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Minimal refactor of existing random API, move samplers implementations to samplers package, implement Sampler<T> by all the Samplers

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Iaroslav 2020-06-08 17:16:57 +07:00
parent bc59f8b287
commit 28062cb096
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32 changed files with 485 additions and 903 deletions
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65
kmath-coroutines/src/commonMain/kotlin/scientifik/kmath/chains/Chain.kt
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@ -19,6 +19,7 @@ package scientifik.kmath.chains
import kotlinx.coroutines.InternalCoroutinesApi
import kotlinx.coroutines.flow.Flow
import kotlinx.coroutines.flow.FlowCollector
import kotlinx.coroutines.flow.flow
import kotlinx.coroutines.sync.Mutex
import kotlinx.coroutines.sync.withLock
@ -27,7 +28,7 @@ import kotlinx.coroutines.sync.withLock
* A not-necessary-Markov chain of some type
* @param R - the chain element type
*/
interface Chain<out R>: Flow<R> {
interface Chain<out R> : Flow<R> {
/**
* Generate next value, changing state if needed
*/
@ -39,13 +40,11 @@ interface Chain<out R>: Flow<R> {
fun fork(): Chain<R>
@OptIn(InternalCoroutinesApi::class)
override suspend fun collect(collector: FlowCollector<R>) {
kotlinx.coroutines.flow.flow {
while (true){
emit(next())
}
}.collect(collector)
}
override suspend fun collect(collector: FlowCollector<R>): Unit = flow {
while (true)
emit(next())
}.collect(collector)
companion object
}
@ -66,24 +65,18 @@ class SimpleChain<out R>(private val gen: suspend () -> R) : Chain<R> {
* A stateless Markov chain
*/
class MarkovChain<out R : Any>(private val seed: suspend () -> R, private val gen: suspend (R) -> R) : Chain<R> {
private val mutex = Mutex()
private val mutex: Mutex = Mutex()
private var value: R? = null
fun value() = value
override suspend fun next(): R {
mutex.withLock {
val newValue = gen(value ?: seed())
value = newValue
return newValue
}
override suspend fun next(): R = mutex.withLock {
val newValue = gen(value ?: seed())
value = newValue
return newValue
}
override fun fork(): Chain<R> {
return MarkovChain(seed = { value ?: seed() }, gen = gen)
}
override fun fork(): Chain<R> = MarkovChain(seed = { value ?: seed() }, gen = gen)
}
/**
@ -97,24 +90,18 @@ class StatefulChain<S, out R>(
private val forkState: ((S) -> S),
private val gen: suspend S.(R) -> R
) : Chain<R> {
private val mutex = Mutex()
private var value: R? = null
fun value() = value
override suspend fun next(): R {
mutex.withLock {
val newValue = state.gen(value ?: state.seed())
value = newValue
return newValue
}
override suspend fun next(): R = mutex.withLock {
val newValue = state.gen(value ?: state.seed())
value = newValue
return newValue
}
override fun fork(): Chain<R> {
return StatefulChain(forkState(state), seed, forkState, gen)
}
override fun fork(): Chain<R> = StatefulChain(forkState(state), seed, forkState, gen)
}
/**
@ -123,9 +110,7 @@ class StatefulChain<S, out R>(
class ConstantChain<out T>(val value: T) : Chain<T> {
override suspend fun next(): T = value
override fun fork(): Chain<T> {
return this
}
override fun fork(): Chain<T> = this
}
/**
@ -143,9 +128,8 @@ fun <T, R> Chain<T>.map(func: suspend (T) -> R): Chain<R> = object : Chain<R> {
fun <T> Chain<T>.filter(block: (T) -> Boolean): Chain<T> = object : Chain<T> {
override suspend fun next(): T {
var next: T
do {
next = this@filter.next()
} while (!block(next))
do next = this@filter.next()
while (!block(next))
return next
}
@ -163,7 +147,9 @@ fun <T, R> Chain<T>.collect(mapper: suspend (Chain<T>) -> R): Chain<R> = object
fun <T, S, R> Chain<T>.collectWithState(state: S, stateFork: (S) -> S, mapper: suspend S.(Chain<T>) -> R): Chain<R> =
object : Chain<R> {
override suspend fun next(): R = state.mapper(this@collectWithState)
override fun fork(): Chain<R> = this@collectWithState.fork().collectWithState(stateFork(state), stateFork, mapper)
override fun fork(): Chain<R> =
this@collectWithState.fork().collectWithState(stateFork(state), stateFork, mapper)
}
/**
@ -171,6 +157,5 @@ fun <T, S, R> Chain<T>.collectWithState(state: S, stateFork: (S) -> S, mapper: s
*/
fun <T, U, R> Chain<T>.zip(other: Chain<U>, block: suspend (T, U) -> R): Chain<R> = object : Chain<R> {
override suspend fun next(): R = block(this@zip.next(), other.next())
override fun fork(): Chain<R> = this@zip.fork().zip(other.fork(), block)
}
}

19
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/UniformRandomProvider.kt
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@ -1,19 +0,0 @@
package scientifik.kmath.commons.rng
interface UniformRandomProvider {
fun nextBytes(bytes: ByteArray)
fun nextBytes(
bytes: ByteArray,
start: Int,
len: Int
)
fun nextInt(): Int
fun nextInt(n: Int): Int
fun nextLong(): Long
fun nextLong(n: Long): Long
fun nextBoolean(): Boolean
fun nextFloat(): Float
fun nextDouble(): Double
}

7
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/SharedStateSampler.kt
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@ -1,7 +0,0 @@
package scientifik.kmath.commons.rng.sampling
import scientifik.kmath.commons.rng.UniformRandomProvider
interface SharedStateSampler<R> {
fun withUniformRandomProvider(rng: UniformRandomProvider): R
}

