Merge pull request #1 from margarita0303/feature/tensors-performance

Feature/tensors performance Adding SVDGolubKahan

benchmarks/build.gradle.kts

@@ -84,6 +84,11 @@ benchmark {
         iterationTimeUnit = "ms"
     }
 
+    configurations.register("svd") {
+        commonConfiguration()
+        include("SVDBenchmark")
+    }
+
     configurations.register("buffer") {
         commonConfiguration()
         include("BufferBenchmark")

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

@@ -0,0 +1,141 @@
+/*
+ * Copyright 2018-2021 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.benchmarks
+import kotlinx.benchmark.Benchmark
+import kotlinx.benchmark.Blackhole
+import kotlinx.benchmark.Scope
+import kotlinx.benchmark.State
+import org.ejml.UtilEjml.assertTrue
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.diagonalEmbedding
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.dot
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.eq
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.svdGolubKahan
+import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.transpose
+import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
+import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.svdPowerMethod
+
+@State(Scope.Benchmark)
+class SVDBenchmark {
+    companion object {
+        val tensorSmall = DoubleTensorAlgebra.randomNormal(intArrayOf(5, 5), 0)
+        val tensorMedium = DoubleTensorAlgebra.randomNormal(intArrayOf(10, 10), 0)
+        val tensorLarge = DoubleTensorAlgebra.randomNormal(intArrayOf(50, 50), 0)
+        val tensorVeryLarge = DoubleTensorAlgebra.randomNormal(intArrayOf(100, 100), 0)
+        val epsilon = 1e-9
+    }
+
+    @Benchmark
+    fun svdPowerMethodSmall(blackhole: Blackhole) {
+        val svd = tensorSmall.svdPowerMethod()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorSmall, epsilon))
+        blackhole.consume(
+            tensorSmall.svdPowerMethod()
+        )
+    }
+
+    @Benchmark
+    fun svdPowerMethodMedium(blackhole: Blackhole) {
+        val svd = tensorMedium.svdPowerMethod()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorMedium, epsilon))
+        blackhole.consume(
+            tensorMedium.svdPowerMethod()
+        )
+    }
+
+    @Benchmark
+    fun svdPowerMethodLarge(blackhole: Blackhole) {
+        val svd = tensorLarge.svdPowerMethod()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorLarge, epsilon))
+        blackhole.consume(
+            tensorLarge.svdPowerMethod()
+        )
+    }
+
+    @Benchmark
+    fun svdPowerMethodVeryLarge(blackhole: Blackhole) {
+        val svd = tensorVeryLarge.svdPowerMethod()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorVeryLarge, epsilon))
+        blackhole.consume(
+            tensorVeryLarge.svdPowerMethod()
+        )
+    }
+
+    @Benchmark
+    fun svdGolubKahanSmall(blackhole: Blackhole) {
+        val svd = tensorSmall.svdGolubKahan()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorSmall, epsilon))
+        blackhole.consume(
+            tensorSmall.svdGolubKahan()
+        )
+    }
+
+    @Benchmark
+    fun svdGolubKahanMedium(blackhole: Blackhole) {
+        val svd = tensorMedium.svdGolubKahan()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorMedium, epsilon))
+        blackhole.consume(
+            tensorMedium.svdGolubKahan()
+        )
+    }
+
+    @Benchmark
+    fun svdGolubKahanLarge(blackhole: Blackhole) {
+        val svd = tensorLarge.svdGolubKahan()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorLarge, epsilon))
+        blackhole.consume(
+            tensorLarge.svdGolubKahan()
+        )
+    }
+
+    @Benchmark
+    fun svdGolubKahanVeryLarge(blackhole: Blackhole) {
+        val svd = tensorVeryLarge.svdGolubKahan()
+        val tensorSVD = svd.first
+            .dot(
+                diagonalEmbedding(svd.second)
+                    .dot(svd.third.transpose())
+            )
+        assertTrue(tensorSVD.eq(tensorVeryLarge, epsilon))
+        blackhole.consume(
+            tensorVeryLarge.svdGolubKahan()
+        )
+    }
+}

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

@@ -27,7 +27,7 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val newThis = broadcast[0]
         val newOther = broadcast[1]
         val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[i] + newOther.mutableBuffer.array()[i]
+            newThis.mutableBuffer[i] + newOther.mutableBuffer[i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
@@ -35,8 +35,8 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
     override fun Tensor<Double>.plusAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.tensor, tensor.shape)
         for (i in 0 until tensor.indices.linearSize) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] +=
+            tensor.mutableBuffer[tensor.bufferStart + i] +=
-                newOther.mutableBuffer.array()[tensor.bufferStart + i]
+                newOther.mutableBuffer[tensor.bufferStart + i]
         }
     }
 
@@ -45,7 +45,7 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val newThis = broadcast[0]
         val newOther = broadcast[1]
         val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[i] - newOther.mutableBuffer.array()[i]
+            newThis.mutableBuffer[i] - newOther.mutableBuffer[i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
@@ -53,8 +53,8 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
     override fun Tensor<Double>.minusAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.tensor, tensor.shape)
         for (i in 0 until tensor.indices.linearSize) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] -=
+            tensor.mutableBuffer[tensor.bufferStart + i] -=
-                newOther.mutableBuffer.array()[tensor.bufferStart + i]
+                newOther.mutableBuffer[tensor.bufferStart + i]
         }
     }
 
@@ -63,8 +63,8 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val newThis = broadcast[0]
         val newOther = broadcast[1]
         val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[newThis.bufferStart + i] *
+            newThis.mutableBuffer[newThis.bufferStart + i] *
-                    newOther.mutableBuffer.array()[newOther.bufferStart + i]
+                    newOther.mutableBuffer[newOther.bufferStart + i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
@@ -72,8 +72,8 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
     override fun Tensor<Double>.timesAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.tensor, tensor.shape)
         for (i in 0 until tensor.indices.linearSize) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] *=
+            tensor.mutableBuffer[tensor.bufferStart + i] *=
-                newOther.mutableBuffer.array()[tensor.bufferStart + i]
+                newOther.mutableBuffer[tensor.bufferStart + i]
         }
     }
 
@@ -82,8 +82,8 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
         val newThis = broadcast[0]
         val newOther = broadcast[1]
         val resBuffer = DoubleArray(newThis.indices.linearSize) { i ->
-            newThis.mutableBuffer.array()[newOther.bufferStart + i] /
+            newThis.mutableBuffer[newOther.bufferStart + i] /
-                    newOther.mutableBuffer.array()[newOther.bufferStart + i]
+                    newOther.mutableBuffer[newOther.bufferStart + i]
         }
         return DoubleTensor(newThis.shape, resBuffer)
     }
@@ -91,8 +91,8 @@ public object BroadcastDoubleTensorAlgebra : DoubleTensorAlgebra() {
     override fun Tensor<Double>.divAssign(arg: StructureND<Double>) {
         val newOther = broadcastTo(arg.tensor, tensor.shape)
         for (i in 0 until tensor.indices.linearSize) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] /=
+            tensor.mutableBuffer[tensor.bufferStart + i] /=
-                newOther.mutableBuffer.array()[tensor.bufferStart + i]
+                newOther.mutableBuffer[tensor.bufferStart + i]
         }
     }
 }

