Optimizing inversion performance
This commit is contained in:
parent
14f05eb1e1
commit
271e762a95
@ -15,19 +15,20 @@ fun main() {
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val n = 5000 // iterations
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val solver = LUSolver.real
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MatrixContext.real.run {
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repeat(50) {
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val res = solver.inverse(matrix)
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}
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val inverseTime = measureTimeMillis {
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repeat(n) {
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val res = solver.inverse(matrix)
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repeat(50) {
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val res = inverse(matrix)
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}
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}
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println("[kmath] Inversion of $n matrices $dim x $dim finished in $inverseTime millis")
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val inverseTime = measureTimeMillis {
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repeat(n) {
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val res = inverse(matrix)
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}
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}
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println("[kmath] Inversion of $n matrices $dim x $dim finished in $inverseTime millis")
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}
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//commons-math
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@ -1,5 +1,6 @@
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package scientifik.kmath.linear
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import scientifik.kmath.operations.RealField
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import scientifik.kmath.operations.Ring
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import scientifik.kmath.structures.*
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@ -17,6 +18,10 @@ class BufferMatrixContext<T : Any, R : Ring<T>>(
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}
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override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
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companion object {
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}
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}
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class BufferMatrix<T : Any>(
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@ -1,16 +1,17 @@
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package scientifik.kmath.linear
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import scientifik.kmath.operations.Field
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import scientifik.kmath.operations.RealField
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import scientifik.kmath.operations.Ring
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import scientifik.kmath.structures.*
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import scientifik.kmath.structures.MutableBuffer.Companion.boxing
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import kotlin.reflect.KClass
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/**
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* Common implementation of [LUPDecompositionFeature]
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*/
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class LUPDecomposition<T : Comparable<T>>(
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class LUPDecomposition<T : Any>(
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private val elementContext: Ring<T>,
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internal val lu: NDStructure<T>,
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val lu: Structure2D<T>,
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val pivot: IntArray,
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private val even: Boolean
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) : LUPDecompositionFeature<T>, DeterminantFeature<T> {
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@ -62,146 +63,222 @@ class LUPDecomposition<T : Comparable<T>>(
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}
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open class BufferAccessor<T : Any>(val type: KClass<T>, val field: Field<T>, val rowNum: Int, val colNum: Int) {
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open operator fun MutableBuffer<T>.get(i: Int, j: Int) = get(i + colNum * j)
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open operator fun MutableBuffer<T>.set(i: Int, j: Int, value: T) {
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set(i + colNum * j, value)
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}
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fun create(init: (i: Int, j: Int) -> T) =
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MutableBuffer.auto(type, rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
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fun create(mat: Structure2D<T>) = create { i, j -> mat[i, j] }
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//TODO optimize wrapper
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fun MutableBuffer<T>.collect(): Structure2D<T> =
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NDStructure.auto(type, rowNum, colNum) { (i, j) -> get(i, j) }.as2D()
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open fun MutableBuffer<T>.innerProduct(row: Int, col: Int, max: Int): T {
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var sum = field.zero
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field.run {
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for (i in 0 until max) {
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sum += get(row, i) * get(i, col)
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}
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}
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return sum
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}
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open fun MutableBuffer<T>.divideInPlace(i: Int, j: Int, factor: T) {
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field.run { set(i, j, get(i, j) / factor) }
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}
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open fun MutableBuffer<T>.subtractInPlace(i: Int, j: Int, lu: MutableBuffer<T>, col: Int) {
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field.run {
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set(i, j, get(i, j) - get(col, j) * lu[i, col])
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}
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}
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}
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/**
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* Common implementation of LUP [LinearSolver] based on commons-math code
