override fun StructureND<Double>.variance(): Double = ndArray.varNumber().toDouble()
+    override fun variance(structureND: StructureND<Double>): Double = structureND.ndArray.varNumber().toDouble()
 }

kmath-optimization/src/commonMain/tmp/minuit/HessianGradientCalculator.kt

@@ -33,7 +33,7 @@ internal class HessianGradientCalculator(fcn: MnFcn, par: MnUserTransformation,
         val g2: RealVector = gradient.getGradientDerivative()
         val gstep: RealVector = gradient.getStep()
         val fcnmin: Double = par.fval()
-        //   std::cout<<"fval: "<<fcnmin<<std::endl;
+        //   standardDiviation::cout<<"fval: "<<fcnmin<<standardDiviation::endl;
         val dfmin: Double = 4.0 * precision().eps2() * (abs(fcnmin) + theFcn.errorDef())
         val n: Int = x.getDimension()
         val dgrd: RealVector = ArrayRealVector(n)

kmath-optimization/src/commonMain/tmp/minuit/MnPosDef.kt

@@ -36,7 +36,7 @@ internal object MnPosDef {
         if (err.size() === 1 && err[0, 0] > prec.eps()) {
             return e
         }
-        //   std::cout<<"MnPosDef init matrix= "<<err<<std::endl;
+        //   standardDiviation::cout<<"MnPosDef init matrix= "<<err<<standardDiviation::endl;
         val epspdf: Double = max(1e-6, prec.eps2())
         var dgmin: Double = err[0, 0]
         for (i in 0 until err.nrow()) {
@@ -66,11 +66,11 @@ internal object MnPosDef {
             }
         }
 
-        //   std::cout<<"MnPosDef p: "<<p<<std::endl;
+        //   standardDiviation::cout<<"MnPosDef p: "<<p<<standardDiviation::endl;
         val eval: RealVector = p.eigenvalues()
         val pmin: Double = eval.getEntry(0)
         var pmax: Double = eval.getEntry(eval.getDimension() - 1)
-        //   std::cout<<"pmin= "<<pmin<<" pmax= "<<pmax<<std::endl;
+        //   standardDiviation::cout<<"pmin= "<<pmin<<" pmax= "<<pmax<<standardDiviation::endl;
         pmax = max(abs(pmax), 1.0)
         if (pmin > epspdf * pmax) {
             return e
@@ -81,9 +81,9 @@ internal object MnPosDef {
             err[i, i] = err[i, i] * (1.0 + padd)
             MINUITPlugin.logStatic(java.lang.Double.toString(eval.getEntry(i)))
         }
-        //   std::cout<<"MnPosDef final matrix: "<<err<<std::endl;
+        //   standardDiviation::cout<<"MnPosDef final matrix: "<<err<<standardDiviation::endl;
         MINUITPlugin.logStatic("matrix forced pos-def by adding $padd to diagonal")
-        //   std::cout<<"eigenvalues: "<<eval<<std::endl;
+        //   standardDiviation::cout<<"eigenvalues: "<<eval<<standardDiviation::endl;
         return MinimumError(err, MnMadePosDef())
     }
 }

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

@@ -52,16 +52,16 @@ public class Mean<T>(
         @Deprecated("Use Long.mean instead")
         public val long: Mean<Long> = Mean(LongRing) { sum, count -> sum / count }
 
-        public fun evaluate(buffer: Buffer<Double>): Double = Double.mean.evaluateBlocking(buffer)
+        public fun evaluate(buffer: Buffer<Double>): Double = DoubleField.mean.evaluateBlocking(buffer)
-        public fun evaluate(buffer: Buffer<Int>): Int = Int.mean.evaluateBlocking(buffer)
+        public fun evaluate(buffer: Buffer<Int>): Int = IntRing.mean.evaluateBlocking(buffer)
-        public fun evaluate(buffer: Buffer<Long>): Long = Long.mean.evaluateBlocking(buffer)
+        public fun evaluate(buffer: Buffer<Long>): Long = LongRing.mean.evaluateBlocking(buffer)
     }
 }
 
 
 //TODO replace with optimized version which respects overflow
-public val Double.Companion.mean: Mean<Double> get() = Mean(DoubleField) { sum, count -> sum / count }
+public val DoubleField.mean: Mean<Double> get() = Mean(DoubleField) { sum, count -> sum / count }
-public val Int.Companion.mean: Mean<Int> get() = Mean(IntRing) { sum, count -> sum / count }
+public val IntRing.mean: Mean<Int> get() = Mean(IntRing) { sum, count -> sum / count }
-public val Long.Companion.mean: Mean<Long> get() = Mean(LongRing) { sum, count -> sum / count }
+public val LongRing.mean: Mean<Long> get() = Mean(LongRing) { sum, count -> sum / count }
 
 

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

@@ -9,6 +9,7 @@ import kotlinx.coroutines.flow.first
 import kotlinx.coroutines.flow.last
 import kotlinx.coroutines.flow.take
 import kotlinx.coroutines.runBlocking
+import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.random.RandomGenerator
 import space.kscience.kmath.random.chain
 import space.kscience.kmath.streaming.chunked
@@ -27,26 +28,26 @@ internal class StatisticTest {
 
     @Test
     fun singleBlockingMean() {
-        val first = runBlocking { chunked.first()}
+        val first = runBlocking { chunked.first() }
-        val res = Double.mean(first)
+        val res = DoubleField.mean(first)
-        assertEquals(0.5,res, 1e-1)
+        assertEquals(0.5, res, 1e-1)
     }
 
     @Test
     fun singleSuspendMean() = runBlocking {
-        val first = runBlocking { chunked.first()}
+        val first = runBlocking { chunked.first() }
-        val res = Double.mean(first)
+        val res = DoubleField.mean(first)
-        assertEquals(0.5,res, 1e-1)
+        assertEquals(0.5, res, 1e-1)
     }
 
     @Test
     fun parallelMean() = runBlocking {
-        val average = Double.mean
+        val average = DoubleField.mean
             .flow(chunked) //create a flow from evaluated results
             .take(100) // Take 100 data chunks from the source and accumulate them
             .last() //get 1e5 data samples average
 
-        assertEquals(0.5,average, 1e-2)
+        assertEquals(0.5, average, 1e-2)
     }
 
 }

kmath-tensorflow/src/test/kotlin/space/kscience/kmath/tensorflow/DoubleTensorFlowOps.kt

@@ -13,6 +13,7 @@ import space.kscience.kmath.nd.structureND
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.sum
+import space.kscience.kmath.tensors.core.randomNormal
 import kotlin.test.assertEquals
 
 @OptIn(UnstableKMathAPI::class)

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

@@ -21,7 +21,7 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> :
     /**
      * @return the mean of all elements in the input tensor.
      */
-    public fun StructureND<T>.mean(): T
+    public fun mean(structureND: StructureND<T>): T
 
     /**
      * Returns the mean of each row of the input tensor in the given dimension [dim].
@@ -34,12 +34,12 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> :
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the mean of each row of the input tensor in the given dimension [dim].
      */
-    public fun StructureND<T>.mean(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun mean(structureND: StructureND<T>, dim: Int, keepDim: Boolean): Tensor<T>
 
     /**
      * @return the standard deviation of all elements in the input tensor.
      */
-    public fun StructureND<T>.std(): T
+    public fun std(structureND: StructureND<T>): T
 
     /**
      * Returns the standard deviation of each row of the input tensor in the given dimension [dim].
@@ -52,12 +52,12 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> :
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the standard deviation of each row of the input tensor in the given dimension [dim].
      */
-    public fun StructureND<T>.std(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun std(structureND: StructureND<T>, dim: Int, keepDim: Boolean): Tensor<T>
 
     /**
      * @return the variance of all elements in the input tensor.
      */
-    public fun StructureND<T>.variance(): T
+    public fun variance(structureND: StructureND<T>): T
 
     /**
      * Returns the variance of each row of the input tensor in the given dimension [dim].
@@ -70,80 +70,45 @@ public interface AnalyticTensorAlgebra<T, A : Field<T>> :
      * @param keepDim whether the output tensor has [dim] retained or not.
      * @return the variance of each row of the input tensor in the given dimension [dim].
      */
-    public fun StructureND<T>.variance(dim: Int, keepDim: Boolean): Tensor<T>
+    public fun variance(structureND: StructureND<T>, dim: Int, keepDim: Boolean): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.exp.html
-    public fun StructureND<T>.exp(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.log.html
-    public fun StructureND<T>.ln(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.sqrt.html
-    public fun StructureND<T>.sqrt(): Tensor<T>
+    override fun sqrt(arg: StructureND<T>): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.cos
-    public fun StructureND<T>.cos(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.acos.html#torch.acos
-    public fun StructureND<T>.acos(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.cosh
-    public fun StructureND<T>.cosh(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.acosh.html#torch.acosh
-    public fun StructureND<T>.acosh(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sin
-    public fun StructureND<T>.sin(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asin
-    public fun StructureND<T>.asin(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.sinh
-    public fun StructureND<T>.sinh(): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.asin.html#torch.asinh
-    public fun StructureND<T>.asinh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.atan.html#torch.tan
-    public fun StructureND<T>.tan(): Tensor<T>
+    override fun tan(arg: StructureND<T>): Tensor<T>
 
