forked from kscience/kmath
commit
df075718db
1
.gitignore
vendored
1
.gitignore
vendored
@ -19,3 +19,4 @@ out/
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!/.idea/copyright/
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!/.idea/copyright/
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!/.idea/scopes/
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!/.idea/scopes/
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/kotlin-js-store/yarn.lock
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@ -52,6 +52,8 @@ kotlin {
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implementation(project(":kmath-viktor"))
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implementation(project(":kmath-viktor"))
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implementation(project(":kmath-jafama"))
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implementation(project(":kmath-jafama"))
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implementation(project(":kmath-multik"))
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implementation(project(":kmath-multik"))
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implementation(projects.kmath.kmathTensorflow)
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implementation("org.tensorflow:tensorflow-core-platform:0.4.0")
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implementation("org.nd4j:nd4j-native:1.0.0-M1")
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implementation("org.nd4j:nd4j-native:1.0.0-M1")
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// uncomment if your system supports AVX2
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// uncomment if your system supports AVX2
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// val os = System.getProperty("os.name")
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// val os = System.getProperty("os.name")
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@ -122,6 +124,11 @@ benchmark {
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include("JafamaBenchmark")
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include("JafamaBenchmark")
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}
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}
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configurations.register("tensorAlgebra") {
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commonConfiguration()
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include("TensorAlgebraBenchmark")
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}
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configurations.register("viktor") {
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configurations.register("viktor") {
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commonConfiguration()
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commonConfiguration()
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include("ViktorBenchmark")
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include("ViktorBenchmark")
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@ -17,7 +17,9 @@ import space.kscience.kmath.multik.multikAlgebra
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.operations.invoke
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import space.kscience.kmath.operations.invoke
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import space.kscience.kmath.structures.Buffer
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import space.kscience.kmath.structures.Buffer
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import space.kscience.kmath.tensorflow.produceWithTF
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
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import space.kscience.kmath.tensors.core.tensorAlgebra
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import kotlin.random.Random
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import kotlin.random.Random
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@State(Scope.Benchmark)
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@State(Scope.Benchmark)
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@ -34,9 +36,6 @@ internal class DotBenchmark {
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random.nextDouble()
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random.nextDouble()
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}
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}
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val tensor1 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12224)
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val tensor2 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12225)
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val cmMatrix1 = CMLinearSpace { matrix1.toCM() }
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val cmMatrix1 = CMLinearSpace { matrix1.toCM() }
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val cmMatrix2 = CMLinearSpace { matrix2.toCM() }
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val cmMatrix2 = CMLinearSpace { matrix2.toCM() }
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@ -44,6 +43,16 @@ internal class DotBenchmark {
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val ejmlMatrix2 = EjmlLinearSpaceDDRM { matrix2.toEjml() }
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val ejmlMatrix2 = EjmlLinearSpaceDDRM { matrix2.toEjml() }
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}
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}
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@Benchmark
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fun tfDot(blackhole: Blackhole) {
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blackhole.consume(
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DoubleField.produceWithTF {
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matrix1 dot matrix1
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}
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)