101
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/AhrensDieterExponentialSampler.kt
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@ -1,101 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.UniformRandomProvider
import kotlin.math.ln
import kotlin.math.pow
class AhrensDieterExponentialSampler : SamplerBase,
SharedStateContinuousSampler {
private val mean: Double
private val rng: UniformRandomProvider
constructor(
rng: UniformRandomProvider,
mean: Double
) : super(null) {
require(mean > 0) { "mean is not strictly positive: $mean" }
this.rng = rng
this.mean = mean
}
private constructor(
rng: UniformRandomProvider,
source: AhrensDieterExponentialSampler
) : super(null) {
this.rng = rng
mean = source.mean
}
override fun sample(): Double {
// Step 1:
var a = 0.0
var u: Double = rng.nextDouble()
// Step 2 and 3:
while (u < 0.5) {
a += EXPONENTIAL_SA_QI.get(
0
)
u *= 2.0
}
// Step 4 (now u >= 0.5):
u += u - 1
// Step 5:
if (u <= EXPONENTIAL_SA_QI.get(
0
)
) {
return mean * (a + u)
}
// Step 6:
var i = 0 // Should be 1, be we iterate before it in while using 0.
var u2: Double = rng.nextDouble()
var umin = u2
// Step 7 and 8:
do {
++i
u2 = rng.nextDouble()
if (u2 < umin) umin = u2
// Step 8:
} while (u > EXPONENTIAL_SA_QI[i]) // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1.
return mean * (a + umin * EXPONENTIAL_SA_QI[0])
}
override fun toString(): String = "Ahrens-Dieter Exponential deviate [$rng]"
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateContinuousSampler =
AhrensDieterExponentialSampler(rng, this)
companion object {
private val EXPONENTIAL_SA_QI = DoubleArray(16)
fun of(
rng: UniformRandomProvider,
mean: Double
): SharedStateContinuousSampler =
AhrensDieterExponentialSampler(
rng,
mean
)
init {
/**
* Filling EXPONENTIAL_SA_QI table.
* Note that we don't want qi = 0 in the table.
*/
val ln2 = ln(2.0)
var qi = 0.0
EXPONENTIAL_SA_QI.indices.forEach { i ->
qi += ln2.pow(i + 1.0) / InternalUtils.factorial(
i + 1
)
EXPONENTIAL_SA_QI[i] = qi
}
}
}
}

50
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/BoxMullerNormalizedGaussianSampler.kt
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@ -1,50 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.UniformRandomProvider
import kotlin.math.*
class BoxMullerNormalizedGaussianSampler(
private val rng: UniformRandomProvider
) :
NormalizedGaussianSampler,
SharedStateContinuousSampler {
private var nextGaussian: Double = Double.NaN
override fun sample(): Double {
val random: Double
if (nextGaussian.isNaN()) {
// Generate a pair of Gaussian numbers.
val x = rng.nextDouble()
val y = rng.nextDouble()
val alpha = 2 * PI * x
val r = sqrt(-2 * ln(y))
// Return the first element of the generated pair.
random = r * cos(alpha)
// Keep second element of the pair for next invocation.
nextGaussian = r * sin(alpha)
} else {
// Use the second element of the pair (generated at the
// previous invocation).
random = nextGaussian
// Both elements of the pair have been used.
nextGaussian = Double.NaN
}
return random
}
override fun toString(): String = "Box-Muller normalized Gaussian deviate [$rng]"
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateContinuousSampler =
BoxMullerNormalizedGaussianSampler(rng)
companion object {
@Suppress("UNCHECKED_CAST")
fun <S> of(rng: UniformRandomProvider): S where S : NormalizedGaussianSampler?, S : SharedStateContinuousSampler? =
BoxMullerNormalizedGaussianSampler(rng) as S
}
}

5
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/ContinuousSampler.kt
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@ -1,5 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
interface ContinuousSampler {
fun sample(): Double
}

5
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/DiscreteSampler.kt
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@ -1,5 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
interface DiscreteSampler {
fun sample(): Int
}

55
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/GaussianSampler.kt
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@ -1,55 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.UniformRandomProvider
class GaussianSampler :
SharedStateContinuousSampler {
private val mean: Double
private val standardDeviation: Double
private val normalized: NormalizedGaussianSampler
constructor(
normalized: NormalizedGaussianSampler,
mean: Double,
standardDeviation: Double
) {
require(standardDeviation > 0) { "standard deviation is not strictly positive: $standardDeviation" }
this.normalized = normalized
this.mean = mean
this.standardDeviation = standardDeviation
}
private constructor(
rng: UniformRandomProvider,
source: GaussianSampler
) {
mean = source.mean
standardDeviation = source.standardDeviation
normalized =
InternalUtils.newNormalizedGaussianSampler(
source.normalized,
rng
)
}
override fun sample(): Double = standardDeviation * normalized.sample() + mean
override fun toString(): String = "Gaussian deviate [$normalized]"
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateContinuousSampler {
return GaussianSampler(rng, this)
}
companion object {
fun of(
normalized: NormalizedGaussianSampler,
mean: Double,
standardDeviation: Double
): SharedStateContinuousSampler =
GaussianSampler(
normalized,
mean,
standardDeviation
)
}
}

