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Optimizing decomposition performance

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This commit is contained in:
Alexander Nozik 2019-04-20 11:43:30 +03:00
parent f1b1010c4d
commit bbc012d8cd
7 changed files with 205 additions and 200 deletions
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2
benchmarks/src/main/kotlin/scientifik/kmath/linear/LinearAlgebraBenchmark.kt
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@ -9,7 +9,7 @@ import kotlin.system.measureTimeMillis
@ExperimentalContracts
fun main() {
val random = Random(12224)
val random = Random(1224)
val dim = 100
//creating invertible matrix
val u = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }

5
build.gradle.kts
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@ -1,9 +1,12 @@
import com.moowork.gradle.node.NodeExtension
import com.moowork.gradle.node.npm.NpmTask
import com.moowork.gradle.node.task.NodeTask
import org.jetbrains.kotlin.gradle.dsl.KotlinMultiplatformExtension
import org.jetbrains.kotlin.gradle.tasks.Kotlin2JsCompile
import org.jetbrains.kotlin.gradle.tasks.KotlinCompile
buildscript {
val kotlinVersion: String by rootProject.extra("1.3.21")
val kotlinVersion: String by rootProject.extra("1.3.30")
val ioVersion: String by rootProject.extra("0.1.5")
val coroutinesVersion: String by rootProject.extra("1.1.1")
val atomicfuVersion: String by rootProject.extra("0.12.1")

13
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/BufferMatrix.kt
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@ -1,5 +1,6 @@
package scientifik.kmath.linear
import scientifik.kmath.operations.RealField
import scientifik.kmath.operations.Ring
import scientifik.kmath.structures.*
@ -23,6 +24,18 @@ class BufferMatrixContext<T : Any, R : Ring<T>>(
}
}
object RealMatrixContext : GenericMatrixContext<Double, RealField> {
override val elementContext = RealField
override inline fun produce(rows: Int, columns: Int, initializer: (i: Int, j: Int) -> Double): Matrix<Double> {
val buffer = DoubleBuffer(rows * columns) { offset -> initializer(offset / columns, offset % columns) }
return BufferMatrix(rows, columns, buffer)
}
override inline fun point(size: Int, initializer: (Int) -> Double): Point<Double> = DoubleBuffer(size,initializer)
}
class BufferMatrix<T : Any>(
override val rowNum: Int,
override val colNum: Int,