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* Specialized LU operations for Doubles
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*/
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class LUSolver<T : Comparable<T>, F : Field<T>>(
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val context: GenericMatrixContext<T, F>,
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val bufferFactory: MutableBufferFactory<T> = ::boxing,
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val singularityCheck: (T) -> Boolean
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) : LinearSolver<T> {
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private fun abs(value: T) =
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if (value > context.elementContext.zero) value else with(context.elementContext) { -value }
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fun buildDecomposition(matrix: Matrix<T>): LUPDecomposition<T> {
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if (matrix.rowNum != matrix.colNum) {
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error("LU decomposition supports only square matrices")
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}
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val m = matrix.colNum
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val pivot = IntArray(matrix.rowNum)
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val lu = Mutable2DStructure.create(matrix.rowNum, matrix.colNum, bufferFactory) { i, j ->
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matrix[i, j]
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}
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with(context.elementContext) {
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// Initialize permutation array and parity
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for (row in 0 until m) {
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pivot[row] = row
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}
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var even = true
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// Loop over columns
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for (col in 0 until m) {
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// upper
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for (row in 0 until col) {
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var sum = lu[row, col]
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for (i in 0 until row) {
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sum -= lu[row, i] * lu[i, col]
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}
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lu[row, col] = sum
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}
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// lower
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val max = (col until m).maxBy { row ->
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var sum = lu[row, col]
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for (i in 0 until col) {
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sum -= lu[row, i] * lu[i, col]
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}
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lu[row, col] = sum
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abs(sum)
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} ?: col
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// Singularity check
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if (singularityCheck(lu[max, col])) {
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error("Singular matrix")
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}
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// Pivot if necessary
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if (max != col) {
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for (i in 0 until m) {
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lu[max, i] = lu[col, i]
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lu[col, i] = lu[max, i]
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}
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val temp = pivot[max]
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pivot[max] = pivot[col]
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pivot[col] = temp
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even = !even
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}
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// Divide the lower elements by the "winning" diagonal elt.
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val luDiag = lu[col, col]
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for (row in col + 1 until m) {
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lu[row, col] = lu[row, col] / luDiag
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}
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}
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return LUPDecomposition(context.elementContext, lu, pivot, even)
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}
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class RealBufferAccessor(rowNum: Int, colNum: Int) : BufferAccessor<Double>(Double::class, RealField, rowNum, colNum) {
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override inline fun MutableBuffer<Double>.get(i: Int, j: Int) = (this as DoubleBuffer).array[i + colNum * j]
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override inline fun MutableBuffer<Double>.set(i: Int, j: Int, value: Double) {
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(this as DoubleBuffer).array[i + colNum * j] = value
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}
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/**
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* Produce a matrix with added decomposition feature
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*/
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fun decompose(matrix: Matrix<T>): Matrix<T> {
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if (matrix.hasFeature<LUPDecomposition<*>>()) {
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return matrix
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} else {
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val decomposition = buildDecomposition(matrix)
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return VirtualMatrix.wrap(matrix, decomposition)
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override fun MutableBuffer<Double>.innerProduct(row: Int, col: Int, max: Int): Double {
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var sum = 0.0
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for (i in 0 until max) {
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sum += get(row, i) * get(i, col)
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}
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return sum
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}
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override fun MutableBuffer<Double>.divideInPlace(i: Int, j: Int, factor: Double) {
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set(i, j, get(i, j) / factor)
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}