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

@@ -89,7 +89,7 @@ public open class DoubleTensorAlgebra :
     }
 
     override fun StructureND<Double>.valueOrNull(): Double? = if (tensor.shape contentEquals intArrayOf(1))
-        tensor.mutableBuffer.array()[tensor.bufferStart] else null
+        tensor.mutableBuffer[tensor.bufferStart] else null
 
     override fun StructureND<Double>.value(): Double = valueOrNull()
         ?: throw IllegalArgumentException("The tensor shape is $shape, but value method is allowed only for shape [1]")
@@ -208,7 +208,7 @@ public open class DoubleTensorAlgebra :
 
     override fun Double.plus(arg: StructureND<Double>): DoubleTensor {
         val resBuffer = DoubleArray(arg.tensor.numElements) { i ->
-            arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i] + this
+            arg.tensor.mutableBuffer[arg.tensor.bufferStart + i] + this
         }
         return DoubleTensor(arg.shape, resBuffer)
     }
@@ -218,35 +218,35 @@ public open class DoubleTensorAlgebra :
     override fun StructureND<Double>.plus(arg: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, arg.tensor)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[i] + arg.tensor.mutableBuffer.array()[i]
+            tensor.mutableBuffer[i] + arg.tensor.mutableBuffer[i]
         }
         return DoubleTensor(tensor.shape, resBuffer)
     }
 
     override fun Tensor<Double>.plusAssign(value: Double) {
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] += value
+            tensor.mutableBuffer[tensor.bufferStart + i] += value
         }
     }
 
     override fun Tensor<Double>.plusAssign(arg: StructureND<Double>) {
         checkShapesCompatible(tensor, arg.tensor)
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] +=
+            tensor.mutableBuffer[tensor.bufferStart + i] +=
-                arg.tensor.mutableBuffer.array()[tensor.bufferStart + i]
+                arg.tensor.mutableBuffer[tensor.bufferStart + i]
         }
     }
 
     override fun Double.minus(arg: StructureND<Double>): DoubleTensor {
         val resBuffer = DoubleArray(arg.tensor.numElements) { i ->
-            this - arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i]
+            this - arg.tensor.mutableBuffer[arg.tensor.bufferStart + i]
         }
         return DoubleTensor(arg.shape, resBuffer)
     }
 
     override fun StructureND<Double>.minus(arg: Double): DoubleTensor {
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] - arg
+            tensor.mutableBuffer[tensor.bufferStart + i] - arg
         }
         return DoubleTensor(tensor.shape, resBuffer)
     }
@@ -254,28 +254,28 @@ public open class DoubleTensorAlgebra :
     override fun StructureND<Double>.minus(arg: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, arg)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[i] - arg.tensor.mutableBuffer.array()[i]
+            tensor.mutableBuffer[i] - arg.tensor.mutableBuffer[i]
         }
         return DoubleTensor(tensor.shape, resBuffer)
     }
 
     override fun Tensor<Double>.minusAssign(value: Double) {
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] -= value
+            tensor.mutableBuffer[tensor.bufferStart + i] -= value
         }
     }
 
     override fun Tensor<Double>.minusAssign(arg: StructureND<Double>) {
         checkShapesCompatible(tensor, arg)
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] -=
+            tensor.mutableBuffer[tensor.bufferStart + i] -=
-                arg.tensor.mutableBuffer.array()[tensor.bufferStart + i]
+                arg.tensor.mutableBuffer[tensor.bufferStart + i]
         }
     }
 
     override fun Double.times(arg: StructureND<Double>): DoubleTensor {
         val resBuffer = DoubleArray(arg.tensor.numElements) { i ->
-            arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i] * this
+            arg.tensor.mutableBuffer[arg.tensor.bufferStart + i] * this
         }
         return DoubleTensor(arg.shape, resBuffer)
     }
@@ -285,36 +285,36 @@ public open class DoubleTensorAlgebra :
     override fun StructureND<Double>.times(arg: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, arg)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] *
+            tensor.mutableBuffer[tensor.bufferStart + i] *
-                    arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i]
+                    arg.tensor.mutableBuffer[arg.tensor.bufferStart + i]
         }
         return DoubleTensor(tensor.shape, resBuffer)
     }
 
     override fun Tensor<Double>.timesAssign(value: Double) {
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] *= value
+            tensor.mutableBuffer[tensor.bufferStart + i] *= value
         }
     }
 
     override fun Tensor<Double>.timesAssign(arg: StructureND<Double>) {
         checkShapesCompatible(tensor, arg)
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] *=
+            tensor.mutableBuffer[tensor.bufferStart + i] *=
-                arg.tensor.mutableBuffer.array()[tensor.bufferStart + i]
+                arg.tensor.mutableBuffer[tensor.bufferStart + i]
         }
     }
 
     override fun Double.div(arg: StructureND<Double>): DoubleTensor {
         val resBuffer = DoubleArray(arg.tensor.numElements) { i ->
-            this / arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i]
+            this / arg.tensor.mutableBuffer[arg.tensor.bufferStart + i]
         }
         return DoubleTensor(arg.shape, resBuffer)
     }
 
     override fun StructureND<Double>.div(arg: Double): DoubleTensor {
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] / arg
+            tensor.mutableBuffer[tensor.bufferStart + i] / arg
         }
         return DoubleTensor(shape, resBuffer)
     }
@@ -322,29 +322,29 @@ public open class DoubleTensorAlgebra :
     override fun StructureND<Double>.div(arg: StructureND<Double>): DoubleTensor {
         checkShapesCompatible(tensor, arg)
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[arg.tensor.bufferStart + i] /
+            tensor.mutableBuffer[arg.tensor.bufferStart + i] /
-                    arg.tensor.mutableBuffer.array()[arg.tensor.bufferStart + i]
+                    arg.tensor.mutableBuffer[arg.tensor.bufferStart + i]
         }
         return DoubleTensor(tensor.shape, resBuffer)
     }
 
     override fun Tensor<Double>.divAssign(value: Double) {
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] /= value
+            tensor.mutableBuffer[tensor.bufferStart + i] /= value
         }
     }
 
     override fun Tensor<Double>.divAssign(arg: StructureND<Double>) {
         checkShapesCompatible(tensor, arg)
         for (i in 0 until tensor.numElements) {
-            tensor.mutableBuffer.array()[tensor.bufferStart + i] /=
+            tensor.mutableBuffer[tensor.bufferStart + i] /=
-                arg.tensor.mutableBuffer.array()[tensor.bufferStart + i]
+                arg.tensor.mutableBuffer[tensor.bufferStart + i]
         }
     }
 
     override fun StructureND<Double>.unaryMinus(): DoubleTensor {
         val resBuffer = DoubleArray(tensor.numElements) { i ->
-            tensor.mutableBuffer.array()[tensor.bufferStart + i].unaryMinus()
+            tensor.mutableBuffer[tensor.bufferStart + i].unaryMinus()
         }
         return DoubleTensor(tensor.shape, resBuffer)
     }
@@ -367,8 +367,8 @@ public open class DoubleTensorAlgebra :
             newMultiIndex[ii] = newMultiIndex[jj].also { newMultiIndex[jj] = newMultiIndex[ii] }
 
             val linearIndex = resTensor.indices.offset(newMultiIndex)
-            resTensor.mutableBuffer.array()[linearIndex] =
+            resTensor.mutableBuffer[linearIndex] =
-                tensor.mutableBuffer.array()[tensor.bufferStart + offset]
+                tensor.mutableBuffer[tensor.bufferStart + offset]
         }
         return resTensor
     }
@@ -833,8 +833,38 @@ public open class DoubleTensorAlgebra :
         return qTensor to rTensor
     }
 
