Separate linear algebra utils into dedicated module
This commit is contained in:
Roland Grinis
parent
51eca003af
commit
d281dfca3a
@ -1,7 +1,5 @@
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package space.kscience.kmath.tensors.core
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import space.kscience.kmath.nd.MutableStructure1D
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import space.kscience.kmath.nd.MutableStructure2D
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import space.kscience.kmath.structures.*
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import space.kscience.kmath.tensors.TensorStructure
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@ -18,9 +16,6 @@ public open class BufferedTensor<T>(
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public val numel: Int
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get() = linearStructure.size
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internal constructor(tensor: BufferedTensor<T>) :
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this(tensor.shape, tensor.buffer, tensor.bufferStart)
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override fun get(index: IntArray): T = buffer[bufferStart + linearStructure.offset(index)]
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override fun set(index: IntArray, value: T) {
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@ -35,39 +30,6 @@ public open class BufferedTensor<T>(
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override fun hashCode(): Int = 0
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internal fun 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 numel step vectorOffset) {
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val vector = BufferedTensor(vectorShape, buffer, offset)
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yield(vector)
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}
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}
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internal fun matrixSequence(): Sequence<BufferedTensor<T>> = sequence {
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check(shape.size >= 2) { "todo" }
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val n = shape.size
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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 numel step matrixOffset) {
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val matrix = BufferedTensor(matrixShape, buffer, offset)
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yield(matrix)
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}
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}
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internal inline fun forEachVector(vectorAction: (BufferedTensor<T>) -> Unit): Unit {
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for (vector in vectorSequence()) {
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vectorAction(vector)
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}
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}
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internal inline fun forEachMatrix(matrixAction: (BufferedTensor<T>) -> Unit): Unit {
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for (matrix in matrixSequence()) {
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matrixAction(matrix)
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}
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}
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}
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public class IntTensor internal constructor(
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@ -1,11 +1,8 @@
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package space.kscience.kmath.tensors.core
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import space.kscience.kmath.nd.MutableStructure1D
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import space.kscience.kmath.nd.MutableStructure2D
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import space.kscience.kmath.tensors.LinearOpsTensorAlgebra
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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.tensors.LinearOpsTensorAlgebra
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import kotlin.math.sqrt
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public class DoubleLinearOpsTensorAlgebra :
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LinearOpsTensorAlgebra<Double, DoubleTensor, IntTensor>,
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@ -15,48 +12,6 @@ public class DoubleLinearOpsTensorAlgebra :
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override fun DoubleTensor.det(): DoubleTensor = detLU()
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private inline fun luHelper(lu: MutableStructure2D<Double>, pivots: MutableStructure1D<Int>, m: Int) {
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for (row in 0 until m) pivots[row] = row
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for (i in 0 until m) {
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var maxVal = -1.0
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var maxInd = i
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for (k in i until m) {
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val absA = kotlin.math.abs(lu[k, i])
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if (absA > maxVal) {
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maxVal = absA
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maxInd = k
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}
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}
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//todo check singularity
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if (maxInd != i) {
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val j = pivots[i]
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pivots[i] = pivots[maxInd]
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pivots[maxInd] = j
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for (k in 0 until m) {
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val tmp = lu[i, k]
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lu[i, k] = lu[maxInd, k]
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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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lu[j, i] /= lu[i, i]
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for (k in i + 1 until m) {
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lu[j, k] -= lu[j, i] * lu[i, k]
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}
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}
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}
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}
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override fun DoubleTensor.lu(): Pair<DoubleTensor, IntTensor> {
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checkSquareMatrix(shape)
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@ -80,37 +35,6 @@ public class DoubleLinearOpsTensorAlgebra :
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}
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private inline 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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) {
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for (i in 0 until n) {
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p[i, pivot[i]] = 1.0
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}
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}
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private inline 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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) {
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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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l[i, j] = 1.0
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}
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if (j < i) {
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l[i, j] = lu[i, j]
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}
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if (j >= i) {
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u[i, j] = lu[i, j]
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}
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}
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}
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}
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override fun luPivot(
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luTensor: DoubleTensor,
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pivotsTensor: IntTensor
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@ -139,27 +63,6 @@ public class DoubleLinearOpsTensorAlgebra :
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}
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private inline 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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) {
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for (i in 0 until n) {
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for (j in 0 until i) {
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var h = a[i, j]
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for (k in 0 until j) {
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h -= l[i, k] * l[j, k]
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}
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l[i, j] = h / l[j, j]
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}
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var h = a[i, i]
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for (j in 0 until i) {
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h -= l[i, j] * l[i, j]
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}
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l[i, i] = sqrt(h)
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}
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}
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override fun DoubleTensor.cholesky(): DoubleTensor {
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// todo checks
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checkSquareMatrix(shape)
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@ -185,14 +88,6 @@ public class DoubleLinearOpsTensorAlgebra :
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TODO("ANDREI")
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}
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private fun luMatrixDet(luTensor: MutableStructure2D<Double>, pivotsTensor: MutableStructure1D<Int>): Double {
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val lu = luTensor.as2D()
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val pivots = pivotsTensor.as1D()
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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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return (0 until m).asSequence().map { lu[it, it] }.fold(sign) { left, right -> left * right }
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}
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public fun DoubleTensor.detLU(): DoubleTensor {
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val (luTensor, pivotsTensor) = lu()
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val n = shape.size