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}
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@Benchmark
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@Benchmark
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fun cmDotWithConversion(blackhole: Blackhole) = CMLinearSpace {
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fun cmDotWithConversion(blackhole: Blackhole) = CMLinearSpace {
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blackhole.consume(matrix1 dot matrix2)
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blackhole.consume(matrix1 dot matrix2)
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@ -64,13 +73,13 @@ internal class DotBenchmark {
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blackhole.consume(matrix1 dot matrix2)
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blackhole.consume(matrix1 dot matrix2)
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}
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}
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// @Benchmark
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@Benchmark
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// fun tensorDot(blackhole: Blackhole) = with(Double.tensorAlgebra) {
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fun tensorDot(blackhole: Blackhole) = with(DoubleField.tensorAlgebra) {
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// blackhole.consume(matrix1 dot matrix2)
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blackhole.consume(matrix1 dot matrix2)
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// }
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}
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@Benchmark
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@Benchmark
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fun multikDot(blackhole: Blackhole) = with(Double.multikAlgebra) {
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fun multikDot(blackhole: Blackhole) = with(DoubleField.multikAlgebra) {
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blackhole.consume(matrix1 dot matrix2)
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blackhole.consume(matrix1 dot matrix2)
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}
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}
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@ -86,6 +95,6 @@ internal class DotBenchmark {
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@Benchmark
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@Benchmark
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fun doubleTensorDot(blackhole: Blackhole) = DoubleTensorAlgebra.invoke {
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fun doubleTensorDot(blackhole: Blackhole) = DoubleTensorAlgebra.invoke {
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blackhole.consume(tensor1 dot tensor2)
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blackhole.consume(matrix1 dot matrix2)
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}
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}
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}
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}
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@ -0,0 +1,37 @@
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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.benchmarks
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import kotlinx.benchmark.Benchmark
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import kotlinx.benchmark.Blackhole
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import kotlinx.benchmark.Scope
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import kotlinx.benchmark.State
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import space.kscience.kmath.linear.linearSpace
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import space.kscience.kmath.linear.matrix
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import space.kscience.kmath.linear.symmetric
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.tensors.core.tensorAlgebra
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import kotlin.random.Random
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@State(Scope.Benchmark)
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internal class TensorAlgebraBenchmark {
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companion object {
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private val random = Random(12224)
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private const val dim = 30
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private val matrix = DoubleField.linearSpace.matrix(dim, dim).symmetric { _, _ -> random.nextDouble() }
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}
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@Benchmark
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fun tensorSymEigSvd(blackhole: Blackhole) = with(Double.tensorAlgebra) {
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blackhole.consume(matrix.symEigSvd(1e-10))
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}
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@Benchmark
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fun tensorSymEigJacobi(blackhole: Blackhole) = with(Double.tensorAlgebra) {
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blackhole.consume(matrix.symEigJacobi(50, 1e-10))
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}
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}
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@ -10,7 +10,7 @@ allprojects {
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}
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}
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group = "space.kscience"
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group = "space.kscience"
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version = "0.3.0-dev-18"
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version = "0.3.0-dev-19"
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}