-    override fun StructureND<Double>.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> =
+    override fun StructureND<Double>.svd(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
-        svd(epsilon = 1e-10)
+        return this.svdGolubKahan()
+    }
+
+    public fun StructureND<Double>.svdGolubKahan(iterations: Int = 30, epsilon: Double = 1e-10): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
+        val size = tensor.dimension
+        val commonShape = tensor.shape.sliceArray(0 until size - 2)
+        val (n, m) = tensor.shape.sliceArray(size - 2 until size)
+        val uTensor = zeros(commonShape + intArrayOf(n, m))
+        val sTensor = zeros(commonShape + intArrayOf(m))
+        val vTensor = zeros(commonShape + intArrayOf(m, m))
+
+        val matrices = tensor.matrices
+        val uTensors = uTensor.matrices
+        val sTensorVectors = sTensor.vectors
+        val vTensors = vTensor.matrices
+
+        for (index in matrices.indices) {
+            val matrix = matrices[index]
+            val matrixSize = matrix.shape.reduce { acc, i -> acc * i }
+            val curMatrix = DoubleTensor(
+                matrix.shape,
+                matrix.mutableBuffer.array()
+                    .slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
+                    .toDoubleArray()
+            )
+            curMatrix.as2D().svdGolubKahanHelper(uTensors[index].as2D(), sTensorVectors[index], vTensors[index].as2D(),
+                iterations, epsilon)
+        }
+
+        return Triple(uTensor, sTensor, vTensor)
+    }
 
     /**
      * Singular Value Decomposition.
@@ -849,7 +879,7 @@ public open class DoubleTensorAlgebra :
      * i.e., the precision with which the cosine approaches 1 in an iterative algorithm.
      * @return a triple `Triple(U, S, V)`.
      */
-    public fun StructureND<Double>.svd(epsilon: Double): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
+    public fun StructureND<Double>.svdPowerMethod(epsilon: Double = 1e-10): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
         val size = tensor.dimension
         val commonShape = tensor.shape.sliceArray(0 until size - 2)
         val (n, m) = tensor.shape.sliceArray(size - 2 until size)
@@ -876,7 +906,7 @@ public open class DoubleTensorAlgebra :
                     .slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
                     .toDoubleArray()
             )
-            svdHelper(curMatrix, usv, m, n, epsilon)
+            svdPowerMethodHelper(curMatrix, usv, m, n, epsilon)
         }
 
         return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
@@ -907,7 +937,7 @@ public open class DoubleTensorAlgebra :
             }
         }
 
-        val (u, s, v) = tensor.svd(epsilon)
+        val (u, s, v) = tensor.svd()
         val shp = s.shape + intArrayOf(1)
         val utv = u.transpose() dot v
         val n = s.shape.last()
@@ -928,18 +958,21 @@ public open class DoubleTensorAlgebra :
 
         var eigenvalueStart = 0
         var eigenvectorStart = 0
+        val eigenvaluesBuffer = eigenvalues.mutableBuffer
+        val eigenvectorsBuffer = eigenvectors.mutableBuffer
+
         for (matrix in tensor.matrixSequence()) {
             val matrix2D = matrix.as2D()
             val (d, v) = matrix2D.jacobiHelper(maxIteration, epsilon)
 
             for (i in 0 until matrix2D.rowNum) {
                 for (j in 0 until matrix2D.colNum) {
-                    eigenvectors.mutableBuffer.array()[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j]
+                    eigenvectorsBuffer[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j]
                 }
             }
 
             for (i in 0 until matrix2D.rowNum) {
-                eigenvalues.mutableBuffer.array()[eigenvalueStart + i] = d[i]
+                eigenvaluesBuffer[eigenvalueStart + i] = d[i]
             }
 
             eigenvalueStart += this.shape.last()
@@ -962,11 +995,11 @@ public open class DoubleTensorAlgebra :
 
         // assume that buffered tensor is square matrix
         operator fun BufferedTensor<Double>.get(i: Int, j: Int): Double {
-            return this.mutableBuffer.array()[bufferStart + i * this.shape[0] + j]
+            return this.mutableBuffer[bufferStart + i * this.shape[0] + j]
         }
 
         operator fun BufferedTensor<Double>.set(i: Int, j: Int, value: Double) {
-            this.mutableBuffer.array()[bufferStart + i * this.shape[0] + j] = value
+            this.mutableBuffer[bufferStart + i * this.shape[0] + j] = value
         }
 
         fun maxOffDiagonal(matrix: BufferedTensor<Double>): Double {

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

@@ -17,6 +17,7 @@ import space.kscience.kmath.tensors.core.DoubleTensor
 import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
 import space.kscience.kmath.tensors.core.IntTensor
 import kotlin.math.abs
+import kotlin.math.max
 import kotlin.math.min
 import kotlin.math.sqrt
 
@@ -299,7 +300,7 @@ internal fun DoubleTensorAlgebra.svd1d(a: DoubleTensor, epsilon: Double = 1e-10)
     }
 }
 
-internal fun DoubleTensorAlgebra.svdHelper(
+internal fun DoubleTensorAlgebra.svdPowerMethodHelper(
     matrix: DoubleTensor,
     USV: Triple<BufferedTensor<Double>, BufferedTensor<Double>, BufferedTensor<Double>>,
     m: Int, n: Int, epsilon: Double,
@@ -307,6 +308,14 @@ internal fun DoubleTensorAlgebra.svdHelper(
     val res = ArrayList<Triple<Double, DoubleTensor, DoubleTensor>>(0)
     val (matrixU, matrixS, matrixV) = USV
 
