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Optimizing inversion performance

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This commit is contained in:
Alexander Nozik 2019-04-09 19:48:53 +03:00
parent 14f05eb1e1
commit 271e762a95
6 changed files with 257 additions and 188 deletions
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7
benchmarks/src/main/kotlin/scientifik/kmath/linear/LinearAlgebraBenchmark.kt
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@ -15,19 +15,20 @@ fun main() {
val n = 5000 // iterations
val solver = LUSolver.real
MatrixContext.real.run {
repeat(50) {
val res = solver.inverse(matrix)
val res = inverse(matrix)
}
val inverseTime = measureTimeMillis {
repeat(n) {
val res = solver.inverse(matrix)
val res = inverse(matrix)
}
}
println("[kmath] Inversion of $n matrices $dim x $dim finished in $inverseTime millis")
}
//commons-math

5
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.*
@ -17,6 +18,10 @@ class BufferMatrixContext<T : Any, R : Ring<T>>(
}
override fun point(size: Int, initializer: (Int) -> T): Point<T> = bufferFactory(size, initializer)
companion object {
}
}
class BufferMatrix<T : Any>(

203
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUPDecomposition.kt
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@ -1,16 +1,17 @@
package scientifik.kmath.linear
import scientifik.kmath.operations.Field
import scientifik.kmath.operations.RealField
import scientifik.kmath.operations.Ring
import scientifik.kmath.structures.*
import scientifik.kmath.structures.MutableBuffer.Companion.boxing
import kotlin.reflect.KClass
/**
* Common implementation of [LUPDecompositionFeature]
*/
class LUPDecomposition<T : Comparable<T>>(
class LUPDecomposition<T : Any>(
private val elementContext: Ring<T>,
internal val lu: NDStructure<T>,
val lu: Structure2D<T>,
val pivot: IntArray,
private val even: Boolean
) : LUPDecompositionFeature<T>, DeterminantFeature<T> {
@ -62,33 +63,102 @@ class LUPDecomposition<T : Comparable<T>>(
}
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])
}
}
}
/**
* Common implementation of LUP [LinearSolver] based on commons-math code
* Specialized LU operations for Doubles
*/
class LUSolver<T : Comparable<T>, F : Field<T>>(
val context: GenericMatrixContext<T, F>,
val bufferFactory: MutableBufferFactory<T> = ::boxing,
val singularityCheck: (T) -> Boolean
) : LinearSolver<T> {
class RealBufferAccessor(rowNum: Int, colNum: Int) : BufferAccessor<Double>(Double::class, RealField, rowNum, colNum) {
override inline fun MutableBuffer<Double>.get(i: Int, j: Int) = (this as DoubleBuffer).array[i + colNum * j]
override inline 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])
}
}
fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.buildAccessor(
type:KClass<T>,
rowNum: Int,
colNum: Int
): BufferAccessor<T> {
return if (elementContext == RealField) {
@Suppress("UNCHECKED_CAST")
RealBufferAccessor(rowNum, colNum) as BufferAccessor<T>
} else {
BufferAccessor(type, elementContext, rowNum, colNum)
}
}
fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.abs(value: T) =
if (value > elementContext.zero) value else with(elementContext) { -value }
private fun abs(value: T) =
if (value > context.elementContext.zero) value else with(context.elementContext) { -value }
fun buildDecomposition(matrix: Matrix<T>): LUPDecomposition<T> {
fun <T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F>.lupDecompose(
type: KClass<T>,
matrix: Matrix<T>,
checkSingular: (T) -> Boolean
): LUPDecomposition<T> {
if (matrix.rowNum != matrix.colNum) {
error("LU decomposition supports only square matrices")
}
val m = matrix.colNum
val pivot = IntArray(matrix.rowNum)
val lu = Mutable2DStructure.create(matrix.rowNum, matrix.colNum, bufferFactory) { i, j ->
matrix[i, j]
}
buildAccessor(type, matrix.rowNum, matrix.colNum).run {
val lu = create(matrix)
with(context.elementContext) {
// Initialize permutation array and parity
for (row in 0 until m) {
pivot[row] = row
@ -100,26 +170,28 @@ class LUSolver<T : Comparable<T>, F : Field<T>>(
// upper
for (row in 0 until col) {
var sum = lu[row, col]
for (i in 0 until row) {
sum -= lu[row, i] * lu[i, col]
}
lu[row, col] = sum
// var sum = lu[row, col]
// for (i in 0 until row) {
// sum -= lu[row, i] * lu[i, col]
// }
val sum = lu.innerProduct(row, col, row)
lu[row, col] = field.run { lu[row, col] - sum }
}
// lower
val max = (col until m).maxBy { row ->
var sum = lu[row, col]
for (i in 0 until col) {
sum -= lu[row, i] * lu[i, col]
}
lu[row, col] = sum
// var sum = lu[row, col]
// for (i in 0 until col) {
// sum -= lu[row, i] * lu[i, col]
// }
// lu[row, col] = sum
val sum = lu.innerProduct(row, col, col)
lu[row, col] = field.run { lu[row, col] - sum }
abs(sum)
} ?: col
// Singularity check
if (singularityCheck(lu[max, col])) {
if (checkSingular(lu[max, col])) {
error("Singular matrix")
}
@ -138,70 +210,75 @@ class LUSolver<T : Comparable<T>, F : Field<T>>(
// Divide the lower elements by the "winning" diagonal elt.
val luDiag = lu[col, col]
for (row in col + 1 until m) {
lu[row, col] = lu[row, col] / luDiag
}
}
return LUPDecomposition(context.elementContext, lu, pivot, even)
lu.divideInPlace(row, col, luDiag)
//lu[row, col] = lu[row, col] / luDiag
}
}
return scientifik.kmath.linear.LUPDecomposition(elementContext, lu.collect(), pivot, even)
/**
* Produce a matrix with added decomposition feature
}
}
/**
* Solve a linear equation **a*x = b**
*/
fun decompose(matrix: Matrix<T>): Matrix<T> {
if (matrix.hasFeature<LUPDecomposition<*>>()) {
return matrix
} else {
val decomposition = buildDecomposition(matrix)
return VirtualMatrix.wrap(matrix, decomposition)
}
}
override fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
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}")
error("Matrix dimension mismatch. Expected ${a.rowNum}, but got ${b.colNum}")
}
// Use existing decomposition if it is provided by matrix
val decomposition = a.getFeature() ?: buildDecomposition(a)
val decomposition = a.getFeature() ?: lupDecompose(type, a, checkSingular)
buildAccessor(type, a.rowNum, a.colNum).run {
val lu = create(decomposition.lu)
with(decomposition) {
with(context.elementContext) {
// Apply permutations to b
val bp = Mutable2DStructure.create(a.rowNum, a.colNum, bufferFactory) { i, j ->
b[pivot[i], j]
val bp = create { i, j ->
b[decomposition.pivot[i], j]
}
// 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[i, j] -= bp[col, j] * lu[i, col]
bp.subtractInPlace(i, j, lu, col)
//bp[i, j] -= bp[col, j] * lu[i, col]
}
}
}
// Solve UX = Y
for (col in a.rowNum - 1 downTo 0) {
val luDiag = lu[col, col]
for (j in 0 until b.colNum) {
bp[col, j] /= lu[col, col]
bp.divideInPlace(col, j, luDiag)
//bp[col, j] /= lu[col, col]
}
for (i in 0 until col) {
for (j in 0 until b.colNum) {
bp[i, j] -= bp[col, j] * lu[i, col]
bp.subtractInPlace(i, j, lu, col)
//bp[i, j] -= bp[col, j] * lu[i, col]
}
}
}
return context.produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
}
}
return produce(a.rowNum, a.colNum) { i, j -> bp[i, j] }
}
override fun inverse(a: Matrix<T>): Matrix<T> = solve(a, context.one(a.rowNum, a.colNum))
companion object {
val real = LUSolver(MatrixContext.real, MutableBuffer.Companion::auto) { 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)
fun GenericMatrixContext<Double, RealField>.inverse(matrix: Matrix<Double>) =
inverse(matrix) { it < 1e-11 }