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override fun MutableBuffer<Double>.subtractInPlace(i: Int, j: Int, lu: MutableBuffer<Double>, col: Int) {
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set(i, j, get(i, j) - get(col, j) * lu[i, col])
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}
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}
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fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.buildAccessor(
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type:KClass<T>,
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rowNum: Int,
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colNum: Int
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): BufferAccessor<T> {
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return if (elementContext == RealField) {
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@Suppress("UNCHECKED_CAST")
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RealBufferAccessor(rowNum, colNum) as BufferAccessor<T>
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} else {
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BufferAccessor(type, elementContext, rowNum, colNum)
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}
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}
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fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T) =
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if (value > elementContext.zero) value else with(elementContext) { -value }
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fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lupDecompose(
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type: KClass<T>,
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matrix: Matrix<T>,
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checkSingular: (T) -> Boolean
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): LUPDecomposition<T> {
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if (matrix.rowNum != matrix.colNum) {
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error("LU decomposition supports only square matrices")
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}
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override fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
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if (b.rowNum != a.colNum) {
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error("Matrix dimension mismatch expected ${a.rowNum}, but got ${b.colNum}")
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val m = matrix.colNum
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val pivot = IntArray(matrix.rowNum)
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buildAccessor(type, matrix.rowNum, matrix.colNum).run {
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val lu = create(matrix)
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// Initialize permutation array and parity
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for (row in 0 until m) {
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pivot[row] = row
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}
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var even = true
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// Use existing decomposition if it is provided by matrix
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val decomposition = a.getFeature() ?: buildDecomposition(a)
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// Loop over columns
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for (col in 0 until m) {
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with(decomposition) {
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with(context.elementContext) {
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// Apply permutations to b
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val bp = Mutable2DStructure.create(a.rowNum, a.colNum, bufferFactory) { i, j ->
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b[pivot[i], j]
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// upper
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for (row in 0 until col) {
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// var sum = lu[row, col]
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// for (i in 0 until row) {
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// sum -= lu[row, i] * lu[i, col]
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// }
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val sum = lu.innerProduct(row, col, row)
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lu[row, col] = field.run { lu[row, col] - sum }
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}
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// lower
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val max = (col until m).maxBy { row ->
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// var sum = lu[row, col]
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// for (i in 0 until col) {
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// sum -= lu[row, i] * lu[i, col]
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// }
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// lu[row, col] = sum
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val sum = lu.innerProduct(row, col, col)
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lu[row, col] = field.run { lu[row, col] - sum }
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abs(sum)
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} ?: col
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// Singularity check
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if (checkSingular(lu[max, col])) {
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error("Singular matrix")
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}
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// Pivot if necessary
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if (max != col) {
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for (i in 0 until m) {
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lu[max, i] = lu[col, i]
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lu[col, i] = lu[max, i]
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}
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val temp = pivot[max]
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pivot[max] = pivot[col]
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pivot[col] = temp
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even = !even
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}
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// Solve LY = b
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for (col in 0 until a.rowNum) {
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for (i in col + 1 until a.rowNum) {
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for (j in 0 until b.colNum) {
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bp[i, j] -= bp[col, j] * lu[i, col]
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}
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}
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}
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// Solve UX = Y
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for (col in a.rowNum - 1 downTo 0) {