     //https://pytorch.org/docs/stable/generated/torch.atan.html#torch.atan
-    public fun StructureND<T>.atan(): Tensor<T>
+    override fun atan(arg: StructureND<T>): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.tanh
-    public fun StructureND<T>.tanh(): Tensor<T>
+    override fun tanh(arg: StructureND<T>): Tensor<T>
-
-    //For information: https://pytorch.org/docs/stable/generated/torch.atanh.html#torch.atanh
-    public fun StructureND<T>.atanh(): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.ceil.html#torch.ceil
-    public fun StructureND<T>.ceil(): Tensor<T>
+    public fun ceil(arg: StructureND<T>): Tensor<T>
 
     //For information: https://pytorch.org/docs/stable/generated/torch.floor.html#torch.floor
-    public fun StructureND<T>.floor(): Tensor<T>
+    public fun floor(structureND: StructureND<T>): Tensor<T>
 
-    override fun sin(arg: StructureND<T>): StructureND<T> = arg.sin()
+    override fun sin(arg: StructureND<T>): StructureND<T> 
 
-    override fun cos(arg: StructureND<T>): StructureND<T> = arg.cos()
+    override fun cos(arg: StructureND<T>): StructureND<T> 
 
-    override fun asin(arg: StructureND<T>): StructureND<T> = arg.asin()
+    override fun asin(arg: StructureND<T>): StructureND<T>
 
-    override fun acos(arg: StructureND<T>): StructureND<T> = arg.acos()
+    override fun acos(arg: StructureND<T>): StructureND<T>
 
-    override fun atan(arg: StructureND<T>): StructureND<T> = arg.atan()
+    override fun exp(arg: StructureND<T>): StructureND<T> 
 
-    override fun exp(arg: StructureND<T>): StructureND<T> = arg.exp()
+    override fun ln(arg: StructureND<T>): StructureND<T>
 
-    override fun ln(arg: StructureND<T>): StructureND<T> = arg.ln()
+    override fun sinh(arg: StructureND<T>): StructureND<T>
 
-    override fun sinh(arg: StructureND<T>): StructureND<T> = arg.sinh()
+    override fun cosh(arg: StructureND<T>): StructureND<T>
 
-    override fun cosh(arg: StructureND<T>): StructureND<T> = arg.cosh()
+    override fun asinh(arg: StructureND<T>): StructureND<T>
 
-    override fun asinh(arg: StructureND<T>): StructureND<T> = arg.asinh()
+    override fun acosh(arg: StructureND<T>): StructureND<T>
 
-    override fun acosh(arg: StructureND<T>): StructureND<T> = arg.acosh()
+    override fun atanh(arg: StructureND<T>): StructureND<T>
-
-    override fun atanh(arg: StructureND<T>): StructureND<T> = arg.atanh()
 }

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

@@ -47,7 +47,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return the batch of `L` matrices.
      */
-    public fun StructureND<T>.cholesky(): StructureND<T>
+    public fun cholesky(structureND: StructureND<T>): StructureND<T>
 
     /**
      * QR decomposition.
@@ -61,7 +61,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return pair of `Q` and `R` tensors.
      */
-    public fun StructureND<T>.qr(): Pair<StructureND<T>, StructureND<T>>
+    public fun qr(structureND: StructureND<T>): Pair<StructureND<T>, StructureND<T>>
 
     /**
      * LUP decomposition
@@ -75,7 +75,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return triple of P, L and U tensors
      */
-    public fun StructureND<T>.lu(): Triple<StructureND<T>, StructureND<T>, StructureND<T>>
+    public fun lu(structureND: StructureND<T>): Triple<StructureND<T>, StructureND<T>, StructureND<T>>
 
     /**
      * Singular Value Decomposition.
@@ -91,7 +91,7 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return triple `Triple(U, S, V)`.
      */
-    public fun StructureND<T>.svd(): Triple<StructureND<T>, StructureND<T>, StructureND<T>>
+    public fun svd(structureND: StructureND<T>): Triple<StructureND<T>, StructureND<T>, StructureND<T>>
 
     /**
      * Returns eigenvalues and eigenvectors of a real symmetric matrix `input` or a batch of real symmetric matrices,
@@ -101,6 +101,6 @@ public interface LinearOpsTensorAlgebra<T, A : Field<T>> : TensorPartialDivision
      * @receiver the `input`.
      * @return a pair `eigenvalues to eigenvectors`
      */
-    public fun StructureND<T>.symEig(): Pair<StructureND<T>, StructureND<T>>
+    public fun symEig(structureND: StructureND<T>): Pair<StructureND<T>, StructureND<T>>
 
 }

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

@@ -10,7 +10,6 @@ import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.*
 import space.kscience.kmath.structures.*
 import space.kscience.kmath.tensors.core.internal.toPrettyString
-import kotlin.jvm.JvmInline
 
 public class OffsetDoubleBuffer(
     override val origin: DoubleBuffer,
@@ -83,9 +82,9 @@ public inline fun OffsetDoubleBuffer.mapInPlace(operation: (Double) -> Double) {
  *
  * [DoubleTensor] always uses row-based strides
  */
-public class DoubleTensor(
+public open class DoubleTensor(
     shape: ShapeND,
-    override val source: OffsetDoubleBuffer,
+    final override val source: OffsetDoubleBuffer,
 ) : BufferedTensor<Double>(shape), MutableStructureNDOfDouble {
 
     init {
@@ -103,7 +102,7 @@ public class DoubleTensor(
         source[indices.offset(index)] = value
     }
 
-    override fun getDouble(index: IntArray): Double = get(index)
+    override fun getDouble(index: IntArray): Double = source[indices.offset(index)]
 
     override fun setDouble(index: IntArray, value: Double) {
         set(index, value)
@@ -112,62 +111,8 @@ 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<PermutedMutableBuffer<Double>>
-        get() = List(colNum) { j ->
-            val indices = IntArray(rowNum) { i -> j + i * colNum }
-            tensor.source.permute(indices)
-        }
-
-    @PerformancePitfall
-    override fun elements(): Sequence<Pair<IntArray, Double>> = tensor.elements()
-    @OptIn(PerformancePitfall::class)
-    override fun get(index: IntArray): Double = tensor[index]
-    override val shape: ShapeND get() = tensor.shape
-}
-
-public fun DoubleTensor.asDoubleTensor2D(): DoubleTensor2D = DoubleTensor2D(this)
-
 public fun DoubleTensor.asDoubleBuffer(): OffsetDoubleBuffer = if (shape.size == 1) {
     source
 } else {
     error("Only 1D tensors could be cast to 1D")
 }
-
-public inline fun DoubleTensor.forEachMatrix(block: (index: IntArray, matrix: DoubleTensor2D) -> Unit) {
-    val n = shape.size
-    check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" }
-    val matrixOffset = shape[n - 1] * shape[n - 2]
-    val matrixShape = ShapeND(shape[n - 2], shape[n - 1])
-
-    val size = matrixShape.linearSize
-    for (i in 0 until linearSize / matrixOffset) {
-        val offset = i * matrixOffset
-        val index = indices.index(offset).sliceArray(0 until (shape.size - 2))
-        block(index, DoubleTensor(matrixShape, source.view(offset, size)).asDoubleTensor2D())
-    }
-}

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor1D.kt

@@ -0,0 +1,45 @@
+/*
+ * 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.misc.PerformancePitfall
+import space.kscience.kmath.nd.MutableStructure1D
+import space.kscience.kmath.nd.ShapeND
+import space.kscience.kmath.structures.MutableBuffer
+
+public class DoubleTensor1D(
+    source: OffsetDoubleBuffer,
+) : DoubleTensor(ShapeND(source.size), source), MutableStructure1D<Double> {
+
+    @PerformancePitfall
+    override fun get(index: IntArray): Double = super<MutableStructure1D>.get(index)
+
+    @PerformancePitfall
+    override fun set(index: IntArray, value: Double) {
+        super<MutableStructure1D>.set(index, value)
+    }
+
+    override val size: Int get() = source.size
+
+    override fun get(index: Int): Double = source[index]
+
+    override fun set(index: Int, value: Double) {
+        source[index] = value
+    }
+
+    override fun copy(): MutableBuffer<Double> = source.copy()
+
+    @PerformancePitfall
+    override fun elements(): Sequence<Pair<IntArray, Double>> = super<MutableStructure1D>.elements()
+}
+
+/**
+ * A zero-copy cast to 1D structure. Changes in resulting structure are reflected on original tensor.
+ */
+public fun DoubleTensor.asDoubleTensor1D(): DoubleTensor1D {
+    require(shape.size == 1) { "Only 1D tensors could be cast to 1D" }
+    return DoubleTensor1D(source)
+}

kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/DoubleTensor2D.kt

@@ -0,0 +1,71 @@
+/*
+ * 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.misc.PerformancePitfall
+import space.kscience.kmath.nd.MutableStructure2D
+import space.kscience.kmath.nd.ShapeND
+import space.kscience.kmath.nd.linearSize
+import space.kscience.kmath.structures.PermutedMutableBuffer
+import space.kscience.kmath.structures.permute
+
+public class DoubleTensor2D(
+    override val rowNum: Int,
+    override val colNum: Int,
+    source: OffsetDoubleBuffer,
+) : DoubleTensor(ShapeND(rowNum, colNum), source), MutableStructure2D<Double> {
+
+    override fun get(i: Int, j: Int): Double = source[i * colNum + j]
+
+    @OptIn(PerformancePitfall::class)
+    override fun get(index: IntArray): Double = getDouble(index)
+
+    override fun set(i: Int, j: Int, value: Double) {
+        source[i * colNum + j] = value
+    }
+
+    @OptIn(PerformancePitfall::class)
+    override val rows: List<OffsetDoubleBuffer>
+        get() = List(rowNum) { i ->
+            source.view(i * colNum, colNum)
+        }
+
+
+    @OptIn(PerformancePitfall::class)
+    override val columns: List<PermutedMutableBuffer<Double>>
+        get() = List(colNum) { j ->
+            val indices = IntArray(rowNum) { i -> j + i * colNum }
+            source.permute(indices)
+        }
+
+    override val shape: ShapeND get() = super<DoubleTensor>.shape
+
+    @PerformancePitfall
+    override fun elements(): Sequence<Pair<IntArray, Double>> = super<MutableStructure2D>.elements()
+}
+
+/**
+ * A zero-copy cast to 2D structure. Changes in resulting structure are reflected on original tensor.
+ */
+public fun DoubleTensor.asDoubleTensor2D(): DoubleTensor2D {
+    require(shape.size == 2) { "Only 2D tensors could be cast to 2D" }
+    return DoubleTensor2D(shape[0], shape[1], source)
+}
+
+
+public inline fun DoubleTensor.forEachMatrix(block: (index: IntArray, matrix: DoubleTensor2D) -> Unit) {
+    val n = shape.size
+    check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" }
+    val matrixOffset = shape[n - 1] * shape[n - 2]
+    val matrixShape = ShapeND(shape[n - 2], shape[n - 1])
+
+    val size = matrixShape.linearSize
+    for (i in 0 until linearSize / matrixOffset) {
+        val offset = i * matrixOffset
+        val index = indices.index(offset).sliceArray(0 until (shape.size - 2))
+        block(index, DoubleTensor(matrixShape, source.view(offset, size)).asDoubleTensor2D())
+    }
+}

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

@@ -11,12 +11,12 @@ 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.operations.DoubleBufferOps
 import space.kscience.kmath.operations.DoubleField
 import space.kscience.kmath.structures.*
 import space.kscience.kmath.tensors.api.AnalyticTensorAlgebra
 import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
 import space.kscience.kmath.tensors.api.Tensor
-import space.kscience.kmath.tensors.api.TensorPartialDivisionAlgebra
 import space.kscience.kmath.tensors.core.internal.*
 import kotlin.math.*
 
@@ -25,7 +25,6 @@ import kotlin.math.*
  */
 @OptIn(PerformancePitfall::class)
 public open class DoubleTensorAlgebra :
-    TensorPartialDivisionAlgebra<Double, DoubleField>,
     AnalyticTensorAlgebra<Double, DoubleField>,
     LinearOpsTensorAlgebra<Double, DoubleField> {
 
@@ -33,6 +32,8 @@ public open class DoubleTensorAlgebra :
 
     override val elementAlgebra: DoubleField get() = DoubleField
 
+    public val bufferAlgebra: DoubleBufferOps get() = DoubleBufferOps
+
 
     /**
      * Applies the [transform] function to each element of the tensor and returns the resulting modified tensor.
@@ -98,6 +99,16 @@ public open class DoubleTensorAlgebra :
     override fun StructureND<Double>.value(): Double = valueOrNull()
         ?: throw IllegalArgumentException("The tensor shape is $shape, but value method is allowed only for shape [1]")
 
+    public fun fromBuffer(shape: ShapeND, buffer: Buffer<Double>): DoubleTensor {
+        checkNotEmptyShape(shape)
+        check(buffer.size > 0) { "Illegal empty buffer provided" }
+        check(buffer.size == shape.linearSize) {
+            "Inconsistent shape $shape for buffer of size ${buffer.size} provided"
+        }
+        return DoubleTensor(shape, buffer.toDoubleBuffer())
+    }
+
+
     /**
      * Constructs a tensor with the specified shape and data.
      *
@@ -105,12 +116,7 @@ public open class DoubleTensorAlgebra :
      * @param array one-dimensional data array.
      * @return tensor with the [shape] shape and [array] data.
      */
-    public fun fromArray(shape: ShapeND, array: DoubleArray): DoubleTensor {
+    public fun fromArray(shape: ShapeND, array: DoubleArray): DoubleTensor = fromBuffer(shape, array.asBuffer())
-        checkNotEmptyShape(shape)
-        checkEmptyDoubleBuffer(array)
-        checkBufferShapeConsistency(shape, array)
-        return DoubleTensor(shape, array.asBuffer())
-    }
 
     /**
      * Constructs a tensor with the specified shape and initializer.
@@ -271,7 +277,7 @@ public open class DoubleTensorAlgebra :
 
     override fun StructureND<Double>.transposed(i: Int, j: Int): Tensor<Double> {
         val actualI = if (i >= 0) i else shape.size + i
-        val actualJ = if(j>=0) j else shape.size + j
+        val actualJ = if (j >= 0) j else shape.size + j
         return asDoubleTensor().permute(
             shape.transposed(actualI, actualJ)
         ) { originIndex ->
@@ -498,48 +504,6 @@ public open class DoubleTensorAlgebra :
         return true
     }
 
-    /**
-     * Returns a tensor of random numbers drawn from normal distributions with `0.0` mean and `1.0` standard deviation.
-     *
-     * @param shape the desired shape for the output tensor.
-     * @param seed the random seed of the pseudo-random number generator.
-     * @return tensor of a given shape filled with numbers from the normal distribution
-     * with `0.0` mean and `1.0` standard deviation.
-     */
-    public fun randomNormal(shape: ShapeND, seed: Long = 0): DoubleTensor =
-        DoubleTensor(shape, DoubleBuffer.randomNormals(shape.linearSize, seed))
-
-    /**
-     * Returns a tensor with the same shape as `input` of random numbers drawn from normal distributions
-     * with `0.0` mean and `1.0` standard deviation.
-     *
-     * @receiver the `input`.
-     * @param seed the random seed of the pseudo-random number generator.
-     * @return a tensor with the same shape as `input` filled with numbers from the normal distribution
-     * with `0.0` mean and `1.0` standard deviation.
-     */
-    public fun Tensor<Double>.randomNormalLike(seed: Long = 0): DoubleTensor =
-        DoubleTensor(shape, DoubleBuffer.randomNormals(shape.linearSize, seed))
-
-    /**
-     * Concatenates a sequence of tensors with equal shapes along the first dimension.
-     *
-     * @param tensors the [List] of tensors with same shapes to concatenate
-     * @return tensor with concatenation result
-     */
-    public fun stack(tensors: List<Tensor<Double>>): DoubleTensor {
-        check(tensors.isNotEmpty()) { "List must have at least 1 element" }
-        val shape = tensors[0].shape
-        check(tensors.all { it.shape contentEquals shape }) { "Tensors must have same shapes" }
-        val resShape = ShapeND(tensors.size) + shape
-//        val resBuffer: List<Double> = tensors.flatMap {
-//            it.asDoubleTensor().source.array.drop(it.asDoubleTensor().bufferStart)
-//                .take(it.asDoubleTensor().linearSize)
-//        }
-        val resBuffer = tensors.map { it.asDoubleTensor().source }.concat()
-        return DoubleTensor(resShape, resBuffer)
-    }
-
     /**
      * Builds tensor from rows of the input tensor.
      *
@@ -631,102 +595,75 @@ public open class DoubleTensorAlgebra :
         }
 
 
-    override fun StructureND<Double>.mean(): Double = sum() / indices.linearSize
+    override fun mean(structureND: StructureND<Double>): Double = structureND.sum() / structureND.indices.linearSize
 
-    override fun StructureND<Double>.mean(dim: Int, keepDim: Boolean): DoubleTensor =
+    override fun mean(structureND: StructureND<Double>, dim: Int, keepDim: Boolean): Tensor<Double> =
-        foldDimToDouble(dim, keepDim) { arr ->
+        structureND.foldDimToDouble(dim, keepDim) { arr ->
-            check(dim < dimension) { "Dimension $dim out of range $dimension" }
+            check(dim < structureND.dimension) { "Dimension $dim out of range ${structureND.dimension}" }
-            arr.sum() / shape[dim]
+            arr.sum() / structureND.shape[dim]
         }
 
-    override fun StructureND<Double>.std(): Double = reduceElements { arr ->
+    override fun std(structureND: StructureND<Double>): Double = structureND.reduceElements { arr ->
-        val mean = arr.array.sum() / indices.linearSize
+        val mean = arr.array.sum() / structureND.indices.linearSize
-        sqrt(arr.array.sumOf { (it - mean) * (it - mean) } / (indices.linearSize - 1))
+        sqrt(arr.array.sumOf { (it - mean) * (it - mean) } / (structureND.indices.linearSize - 1))
     }
 
-    override fun StructureND<Double>.std(dim: Int, keepDim: Boolean): DoubleTensor = foldDimToDouble(
+    override fun std(structureND: StructureND<Double>, dim: Int, keepDim: Boolean): Tensor<Double> =
-        dim,
+        structureND.foldDimToDouble(
-        keepDim
+            dim,
-    ) { arr ->
+            keepDim
-        check(dim < dimension) { "Dimension $dim out of range $dimension" }
+        ) { arr ->
-        val mean = arr.sum() / shape[dim]
+            check(dim < structureND.dimension) { "Dimension $dim out of range ${structureND.dimension}" }
-        sqrt(arr.sumOf { (it - mean) * (it - mean) } / (shape[dim] - 1))
+            val mean = arr.sum() / structureND.shape[dim]
-    }
+            sqrt(arr.sumOf { (it - mean) * (it - mean) } / (structureND.shape[dim] - 1))
+        }
 
