QOW is working more or less
This commit is contained in:
parent
9b8da4cdcc
commit
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@ -20,6 +20,7 @@ dependencies {
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implementation(project(":kmath-coroutines"))
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implementation(project(":kmath-coroutines"))
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implementation(project(":kmath-commons"))
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implementation(project(":kmath-commons"))
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implementation(project(":kmath-complex"))
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implementation(project(":kmath-complex"))
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implementation(project(":kmath-optimization"))
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implementation(project(":kmath-stat"))
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implementation(project(":kmath-stat"))
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implementation(project(":kmath-viktor"))
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implementation(project(":kmath-viktor"))
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implementation(project(":kmath-dimensions"))
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implementation(project(":kmath-dimensions"))
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@ -3,19 +3,17 @@
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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*/
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package space.kscience.kmath.commons.fit
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package space.kscience.kmath.fit
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import kotlinx.html.br
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import kotlinx.html.br
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import kotlinx.html.h3
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import kotlinx.html.h3
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import space.kscience.kmath.commons.expressions.DSProcessor
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import space.kscience.kmath.commons.expressions.DSProcessor
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import space.kscience.kmath.commons.optimization.CMOptimizer
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import space.kscience.kmath.commons.optimization.CMOptimizer
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import space.kscience.kmath.distributions.NormalDistribution
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import space.kscience.kmath.distributions.NormalDistribution
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import space.kscience.kmath.expressions.binding
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import space.kscience.kmath.expressions.chiSquaredExpression
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import space.kscience.kmath.expressions.chiSquaredExpression
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import space.kscience.kmath.expressions.symbol
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import space.kscience.kmath.expressions.symbol
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import space.kscience.kmath.optimization.FunctionOptimizationTarget
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import space.kscience.kmath.optimization.*
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import space.kscience.kmath.optimization.optimizeWith
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import space.kscience.kmath.optimization.resultPoint
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import space.kscience.kmath.optimization.resultValue
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import space.kscience.kmath.real.DoubleVector
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import space.kscience.kmath.real.DoubleVector
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import space.kscience.kmath.real.map
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import space.kscience.kmath.real.map
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import space.kscience.kmath.real.step
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import space.kscience.kmath.real.step
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@ -25,6 +23,7 @@ import space.kscience.kmath.structures.toList
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import space.kscience.plotly.*
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import space.kscience.plotly.*
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import space.kscience.plotly.models.ScatterMode
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import space.kscience.plotly.models.ScatterMode
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import space.kscience.plotly.models.TraceValues
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import space.kscience.plotly.models.TraceValues
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import kotlin.math.abs
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import kotlin.math.pow
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import kotlin.math.pow
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import kotlin.math.sqrt
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import kotlin.math.sqrt
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@ -45,7 +44,7 @@ operator fun TraceValues.invoke(vector: DoubleVector) {
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*/
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*/
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suspend fun main() {
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suspend fun main() {
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//A generator for a normally distributed values
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//A generator for a normally distributed values
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val generator = NormalDistribution(2.0, 7.0)
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val generator = NormalDistribution(0.0, 1.0)
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//A chain/flow of random values with the given seed
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//A chain/flow of random values with the given seed
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val chain = generator.sample(RandomGenerator.default(112667))
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val chain = generator.sample(RandomGenerator.default(112667))
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@ -56,7 +55,7 @@ suspend fun main() {
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//Perform an operation on each x value (much more effective, than numpy)
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//Perform an operation on each x value (much more effective, than numpy)
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val y = x.map {
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val y = x.map { it ->
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val value = it.pow(2) + it + 1
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val value = it.pow(2) + it + 1
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value + chain.next() * sqrt(value)
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value + chain.next() * sqrt(value)
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}
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}
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105
examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt
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105
examples/src/main/kotlin/space/kscience/kmath/fit/qowFit.kt
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@ -0,0 +1,105 @@
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.fit
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import kotlinx.html.br
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import kotlinx.html.h3
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import space.kscience.kmath.commons.expressions.DSProcessor
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import space.kscience.kmath.data.XYErrorColumnarData
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import space.kscience.kmath.distributions.NormalDistribution
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import space.kscience.kmath.expressions.Symbol
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import space.kscience.kmath.expressions.binding
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import space.kscience.kmath.expressions.symbol
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import space.kscience.kmath.optimization.QowOptimizer
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import space.kscience.kmath.optimization.fitWith
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import space.kscience.kmath.optimization.resultPoint
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import space.kscience.kmath.real.map
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import space.kscience.kmath.real.step
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import space.kscience.kmath.stat.RandomGenerator
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import space.kscience.kmath.structures.asIterable
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import space.kscience.kmath.structures.toList
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import space.kscience.plotly.*
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import space.kscience.plotly.models.ScatterMode
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import kotlin.math.abs
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import kotlin.math.pow
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import kotlin.math.sqrt
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// Forward declaration of symbols that will be used in expressions.
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private val a by symbol
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private val b by symbol
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private val c by symbol
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/**
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* Least squares fie with auto-differentiation. Uses `kmath-commons` and `kmath-for-real` modules.
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*/
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suspend fun main() {
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//A generator for a normally distributed values
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val generator = NormalDistribution(0.0, 1.0)
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//A chain/flow of random values with the given seed
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val chain = generator.sample(RandomGenerator.default(112667))
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//Create a uniformly distributed x values like numpy.arrange
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val x = 1.0..100.0 step 1.0
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//Perform an operation on each x value (much more effective, than numpy)
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val y = x.map { it ->
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val value = it.pow(2) + it + 100
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value + chain.next() * sqrt(value)
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}
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// this will also work, but less effective:
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// val y = x.pow(2)+ x + 1 + chain.nextDouble()
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// create same errors for all xs
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val yErr = y.map { sqrt(abs(it)) }
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require(yErr.asIterable().all { it > 0 }) { "All errors must be strictly positive" }
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val result = XYErrorColumnarData.of(x, y, yErr).fitWith(
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QowOptimizer,
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DSProcessor,
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mapOf(a to 1.0, b to 1.2, c to 99.0)
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) { arg ->
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//bind variables to autodiff context
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val a by binding
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val b by binding
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//Include default value for c if it is not provided as a parameter
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val c = bindSymbolOrNull(c) ?: one
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a * arg.pow(2) + b * arg + c
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}
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//display a page with plot and numerical results
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val page = Plotly.page {
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plot {
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scatter {
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mode = ScatterMode.markers
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x(x)
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y(y)
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error_y {
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array = yErr.toList()
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}
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name = "data"
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}
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scatter {
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mode = ScatterMode.lines
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x(x)
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y(x.map { result.model(result.resultPoint + (Symbol.x to it)) })
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name = "fit"
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}
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}
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br()
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h3 {
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+"Fit result: ${result.resultPoint}"
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}
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// h3 {
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// +"Chi2/dof = ${result.resultValue / (x.size - 3)}"
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// }
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}
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page.makeFile()
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}
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@ -22,7 +22,7 @@ fun main(): Unit = DoubleField {
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}
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}
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//Define a function in a nd space
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//Define a function in a nd space
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val function: (Double) -> StructureND<Double> = { x: Double -> 3 * number(x).pow(2) + 2 * diagonal(x) + 1 }
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val function: (Double) -> StructureND<Double> = { x: Double -> 3 * x.pow(2) + 2 * diagonal(x) + 1 }
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//get the result of the integration
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//get the result of the integration
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val result = gaussIntegrator.integrate(0.0..10.0, function = function)
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val result = gaussIntegrator.integrate(0.0..10.0, function = function)
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@ -9,6 +9,7 @@ dependencies {
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api(project(":kmath-core"))
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api(project(":kmath-core"))
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api(project(":kmath-complex"))
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api(project(":kmath-complex"))
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api(project(":kmath-coroutines"))