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}
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subprojects {
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subprojects {
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@ -5,8 +5,8 @@
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package space.kscience.kmath.functions
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package space.kscience.kmath.functions
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import space.kscience.kmath.interpolation.SplineInterpolator
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import space.kscience.kmath.interpolation.interpolatePolynomials
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import space.kscience.kmath.interpolation.interpolatePolynomials
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import space.kscience.kmath.interpolation.splineInterpolator
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import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.operations.DoubleField
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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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@ -28,7 +28,7 @@ fun main() {
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val xs = 0.0..100.0 step 0.5
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val xs = 0.0..100.0 step 0.5
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val ys = xs.map(function)
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val ys = xs.map(function)
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val polynomial: PiecewisePolynomial<Double> = SplineInterpolator.double.interpolatePolynomials(xs, ys)
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val polynomial: PiecewisePolynomial<Double> = DoubleField.splineInterpolator.interpolatePolynomials(xs, ys)
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val polyFunction = polynomial.asFunction(DoubleField, 0.0)
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val polyFunction = polynomial.asFunction(DoubleField, 0.0)
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@ -28,6 +28,8 @@ public fun <T : Comparable<T>> PiecewisePolynomial<T>.integrate(algebra: Field<T
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/**
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/**
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* Compute definite integral of given [PiecewisePolynomial] piece by piece in a given [range]
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* Compute definite integral of given [PiecewisePolynomial] piece by piece in a given [range]
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* Requires [UnivariateIntegrationNodes] or [IntegrationRange] and [IntegrandMaxCalls]
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* Requires [UnivariateIntegrationNodes] or [IntegrationRange] and [IntegrandMaxCalls]
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*
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* TODO use context receiver for algebra
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*/
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*/
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@UnstableKMathAPI
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@UnstableKMathAPI
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public fun <T : Comparable<T>> PiecewisePolynomial<T>.integrate(
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public fun <T : Comparable<T>> PiecewisePolynomial<T>.integrate(
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@ -98,6 +100,7 @@ public object DoubleSplineIntegrator : UnivariateIntegrator<Double> {
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}
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}
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}
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}
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@Suppress("unused")
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@UnstableKMathAPI
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@UnstableKMathAPI
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public inline val DoubleField.splineIntegrator: UnivariateIntegrator<Double>
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public inline val DoubleField.splineIntegrator: UnivariateIntegrator<Double>
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get() = DoubleSplineIntegrator
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get() = DoubleSplineIntegrator
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@ -9,6 +9,7 @@ package space.kscience.kmath.interpolation
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import space.kscience.kmath.data.XYColumnarData
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import space.kscience.kmath.data.XYColumnarData
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import space.kscience.kmath.functions.PiecewisePolynomial
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import space.kscience.kmath.functions.PiecewisePolynomial
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import space.kscience.kmath.functions.asFunction
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import space.kscience.kmath.functions.value
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import space.kscience.kmath.functions.value
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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.operations.Ring
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import space.kscience.kmath.operations.Ring
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@ -59,3 +60,33 @@ public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolatePolynomials(
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val pointSet = XYColumnarData.of(data.map { it.first }.asBuffer(), data.map { it.second }.asBuffer())
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val pointSet = XYColumnarData.of(data.map { it.first }.asBuffer(), data.map { it.second }.asBuffer())