251
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/LargenMeanPoissonSampler.kt
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@ -1,251 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.UniformRandomProvider
import kotlin.math.*
class LargeMeanPoissonSampler :
SharedStateDiscreteSampler {
private val rng: UniformRandomProvider
private val exponential: SharedStateContinuousSampler
private val gaussian: SharedStateContinuousSampler
private val factorialLog: InternalUtils.FactorialLog
private val lambda: Double
private val logLambda: Double
private val logLambdaFactorial: Double
private val delta: Double
private val halfDelta: Double
private val twolpd: Double
private val p1: Double
private val p2: Double
private val c1: Double
private val smallMeanPoissonSampler: SharedStateDiscreteSampler
constructor(
rng: UniformRandomProvider,
mean: Double
) {
require(mean >= 1) { "mean is not >= 1: $mean" }
// The algorithm is not valid if Math.floor(mean) is not an integer.
require(mean <= MAX_MEAN) { "mean $mean > $MAX_MEAN" }
this.rng = rng
gaussian =
ZigguratNormalizedGaussianSampler(rng)
exponential =
AhrensDieterExponentialSampler.of(
rng,
1.0
)
// Plain constructor uses the uncached function.
factorialLog = NO_CACHE_FACTORIAL_LOG!!
// Cache values used in the algorithm
lambda = floor(mean)
logLambda = ln(lambda)
logLambdaFactorial = getFactorialLog(lambda.toInt())
delta = sqrt(lambda * ln(32 * lambda / PI + 1))
halfDelta = delta / 2
twolpd = 2 * lambda + delta
c1 = 1 / (8 * lambda)
val a1: Double = sqrt(PI * twolpd) * exp(c1)
val a2: Double = twolpd / delta * exp(-delta * (1 + delta) / twolpd)
val aSum = a1 + a2 + 1
p1 = a1 / aSum
p2 = a2 / aSum
// The algorithm requires a Poisson sample from the remaining lambda fraction.
val lambdaFractional = mean - lambda
smallMeanPoissonSampler =
if (lambdaFractional < Double.MIN_VALUE) NO_SMALL_MEAN_POISSON_SAMPLER else // Not used.
KempSmallMeanPoissonSampler.of(
rng,
lambdaFractional
)
}
internal constructor(
rng: UniformRandomProvider,
state: LargeMeanPoissonSamplerState,
lambdaFractional: Double
) {
require(!(lambdaFractional < 0 || lambdaFractional >= 1)) { "lambdaFractional must be in the range 0 (inclusive) to 1 (exclusive): $lambdaFractional" }
this.rng = rng
gaussian =
ZigguratNormalizedGaussianSampler(rng)
exponential =
AhrensDieterExponentialSampler.of(
rng,
1.0
)
// Plain constructor uses the uncached function.
factorialLog = NO_CACHE_FACTORIAL_LOG!!
// Use the state to initialise the algorithm
lambda = state.lambdaRaw
logLambda = state.logLambda
logLambdaFactorial = state.logLambdaFactorial
delta = state.delta
halfDelta = state.halfDelta
twolpd = state.twolpd
p1 = state.p1
p2 = state.p2
c1 = state.c1
// The algorithm requires a Poisson sample from the remaining lambda fraction.
smallMeanPoissonSampler =
if (lambdaFractional < Double.MIN_VALUE)
NO_SMALL_MEAN_POISSON_SAMPLER
else // Not used.
KempSmallMeanPoissonSampler.of(
rng,
lambdaFractional
)
}
/**
* @param rng Generator of uniformly distributed random numbers.
* @param source Source to copy.
*/
private constructor(
rng: UniformRandomProvider,
source: LargeMeanPoissonSampler
) {
this.rng = rng
gaussian = source.gaussian.withUniformRandomProvider(rng)!!
exponential = source.exponential.withUniformRandomProvider(rng)!!
// Reuse the cache
factorialLog = source.factorialLog
lambda = source.lambda
logLambda = source.logLambda
logLambdaFactorial = source.logLambdaFactorial
delta = source.delta
halfDelta = source.halfDelta
twolpd = source.twolpd
p1 = source.p1
p2 = source.p2
c1 = source.c1
// Share the state of the small sampler
smallMeanPoissonSampler = source.smallMeanPoissonSampler.withUniformRandomProvider(rng)!!
}
/** {@inheritDoc} */
override fun sample(): Int {
// This will never be null. It may be a no-op delegate that returns zero.
val y2: Int = smallMeanPoissonSampler.sample()
var x: Double
var y: Double
var v: Double
var a: Int
var t: Double
var qr: Double
var qa: Double
while (true) {
// Step 1:
val u = rng.nextDouble()
if (u <= p1) {
// Step 2:
val n = gaussian.sample()
x = n * sqrt(lambda + halfDelta) - 0.5
if (x > delta || x < -lambda) continue
y = if (x < 0) floor(x) else ceil(x)
val e = exponential.sample()
v = -e - 0.5 * n * n + c1
} else {
// Step 3:
if (u > p1 + p2) {
y = lambda
break
}
x = delta + twolpd / delta * exponential.sample()
y = ceil(x)
v = -exponential.sample() - delta * (x + 1) / twolpd
}
// The Squeeze Principle
// Step 4.1:
a = if (x < 0) 1 else 0
t = y * (y + 1) / (2 * lambda)
// Step 4.2
if (v < -t && a == 0) {
y += lambda
break
}
// Step 4.3:
qr = t * ((2 * y + 1) / (6 * lambda) - 1)
qa = qr - t * t / (3 * (lambda + a * (y + 1)))
// Step 4.4:
if (v < qa) {
y += lambda
break
}
// Step 4.5:
if (v > qr) continue
// Step 4.6:
if (v < y * logLambda - getFactorialLog((y + lambda).toInt()) + logLambdaFactorial) {
y += lambda
break
}
}
return min(y2 + y.toLong(), Int.MAX_VALUE.toLong()).toInt()
}
private fun getFactorialLog(n: Int): Double = factorialLog.value(n)
override fun toString(): String = "Large Mean Poisson deviate [$rng]"
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateDiscreteSampler =
LargeMeanPoissonSampler(rng, this)
val state: LargeMeanPoissonSamplerState
get() = LargeMeanPoissonSamplerState(
lambda, logLambda, logLambdaFactorial,
delta, halfDelta, twolpd, p1, p2, c1
)
class LargeMeanPoissonSamplerState(
val lambdaRaw: Double,
val logLambda: Double,
val logLambdaFactorial: Double,
val delta: Double,
val halfDelta: Double,
val twolpd: Double,
val p1: Double,
val p2: Double,
val c1: Double
) {
fun getLambda(): Int = lambdaRaw.toInt()
}
companion object {
private const val MAX_MEAN = 0.5 * Int.MAX_VALUE
private var NO_CACHE_FACTORIAL_LOG: InternalUtils.FactorialLog? = null
private val NO_SMALL_MEAN_POISSON_SAMPLER: SharedStateDiscreteSampler =
object : SharedStateDiscreteSampler {
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateDiscreteSampler =
// No requirement for RNG
this
override fun sample(): Int =// No Poisson sample
0
}
fun of(
rng: UniformRandomProvider,
mean: Double
): SharedStateDiscreteSampler =
LargeMeanPoissonSampler(rng, mean)
init {
// Create without a cache.
NO_CACHE_FACTORIAL_LOG =
InternalUtils.FactorialLog.create()
}
}
}

4
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/NormalizedGaussianSampler.kt
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@ -1,4 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
interface NormalizedGaussianSampler :
ContinuousSampler

40
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/PoissonSampler.kt
View File

@ -1,40 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.UniformRandomProvider
class PoissonSampler(
rng: UniformRandomProvider,
mean: Double
) : SamplerBase(null),
SharedStateDiscreteSampler {
private val poissonSamplerDelegate: SharedStateDiscreteSampler
override fun sample(): Int = poissonSamplerDelegate.sample()
override fun toString(): String = poissonSamplerDelegate.toString()
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateDiscreteSampler? =
// Direct return of the optimised sampler
poissonSamplerDelegate.withUniformRandomProvider(rng)
companion object {
const val PIVOT = 40.0
fun of(
rng: UniformRandomProvider,
mean: Double
): SharedStateDiscreteSampler =// Each sampler should check the input arguments.
if (mean < PIVOT) SmallMeanPoissonSampler.of(
rng,
mean
) else LargeMeanPoissonSampler.of(
rng,
mean
)
}
init {
// Delegate all work to specialised samplers.
poissonSamplerDelegate =
of(rng, mean)
}
}

12
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/SamplerBase.kt
View File

@ -1,12 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.UniformRandomProvider
@Deprecated("Since version 1.1. Class intended for internal use only.")
open class SamplerBase protected constructor(private val rng: UniformRandomProvider?) {
protected fun nextDouble(): Double = rng!!.nextDouble()
protected fun nextInt(): Int = rng!!.nextInt()
protected fun nextInt(max: Int): Int = rng!!.nextInt(max)
protected fun nextLong(): Long = rng!!.nextLong()
override fun toString(): String = "rng=$rng"
}