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api(project(":kmath-coroutines"))
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api(project(":kmath-optimization"))
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api(project(":kmath-stat"))
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api(project(":kmath-stat"))
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api(project(":kmath-functions"))
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api(project(":kmath-functions"))
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api("org.apache.commons:commons-math3:3.6.1")
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api("org.apache.commons:commons-math3:3.6.1")
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@ -18,6 +18,7 @@ import space.kscience.kmath.expressions.SymbolIndexer
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import space.kscience.kmath.expressions.derivative
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import space.kscience.kmath.expressions.derivative
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import space.kscience.kmath.expressions.withSymbols
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import space.kscience.kmath.expressions.withSymbols
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.misc.log
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import space.kscience.kmath.optimization.*
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import space.kscience.kmath.optimization.*
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import kotlin.collections.set
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import kotlin.collections.set
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import kotlin.reflect.KClass
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import kotlin.reflect.KClass
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@ -108,15 +109,17 @@ public object CMOptimizer : Optimizer<Double, FunctionOptimization<Double>> {
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val objectiveFunction = ObjectiveFunction {
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val objectiveFunction = ObjectiveFunction {
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val args = startPoint + it.toMap()
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val args = startPoint + it.toMap()
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problem.expression(args)
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val res = problem.expression(args)
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res
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}
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}
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addOptimizationData(objectiveFunction)
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addOptimizationData(objectiveFunction)
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val gradientFunction = ObjectiveFunctionGradient {
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val gradientFunction = ObjectiveFunctionGradient {
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val args = startPoint + it.toMap()
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val args = startPoint + it.toMap()
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DoubleArray(symbols.size) { index ->
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val res = DoubleArray(symbols.size) { index ->
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problem.expression.derivative(symbols[index])(args)
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problem.expression.derivative(symbols[index])(args)
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}
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}
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res
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}
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}
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addOptimizationData(gradientFunction)
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addOptimizationData(gradientFunction)
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@ -42,8 +42,8 @@ internal class AutoDiffTest {
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@Test
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@Test
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fun autoDifTest() {
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fun autoDifTest() {
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val f = DerivativeStructureExpression {
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val f = DerivativeStructureExpression {
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val x by binding()
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val x by binding
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val y by binding()
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val y by binding
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x.pow(2) + 2 * x * y + y.pow(2) + 1
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x.pow(2) + 2 * x * y + y.pow(2) + 1
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}
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}
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@ -15,6 +15,7 @@ import space.kscience.kmath.expressions.chiSquaredExpression
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import space.kscience.kmath.expressions.symbol
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import space.kscience.kmath.expressions.symbol
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import space.kscience.kmath.optimization.*
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import space.kscience.kmath.optimization.*
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import space.kscience.kmath.stat.RandomGenerator
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import space.kscience.kmath.stat.RandomGenerator
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import space.kscience.kmath.structures.DoubleBuffer
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import space.kscience.kmath.structures.asBuffer
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import space.kscience.kmath.structures.asBuffer
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import space.kscience.kmath.structures.map
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import space.kscience.kmath.structures.map
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import kotlin.math.pow
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import kotlin.math.pow
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@ -58,7 +59,7 @@ internal class OptimizeTest {
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it.pow(2) + it + 1 + chain.next()
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it.pow(2) + it + 1 + chain.next()
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}
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}
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val yErr = List(x.size) { sigma }.asBuffer()
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val yErr = DoubleBuffer(x.size) { sigma }
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val chi2 = DSProcessor.chiSquaredExpression(
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val chi2 = DSProcessor.chiSquaredExpression(
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x, y, yErr
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x, y, yErr
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@ -32,19 +32,21 @@ public interface XYColumnarData<out T, out X : T, out Y : T> : ColumnarData<T> {
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Symbol.y -> y
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Symbol.y -> y
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else -> null
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else -> null
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}
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}
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}
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@Suppress("FunctionName")
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public companion object{
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@UnstableKMathAPI
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@UnstableKMathAPI
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public fun <T, X : T, Y : T> XYColumnarData(x: Buffer<X>, y: Buffer<Y>): XYColumnarData<T, X, Y> {
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public fun <T, X : T, Y : T> of(x: Buffer<X>, y: Buffer<Y>): XYColumnarData<T, X, Y> {
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require(x.size == y.size) { "Buffer size mismatch. x buffer size is ${x.size}, y buffer size is ${y.size}" }
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require(x.size == y.size) { "Buffer size mismatch. x buffer size is ${x.size}, y buffer size is ${y.size}" }
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return object : XYColumnarData<T, X, Y> {
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return object : XYColumnarData<T, X, Y> {
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override val size: Int = x.size
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override val size: Int = x.size
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override val x: Buffer<X> = x
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override val x: Buffer<X> = x
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override val y: Buffer<Y> = y
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override val y: Buffer<Y> = y
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}
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}
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}
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}
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}
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}
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/**
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/**
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* Represent a [ColumnarData] as an [XYColumnarData]. The presence or respective columns is checked on creation.
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* Represent a [ColumnarData] as an [XYColumnarData]. The presence or respective columns is checked on creation.
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*/
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*/
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@ -5,15 +5,13 @@
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package space.kscience.kmath.data
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package space.kscience.kmath.data
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import space.kscience.kmath.data.XYErrorColumnarData.Companion
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import space.kscience.kmath.expressions.Symbol
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import space.kscience.kmath.expressions.Symbol
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import space.kscience.kmath.expressions.symbol
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.misc.UnstableKMathAPI
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import space.kscience.kmath.structures.Buffer
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import space.kscience.kmath.structures.Buffer
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/**
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/**
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* A [ColumnarData] with additional [Companion.yErr] column for an [Symbol.y] error
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* A [ColumnarData] with additional [Symbol.yError] column for an [Symbol.y] error
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* Inherits [XYColumnarData].
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* Inherits [XYColumnarData].
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*/
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*/
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@UnstableKMathAPI
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@UnstableKMathAPI
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@ -23,11 +21,24 @@ public interface XYErrorColumnarData<T, out X : T, out Y : T> : XYColumnarData<T
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override fun get(symbol: Symbol): Buffer<T> = when (symbol) {
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override fun get(symbol: Symbol): Buffer<T> = when (symbol) {
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Symbol.x -> x
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Symbol.x -> x
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Symbol.y -> y
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Symbol.y -> y
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Companion.yErr -> yErr
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Symbol.yError -> yErr
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else -> error("A column for symbol $symbol not found")
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else -> error("A column for symbol $symbol not found")
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}
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}
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public companion object{
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public companion object {
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public val yErr: Symbol by symbol
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public fun <T, X : T, Y : T> of(
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x: Buffer<X>, y: Buffer<Y>, yErr: Buffer<Y>
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): XYErrorColumnarData<T, X, Y> {
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require(x.size == y.size) { "Buffer size mismatch. x buffer size is ${x.size}, y buffer size is ${y.size}" }
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require(y.size == yErr.size) { "Buffer size mismatch. y buffer size is ${x.size}, yErr buffer size is ${y.size}" }
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return object : XYErrorColumnarData<T, X, Y> {
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override val size: Int = x.size
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override val x: Buffer<X> = x
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override val y: Buffer<Y> = y
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override val yErr: Buffer<Y> = yErr
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}
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}
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}
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}
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}
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}
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@ -68,6 +68,7 @@ public interface ExpressionAlgebra<in T, E> : Algebra<E> {
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/**
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/**
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* Bind a symbol by name inside the [ExpressionAlgebra]
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* Bind a symbol by name inside the [ExpressionAlgebra]
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*/
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*/
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public fun <T, E> ExpressionAlgebra<T, E>.binding(): ReadOnlyProperty<Any?, E> = ReadOnlyProperty { _, property ->
|
public val <T, E> ExpressionAlgebra<T, E>.binding: ReadOnlyProperty<Any?, E>
|
||||||
bindSymbol(property.name) ?: error("A variable with name ${property.name} does not exist")
|
get() = ReadOnlyProperty { _, property ->
|
||||||
}
|
bindSymbol(property.name) ?: error("A variable with name ${property.name} does not exist")
|
||||||
|
}
|
||||||
|
@ -7,13 +7,18 @@ package space.kscience.kmath.expressions
|
|||||||
|
|
||||||
import space.kscience.kmath.operations.ExtendedField
|
import space.kscience.kmath.operations.ExtendedField
|
||||||
import space.kscience.kmath.structures.Buffer
|
import space.kscience.kmath.structures.Buffer
|
||||||
|
import space.kscience.kmath.structures.asIterable
|
||||||
import space.kscience.kmath.structures.indices
|
import space.kscience.kmath.structures.indices
|
||||||
|
import kotlin.jvm.JvmName
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic
|
* Generate a chi squared expression from given x-y-sigma data and inline model. Provides automatic
|
||||||
* differentiation.
