forked from kscience/kmath
Slight adjustment to tensor internals
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c8621ee5b7
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@ -5,8 +5,10 @@
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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.as1D
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import space.kscience.kmath.nd.as2D
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import space.kscience.kmath.structures.indices
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import space.kscience.kmath.tensors.api.AnalyticTensorAlgebra
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import space.kscience.kmath.tensors.api.LinearOpsTensorAlgebra
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import space.kscience.kmath.tensors.api.Tensor
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@ -813,28 +815,32 @@ public open class DoubleTensorAlgebra :
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val sTensor = zeros(commonShape + intArrayOf(min(n, m)))
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val vTensor = zeros(commonShape + intArrayOf(min(n, m), m))
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tensor.matrixSequence()
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.zip(
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uTensor.matrixSequence()
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.zip(
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sTensor.vectorSequence()
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.zip(vTensor.matrixSequence())
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)
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).forEach { (matrix, USV) ->
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val matrixSize = matrix.shape.reduce { acc, i -> acc * i }
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val curMatrix = DoubleTensor(
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matrix.shape,
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matrix.mutableBuffer.array().slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
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.toDoubleArray()
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)
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svdHelper(curMatrix, USV, m, n, epsilon)
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}
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val matrices = tensor.matrices
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val uTensors = uTensor.matrices
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val sTensorVectors = sTensor.vectors
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val vTensors = vTensor.matrices
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for (index in matrices.indices) {
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val matrix = matrices[index]
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val usv = Triple(
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uTensors[index],
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sTensorVectors[index],
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vTensors[index]
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)
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val matrixSize = matrix.shape.reduce { acc, i -> acc * i }
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val curMatrix = DoubleTensor(
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matrix.shape,
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matrix.mutableBuffer.array()
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.slice(matrix.bufferStart until matrix.bufferStart + matrixSize)
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.toDoubleArray()
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)
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svdHelper(curMatrix, usv, m, n, epsilon)
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}
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return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
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}
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override fun Tensor<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> =
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symEig(epsilon = 1e-15)
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override fun Tensor<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEig(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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@ -846,12 +852,26 @@ public open class DoubleTensorAlgebra :
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*/
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public fun Tensor<Double>.symEig(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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for (i in 0 until n) {
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for (j in 0 until n) {
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if (i == j) {
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this[i, j] = sign(this[i, j])
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} else {
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this[i, j] = 0.0
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}
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}
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}
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}
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val (u, s, v) = tensor.svd(epsilon)
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val shp = s.shape + intArrayOf(1)
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val utv = u.transpose() dot v
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val n = s.shape.last()
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for (matrix in utv.matrixSequence())
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cleanSymHelper(matrix.as2D(), n)
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for (matrix in utv.matrixSequence()) {
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matrix.as2D().cleanSym(n)
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}
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val eig = (utv dot s.view(shp)).view(s.shape)
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return eig to v
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@ -10,41 +10,54 @@ import space.kscience.kmath.nd.MutableStructure2D
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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.operations.invoke
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import space.kscience.kmath.tensors.core.*
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import space.kscience.kmath.structures.VirtualBuffer
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import space.kscience.kmath.structures.asSequence
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import space.kscience.kmath.tensors.core.BufferedTensor
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import space.kscience.kmath.tensors.core.DoubleTensor
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.valueOrNull
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import space.kscience.kmath.tensors.core.IntTensor
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import kotlin.math.abs
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import kotlin.math.min
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import kotlin.math.sign
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import kotlin.math.sqrt
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internal val <T> BufferedTensor<T>.vectors: VirtualBuffer<BufferedTensor<T>>
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get() {
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val n = shape.size
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val vectorOffset = shape[n - 1]
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val vectorShape = intArrayOf(shape.last())
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internal fun <T> BufferedTensor<T>.vectorSequence(): Sequence<BufferedTensor<T>> = sequence {
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val n = shape.size
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val vectorOffset = shape[n - 1]
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val vectorShape = intArrayOf(shape.last())
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for (offset in 0 until numElements step vectorOffset) {
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val vector = BufferedTensor(vectorShape, mutableBuffer, bufferStart + offset)
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yield(vector)
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return VirtualBuffer(numElements / vectorOffset) { index ->
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val offset = index * vectorOffset
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BufferedTensor(vectorShape, mutableBuffer, bufferStart + offset)
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}
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}
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}
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internal fun <T> BufferedTensor<T>.matrixSequence(): Sequence<BufferedTensor<T>> = sequence {
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val n = shape.size
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check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" }
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val matrixOffset = shape[n - 1] * shape[n - 2]
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val matrixShape = intArrayOf(shape[n - 2], shape[n - 1])