7
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/SharedStateContinuousSampler.kt
View File

@ -1,7 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.sampling.SharedStateSampler
interface SharedStateContinuousSampler : ContinuousSampler,
SharedStateSampler<SharedStateContinuousSampler?> {
}

7
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/SharedStateDiscreteSampler.kt
View File

@ -1,7 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.sampling.SharedStateSampler
interface SharedStateDiscreteSampler : DiscreteSampler,
SharedStateSampler<SharedStateDiscreteSampler?> { // Composite interface
}

60
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/SmallMeanPoissonSampler.kt
View File

@ -1,60 +0,0 @@
package scientifik.kmath.commons.rng.sampling.distribution
import scientifik.kmath.commons.rng.UniformRandomProvider
import kotlin.math.ceil
import kotlin.math.exp
class SmallMeanPoissonSampler :
SharedStateDiscreteSampler {
private val p0: Double
private val limit: Int
private val rng: UniformRandomProvider
constructor(
rng: UniformRandomProvider,
mean: Double
) {
this.rng = rng
require(mean > 0) { "mean is not strictly positive: $mean" }
p0 = exp(-mean)
limit = (if (p0 > 0) ceil(1000 * mean) else throw IllegalArgumentException("No p(x=0) probability for mean: $mean")).toInt()
// This excludes NaN values for the mean
// else
// The returned sample is bounded by 1000 * mean
}
private constructor(
rng: UniformRandomProvider,
source: SmallMeanPoissonSampler
) {
this.rng = rng
p0 = source.p0
limit = source.limit
}
override fun sample(): Int {
var n = 0
var r = 1.0
while (n < limit) {
r *= rng.nextDouble()
if (r >= p0) n++ else break
}
return n
}
override fun toString(): String = "Small Mean Poisson deviate [$rng]"
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateDiscreteSampler =
SmallMeanPoissonSampler(rng, this)
companion object {
fun of(
rng: UniformRandomProvider,
mean: Double
): SharedStateDiscreteSampler =
SmallMeanPoissonSampler(rng, mean)
}
}

3
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/Distribution.kt
View File

@ -1,5 +1,6 @@
package scientifik.kmath.prob
import kotlinx.coroutines.flow.first
import scientifik.kmath.chains.Chain
import scientifik.kmath.chains.collect
import scientifik.kmath.structures.Buffer
@ -69,6 +70,8 @@ fun <T : Any> Sampler<T>.sampleBuffer(
}
}
suspend fun <T : Any> Sampler<T>.next(generator: RandomGenerator) = sample(generator).first()
/**
* Generate a bunch of samples from real distributions
*/

1
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/FactorizedDistribution.kt
View File

@ -12,7 +12,6 @@ interface NamedDistribution<T> : Distribution<Map<String, T>>
* A multivariate distribution that has independent distributions for separate axis
*/
class FactorizedDistribution<T>(val distributions: Collection<NamedDistribution<T>>) : NamedDistribution<T> {
override fun probability(arg: Map<String, T>): Double {
return distributions.fold(1.0) { acc, distr -> acc * distr.probability(arg) }
}

10
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/RandomGenerator.kt
View File

@ -7,13 +7,11 @@ import kotlin.random.Random
*/
interface RandomGenerator {
fun nextBoolean(): Boolean
fun nextDouble(): Double
fun nextInt(): Int
fun nextInt(until: Int): Int
fun nextLong(): Long
fun nextLong(until: Long): Long
fun fillBytes(array: ByteArray, fromIndex: Int = 0, toIndex: Int = array.size)
fun nextBytes(size: Int): ByteArray = ByteArray(size).also { fillBytes(it) }
@ -28,21 +26,16 @@ interface RandomGenerator {
companion object {
val default by lazy { DefaultGenerator() }
fun default(seed: Long) = DefaultGenerator(Random(seed))
}
}
inline class DefaultGenerator(val random: Random = Random) : RandomGenerator {
inline class DefaultGenerator(private val random: Random = Random) : RandomGenerator {
override fun nextBoolean(): Boolean = random.nextBoolean()
override fun nextDouble(): Double = random.nextDouble()
override fun nextInt(): Int = random.nextInt()
override fun nextInt(until: Int): Int = random.nextInt(until)
override fun nextLong(): Long = random.nextLong()
override fun nextLong(until: Long): Long = random.nextLong(until)
override fun fillBytes(array: ByteArray, fromIndex: Int, toIndex: Int) {
@ -50,6 +43,5 @@ inline class DefaultGenerator(val random: Random = Random) : RandomGenerator {
}
override fun nextBytes(size: Int): ByteArray = random.nextBytes(size)
override fun fork(): RandomGenerator = RandomGenerator.default(random.nextLong())
}

68
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/AhrensDieterExponentialSampler.kt Normal file
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@ -0,0 +1,68 @@
package scientifik.kmath.prob.samplers
import scientifik.kmath.chains.Chain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
import scientifik.kmath.prob.chain
import kotlin.math.ln
import kotlin.math.pow
class AhrensDieterExponentialSampler(val mean: Double) : Sampler<Double> {
init {
require(mean > 0) { "mean is not strictly positive: $mean" }
}
override fun sample(generator: RandomGenerator): Chain<Double> = generator.chain {
// Step 1:
var a = 0.0
var u = nextDouble()
// Step 2 and 3:
while (u < 0.5) {
a += EXPONENTIAL_SA_QI[0]
u *= 2.0
}
// Step 4 (now u >= 0.5):
u += u - 1
// Step 5:
if (u <= EXPONENTIAL_SA_QI[0]) return@chain mean * (a + u)
// Step 6:
var i = 0 // Should be 1, be we iterate before it in while using 0.
var u2 = nextDouble()
var umin = u2
// Step 7 and 8:
do {
++i
u2 = nextDouble()
if (u2 < umin) umin = u2
// Step 8:
} while (u > EXPONENTIAL_SA_QI[i]) // Ensured to exit since EXPONENTIAL_SA_QI[MAX] = 1.
mean * (a + umin * EXPONENTIAL_SA_QI[0])
}
override fun toString(): String = "Ahrens-Dieter Exponential deviate"
companion object {
private val EXPONENTIAL_SA_QI = DoubleArray(16)
fun of(mean: Double): Sampler<Double> =
AhrensDieterExponentialSampler(mean)
init {
/**
* Filling EXPONENTIAL_SA_QI table.
* Note that we don't want qi = 0 in the table.
*/
val ln2 = ln(2.0)
var qi = 0.0
EXPONENTIAL_SA_QI.indices.forEach { i ->
qi += ln2.pow(i + 1.0) / InternalUtils.factorial(i + 1)
EXPONENTIAL_SA_QI[i] = qi
}
}
}
}