|
* differentiation.
|
||||||
|
*
|
||||||
|
* **WARNING** All elements of [yErr] must be positive.
|
||||||
*/
|
*/
|
||||||
public fun <T : Any, I : Any, A> AutoDiffProcessor<T, I, A>.chiSquaredExpression(
|
@JvmName("genericChiSquaredExpression")
|
||||||
|
public fun <T : Comparable<T>, I : Any, A> AutoDiffProcessor<T, I, A>.chiSquaredExpression(
|
||||||
x: Buffer<T>,
|
x: Buffer<T>,
|
||||||
y: Buffer<T>,
|
y: Buffer<T>,
|
||||||
yErr: Buffer<T>,
|
yErr: Buffer<T>,
|
||||||
@ -35,4 +40,14 @@ public fun <T : Any, I : Any, A> AutoDiffProcessor<T, I, A>.chiSquaredExpression
|
|||||||
|
|
||||||
sum
|
sum
|
||||||
}
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
public fun <I : Any, A> AutoDiffProcessor<Double, I, A>.chiSquaredExpression(
|
||||||
|
x: Buffer<Double>,
|
||||||
|
y: Buffer<Double>,
|
||||||
|
yErr: Buffer<Double>,
|
||||||
|
model: A.(I) -> I,
|
||||||
|
): DifferentiableExpression<Double> where A : ExtendedField<I>, A : ExpressionAlgebra<Double, I> {
|
||||||
|
require(yErr.asIterable().all { it > 0.0 }) { "All errors must be strictly positive" }
|
||||||
|
return chiSquaredExpression<Double, I, A>(x, y, yErr, model)
|
||||||
}
|
}
|
@ -5,6 +5,7 @@
|
|||||||
|
|
||||||
package space.kscience.kmath.misc
|
package space.kscience.kmath.misc
|
||||||
|
|
||||||
|
import kotlin.jvm.JvmInline
|
||||||
import kotlin.reflect.KClass
|
import kotlin.reflect.KClass
|
||||||
|
|
||||||
/**
|
/**
|
||||||
@ -29,7 +30,8 @@ public interface Feature<F : Feature<F>> {
|
|||||||
/**
|
/**
|
||||||
* A container for a set of features
|
* A container for a set of features
|
||||||
*/
|
*/
|
||||||
public class FeatureSet<F : Feature<F>> private constructor(public val features: Map<FeatureKey<F>, F>) : Featured<F> {
|
@JvmInline
|
||||||
|
public value class FeatureSet<F : Feature<F>> private constructor(public val features: Map<FeatureKey<F>, F>) : Featured<F> {
|
||||||
@Suppress("UNCHECKED_CAST")
|
@Suppress("UNCHECKED_CAST")
|
||||||
override fun <T : F> getFeature(type: FeatureKey<T>): T? = features[type]?.let { it as T }
|
override fun <T : F> getFeature(type: FeatureKey<T>): T? = features[type]?.let { it as T }
|
||||||
|
|
||||||
@ -48,6 +50,9 @@ public class FeatureSet<F : Feature<F>> private constructor(public val features:
|
|||||||
|
|
||||||
public operator fun iterator(): Iterator<F> = features.values.iterator()
|
public operator fun iterator(): Iterator<F> = features.values.iterator()
|
||||||
|
|
||||||
|
override fun toString(): String = features.values.joinToString(prefix = "[ ", postfix = " ]")
|
||||||
|
|
||||||
|
|
||||||
public companion object {
|
public companion object {
|
||||||
public fun <F : Feature<F>> of(vararg features: F): FeatureSet<F> = FeatureSet(features.associateBy { it.key })
|
public fun <F : Feature<F>> of(vararg features: F): FeatureSet<F> = FeatureSet(features.associateBy { it.key })
|
||||||
public fun <F : Feature<F>> of(features: Iterable<F>): FeatureSet<F> =
|
public fun <F : Feature<F>> of(features: Iterable<F>): FeatureSet<F> =
|
||||||
|
@ -5,10 +5,18 @@
|
|||||||
|
|
||||||
package space.kscience.kmath.misc
|
package space.kscience.kmath.misc
|
||||||
|
|
||||||
public interface Loggable {
|
import space.kscience.kmath.misc.Loggable.Companion.INFO
|
||||||
public fun log(tag: String = INFO, block: () -> String)
|
|
||||||
|
public fun interface Loggable {
|
||||||
|
public fun log(tag: String, block: () -> String)
|
||||||
|
|
||||||
public companion object {
|
public companion object {
|
||||||
public const val INFO: String = "INFO"
|
public const val INFO: String = "INFO"
|
||||||
|
|
||||||
|
public val console: Loggable = Loggable { tag, block ->
|
||||||
|
println("[$tag] ${block()}")
|
||||||
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
public fun Loggable.log(block: () -> String): Unit = log(INFO, block)
|
@ -16,7 +16,7 @@ class ExpressionFieldTest {
|
|||||||
@Test
|
@Test
|
||||||
fun testExpression() {
|
fun testExpression() {
|
||||||
val expression = with(FunctionalExpressionField(DoubleField)) {
|
val expression = with(FunctionalExpressionField(DoubleField)) {
|
||||||
val x by binding()
|
val x by binding
|
||||||
x * x + 2 * x + one
|
x * x + 2 * x + one
|
||||||
}
|
}
|
||||||
|
|
||||||
@ -27,7 +27,7 @@ class ExpressionFieldTest {
|
|||||||
@Test
|
@Test
|
||||||
fun separateContext() {
|
fun separateContext() {
|
||||||
fun <T> FunctionalExpressionField<T, *>.expression(): Expression<T> {
|
fun <T> FunctionalExpressionField<T, *>.expression(): Expression<T> {
|
||||||
val x by binding()
|
val x by binding
|
||||||
return x * x + 2 * x + one
|
return x * x + 2 * x + one
|
||||||
}
|
}
|
||||||
|
|
||||||
@ -38,7 +38,7 @@ class ExpressionFieldTest {
|
|||||||
@Test
|
@Test
|
||||||
fun valueExpression() {
|
fun valueExpression() {
|
||||||
val expressionBuilder: FunctionalExpressionField<Double, *>.() -> Expression<Double> = {
|
val expressionBuilder: FunctionalExpressionField<Double, *>.() -> Expression<Double> = {
|
||||||
val x by binding()
|
val x by binding
|
||||||
x * x + 2 * x + one
|
x * x + 2 * x + one
|
||||||
}
|
}
|
||||||
|
|
||||||
|
@ -73,7 +73,8 @@ public class GaussIntegrator<T : Any>(
|
|||||||
}
|
}
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Create a Gauss-Legendre integrator for this field.
|
* Create a Gauss integrator for this field. By default, uses Legendre rule to compute points and weights.
|
||||||
|
* Custom rules could be provided by [GaussIntegratorRuleFactory] feature.
