forked from kscience/kmath
Merge pull request #461 from ivandev0/kylchik/jacobi
Jacobi eigenvalue algorithm
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commit
c80f70fe0f
@ -124,6 +124,11 @@ benchmark {
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include("JafamaBenchmark")
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}
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configurations.register("tensorAlgebra") {
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commonConfiguration()
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include("TensorAlgebraBenchmark")
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}
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configurations.register("viktor") {
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commonConfiguration()
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include("ViktorBenchmark")
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@ -15,10 +15,8 @@ import space.kscience.kmath.linear.invoke
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import space.kscience.kmath.linear.linearSpace
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import space.kscience.kmath.multik.multikAlgebra
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.operations.invoke
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import space.kscience.kmath.structures.Buffer
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import space.kscience.kmath.tensorflow.produceWithTF
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
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import space.kscience.kmath.tensors.core.tensorAlgebra
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import kotlin.random.Random
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@ -36,9 +34,6 @@ internal class DotBenchmark {
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random.nextDouble()
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}
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val tensor1 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12224)
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val tensor2 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12225)
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val cmMatrix1 = CMLinearSpace { matrix1.toCM() }
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val cmMatrix2 = CMLinearSpace { matrix2.toCM() }
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@ -48,10 +43,10 @@ internal class DotBenchmark {
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@Benchmark
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fun tfDot(blackhole: Blackhole){
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fun tfDot(blackhole: Blackhole) {
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blackhole.consume(
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DoubleField.produceWithTF {
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tensor1 dot tensor2
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matrix1 dot matrix1
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}
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)
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}
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@ -95,9 +90,4 @@ internal class DotBenchmark {
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fun doubleDot(blackhole: Blackhole) = with(DoubleField.linearSpace) {
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blackhole.consume(matrix1 dot matrix2)
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}
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@Benchmark
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fun doubleTensorDot(blackhole: Blackhole) = DoubleTensorAlgebra.invoke {
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blackhole.consume(tensor1 dot tensor2)
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}
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}
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@ -0,0 +1,37 @@
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.benchmarks
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import kotlinx.benchmark.Benchmark
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import kotlinx.benchmark.Blackhole
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import kotlinx.benchmark.Scope
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import kotlinx.benchmark.State
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import space.kscience.kmath.linear.linearSpace
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import space.kscience.kmath.linear.matrix
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import space.kscience.kmath.linear.symmetric
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.tensors.core.tensorAlgebra
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import kotlin.random.Random
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@State(Scope.Benchmark)
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internal class TensorAlgebraBenchmark {
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companion object {
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private val random = Random(12224)
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private const val dim = 30
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private val matrix = DoubleField.linearSpace.matrix(dim, dim).symmetric { _, _ -> random.nextDouble() }
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}
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@Benchmark
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fun tensorSymEigSvd(blackhole: Blackhole) = with(Double.tensorAlgebra) {
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blackhole.consume(matrix.symEigSvd(1e-10))
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}
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@Benchmark
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fun tensorSymEigJacobi(blackhole: Blackhole) = with(Double.tensorAlgebra) {
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blackhole.consume(matrix.symEigJacobi(50, 1e-10))
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}
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}
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@ -9,10 +9,7 @@
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package space.kscience.kmath.tensors.core
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import space.kscience.kmath.misc.PerformancePitfall
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import space.kscience.kmath.nd.MutableStructure2D
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import space.kscience.kmath.nd.StructureND
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import space.kscience.kmath.nd.as1D
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import space.kscience.kmath.nd.as2D
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import space.kscience.kmath.nd.*
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.structures.MutableBuffer
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import space.kscience.kmath.structures.indices
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@ -885,7 +882,7 @@ public open class DoubleTensorAlgebra :
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return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
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}
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override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEig(epsilon = 1e-15)
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override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEigJacobi(maxIteration = 50, epsilon = 1e-15)
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/**
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* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
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@ -895,7 +892,7 @@ public open class DoubleTensorAlgebra :
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* and when the cosine approaches 1 in the SVD algorithm.
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* @return a pair `eigenvalues to eigenvectors`.