40
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/Mutable2DStructure.kt
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@ -1,40 +0,0 @@
package scientifik.kmath.linear
import scientifik.kmath.structures.MutableBuffer
import scientifik.kmath.structures.MutableBufferFactory
import scientifik.kmath.structures.MutableNDStructure
class Mutable2DStructure<T>(val rowNum: Int, val colNum: Int, val buffer: MutableBuffer<T>) : MutableNDStructure<T> {
override val shape: IntArray
get() = intArrayOf(rowNum, colNum)
operator fun get(i: Int, j: Int): T = buffer[i * colNum + j]
override fun get(index: IntArray): T = get(index[0], index[1])
override fun elements(): Sequence<Pair<IntArray, T>> = sequence {
for (i in 0 until rowNum) {
for (j in 0 until colNum) {
yield(intArrayOf(i, j) to get(i, j))
}
}
}
operator fun set(i: Int, j: Int, value: T) {
buffer[i * colNum + j] = value
}
override fun set(index: IntArray, value: T) = set(index[0], index[1], value)
companion object {
fun <T> create(
rowNum: Int,
colNum: Int,
bufferFactory: MutableBufferFactory<T>,
init: (i: Int, j: Int) -> T
): Mutable2DStructure<T> {
val buffer = bufferFactory(rowNum * colNum) { offset -> init(offset / colNum, offset % colNum) }
return Mutable2DStructure(rowNum, colNum, buffer)
}
}
}

33
kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/Buffers.kt
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@ -2,6 +2,7 @@ package scientifik.kmath.structures
import scientifik.kmath.operations.Complex
import scientifik.kmath.operations.complex
import kotlin.reflect.KClass
typealias BufferFactory<T> = (Int, (Int) -> T) -> Buffer<T>
@ -41,13 +42,10 @@ interface Buffer<T> {
*/
inline fun <T> boxing(size: Int, initializer: (Int) -> T): Buffer<T> = ListBuffer(List(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> {
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) })
}
}
}

15
kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDStructure.kt
View File

@ -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)
}