Improve Jacobi algorithm readability by extracting some logic into helper fun
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Ivan Kylchik
parent
7a72a0b979
commit
7aff774bc1
@ -10,6 +10,7 @@ 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.Structure2D
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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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@ -885,7 +886,7 @@ 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(epsilon = 1e-10)
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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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@ -922,96 +923,99 @@ public open class DoubleTensorAlgebra :
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return eig to v
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}
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// TODO
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// 1. Cyclic method
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// 2. Sort eigenvalues
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public fun StructureND<Double>.symEig(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
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public fun StructureND<Double>.symEigJacobi(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
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checkSymmetric(tensor, epsilon)
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val ii = tensor.minusIndex(-2)
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val jj = tensor.minusIndex(-1)
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val n = tensor.numElements
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val size = this.dimension
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val commonShape = this.shape.sliceArray(0 until size - 2) + intArrayOf(1, 1)
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val s = zeros(this.shape)
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val eigenvalues = zeros(this.shape.sliceArray(0 until size - 1))
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var d = this.copy()
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var s = diagonalEmbedding(ones(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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matrix.as2D().jacobiHelper(eigenvalues, s, eigenvalueStart, eigenvectorStart, epsilon)
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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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// TODO sort eigenvalues
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return eigenvalues to s
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}
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private fun MutableStructure2D<Double>.jacobiHelper(
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eigenvalues: DoubleTensor,
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eigenvectors: DoubleTensor,
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eigenvalueStart: Int,
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eigenvectorStart: Int,
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epsilon: Double
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) {
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var d = this
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var s = eye(this.shape[0])
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// TODO implement cyclic method
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do {
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// 1. Find max element by abs value that is not on diagonal
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val buffer = MutableBuffer.boxing(commonShape.reduce(Int::times)) { Triple(0.0, 0, 0) }
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val maxOffDiagonalElements = BufferedTensor(commonShape, buffer, 0)
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for (offset in 0 until n) {
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val multiIndex = d.linearStructure.index(offset)
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if (multiIndex[ii] != multiIndex[jj]) {
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val value = d.mutableBuffer.array()[offset]
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val commonIndex = multiIndex.sliceArray(0 until size - 2) + intArrayOf(0, 0)
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if (abs(value) > maxOffDiagonalElements[commonIndex].first) {
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maxOffDiagonalElements[commonIndex] = Triple(abs(value), multiIndex[ii], multiIndex[jj])
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var maxOffDiagonalElement = 0.0
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var maxElementIndex = Pair(0, 0)
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for (i in 0 until this.rowNum) {
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for (j in 0 until this.colNum) {
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if (i == j) continue
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if (abs(d[i, j]) > maxOffDiagonalElement) {
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maxOffDiagonalElement = abs(d[i, j])
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maxElementIndex = i to j
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}
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}
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}
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// 2. Evaluate "rotation" angle
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val angles = zeros(commonShape)
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for (offset in 0 until maxOffDiagonalElements.numElements) {
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val (_, i, j) = maxOffDiagonalElements.mutableBuffer[offset]
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val multiIndex = maxOffDiagonalElements.linearStructure.index(offset)
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val dIJ = d[maxElementIndex.first, maxElementIndex.second]
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val dII = d[maxElementIndex.first, maxElementIndex.first]
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val dJJ = d[maxElementIndex.second, maxElementIndex.second]
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val dIJ = d.mutableBuffer[d.linearStructure.offset(multiIndex.also { it[ii] = i; it[jj] = j })]
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val dII = d.mutableBuffer[d.linearStructure.offset(multiIndex.also { it[ii] = i; it[jj] = i })]
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val dJJ = d.mutableBuffer[d.linearStructure.offset(multiIndex.also { it[ii] = j; it[jj] = j })]
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angles.mutableBuffer.array()[offset] = if (dII == dJJ) {
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if (dIJ > 0) PI / 4 else -PI / 4
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} else {
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0.5 * atan(2 * dIJ / (dJJ - dII))
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}
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val angle = if (dII == dJJ) {
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if (dIJ > 0) PI / 4 else -PI / 4
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} else {
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0.5 * atan(2 * dIJ / (dJJ - dII))
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}
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// 3. Build rotation tensor `s1`
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val s1 = diagonalEmbedding(ones(this.shape.sliceArray(0 until size - 1)))
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for (offset in 0 until n) {
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val multiIndex = d.linearStructure.index(offset)
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val commonIndex = multiIndex.sliceArray(0 until size - 2) + intArrayOf(0, 0)
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val (_, i, j) = maxOffDiagonalElements[commonIndex]
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val angleValue = angles[commonIndex]
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s1.mutableBuffer.array()[offset] = when {
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multiIndex[ii] == i && multiIndex[jj] == i || multiIndex[ii] == j && multiIndex[jj] == j -> cos(angleValue)
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multiIndex[ii] == i && multiIndex[jj] == j -> sin(angleValue)
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multiIndex[ii] == j && multiIndex[jj] == i -> -sin(angleValue)
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else -> s1.mutableBuffer.array()[offset]
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val s1 = eye(this.rowNum)
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for (i in 0 until this.rowNum) {
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for (j in 0 until this.colNum) {
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s1.mutableBuffer.array()[i * this.rowNum + j] = when {
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maxElementIndex.first == i && maxElementIndex.first == j -> cos(angle)
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maxElementIndex.second == i && maxElementIndex.second == j -> cos(angle)
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maxElementIndex.first == i && maxElementIndex.second == j -> sin(angle)
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maxElementIndex.first == j && maxElementIndex.second == i -> -sin(angle)
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else -> s1.mutableBuffer.array()[i * this.rowNum + j]
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}
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}
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}
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// 4. Evaluate new tensor
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d = (s1.transpose() dot d) dot s1
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d = ((s1.transpose() dot d) dot s1).as2D()
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s = s dot s1
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if (d.isDiagonal(epsilon)) break
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} while(true)
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val eigenvalues = zeros(d.shape.sliceArray(0 until size - 1))
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for (offset in 0 until n) {
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val multiIndex = d.linearStructure.index(offset)
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if (multiIndex[ii] == multiIndex[jj]) {
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eigenvalues[multiIndex.sliceArray(0 until size - 1)] = d.mutableBuffer.array()[offset]
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// 5. Copy result
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for (i in 0 until this.rowNum) {
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for (j in 0 until this.colNum) {
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eigenvectors.mutableBuffer.array()[eigenvectorStart + i * this.rowNum + j] = s.mutableBuffer.array()[i * this.rowNum + j]
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}
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}
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return eigenvalues to s
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for (i in 0 until this.rowNum) {
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eigenvalues.mutableBuffer.array()[eigenvalueStart + i] = d[i, i]
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}
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}
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public fun StructureND<Double>.isDiagonal(epsilon: Double = 1e-9): Boolean {
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val ii = tensor.minusIndex(-2)
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val jj = tensor.minusIndex(-1)
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for (offset in 0 until tensor.numElements) {
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val multiIndex = tensor.linearStructure.index(offset)
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if (multiIndex[ii] != multiIndex[jj] && abs(tensor.mutableBuffer.array()[offset]) > epsilon) {
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return false
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public fun Structure2D<Double>.isDiagonal(epsilon: Double = 1e-9): Boolean {
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for (i in 0 until this.rowNum) {
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for (j in 0 until this.colNum) {
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if (i != j && abs(this[i, j]) > epsilon) {
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return false
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}
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}
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}
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