Optimizing decomposition performance
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@ -9,7 +9,7 @@ import kotlin.system.measureTimeMillis
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@ExperimentalContracts
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fun main() {
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val random = Random(12224)
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val random = Random(1224)
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val dim = 100
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//creating invertible matrix
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val u = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
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@ -1,9 +1,12 @@
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import com.moowork.gradle.node.NodeExtension
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import com.moowork.gradle.node.npm.NpmTask
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import com.moowork.gradle.node.task.NodeTask
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import org.jetbrains.kotlin.gradle.dsl.KotlinMultiplatformExtension
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import org.jetbrains.kotlin.gradle.tasks.Kotlin2JsCompile
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import org.jetbrains.kotlin.gradle.tasks.KotlinCompile
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buildscript {
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val kotlinVersion: String by rootProject.extra("1.3.21")
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val kotlinVersion: String by rootProject.extra("1.3.30")
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val ioVersion: String by rootProject.extra("0.1.5")
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val coroutinesVersion: String by rootProject.extra("1.1.1")
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val atomicfuVersion: String by rootProject.extra("0.12.1")
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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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@ -23,6 +24,18 @@ class BufferMatrixContext<T : Any, R : Ring<T>>(
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}
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}
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object RealMatrixContext : GenericMatrixContext<Double, RealField> {
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override val elementContext = RealField
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override inline fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> Double): Matrix<Double> {
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val buffer = DoubleBuffer(rows * columns) { offset -> initializer(offset / columns, offset % columns) }
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return BufferMatrix(rows, columns, buffer)
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}
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override inline fun point(size: Int, initializer: (Int) -> Double): Point<Double> = DoubleBuffer(size,initializer)
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}
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class BufferMatrix<T : Any>(
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override val rowNum: Int,
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override val colNum: Int,
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@ -3,22 +3,22 @@ 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 kotlin.contracts.ExperimentalContracts
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import kotlin.contracts.InvocationKind
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import kotlin.contracts.contract
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import kotlin.reflect.KClass
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import scientifik.kmath.structures.BufferAccessor2D
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import scientifik.kmath.structures.Matrix
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import scientifik.kmath.structures.Structure2D
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/**
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* Common implementation of [LUPDecompositionFeature]
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*/
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class LUPDecomposition<T : Any>(
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private val elementContext: Ring<T>,
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val context: GenericMatrixContext<T, out Field<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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val elementContext get() = context.elementContext
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/**
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* Returns the matrix L of the decomposition.
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*
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@ -66,102 +66,14 @@ class LUPDecomposition<T : Any>(
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}
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internal open class BufferAccessor<T : Any>(
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val type: KClass<T>,
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val field: Field<T>,
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val rowNum: Int,
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val colNum: Int
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) {
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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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* Specialized LU operations for Doubles
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*/
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private class RealBufferAccessor(rowNum: Int, colNum: Int) :
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BufferAccessor<Double>(Double::class, RealField, rowNum, colNum) {
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override fun MutableBuffer<Double>.get(i: Int, j: Int) = (this as DoubleBuffer).array[i + colNum * j]
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override 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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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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@ExperimentalContracts
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private inline fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.withAccessor(
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type: KClass<T>,
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rowNum: Int,
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colNum: Int,
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block: BufferAccessor<T>.() -> Unit
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) {
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contract {
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callsInPlace(block, InvocationKind.EXACTLY_ONCE)
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}
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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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}.run(block)
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}
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private fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T) =