|
||||||
* @see [GaussIntegrator]
|
* @see [GaussIntegrator]
|
||||||
*/
|
*/
|
||||||
public val <T : Any> Field<T>.gaussIntegrator: GaussIntegrator<T> get() = GaussIntegrator(this)
|
public val <T : Any> Field<T>.gaussIntegrator: GaussIntegrator<T> get() = GaussIntegrator(this)
|
||||||
|
@ -42,20 +42,20 @@ public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolatePolynomials(
|
|||||||
x: Buffer<T>,
|
x: Buffer<T>,
|
||||||
y: Buffer<T>,
|
y: Buffer<T>,
|
||||||
): PiecewisePolynomial<T> {
|
): PiecewisePolynomial<T> {
|
||||||
val pointSet = XYColumnarData(x, y)
|
val pointSet = XYColumnarData.of(x, y)
|
||||||
return interpolatePolynomials(pointSet)
|
return interpolatePolynomials(pointSet)
|
||||||
}
|
}
|
||||||
|
|
||||||
public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolatePolynomials(
|
public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolatePolynomials(
|
||||||
data: Map<T, T>,
|
data: Map<T, T>,
|
||||||
): PiecewisePolynomial<T> {
|
): PiecewisePolynomial<T> {
|
||||||
val pointSet = XYColumnarData(data.keys.toList().asBuffer(), data.values.toList().asBuffer())
|
val pointSet = XYColumnarData.of(data.keys.toList().asBuffer(), data.values.toList().asBuffer())
|
||||||
return interpolatePolynomials(pointSet)
|
return interpolatePolynomials(pointSet)
|
||||||
}
|
}
|
||||||
|
|
||||||
public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolatePolynomials(
|
public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolatePolynomials(
|
||||||
data: List<Pair<T, T>>,
|
data: List<Pair<T, T>>,
|
||||||
): PiecewisePolynomial<T> {
|
): PiecewisePolynomial<T> {
|
||||||
val pointSet = XYColumnarData(data.map { it.first }.asBuffer(), data.map { it.second }.asBuffer())
|
val pointSet = XYColumnarData.of(data.map { it.first }.asBuffer(), data.map { it.second }.asBuffer())
|
||||||
return interpolatePolynomials(pointSet)
|
return interpolatePolynomials(pointSet)
|
||||||
}
|
}
|
||||||
|
20
kmath-optimization/build.gradle.kts
Normal file
20
kmath-optimization/build.gradle.kts
Normal file
@ -0,0 +1,20 @@
|
|||||||
|
plugins {
|
||||||
|
id("ru.mipt.npm.gradle.mpp")
|
||||||
|
id("ru.mipt.npm.gradle.native")
|
||||||
|
}
|
||||||
|
|
||||||
|
kscience {
|
||||||
|
useAtomic()
|
||||||
|
}
|
||||||
|
|
||||||
|
kotlin.sourceSets {
|
||||||
|
commonMain {
|
||||||
|
dependencies {
|
||||||
|
api(project(":kmath-coroutines"))
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
readme {
|
||||||
|
maturity = ru.mipt.npm.gradle.Maturity.EXPERIMENTAL
|
||||||
|
}
|
@ -5,13 +5,11 @@
|
|||||||
|
|
||||||
package space.kscience.kmath.optimization
|
package space.kscience.kmath.optimization
|
||||||
|
|
||||||
import space.kscience.kmath.expressions.*
|
import space.kscience.kmath.expressions.DifferentiableExpression
|
||||||
|
import space.kscience.kmath.expressions.Symbol
|
||||||
import space.kscience.kmath.misc.FeatureSet
|
import space.kscience.kmath.misc.FeatureSet
|
||||||
import space.kscience.kmath.operations.ExtendedField
|
|
||||||
import space.kscience.kmath.structures.Buffer
|
|
||||||
import space.kscience.kmath.structures.indices
|
|
||||||
|
|
||||||
public class OptimizationValue<T>(public val value: T) : OptimizationFeature{
|
public class OptimizationValue<T>(public val value: T) : OptimizationFeature {
|
||||||
override fun toString(): String = "Value($value)"
|
override fun toString(): String = "Value($value)"
|
||||||
}
|
}
|
||||||
|
|
||||||
@ -23,9 +21,28 @@ public enum class FunctionOptimizationTarget : OptimizationFeature {
|
|||||||
public class FunctionOptimization<T>(
|
public class FunctionOptimization<T>(
|
||||||
override val features: FeatureSet<OptimizationFeature>,
|
override val features: FeatureSet<OptimizationFeature>,
|
||||||
public val expression: DifferentiableExpression<T>,
|
public val expression: DifferentiableExpression<T>,
|
||||||
) : OptimizationProblem<T>{
|
) : OptimizationProblem<T> {
|
||||||
|
|
||||||
public companion object
|
|
||||||
|
override fun equals(other: Any?): Boolean {
|
||||||
|
if (this === other) return true
|
||||||
|
if (other == null || this::class != other::class) return false
|
||||||
|
|
||||||
|
other as FunctionOptimization<*>
|
||||||
|
|
||||||
|
if (features != other.features) return false
|
||||||
|
if (expression != other.expression) return false
|
||||||
|
|
||||||
|
return true
|
||||||
|
}
|
||||||
|
|
||||||
|
override fun hashCode(): Int {
|
||||||
|
var result = features.hashCode()
|
||||||
|
result = 31 * result + expression.hashCode()
|
||||||
|
return result
|
||||||
|
}
|
||||||
|
|
||||||
|
override fun toString(): String = "FunctionOptimization(features=$features)"
|
||||||
}
|
}
|
||||||
|
|
||||||
public fun <T> FunctionOptimization<T>.withFeatures(
|
public fun <T> FunctionOptimization<T>.withFeatures(
|
||||||
@ -47,7 +64,7 @@ public suspend fun <T : Any> DifferentiableExpression<T>.optimizeWith(
|
|||||||
return optimizer.optimize(problem)
|
return optimizer.optimize(problem)
|
||||||
}
|
}
|
||||||
|
|
||||||
public val <T> FunctionOptimization<T>.resultValueOrNull:T?
|
public val <T> FunctionOptimization<T>.resultValueOrNull: T?
|
||||||
get() = getFeature<OptimizationResult<T>>()?.point?.let { expression(it) }
|
get() = getFeature<OptimizationResult<T>>()?.point?.let { expression(it) }
|
||||||
|
|
||||||
public val <T> FunctionOptimization<T>.resultValue: T
|
public val <T> FunctionOptimization<T>.resultValue: T
|
@ -72,15 +72,15 @@ public suspend fun <T> DifferentiableExpression<T>.optimizeWith(
|
|||||||
public class XYOptimizationBuilder(
|
public class XYOptimizationBuilder(
|
||||||
public val data: XYColumnarData<Double, Double, Double>,
|
public val data: XYColumnarData<Double, Double, Double>,
|
||||||
public val model: DifferentiableExpression<Double>,
|
public val model: DifferentiableExpression<Double>,
|
||||||
) : OptimizationBuilder<Double, XYOptimization>() {
|
) : OptimizationBuilder<Double, XYFit>() {
|
||||||
|
|
||||||
public var pointToCurveDistance: PointToCurveDistance = PointToCurveDistance.byY
|
public var pointToCurveDistance: PointToCurveDistance = PointToCurveDistance.byY
|
||||||
public var pointWeight: PointWeight = PointWeight.byYSigma
|
public var pointWeight: PointWeight = PointWeight.byYSigma
|
||||||
|
|
||||||
override fun build(): XYOptimization = XYOptimization(
|
override fun build(): XYFit = XYFit(
|
||||||
FeatureSet.of(features),
|
|
||||||
data,
|
data,
|
||||||
model,
|
model,
|
||||||
|
FeatureSet.of(features),
|
||||||
pointToCurveDistance,
|
pointToCurveDistance,
|
||||||
pointWeight
|
pointWeight
|
||||||
)
|
)
|
||||||
@ -90,4 +90,4 @@ public fun XYOptimization(
|
|||||||
data: XYColumnarData<Double, Double, Double>,
|
data: XYColumnarData<Double, Double, Double>,
|
||||||
model: DifferentiableExpression<Double>,
|
model: DifferentiableExpression<Double>,
|
||||||
builder: XYOptimizationBuilder.() -> Unit,
|
builder: XYOptimizationBuilder.() -> Unit,
|
||||||
): XYOptimization = XYOptimizationBuilder(data, model).apply(builder).build()
|
): XYFit = XYOptimizationBuilder(data, model).apply(builder).build()
|
@ -11,6 +11,7 @@ import space.kscience.kmath.expressions.SymbolIndexer
|
|||||||
import space.kscience.kmath.expressions.derivative
|
import space.kscience.kmath.expressions.derivative
|
||||||
import space.kscience.kmath.linear.*
|
import space.kscience.kmath.linear.*
|
||||||
import space.kscience.kmath.misc.UnstableKMathAPI
|
import space.kscience.kmath.misc.UnstableKMathAPI
|
||||||
|
import space.kscience.kmath.misc.log
|
||||||
import space.kscience.kmath.operations.DoubleField
|
import space.kscience.kmath.operations.DoubleField
|
||||||
import space.kscience.kmath.structures.DoubleBuffer
|
import space.kscience.kmath.structures.DoubleBuffer
|
||||||
import space.kscience.kmath.structures.DoubleL2Norm
|
import space.kscience.kmath.structures.DoubleL2Norm
|
||||||
@ -21,14 +22,14 @@ import space.kscience.kmath.structures.DoubleL2Norm
|
|||||||
* See [the article](http://arxiv.org/abs/physics/0604127).