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for (offset in 0 until numElements step matrixOffset) {
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val matrix = BufferedTensor(matrixShape, mutableBuffer, bufferStart + offset)
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yield(matrix)
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internal fun <T> BufferedTensor<T>.vectorSequence(): Sequence<BufferedTensor<T>> = vectors.asSequence()
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/**
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* A random access alternative to [matrixSequence]
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*/
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internal val <T> BufferedTensor<T>.matrices: VirtualBuffer<BufferedTensor<T>>
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get() {
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val n = shape.size
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check(n >= 2) { "Expected tensor with 2 or more dimensions, got size $n" }
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val matrixOffset = shape[n - 1] * shape[n - 2]
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val matrixShape = intArrayOf(shape[n - 2], shape[n - 1])
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return VirtualBuffer(numElements / matrixOffset) { index ->
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val offset = index * matrixOffset
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BufferedTensor(matrixShape, mutableBuffer, bufferStart + offset)
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}
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}
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}
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internal fun <T> BufferedTensor<T>.matrixSequence(): Sequence<BufferedTensor<T>> = matrices.asSequence()
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internal fun dotHelper(
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a: MutableStructure2D<Double>,
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b: MutableStructure2D<Double>,
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res: MutableStructure2D<Double>,
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l: Int, m: Int, n: Int
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l: Int, m: Int, n: Int,
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) {
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for (i in 0 until l) {
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for (j in 0 until n) {
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@ -60,7 +73,7 @@ internal fun dotHelper(
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internal fun luHelper(
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lu: MutableStructure2D<Double>,
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pivots: MutableStructure1D<Int>,
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epsilon: Double
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epsilon: Double,
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): Boolean {
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val m = lu.rowNum
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@ -122,7 +135,7 @@ internal fun <T> BufferedTensor<T>.setUpPivots(): IntTensor {
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internal fun DoubleTensorAlgebra.computeLU(
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tensor: DoubleTensor,
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epsilon: Double
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epsilon: Double,
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): Pair<DoubleTensor, IntTensor>? {
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checkSquareMatrix(tensor.shape)
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@ -139,7 +152,7 @@ internal fun DoubleTensorAlgebra.computeLU(
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internal fun pivInit(
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p: MutableStructure2D<Double>,
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pivot: MutableStructure1D<Int>,
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n: Int
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n: Int,
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) {
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for (i in 0 until n) {
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p[i, pivot[i]] = 1.0
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@ -150,7 +163,7 @@ internal fun luPivotHelper(
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l: MutableStructure2D<Double>,
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u: MutableStructure2D<Double>,
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lu: MutableStructure2D<Double>,
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n: Int
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n: Int,
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) {
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for (i in 0 until n) {
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for (j in 0 until n) {
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@ -170,7 +183,7 @@ internal fun luPivotHelper(
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internal fun choleskyHelper(
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a: MutableStructure2D<Double>,
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l: MutableStructure2D<Double>,
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n: Int
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n: Int,
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) {
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for (i in 0 until n) {
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for (j in 0 until i) {
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@ -200,7 +213,7 @@ internal fun luMatrixDet(lu: MutableStructure2D<Double>, pivots: MutableStructur
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internal fun luMatrixInv(
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lu: MutableStructure2D<Double>,
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pivots: MutableStructure1D<Int>,
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invMatrix: MutableStructure2D<Double>
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invMatrix: MutableStructure2D<Double>,
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) {
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val m = lu.shape[0]
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@ -227,7 +240,7 @@ internal fun luMatrixInv(
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internal fun DoubleTensorAlgebra.qrHelper(
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matrix: DoubleTensor,
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q: DoubleTensor,
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r: MutableStructure2D<Double>
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r: MutableStructure2D<Double>,
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) {
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checkSquareMatrix(matrix.shape)
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val n = matrix.shape[0]
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@ -280,12 +293,11 @@ internal fun DoubleTensorAlgebra.svd1d(a: DoubleTensor, epsilon: Double = 1e-10)
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internal fun DoubleTensorAlgebra.svdHelper(
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matrix: DoubleTensor,
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USV: Pair<BufferedTensor<Double>, Pair<BufferedTensor<Double>, BufferedTensor<Double>>>,
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m: Int, n: Int, epsilon: Double
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USV: Triple<BufferedTensor<Double>, BufferedTensor<Double>, BufferedTensor<Double>>,
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m: Int, n: Int, epsilon: Double,
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) {
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val res = ArrayList<Triple<Double, DoubleTensor, DoubleTensor>>(0)
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val (matrixU, SV) = USV
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val (matrixS, matrixV) = SV
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val (matrixU, matrixS, matrixV) = USV
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for (k in 0 until min(n, m)) {
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var a = matrix.copy()
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@ -329,14 +341,3 @@ internal fun DoubleTensorAlgebra.svdHelper(
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matrixV.mutableBuffer.array()[matrixV.bufferStart + i] = vBuffer[i]
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}
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}
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internal fun cleanSymHelper(matrix: MutableStructure2D<Double>, n: Int) {
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for (i in 0 until n)
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for (j in 0 until n) {
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if (i == j) {
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matrix[i, j] = sign(matrix[i, j])
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} else {
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matrix[i, j] = 0.0
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}
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}
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}
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