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Code refactoring, implement NormalDistribution

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This commit is contained in:
Iaroslav Postovalov 2020-10-15 23:52:50 +07:00
parent 26d81bddb5
commit 0c6fff3878
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GPG Key ID: 46E15E4A31B3BCD7
10 changed files with 45 additions and 142 deletions
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6
kmath-commons/src/main/kotlin/kscience/kmath/commons/expressions/DiffExpression.kt
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@ -33,10 +33,7 @@ public class DerivativeStructureField(
variables[name] ?: default ?: error("A variable with name $name does not exist")
public fun Number.const(): DerivativeStructure = DerivativeStructure(order, parameters.size, toDouble())
public fun DerivativeStructure.deriv(parName: String, order: Int = 1): Double {
return deriv(mapOf(parName to order))
}
public fun DerivativeStructure.deriv(parName: String, order: Int = 1): Double = deriv(mapOf(parName to order))
public fun DerivativeStructure.deriv(orders: Map<String, Int>): Double {
return getPartialDerivative(*parameters.keys.map { orders[it] ?: 0 }.toIntArray())
@ -75,7 +72,6 @@ public class DerivativeStructureField(
public fun power(arg: DerivativeStructure, pow: DerivativeStructure): DerivativeStructure = arg.pow(pow)
public override fun exp(arg: DerivativeStructure): DerivativeStructure = arg.exp()
public override fun ln(arg: DerivativeStructure): DerivativeStructure = arg.log()
public override operator fun DerivativeStructure.plus(b: Number): DerivativeStructure = add(b.toDouble())
public override operator fun DerivativeStructure.minus(b: Number): DerivativeStructure = subtract(b.toDouble())
public override operator fun Number.plus(b: DerivativeStructure): DerivativeStructure = b + this

12
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/Distribution.kt
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@ -6,7 +6,7 @@ import kscience.kmath.chains.collect
import kscience.kmath.structures.Buffer
import kscience.kmath.structures.BufferFactory
public interface Sampler<T : Any> {
public fun interface Sampler<T : Any> {
public fun sample(generator: RandomGenerator): Chain<T>
}
@ -20,11 +20,7 @@ public interface Distribution<T : Any> : Sampler<T> {
*/
public fun probability(arg: T): Double
/**
* Create a chain of samples from this distribution.
* The chain is not guaranteed to be stateless, but different sample chains should be independent.
*/
override fun sample(generator: RandomGenerator): Chain<T>
public override fun sample(generator: RandomGenerator): Chain<T>
/**
* An empty companion. Distribution factories should be written as its extensions
@ -63,9 +59,7 @@ public fun <T : Any> Sampler<T>.sampleBuffer(
//clear list from previous run
tmp.clear()
//Fill list
repeat(size) {
tmp.add(chain.next())
}
repeat(size) { tmp.add(chain.next()) }
//return new buffer with elements from tmp
bufferFactory(size) { tmp[it] }
}

30
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/distributions/NormalDistribution.kt Normal file
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@ -0,0 +1,30 @@
package kscience.kmath.prob.distributions
import kscience.kmath.chains.Chain
import kscience.kmath.prob.RandomGenerator
import kscience.kmath.prob.UnivariateDistribution
import kscience.kmath.prob.internal.InternalErf
import kscience.kmath.prob.samplers.GaussianSampler
import kotlin.math.*
public inline class NormalDistribution(public val sampler: GaussianSampler) : UnivariateDistribution<Double> {
public override fun probability(arg: Double): Double {
val x1 = (arg - sampler.mean) / sampler.standardDeviation
return exp(-0.5 * x1 * x1 - (ln(sampler.standardDeviation) + 0.5 * ln(2 * PI)))
}
public override fun sample(generator: RandomGenerator): Chain<Double> = sampler.sample(generator)
public override fun cumulative(arg: Double): Double {
val dev = arg - sampler.mean
return when {
abs(dev) > 40 * sampler.standardDeviation -> if (dev < 0) 0.0 else 1.0
else -> 0.5 * InternalErf.erfc(-dev / (sampler.standardDeviation * SQRT2))
}
}
private companion object {
private val SQRT2 = sqrt(2.0)
}
}