257
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUPDecomposition.kt
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@ -3,22 +3,22 @@ package scientifik.kmath.linear
import scientifik.kmath.operations.Field
import scientifik.kmath.operations.RealField
import scientifik.kmath.operations.Ring
import scientifik.kmath.structures.*
import kotlin.contracts.ExperimentalContracts
import kotlin.contracts.InvocationKind
import kotlin.contracts.contract
import kotlin.reflect.KClass
import scientifik.kmath.structures.BufferAccessor2D
import scientifik.kmath.structures.Matrix
import scientifik.kmath.structures.Structure2D
/**
* Common implementation of [LUPDecompositionFeature]
*/
class LUPDecomposition<T : Any>(
private val elementContext: Ring<T>,
val context: GenericMatrixContext<T, out Field<T>>,
val lu: Structure2D<T>,
val pivot: IntArray,
private val even: Boolean
) : LUPDecompositionFeature<T>, DeterminantFeature<T> {
val elementContext get() = context.elementContext
/**
* Returns the matrix L of the decomposition.
*
@ -66,102 +66,14 @@ class LUPDecomposition<T : Any>(
}
internal open class BufferAccessor<T : Any>(
val type: KClass<T>,
val field: Field<T>,
val rowNum: Int,
val colNum: Int
) {
open operator fun MutableBuffer<T>.get(i: Int, j: Int) = get(i + colNum * j)
open operator fun MutableBuffer<T>.set(i: Int, j: Int, value: T) {
set(i + colNum * j, value)
}
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()
open fun MutableBuffer<T>.innerProduct(row: Int, col: Int, max: Int): T {
var sum = field.zero
field.run {
for (i in 0 until max) {
sum += get(row, i) * get(i, col)
}
}
return sum
}
open fun MutableBuffer<T>.divideInPlace(i: Int, j: Int, factor: T) {
field.run { set(i, j, get(i, j) / factor) }
}
open fun MutableBuffer<T>.subtractInPlace(i: Int, j: Int, lu: MutableBuffer<T>, col: Int) {
field.run {
set(i, j, get(i, j) - get(col, j) * lu[i, col])
}
}
}
/**
* Specialized LU operations for Doubles
*/
private class RealBufferAccessor(rowNum: Int, colNum: Int) :
BufferAccessor<Double>(Double::class, RealField, rowNum, colNum) {
override fun MutableBuffer<Double>.get(i: Int, j: Int) = (this as DoubleBuffer).array[i + colNum * j]
override fun MutableBuffer<Double>.set(i: Int, j: Int, value: Double) {
(this as DoubleBuffer).array[i + colNum * j] = value
}
override fun MutableBuffer<Double>.innerProduct(row: Int, col: Int, max: Int): Double {
var sum = 0.0
for (i in 0 until max) {
sum += get(row, i) * get(i, col)
}
return sum
}
override fun MutableBuffer<Double>.divideInPlace(i: Int, j: Int, factor: Double) {
set(i, j, get(i, j) / factor)
}
override fun MutableBuffer<Double>.subtractInPlace(i: Int, j: Int, lu: MutableBuffer<Double>, col: Int) {
set(i, j, get(i, j) - get(col, j) * lu[i, col])
}
}
@ExperimentalContracts
private inline fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.withAccessor(
type: KClass<T>,
rowNum: Int,
colNum: Int,
block: BufferAccessor<T>.() -> Unit
) {
contract {
callsInPlace(block, InvocationKind.EXACTLY_ONCE)
}
if (elementContext == RealField) {
@Suppress("UNCHECKED_CAST")
RealBufferAccessor(rowNum, colNum) as BufferAccessor<T>
} else {
BufferAccessor(type, elementContext, rowNum, colNum)
}.run(block)
}
private fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T) =
fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T) =
if (value > elementContext.zero) value else with(elementContext) { -value }
/**
* Create a lup decomposition of generic matrix
*/
@ExperimentalContracts
fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
type: KClass<T>,
inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
matrix: Matrix<T>,
checkSingular: (T) -> Boolean
): LUPDecomposition<T> {
@ -169,11 +81,12 @@ fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
error("LU decomposition supports only square matrices")
}
val m = matrix.colNum
val pivot = IntArray(matrix.rowNum)
withAccessor(type, matrix.rowNum, matrix.colNum) {
//TODO just waits for KEEP-176
BufferAccessor2D(T::class, matrix.rowNum, matrix.colNum).run {
elementContext.run {
val lu = create(matrix)
@ -183,32 +96,56 @@ fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
}
var even = true
// Initialize permutation array and parity
for (row in 0 until m) {
pivot[row] = row
}
var singular = false
// Loop over columns
for (col in 0 until m) {
// upper
for (row in 0 until col) {
val sum = lu.innerProduct(row, col, row)
lu[row, col] = field.run { lu[row, col] - sum }
val luRow = lu.row(row)
var sum = luRow[col]
for (i in 0 until row) {
sum -= luRow[i] * lu[i, col]
}
luRow[col] = sum
}
// lower
val max = (col until m).maxBy { row ->
val sum = lu.innerProduct(row, col, col)
lu[row, col] = field.run { lu[row, col] - sum }
abs(sum)
} ?: col
var max = col // permutation row
var largest = -one
for (row in col until m) {
val luRow = lu.row(row)
var sum = luRow[col]
for (i in 0 until col) {
sum -= luRow[i] * lu[i, col]
}
luRow[col] = sum
// maintain best permutation choice
if (abs(sum) > largest) {
largest = abs(sum)
max = row
}
}
// Singularity check
if (checkSingular(lu[max, col])) {
error("Singular matrix")
if (checkSingular(abs(lu[max, col]))) {
error("The matrix is singular")
}
// Pivot if necessary
if (max != col) {