37
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/BoxMullerNormalizedGaussianSampler.kt Normal file
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@ -0,0 +1,37 @@
package scientifik.kmath.prob.samplers
import scientifik.kmath.chains.Chain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
import scientifik.kmath.prob.chain
import kotlin.math.*
class BoxMullerNormalizedGaussianSampler : NormalizedGaussianSampler, Sampler<Double> {
private var nextGaussian: Double = Double.NaN
override fun sample(generator: RandomGenerator): Chain<Double> = generator.chain {
val random: Double
if (nextGaussian.isNaN()) {
// Generate a pair of Gaussian numbers.
val x = nextDouble()
val y = nextDouble()
val alpha = 2 * PI * x
val r = sqrt(-2 * ln(y))
// Return the first element of the generated pair.
random = r * cos(alpha)
// Keep second element of the pair for next invocation.
nextGaussian = r * sin(alpha)
} else {
// Use the second element of the pair (generated at the
// previous invocation).
random = nextGaussian
// Both elements of the pair have been used.
nextGaussian = Double.NaN
}
random
}
override fun toString(): String = "Box-Muller normalized Gaussian deviate"
}

34
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/GaussianSampler.kt Normal file
View File

@ -0,0 +1,34 @@
package scientifik.kmath.prob.samplers
import scientifik.kmath.chains.Chain
import scientifik.kmath.chains.map
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
class GaussianSampler(
private val mean: Double,
private val standardDeviation: Double,
private val normalized: NormalizedGaussianSampler
) : Sampler<Double> {
init {
require(standardDeviation > 0) { "standard deviation is not strictly positive: $standardDeviation" }
}
override fun sample(generator: RandomGenerator): Chain<Double> =
normalized.sample(generator).map { standardDeviation * it + mean }
override fun toString(): String = "Gaussian deviate [$normalized]"
companion object {
fun of(
normalized: NormalizedGaussianSampler,
mean: Double,
standardDeviation: Double
) = GaussianSampler(
mean,
standardDeviation,
normalized
)
}
}

4
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/InternalGamma.kt → kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/InternalGamma.kt
View File

@ -1,10 +1,10 @@
package scientifik.kmath.commons.rng.sampling.distribution
package scientifik.kmath.prob.samplers
import kotlin.math.PI
import kotlin.math.ln
internal object InternalGamma {
const val LANCZOS_G = 607.0 / 128.0
private const val LANCZOS_G = 607.0 / 128.0
private val LANCZOS_COEFFICIENTS = doubleArrayOf(
0.99999999999999709182,

50
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/InternalUtils.kt → kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/InternalUtils.kt
View File

@ -1,7 +1,5 @@
package scientifik.kmath.commons.rng.sampling.distribution
package scientifik.kmath.prob.samplers
import scientifik.kmath.commons.rng.UniformRandomProvider
import scientifik.kmath.commons.rng.sampling.SharedStateSampler
import kotlin.math.ln
import kotlin.math.min
@ -20,8 +18,8 @@ internal object InternalUtils {
fun factorial(n: Int): Long = FACTORIALS[n]
fun validateProbabilities(probabilities: DoubleArray?): Double {
require(!(probabilities == null || probabilities.isEmpty())) { "Probabilities must not be empty." }
fun validateProbabilities(probabilities: DoubleArray): Double {
require(probabilities.isNotEmpty()) { "Probabilities must not be empty." }
var sumProb = 0.0
probabilities.forEach { prob ->
@ -33,23 +31,10 @@ internal object InternalUtils {
return sumProb
}
fun validateProbability(probability: Double): Unit =
require(!(probability < 0 || probability.isInfinite() || probability.isNaN())) { "Invalid probability: $probability" }
fun newNormalizedGaussianSampler(
sampler: NormalizedGaussianSampler,
rng: UniformRandomProvider
): NormalizedGaussianSampler {
if (sampler !is SharedStateSampler<*>) throw UnsupportedOperationException("The underlying sampler cannot share state")
val newSampler: Any =
(sampler as SharedStateSampler<*>).withUniformRandomProvider(rng) as? NormalizedGaussianSampler
?: throw UnsupportedOperationException(
"The underlying sampler did not create a normalized Gaussian sampler"
)
return newSampler as NormalizedGaussianSampler
}
private fun validateProbability(probability: Double): Unit =
require(!(probability < 0 || probability.isInfinite() || probability.isNaN())) {
"Invalid probability: $probability"
}
class FactorialLog private constructor(
numValues: Int,
@ -68,23 +53,19 @@ internal object InternalUtils {
BEGIN_LOG_FACTORIALS, endCopy)
}
// All values to be computed
else
endCopy =
BEGIN_LOG_FACTORIALS
else endCopy = BEGIN_LOG_FACTORIALS
// Compute remaining values.
(endCopy until numValues).forEach { i ->
if (i < FACTORIALS.size) logFactorials[i] = ln(
FACTORIALS[i].toDouble()) else logFactorials[i] =
logFactorials[i - 1] + ln(i.toDouble())
if (i < FACTORIALS.size)
logFactorials[i] = ln(FACTORIALS[i].toDouble())
else
logFactorials[i] = logFactorials[i - 1] + ln(i.toDouble())
}
}
fun withCache(cacheSize: Int): FactorialLog =
FactorialLog(
cacheSize,
logFactorials
)
FactorialLog(cacheSize, logFactorials)
fun value(n: Int): Double {
if (n < logFactorials.size)
@ -98,10 +79,7 @@ internal object InternalUtils {
companion object {
fun create(): FactorialLog =
FactorialLog(
0,
null
)
FactorialLog(0, null)
}
}
}

35
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/KempSmallMeanPoissonSampler.kt → kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/KempSmallMeanPoissonSampler.kt
View File