|
* See [the article](http://arxiv.org/abs/physics/0604127).
|
||||||
*/
|
*/
|
||||||
@UnstableKMathAPI
|
@UnstableKMathAPI
|
||||||
public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
public object QowOptimizer : Optimizer<Double, XYFit> {
|
||||||
|
|
||||||
private val linearSpace: LinearSpace<Double, DoubleField> = LinearSpace.double
|
private val linearSpace: LinearSpace<Double, DoubleField> = LinearSpace.double
|
||||||
private val solver: LinearSolver<Double> = linearSpace.lupSolver()
|
private val solver: LinearSolver<Double> = linearSpace.lupSolver()
|
||||||
|
|
||||||
@OptIn(UnstableKMathAPI::class)
|
@OptIn(UnstableKMathAPI::class)
|
||||||
private inner class QoWeight(
|
private class QoWeight(
|
||||||
val problem: XYOptimization,
|
val problem: XYFit,
|
||||||
val parameters: Map<Symbol, Double>,
|
val parameters: Map<Symbol, Double>,
|
||||||
) : Map<Symbol, Double> by parameters, SymbolIndexer {
|
) : Map<Symbol, Double> by parameters, SymbolIndexer {
|
||||||
override val symbols: List<Symbol> = parameters.keys.toList()
|
override val symbols: List<Symbol> = parameters.keys.toList()
|
||||||
@ -39,8 +40,8 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
* Derivatives of the spectrum over parameters. First index in the point number, second one - index of parameter
|
* Derivatives of the spectrum over parameters. First index in the point number, second one - index of parameter
|
||||||
*/
|
*/
|
||||||
val derivs: Matrix<Double> by lazy {
|
val derivs: Matrix<Double> by lazy {
|
||||||
linearSpace.buildMatrix(problem.data.size, symbols.size) { i, k ->
|
linearSpace.buildMatrix(problem.data.size, symbols.size) { d, s ->
|
||||||
problem.distance(i).derivative(symbols[k])(parameters)
|
problem.distance(d).derivative(symbols[s])(parameters)
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
@ -48,25 +49,27 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
* Array of dispersions in each point
|
* Array of dispersions in each point
|
||||||
*/
|
*/
|
||||||
val dispersion: Point<Double> by lazy {
|
val dispersion: Point<Double> by lazy {
|
||||||
DoubleBuffer(problem.data.size) { i ->
|
DoubleBuffer(problem.data.size) { d ->
|
||||||
problem.weight(i).invoke(parameters)
|
problem.weight(d).invoke(parameters)
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
val prior: DifferentiableExpression<Double>? get() = problem.getFeature<OptimizationPrior<Double>>()
|
val prior: DifferentiableExpression<Double>? get() = problem.getFeature<OptimizationPrior<Double>>()
|
||||||
|
|
||||||
|
override fun toString(): String = parameters.toString()
|
||||||
}
|
}
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* The signed distance from the model to the [i]-th point of data.
|
* The signed distance from the model to the [d]-th point of data.
|
||||||
*/
|
*/
|
||||||
private fun QoWeight.distance(i: Int, parameters: Map<Symbol, Double>): Double = problem.distance(i)(parameters)
|
private fun QoWeight.distance(d: Int, parameters: Map<Symbol, Double>): Double = problem.distance(d)(parameters)
|
||||||
|
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* The derivative of [distance]
|
* The derivative of [distance]
|
||||||
*/
|
*/
|
||||||
private fun QoWeight.distanceDerivative(symbol: Symbol, i: Int, parameters: Map<Symbol, Double>): Double =
|
private fun QoWeight.distanceDerivative(symbol: Symbol, d: Int, parameters: Map<Symbol, Double>): Double =
|
||||||
problem.distance(i).derivative(symbol)(parameters)
|
problem.distance(d).derivative(symbol)(parameters)
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Теоретическая ковариация весовых функций.
|
* Теоретическая ковариация весовых функций.
|
||||||
@ -74,8 +77,8 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
* D(\phi)=E(\phi_k(\theta_0) \phi_l(\theta_0))= disDeriv_k * disDeriv_l /sigma^2
|
* D(\phi)=E(\phi_k(\theta_0) \phi_l(\theta_0))= disDeriv_k * disDeriv_l /sigma^2
|
||||||
*/
|
*/
|
||||||
private fun QoWeight.covarF(): Matrix<Double> =
|
private fun QoWeight.covarF(): Matrix<Double> =
|
||||||
linearSpace.matrix(size, size).symmetric { k, l ->
|
linearSpace.matrix(size, size).symmetric { s1, s2 ->
|
||||||
(0 until data.size).sumOf { i -> derivs[k, i] * derivs[l, i] / dispersion[i] }
|
(0 until data.size).sumOf { d -> derivs[d, s1] * derivs[d, s2] / dispersion[d] }
|
||||||
}
|
}
|
||||||
|
|
||||||
/**
|
/**
|
||||||
@ -89,12 +92,12 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
* количество вызывов функции будет dim^2 вместо dim Первый индекс -
|
* количество вызывов функции будет dim^2 вместо dim Первый индекс -
|
||||||
* номер точки, второй - номер переменной, по которой берется производная
|
* номер точки, второй - номер переменной, по которой берется производная
|
||||||
*/
|
*/
|
||||||
val eqvalues = linearSpace.buildMatrix(data.size, size) { i, l ->
|
val eqvalues = linearSpace.buildMatrix(data.size, size) { d, s ->
|
||||||
distance(i, theta) * derivs[l, i] / dispersion[i]
|
distance(d, theta) * derivs[d, s] / dispersion[d]
|
||||||
}
|
}
|
||||||
|
|
||||||
buildMatrix(size, size) { k, l ->
|
buildMatrix(size, size) { s1, s2 ->
|
||||||
(0 until data.size).sumOf { i -> eqvalues[i, l] * eqvalues[i, k] }
|
(0 until data.size).sumOf { d -> eqvalues[d, s2] * eqvalues[d, s1] }
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
@ -106,20 +109,20 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
): Matrix<Double> = with(linearSpace) {
|
): Matrix<Double> = with(linearSpace) {
|
||||||
//Возвращает производную k-того Eq по l-тому параметру
|
//Возвращает производную k-того Eq по l-тому параметру
|
||||||
//val res = Array(fitDim) { DoubleArray(fitDim) }
|
//val res = Array(fitDim) { DoubleArray(fitDim) }
|
||||||
val sderiv = buildMatrix(data.size, size) { i, l ->
|
val sderiv = buildMatrix(data.size, size) { d, s ->
|
||||||
distanceDerivative(symbols[l], i, theta)
|
distanceDerivative(symbols[s], d, theta)
|
||||||
}
|
}
|
||||||
|
|
||||||
buildMatrix(size, size) { k, l ->
|
buildMatrix(size, size) { s1, s2 ->
|
||||||
val base = (0 until data.size).sumOf { i ->
|
val base = (0 until data.size).sumOf { d ->
|
||||||
require(dispersion[i] > 0)
|
require(dispersion[d] > 0)
|
||||||
sderiv[i, l] * derivs[k, i] / dispersion[i]
|
sderiv[d, s2] * derivs[d, s1] / dispersion[d]
|
||||||
}
|
}
|
||||||
prior?.let { prior ->
|
prior?.let { prior ->
|
||||||
//Check if this one is correct
|
//Check if this one is correct
|
||||||
val pi = prior(theta)