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@ -213,33 +108,6 @@ public class DoubleLinearOpsTensorAlgebra :
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return detTensor
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}
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private 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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) {
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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) = lu()
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val invTensor = luTensor.zeroesLike()
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@ -1,8 +1,7 @@
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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.as2D
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import space.kscience.kmath.tensors.TensorPartialDivisionAlgebra
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import space.kscience.kmath.nd.as2D
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import kotlin.math.abs
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public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double, DoubleTensor> {
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@ -230,23 +229,6 @@ public open class DoubleTensorAlgebra : TensorPartialDivisionAlgebra<Double, Dou
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return this.view(other.shape)
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}
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private inline 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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) {
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for (i in 0 until l) {
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for (j in 0 until n) {
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var curr = 0.0
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for (k in 0 until m) {
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curr += a[i, k] * b[k, j]
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}
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res[i, j] = curr
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}
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}
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}
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override fun DoubleTensor.dot(other: DoubleTensor): DoubleTensor {
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if (this.shape.size == 1 && other.shape.size == 1) {
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return DoubleTensor(intArrayOf(1), doubleArrayOf(this.times(other).buffer.array().sum()))
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@ -0,0 +1,188 @@
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package space.kscience.kmath.tensors.core
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import space.kscience.kmath.nd.MutableStructure1D
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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 kotlin.math.sqrt
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internal inline 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 numel step vectorOffset) {
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val vector = BufferedTensor(vectorShape, buffer, offset)
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yield(vector)
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}
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}
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internal inline fun <T> BufferedTensor<T>.matrixSequence(): Sequence<BufferedTensor<T>> = sequence {
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check(shape.size >= 2) { "todo" }
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val n = shape.size
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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 numel step matrixOffset) {
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val matrix = BufferedTensor(matrixShape, buffer, offset)
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yield(matrix)
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}
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}
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internal inline fun <T> BufferedTensor<T>.forEachVector(vectorAction: (BufferedTensor<T>) -> Unit): Unit {
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for (vector in vectorSequence()) {
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vectorAction(vector)
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}
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}
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internal inline fun <T> BufferedTensor<T>.forEachMatrix(matrixAction: (BufferedTensor<T>) -> Unit): Unit {
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for (matrix in matrixSequence()) {
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matrixAction(matrix)
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}
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}
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internal inline 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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) {
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for (i in 0 until l) {
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for (j in 0 until n) {
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var curr = 0.0
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for (k in 0 until m) {
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curr += a[i, k] * b[k, j]
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}
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res[i, j] = curr
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}
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}
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}
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internal inline fun luHelper(lu: MutableStructure2D<Double>, pivots: MutableStructure1D<Int>, m: Int) {
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for (row in 0 until m) pivots[row] = row
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for (i in 0 until m) {
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var maxVal = -1.0
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var maxInd = i
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for (k in i until m) {
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val absA = kotlin.math.abs(lu[k, i])
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if (absA > maxVal) {
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maxVal = absA
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maxInd = k
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}
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}
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//todo check singularity
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if (maxInd != i) {
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val j = pivots[i]
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pivots[i] = pivots[maxInd]
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pivots[maxInd] = j
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for (k in 0 until m) {
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val tmp = lu[i, k]
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lu[i, k] = lu[maxInd, k]
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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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lu[j, i] /= lu[i, i]
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for (k in i + 1 until m) {
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lu[j, k] -= lu[j, i] * lu[i, k]
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}
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}
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}
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}
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internal inline 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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) {
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for (i in 0 until n) {
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p[i, pivot[i]] = 1.0
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}
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}
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internal inline 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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) {
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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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l[i, j] = 1.0
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}
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if (j < i) {
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l[i, j] = lu[i, j]
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}
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if (j >= i) {
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u[i, j] = lu[i, j]
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}
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}
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}
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}
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internal inline 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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) {
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for (i in 0 until n) {
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for (j in 0 until i) {
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var h = a[i, j]
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for (k in 0 until j) {
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h -= l[i, k] * l[j, k]
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}
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l[i, j] = h / l[j, j]
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}
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var h = a[i, i]
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for (j in 0 until i) {
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h -= l[i, j] * l[i, j]
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}
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l[i, i] = sqrt(h)
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}
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}
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internal inline fun luMatrixDet(luTensor: MutableStructure2D<Double>, pivotsTensor: MutableStructure1D<Int>): Double {
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val lu = luTensor.as2D()
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val pivots = pivotsTensor.as1D()
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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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return (0 until m).asSequence().map { lu[it, it] }.fold(sign) { left, right -> left * right }
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}
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internal inline 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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) {
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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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