-    override fun StructureND<Double>.variance(): Double = reduceElements { arr ->
+    override fun variance(structureND: StructureND<Double>): Double = structureND.reduceElements { arr ->
-        val linearSize = indices.linearSize
+        val linearSize = structureND.indices.linearSize
         val mean = arr.array.sum() / linearSize
         arr.array.sumOf { (it - mean) * (it - mean) } / (linearSize - 1)
     }
 
-    override fun StructureND<Double>.variance(dim: Int, keepDim: Boolean): DoubleTensor = foldDimToDouble(
+    override fun variance(structureND: StructureND<Double>, dim: Int, keepDim: Boolean): Tensor<Double> =
-        dim,
+        structureND.foldDimToDouble(
-        keepDim
+            dim,
-    ) { arr ->
+            keepDim
-        check(dim < dimension) { "Dimension $dim out of range $dimension" }
+        ) { arr ->
-        val mean = arr.sum() / shape[dim]
+            check(dim < structureND.dimension) { "Dimension $dim out of range ${structureND.dimension}" }
-        arr.sumOf { (it - mean) * (it - mean) } / (shape[dim] - 1)
+            val mean = arr.sum() / structureND.shape[dim]
-    }
+            arr.sumOf { (it - mean) * (it - mean) } / (structureND.shape[dim] - 1)
-
-    private fun cov(x: StructureND<Double>, y: StructureND<Double>): Double {
-        val n = x.shape[0]
-        return ((x - x.mean()) * (y - y.mean())).mean() * n / (n - 1)
-    }
-
-    /**
-     * Returns the covariance matrix `M` of given vectors.
-     *
-     * `M[i, j]` contains covariance of `i`-th and `j`-th given vectors
-     *
-     * @param tensors the [List] of 1-dimensional tensors with same shape
-     * @return `M`.
-     */
-    public fun cov(tensors: List<StructureND<Double>>): DoubleTensor {
-        check(tensors.isNotEmpty()) { "List must have at least 1 element" }
-        val n = tensors.size
-        val m = tensors[0].shape[0]
-        check(tensors.all { it.shape contentEquals ShapeND(m) }) { "Tensors must have same shapes" }
-        val resTensor = DoubleTensor(
-            ShapeND(n, n),
-            DoubleBuffer(n * n) { 0.0 }
-        )
-        for (i in 0 until n) {
-            for (j in 0 until n) {
-                resTensor[intArrayOf(i, j)] = cov(tensors[i], tensors[j])
-            }
         }
-        return resTensor
-    }
 
-    override fun StructureND<Double>.exp(): DoubleTensor = map { exp(it) }
 
-    override fun StructureND<Double>.ln(): DoubleTensor = map { ln(it) }
+    override fun exp(arg: StructureND<Double>): DoubleTensor = arg.map { this.exp(it) }
 
-    override fun StructureND<Double>.sqrt(): DoubleTensor = map { sqrt(it) }
+    override fun ln(arg: StructureND<Double>): DoubleTensor = arg.map { this.ln(it) }
 
-    override fun StructureND<Double>.cos(): DoubleTensor = map { cos(it) }
+    override fun sqrt(arg: StructureND<Double>): DoubleTensor = arg.map { this.sqrt(it) }
 
-    override fun StructureND<Double>.acos(): DoubleTensor = map { acos(it) }
+    override fun cos(arg: StructureND<Double>): DoubleTensor = arg.map { this.cos(it) }
 
-    override fun StructureND<Double>.cosh(): DoubleTensor = map { cosh(it) }
+    override fun acos(arg: StructureND<Double>): DoubleTensor = arg.map { this.acos(it) }
 
-    override fun StructureND<Double>.acosh(): DoubleTensor = map { acosh(it) }
+    override fun cosh(arg: StructureND<Double>): DoubleTensor = arg.map { this.cosh(it) }
 
-    override fun StructureND<Double>.sin(): DoubleTensor = map { sin(it) }
+    override fun acosh(arg: StructureND<Double>): DoubleTensor = arg.map { this.acosh(it) }
 
-    override fun StructureND<Double>.asin(): DoubleTensor = map { asin(it) }
+    override fun sin(arg: StructureND<Double>): DoubleTensor = arg.map { this.sin(it) }
 
-    override fun StructureND<Double>.sinh(): DoubleTensor = map { sinh(it) }
+    override fun asin(arg: StructureND<Double>): DoubleTensor = arg.map { this.asin(it) }
 
-    override fun StructureND<Double>.asinh(): DoubleTensor = map { asinh(it) }
+    override fun sinh(arg: StructureND<Double>): DoubleTensor = arg.map { this.sinh(it) }
 
-    override fun StructureND<Double>.tan(): DoubleTensor = map { tan(it) }
+    override fun asinh(arg: StructureND<Double>): DoubleTensor = arg.map { this.asinh(it) }
 
-    override fun StructureND<Double>.atan(): DoubleTensor = map { atan(it) }
+    override fun tan(arg: StructureND<Double>): DoubleTensor = arg.map { this.tan(it) }
 
-    override fun StructureND<Double>.tanh(): DoubleTensor = map { tanh(it) }
+    override fun atan(arg: StructureND<Double>): DoubleTensor = arg.map { this.atan(it) }
 
-    override fun StructureND<Double>.atanh(): DoubleTensor = map { atanh(it) }
+    override fun tanh(arg: StructureND<Double>): DoubleTensor = arg.map { this.tanh(it) }
+
+    override fun atanh(arg: StructureND<Double>): DoubleTensor = arg.map { this.atanh(it) }
 
     override fun power(arg: StructureND<Double>, pow: Number): StructureND<Double> = if (pow is Int) {
         arg.map { it.pow(pow) }
@@ -734,115 +671,26 @@ public open class DoubleTensorAlgebra :
         arg.map { it.pow(pow.toDouble()) }
     }
 
-    override fun StructureND<Double>.ceil(): DoubleTensor = map { ceil(it) }
+    override fun ceil(arg: StructureND<Double>): DoubleTensor = arg.map { ceil(it) }
 
-    override fun StructureND<Double>.floor(): DoubleTensor = map { floor(it) }
+    override fun floor(structureND: StructureND<Double>): DoubleTensor = structureND.map { floor(it) }
 
-    override fun StructureND<Double>.inv(): DoubleTensor = invLU(1e-9)
+    override fun StructureND<Double>.inv(): DoubleTensor = invLU(this, 1e-9)
 
-    override fun StructureND<Double>.det(): DoubleTensor = detLU(1e-9)
+    override fun StructureND<Double>.det(): DoubleTensor = detLU(this, 1e-9)
 
-    /**
+    override fun lu(structureND: StructureND<Double>): Triple<DoubleTensor, DoubleTensor, DoubleTensor> =
-     * Computes the LU factorization of a matrix or batches of matrices `input`.
+        lu(structureND, 1e-9)
-     * Returns a tuple containing the LU factorization and pivots of `input`.
-     *
-     * @param epsilon permissible error when comparing the determinant of a matrix with zero
-     * @return pair of `factorization` and `pivots`.
-     * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor.
-     * The `pivots`  has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows.
-     */
-    public fun StructureND<Double>.luFactor(epsilon: Double): Pair<DoubleTensor, IntTensor> =
-        computeLU(this, epsilon)
-            ?: throw IllegalArgumentException("Tensor contains matrices which are singular at precision $epsilon")
 
-    /**
+    override fun cholesky(structureND: StructureND<Double>): DoubleTensor = cholesky(structureND, 1e-6)
-     * Computes the LU factorization of a matrix or batches of matrices `input`.
-     * Returns a tuple containing the LU factorization and pivots of `input`.
-     * Uses an error of ``1e-9`` when calculating whether a matrix is degenerate.
-     *
-     * @return pair of `factorization` and `pivots`.
-     * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor.
-     * The `pivots`  has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows.
-     */
-    public fun StructureND<Double>.luFactor(): Pair<DoubleTensor, IntTensor> = luFactor(1e-9)
 