|
val pi = prior(theta)
|
||||||
val deriv1 = prior.derivative(symbols[k])(theta)
|
val deriv1 = prior.derivative(symbols[s1])(theta)
|
||||||
val deriv2 = prior.derivative(symbols[l])(theta)
|
val deriv2 = prior.derivative(symbols[s2])(theta)
|
||||||
base + deriv1 * deriv2 / pi / pi
|
base + deriv1 * deriv2 / pi / pi
|
||||||
} ?: base
|
} ?: base
|
||||||
}
|
}
|
||||||
@ -130,13 +133,13 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
* Значения уравнений метода квазиоптимальных весов
|
* Значения уравнений метода квазиоптимальных весов
|
||||||
*/
|
*/
|
||||||
private fun QoWeight.getEqValues(theta: Map<Symbol, Double> = this): Point<Double> {
|
private fun QoWeight.getEqValues(theta: Map<Symbol, Double> = this): Point<Double> {
|
||||||
val distances = DoubleBuffer(data.size) { i -> distance(i, theta) }
|
val distances = DoubleBuffer(data.size) { d -> distance(d, theta) }
|
||||||
|
|
||||||
return DoubleBuffer(size) { k ->
|
return DoubleBuffer(size) { s ->
|
||||||
val base = (0 until data.size).sumOf { i -> distances[i] * derivs[k, i] / dispersion[i] }
|
val base = (0 until data.size).sumOf { d -> distances[d] * derivs[d, s] / dispersion[d] }
|
||||||
//Поправка на априорную вероятность
|
//Поправка на априорную вероятность
|
||||||
prior?.let { prior ->
|
prior?.let { prior ->
|
||||||
base - prior.derivative(symbols[k])(theta) / prior(theta)
|
base - prior.derivative(symbols[s])(theta) / prior(theta)
|
||||||
} ?: base
|
} ?: base
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
@ -163,15 +166,15 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
|
|
||||||
val logger = problem.getFeature<OptimizationLog>()
|
val logger = problem.getFeature<OptimizationLog>()
|
||||||
|
|
||||||
var dis: Double//норма невязки
|
var dis: Double //discrepancy value
|
||||||
// Для удобства работаем всегда с полным набором параметров
|
// Working with the full set of parameters
|
||||||
var par = problem.startPoint
|
var par = problem.startPoint
|
||||||
|
|
||||||
logger?.log { "Starting newtonian iteration from: \n\t$par" }
|
logger?.log { "Starting newtonian iteration from: \n\t$par" }
|
||||||
|
|
||||||
var eqvalues = getEqValues(par)//значения функций
|
var eqvalues = getEqValues(par) //Values of the weight functions
|
||||||
|
|
||||||
dis = DoubleL2Norm.norm(eqvalues)// невязка
|
dis = DoubleL2Norm.norm(eqvalues) // discrepancy
|
||||||
logger?.log { "Starting discrepancy is $dis" }
|
logger?.log { "Starting discrepancy is $dis" }
|
||||||
var i = 0
|
var i = 0
|
||||||
var flag = false
|
var flag = false
|
||||||
@ -238,7 +241,8 @@ public class QowOptimizer : Optimizer<Double, XYOptimization> {
|
|||||||
return covar
|
return covar
|
||||||
}
|
}
|
||||||
|
|
||||||
override suspend fun optimize(problem: XYOptimization): XYOptimization {
|
override suspend fun optimize(problem: XYFit): XYFit {
|
||||||
|
val qowSteps = 2
|
||||||
val initialWeight = QoWeight(problem, problem.startPoint)
|
val initialWeight = QoWeight(problem, problem.startPoint)
|
||||||
val res = initialWeight.newtonianRun()
|
val res = initialWeight.newtonianRun()
|
||||||
return res.problem.withFeature(OptimizationResult(res.parameters))
|
return res.problem.withFeature(OptimizationResult(res.parameters))
|
@ -0,0 +1,125 @@
|
|||||||
|
/*
|
||||||
|
* Copyright 2018-2021 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.
|
||||||
|
*/
|
||||||
|
@file:OptIn(UnstableKMathAPI::class)
|
||||||
|
|
||||||
|
package space.kscience.kmath.optimization
|
||||||
|
|
||||||
|
import space.kscience.kmath.data.XYColumnarData
|
||||||
|
import space.kscience.kmath.expressions.*
|
||||||
|
import space.kscience.kmath.misc.FeatureSet
|
||||||
|
import space.kscience.kmath.misc.Loggable
|
||||||
|
import space.kscience.kmath.misc.UnstableKMathAPI
|
||||||
|
import space.kscience.kmath.operations.ExtendedField
|
||||||
|
import space.kscience.kmath.operations.bindSymbol
|
||||||
|
import kotlin.math.pow
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Specify the way to compute distance from point to the curve as DifferentiableExpression
|
||||||
|
*/
|
||||||
|
public interface PointToCurveDistance : OptimizationFeature {
|
||||||
|
public fun distance(problem: XYFit, index: Int): DifferentiableExpression<Double>
|
||||||
|
|
||||||
|
public companion object {
|
||||||
|
public val byY: PointToCurveDistance = object : PointToCurveDistance {
|
||||||
|
override fun distance(problem: XYFit, index: Int): DifferentiableExpression<Double> {
|
||||||
|
val x = problem.data.x[index]
|
||||||
|
val y = problem.data.y[index]
|
||||||
|
|
||||||
|
return object : DifferentiableExpression<Double> {
|
||||||
|
override fun derivativeOrNull(
|
||||||
|
symbols: List<Symbol>
|
||||||
|
): Expression<Double>? = problem.model.derivativeOrNull(symbols)?.let { derivExpression ->
|
||||||
|
Expression { arguments ->
|
||||||
|
derivExpression.invoke(arguments + (Symbol.x to x))
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
override fun invoke(arguments: Map<Symbol, Double>): Double =
|
||||||
|
problem.model(arguments + (Symbol.x to x)) - y
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
override fun toString(): String = "PointToCurveDistanceByY"
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Compute a wight of the point. The more the weight, the more impact this point will have on the fit.
|
||||||
|
* By default, uses Dispersion^-1
|
||||||
|
*/
|
||||||
|
public interface PointWeight : OptimizationFeature {
|
||||||
|
public fun weight(problem: XYFit, index: Int): DifferentiableExpression<Double>
|
||||||
|
|
||||||
|
public companion object {
|
||||||
|
public fun bySigma(sigmaSymbol: Symbol): PointWeight = object : PointWeight {
|
||||||
|
override fun weight(problem: XYFit, index: Int): DifferentiableExpression<Double> =
|
||||||
|
object : DifferentiableExpression<Double> {
|
||||||
|
override fun invoke(arguments: Map<Symbol, Double>): Double {
|
||||||
|
return problem.data[sigmaSymbol]?.get(index)?.pow(-2) ?: 1.0
|
||||||
|
}
|
||||||
|
|
||||||
|
override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double> = Expression { 0.0 }
|
||||||
|
}
|
||||||
|
|
||||||
|
override fun toString(): String = "PointWeightBySigma($sigmaSymbol)"
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
public val byYSigma: PointWeight = bySigma(Symbol.yError)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* A fit problem for X-Y-Yerr data. Also known as "least-squares" problem.