@ -1,14 +1,16 @@
package scientifik.kmath.commons.rng.sampling.distribution
package scientifik.kmath.prob.samplers
import scientifik.kmath.commons.rng.UniformRandomProvider
import scientifik.kmath.chains.Chain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
import scientifik.kmath.prob.chain
import kotlin.math.exp
class KempSmallMeanPoissonSampler private constructor(
private val rng: UniformRandomProvider,
private val p0: Double,
private val mean: Double
) : SharedStateDiscreteSampler {
override fun sample(): Int {
) : Sampler<Int> {
override fun sample(generator: RandomGenerator): Chain<Int> = generator.chain {
// Note on the algorithm:
// - X is the unknown sample deviate (the output of the algorithm)
// - x is the current value from the distribution
@ -16,7 +18,7 @@ class KempSmallMeanPoissonSampler private constructor(
// - u is effectively the cumulative probability that the sample X
// is equal or above the current value x, p(X>=x)
// So if p(X>=x) > p(X=x) the sample must be above x, otherwise it is x
var u = rng.nextDouble()
var u = nextDouble()
var x = 0
var p = p0
@ -28,31 +30,20 @@ class KempSmallMeanPoissonSampler private constructor(
// The algorithm listed in Kemp (1981) does not check that the rolling probability
// is positive. This check is added to ensure no errors when the limit of the summation
// 1 - sum(p(x)) is above 0 due to cumulative error in floating point arithmetic.
if (p == 0.0) return x
if (p == 0.0) return@chain x
}
return x
x
}
override fun toString(): String = "Kemp Small Mean Poisson deviate [$rng]"
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateDiscreteSampler =
KempSmallMeanPoissonSampler(rng, p0, mean)
override fun toString(): String = "Kemp Small Mean Poisson deviate"
companion object {
fun of(
rng: UniformRandomProvider,
mean: Double
): SharedStateDiscreteSampler {
fun of(mean: Double): KempSmallMeanPoissonSampler {
require(mean > 0) { "Mean is not strictly positive: $mean" }
val p0: Double = exp(-mean)
// Probability must be positive. As mean increases then p(0) decreases.
if (p0 > 0) return KempSmallMeanPoissonSampler(
rng,
p0,
mean
)
if (p0 > 0) return KempSmallMeanPoissonSampler(p0, mean)
throw IllegalArgumentException("No probability for mean: $mean")
}
}

132
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/LargeMeanPoissonSampler.kt Normal file
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@ -0,0 +1,132 @@
package scientifik.kmath.prob.samplers
import kotlinx.coroutines.flow.first
import scientifik.kmath.chains.Chain
import scientifik.kmath.chains.ConstantChain
import scientifik.kmath.chains.SimpleChain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
import scientifik.kmath.prob.next
import kotlin.math.*
class LargeMeanPoissonSampler(val mean: Double) : Sampler<Int> {
private val exponential: Sampler<Double> =
AhrensDieterExponentialSampler.of(1.0)
private val gaussian: Sampler<Double> =
ZigguratNormalizedGaussianSampler()
private val factorialLog: InternalUtils.FactorialLog = NO_CACHE_FACTORIAL_LOG!!
private val lambda: Double = floor(mean)
private val logLambda: Double = ln(lambda)
private val logLambdaFactorial: Double = getFactorialLog(lambda.toInt())
private val delta: Double = sqrt(lambda * ln(32 * lambda / PI + 1))
private val halfDelta: Double = delta / 2
private val twolpd: Double = 2 * lambda + delta
private val c1: Double = 1 / (8 * lambda)
private val a1: Double = sqrt(PI * twolpd) * exp(c1)
private val a2: Double = twolpd / delta * exp(-delta * (1 + delta) / twolpd)
private val aSum: Double = a1 + a2 + 1
private val p1: Double = a1 / aSum
private val p2: Double = a2 / aSum
private val smallMeanPoissonSampler: Sampler<Int> = if (mean - lambda < Double.MIN_VALUE)
NO_SMALL_MEAN_POISSON_SAMPLER
else // Not used.
KempSmallMeanPoissonSampler.of(mean - lambda)
init {
require(mean >= 1) { "mean is not >= 1: $mean" }
// The algorithm is not valid if Math.floor(mean) is not an integer.
require(mean <= MAX_MEAN) { "mean $mean > $MAX_MEAN" }
}
override fun sample(generator: RandomGenerator): Chain<Int> = SimpleChain {
// This will never be null. It may be a no-op delegate that returns zero.
val y2 = smallMeanPoissonSampler.next(generator)
var x: Double
var y: Double
var v: Double
var a: Int
var t: Double
var qr: Double
var qa: Double
while (true) {
// Step 1:
val u = generator.nextDouble()
if (u <= p1) {
// Step 2:
val n = gaussian.next(generator)
x = n * sqrt(lambda + halfDelta) - 0.5
if (x > delta || x < -lambda) continue
y = if (x < 0) floor(x) else ceil(x)
val e = exponential.next(generator)
v = -e - 0.5 * n * n + c1
} else {
// Step 3:
if (u > p1 + p2) {
y = lambda
break
}
x = delta + twolpd / delta * exponential.next(generator)
y = ceil(x)
v = -exponential.next(generator) - delta * (x + 1) / twolpd
}
// The Squeeze Principle
// Step 4.1:
a = if (x < 0) 1 else 0
t = y * (y + 1) / (2 * lambda)
// Step 4.2
if (v < -t && a == 0) {
y += lambda
break
}
// Step 4.3:
qr = t * ((2 * y + 1) / (6 * lambda) - 1)
qa = qr - t * t / (3 * (lambda + a * (y + 1)))
// Step 4.4:
if (v < qa) {
y += lambda
break
}
// Step 4.5:
if (v > qr) continue
// Step 4.6:
if (v < y * logLambda - getFactorialLog((y + lambda).toInt()) + logLambdaFactorial) {
y += lambda
break
}
}
min(y2 + y.toLong(), Int.MAX_VALUE.toLong()).toInt()
}
private fun getFactorialLog(n: Int): Double = factorialLog.value(n)
override fun toString(): String = "Large Mean Poisson deviate"
companion object {
private const val MAX_MEAN = 0.5 * Int.MAX_VALUE
private var NO_CACHE_FACTORIAL_LOG: InternalUtils.FactorialLog? = null
private val NO_SMALL_MEAN_POISSON_SAMPLER = object : Sampler<Int> {
override fun sample(generator: RandomGenerator): Chain<Int> = ConstantChain(0)
}
fun of(mean: Double): LargeMeanPoissonSampler =
LargeMeanPoissonSampler(mean)
init {
// Create without a cache.
NO_CACHE_FACTORIAL_LOG =
InternalUtils.FactorialLog.create()
}
}
}

42
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/MarsagliaNormalizedGaussianSampler.kt → kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/MarsagliaNormalizedGaussianSampler.kt
View File

