lu inv and det complete + tests
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@ -13,7 +13,7 @@ public interface LinearOpsTensorAlgebra<T, TensorType : TensorStructure<T>, Inde
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//https://pytorch.org/docs/stable/linalg.html#torch.linalg.qr
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public fun TensorType.qr(): TensorType
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//https://pytorch.org/docs/stable/generated/torch.lu.html
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//htt ps://pytorch.org/docs/stable/generated/torch.lu.html
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public fun TensorType.lu(): Pair<TensorType, IndexTensorType>
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//https://pytorch.org/docs/stable/generated/torch.lu_unpack.html
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@ -1,5 +1,8 @@
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package space.kscience.kmath.tensors.core
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import space.kscience.kmath.nd.MutableStructure2D
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import space.kscience.kmath.nd.Structure1D
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import space.kscience.kmath.nd.Structure2D
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import space.kscience.kmath.tensors.LinearOpsTensorAlgebra
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import kotlin.math.sqrt
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@ -20,6 +23,8 @@ public class DoubleLinearOpsTensorAlgebra :
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val n = shape.size
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val m = shape.last()
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val pivotsShape = IntArray(n - 1) { i -> shape[i] }
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pivotsShape[n - 2] = m + 1
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val pivotsTensor = IntTensor(
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pivotsShape,
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IntArray(pivotsShape.reduce(Int::times)) { 0 }
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@ -54,6 +59,8 @@ public class DoubleLinearOpsTensorAlgebra :
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lu[maxInd, k] = tmp
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}
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pivots[m] += 1
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}
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for (j in i + 1 until m) {
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@ -146,6 +153,78 @@ public class DoubleLinearOpsTensorAlgebra :
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TODO("ANDREI")
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}
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private fun luMatrixDet(lu: Structure2D<Double>, pivots: Structure1D<Int>): Double {
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val m = lu.shape[0]
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val sign = if((pivots[m] - m) % 2 == 0) 1.0 else -1.0
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var det = sign
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for (i in 0 until m){
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det *= lu[i, i]
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}
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return det
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}
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public fun DoubleTensor.detLU(): DoubleTensor {
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val (luTensor, pivotsTensor) = this.lu()
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val n = shape.size
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val detTensorShape = IntArray(n - 1) { i -> shape[i] }
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detTensorShape[n - 2] = 1
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val resBuffer = DoubleArray(detTensorShape.reduce(Int::times)) { 0.0 }
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val detTensor = DoubleTensor(
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detTensorShape,
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resBuffer
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)
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luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).forEachIndexed { index, (luMatrix, pivots) ->
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resBuffer[index] = luMatrixDet(luMatrix, pivots)
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}
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return detTensor
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}
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private fun luMatrixInv(
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lu: Structure2D<Double>,
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pivots: Structure1D<Int>,
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invMatrix : MutableStructure2D<Double>
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): Unit {
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val m = lu.shape[0]
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for (j in 0 until m) {
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for (i in 0 until m) {
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if (pivots[i] == j){
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invMatrix[i, j] = 1.0
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}
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for (k in 0 until i){
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invMatrix[i, j] -= lu[i, k] * invMatrix[k, j]
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}
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}
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for (i in m - 1 downTo 0) {
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for (k in i + 1 until m) {
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invMatrix[i, j] -= lu[i, k] * invMatrix[k, j]
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}
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invMatrix[i, j] /= lu[i, i]
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}
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}
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}
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public fun DoubleTensor.invLU(): DoubleTensor {
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val (luTensor, pivotsTensor) = this.lu()
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val n = shape.size
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val invTensor = luTensor.zeroesLike()
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for (
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(luP, invMatrix) in
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luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).zip(invTensor.matrixSequence())
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) {
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val (lu, pivots) = luP
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luMatrixInv(lu, pivots, invMatrix)
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}
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return invTensor
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}
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}
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public inline fun <R> DoubleLinearOpsTensorAlgebra(block: DoubleLinearOpsTensorAlgebra.() -> R): R =
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@ -1,5 +1,8 @@
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package space.kscience.kmath.tensors.core
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import space.kscience.kmath.linear.Matrix
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import space.kscience.kmath.nd.MutableStructure2D
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import space.kscience.kmath.nd.Structure2D
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import space.kscience.kmath.tensors.TensorPartialDivisionAlgebra
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import kotlin.math.abs
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@ -262,7 +265,31 @@ public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double, Dou
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}
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override fun DoubleTensor.det(): DoubleTensor {
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TODO("ANDREI")
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TODO()
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/*
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checkSquareMatrix(shape)
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val n = shape.size
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val m = shape.last()
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val detTensorShape = IntArray(n - 1) { i -> shape[i] }
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detTensorShape[n - 1] = 1
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val resBuffer = DoubleArray(detTensorShape.reduce(Int::times)) { 0.0 }
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val detTensor = DoubleTensor(
