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Merge remote-tracking branch 'space/dev' into dev

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This commit is contained in:
Alexander Nozik 2023-05-09 19:01:56 +03:00
commit 4dbcaca87c
5 changed files with 183 additions and 2 deletions
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2
kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/_generated.kt
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@ -19,9 +19,9 @@ import org.ejml.sparse.csc.factory.DecompositionFactory_DSCC
import org.ejml.sparse.csc.factory.DecompositionFactory_FSCC
import org.ejml.sparse.csc.factory.LinearSolverFactory_DSCC
import org.ejml.sparse.csc.factory.LinearSolverFactory_FSCC
import space.kscience.kmath.UnstableKMathAPI
import space.kscience.kmath.linear.*
import space.kscience.kmath.linear.Matrix
import space.kscience.kmath.UnstableKMathAPI
import space.kscience.kmath.nd.StructureFeature
import space.kscience.kmath.operations.DoubleField
import space.kscience.kmath.operations.FloatField

24
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/distributions/zSNormalCdf.kt Normal file
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@ -0,0 +1,24 @@
/*
* Copyright 2018-2023 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.distributions
import space.kscience.kmath.operations.DoubleField.pow
import kotlin.math.PI
import kotlin.math.absoluteValue
import kotlin.math.exp
/**
* Zelen & Severo approximation for the standard normal CDF.
* The error is bounded by 7.5 * 10e-8.
* */
public fun zSNormalCDF(x: Double): Double {
val t = 1 / (1 + 0.2316419 * x.absoluteValue)
val summ = 0.319381530*t - 0.356563782*t.pow(2) + 1.781477937*t.pow(3) - 1.821255978*t.pow(4) + 1.330274429*t.pow(5)
val temp = summ * exp(-x.absoluteValue.pow(2) / 2) / (2 * PI).pow(0.5)
return if (x >= 0) 1 - temp else temp
}

15
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/SeriesAlgebra.kt
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@ -191,7 +191,7 @@ public open class SeriesAlgebra<T, out A : Ring<T>, out BA : BufferAlgebra<T, A>
crossinline operation: A.(left: T, right: T) -> T,
): Series<T> {
val newRange = offsetIndices.intersect(other.offsetIndices)
return seriesByOffset(startOffset = newRange.first, size = newRange.last - newRange.first) { offset ->
return seriesByOffset(startOffset = newRange.first, size = newRange.last + 1 - newRange.first) { offset ->
elementAlgebra.operation(
getByOffset(offset),
other.getByOffset(offset)
@ -199,12 +199,25 @@ public open class SeriesAlgebra<T, out A : Ring<T>, out BA : BufferAlgebra<T, A>
}
}
/**
* Zip buffer with itself, but shifted
* */
public inline fun Buffer<T>.zipWithShift(
shift: Int = 1,
crossinline operation: A.(left: T, right: T) -> T
): Buffer<T> {
val shifted = this.moveBy(shift)
return zip(shifted, operation)
}
override fun Buffer<T>.unaryMinus(): Buffer<T> = map { -it }
override fun add(left: Buffer<T>, right: Buffer<T>): Series<T> = left.zip(right) { l, r -> l + r }
override fun multiply(left: Buffer<T>, right: Buffer<T>): Buffer<T> = left.zip(right) { l, r -> l * r }
public fun Buffer<T>.difference(shift: Int=1): Buffer<T> = this.zipWithShift(shift) {l, r -> r - l}
public companion object
}