+    val matrixUStart = matrixU.bufferStart
+    val matrixSStart = matrixS.bufferStart
+    val matrixVStart = matrixV.bufferStart
+
+    val matrixUBuffer = matrixU.mutableBuffer
+    val matrixSBuffer = matrixS.mutableBuffer
+    val matrixVBuffer = matrixV.mutableBuffer
+
     for (k in 0 until min(n, m)) {
         var a = matrix.copy()
         for ((singularValue, u, v) in res.slice(0 until k)) {
@@ -340,12 +349,307 @@ internal fun DoubleTensorAlgebra.svdHelper(
     val uBuffer = res.map { it.second }.flatMap { it.mutableBuffer.array().toList() }.toDoubleArray()
     val vBuffer = res.map { it.third }.flatMap { it.mutableBuffer.array().toList() }.toDoubleArray()
     for (i in uBuffer.indices) {
-        matrixU.mutableBuffer.array()[matrixU.bufferStart + i] = uBuffer[i]
+        matrixUBuffer[matrixUStart + i] = uBuffer[i]
     }
     for (i in s.indices) {
-        matrixS.mutableBuffer.array()[matrixS.bufferStart + i] = s[i]
+        matrixSBuffer[matrixSStart + i] = s[i]
     }
     for (i in vBuffer.indices) {
-        matrixV.mutableBuffer.array()[matrixV.bufferStart + i] = vBuffer[i]
+        matrixVBuffer[matrixVStart + i] = vBuffer[i]
+    }
+}
+
+private fun pythag(a: Double, b: Double): Double {
+    val at: Double = abs(a)
+    val bt: Double = abs(b)
+    val ct: Double
+    val result: Double
+    if (at > bt) {
+        ct = bt / at
+        result = at * sqrt(1.0 + ct * ct)
+    } else if (bt > 0.0) {
+        ct = at / bt
+        result = bt * sqrt(1.0 + ct * ct)
+    } else result = 0.0
+    return result
+}
+
+private fun SIGN(a: Double, b: Double): Double {
+    if (b >= 0.0)
+        return abs(a)
+    else
+        return -abs(a)
+}
+internal fun MutableStructure2D<Double>.svdGolubKahanHelper(u: MutableStructure2D<Double>, w: BufferedTensor<Double>,
+                                                            v: MutableStructure2D<Double>, iterations: Int, epsilon: Double) {
+    val shape = this.shape
+    val m = shape.component1()
+    val n = shape.component2()
+    var f = 0.0
+    val rv1 = DoubleArray(n)
+    var s = 0.0
+    var scale = 0.0
+    var anorm = 0.0
+    var g = 0.0
+    var l = 0
+
+    val wStart = w.bufferStart
+    val wBuffer = w.mutableBuffer
+
+    for (i in 0 until n) {
+        /* left-hand reduction */
+        l = i + 1
+        rv1[i] = scale * g
+        g = 0.0
+        s = 0.0
+        scale = 0.0
+        if (i < m) {
+            for (k in i until m) {
+                scale += abs(this[k, i]);
+            }
+            if (abs(scale) > epsilon) {
+                for (k in i until m) {
+                    this[k, i] = (this[k, i] / scale)
+                    s += this[k, i] * this[k, i]
+                }
+                f = this[i, i]
+                if (f >= 0) {
+                    g = (-1) * abs(sqrt(s))
+                } else {
+                    g = abs(sqrt(s))
+                }
+                val h = f * g - s
+                this[i, i] = f - g
+                if (i != n - 1) {
+                    for (j in l until n) {
+                        s = 0.0
+                        for (k in i until m) {
+                            s += this[k, i] * this[k, j]
+                        }
+                        f = s / h
+                        for (k in i until m) {
+                            this[k, j] += f * this[k, i]
+                        }
+                    }
+                }
+                for (k in i until m) {
+                    this[k, i] = this[k, i] * scale
+                }
+            }
+        }
+
+        wBuffer[wStart + i] = scale * g
+        /* right-hand reduction */
+        g = 0.0
+        s = 0.0
+        scale = 0.0
+        if (i < m && i != n - 1) {
+            for (k in l until n) {
+                scale += abs(this[i, k])
+            }
+            if (abs(scale) > epsilon) {
+                for (k in l until n) {
+                    this[i, k] = this[i, k] / scale
+                    s += this[i, k] * this[i, k]
+                }
+                f = this[i, l]
+                if (f >= 0) {
+                    g = (-1) * abs(sqrt(s))
+                } else {
+                    g = abs(sqrt(s))
+                }
+                val h = f * g - s
+                this[i, l] = f - g
+                for (k in l until n) {
+                    rv1[k] = this[i, k] / h
+                }
+                if (i != m - 1) {
+                    for (j in l until m) {
+                        s = 0.0
+                        for (k in l until n) {
+                            s += this[j, k] * this[i, k]
+                        }
+                        for (k in l until n) {
+                            this[j, k] += s * rv1[k]
+                        }
+                    }
+                }
+                for (k in l until n) {
+                    this[i, k] = this[i, k] * scale
+                }
+            }
+        }
+        anorm = max(anorm, (abs(wBuffer[wStart + i]) + abs(rv1[i])));
+    }
+
+    for (i in n - 1 downTo 0) {
+        if (i < n - 1) {
+            if (abs(g) > epsilon) {
+                for (j in l until n) {
+                    v[j, i] = (this[i, j] / this[i, l]) / g
+                }
+                for (j in l until n) {
+                    s = 0.0
+                    for (k in l until n)
+                        s += this[i, k] * v[k, j]
+                    for (k in l until n)
+                        v[k, j] += s * v[k, i]
+                }
+            }
+            for (j in l until n) {
+                v[i, j] = 0.0
+                v[j, i] = 0.0
+            }
+        }
+        v[i, i] = 1.0
+        g = rv1[i]
+        l = i
+    }
+
+    for (i in min(n, m) - 1 downTo 0) {
+        l = i + 1
+        g =  wBuffer[wStart + i]
+        for (j in l until n) {
+            this[i, j] = 0.0
+        }
+        if (abs(g) > epsilon) {
+            g = 1.0 / g
+            for (j in l until n) {
+                s = 0.0
+                for (k in l until m) {
+                    s += this[k, i] * this[k, j]
+                }
+                f = (s / this[i, i]) * g
+                for (k in i until m) {
+                    this[k, j] += f * this[k, i]
+                }
+            }
+            for (j in i until m) {
+                this[j, i] *= g
+            }
+        } else {
+            for (j in i until m) {
+                this[j, i] = 0.0
+            }
+        }
+        this[i, i] += 1.0
+    }
+
+    var flag = 0
+    var nm = 0
+    var c = 0.0
+    var h = 0.0
+    var y = 0.0
+    var z = 0.0
+    var x = 0.0
+    for (k in n - 1 downTo 0) {
+        for (its in 1 until iterations) {
+            flag = 1
+            for (newl in k downTo 0) {
+                nm = newl - 1
+                if (abs(rv1[newl]) + anorm == anorm) {
+                    flag = 0
+                    l = newl
+                    break
+                }
+                if (abs(wBuffer[wStart + nm]) + anorm == anorm) {
+                    l = newl
+                    break
+                }
+            }
+
+            if (flag != 0) {
+                c = 0.0
+                s = 1.0
+                for (i in l until k + 1) {
+                    f = s * rv1[i]
+                    rv1[i] = c * rv1[i]
+                    if (abs(f) + anorm == anorm) {
+                        break
+                    }
+                    g = wBuffer[wStart + i]
+                    h = pythag(f, g)
+                    wBuffer[wStart + i] = h
+                    h = 1.0 / h
+                    c = g * h
+                    s = (-f) * h
+                    for (j in 0 until m) {
+                        y = this[j, nm]
+                        z = this[j, i]
+                        this[j, nm] = y * c + z * s
+                        this[j, i] = z * c - y * s
+                    }
+                }
+            }
+
+            z =  wBuffer[wStart + k]
+            if (l == k) {
+                if (z < 0.0) {
+                    wBuffer[wStart + k] = -z
+                    for (j in 0 until n)
+                        v[j, k] = -v[j, k]
+                }
+                break
+            }
+
+            x =  wBuffer[wStart + l]
+            nm = k - 1
+            y =  wBuffer[wStart + nm]
+            g = rv1[nm]
+            h = rv1[k]
+            f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y)
+            g = pythag(f, 1.0)
+            f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x
+            c = 1.0
+            s = 1.0
+
+            var i = 0
+            for (j in l until nm + 1) {
+                i = j + 1
+                g = rv1[i]
+                y = wBuffer[wStart + i]
+                h = s * g
+                g = c * g
+                z = pythag(f, h)
+                rv1[j] = z
+                c = f / z
+                s = h / z
+                f = x * c + g * s
+                g = g * c - x * s
+                h = y * s
+                y *= c
+
+                for (jj in 0 until n) {
+                    x = v[jj, j];
+                    z = v[jj, i];
+                    v[jj, j] = x * c + z * s;
+                    v[jj, i] = z * c - x * s;
+                }
+                z = pythag(f, h)
+                wBuffer[wStart + j] = z
+                if (abs(z) > epsilon) {
+                    z = 1.0 / z
+                    c = f * z
+                    s = h * z
+                }
+                f = c * g + s * y
+                x = c * y - s * g
+                for (jj in 0 until m) {
+                    y = this[jj, j]
+                    z = this[jj, i]
+                    this[jj, j] = y * c + z * s
+                    this[jj, i] = z * c - y * s
+                }
+            }
+            rv1[l] = 0.0
+            rv1[k] = f
+            wBuffer[wStart + k] = x
+        }
+    }
+
+    for (i in 0 until n) {
+        for (j in 0 until m) {
+            u[j, i] = this[j, i]
+        }
     }
 }