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return interpolatePolynomials(pointSet)
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return interpolatePolynomials(pointSet)
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}
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}
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public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
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x: Buffer<T>,
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y: Buffer<T>,
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): (T) -> T? = interpolatePolynomials(x, y).asFunction(algebra)
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public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
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data: Map<T, T>,
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): (T) -> T? = interpolatePolynomials(data).asFunction(algebra)
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public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
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data: List<Pair<T, T>>,
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): (T) -> T? = interpolatePolynomials(data).asFunction(algebra)
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public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
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x: Buffer<T>,
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y: Buffer<T>,
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defaultValue: T,
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): (T) -> T = interpolatePolynomials(x, y).asFunction(algebra, defaultValue)
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public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
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data: Map<T, T>,
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defaultValue: T,
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): (T) -> T = interpolatePolynomials(data).asFunction(algebra, defaultValue)
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public fun <T : Comparable<T>> PolynomialInterpolator<T>.interpolate(
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data: List<Pair<T, T>>,
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defaultValue: T,
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): (T) -> T = interpolatePolynomials(data).asFunction(algebra, defaultValue)
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@ -22,6 +22,7 @@ internal fun <T : Comparable<T>> insureSorted(points: XYColumnarData<*, T, *>) {
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* Reference JVM implementation: https://github.com/apache/commons-math/blob/master/src/main/java/org/apache/commons/math4/analysis/interpolation/LinearInterpolator.java
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* Reference JVM implementation: https://github.com/apache/commons-math/blob/master/src/main/java/org/apache/commons/math4/analysis/interpolation/LinearInterpolator.java
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*/
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*/
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public class LinearInterpolator<T : Comparable<T>>(override val algebra: Field<T>) : PolynomialInterpolator<T> {
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public class LinearInterpolator<T : Comparable<T>>(override val algebra: Field<T>) : PolynomialInterpolator<T> {
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@OptIn(UnstableKMathAPI::class)
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@OptIn(UnstableKMathAPI::class)
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override fun interpolatePolynomials(points: XYColumnarData<T, T, T>): PiecewisePolynomial<T> = algebra {
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override fun interpolatePolynomials(points: XYColumnarData<T, T, T>): PiecewisePolynomial<T> = algebra {
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require(points.size > 0) { "Point array should not be empty" }
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require(points.size > 0) { "Point array should not be empty" }
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@ -37,3 +38,6 @@ public class LinearInterpolator<T : Comparable<T>>(override val algebra: Field<T
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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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public val <T : Comparable<T>> Field<T>.linearInterpolator: LinearInterpolator<T>
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get() = LinearInterpolator(this)
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@ -63,8 +63,8 @@ public class SplineInterpolator<T : Comparable<T>>(
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//Shift coefficients to represent absolute polynomial instead of one with an offset
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//Shift coefficients to represent absolute polynomial instead of one with an offset
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val polynomial = Polynomial(
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val polynomial = Polynomial(
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a - b * x0 + c * x02 - d * x03,
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a - b * x0 + c * x02 - d * x03,
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b - 2*c*x0 + 3*d*x02,
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b - 2 * c * x0 + 3 * d * x02,
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c - 3*d*x0,
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c - 3 * d * x0,
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d
|
d
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)
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)
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cOld = c
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cOld = c
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@ -72,8 +72,12 @@ public class SplineInterpolator<T : Comparable<T>>(