|
||||||
|
*/
|
||||||
|
public class XYFit(
|
||||||
|
public val data: XYColumnarData<Double, Double, Double>,
|
||||||
|
public val model: DifferentiableExpression<Double>,
|
||||||
|
override val features: FeatureSet<OptimizationFeature>,
|
||||||
|
internal val pointToCurveDistance: PointToCurveDistance = PointToCurveDistance.byY,
|
||||||
|
internal val pointWeight: PointWeight = PointWeight.byYSigma,
|
||||||
|
) : OptimizationProblem<Double> {
|
||||||
|
public fun distance(index: Int): DifferentiableExpression<Double> = pointToCurveDistance.distance(this, index)
|
||||||
|
|
||||||
|
public fun weight(index: Int): DifferentiableExpression<Double> = pointWeight.weight(this, index)
|
||||||
|
}
|
||||||
|
|
||||||
|
public fun XYFit.withFeature(vararg features: OptimizationFeature): XYFit {
|
||||||
|
return XYFit(data, model, this.features.with(*features), pointToCurveDistance, pointWeight)
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Fit given dta with
|
||||||
|
*/
|
||||||
|
public suspend fun <I : Any, A> XYColumnarData<Double, Double, Double>.fitWith(
|
||||||
|
optimizer: Optimizer<Double, XYFit>,
|
||||||
|
processor: AutoDiffProcessor<Double, I, A>,
|
||||||
|
startingPoint: Map<Symbol, Double>,
|
||||||
|
vararg features: OptimizationFeature = emptyArray(),
|
||||||
|
xSymbol: Symbol = Symbol.x,
|
||||||
|
pointToCurveDistance: PointToCurveDistance = PointToCurveDistance.byY,
|
||||||
|
pointWeight: PointWeight = PointWeight.byYSigma,
|
||||||
|
model: A.(I) -> I
|
||||||
|
): XYFit where A : ExtendedField<I>, A : ExpressionAlgebra<Double, I> {
|
||||||
|
val modelExpression = processor.differentiate {
|
||||||
|
val x = bindSymbol(xSymbol)
|
||||||
|
model(x)
|
||||||
|
}
|
||||||
|
|
||||||
|
var actualFeatures = FeatureSet.of(*features, OptimizationStartPoint(startingPoint))
|
||||||
|
|
||||||
|
if (actualFeatures.getFeature<OptimizationLog>() == null) {
|
||||||
|
actualFeatures = actualFeatures.with(OptimizationLog(Loggable.console))
|
||||||
|
}
|
||||||
|
val problem = XYFit(
|
||||||
|
this,
|
||||||
|
modelExpression,
|
||||||
|
actualFeatures,
|
||||||
|
pointToCurveDistance,
|
||||||
|
pointWeight
|
||||||
|
)
|
||||||
|
return optimizer.optimize(problem)
|
||||||
|
}
|
@ -0,0 +1,66 @@
|
|||||||
|
/*
|
||||||
|
* Copyright 2018-2021 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.optimization
|
||||||
|
|
||||||
|
import space.kscience.kmath.data.XYColumnarData
|
||||||
|
import space.kscience.kmath.data.indices
|
||||||
|
import space.kscience.kmath.expressions.DifferentiableExpression
|
||||||
|
import space.kscience.kmath.expressions.Expression
|
||||||
|
import space.kscience.kmath.expressions.Symbol
|
||||||
|
import space.kscience.kmath.expressions.derivative
|
||||||
|
import space.kscience.kmath.misc.UnstableKMathAPI
|
||||||
|
import kotlin.math.PI
|
||||||
|
import kotlin.math.ln
|
||||||
|
import kotlin.math.pow
|
||||||
|
import kotlin.math.sqrt
|
||||||
|
|
||||||
|
|
||||||
|
private val oneOver2Pi = 1.0 / sqrt(2 * PI)
|
||||||
|
|
||||||
|
@UnstableKMathAPI
|
||||||
|
internal fun XYFit.logLikelihood(): DifferentiableExpression<Double> = object : DifferentiableExpression<Double> {
|
||||||
|
override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double> = Expression { arguments ->
|
||||||
|
data.indices.sumOf { index ->
|
||||||
|
val d = distance(index)(arguments)
|
||||||
|
val weight = weight(index)(arguments)
|
||||||
|
val weightDerivative = weight(index)(arguments)
|
||||||
|
|
||||||
|
// -1 / (sqrt(2 PI) * sigma) + 2 (x-mu)/ 2 sigma^2 * d mu/ d theta - (x-mu)^2 / 2 * d w/ d theta
|
||||||
|
return@sumOf -oneOver2Pi * sqrt(weight) + //offset derivative
|
||||||
|
d * model.derivative(symbols)(arguments) * weight - //model derivative
|
||||||
|
d.pow(2) * weightDerivative / 2 //weight derivative
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
override fun invoke(arguments: Map<Symbol, Double>): Double {
|
||||||
|
return data.indices.sumOf { index ->
|
||||||
|
val d = distance(index)(arguments)
|
||||||
|
val weight = weight(index)(arguments)
|
||||||
|
//1/sqrt(2 PI sigma^2) - (x-mu)^2/ (2 * sigma^2)
|
||||||
|
oneOver2Pi * ln(weight) - d.pow(2) * weight
|
||||||
|
} / 2
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Optimize given XY (least squares) [problem] using this function [Optimizer].
|
||||||
|
* The problem is treated as maximum likelihood problem and is done via maximizing logarithmic likelihood, respecting
|
||||||
|
* possible weight dependency on the model and parameters.
|
||||||
|
*/
|
||||||
|
@UnstableKMathAPI
|
||||||
|
public suspend fun Optimizer<Double, FunctionOptimization<Double>>.maximumLogLikelihood(problem: XYFit): XYFit {
|
||||||
|
val functionOptimization = FunctionOptimization(problem.features, problem.logLikelihood())
|
||||||
|
val result = optimize(functionOptimization.withFeatures(FunctionOptimizationTarget.MAXIMIZE))
|
||||||
|
return XYFit(problem.data, problem.model, result.features)
|
||||||
|
}
|
||||||
|
|
||||||
|
@UnstableKMathAPI
|
||||||
|
public suspend fun Optimizer<Double, FunctionOptimization<Double>>.maximumLogLikelihood(
|
||||||
|
data: XYColumnarData<Double, Double, Double>,
|
||||||
|
model: DifferentiableExpression<Double>,
|
||||||
|
builder: XYOptimizationBuilder.() -> Unit,
|
||||||
|
): XYFit = maximumLogLikelihood(XYOptimization(data, model, builder))
|
@ -1,6 +1,5 @@
|
|||||||
plugins {
|
plugins {
|
||||||
kotlin("multiplatform")
|
id("ru.mipt.npm.gradle.mpp")
|
||||||
id("ru.mipt.npm.gradle.common")
|
|
||||||
id("ru.mipt.npm.gradle.native")
|
id("ru.mipt.npm.gradle.native")
|
||||||
}
|
}
|
||||||
|
|
||||||
|
@ -1,189 +0,0 @@
|
|||||||
/*
|
|
||||||
* Copyright 2018-2021 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.
|
|
||||||
*/
|
|
||||||
@file:OptIn(UnstableKMathAPI::class)
|
|
||||||
|
|
||||||
package space.kscience.kmath.optimization
|
|
||||||
|
|
||||||
import space.kscience.kmath.data.XYColumnarData
|
|
||||||
import space.kscience.kmath.data.indices
|
|
||||||
import space.kscience.kmath.expressions.DifferentiableExpression
|
|
||||||
import space.kscience.kmath.expressions.Expression
|
|
||||||
import space.kscience.kmath.expressions.Symbol
|
|
||||||
import space.kscience.kmath.expressions.derivative
|
|
||||||
import space.kscience.kmath.misc.FeatureSet
|
|
||||||
import space.kscience.kmath.misc.UnstableKMathAPI
|
|
||||||
import kotlin.math.PI
|
|
||||||
import kotlin.math.ln
|
|
||||||
import kotlin.math.pow
|
|
||||||
import kotlin.math.sqrt
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Specify the way to compute distance from point to the curve as DifferentiableExpression
|
|
||||||
*/
|
|
||||||
public interface PointToCurveDistance : OptimizationFeature {
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|
||||||
public fun distance(problem: XYOptimization, index: Int): DifferentiableExpression<Double>
|
|
||||||
|
|
||||||
public companion object {
|
|
||||||
public val byY: PointToCurveDistance = object : PointToCurveDistance {
|
|
||||||
override fun distance(problem: XYOptimization, index: Int): DifferentiableExpression<Double> {
|
|
||||||
|
|
||||||
val x = problem.data.x[index]
|
|
||||||
val y = problem.data.y[index]
|
|
||||||
return object : DifferentiableExpression<Double> {
|
|
||||||
override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double>? =
|
|
||||||
problem.model.derivativeOrNull(symbols)
|
|
||||||
|
|
||||||
override fun invoke(arguments: Map<Symbol, Double>): Double =
|
|
||||||
problem.model(arguments + (Symbol.x to x)) - y
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
override fun toString(): String = "PointToCurveDistanceByY"
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Compute a wight of the point. The more the weight, the more impact this point will have on the fit.