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

@@ -12,110 +12,250 @@ import kotlin.test.assertTrue
 
 internal class TestDoubleAnalyticTensorAlgebra {
 
-    val shape = intArrayOf(2, 1, 3, 2)
+    val shapeWithNegative = intArrayOf(4)
-    val buffer = doubleArrayOf(
+    val bufferWithNegative = doubleArrayOf(9.3348, -7.5889,  -1.2005, 1.1584)
-        27.1, 20.0, 19.84,
+    val tensorWithNegative = DoubleTensor(shapeWithNegative, bufferWithNegative)
-        23.123, 3.0, 2.0,
 
-        3.23, 133.7, 25.3,
+    val shape1 = intArrayOf(4)
-        100.3, 11.0, 12.012
+    val buffer1 = doubleArrayOf(1.3348, 1.5889,  1.2005, 1.1584)
-    )
+    val tensor1 = DoubleTensor(shape1, buffer1)
-    val tensor = DoubleTensor(shape, buffer)
+
+    val shape2 = intArrayOf(2, 2)
+    val buffer2 = doubleArrayOf(1.0, 9.456, 3.0, 4.0)
+    val tensor2 = DoubleTensor(shape2, buffer2)
+
+    val shape3 = intArrayOf(2, 3, 2)
+    val buffer3 = doubleArrayOf(1.0, 9.456, 7.0, 2.123, 1.0, 9.456, 30.8888, 6.0, 1.0, 9.456, 3.0, 4.99)
+    val tensor3 = DoubleTensor(shape3, buffer3)
+
+    val shape4 = intArrayOf(2, 1, 3, 2)
+    val buffer4 = doubleArrayOf(27.1, 20.0, 19.84, 23.123, 3.0, 2.0, 3.23, 133.7, 25.3, 100.3, 11.0, 12.012)
+    val tensor4 = DoubleTensor(shape4, buffer4)
+
+    val bufferWithNegativeMod1 = bufferWithNegative.map { x -> x % 1 }.toDoubleArray()
+    val tensorWithNegativeMod1 = DoubleTensor(shapeWithNegative, bufferWithNegativeMod1)
+
+    val buffer1Mod1 = buffer1.map { x -> x % 1 }.toDoubleArray()
+    val tensor1Mod1 = DoubleTensor(shape1, buffer1Mod1)
+
+    val buffer2Mod1 = buffer2.map { x -> x % 1 }.toDoubleArray()
+    val tensor2Mod1 = DoubleTensor(shape2, buffer2Mod1)
+
+    val buffer3Mod1 = buffer3.map { x -> x % 1 }.toDoubleArray()
+    val tensor3Mod1 = DoubleTensor(shape3, buffer3Mod1)
+
+    val buffer4Mod1 = buffer4.map { x -> x % 1 }.toDoubleArray()
+    val tensor4Mod1 = DoubleTensor(shape4, buffer4Mod1)
 
     fun DoubleArray.fmap(transform: (Double) -> Double): DoubleArray {
         return this.map(transform).toDoubleArray()
     }
 
-    fun expectedTensor(transform: (Double) -> Double): DoubleTensor {
+    fun expectedTensorWithNegative(transform: (Double) -> Double): DoubleTensor {
-        return DoubleTensor(shape, buffer.fmap(transform))
+        return DoubleTensor(shapeWithNegative, bufferWithNegative.fmap(transform))
+    }
+
+    fun expectedTensor1(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape1, buffer1.fmap(transform))
+    }
+
+    fun expectedTensor2(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape2, buffer2.fmap(transform))
+    }
+
+    fun expectedTensor3(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape3, buffer3.fmap(transform))
+    }
+
+    fun expectedTensor4(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape4, buffer4.fmap(transform))
+    }
+
+    fun expectedTensorWithNegativeMod1(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shapeWithNegative, bufferWithNegativeMod1.fmap(transform))
+    }
+
+    fun expectedTensor1Mod1(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape1, buffer1Mod1.fmap(transform))
+    }
+
+    fun expectedTensor2Mod1(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape2, buffer2Mod1.fmap(transform))
+    }
+
+    fun expectedTensor3Mod1(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape3, buffer3Mod1.fmap(transform))
+    }
+
+    fun expectedTensor4Mod1(transform: (Double) -> Double): DoubleTensor {
+        return DoubleTensor(shape4, buffer4Mod1.fmap(transform))
     }
 
     @Test
     fun testExp() = DoubleTensorAlgebra {
-        assertTrue { tensor.exp() eq expectedTensor(::exp) }
+        assertTrue { tensorWithNegative.exp() eq expectedTensorWithNegative(::exp) }
+        assertTrue { tensor1.exp() eq expectedTensor1(::exp) }
+        assertTrue { tensor2.exp() eq expectedTensor2(::exp) }
+        assertTrue { tensor3.exp() eq expectedTensor3(::exp) }
+        assertTrue { tensor4.exp() eq expectedTensor4(::exp) }
     }
 
     @Test
     fun testLog() = DoubleTensorAlgebra {
-        assertTrue { tensor.ln() eq expectedTensor(::ln) }
+        assertTrue { tensor1.ln() eq expectedTensor1(::ln) }
+        assertTrue { tensor2.ln() eq expectedTensor2(::ln) }
+        assertTrue { tensor3.ln() eq expectedTensor3(::ln) }
+        assertTrue { tensor4.ln() eq expectedTensor4(::ln) }
     }
 
     @Test
     fun testSqrt() = DoubleTensorAlgebra {
-        assertTrue { tensor.sqrt() eq expectedTensor(::sqrt) }
+        assertTrue { tensor1.sqrt() eq expectedTensor1(::sqrt) }
+        assertTrue { tensor2.sqrt() eq expectedTensor2(::sqrt) }
+        assertTrue { tensor3.sqrt() eq expectedTensor3(::sqrt) }
+        assertTrue { tensor4.sqrt() eq expectedTensor4(::sqrt) }
     }
 
     @Test
     fun testCos() = DoubleTensorAlgebra {
-        assertTrue { tensor.cos() eq expectedTensor(::cos) }
+        assertTrue { tensorWithNegative.cos() eq expectedTensorWithNegative(::cos) }
+        assertTrue { tensor1.cos() eq expectedTensor1(::cos) }
+        assertTrue { tensor2.cos() eq expectedTensor2(::cos) }
+        assertTrue { tensor3.cos() eq expectedTensor3(::cos) }
+        assertTrue { tensor4.cos() eq expectedTensor4(::cos) }
     }
 
+    @Test
+    fun testAcos() = DoubleTensorAlgebra {
+        assertTrue { tensorWithNegativeMod1.acos() eq expectedTensorWithNegativeMod1(::acos) }
+        assertTrue { tensor1Mod1.acos() eq expectedTensor1Mod1(::acos) }
+        assertTrue { tensor2Mod1.acos() eq expectedTensor2Mod1(::acos) }
+        assertTrue { tensor3Mod1.acos() eq expectedTensor3Mod1(::acos) }
+        assertTrue { tensor4Mod1.acos() eq expectedTensor4Mod1(::acos) }
+    }
 