72
kmath-stat/src/commonMain/kotlin/space/kscience/kmath/series/VarianceRatioTest.kt Normal file
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@ -0,0 +1,72 @@
/*
* Copyright 2018-2023 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.series
import space.kscience.kmath.distributions.zSNormalCDF
import space.kscience.kmath.operations.DoubleField.pow
import space.kscience.kmath.operations.fold
import kotlin.math.absoluteValue
/**
* Container class for Variance Ratio Test result:
* ratio itself, corresponding Z-score, also it's p-value
* **/
public data class VarianceRatioTestResult(val varianceRatio: Double=1.0, val zScore: Double=0.0, val pValue: Double=0.5)
/**
* Calculates the Z-statistic and the p-value for the Lo and MacKinlay's Variance Ratio test (1987)
* under Homoscedastic or Heteroscedstic assumptions
* with two-sided p-value test
* https://ssrn.com/abstract=346975
* **/
public fun SeriesAlgebra<Double, *, *, *>.varianceRatioTest(series: Series<Double>, shift: Int, homoscedastic: Boolean=true): VarianceRatioTestResult {
require(shift > 1) {"Shift must be greater than one"}
require(shift < series.size) {"Shift must be smaller than sample size"}
val sum = { x: Double, y: Double -> x + y }
val mean = series.fold(0.0, sum) / series.size
val demeanedSquares = series.map { (it - mean).pow(2) }
val variance = demeanedSquares.fold(0.0, sum)
if (variance == 0.0) return VarianceRatioTestResult()
var seriesAgg = series
for (i in 1..<shift) {
seriesAgg = seriesAgg.zip(series.moveTo(i)) { v1, v2 -> v1 + v2 }
}
val demeanedSquaresAgg = seriesAgg.map { (it - shift * mean).pow(2) }
val varianceAgg = demeanedSquaresAgg.fold(0.0, sum)
val varianceRatio =
varianceAgg * (series.size.toDouble() - 1) / variance / (series.size.toDouble() - shift.toDouble() + 1) / (1 - shift.toDouble()/series.size.toDouble()) / shift.toDouble()
// calculating asymptotic variance
val phi = if (homoscedastic) { // under homoscedastic null hypothesis
2 * (2 * shift - 1.0) * (shift - 1.0) / (3 * shift * series.size)
} else { // under heteroscedastic null hypothesis
var accumulator = 0.0
for (j in 1..<shift) {
val temp = demeanedSquares
val delta = series.size * temp.zipWithShift(j) { v1, v2 -> v1 * v2 }.fold(0.0, sum) / variance.pow(2)
accumulator += delta * 4 * (shift - j).toDouble().pow(2) / shift.toDouble().pow(2)
}
accumulator
}
val zScore = (varianceRatio - 1) / phi.pow(0.5)
val pValue = 2*(1 - zSNormalCDF(zScore.absoluteValue))
return VarianceRatioTestResult(varianceRatio, zScore, pValue)
}

72
kmath-stat/src/commonTest/kotlin/space/kscience/kmath/series/TestVarianceRatioTest.kt Normal file
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@ -0,0 +1,72 @@
/*
* Copyright 2018-2023 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.series
import space.kscience.kmath.operations.algebra
import space.kscience.kmath.operations.bufferAlgebra
import kotlin.math.PI
import kotlin.test.Test
import kotlin.test.assertEquals
class TestVarianceRatioTest {
@Test
fun monotonicData() {
with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
val monotonicData = series(10) { it * 1.0 }
val resultHomo = varianceRatioTest(monotonicData, 2, homoscedastic = true)
assertEquals(1.818181, resultHomo.varianceRatio, 1e-6)
// homoscedastic zScore
assertEquals(2.587318, resultHomo.zScore, 1e-6)
assertEquals(.0096, resultHomo.pValue, 1e-4)
val resultHetero = varianceRatioTest(monotonicData, 2, homoscedastic = false)
// heteroscedastic zScore
assertEquals(0.819424, resultHetero.zScore, 1e-6)
assertEquals(.4125, resultHetero.pValue, 1e-4)
}
}
@Test
fun volatileData() {
with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
val volatileData = series(10) { sin(PI * it + PI/2) + 1.0}
val resultHomo = varianceRatioTest(volatileData, 2)
assertEquals(0.0, resultHomo.varianceRatio, 1e-6)
// homoscedastic zScore
assertEquals(-3.162277, resultHomo.zScore, 1e-6)
assertEquals(.0015, resultHomo.pValue, 1e-4)
val resultHetero = varianceRatioTest(volatileData, 2, homoscedastic = false)
// heteroscedastic zScore
assertEquals(-1.0540925, resultHetero.zScore, 1e-6)
assertEquals(.2918, resultHetero.pValue, 1e-4)
}
}
@Test
fun negativeData() {
with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
val negativeData = series(10) { sin(it * 1.2)}
val resultHomo = varianceRatioTest(negativeData, 3)
assertEquals(1.240031, resultHomo.varianceRatio, 1e-6)
// homoscedastic zScore
assertEquals(0.509183, resultHomo.zScore, 1e-6)
val resultHetero = varianceRatioTest(negativeData, 3, homoscedastic = false)
// heteroscedastic zScore
assertEquals(0.209202, resultHetero.zScore, 1e-6)
}
}
@Test
fun zeroVolatility() {
with(Double.algebra.bufferAlgebra.seriesAlgebra()) {
val zeroVolData = series(10) { 0.0 }
val result = varianceRatioTest(zeroVolData, 4)
assertEquals(1.0, result.varianceRatio, 1e-6)
assertEquals(0.0, result.zScore, 1e-6)
assertEquals(0.5, result.pValue, 1e-4)
}
}
}