@ -1,35 +1,42 @@
package scientifik.kmath.commons.rng.sampling.distribution
package scientifik.kmath.prob.samplers
import scientifik.kmath.commons.rng.UniformRandomProvider
import scientifik.kmath.chains.Chain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
import scientifik.kmath.prob.chain
import kotlin.math.ln
import kotlin.math.sqrt
class MarsagliaNormalizedGaussianSampler(private val rng: UniformRandomProvider) :
NormalizedGaussianSampler,
SharedStateContinuousSampler {
class MarsagliaNormalizedGaussianSampler : NormalizedGaussianSampler, Sampler<Double> {
private var nextGaussian = Double.NaN
override fun sample(): Double {
override fun sample(generator: RandomGenerator): Chain<Double> = generator.chain {
if (nextGaussian.isNaN()) {
val alpha: Double
var x: Double
// Rejection scheme for selecting a pair that lies within the unit circle.
while (true) {
// Generate a pair of numbers within [-1 , 1).
val x = 2.0 * rng.nextDouble() - 1.0
val y = 2.0 * rng.nextDouble() - 1.0
x = 2.0 * generator.nextDouble() - 1.0
val y = 2.0 * generator.nextDouble() - 1.0
val r2 = x * x + y * y
if (r2 < 1 && r2 > 0) {
// Pair (x, y) is within unit circle.
val alpha = sqrt(-2 * ln(r2) / r2)
alpha = sqrt(-2 * ln(r2) / r2)
// Keep second element of the pair for next invocation.
nextGaussian = alpha * y
// Return the first element of the generated pair.
return alpha * x
break
}
// Pair is not within the unit circle: Generate another one.
}
// Return the first element of the generated pair.
alpha * x
} else {
// Use the second element of the pair (generated at the
// previous invocation).
@ -37,18 +44,9 @@ class MarsagliaNormalizedGaussianSampler(private val rng: UniformRandomProvider)
// Both elements of the pair have been used.
nextGaussian = Double.NaN
return r
r
}
}
override fun toString(): String = "Box-Muller (with rejection) normalized Gaussian deviate [$rng]"
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateContinuousSampler =
MarsagliaNormalizedGaussianSampler(rng)
companion object {
@Suppress("UNCHECKED_CAST")
fun <S> of(rng: UniformRandomProvider): S where S : NormalizedGaussianSampler?, S : SharedStateContinuousSampler? =
MarsagliaNormalizedGaussianSampler(rng) as S
}
override fun toString(): String = "Box-Muller (with rejection) normalized Gaussian deviate"
}

5
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/NormalizedGaussianSampler.kt Normal file
View File

@ -0,0 +1,5 @@
package scientifik.kmath.prob.samplers
import scientifik.kmath.prob.Sampler
interface NormalizedGaussianSampler : Sampler<Double>

29
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/PoissonSampler.kt Normal file
View File

@ -0,0 +1,29 @@
package scientifik.kmath.prob.samplers
import scientifik.kmath.chains.Chain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
class PoissonSampler(
mean: Double
) : Sampler<Int> {
private val poissonSamplerDelegate: Sampler<Int>
init {
// Delegate all work to specialised samplers.
poissonSamplerDelegate = of(mean)
}
override fun sample(generator: RandomGenerator): Chain<Int> = poissonSamplerDelegate.sample(generator)
override fun toString(): String = poissonSamplerDelegate.toString()
companion object {
private const val PIVOT = 40.0
fun of(mean: Double) =// Each sampler should check the input arguments.
if (mean < PIVOT) SmallMeanPoissonSampler.of(
mean
) else LargeMeanPoissonSampler.of(mean)
}
}

43
kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/SmallMeanPoissonSampler.kt Normal file
View File

@ -0,0 +1,43 @@
package scientifik.kmath.prob.samplers
import scientifik.kmath.chains.Chain
import scientifik.kmath.chains.SimpleChain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
import scientifik.kmath.prob.chain
import kotlin.math.ceil
import kotlin.math.exp
class SmallMeanPoissonSampler(mean: Double) : Sampler<Int> {
private val p0: Double
private val limit: Int
init {
require(mean > 0) { "mean is not strictly positive: $mean" }
p0 = exp(-mean)
limit = (if (p0 > 0)
ceil(1000 * mean)
else
throw IllegalArgumentException("No p(x=0) probability for mean: $mean")).toInt()
}
override fun sample(generator: RandomGenerator): Chain<Int> = generator.chain {
var n = 0
var r = 1.0
while (n < limit) {
r *= nextDouble()
if (r >= p0) n++ else break
}
n
}
override fun toString(): String = "Small Mean Poisson deviate"
companion object {
fun of(mean: Double): SmallMeanPoissonSampler =
SmallMeanPoissonSampler(mean)
}
}

118
kmath-prob/src/commonMain/kotlin/scientifik/kmath/commons/rng/sampling/distribution/ZigguratNormalizedGaussianSampler.kt → kmath-prob/src/commonMain/kotlin/scientifik/kmath/prob/samplers/ZigguratNormalizedGaussianSampler.kt
View File

@ -1,38 +1,76 @@
package scientifik.kmath.commons.rng.sampling.distribution
package scientifik.kmath.prob.samplers
import scientifik.kmath.commons.rng.UniformRandomProvider
import scientifik.kmath.chains.Chain
import scientifik.kmath.chains.SimpleChain
import scientifik.kmath.prob.RandomGenerator
import scientifik.kmath.prob.Sampler
import scientifik.kmath.prob.chain
import kotlin.math.*
class ZigguratNormalizedGaussianSampler(private val rng: UniformRandomProvider) :
NormalizedGaussianSampler,
SharedStateContinuousSampler {
class ZigguratNormalizedGaussianSampler() :
NormalizedGaussianSampler, Sampler<Double> {
private fun sampleOne(generator: RandomGenerator): Double {
val j = generator.nextLong()
val i = (j and LAST.toLong()).toInt()
return if (abs(j) < K[i]) j * W[i] else fix(generator, j, i)
}
override fun sample(generator: RandomGenerator): Chain<Double> = generator.chain { sampleOne(this) }
override fun toString(): String = "Ziggurat normalized Gaussian deviate"
private fun fix(
generator: RandomGenerator,
hz: Long,
iz: Int
): Double {
var x: Double
var y: Double
x = hz * W[iz]
return if (iz == 0) {
// Base strip.
// This branch is called about 5.7624515E-4 times per sample.
do {
y = -ln(generator.nextDouble())
x = -ln(generator.nextDouble()) * ONE_OVER_R
} while (y + y < x * x)
val out = R + x
if (hz > 0) out else -out
} else {
// Wedge of other strips.
// This branch is called about 0.027323 times per sample.
// else
// Try again.
// This branch is called about 0.012362 times per sample.
if (F[iz] + generator.nextDouble() * (F[iz - 1] - F[iz]) < gauss(
x
)
) x else sampleOne(generator)
}
}
companion object {
private const val R = 3.442619855899
private const val R: Double = 3.442619855899
private const val ONE_OVER_R: Double = 1 / R
private const val V = 9.91256303526217e-3
private val MAX: Double = 2.0.pow(63.0)
private val ONE_OVER_MAX: Double = 1.0 / MAX
private const val LEN = 128
private const val LEN: Int = 128
private const val LAST: Int = LEN - 1
private val K = LongArray(LEN)
private val W = DoubleArray(LEN)
private val F = DoubleArray(LEN)
private val K: LongArray = LongArray(LEN)
private val W: DoubleArray = DoubleArray(LEN)
private val F: DoubleArray = DoubleArray(LEN)
private fun gauss(x: Double): Double = exp(-0.5 * x * x)
@Suppress("UNCHECKED_CAST")
fun <S> of(rng: UniformRandomProvider): S where S : NormalizedGaussianSampler?, S : SharedStateContinuousSampler? =
ZigguratNormalizedGaussianSampler(rng) as S
init {
// Filling the tables.
var d =
R
var d = R
var t = d
var fd =
gauss(
d
)
gauss(d)
val q = V / fd
K[0] = (d / q * MAX).toLong()
K[1] = 0
@ -54,46 +92,4 @@ class ZigguratNormalizedGaussianSampler(private val rng: UniformRandomProvider)
}
}
}
override fun sample(): Double {
val j = rng.nextLong()
val i = (j and LAST.toLong()).toInt()
return if (abs(j) < K[i]) j * W[i] else fix(j, i)
}
override fun toString(): String = "Ziggurat normalized Gaussian deviate [$rng]"
private fun fix(
hz: Long,
iz: Int
): Double {
var x: Double
var y: Double
x = hz * W[iz]
return if (iz == 0) {
// Base strip.
// This branch is called about 5.7624515E-4 times per sample.
do {
y = -ln(rng.nextDouble())
x = -ln(rng.nextDouble()) * ONE_OVER_R
} while (y + y < x * x)
val out = R + x
if (hz > 0) out else -out
} else {
// Wedge of other strips.
// This branch is called about 0.027323 times per sample.
// else
// Try again.
// This branch is called about 0.012362 times per sample.
if (F[iz] + rng.nextDouble() * (F[iz - 1] - F[iz]) < gauss(
x
)
) x else sample()
}
}
override fun withUniformRandomProvider(rng: UniformRandomProvider): SharedStateContinuousSampler =
ZigguratNormalizedGaussianSampler(rng)
}