     @Test
     fun testCosh() = DoubleTensorAlgebra {
-        assertTrue { tensor.cosh() eq expectedTensor(::cosh) }
+        assertTrue { tensorWithNegative.cosh() eq expectedTensorWithNegative(::cosh) }
+        assertTrue { tensor1.cosh() eq expectedTensor1(::cosh) }
+        assertTrue { tensor2.cosh() eq expectedTensor2(::cosh) }
+        assertTrue { tensor3.cosh() eq expectedTensor3(::cosh) }
+        assertTrue { tensor4.cosh() eq expectedTensor4(::cosh) }
     }
 
     @Test
     fun testAcosh() = DoubleTensorAlgebra {
-        assertTrue { tensor.acosh() eq expectedTensor(::acosh) }
+        assertTrue { tensor1.acosh() eq expectedTensor1(::acosh) }
+        assertTrue { tensor2.acosh() eq expectedTensor2(::acosh) }
+        assertTrue { tensor3.acosh() eq expectedTensor3(::acosh) }
+        assertTrue { tensor4.acosh() eq expectedTensor4(::acosh) }
     }
 
     @Test
     fun testSin() = DoubleTensorAlgebra {
-        assertTrue { tensor.sin() eq expectedTensor(::sin) }
+        assertTrue { tensorWithNegative.sin() eq expectedTensorWithNegative(::sin) }
+        assertTrue { tensor1.sin() eq expectedTensor1(::sin) }
+        assertTrue { tensor2.sin() eq expectedTensor2(::sin) }
+        assertTrue { tensor3.sin() eq expectedTensor3(::sin) }
+        assertTrue { tensor4.sin() eq expectedTensor4(::sin) }
+    }
+
+    @Test
+    fun testAsin() = DoubleTensorAlgebra {
+        assertTrue { tensorWithNegativeMod1.asin() eq expectedTensorWithNegativeMod1(::asin) }
+        assertTrue { tensor1Mod1.asin() eq expectedTensor1Mod1(::asin) }
+        assertTrue { tensor2Mod1.asin() eq expectedTensor2Mod1(::asin) }
+        assertTrue { tensor3Mod1.asin() eq expectedTensor3Mod1(::asin) }
+        assertTrue { tensor4Mod1.asin() eq expectedTensor4Mod1(::asin) }
     }
 
     @Test
     fun testSinh() = DoubleTensorAlgebra {
-        assertTrue { tensor.sinh() eq expectedTensor(::sinh) }
+        assertTrue { tensorWithNegative.sinh() eq expectedTensorWithNegative(::sinh) }
+        assertTrue { tensor1.sinh() eq expectedTensor1(::sinh) }
+        assertTrue { tensor2.sinh() eq expectedTensor2(::sinh) }
+        assertTrue { tensor3.sinh() eq expectedTensor3(::sinh) }
+        assertTrue { tensor4.sinh() eq expectedTensor4(::sinh) }
     }
 
     @Test
     fun testAsinh() = DoubleTensorAlgebra {
-        assertTrue { tensor.asinh() eq expectedTensor(::asinh) }
+        assertTrue { tensorWithNegative.asinh() eq expectedTensorWithNegative(::asinh) }
+        assertTrue { tensor1.asinh() eq expectedTensor1(::asinh) }
+        assertTrue { tensor2.asinh() eq expectedTensor2(::asinh) }
+        assertTrue { tensor3.asinh() eq expectedTensor3(::asinh) }
+        assertTrue { tensor4.asinh() eq expectedTensor4(::asinh) }
     }
 
     @Test
     fun testTan() = DoubleTensorAlgebra {
-        assertTrue { tensor.tan() eq expectedTensor(::tan) }
+        assertTrue { tensorWithNegative.tan() eq expectedTensorWithNegative(::tan) }
+        assertTrue { tensor1.tan() eq expectedTensor1(::tan) }
+        assertTrue { tensor2.tan() eq expectedTensor2(::tan) }
+        assertTrue { tensor3.tan() eq expectedTensor3(::tan) }
+        assertTrue { tensor4.tan() eq expectedTensor4(::tan) }
     }
 
     @Test
     fun testAtan() = DoubleTensorAlgebra {
-        assertTrue { tensor.atan() eq expectedTensor(::atan) }
+        assertTrue { tensorWithNegative.atan() eq expectedTensorWithNegative(::atan) }
+        assertTrue { tensor1.atan() eq expectedTensor1(::atan) }
+        assertTrue { tensor2.atan() eq expectedTensor2(::atan) }
+        assertTrue { tensor3.atan() eq expectedTensor3(::atan) }
+        assertTrue { tensor4.atan() eq expectedTensor4(::atan) }
     }
 
     @Test
     fun testTanh() = DoubleTensorAlgebra {
-        assertTrue { tensor.tanh() eq expectedTensor(::tanh) }
+        assertTrue { tensorWithNegative.tanh() eq expectedTensorWithNegative(::tanh) }
+        assertTrue { tensor1.tanh() eq expectedTensor1(::tanh) }
+        assertTrue { tensor2.tanh() eq expectedTensor2(::tanh) }
+        assertTrue { tensor3.tanh() eq expectedTensor3(::tanh) }
+        assertTrue { tensor4.tanh() eq expectedTensor4(::tanh) }
+    }
+
+    @Test
+    fun testAtanh() = DoubleTensorAlgebra {
+        assertTrue { tensorWithNegativeMod1.atanh() eq expectedTensorWithNegativeMod1(::atanh) }
+        assertTrue { tensor1Mod1.atanh() eq expectedTensor1Mod1(::atanh) }
+        assertTrue { tensor2Mod1.atanh() eq expectedTensor2Mod1(::atanh) }
+        assertTrue { tensor3Mod1.atanh() eq expectedTensor3Mod1(::atanh) }
+        assertTrue { tensor4Mod1.atanh() eq expectedTensor4Mod1(::atanh) }
     }
 
     @Test
     fun testCeil() = DoubleTensorAlgebra {
-        assertTrue { tensor.ceil() eq expectedTensor(::ceil) }
+        assertTrue { tensorWithNegative.ceil() eq expectedTensorWithNegative(::ceil) }
+        assertTrue { tensor1.ceil() eq expectedTensor1(::ceil) }
+        assertTrue { tensor2.ceil() eq expectedTensor2(::ceil) }
+        assertTrue { tensor3.ceil() eq expectedTensor3(::ceil) }
+        assertTrue { tensor4.ceil() eq expectedTensor4(::ceil) }
     }
 
     @Test
     fun testFloor() = DoubleTensorAlgebra {
-        assertTrue { tensor.floor() eq expectedTensor(::floor) }
+        assertTrue { tensorWithNegative.floor() eq expectedTensorWithNegative(::floor) }
+        assertTrue { tensor1.floor() eq expectedTensor1(::floor) }
+        assertTrue { tensor2.floor() eq expectedTensor2(::floor) }
+        assertTrue { tensor3.floor() eq expectedTensor3(::floor) }
+        assertTrue { tensor4.floor() eq expectedTensor4(::floor) }
     }
 
-    val shape2 = intArrayOf(2, 2)
+    val shape5 = intArrayOf(2, 2)
-    val buffer2 = doubleArrayOf(
+    val buffer5 = doubleArrayOf(
         1.0, 2.0,
         -3.0, 4.0
     )
-    val tensor2 = DoubleTensor(shape2, buffer2)
+    val tensor5 = DoubleTensor(shape5, buffer5)
 