-    /**
+    override fun qr(structureND: StructureND<Double>): Pair<DoubleTensor, DoubleTensor> {
-     * Unpacks the data and pivots from a LU factorization of a tensor.
+        checkSquareMatrix(structureND.shape)
-     * Given a tensor [luTensor], return tensors `Triple(P, L, U)` satisfying `P dot luTensor = L dot U`,
+        val qTensor = zeroesLike(structureND)
-     * with `P` being a permutation matrix or batch of matrices,
+        val rTensor = zeroesLike(structureND)
-     * `L` being a lower triangular matrix or batch of matrices,
-     * `U` being an upper triangular matrix or batch of matrices.
-     *
-     * @param luTensor the packed LU factorization data
-     * @param pivotsTensor the packed LU factorization pivots
-     * @return triple of `P`, `L` and `U` tensors
-     */
-    public fun luPivot(
-        luTensor: StructureND<Double>,
-        pivotsTensor: Tensor<Int>,
-    ): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
-        checkSquareMatrix(luTensor.shape)
-        check(
-            luTensor.shape.first(luTensor.shape.size - 2) contentEquals pivotsTensor.shape.first(pivotsTensor.shape.size - 1) ||
-                    luTensor.shape.last() == pivotsTensor.shape.last() - 1
-        ) { "Inappropriate shapes of input tensors" }
-
-        val n = luTensor.shape.last()
-        val pTensor = zeroesLike(luTensor)
-        pTensor
-            .matrixSequence()
-            .zip(pivotsTensor.asIntTensor().vectorSequence())
-            .forEach { (p, pivot) -> pivInit(p.asDoubleTensor2D(), pivot.as1D(), n) }
-
-        val lTensor = zeroesLike(luTensor)
-        val uTensor = zeroesLike(luTensor)
-
-        lTensor.matrixSequence()
-            .zip(uTensor.matrixSequence())
-            .zip(luTensor.asDoubleTensor().matrixSequence())
-            .forEach { (pairLU, lu) ->
-                val (l, u) = pairLU
-                luPivotHelper(l.asDoubleTensor2D(), u.asDoubleTensor2D(), lu.asDoubleTensor2D(), n)
-            }
-
-        return Triple(pTensor, lTensor, uTensor)
-    }
-
-    /**
-     * QR decomposition.
-     *
-     * Computes the QR decomposition of a matrix or a batch of matrices, and returns a pair `Q to R` of tensors.
-     * Given a tensor `input`, return tensors `Q to R` satisfying `input == Q dot R`,
-     * with `Q` being an orthogonal matrix or batch of orthogonal matrices
-     * and `R` being an upper triangular matrix or batch of upper triangular matrices.
-     *
-     * @receiver the `input`.
-     * @param epsilon the permissible error when comparing tensors for equality.
-     * Used when checking the positive definiteness of the input matrix or matrices.
-     * @return a pair of `Q` and `R` tensors.
-     */
-    public fun StructureND<Double>.cholesky(epsilon: Double): DoubleTensor {
-        checkSquareMatrix(shape)
-        checkPositiveDefinite(asDoubleTensor(), epsilon)
-
-        val n = shape.last()
-        val lTensor = zeroesLike(this)
-
-        for ((a, l) in asDoubleTensor().matrixSequence().zip(lTensor.matrixSequence()))
-            for (i in 0 until n) choleskyHelper(a.asDoubleTensor2D(), l.asDoubleTensor2D(), n)
-
-        return lTensor
-    }
-
-    override fun StructureND<Double>.cholesky(): DoubleTensor = cholesky(1e-6)
-
-    override fun StructureND<Double>.qr(): Pair<DoubleTensor, DoubleTensor> {
-        checkSquareMatrix(shape)
-        val qTensor = zeroesLike(this)
-        val rTensor = zeroesLike(this)
 
         //TODO replace with cycle
-        asDoubleTensor().matrixSequence()
+        structureND.asDoubleTensor().matrixSequence()
             .zip(
                 (qTensor.matrixSequence()
                     .zip(rTensor.matrixSequence()))
@@ -854,200 +702,14 @@ public open class DoubleTensorAlgebra :
         return qTensor to rTensor
     }
 
-    override fun StructureND<Double>.svd(): Triple<StructureND<Double>, StructureND<Double>, StructureND<Double>> =
+    override fun svd(
-        svd(epsilon = 1e-10)
+        structureND: StructureND<Double>,
+    ): Triple<StructureND<Double>, StructureND<Double>, StructureND<Double>> =
+        svd(structureND = structureND, epsilon = 1e-10)
 
+    override fun symEig(structureND: StructureND<Double>): Pair<DoubleTensor, DoubleTensor> =
+        symEigJacobi(structureND = structureND, maxIteration = 50, epsilon = 1e-15)
 
-    /**
-     * Singular Value Decomposition.
-     *
-     * Computes the singular value decomposition of either a matrix or batch of matrices `input`.
-     * The singular value decomposition is represented as a triple `Triple(U, S, V)`,
-     * such that `input == U dot diagonalEmbedding(S) dot V.transpose()`.
-     * If `input` is a batch of tensors, then U, S, and Vh are also batched with the same batch dimensions as `input.
-     *
-     * @receiver the `input`.
-     * @param epsilon permissible error when calculating the dot product of vectors
-     * i.e., the precision with which the cosine approaches 1 in an iterative algorithm.
-     * @return a triple `Triple(U, S, V)`.
-     */
-    public fun StructureND<Double>.svd(epsilon: Double): Triple<StructureND<Double>, StructureND<Double>, StructureND<Double>> {
-        val size = dimension
-        val commonShape = shape.slice(0 until size - 2)
-        val (n, m) = shape.slice(size - 2 until size)
-        val uTensor = zeros(commonShape + ShapeND(min(n, m), n))
-        val sTensor = zeros(commonShape + ShapeND(min(n, m)))
-        val vTensor = zeros(commonShape + ShapeND(min(n, m), m))
-
-        val matrices = asDoubleTensor().matrices
-        val uTensors = uTensor.matrices
-        val sTensorVectors = sTensor.vectors
-        val vTensors = vTensor.matrices
-
-        for (index in matrices.indices) {
-            val matrix = matrices[index]
-            val usv = Triple(
-                uTensors[index],
-                sTensorVectors[index],
-                vTensors[index]
-            )
-            val matrixSize = matrix.shape.linearSize
-            val curMatrix = DoubleTensor(
-                matrix.shape,
-                matrix.source.view(0, matrixSize)
-            )
-            svdHelper(curMatrix, usv, m, n, epsilon)
-        }
-
-        return Triple(uTensor.transposed(), sTensor, vTensor.transposed())
-    }
-
-    override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> =
-        symEigJacobi(maxIteration = 50, epsilon = 1e-15)
-
-    /**
-     * Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
-     * represented by a pair `eigenvalues to eigenvectors`.
-     *
-     * @param epsilon the permissible error when comparing tensors for equality
-     * and when the cosine approaches 1 in the SVD algorithm.
-     * @return a pair `eigenvalues to eigenvectors`.
-     */
-    public fun StructureND<Double>.symEigSvd(epsilon: Double): Pair<DoubleTensor, StructureND<Double>> {
-        //TODO optimize conversion
-        checkSymmetric(asDoubleTensor(), epsilon)
-
-        fun MutableStructure2D<Double>.cleanSym(n: Int) {
-            for (i in 0 until n) {
-                for (j in 0 until n) {
-                    if (i == j) {
-                        this[i, j] = sign(this[i, j])
-                    } else {
-                        this[i, j] = 0.0
-                    }
-                }
-            }
-        }
-
-        val (u, s, v) = svd(epsilon)
-        val shp = s.shape + intArrayOf(1)
-        val utv = u.transposed() matmul v
-        val n = s.shape.last()
-        for (matrix in utv.matrixSequence()) {
-            matrix.asDoubleTensor2D().cleanSym(n)
-        }
-
-        val eig = (utv dot s.asDoubleTensor().view(shp)).view(s.shape)
-        return eig to v
-    }
-
-    public fun StructureND<Double>.symEigJacobi(maxIteration: Int, epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
-        //TODO optimize conversion
-        checkSymmetric(asDoubleTensor(), epsilon)
-
-        val size = this.dimension
-        val eigenvectors = zeros(shape)
-        val eigenvalues = zeros(shape.slice(0 until size - 1))
-
-        var eigenvalueStart = 0
-        var eigenvectorStart = 0
-        for (matrix in asDoubleTensor().matrixSequence()) {
-            val matrix2D = matrix.asDoubleTensor2D()
-            val (d, v) = matrix2D.jacobiHelper(maxIteration, epsilon)
-
-            for (i in 0 until matrix2D.rowNum) {
-                for (j in 0 until matrix2D.colNum) {
-                    eigenvectors.source[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j]
-                }
-            }
-
-            for (i in 0 until matrix2D.rowNum) {
-                eigenvalues.source[eigenvalueStart + i] = d[i]
-            }
-
-            eigenvalueStart += this.shape.last()
-            eigenvectorStart += this.shape.last() * this.shape.last()
-        }
-
-        return eigenvalues to eigenvectors
-    }
-
-    /**
-     * Computes the determinant of a square matrix input, or of each square matrix in a batched input
-     * using LU factorization algorithm.
-     *
-     * @param epsilon the error in the LU algorithm&mdash;permissible error when comparing the determinant of a matrix
-     * with zero.
-     * @return the determinant.
-     */
-    public fun StructureND<Double>.detLU(epsilon: Double = 1e-9): DoubleTensor {
-        checkSquareMatrix(shape)
-        //TODO check for unnecessary copies
-        val luTensor = copyToTensor()
-        val pivotsTensor = setUpPivots()
-
-        val n = shape.size
-
-        val detTensorShape = ShapeND(IntArray(n - 1) { i -> shape[i] }.apply {
-            set(n - 2, 1)
-        })
-
-        val resBuffer = DoubleBuffer(detTensorShape.linearSize) { 0.0 }
-
-        val detTensor = DoubleTensor(
-            detTensorShape,
-            resBuffer
-        )
-
-        luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).forEachIndexed { index, (lu, pivots) ->
-            resBuffer[index] = if (luHelper(lu.asDoubleTensor2D(), pivots.as1D(), epsilon))
-                0.0 else luMatrixDet(lu.asDoubleTensor2D(), pivots.as1D())
-        }
-
-        return detTensor
-    }
-
-    /**
-     * Computes the multiplicative inverse matrix of a square matrix input, or of each square matrix in a batched input
-     * using LU factorization algorithm.
-     * Given a square matrix `a`, return the matrix `aInv` satisfying
-     * `a dot aInv == aInv dot a == eye(a.shape[0])`.
-     *
-     * @param epsilon error in the LU algorithm&mdash;permissible error when comparing the determinant of a matrix with zero
-     * @return the multiplicative inverse of a matrix.
-     */
-    public fun StructureND<Double>.invLU(epsilon: Double = 1e-9): DoubleTensor {
-        val (luTensor, pivotsTensor) = luFactor(epsilon)
-        val invTensor = zeroesLike(luTensor)
-
-        //TODO replace sequence with a cycle
-        val seq = luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).zip(invTensor.matrixSequence())
-        for ((luP, invMatrix) in seq) {
-            val (lu, pivots) = luP
-            luMatrixInv(lu.asDoubleTensor2D(), pivots.as1D(), invMatrix.asDoubleTensor2D())
-        }
-
-        return invTensor
-    }
-
-    /**
-     * LUP decomposition.
-     *
-     * Computes the LUP decomposition of a matrix or a batch of matrices.
-     * Given a tensor `input`, return tensors `Triple(P, L, U)` satisfying `P dot input == L dot U`,
-     * with `P` being a permutation matrix or batch of matrices,
-     * `L` being a lower triangular matrix or batch of matrices,
-     * `U` being an upper triangular matrix or batch of matrices.
-     *
-     * @param epsilon permissible error when comparing the determinant of a matrix with zero.
-     * @return triple of `P`, `L` and `U` tensors.
-     */
-    public fun StructureND<Double>.lu(epsilon: Double = 1e-9): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
-        val (lu, pivots) = luFactor(epsilon)
-        return luPivot(lu, pivots)
-    }
-
-    override fun StructureND<Double>.lu(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> = lu(1e-9)
 }
 