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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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/**
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* Create a lup decomposition of generic matrix
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*/
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@ExperimentalContracts
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fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
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type: KClass<T>,
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inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
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matrix: Matrix<T>,
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checkSingular: (T) -> Boolean
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): LUPDecomposition<T> {
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@ -169,133 +81,166 @@ fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
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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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withAccessor(type, matrix.rowNum, matrix.colNum) {
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//TODO just waits for KEEP-176
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BufferAccessor2D(T::class, matrix.rowNum, matrix.colNum).run {
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elementContext.run {
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val lu = create(matrix)
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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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// 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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val sum = lu.innerProduct(row, col, row)
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lu[row, col] = field.run { lu[row, col] - sum }
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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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// lower
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val max = (col until m).maxBy { row ->
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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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// 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 singular = false
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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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// 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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val luRow = lu.row(row)
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var sum = luRow[col]
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for (i in 0 until row) {
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sum -= luRow[i] * lu[i, col]
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}
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luRow[col] = sum
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}
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// lower
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var max = col // permutation row
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var largest = -one
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for (row in col until m) {
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val luRow = lu.row(row)
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var sum = luRow[col]
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for (i in 0 until col) {
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sum -= luRow[i] * lu[i, col]
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}
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luRow[col] = sum
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// maintain best permutation choice
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if (abs(sum) > largest) {
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largest = abs(sum)
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max = row
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}
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}
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// Singularity check
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if (checkSingular(abs(lu[max, col]))) {
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error("The matrix is singular")
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}
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// Pivot if necessary
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if (max != col) {
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val luMax = lu.row(max)
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val luCol = lu.row(col)
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for (i in 0 until m) {
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val tmp = luMax[i]
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luMax[i] = luCol[i]
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luCol[i] = tmp
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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] /= luDiag
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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.divideInPlace(row, col, luDiag)
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//lu[row, col] = lu[row, col] / luDiag
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}
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return LUPDecomposition(this@lup, lu.collect(), pivot, even)
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}
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}
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}
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fun GenericMatrixContext<Double, RealField>.lup(matrix: Matrix<Double>) = lup(matrix) { it < 1e-11 }
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inline fun <reified T : Any> LUPDecomposition<T>.solve(matrix: Matrix<T>): Matrix<T> {
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if (matrix.rowNum != pivot.size) {
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error("Matrix dimension mismatch. Expected ${pivot.size}, but got ${matrix.colNum}")
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}
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BufferAccessor2D(T::class, matrix.rowNum, matrix.colNum).run {
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elementContext.run {
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val lu = create{i,j-> this@solve.lu[i,j]}
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// Apply permutations to b
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val bp = create { i, j -> zero }
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for (row in 0 until pivot.size) {
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val bpRow = bp.row(row)
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val pRow = pivot[row]
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for (col in 0 until matrix.colNum) {
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bpRow[col] = matrix[pRow, col]
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}
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}
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// Solve LY = b
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for (col in 0 until pivot.size) {
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val bpCol = bp.row(col)