val luMax = lu.row(max)
val luCol = lu.row(col)
for (i in 0 until m) {
lu[max, i] = lu[col, i]
lu[col, i] = lu[max, i]
val tmp = luMax[i]
luMax[i] = luCol[i]
luCol[i] = tmp
}
val temp = pivot[max]
pivot[max] = pivot[col]
@ -219,83 +156,91 @@ fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lup(
// Divide the lower elements by the "winning" diagonal elt.
val luDiag = lu[col, col]
for (row in col + 1 until m) {
lu.divideInPlace(row, col, luDiag)
//lu[row, col] = lu[row, col] / luDiag
lu[row, col] /= luDiag
}
}
return LUPDecomposition(elementContext, lu.collect(), pivot, even)
return LUPDecomposition(this@lup, lu.collect(), pivot, even)
}
}
}
@ExperimentalContracts
fun GenericMatrixContext<Double, RealField>.lup(matrix: Matrix<Double>) = lup(Double::class, matrix) { it < 1e-11 }
fun GenericMatrixContext<Double, RealField>.lup(matrix: Matrix<Double>) = lup(matrix) { it < 1e-11 }
/**
* Solve a linear equation **a*x = b**
*/
@ExperimentalContracts
fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.solve(
type: KClass<T>,
a: Matrix<T>,
b: Matrix<T>,
checkSingular: (T) -> Boolean
): Matrix<T> {
if (b.rowNum != a.colNum) {
error("Matrix dimension mismatch. Expected ${a.rowNum}, but got ${b.colNum}")
inline fun <reified T : Any> LUPDecomposition<T>.solve(matrix: Matrix<T>): Matrix<T> {
if (matrix.rowNum != pivot.size) {
error("Matrix dimension mismatch. Expected ${pivot.size}, but got ${matrix.colNum}")
}
// Use existing decomposition if it is provided by matrix
val decomposition = a.getFeature() ?: lup(type, a, checkSingular)
BufferAccessor2D(T::class, matrix.rowNum, matrix.colNum).run {
elementContext.run {
withAccessor(type, a.rowNum, a.colNum) {
val lu = create(decomposition.lu)
val lu = create{i,j-> this@solve.lu[i,j]}
// Apply permutations to b
val bp = create { i, j ->
b[decomposition.pivot[i], j]
val bp = create { i, j -> zero }
for (row in 0 until pivot.size) {
val bpRow = bp.row(row)
val pRow = pivot[row]
for (col in 0 until matrix.colNum) {
bpRow[col] = matrix[pRow, col]
}
}
// Solve LY = b
for (col in 0 until a.rowNum) {
for (i in col + 1 until a.rowNum) {
for (j in 0 until b.colNum) {
bp.subtractInPlace(i, j, lu, col)
//bp[i, j] -= bp[col, j] * lu[i, col]
for (col in 0 until pivot.size) {
val bpCol = bp.row(col)
for (i in col + 1 until pivot.size) {
val bpI = bp.row(i)
val luICol = lu[i, col]
for (j in 0 until matrix.colNum) {
bpI[j] -= bpCol[j] * luICol
}
}
}
// Solve UX = Y
for (col in a.rowNum - 1 downTo 0) {
for (col in pivot.size - 1 downTo 0) {
val bpCol = bp.row(col)
val luDiag = lu[col, col]
for (j in 0 until b.colNum) {
bp.divideInPlace(col, j, luDiag)
//bp[col, j] /= lu[col, col]
for (j in 0 until matrix.colNum) {
bpCol[j] /= luDiag
}
for (i in 0 until col) {
for (j in 0 until b.colNum) {
bp.subtractInPlace(i, j, lu, col)
//bp[i, j] -= bp[col, j] * lu[i, col]
val bpI = bp.row(i)
val luICol = lu[i, col]
for (j in 0 until matrix.colNum) {
bpI[j] -= bpCol[j] * luICol
}
}
}
return produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
return context.produce(pivot.size, matrix.colNum) { i, j -> bp[i, j] }
}
}
}
@ExperimentalContracts
fun GenericMatrixContext<Double, RealField>.solve(a: Matrix<Double>, b: Matrix<Double>) =
solve(Double::class, a, b) { it < 1e-11 }
@ExperimentalContracts
/**
* Solve a linear equation **a*x = b**
*/
inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.solve(
a: Matrix<T>,
b: Matrix<T>,
crossinline checkSingular: (T) -> Boolean
): Matrix<T> {
// Use existing decomposition if it is provided by matrix
val decomposition = a.getFeature() ?: lup(a, checkSingular)
return decomposition.solve(b)
}
fun RealMatrixContext.solve(a: Matrix<Double>, b: Matrix<Double>) =
solve(a, b) { it < 1e-11 }
inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.inverse(
matrix: Matrix<T>,
noinline checkSingular: (T) -> Boolean
) =
solve(T::class, matrix, one(matrix.rowNum, matrix.colNum), checkSingular)
) = solve(matrix, one(matrix.rowNum, matrix.colNum), checkSingular)
@ExperimentalContracts
fun GenericMatrixContext<Double, RealField>.inverse(matrix: Matrix<Double>) =
inverse(matrix) { it < 1e-11 }
fun RealMatrixContext.inverse(matrix: Matrix<Double>) =
solve(matrix, one(matrix.rowNum, matrix.colNum)) { it < 1e-11 }

3
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/MatrixContext.kt
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@ -1,6 +1,5 @@
package scientifik.kmath.linear
import scientifik.kmath.operations.RealField
import scientifik.kmath.operations.Ring
import scientifik.kmath.operations.SpaceOperations
import scientifik.kmath.operations.sum
@ -30,7 +29,7 @@ interface MatrixContext<T : Any> : SpaceOperations<Matrix<T>> {
/**
* Non-boxing double matrix
*/
val real = BufferMatrixContext(RealField, Buffer.Companion::auto)
val real = RealMatrixContext
/**
* A structured matrix with custom buffer

45
kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferAccessor2D.kt Normal file
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@ -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)
}

2
kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
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@ -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>