 public val Double.Companion.tensorAlgebra: DoubleTensorAlgebra get() = DoubleTensorAlgebra

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

@@ -13,6 +13,7 @@ import space.kscience.kmath.tensors.api.Tensor
 import space.kscience.kmath.tensors.core.DoubleTensor
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
 import space.kscience.kmath.tensors.core.asDoubleTensor
+import space.kscience.kmath.tensors.core.detLU
 
 
 internal fun checkNotEmptyShape(shape: ShapeND) =
@@ -26,7 +27,7 @@ internal fun checkEmptyDoubleBuffer(buffer: DoubleArray) = check(buffer.isNotEmp
 
 internal fun checkBufferShapeConsistency(shape: ShapeND, buffer: DoubleArray) =
     check(buffer.size == shape.linearSize) {
-        "Inconsistent shape ${shape} for buffer of size ${buffer.size} provided"
+        "Inconsistent shape $shape for buffer of size ${buffer.size} provided"
     }
 
 @PublishedApi
@@ -62,7 +63,7 @@ internal fun DoubleTensorAlgebra.checkSymmetric(
 internal fun DoubleTensorAlgebra.checkPositiveDefinite(tensor: DoubleTensor, epsilon: Double = 1e-6) {
     checkSymmetric(tensor, epsilon)
     for (mat in tensor.matrixSequence())
-        check(mat.asDoubleTensor().detLU().value() > 0.0) {
+        check(detLU(mat.asDoubleTensor()).value() > 0.0) {
-            "Tensor contains matrices which are not positive definite ${mat.asDoubleTensor().detLU().value()}"
+            "Tensor contains matrices which are not positive definite ${detLU(mat.asDoubleTensor()).value()}"
         }
 }

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

@@ -227,7 +227,7 @@ internal fun DoubleTensorAlgebra.qrHelper(
                 }
             }
         }
-        r[j, j] = DoubleTensorAlgebra { (v dot v).sqrt().value() }
+        r[j, j] = DoubleTensorAlgebra { sqrt((v dot v)).value() }
         for (i in 0 until n) {
             qM[i, j] = vv[i] / r[j, j]
         }
@@ -250,7 +250,7 @@ internal fun DoubleTensorAlgebra.svd1d(a: DoubleTensor, epsilon: Double = 1e-10)
     while (true) {
         lastV = v
         v = b.dot(lastV)
-        val norm = DoubleTensorAlgebra { (v dot v).sqrt().value() }
+        val norm = DoubleTensorAlgebra { sqrt((v dot v)).value() }
         v = v.times(1.0 / norm)
         if (abs(v.dot(lastV).value()) > 1 - epsilon) {
             return v
@@ -283,12 +283,12 @@ internal fun DoubleTensorAlgebra.svdHelper(
         if (n > m) {
             v = svd1d(a, epsilon)
             u = matrix.dot(v)
-            norm = DoubleTensorAlgebra { (u dot u).sqrt().value() }
+            norm = DoubleTensorAlgebra { sqrt((u dot u)).value() }
             u = u.times(1.0 / norm)
         } else {
             u = svd1d(a, epsilon)
             v = matrix.transposed(0, 1).dot(u)
-            norm = DoubleTensorAlgebra { (v dot v).sqrt().value() }
+            norm = DoubleTensorAlgebra { sqrt((v dot v)).value() }
             v = v.times(1.0 / norm)
         }
 