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for (i in col + 1 until pivot.size) {
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val bpI = bp.row(i)
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val luICol = lu[i, col]
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for (j in 0 until matrix.colNum) {
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bpI[j] -= bpCol[j] * luICol
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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 pivot.size - 1 downTo 0) {
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val bpCol = bp.row(col)
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val luDiag = lu[col, col]
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for (j in 0 until matrix.colNum) {
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bpCol[j] /= luDiag
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}
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for (i in 0 until col) {
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val bpI = bp.row(i)
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val luICol = lu[i, col]
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for (j in 0 until matrix.colNum) {
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bpI[j] -= bpCol[j] * luICol
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}
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}
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}
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return context.produce(pivot.size, matrix.colNum) { i, j -> bp[i, j] }
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}
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return LUPDecomposition(elementContext, lu.collect(), pivot, even)
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}
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}
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@ExperimentalContracts
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fun GenericMatrixContext<Double, RealField>.lup(matrix: Matrix<Double>) = lup(Double::class, matrix) { it < 1e-11 }
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/**
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* Solve a linear equation **a*x = b**
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*/
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@ExperimentalContracts
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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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inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.solve(
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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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crossinline 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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// Use existing decomposition if it is provided by matrix
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val decomposition = a.getFeature() ?: lup(type, a, checkSingular)
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withAccessor(type, a.rowNum, a.colNum) {
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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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val decomposition = a.getFeature() ?: lup(a, checkSingular)
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return decomposition.solve(b)
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}
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@ExperimentalContracts
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fun GenericMatrixContext<Double, RealField>.solve(a: Matrix<Double>, b: Matrix<Double>) =
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solve(Double::class, a, b) { it < 1e-11 }
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fun RealMatrixContext.solve(a: Matrix<Double>, b: Matrix<Double>) =
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solve(a, b) { it < 1e-11 }
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@ExperimentalContracts
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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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) = solve(matrix, one(matrix.rowNum, matrix.colNum), checkSingular)
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@ExperimentalContracts
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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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fun RealMatrixContext.inverse(matrix: Matrix<Double>) =
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solve(matrix, one(matrix.rowNum, matrix.colNum)) { it < 1e-11 }
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@ -1,6 +1,5 @@
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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.operations.SpaceOperations
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import scientifik.kmath.operations.sum
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@ -30,7 +29,7 @@ interface MatrixContext<T : Any> : SpaceOperations<Matrix<T>> {
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/**
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* Non-boxing double matrix
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*/
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val real = BufferMatrixContext(RealField, Buffer.Companion::auto)
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val real = RealMatrixContext
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/**
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* A structured matrix with custom buffer
|
||||
|
||||
@ -0,0 +1,45 @@
|
||||
package scientifik.kmath.structures
|
||||
|
||||
import kotlin.reflect.KClass
|
||||
|
||||
/**
|
||||
* A context that allows to operate on a [MutableBuffer] as on 2d array
|
||||
*/
|
||||
class BufferAccessor2D<T : Any>(val type: KClass<T>, val rowNum: Int, val colNum: Int) {
|
||||
|
||||
inline operator fun Buffer<T>.get(i: Int, j: Int) = get(i + colNum * j)
|
||||
|
||||
inline operator fun MutableBuffer<T>.set(i: Int, j: Int, value: T) {
|
||||
set(i + colNum * j, value)
|
||||
}
|
||||
|
||||
inline fun create(init: (i: Int, j: Int) -> T) =
|
||||
MutableBuffer.auto(type, rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
|
||||
|
||||
fun create(mat: Structure2D<T>) = create { i, j -> mat[i, j] }
|
||||
|
||||
//TODO optimize wrapper
|
||||
fun MutableBuffer<T>.collect(): Structure2D<T> =
|
||||
NDStructure.auto(type, rowNum, colNum) { (i, j) -> get(i, j) }.as2D()
|
||||
|
||||
|
||||
inner class Row(val buffer: MutableBuffer<T>, val rowIndex: Int) : MutableBuffer<T> {
|
||||
override val size: Int get() = colNum
|
||||
|
||||
override fun get(index: Int): T = buffer[rowIndex, index]
|
||||
|
||||
override fun set(index: Int, value: T) {
|
||||
buffer[rowIndex, index] = value
|
||||
}
|
||||
|
||||
override fun copy(): MutableBuffer<T> = MutableBuffer.auto(type, colNum) { get(it) }
|
||||
|
||||
override fun iterator(): Iterator<T> = (0 until colNum).map(::get).iterator()
|
||||
|
||||
}
|
||||
|
||||
/**
|
||||
* Get row
|
||||
*/
|
||||
fun MutableBuffer<T>.row(i: Int) = Row(this, i)
|
||||
}
|
||||
@ -84,7 +84,7 @@ interface MutableBuffer<T> : Buffer<T> {
|
||||
MutableListBuffer(MutableList(size, initializer))
|
||||
|
||||
@Suppress("UNCHECKED_CAST")
|
||||
inline fun <T : Any> auto(type: KClass<T>, size: Int, initializer: (Int) -> T): MutableBuffer<T> {
|
||||
inline fun <T : Any> auto(type: KClass<out 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>
|
||||
|
||||
Loading…
Reference in New Issue
Block a user