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detTensorShape,
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resBuffer
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)
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this.matrixSequence().forEachIndexed{i, matrix ->
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// todo need Matrix determinant algo
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// todo resBuffer[i] = matrix.det()
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}
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return detTensor
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*/
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}
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override fun DoubleTensor.square(): DoubleTensor {
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@ -294,7 +321,7 @@ public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double, Dou
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}
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public fun DoubleTensor.contentEquals(other: DoubleTensor, eqFunction: (Double, Double) -> Boolean): Boolean {
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if (!(this.shape contentEquals other.shape)){
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if (!(this.shape contentEquals other.shape)) {
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return false
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}
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return this.eq(other, eqFunction)
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@ -303,10 +330,10 @@ public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double, Dou
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public fun DoubleTensor.eq(other: DoubleTensor, eqFunction: (Double, Double) -> Boolean): Boolean {
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// todo broadcasting checking
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val n = this.linearStructure.size
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if (n != other.linearStructure.size){
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if (n != other.linearStructure.size) {
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return false
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}
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for (i in 0 until n){
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for (i in 0 until n) {
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if (!eqFunction(this.buffer[this.bufferStart + i], other.buffer[other.bufferStart + i])) {
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return false
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}
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@ -3,7 +3,6 @@ package space.kscience.kmath.tensors.core
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import kotlin.math.abs
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import kotlin.math.exp
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertTrue
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class TestDoubleAnalyticTensorAlgebra {
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@ -16,9 +15,9 @@ class TestDoubleAnalyticTensorAlgebra {
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return this.map(transform).toDoubleArray()
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}
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fun DoubleArray.deltaEqual(other: DoubleArray, delta: Double = 1e-5): Boolean {
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fun DoubleArray.epsEqual(other: DoubleArray, eps: Double = 1e-5): Boolean {
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for ((elem1, elem2) in this.asSequence().zip(other.asSequence())) {
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if (abs(elem1 - elem2) > delta) {
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if (abs(elem1 - elem2) > eps) {
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return false
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}
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}
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@ -29,7 +28,7 @@ class TestDoubleAnalyticTensorAlgebra {
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fun testExp() = DoubleAnalyticTensorAlgebra {
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tensor.exp().let {
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assertTrue { shape contentEquals it.shape }
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assertTrue { buffer.fmap(::exp).deltaEqual(it.buffer.array())}
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assertTrue { buffer.fmap(::exp).epsEqual(it.buffer.array())}
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}
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}
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}
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@ -0,0 +1,73 @@
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package space.kscience.kmath.tensors.core
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import kotlin.math.abs
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import kotlin.math.exp
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertTrue
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class TestDoubleLinearOpsTensorAlgebra {
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private val eps = 1e-5
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private fun Double.epsEqual(other: Double): Boolean {
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return abs(this - other) < eps
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}
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fun DoubleArray.epsEqual(other: DoubleArray, eps: Double = 1e-5): Boolean {
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for ((elem1, elem2) in this.asSequence().zip(other.asSequence())) {
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if (abs(elem1 - elem2) > eps) {
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return false
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}
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}
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return true
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}
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@Test
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fun testDetLU() = DoubleLinearOpsTensorAlgebra {
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val tensor = fromArray(
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intArrayOf(2, 2, 2),
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doubleArrayOf(
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1.0, 3.0,
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1.0, 2.0,
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1.5, 1.0,
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10.0, 2.0
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)
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)
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val expectedShape = intArrayOf(2, 1)
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val expectedBuffer = doubleArrayOf(
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-1.0,
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-7.0
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)
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val detTensor = tensor.detLU()
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assertTrue { detTensor.shape contentEquals expectedShape }
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assertTrue { detTensor.buffer.array().epsEqual(expectedBuffer) }
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}
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@Test
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fun testInvLU() = DoubleLinearOpsTensorAlgebra {
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val tensor = fromArray(
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intArrayOf(2, 2, 2),
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doubleArrayOf(
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1.0, 0.0,
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0.0, 2.0,
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1.0, 1.0,
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1.0, 0.0
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)
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)
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val expectedShape = intArrayOf(2, 2, 2)
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val expectedBuffer = doubleArrayOf(
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1.0, 0.0,
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0.0, 0.5,
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0.0, 1.0,
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1.0, -1.0
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)
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val invTensor = tensor.invLU()
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assertTrue { invTensor.shape contentEquals expectedShape }
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assertTrue { invTensor.buffer.array().epsEqual(expectedBuffer) }
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}
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}
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