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for (j in 0 until b.colNum) {
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bp[col, j] /= lu[col, col]
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}
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for (i in 0 until col) {
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for (j in 0 until b.colNum) {
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bp[i, j] -= bp[col, j] * lu[i, col]
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}
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}
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}
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return context.produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
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// Divide the lower elements by the "winning" diagonal elt.
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val luDiag = lu[col, col]
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for (row in col + 1 until m) {
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lu.divideInPlace(row, col, luDiag)
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//lu[row, col] = lu[row, col] / luDiag
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}
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}
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return scientifik.kmath.linear.LUPDecomposition(elementContext, lu.collect(), pivot, even)
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}
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}
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/**
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* Solve a linear equation **a*x = b**
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*/
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fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.solve(
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type: KClass<T>,
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a: Matrix<T>,
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b: Matrix<T>,
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checkSingular: (T) -> Boolean
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): Matrix<T> {
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if (b.rowNum != a.colNum) {
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error("Matrix dimension mismatch. Expected ${a.rowNum}, but got ${b.colNum}")
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}
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override fun inverse(a: Matrix<T>): Matrix<T> = solve(a, context.one(a.rowNum, a.colNum))
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// Use existing decomposition if it is provided by matrix
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val decomposition = a.getFeature() ?: lupDecompose(type, a, checkSingular)
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companion object {
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val real = LUSolver(MatrixContext.real, MutableBuffer.Companion::auto) { it < 1e-11 }
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buildAccessor(type, a.rowNum, a.colNum).run {
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val lu = create(decomposition.lu)
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// Apply permutations to b
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val bp = create { i, j ->
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b[decomposition.pivot[i], j]
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}
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// Solve LY = b
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for (col in 0 until a.rowNum) {
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for (i in col + 1 until a.rowNum) {
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for (j in 0 until b.colNum) {
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bp.subtractInPlace(i, j, lu, col)
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//bp[i, j] -= bp[col, j] * lu[i, col]
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}
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}
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}
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// Solve UX = Y
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for (col in a.rowNum - 1 downTo 0) {
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val luDiag = lu[col, col]
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for (j in 0 until b.colNum) {
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bp.divideInPlace(col, j, luDiag)
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//bp[col, j] /= lu[col, col]
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}
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for (i in 0 until col) {
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for (j in 0 until b.colNum) {
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bp.subtractInPlace(i, j, lu, col)
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//bp[i, j] -= bp[col, j] * lu[i, col]
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}
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}
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}
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return produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
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}
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}
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}
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inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.inverse(
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matrix: Matrix<T>,
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noinline checkSingular: (T) -> Boolean
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) =
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solve(T::class, matrix, one(matrix.rowNum, matrix.colNum), checkSingular)
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fun GenericMatrixContext<Double, RealField>.inverse(matrix: Matrix<Double>) =
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inverse(matrix) { it < 1e-11 }
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@ -1,40 +0,0 @@
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package scientifik.kmath.linear
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import scientifik.kmath.structures.MutableBuffer
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import scientifik.kmath.structures.MutableBufferFactory
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import scientifik.kmath.structures.MutableNDStructure
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class Mutable2DStructure<T>(val rowNum: Int, val colNum: Int, val buffer: MutableBuffer<T>) : MutableNDStructure<T> {
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override val shape: IntArray
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get() = intArrayOf(rowNum, colNum)
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operator fun get(i: Int, j: Int): T = buffer[i * colNum + j]
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override fun get(index: IntArray): T = get(index[0], index[1])
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override fun elements(): Sequence<Pair<IntArray, T>> = sequence {