1
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/samplers/AhrensDieterExponentialSampler.kt
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@ -4,6 +4,7 @@ import kscience.kmath.chains.Chain
import kscience.kmath.prob.RandomGenerator
import kscience.kmath.prob.Sampler
import kscience.kmath.prob.chain
import kscience.kmath.prob.internal.InternalUtils
import kotlin.math.ln
import kotlin.math.pow

1
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/samplers/AliasMethodDiscreteSampler.kt
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@ -4,6 +4,7 @@ import kscience.kmath.chains.Chain
import kscience.kmath.prob.RandomGenerator
import kscience.kmath.prob.Sampler
import kscience.kmath.prob.chain
import kscience.kmath.prob.internal.InternalUtils
import kotlin.math.ceil
import kotlin.math.max
import kotlin.math.min

7
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/samplers/GaussianSampler.kt
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@ -10,10 +10,13 @@ import kscience.kmath.prob.Sampler
*
* Based on Commons RNG implementation.
* See https://commons.apache.org/proper/commons-rng/commons-rng-sampling/apidocs/org/apache/commons/rng/sampling/distribution/GaussianSampler.html
*
* @property mean the mean of the distribution.
* @property standardDeviation the variance of the distribution.
*/
public class GaussianSampler private constructor(
private val mean: Double,
private val standardDeviation: Double,
public val mean: Double,
public val standardDeviation: Double,
private val normalized: NormalizedGaussianSampler
) : Sampler<Double> {
public override fun sample(generator: RandomGenerator): Chain<Double> = normalized

41
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/samplers/InternalGamma.kt
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@ -1,43 +1,2 @@
package kscience.kmath.prob.samplers
import kotlin.math.PI
import kotlin.math.ln
internal object InternalGamma {
private const val LANCZOS_G = 607.0 / 128.0
private val LANCZOS_COEFFICIENTS = doubleArrayOf(
0.99999999999999709182,
57.156235665862923517,
-59.597960355475491248,
14.136097974741747174,
-0.49191381609762019978,
.33994649984811888699e-4,
.46523628927048575665e-4,
-.98374475304879564677e-4,
.15808870322491248884e-3,
-.21026444172410488319e-3,
.21743961811521264320e-3,
-.16431810653676389022e-3,
.84418223983852743293e-4,
-.26190838401581408670e-4,
.36899182659531622704e-5
)
private val HALF_LOG_2_PI: Double = 0.5 * ln(2.0 * PI)
fun logGamma(x: Double): Double {
// Stripped-down version of the same method defined in "Commons Math":
// Unused "if" branches (for when x < 8) have been removed here since
// this method is only used (by class "InternalUtils") in order to
// compute log(n!) for x > 20.
val sum = lanczos(x)
val tmp = x + LANCZOS_G + 0.5
return (x + 0.5) * ln(tmp) - tmp + HALF_LOG_2_PI + ln(sum / x)
}
private fun lanczos(x: Double): Double {
val sum = (LANCZOS_COEFFICIENTS.size - 1 downTo 1).sumByDouble { LANCZOS_COEFFICIENTS[it] / (x + it) }
return sum + LANCZOS_COEFFICIENTS[0]
}
}