     @Test
     fun testMin() = DoubleTensorAlgebra {
-        assertTrue { tensor2.min() == -3.0 }
+        assertTrue { tensor5.min() == -3.0 }
-        assertTrue { tensor2.min(0, true) eq fromArray(
+        assertTrue { tensor5.min(0, true) eq fromArray(
             intArrayOf(1, 2),
             doubleArrayOf(-3.0, 2.0)
         )}
-        assertTrue { tensor2.min(1, false) eq fromArray(
+        assertTrue { tensor5.min(1, false) eq fromArray(
             intArrayOf(2),
             doubleArrayOf(1.0, -3.0)
         )}
@@ -123,12 +263,12 @@ internal class TestDoubleAnalyticTensorAlgebra {
 
     @Test
     fun testMax() = DoubleTensorAlgebra {
-        assertTrue { tensor2.max() == 4.0 }
+        assertTrue { tensor5.max() == 4.0 }
-        assertTrue { tensor2.max(0, true) eq fromArray(
+        assertTrue { tensor5.max(0, true) eq fromArray(
             intArrayOf(1, 2),
             doubleArrayOf(1.0, 4.0)
         )}
-        assertTrue { tensor2.max(1, false) eq fromArray(
+        assertTrue { tensor5.max(1, false) eq fromArray(
             intArrayOf(2),
             doubleArrayOf(2.0, 4.0)
         )}
@@ -136,12 +276,12 @@ internal class TestDoubleAnalyticTensorAlgebra {
 
     @Test
     fun testSum() = DoubleTensorAlgebra {
-        assertTrue { tensor2.sum() == 4.0 }
+        assertTrue { tensor5.sum() == 4.0 }
-        assertTrue { tensor2.sum(0, true) eq fromArray(
+        assertTrue { tensor5.sum(0, true) eq fromArray(
             intArrayOf(1, 2),
             doubleArrayOf(-2.0, 6.0)
         )}
-        assertTrue { tensor2.sum(1, false) eq fromArray(
+        assertTrue { tensor5.sum(1, false) eq fromArray(
             intArrayOf(2),
             doubleArrayOf(3.0, 1.0)
         )}
@@ -149,15 +289,24 @@ internal class TestDoubleAnalyticTensorAlgebra {
 
     @Test
     fun testMean() = DoubleTensorAlgebra {
-        assertTrue { tensor2.mean() == 1.0 }
+        assertTrue { tensor5.mean() == 1.0 }
-        assertTrue { tensor2.mean(0, true) eq fromArray(
+        assertTrue { tensor5.mean(0, true) eq fromArray(
             intArrayOf(1, 2),
             doubleArrayOf(-1.0, 3.0)
         )}
-        assertTrue { tensor2.mean(1, false) eq fromArray(
+        assertTrue { tensor5.mean(1, false) eq fromArray(
             intArrayOf(2),
             doubleArrayOf(1.5, 0.5)
         )}
     }
 
+    @Test
+    fun testStd() = DoubleTensorAlgebra {
+        assertTrue { floor(tensor5.std() * 10000 ) / 10000 == 2.9439 }
+    }
+
+    @Test
+    fun testVariance() = DoubleTensorAlgebra {
+        assertTrue { floor(tensor5.variance() * 10000 ) / 10000 == 8.6666 }
+    }
 }

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

@@ -156,23 +156,12 @@ internal class TestDoubleLinearOpsTensorAlgebra {
 
         val res = svd1d(tensor2)
 
+        val resBuffer = res.mutableBuffer
+        val resStart = res.bufferStart
+
         assertTrue(res.shape contentEquals intArrayOf(2))
-        assertTrue { abs(abs(res.mutableBuffer.array()[res.bufferStart]) - 0.386) < 0.01 }
+        assertTrue { abs(abs(resBuffer[resStart]) - 0.386) < 0.01 }
-        assertTrue { abs(abs(res.mutableBuffer.array()[res.bufferStart + 1]) - 0.922) < 0.01 }
+        assertTrue { abs(abs(resBuffer[resStart + 1]) - 0.922) < 0.01 }
-    }
-
-    @Test
-    fun testSVD() = DoubleTensorAlgebra{
-        testSVDFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
-        testSVDFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
-    }
-
-    @Test
-    fun testBatchedSVD() = DoubleTensorAlgebra {
-        val tensor = randomNormal(intArrayOf(2, 5, 3), 0)
-        val (tensorU, tensorS, tensorV) = tensor.svd()
-        val tensorSVD = tensorU dot (diagonalEmbedding(tensorS) dot tensorV.transpose())
-        assertTrue(tensor.eq(tensorSVD))
     }
 
     @Test
@@ -184,13 +173,130 @@ internal class TestDoubleLinearOpsTensorAlgebra {
         assertTrue(tensorSigma.eq(tensorSigmaCalc))
     }
 
+    @Test
+    fun testSVD() = DoubleTensorAlgebra{
+        testSVDFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
+        testSVDFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
+        val buffer1 = doubleArrayOf(
+            1.000000, 2.000000, 3.000000,
+            2.000000, 3.000000, 4.000000,
+            3.000000, 4.000000, 5.000000,
+            4.000000, 5.000000, 6.000000,
+            5.000000, 6.000000, 9.000000
+        )
+        testSVDFor(fromArray(intArrayOf(5, 3), buffer1))
+        val buffer2 = doubleArrayOf(
+            1.0, 2.0, 3.0, 2.0, 3.0,
+            4.0, 3.0, 4.0, 5.0, 4.0,
+            5.0, 6.0, 5.0, 6.0, 7.0
+        )
+        testSVDFor(fromArray(intArrayOf(3, 5), buffer2))
+    }
 
+    @Test
+    fun testBatchedSVD() = DoubleTensorAlgebra{
+        val tensor1 = randomNormal(intArrayOf(2, 5, 3), 0)
+        testSVDFor(tensor1)
+        val tensor2 = DoubleTensorAlgebra.randomNormal(intArrayOf(30, 30, 30), 0)
+        testSVDFor(tensor2)
+    }
+
+    @Test
+    fun testSVDGolubKahan() = DoubleTensorAlgebra{
+        testSVDGolubKahanFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
+        testSVDGolubKahanFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
+        val buffer1 = doubleArrayOf(
+            1.000000, 2.000000, 3.000000,
+            2.000000, 3.000000, 4.000000,
+            3.000000, 4.000000, 5.000000,
+            4.000000, 5.000000, 6.000000,
+            5.000000, 6.000000, 9.000000
+        )
+        testSVDGolubKahanFor(fromArray(intArrayOf(5, 3), buffer1))
+        val buffer2 = doubleArrayOf(
+            1.0, 2.0, 3.0, 2.0, 3.0,
+            4.0, 3.0, 4.0, 5.0, 4.0,
+            5.0, 6.0, 5.0, 6.0, 7.0
+        )
+        testSVDGolubKahanFor(fromArray(intArrayOf(3, 5), buffer2))
+    }
+
+    @Test
+    fun testBatchedSVDGolubKahan() = DoubleTensorAlgebra{
+        val tensor1 = randomNormal(intArrayOf(2, 5, 3), 0)
+        testSVDGolubKahanFor(tensor1)
+        val tensor2 = DoubleTensorAlgebra.randomNormal(intArrayOf(30, 30, 30), 0)
+        testSVDGolubKahanFor(tensor2)
+    }
+
+    @Test
+    fun testSVDPowerMethod() = DoubleTensorAlgebra{
+        testSVDPowerMethodFor(fromArray(intArrayOf(2, 3), doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)))
+        testSVDPowerMethodFor(fromArray(intArrayOf(2, 2), doubleArrayOf(-1.0, 0.0, 239.0, 238.0)))
+        val buffer1 = doubleArrayOf(
+            1.000000, 2.000000, 3.000000,
+            2.000000, 3.000000, 4.000000,
+            3.000000, 4.000000, 5.000000,
+            4.000000, 5.000000, 6.000000,
+            5.000000, 6.000000, 9.000000
+        )
+        testSVDPowerMethodFor(fromArray(intArrayOf(5, 3), buffer1))
+        val buffer2 = doubleArrayOf(
+            1.0, 2.0, 3.0, 2.0, 3.0,
+            4.0, 3.0, 4.0, 5.0, 4.0,
+            5.0, 6.0, 5.0, 6.0, 7.0
+        )
+        testSVDPowerMethodFor(fromArray(intArrayOf(3, 5), buffer2))
+    }
+
+    @Test
+    fun testBatchedSVDPowerMethod() = DoubleTensorAlgebra {
+        val tensor1 = randomNormal(intArrayOf(2, 5, 3), 0)
+        testSVDPowerMethodFor(tensor1)
+        val tensor2 = DoubleTensorAlgebra.randomNormal(intArrayOf(30, 30, 30), 0)
+        testSVDPowerMethodFor(tensor2)
+    }
+
+//    @Test
+//    fun testSVDPowerMethodError() = DoubleTensorAlgebra{
+//       val buffer = doubleArrayOf(
+//            1.000000, 2.000000, 3.000000,
+//            2.000000, 3.000000, 4.000000,
+//            3.000000, 4.000000, 5.000000,
+//            4.000000, 5.000000, 6.000000,
+//            5.000000, 6.000000, 7.000000
+//        )
+//        testSVDPowerMethodFor(fromArray(intArrayOf(5, 3), buffer))
+//    }
 }
 