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for (i in 0 until rowNum) {
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for (j in 0 until colNum) {
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yield(intArrayOf(i, j) to get(i, j))
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}
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}
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}
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operator fun set(i: Int, j: Int, value: T) {
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buffer[i * colNum + j] = value
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}
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override fun set(index: IntArray, value: T) = set(index[0], index[1], value)
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companion object {
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fun <T> create(
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rowNum: Int,
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colNum: Int,
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bufferFactory: MutableBufferFactory<T>,
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init: (i: Int, j: Int) -> T
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): Mutable2DStructure<T> {
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val buffer = bufferFactory(rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
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return Mutable2DStructure(rowNum, colNum, buffer)
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}
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}
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}
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@ -2,6 +2,7 @@ package scientifik.kmath.structures
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import scientifik.kmath.operations.Complex
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import scientifik.kmath.operations.complex
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import kotlin.reflect.KClass
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typealias BufferFactory<T> = (Int, (Int) -> T) -> Buffer<T>
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@ -41,13 +42,10 @@ interface Buffer<T> {
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*/
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inline fun <T> boxing(size: Int, initializer: (Int) -> T): Buffer<T> = ListBuffer(List(size, initializer))
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/**
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* Create most appropriate immutable buffer for given type avoiding boxing wherever possible
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*/
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@Suppress("UNCHECKED_CAST")
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inline fun <reified T : Any> auto(size: Int, crossinline initializer: (Int) -> T): Buffer<T> {
|
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inline fun <T : Any> auto(type: KClass<T>, size: Int, crossinline initializer: (Int) -> T): Buffer<T> {
|
||||
//TODO add resolution based on Annotation or companion resolution
|
||||
return when (T::class) {
|
||||
return when (type) {
|
||||
Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as Buffer<T>
|
||||
Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as Buffer<T>
|
||||
Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as Buffer<T>
|
||||
@ -56,6 +54,13 @@ interface Buffer<T> {
|
||||
else -> boxing(size, initializer)
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Create most appropriate immutable buffer for given type avoiding boxing wherever possible
|
||||
*/
|
||||
@Suppress("UNCHECKED_CAST")
|
||||
inline fun <reified T : Any> auto(size: Int, crossinline initializer: (Int) -> T): Buffer<T> =
|
||||
auto(T::class, size, initializer)
|
||||
}
|
||||
}
|
||||
|
||||
@ -78,12 +83,9 @@ interface MutableBuffer<T> : Buffer<T> {
|
||||
inline fun <T> boxing(size: Int, initializer: (Int) -> T): MutableBuffer<T> =
|
||||
MutableListBuffer(MutableList(size, initializer))
|
||||
|
||||
/**
|
||||
* Create most appropriate mutable buffer for given type avoiding boxing wherever possible
|
||||
*/
|
||||
@Suppress("UNCHECKED_CAST")
|
||||
inline fun <reified T : Any> auto(size: Int, initializer: (Int) -> T): MutableBuffer<T> {
|
||||
return when (T::class) {
|
||||
inline fun <T : Any> auto(type: KClass<T>, size: Int, initializer: (Int) -> T): MutableBuffer<T> {
|
||||
return when (type) {
|
||||
Double::class -> DoubleBuffer(DoubleArray(size) { initializer(it) as Double }) as MutableBuffer<T>
|
||||
Short::class -> ShortBuffer(ShortArray(size) { initializer(it) as Short }) as MutableBuffer<T>
|
||||
Int::class -> IntBuffer(IntArray(size) { initializer(it) as Int }) as MutableBuffer<T>
|
||||
@ -91,6 +93,17 @@ interface MutableBuffer<T> : Buffer<T> {
|
||||
else -> boxing(size, initializer)
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Create most appropriate mutable buffer for given type avoiding boxing wherever possible
|
||||
*/
|
||||
@Suppress("UNCHECKED_CAST")
|
||||
inline fun <reified T : Any> auto(size: Int, initializer: (Int) -> T): MutableBuffer<T> =
|
||||
auto(T::class, size, initializer)
|
||||
|
||||
val real: MutableBufferFactory<Double> = { size: Int, initializer: (Int) -> Double ->
|
||||
DoubleBuffer(DoubleArray(size) { initializer(it) })
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
@ -1,5 +1,8 @@
|
||||
package scientifik.kmath.structures
|
||||
|
||||
import kotlin.jvm.JvmName
|
||||
import kotlin.reflect.KClass
|
||||
|
||||
|
||||
interface NDStructure<T> {
|
||||
|
||||
@ -40,6 +43,9 @@ interface NDStructure<T> {
|
||||
inline fun <reified T : Any> auto(strides: Strides, crossinline initializer: (IntArray) -> T) =
|
||||
BufferNDStructure(strides, Buffer.auto(strides.linearSize) { i -> initializer(strides.index(i)) })
|
||||
|
||||
inline fun <T : Any> auto(type: KClass<T>, strides: Strides, crossinline initializer: (IntArray) -> T) =
|
||||
BufferNDStructure(strides, Buffer.auto(type, strides.linearSize) { i -> initializer(strides.index(i)) })
|
||||
|
||||
fun <T> build(
|
||||
shape: IntArray,
|
||||
bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
|
||||
@ -48,6 +54,13 @@ interface NDStructure<T> {
|
||||
|
||||
inline fun <reified T : Any> auto(shape: IntArray, crossinline initializer: (IntArray) -> T) =
|
||||
auto(DefaultStrides(shape), initializer)
|
||||
|
||||
@JvmName("autoVarArg")
|
||||
inline fun <reified T : Any> auto(vararg shape: Int, crossinline initializer: (IntArray) -> T) =
|
||||
auto(DefaultStrides(shape), initializer)
|
||||
|
||||
inline fun <T : Any> auto(type: KClass<T>, vararg shape: Int, crossinline initializer: (IntArray) -> T) =
|
||||
auto(type, DefaultStrides(shape), initializer)
|
||||
}
|
||||
}
|
||||
|
||||
@ -57,7 +70,7 @@ interface MutableNDStructure<T> : NDStructure<T> {
|
||||
operator fun set(index: IntArray, value: T)
|
||||
}
|
||||
|
||||
fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) -> T) {
|
||||
inline fun <T> MutableNDStructure<T>.mapInPlace(action: (IntArray, T) -> T) {
|
||||
elements().forEach { (index, oldValue) ->
|
||||
this[index] = action(index, oldValue)
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user