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}
|
}
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}
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}
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}
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}
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public companion object {
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public val double: SplineInterpolator<Double> = SplineInterpolator(DoubleField, ::DoubleBuffer)
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}
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}
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}
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|
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|
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public fun <T : Comparable<T>> Field<T>.splineInterpolator(
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|
bufferFactory: MutableBufferFactory<T>,
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|
): SplineInterpolator<T> = SplineInterpolator(this, bufferFactory)
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|
|
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public val DoubleField.splineInterpolator: SplineInterpolator<Double>
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get() = SplineInterpolator(this, ::DoubleBuffer)
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@ -5,8 +5,6 @@
|
|||||||
|
|
||||||
package space.kscience.kmath.interpolation
|
package space.kscience.kmath.interpolation
|
||||||
|
|
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import space.kscience.kmath.functions.PiecewisePolynomial
|
|
||||||
import space.kscience.kmath.functions.asFunction
|
|
||||||
import space.kscience.kmath.operations.DoubleField
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import space.kscience.kmath.operations.DoubleField
|
||||||
import kotlin.test.Test
|
import kotlin.test.Test
|
||||||
import kotlin.test.assertEquals
|
import kotlin.test.assertEquals
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||||||
@ -21,8 +19,8 @@ internal class LinearInterpolatorTest {
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3.0 to 4.0
|
3.0 to 4.0
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)
|
)
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|
|
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val polynomial: PiecewisePolynomial<Double> = LinearInterpolator(DoubleField).interpolatePolynomials(data)
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//val polynomial: PiecewisePolynomial<Double> = DoubleField.linearInterpolator.interpolatePolynomials(data)
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val function = polynomial.asFunction(DoubleField)
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val function = DoubleField.linearInterpolator.interpolate(data)
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assertEquals(null, function(-1.0))
|
assertEquals(null, function(-1.0))
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assertEquals(0.5, function(0.5))
|
assertEquals(0.5, function(0.5))
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assertEquals(2.0, function(1.5))
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assertEquals(2.0, function(1.5))
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||||||
|
@ -5,8 +5,6 @@
|
|||||||
|
|
||||||
package space.kscience.kmath.interpolation
|
package space.kscience.kmath.interpolation
|
||||||
|
|
||||||
import space.kscience.kmath.functions.PiecewisePolynomial
|
|
||||||
import space.kscience.kmath.functions.asFunction
|
|
||||||
import space.kscience.kmath.operations.DoubleField
|
import space.kscience.kmath.operations.DoubleField
|
||||||
import kotlin.math.PI
|
import kotlin.math.PI
|
||||||
import kotlin.math.sin
|
import kotlin.math.sin
|
||||||
@ -21,9 +19,10 @@ internal class SplineInterpolatorTest {
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|||||||
x to sin(x)
|
x to sin(x)
|
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}
|
}
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|
|
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val polynomial: PiecewisePolynomial<Double> = SplineInterpolator.double.interpolatePolynomials(data)
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//val polynomial: PiecewisePolynomial<Double> = DoubleField.splineInterpolator.interpolatePolynomials(data)
|
||||||
|
|
||||||
|
val function = DoubleField.splineInterpolator.interpolate(data, Double.NaN)
|
||||||
|
|
||||||
val function = polynomial.asFunction(DoubleField, Double.NaN)
|
|
||||||
assertEquals(Double.NaN, function(-1.0))
|
assertEquals(Double.NaN, function(-1.0))
|
||||||
assertEquals(sin(0.5), function(0.5), 0.1)
|
assertEquals(sin(0.5), function(0.5), 0.1)
|
||||||
assertEquals(sin(1.5), function(1.5), 0.1)
|
assertEquals(sin(1.5), function(1.5), 0.1)
|
||||||
|
@ -6,13 +6,38 @@
|
|||||||
package space.kscience.kmath.multik
|
package space.kscience.kmath.multik
|
||||||
|
|
||||||
import org.junit.jupiter.api.Test
|
import org.junit.jupiter.api.Test
|
||||||
|
import space.kscience.kmath.nd.StructureND
|
||||||
import space.kscience.kmath.nd.one
|
import space.kscience.kmath.nd.one
|
||||||
import space.kscience.kmath.operations.DoubleField
|
import space.kscience.kmath.operations.DoubleField
|
||||||
import space.kscience.kmath.operations.invoke
|
import space.kscience.kmath.operations.invoke
|
||||||
|
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
|
||||||
|
import space.kscience.kmath.tensors.core.tensorAlgebra
|
||||||
|
import kotlin.test.assertTrue
|
||||||
|
|
||||||
internal class MultikNDTest {
|
internal class MultikNDTest {
|
||||||
@Test
|
@Test
|
||||||
fun basicAlgebra(): Unit = DoubleField.multikAlgebra{
|
fun basicAlgebra(): Unit = DoubleField.multikAlgebra{
|
||||||
one(2,2) + 1.0
|
one(2,2) + 1.0
|
||||||
}
|
}
|
||||||
|
|
||||||
|
@Test
|
||||||
|
fun dotResult(){
|
||||||
|
val dim = 100
|
||||||
|
|
||||||
|