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*/
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public fun StructureND<Double>.symEig(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
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public fun StructureND<Double>.symEigSvd(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
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checkSymmetric(tensor, epsilon)
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fun MutableStructure2D<Double>.cleanSym(n: Int) {
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@ -922,6 +919,151 @@ public open class DoubleTensorAlgebra :
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return eig to v
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}
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public fun StructureND<Double>.symEigJacobi(maxIteration: Int, epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
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checkSymmetric(tensor, epsilon)
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val size = this.dimension
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val eigenvectors = zeros(this.shape)
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val eigenvalues = zeros(this.shape.sliceArray(0 until size - 1))
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var eigenvalueStart = 0
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var eigenvectorStart = 0
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for (matrix in tensor.matrixSequence()) {
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val matrix2D = matrix.as2D()
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val (d, v) = matrix2D.jacobiHelper(maxIteration, epsilon)
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for (i in 0 until matrix2D.rowNum) {
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for (j in 0 until matrix2D.colNum) {
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eigenvectors.mutableBuffer.array()[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j]
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}
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}
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for (i in 0 until matrix2D.rowNum) {
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eigenvalues.mutableBuffer.array()[eigenvalueStart + i] = d[i]
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}
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eigenvalueStart += this.shape.last()
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eigenvectorStart += this.shape.last() * this.shape.last()
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}
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return eigenvalues to eigenvectors
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}
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private fun MutableStructure2D<Double>.jacobiHelper(
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maxIteration: Int,
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epsilon: Double
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): Pair<Structure1D<Double>, Structure2D<Double>> {
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val n = this.shape[0]
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val A_ = this.copy()
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val V = eye(n)
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val D = DoubleTensor(intArrayOf(n), (0 until this.rowNum).map { this[it, it] }.toDoubleArray()).as1D()
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val B = DoubleTensor(intArrayOf(n), (0 until this.rowNum).map { this[it, it] }.toDoubleArray()).as1D()
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val Z = zeros(intArrayOf(n)).as1D()
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// assume that buffered tensor is square matrix
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operator fun BufferedTensor<Double>.get(i: Int, j: Int): Double {
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return this.mutableBuffer.array()[bufferStart + i * this.shape[0] + j]
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}
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operator fun BufferedTensor<Double>.set(i: Int, j: Int, value: Double) {
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this.mutableBuffer.array()[bufferStart + i * this.shape[0] + j] = value
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}
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fun maxOffDiagonal(matrix: BufferedTensor<Double>): Double {
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var maxOffDiagonalElement = 0.0
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for (i in 0 until n - 1) {
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for (j in i + 1 until n) {
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maxOffDiagonalElement = max(maxOffDiagonalElement, abs(matrix[i, j]))
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}
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}
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return maxOffDiagonalElement
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}
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fun rotate(a: BufferedTensor<Double>, s: Double, tau: Double, i: Int, j: Int, k: Int, l: Int) {
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val g = a[i, j]
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val h = a[k, l]
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a[i, j] = g - s * (h + g * tau)
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a[k, l] = h + s * (g - h * tau)
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}
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fun jacobiIteration(
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a: BufferedTensor<Double>,
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v: BufferedTensor<Double>,
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d: MutableStructure1D<Double>,
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z: MutableStructure1D<Double>,
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) {
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for (ip in 0 until n - 1) {
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for (iq in ip + 1 until n) {
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val g = 100.0 * abs(a[ip, iq])
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if (g <= epsilon * abs(d[ip]) && g <= epsilon * abs(d[iq])) {
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a[ip, iq] = 0.0
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continue
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}
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var h = d[iq] - d[ip]
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val t = when {
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g <= epsilon * abs(h) -> (a[ip, iq]) / h
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else -> {
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val theta = 0.5 * h / (a[ip, iq])
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val denominator = abs(theta) + sqrt(1.0 + theta * theta)
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if (theta < 0.0) -1.0 / denominator else 1.0 / denominator
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}
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}
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val c = 1.0 / sqrt(1 + t * t)
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val s = t * c
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val tau = s / (1.0 + c)
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h = t * a[ip, iq]
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z[ip] -= h
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z[iq] += h
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d[ip] -= h
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d[iq] += h
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a[ip, iq] = 0.0
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for (j in 0 until ip) {
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rotate(a, s, tau, j, ip, j, iq)
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}
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for (j in (ip + 1) until iq) {
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rotate(a, s, tau, ip, j, j, iq)
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}
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for (j in (iq + 1) until n) {
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rotate(a, s, tau, ip, j, iq, j)
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}
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for (j in 0 until n) {
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rotate(v, s, tau, j, ip, j, iq)
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}
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}
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}
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}
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fun updateDiagonal(
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d: MutableStructure1D<Double>,
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z: MutableStructure1D<Double>,
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b: MutableStructure1D<Double>,
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) {
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for (ip in 0 until d.size) {
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b[ip] += z[ip]
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d[ip] = b[ip]
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z[ip] = 0.0
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}
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}
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var sm = maxOffDiagonal(A_)
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for (iteration in 0 until maxIteration) {
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if (sm < epsilon) {
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break
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}
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jacobiIteration(A_, V, D, Z)
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updateDiagonal(D, Z, B)
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sm = maxOffDiagonal(A_)
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}
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// TODO sort eigenvalues
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return D to V.as2D()
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}
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/**
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* Computes the determinant of a square matrix input, or of each square matrix in a batched input
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* using LU factorization algorithm.
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