76
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/samplers/InternalUtils.kt
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@ -1,78 +1,2 @@
package kscience.kmath.prob.samplers
import kotlin.math.ln
import kotlin.math.min
internal object InternalUtils {
private val FACTORIALS = longArrayOf(
1L, 1L, 2L,
6L, 24L, 120L,
720L, 5040L, 40320L,
362880L, 3628800L, 39916800L,
479001600L, 6227020800L, 87178291200L,
1307674368000L, 20922789888000L, 355687428096000L,
6402373705728000L, 121645100408832000L, 2432902008176640000L
)
private const val BEGIN_LOG_FACTORIALS = 2
fun factorial(n: Int): Long = FACTORIALS[n]
fun validateProbabilities(probabilities: DoubleArray?): Double {
require(!(probabilities == null || probabilities.isEmpty())) { "Probabilities must not be empty." }
var sumProb = 0.0
probabilities.forEach { prob ->
validateProbability(prob)
sumProb += prob
}
require(!(sumProb.isInfinite() || sumProb <= 0)) { "Invalid sum of probabilities: $sumProb" }
return sumProb
}
private fun validateProbability(probability: Double): Unit =
require(!(probability < 0 || probability.isInfinite() || probability.isNaN())) { "Invalid probability: $probability" }
class FactorialLog private constructor(
numValues: Int,
cache: DoubleArray?
) {
private val logFactorials: DoubleArray = DoubleArray(numValues)
init {
val endCopy: Int
if (cache != null && cache.size > BEGIN_LOG_FACTORIALS) {
// Copy available values.
endCopy = min(cache.size, numValues)
cache.copyInto(
logFactorials,
BEGIN_LOG_FACTORIALS,
BEGIN_LOG_FACTORIALS, endCopy
)
}
// All values to be computed
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())
}
}
fun value(n: Int): Double {
if (n < logFactorials.size)
return logFactorials[n]
return if (n < FACTORIALS.size) ln(FACTORIALS[n].toDouble()) else InternalGamma.logGamma(n + 1.0)
}
companion object {
fun create(): FactorialLog = FactorialLog(0, null)
}
}
}

8
kmath-prob/src/commonMain/kotlin/kscience/kmath/prob/samplers/LargeMeanPoissonSampler.kt
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@ -5,6 +5,7 @@ import kscience.kmath.chains.ConstantChain
import kscience.kmath.prob.RandomGenerator
import kscience.kmath.prob.Sampler
import kscience.kmath.prob.chain
import kscience.kmath.prob.internal.InternalUtils
import kscience.kmath.prob.next
import kotlin.math.*
@ -111,16 +112,13 @@ public class LargeMeanPoissonSampler private constructor(public val mean: Double
}
private fun getFactorialLog(n: Int): Double = factorialLog.value(n)
override fun toString(): String = "Large Mean Poisson deviate"
public override fun toString(): String = "Large Mean Poisson deviate"
public companion object {
private const val MAX_MEAN: Double = 0.5 * Int.MAX_VALUE
private val NO_CACHE_FACTORIAL_LOG: InternalUtils.FactorialLog = InternalUtils.FactorialLog.create()
private val NO_SMALL_MEAN_POISSON_SAMPLER: Sampler<Int> = object : Sampler<Int> {
override fun sample(generator: RandomGenerator): Chain<Int> = ConstantChain(0)
}
private val NO_SMALL_MEAN_POISSON_SAMPLER: Sampler<Int> = Sampler { ConstantChain(0) }
public fun of(mean: Double): LargeMeanPoissonSampler {
require(mean >= 1) { "mean is not >= 1: $mean" }

5
kmath-prob/src/jvmMain/kotlin/kscience/kmath/prob/RandomSourceGenerator.kt
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@ -26,10 +26,7 @@ public class RandomSourceGenerator(public val source: RandomSource, seed: Long?)
public inline class RandomGeneratorProvider(public val generator: RandomGenerator) : UniformRandomProvider {
public override fun nextBoolean(): Boolean = generator.nextBoolean()
public override fun nextFloat(): Float = generator.nextDouble().toFloat()
public override fun nextBytes(bytes: ByteArray) {
generator.fillBytes(bytes)
}
public override fun nextBytes(bytes: ByteArray): Unit = generator.fillBytes(bytes)
public override fun nextBytes(bytes: ByteArray, start: Int, len: Int) {
generator.fillBytes(bytes, start, start + len)