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

@@ -0,0 +1,370 @@
+/*
+ * 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.*
+import space.kscience.kmath.operations.covariance
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.DoubleBuffer
+import space.kscience.kmath.tensors.api.Tensor
+import space.kscience.kmath.tensors.core.internal.*
+import kotlin.math.min
+import kotlin.math.sign
+
+
+/**
+ * Returns a tensor of random numbers drawn from normal distributions with `0.0` mean and `1.0` standard deviation.
+ *
+ * @param shape the desired shape for the output tensor.
+ * @param seed the random seed of the pseudo-random number generator.
+ * @return tensor of a given shape filled with numbers from the normal distribution
+ * with `0.0` mean and `1.0` standard deviation.
+ */
+public fun DoubleTensorAlgebra.randomNormal(shape: ShapeND, seed: Long = 0): DoubleTensor =
+    fromBuffer(shape, DoubleBuffer.randomNormals(shape.linearSize, seed))
+
+/**
+ * Returns a tensor with the same shape as `input` of random numbers drawn from normal distributions
+ * with `0.0` mean and `1.0` standard deviation.
+ *
+ * @receiver the `input`.
+ * @param seed the random seed of the pseudo-random number generator.
+ * @return a tensor with the same shape as `input` filled with numbers from the normal distribution
+ * with `0.0` mean and `1.0` standard deviation.
+ */
+public fun DoubleTensorAlgebra.randomNormalLike(structure: WithShape, seed: Long = 0): DoubleTensor =
+    DoubleTensor(structure.shape, DoubleBuffer.randomNormals(structure.shape.linearSize, seed))
+
+/**
+ * Concatenates a sequence of tensors with equal shapes along the first dimension.
+ *
+ * @param tensors the [List] of tensors with same shapes to concatenate
+ * @return tensor with concatenation result
+ */
+public fun stack(tensors: List<Tensor<Double>>): DoubleTensor {
+    check(tensors.isNotEmpty()) { "List must have at least 1 element" }
+    val shape = tensors[0].shape
+    check(tensors.all { it.shape contentEquals shape }) { "Tensors must have same shapes" }
+    val resShape = ShapeND(tensors.size) + shape
+//        val resBuffer: List<Double> = tensors.flatMap {
+//            it.asDoubleTensor().source.array.drop(it.asDoubleTensor().bufferStart)
+//                .take(it.asDoubleTensor().linearSize)
+//        }
+    val resBuffer = tensors.map { it.asDoubleTensor().source }.concat()
+    return DoubleTensor(resShape, resBuffer)
+}
+
+/**
+ * Computes the LU factorization of a matrix or batches of matrices `input`.
+ * Returns a tuple containing the LU factorization and pivots of `input`.
+ *
+ * @param epsilon permissible error when comparing the determinant of a matrix with zero default is 1e-9
+ * @return pair of `factorization` and `pivots`.
+ * The `factorization` has the shape ``(*, m, n)``, where``(*, m, n)`` is the shape of the `input` tensor.
+ * The `pivots`  has the shape ``(∗, min(m, n))``. `pivots` stores all the intermediate transpositions of rows.
+ */
+public fun DoubleTensorAlgebra.luFactor(
+    structureND: StructureND<Double>,
+    epsilon: Double = 1e-9,
+): Pair<DoubleTensor, IntTensor> =
+    computeLU(structureND, epsilon)
+        ?: throw IllegalArgumentException("Tensor contains matrices which are singular at precision $epsilon")
+
+
+/**
+ * Unpacks the data and pivots from a LU factorization of a tensor.
+ * Given a tensor [luTensor], return tensors `Triple(P, L, U)` satisfying `P dot luTensor = L dot U`,
+ * with `P` being a permutation matrix or batch of matrices,
+ * `L` being a lower triangular matrix or batch of matrices,
+ * `U` being an upper triangular matrix or batch of matrices.
+ *
+ * @param luTensor the packed LU factorization data
+ * @param pivotsTensor the packed LU factorization pivots
+ * @return triple of `P`, `L` and `U` tensors
+ */
+public fun DoubleTensorAlgebra.luPivot(
+    luTensor: StructureND<Double>,
+    pivotsTensor: Tensor<Int>,
+): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
+    checkSquareMatrix(luTensor.shape)
+    check(
+        luTensor.shape.first(luTensor.shape.size - 2) contentEquals pivotsTensor.shape.first(pivotsTensor.shape.size - 1) ||
+                luTensor.shape.last() == pivotsTensor.shape.last() - 1
+    ) { "Inappropriate shapes of input tensors" }
+
+    val n = luTensor.shape.last()
+    val pTensor = zeroesLike(luTensor)
+    pTensor
+        .matrixSequence()
+        .zip(pivotsTensor.asIntTensor().vectorSequence())
+        .forEach { (p, pivot) -> pivInit(p.asDoubleTensor2D(), pivot.as1D(), n) }
+
+    val lTensor = zeroesLike(luTensor)
+    val uTensor = zeroesLike(luTensor)
+
+    lTensor.matrixSequence()
+        .zip(uTensor.matrixSequence())
+        .zip(luTensor.asDoubleTensor().matrixSequence())
+        .forEach { (pairLU, lu) ->
+            val (l, u) = pairLU
+            luPivotHelper(l.asDoubleTensor2D(), u.asDoubleTensor2D(), lu.asDoubleTensor2D(), n)
+        }
+
+    return Triple(pTensor, lTensor, uTensor)
+}
+
+
+/**
+ * LUP decomposition.
+ *
+ * Computes the LUP decomposition of a matrix or a batch of matrices.
+ * Given a tensor `input`, return tensors `Triple(P, L, U)` satisfying `P dot input == L dot U`,
+ * with `P` being a permutation matrix or batch of matrices,
+ * `L` being a lower triangular matrix or batch of matrices,
+ * `U` being an upper triangular matrix or batch of matrices.
+ *
+ * @param epsilon permissible error when comparing the determinant of a matrix with zero.
+ * @return triple of `P`, `L` and `U` tensors.
+ */
+public fun DoubleTensorAlgebra.lu(
+    structureND: StructureND<Double>,
+    epsilon: Double = 1e-9,
+): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
+    val (lu, pivots) = luFactor(structureND, epsilon)
+    return luPivot(lu, pivots)
+}
+
+
+/**
+ * QR decomposition.
+ *
+ * Computes the QR decomposition of a matrix or a batch of matrices, and returns a pair `Q to R` of tensors.
+ * Given a tensor `input`, return tensors `Q to R` satisfying `input == Q dot R`,
+ * with `Q` being an orthogonal matrix or batch of orthogonal matrices
+ * and `R` being an upper triangular matrix or batch of upper triangular matrices.
+ *
+ * @receiver the `input`.
+ * @param epsilon the permissible error when comparing tensors for equality. The default is 1e-6
+ * Used when checking the positive definiteness of the input matrix or matrices.
+ * @return a pair of `Q` and `R` tensors.
+ */
+public fun DoubleTensorAlgebra.cholesky(structureND: StructureND<Double>, epsilon: Double = 1e-6): DoubleTensor {
+    checkSquareMatrix(structureND.shape)
+    checkPositiveDefinite(structureND.asDoubleTensor(), epsilon)
+
+    val n = structureND.shape.last()
+    val lTensor = zeroesLike(structureND)
+
+    for ((a, l) in structureND.asDoubleTensor().matrixSequence().zip(lTensor.matrixSequence()))
+        for (i in 0 until n) choleskyHelper(a.asDoubleTensor2D(), l.asDoubleTensor2D(), n)
+
+    return lTensor
+}
+
+
+/**
+ * Singular Value Decomposition.
+ *
+ * Computes the singular value decomposition of either a matrix or batch of matrices `input`.
+ * The singular value decomposition is represented as a triple `Triple(U, S, V)`,
+ * such that `input == U dot diagonalEmbedding(S) dot V.transpose()`.
+ * If `input` is a batch of tensors, then U, S, and Vh are also batched with the same batch dimensions as `input.
+ *
+ * @receiver the `input`.
+ * @param epsilon permissible error when calculating the dot product of vectors
+ * i.e., the precision with which the cosine approaches 1 in an iterative algorithm.
+ * @return a triple `Triple(U, S, V)`.
+ */
+public fun DoubleTensorAlgebra.svd(
+    structureND: StructureND<Double>,
+    epsilon: Double,
+): Triple<StructureND<Double>, StructureND<Double>, StructureND<Double>> {
+    val size = structureND.dimension
+    val commonShape = structureND.shape.slice(0 until size - 2)
+    val (n, m) = structureND.shape.slice(size - 2 until size)
+    val uTensor = zeros(commonShape + ShapeND(min(n, m), n))
+    val sTensor = zeros(commonShape + ShapeND(min(n, m)))
+    val vTensor = zeros(commonShape + ShapeND(min(n, m), m))
+
+    val matrices = structureND.asDoubleTensor().matrices
+    val uTensors = uTensor.matrices
+    val sTensorVectors = sTensor.vectors
+    val vTensors = vTensor.matrices
+
+    for (index in matrices.indices) {
+        val matrix = matrices[index]
+        val usv = Triple(
+            uTensors[index],
+            sTensorVectors[index],
+            vTensors[index]
+        )
+        val matrixSize = matrix.shape.linearSize
+        val curMatrix = DoubleTensor(
+            matrix.shape,
+            matrix.source.view(0, matrixSize)
+        )
+        svdHelper(curMatrix, usv, m, n, epsilon)
+    }
+
+    return Triple(uTensor.transposed(), sTensor, vTensor.transposed())
+}
+
+/**
+ * Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
+ * represented by a pair `eigenvalues to eigenvectors`.
+ *
+ * @param epsilon the permissible error when comparing tensors for equality
+ * and when the cosine approaches 1 in the SVD algorithm.
+ * @return a pair `eigenvalues to eigenvectors`.
+ */
+public fun DoubleTensorAlgebra.symEigSvd(
+    structureND: StructureND<Double>,
+    epsilon: Double,
+): Pair<DoubleTensor, StructureND<Double>> {
+    //TODO optimize conversion
+    checkSymmetric(structureND.asDoubleTensor(), epsilon)
+
+    fun MutableStructure2D<Double>.cleanSym(n: Int) {
+        for (i in 0 until n) {
+            for (j in 0 until n) {
+                if (i == j) {
+                    this[i, j] = sign(this[i, j])
+                } else {
+                    this[i, j] = 0.0
+                }
+            }
+        }
+    }
+
+    val (u, s, v) = svd(structureND, epsilon)
+    val shp = s.shape + intArrayOf(1)
+    val utv = u.transposed() matmul v
+    val n = s.shape.last()
+    for (matrix in utv.matrixSequence()) {
+        matrix.asDoubleTensor2D().cleanSym(n)
+    }
+
+    val eig = (utv dot s.asDoubleTensor().view(shp)).view(s.shape)
+    return eig to v
+}
+
+public fun DoubleTensorAlgebra.symEigJacobi(
+    structureND: StructureND<Double>,
+    maxIteration: Int,
+    epsilon: Double,
+): Pair<DoubleTensor, DoubleTensor> {
+    //TODO optimize conversion
+    checkSymmetric(structureND.asDoubleTensor(), epsilon)
+
+    val size = structureND.dimension
+    val eigenvectors = zeros(structureND.shape)
+    val eigenvalues = zeros(structureND.shape.slice(0 until size - 1))
+
+    var eigenvalueStart = 0
+    var eigenvectorStart = 0
+    for (matrix in structureND.asDoubleTensor().matrixSequence()) {
+        val matrix2D = matrix.asDoubleTensor2D()
+        val (d, v) = matrix2D.jacobiHelper(maxIteration, epsilon)
+
+        for (i in 0 until matrix2D.rowNum) {
+            for (j in 0 until matrix2D.colNum) {
+                eigenvectors.source[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j]
+            }
+        }
+
+        for (i in 0 until matrix2D.rowNum) {
+            eigenvalues.source[eigenvalueStart + i] = d[i]
+        }
+
+        eigenvalueStart += structureND.shape.last()
+        eigenvectorStart += structureND.shape.last() * structureND.shape.last()
+    }
+
+    return eigenvalues to eigenvectors
+}
+
+/**
+ * Computes the determinant of a square matrix input, or of each square matrix in a batched input
+ * using LU factorization algorithm.
+ *
+ * @param epsilon the error in the LU algorithm&mdash;permissible error when comparing the determinant of a matrix
+ * with zero.
+ * @return the determinant.
+ */
+public fun DoubleTensorAlgebra.detLU(structureND: StructureND<Double>, epsilon: Double = 1e-9): DoubleTensor {
+    checkSquareMatrix(structureND.shape)
+    //TODO check for unnecessary copies
+    val luTensor = structureND.copyToTensor()
+    val pivotsTensor = structureND.setUpPivots()
+
+    val n = structureND.shape.size
+
+    val detTensorShape = ShapeND(IntArray(n - 1) { i -> structureND.shape[i] }.apply {
+        set(n - 2, 1)
+    })
+
+    val resBuffer = DoubleBuffer(detTensorShape.linearSize) { 0.0 }
+
+    val detTensor = DoubleTensor(
+        detTensorShape,
+        resBuffer
+    )
+
+    luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).forEachIndexed { index, (lu, pivots) ->
+        resBuffer[index] = if (luHelper(lu.asDoubleTensor2D(), pivots.as1D(), epsilon))
+            0.0 else luMatrixDet(lu.asDoubleTensor2D(), pivots.as1D())
+    }
+
+    return detTensor
+}
+
+/**
+ * Computes the multiplicative inverse matrix of a square matrix input, or of each square matrix in a batched input
+ * using LU factorization algorithm.
+ * Given a square matrix `a`, return the matrix `aInv` satisfying
+ * `a dot aInv == aInv dot a == eye(a.shape[0])`.
+ *
+ * @param epsilon error in the LU algorithm&mdash;permissible error when comparing the determinant of a matrix with zero
+ * @return the multiplicative inverse of a matrix.
+ */
+public fun DoubleTensorAlgebra.invLU(structureND: StructureND<Double>, epsilon: Double = 1e-9): DoubleTensor {
+    val (luTensor, pivotsTensor) = luFactor(structureND, epsilon)
+    val invTensor = zeroesLike(luTensor)
+
+    //TODO replace sequence with a cycle
+    val seq = luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).zip(invTensor.matrixSequence())
+    for ((luP, invMatrix) in seq) {
+        val (lu, pivots) = luP
+        luMatrixInv(lu.asDoubleTensor2D(), pivots.as1D(), invMatrix.asDoubleTensor2D())
+    }
+
+    return invTensor
+}
+
+/**
+ * Returns the covariance matrix `M` of given vectors.
+ *
+ * `M[i, j]` contains covariance of `i`-th and `j`-th given vectors
+ *
+ * @param vectors the [List] of 1-dimensional tensors with same shape
+ * @return `M`.
+ */
+public fun DoubleTensorAlgebra.covariance(vectors: List<Buffer<Double>>): DoubleTensor {
+    check(vectors.isNotEmpty()) { "List must have at least 1 element" }
+    val n = vectors.size
+    val m = vectors[0].size
+    check(vectors.all { it.size == m }) { "Vectors must have same shapes" }
+    val resTensor = DoubleTensor(
+        ShapeND(n, n),
+        DoubleBuffer(n * n) { 0.0 }
+    )
+    for (i in 0 until n) {
+        for (j in 0 until n) {
+            resTensor[intArrayOf(i, j)] = bufferAlgebra.covariance(vectors[i], vectors[j])
+        }
+    }
+    return resTensor
+}