66
kmath-prob/src/jvmMain/kotlin/scientifik/kmath/prob/DistributionsJVM.kt
View File

@ -1,66 +0,0 @@
package scientifik.kmath.prob
import scientifik.kmath.commons.rng.sampling.distribution.ContinuousSampler
import scientifik.kmath.commons.rng.sampling.distribution.DiscreteSampler
import scientifik.kmath.commons.rng.sampling.distribution.GaussianSampler
import scientifik.kmath.commons.rng.sampling.distribution.PoissonSampler
import kotlin.math.PI
import kotlin.math.exp
import kotlin.math.pow
import kotlin.math.sqrt
fun Distribution.Companion.normal(
method: NormalSamplerMethod = NormalSamplerMethod.Ziggurat
): Distribution<Double> = object : ContinuousSamplerDistribution() {
override fun buildCMSampler(generator: RandomGenerator): ContinuousSampler {
val provider = generator.asUniformRandomProvider()
return normalSampler(method, provider)
}
override fun probability(arg: Double): Double {
return exp(-arg.pow(2) / 2) / sqrt(PI * 2)
}
}
fun Distribution.Companion.normal(
mean: Double,
sigma: Double,
method: NormalSamplerMethod = NormalSamplerMethod.Ziggurat
): ContinuousSamplerDistribution = object : ContinuousSamplerDistribution() {
private val sigma2 = sigma.pow(2)
private val norm = sigma * sqrt(PI * 2)
override fun buildCMSampler(generator: RandomGenerator): ContinuousSampler {
val provider = generator.asUniformRandomProvider()
val normalizedSampler = normalSampler(method, provider)
return GaussianSampler(
normalizedSampler,
mean,
sigma
)
}
override fun probability(arg: Double): Double {
return exp(-(arg - mean).pow(2) / 2 / sigma2) / norm
}
}
fun Distribution.Companion.poisson(
lambda: Double
): DiscreteSamplerDistribution = object : DiscreteSamplerDistribution() {
override fun buildSampler(generator: RandomGenerator): DiscreteSampler {
return PoissonSampler.of(generator.asUniformRandomProvider(), lambda)
}
private val computedProb: HashMap<Int, Double> = hashMapOf(0 to exp(-lambda))
override fun probability(arg: Int): Double {
require(arg >= 0) { "The argument must be >= 0" }
return if (arg > 40)
exp(-(arg - lambda).pow(2) / 2 / lambda) / sqrt(2 * PI * lambda)
else
computedProb.getOrPut(arg) { probability(arg - 1) * lambda / arg }
}
}

23
kmath-prob/src/jvmMain/kotlin/scientifik/kmath/prob/RandomSourceGenerator.kt
View File

@ -1,11 +1,10 @@
package scientifik.kmath.prob
import org.apache.commons.rng.simple.RandomSource
import scientifik.kmath.commons.rng.UniformRandomProvider
class RandomSourceGenerator(val source: RandomSource, seed: Long?) :
class RandomSourceGenerator(private val source: RandomSource, seed: Long?) :
RandomGenerator {
internal val random = seed?.let {
private val random = seed?.let {
RandomSource.create(source, seed)
} ?: RandomSource.create(source)
@ -24,24 +23,6 @@ class RandomSourceGenerator(val source: RandomSource, seed: Long?) :
override fun fork(): RandomGenerator = RandomSourceGenerator(source, nextLong())
}
/**
* Represent this [RandomGenerator] as commons-rng [UniformRandomProvider] preserving and mirroring its current state.
* Getting new value from one of those changes the state of another.
*/
fun RandomGenerator.asUniformRandomProvider(): UniformRandomProvider = if (this is RandomSourceGenerator) {
object : UniformRandomProvider {
override fun nextBytes(bytes: ByteArray) = random.nextBytes(bytes)
override fun nextBytes(bytes: ByteArray, start: Int, len: Int) = random.nextBytes(bytes, start, len)
override fun nextInt(): Int = random.nextInt()
override fun nextInt(n: Int): Int = random.nextInt(n)
override fun nextLong(): Long = random.nextLong()
override fun nextLong(n: Long): Long = random.nextLong(n)
override fun nextBoolean(): Boolean = random.nextBoolean()
override fun nextFloat(): Float = random.nextFloat()
override fun nextDouble(): Double = random.nextDouble()
}
} else RandomGeneratorProvider(this)
fun RandomGenerator.Companion.fromSource(source: RandomSource, seed: Long? = null): RandomSourceGenerator =
RandomSourceGenerator(source, seed)