-
+private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor) {
-private fun DoubleTensorAlgebra.testSVDFor(tensor: DoubleTensor, epsilon: Double = 1e-10) {
     val svd = tensor.svd()
 
+    val tensorSVD = svd.first
+        .dot(
+            diagonalEmbedding(svd.second)
+                .dot(svd.third.transpose())
+        )
+
+    assertTrue(tensor.eq(tensorSVD))
+}
+
+private fun DoubleTensorAlgebra.testSVDGolubKahanFor(tensor: DoubleTensor, epsilon: Double = 1e-10) {
+    val svd = tensor.svdGolubKahan()
+
+    val tensorSVD = svd.first
+        .dot(
+            diagonalEmbedding(svd.second)
+                .dot(svd.third.transpose())
+        )
+
+    assertTrue(tensor.eq(tensorSVD, epsilon))
+}
+
+private fun DoubleTensorAlgebra.testSVDPowerMethodFor(tensor: DoubleTensor, epsilon: Double = 1e-10) {
+    val svd = tensor.svdPowerMethod()
+
     val tensorSVD = svd.first
         .dot(
             diagonalEmbedding(svd.second)

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

@@ -23,6 +23,44 @@ import kotlin.test.assertTrue
 
 internal class TestDoubleTensor {
 
+    @Test
+    fun testFullLike() = DoubleTensorAlgebra {
+        val shape = intArrayOf(2, 3)
+        val buffer = doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)
+        val tensor = DoubleTensor(shape, buffer)
+        val value = 12.5
+        assertTrue { tensor.fullLike(value) eq DoubleTensor(shape, buffer.map { value }.toDoubleArray() ) }
+    }
+
+    @Test
+    fun testOnesLike() = DoubleTensorAlgebra {
+        val shape = intArrayOf(2, 3)
+        val buffer = doubleArrayOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0)
+        val tensor = DoubleTensor(shape, buffer)
+        assertTrue { tensor.onesLike() eq DoubleTensor(shape, buffer.map { 1.0 }.toDoubleArray() ) }
+    }
+
+    @Test
+    fun testRowsByIndices() = DoubleTensorAlgebra {
+        val shape = intArrayOf(2, 2)
+        val buffer = doubleArrayOf(1.0, 2.0, -3.0, 4.0)
+        val tensor = fromArray(shape, buffer)
+        assertTrue { tensor.rowsByIndices(intArrayOf(0)) eq DoubleTensor(intArrayOf(1, 2), doubleArrayOf(1.0, 2.0)) }
+        assertTrue { tensor.rowsByIndices(intArrayOf(0, 1)) eq tensor }
+    }
+
+    @Test
+    fun testTimes() = DoubleTensorAlgebra {
+        val shape = intArrayOf(2, 2)
+        val buffer = doubleArrayOf(1.0, 2.0, -3.0, 4.0)
+        val tensor = DoubleTensor(shape, buffer)
+        val value = 3
+        assertTrue { tensor.times(value).toBufferedTensor() eq DoubleTensor(shape, buffer.map { x -> 3 * x }.toDoubleArray()) }
+        val buffer2 = doubleArrayOf(7.0, -8.0, -5.0, 2.0)
+        val tensor2 = DoubleTensor(shape, buffer2)
+        assertTrue {tensor.times(tensor2).toBufferedTensor() eq DoubleTensor(shape, doubleArrayOf(7.0, -16.0, 15.0, 8.0)) }
+    }
+
     @Test
     fun testValue() = DoubleTensorAlgebra {
         val value = 12.5

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

@@ -132,6 +132,27 @@ internal class TestDoubleTensorAlgebra {
             468.0, 501.0, 534.0, 594.0, 636.0, 678.0, 720.0, 771.0, 822.0
         ))
         assertTrue(res45.shape contentEquals intArrayOf(2, 3, 3))
+
+        val oneDimTensor1 = fromArray(intArrayOf(3), doubleArrayOf(1.0, 2.0, 3.0))
+        val oneDimTensor2 = fromArray(intArrayOf(3), doubleArrayOf(4.0, 5.0, 6.0))
+        val resOneDimTensors = oneDimTensor1.dot(oneDimTensor2)
+        assertTrue(resOneDimTensors.mutableBuffer.array() contentEquals doubleArrayOf(32.0))
+        assertTrue(resOneDimTensors.shape contentEquals intArrayOf(1))
+
+        val twoDimTensor1 = fromArray(intArrayOf(2, 2), doubleArrayOf(1.0, 2.0, 3.0, 4.0))
+        val twoDimTensor2 = fromArray(intArrayOf(2, 2), doubleArrayOf(5.0, 6.0, 7.0, 8.0))
+        val resTwoDimTensors = twoDimTensor1.dot(twoDimTensor2)
+        assertTrue(resTwoDimTensors.mutableBuffer.array() contentEquals doubleArrayOf(19.0, 22.0, 43.0, 50.0))
+        assertTrue(resTwoDimTensors.shape contentEquals intArrayOf(2, 2))
+
+        val oneDimTensor3 = fromArray(intArrayOf(2), doubleArrayOf(1.0, 2.0))
+        val resOneDimTensorOnTwoDimTensor = oneDimTensor3.dot(twoDimTensor1)
+        assertTrue(resOneDimTensorOnTwoDimTensor.mutableBuffer.array() contentEquals doubleArrayOf(7.0, 10.0))
+        assertTrue(resOneDimTensorOnTwoDimTensor.shape contentEquals intArrayOf(2))
+
+        val resTwoDimTensorOnOneDimTensor = twoDimTensor1.dot(oneDimTensor3)
+        assertTrue(resTwoDimTensorOnOneDimTensor.mutableBuffer.array() contentEquals doubleArrayOf(5.0, 11.0))
+        assertTrue(resTwoDimTensorOnOneDimTensor.shape contentEquals intArrayOf(2))
     }
 
     @Test