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

@@ -34,73 +34,73 @@ internal class TestDoubleAnalyticTensorAlgebra {
 
     @Test
     fun testExp() = DoubleTensorAlgebra {
-        assertTrue { tensor.exp() eq expectedTensor(::exp) }
+        assertTrue { exp(tensor) eq expectedTensor(::exp) }
     }
 
     @Test
     fun testLog() = DoubleTensorAlgebra {
-        assertTrue { tensor.ln() eq expectedTensor(::ln) }
+        assertTrue { ln(tensor) eq expectedTensor(::ln) }
     }
 
     @Test
     fun testSqrt() = DoubleTensorAlgebra {
-        assertTrue { tensor.sqrt() eq expectedTensor(::sqrt) }
+        assertTrue { sqrt(tensor) eq expectedTensor(::sqrt) }
     }
 
     @Test
     fun testCos() = DoubleTensorAlgebra {
-        assertTrue { tensor.cos() eq expectedTensor(::cos) }
+        assertTrue { cos(tensor) eq expectedTensor(::cos) }
     }
 
 
     @Test
     fun testCosh() = DoubleTensorAlgebra {
-        assertTrue { tensor.cosh() eq expectedTensor(::cosh) }
+        assertTrue { cosh(tensor) eq expectedTensor(::cosh) }
     }
 
     @Test
     fun testAcosh() = DoubleTensorAlgebra {
-        assertTrue { tensor.acosh() eq expectedTensor(::acosh) }
+        assertTrue { acosh(tensor) eq expectedTensor(::acosh) }
     }
 
     @Test
     fun testSin() = DoubleTensorAlgebra {
-        assertTrue { tensor.sin() eq expectedTensor(::sin) }
+        assertTrue { sin(tensor) eq expectedTensor(::sin) }
     }
 
     @Test
     fun testSinh() = DoubleTensorAlgebra {
-        assertTrue { tensor.sinh() eq expectedTensor(::sinh) }
+        assertTrue { sinh(tensor) eq expectedTensor(::sinh) }
     }
 
     @Test
     fun testAsinh() = DoubleTensorAlgebra {
-        assertTrue { tensor.asinh() eq expectedTensor(::asinh) }
+        assertTrue { asinh(tensor) eq expectedTensor(::asinh) }
     }
 
     @Test
     fun testTan() = DoubleTensorAlgebra {
-        assertTrue { tensor.tan() eq expectedTensor(::tan) }
+        assertTrue { tan(tensor) eq expectedTensor(::tan) }
     }
 
     @Test
     fun testAtan() = DoubleTensorAlgebra {
-        assertTrue { tensor.atan() eq expectedTensor(::atan) }
+        assertTrue { atan(tensor) eq expectedTensor(::atan) }
     }
 
     @Test
     fun testTanh() = DoubleTensorAlgebra {
-        assertTrue { tensor.tanh() eq expectedTensor(::tanh) }
+        assertTrue { tanh(tensor) eq expectedTensor(::tanh) }
     }
 
     @Test
     fun testCeil() = DoubleTensorAlgebra {
-        assertTrue { tensor.ceil() eq expectedTensor(::ceil) }
+        assertTrue { ceil(tensor) eq expectedTensor(::ceil) }
     }
 
     @Test
     fun testFloor() = DoubleTensorAlgebra {
-        assertTrue { tensor.floor() eq expectedTensor(::floor) }
+        assertTrue { floor(tensor) eq expectedTensor(::floor) }
     }
 
     val shape2 = ShapeND(2, 2)
@@ -163,15 +163,15 @@ internal class TestDoubleAnalyticTensorAlgebra {
 
     @Test
     fun testMean() = DoubleTensorAlgebra {
-        assertTrue { tensor2.mean() == 1.0 }
+        assertTrue { mean(tensor2) == 1.0 }
         assertTrue {
-            tensor2.mean(0, true) eq fromArray(
+            mean(tensor2, 0, true) eq fromArray(
                 ShapeND(1, 2),
                 doubleArrayOf(-1.0, 3.0)
             )
         }
         assertTrue {
-            tensor2.mean(1, false) eq fromArray(
+            mean(tensor2, 1, false) eq fromArray(
                 ShapeND(2),
                 doubleArrayOf(1.5, 0.5)
             )

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

@@ -35,7 +35,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
                 -7.0
             )
         )
-        val detTensor = tensor.detLU()
+        val detTensor = detLU(tensor)
 
         assertTrue(detTensor.eq(expectedTensor))
 
@@ -88,7 +88,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
             )
         )
 
-        val invTensor = tensor.invLU()
+        val invTensor = invLU(tensor)
         assertTrue(invTensor.eq(expectedTensor))
     }
 
@@ -111,7 +111,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
 
         val tensor = fromArray(shape, buffer)
 
-        val (q, r) = tensor.qr()
+        val (q, r) = qr(tensor)
 
         assertTrue { q.shape contentEquals shape }
         assertTrue { r.shape contentEquals shape }
@@ -131,7 +131,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
         )
         val tensor = fromArray(shape, buffer)
 
-        val (p, l, u) = tensor.lu()
+        val (p, l, u) = lu(tensor)
 
         assertTrue { p.shape contentEquals shape }
         assertTrue { l.shape contentEquals shape }
@@ -146,7 +146,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
         val sigma = (tensor matmul tensor.transposed()) + diagonalEmbedding(
             fromArray(ShapeND(2, 5), DoubleArray(10) { 0.1 })
         )
-        val low = sigma.cholesky()
+        val low = cholesky(sigma)
         val sigmChol = low matmul low.transposed()
         assertTrue(sigma.eq(sigmChol))
     }
@@ -171,7 +171,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
     @Test
     fun testBatchedSVD() = DoubleTensorAlgebra {
         val tensor = randomNormal(ShapeND(2, 5, 3), 0)
-        val (tensorU, tensorS, tensorV) = tensor.svd()
+        val (tensorU, tensorS, tensorV) = svd(tensor)
         val tensorSVD = tensorU matmul (diagonalEmbedding(tensorS) matmul tensorV.transposed())
         assertTrue(tensor.eq(tensorSVD))
     }
@@ -180,7 +180,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
     fun testBatchedSymEig() = DoubleTensorAlgebra {
         val tensor = randomNormal(shape = ShapeND(2, 3, 3), 0)
         val tensorSigma = tensor + tensor.transposed()
-        val (tensorS, tensorV) = tensorSigma.symEig()
+        val (tensorS, tensorV) = symEig(tensorSigma)
         val tensorSigmaCalc = tensorV matmul (diagonalEmbedding(tensorS) matmul tensorV.transposed())
         assertTrue(tensorSigma.eq(tensorSigmaCalc))
     }
@@ -190,7 +190,7 @@ internal class TestDoubleLinearOpsTensorAlgebra {
 
 
 private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor, epsilon: Double = 1e-10) {
-    val svd = tensor.svd()
+    val svd = svd(tensor)
 
     val tensorSVD = svd.first
         .dot(