|
|
||||||
* By default uses Dispersion^-1
|
|
||||||
*/
|
|
||||||
public interface PointWeight : OptimizationFeature {
|
|
||||||
public fun weight(problem: XYOptimization, index: Int): DifferentiableExpression<Double>
|
|
||||||
|
|
||||||
public companion object {
|
|
||||||
public fun bySigma(sigmaSymbol: Symbol): PointWeight = object : PointWeight {
|
|
||||||
override fun weight(problem: XYOptimization, index: Int): DifferentiableExpression<Double> =
|
|
||||||
object : DifferentiableExpression<Double> {
|
|
||||||
override fun invoke(arguments: Map<Symbol, Double>): Double {
|
|
||||||
return problem.data[sigmaSymbol]?.get(index)?.pow(-2) ?: 1.0
|
|
||||||
}
|
|
||||||
|
|
||||||
override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double> = Expression { 0.0 }
|
|
||||||
}
|
|
||||||
|
|
||||||
override fun toString(): String = "PointWeightBySigma($sigmaSymbol)"
|
|
||||||
|
|
||||||
}
|
|
||||||
|
|
||||||
public val byYSigma: PointWeight = bySigma(Symbol.yError)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* An optimization for XY data.
|
|
||||||
*/
|
|
||||||
public class XYOptimization(
|
|
||||||
override val features: FeatureSet<OptimizationFeature>,
|
|
||||||
public val data: XYColumnarData<Double, Double, Double>,
|
|
||||||
public val model: DifferentiableExpression<Double>,
|
|
||||||
internal val pointToCurveDistance: PointToCurveDistance = PointToCurveDistance.byY,
|
|
||||||
internal val pointWeight: PointWeight = PointWeight.byYSigma,
|
|
||||||
) : OptimizationProblem<Double> {
|
|
||||||
public fun distance(index: Int): DifferentiableExpression<Double> = pointToCurveDistance.distance(this, index)
|
|
||||||
|
|
||||||
public fun weight(index: Int): DifferentiableExpression<Double> = pointWeight.weight(this, index)
|
|
||||||
}
|
|
||||||
|
|
||||||
public fun XYOptimization.withFeature(vararg features: OptimizationFeature): XYOptimization {
|
|
||||||
return XYOptimization(this.features.with(*features), data, model, pointToCurveDistance, pointWeight)
|
|
||||||
}
|
|
||||||
|
|
||||||
private val oneOver2Pi = 1.0 / sqrt(2 * PI)
|
|
||||||
|
|
||||||
internal fun XYOptimization.likelihood(): DifferentiableExpression<Double> = object : DifferentiableExpression<Double> {
|
|
||||||
override fun derivativeOrNull(symbols: List<Symbol>): Expression<Double> = Expression { arguments ->
|
|
||||||
data.indices.sumOf { index ->
|
|
||||||
|
|
||||||
val d = distance(index)(arguments)
|
|
||||||
val weight = weight(index)(arguments)
|
|
||||||
val weightDerivative = weight(index)(arguments)
|
|
||||||
|
|
||||||
// -1 / (sqrt(2 PI) * sigma) + 2 (x-mu)/ 2 sigma^2 * d mu/ d theta - (x-mu)^2 / 2 * d w/ d theta
|
|
||||||
return@sumOf -oneOver2Pi * sqrt(weight) + //offset derivative
|
|
||||||
d * model.derivative(symbols)(arguments) * weight - //model derivative
|
|
||||||
d.pow(2) * weightDerivative / 2 //weight derivative
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
override fun invoke(arguments: Map<Symbol, Double>): Double {
|
|
||||||
return data.indices.sumOf { index ->
|
|
||||||
val d = distance(index)(arguments)
|
|
||||||
val weight = weight(index)(arguments)
|
|
||||||
//1/sqrt(2 PI sigma^2) - (x-mu)^2/ (2 * sigma^2)
|
|
||||||
oneOver2Pi * ln(weight) - d.pow(2) * weight
|
|
||||||
} / 2
|
|
||||||
}
|
|
||||||
|
|
||||||
}
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Optimize given XY (least squares) [problem] using this function [Optimizer].
|
|
||||||
* The problem is treated as maximum likelihood problem and is done via maximizing logarithmic likelihood, respecting
|
|
||||||
* possible weight dependency on the model and parameters.
|
|
||||||
*/
|
|
||||||
public suspend fun Optimizer<Double, FunctionOptimization<Double>>.maximumLogLikelihood(problem: XYOptimization): XYOptimization {
|
|
||||||
val functionOptimization = FunctionOptimization(problem.features, problem.likelihood())
|
|
||||||
val result = optimize(functionOptimization.withFeatures(FunctionOptimizationTarget.MAXIMIZE))
|
|
||||||
return XYOptimization(result.features, problem.data, problem.model)
|
|
||||||
}
|
|
||||||
|
|
||||||
public suspend fun Optimizer<Double, FunctionOptimization<Double>>.maximumLogLikelihood(
|
|
||||||
data: XYColumnarData<Double, Double, Double>,
|
|
||||||
model: DifferentiableExpression<Double>,
|
|
||||||
builder: XYOptimizationBuilder.() -> Unit,
|
|
||||||
): XYOptimization = maximumLogLikelihood(XYOptimization(data, model, builder))
|
|
||||||
|
|
||||||
//public suspend fun XYColumnarData<Double, Double, Double>.fitWith(
|
|
||||||
// optimizer: XYOptimization,
|
|
||||||
// problemBuilder: XYOptimizationBuilder.() -> Unit = {},
|
|
||||||
//
|
|
||||||
//)
|
|
||||||
|
|
||||||
|
|
||||||
//
|
|
||||||
//@UnstableKMathAPI
|
|
||||||
//public interface XYFit<T> : OptimizationProblem {
|
|
||||||
//
|
|
||||||
// public val algebra: Field<T>
|
|
||||||
//
|
|
||||||
// /**
|
|
||||||
// * Set X-Y data for this fit optionally including x and y errors
|
|
||||||
// */
|
|
||||||
// public fun data(
|
|
||||||
// dataSet: ColumnarData<T>,
|
|
||||||
// xSymbol: Symbol,
|
|
||||||
// ySymbol: Symbol,
|
|
||||||
// xErrSymbol: Symbol? = null,
|
|
||||||
// yErrSymbol: Symbol? = null,
|
|
||||||
// )
|
|
||||||
//
|
|
||||||
// public fun model(model: (T) -> DifferentiableExpression<T, *>)
|
|
||||||
//
|
|
||||||
// /**
|
|
||||||
// * Set the differentiable model for this fit
|
|
||||||
// */
|
|
||||||
// public fun <I : Any, A> model(
|
|
||||||
// autoDiff: AutoDiffProcessor<T, I, A, Expression<T>>,
|
|
||||||
// modelFunction: A.(I) -> I,
|
|
||||||
// ): Unit where A : ExtendedField<I>, A : ExpressionAlgebra<T, I> = model { arg ->
|
|
||||||
// autoDiff.process { modelFunction(const(arg)) }
|
|
||||||
// }
|
|
||||||
//}
|
|
||||||
|
|
||||||
//
|
|
||||||
///**
|
|
||||||
// * Define a chi-squared-based objective function
|
|
||||||
// */
|
|
||||||
//public fun <T : Any, I : Any, A> FunctionOptimization<T>.chiSquared(
|
|
||||||
// autoDiff: AutoDiffProcessor<T, I, A, Expression<T>>,
|
|
||||||
// x: Buffer<T>,
|
|
||||||
// y: Buffer<T>,
|
|
||||||
// yErr: Buffer<T>,
|
|
||||||
// model: A.(I) -> I,
|
|
||||||
//) where A : ExtendedField<I>, A : ExpressionAlgebra<T, I> {
|
|
||||||
// val chiSquared = FunctionOptimization.chiSquared(autoDiff, x, y, yErr, model)
|
|
||||||
// function(chiSquared)
|
|
||||||
// maximize = false
|
|
||||||
//}
|
|
@ -26,6 +26,7 @@ include(
|
|||||||
":kmath-histograms",
|
":kmath-histograms",
|
||||||
":kmath-commons",
|
":kmath-commons",
|
||||||
":kmath-viktor",
|
":kmath-viktor",
|
||||||
|
":kmath-optimization",
|
||||||
":kmath-stat",
|
":kmath-stat",
|
||||||
":kmath-nd4j",
|
":kmath-nd4j",
|
||||||
":kmath-dimensions",
|
":kmath-dimensions",
|
||||||
|
Loading…
Reference in New Issue
Block a user