val tensor1 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12224)
|
||||||
|
val tensor2 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12225)
|
||||||
|
|
||||||
|
val multikResult = with(DoubleField.multikAlgebra){
|
||||||
|
tensor1 dot tensor2
|
||||||
|
}
|
||||||
|
|
||||||
|
val defaultResult = with(DoubleField.tensorAlgebra){
|
||||||
|
tensor1 dot tensor2
|
||||||
|
}
|
||||||
|
|
||||||
|
assertTrue {
|
||||||
|
StructureND.contentEquals(multikResult, defaultResult)
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
}
|
}
|
@ -199,8 +199,9 @@ public abstract class TensorFlowAlgebra<T, TT : TNumber, A : Ring<T>> internal c
|
|||||||
|
|
||||||
override fun StructureND<T>.dot(other: StructureND<T>): TensorFlowOutput<T, TT> = operate(other) { l, r ->
|
override fun StructureND<T>.dot(other: StructureND<T>): TensorFlowOutput<T, TT> = operate(other) { l, r ->
|
||||||
ops.linalg.matMul(
|
ops.linalg.matMul(
|
||||||
if (l.asTensor().shape().numDimensions() == 1) ops.expandDims(l, ops.constant(0)) else l,
|
if (l.shape().numDimensions() == 1) ops.expandDims(l, ops.constant(0)) else l,
|
||||||
if (r.asTensor().shape().numDimensions() == 1) ops.expandDims(r, ops.constant(-1)) else r)
|
if (r.shape().numDimensions() == 1) ops.expandDims(r, ops.constant(-1)) else r
|
||||||
|
)
|
||||||
}
|
}
|
||||||
|
|
||||||
override fun diagonalEmbedding(
|
override fun diagonalEmbedding(
|
||||||
|
@ -4,6 +4,8 @@ import org.junit.jupiter.api.Test
|
|||||||
import space.kscience.kmath.nd.get
|
import space.kscience.kmath.nd.get
|
||||||
import space.kscience.kmath.nd.structureND
|
import space.kscience.kmath.nd.structureND
|
||||||
import space.kscience.kmath.operations.DoubleField
|
import space.kscience.kmath.operations.DoubleField
|
||||||
|
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
|
||||||
|
import space.kscience.kmath.tensors.core.DoubleTensorAlgebra.Companion.sum
|
||||||
import kotlin.test.assertEquals
|
import kotlin.test.assertEquals
|
||||||
|
|
||||||
class DoubleTensorFlowOps {
|
class DoubleTensorFlowOps {
|
||||||
@ -18,6 +20,18 @@ class DoubleTensorFlowOps {
|
|||||||
assertEquals(3.0, res[0, 0])
|
assertEquals(3.0, res[0, 0])
|
||||||
}
|
}
|
||||||
|
|
||||||
|
@Test
|
||||||
|
fun dot(){
|
||||||
|
val dim = 1000
|
||||||
|
|
||||||
|
val tensor1 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12224)
|
||||||
|
val tensor2 = DoubleTensorAlgebra.randomNormal(shape = intArrayOf(dim, dim), 12225)
|
||||||
|
|
||||||
|
DoubleField.produceWithTF {
|
||||||
|
tensor1 dot tensor2
|
||||||
|
}.sum()
|
||||||
|
}
|
||||||
|
|
||||||
@Test
|
@Test
|
||||||
fun extensionOps(){
|
fun extensionOps(){
|
||||||
val res = DoubleField.produceWithTF {
|
val res = DoubleField.produceWithTF {
|
||||||
|
@ -9,10 +9,7 @@
|
|||||||
package space.kscience.kmath.tensors.core
|
package space.kscience.kmath.tensors.core
|
||||||
|
|
||||||
import space.kscience.kmath.misc.PerformancePitfall
|
import space.kscience.kmath.misc.PerformancePitfall
|
||||||
import space.kscience.kmath.nd.MutableStructure2D
|
import space.kscience.kmath.nd.*
|
||||||
import space.kscience.kmath.nd.StructureND
|
|
||||||
import space.kscience.kmath.nd.as1D
|
|
||||||
import space.kscience.kmath.nd.as2D
|
|
||||||
import space.kscience.kmath.operations.DoubleField
|
import space.kscience.kmath.operations.DoubleField
|
||||||
import space.kscience.kmath.structures.MutableBuffer
|
import space.kscience.kmath.structures.MutableBuffer
|
||||||
import space.kscience.kmath.structures.indices
|
import space.kscience.kmath.structures.indices
|
||||||
@ -885,7 +882,7 @@ public open class DoubleTensorAlgebra :
|
|||||||
return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
|
return Triple(uTensor.transpose(), sTensor, vTensor.transpose())
|
||||||
}
|
}
|
||||||
|
|
||||||
override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEig(epsilon = 1e-15)
|
override fun StructureND<Double>.symEig(): Pair<DoubleTensor, DoubleTensor> = symEigJacobi(maxIteration = 50, epsilon = 1e-15)
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
|
* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
|
||||||
@ -895,7 +892,7 @@ public open class DoubleTensorAlgebra :
|
|||||||
* and when the cosine approaches 1 in the SVD algorithm.
|
* and when the cosine approaches 1 in the SVD algorithm.
|
||||||
* @return a pair `eigenvalues to eigenvectors`.
|
* @return a pair `eigenvalues to eigenvectors`.
|
||||||
*/
|
*/
|
||||||
public fun StructureND<Double>.symEig(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
|
public fun StructureND<Double>.symEigSvd(epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
|
||||||
checkSymmetric(tensor, epsilon)
|
checkSymmetric(tensor, epsilon)
|
||||||
|
|
||||||
fun MutableStructure2D<Double>.cleanSym(n: Int) {
|
fun MutableStructure2D<Double>.cleanSym(n: Int) {
|
||||||
@ -922,6 +919,151 @@ public open class DoubleTensorAlgebra :
|
|||||||
return eig to v
|
return eig to v
|
||||||
}
|
}
|
||||||
|
|
||||||
|
public fun StructureND<Double>.symEigJacobi(maxIteration: Int, epsilon: Double): Pair<DoubleTensor, DoubleTensor> {
|
||||||
|
checkSymmetric(tensor, epsilon)
|
||||||
|
|
||||||
|
val size = this.dimension
|
||||||
|
val eigenvectors = zeros(this.shape)
|
||||||
|
val eigenvalues = zeros(this.shape.sliceArray(0 until size - 1))
|
||||||
|
|
||||||
|
var eigenvalueStart = 0
|
||||||
|
var eigenvectorStart = 0
|
||||||
|
for (matrix in tensor.matrixSequence()) {
|
||||||
|
val matrix2D = matrix.as2D()
|
||||||
|
val (d, v) = matrix2D.jacobiHelper(maxIteration, epsilon)
|
||||||
|
|
||||||
|
for (i in 0 until matrix2D.rowNum) {
|
||||||
|
for (j in 0 until matrix2D.colNum) {
|
||||||
|
eigenvectors.mutableBuffer.array()[eigenvectorStart + i * matrix2D.rowNum + j] = v[i, j]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for (i in 0 until matrix2D.rowNum) {
|
||||||
|
eigenvalues.mutableBuffer.array()[eigenvalueStart + i] = d[i]
|
||||||
|
}
|
||||||
|
|
||||||
|
eigenvalueStart += this.shape.last()
|
||||||
|
eigenvectorStart += this.shape.last() * this.shape.last()
|
||||||
|
}
|
||||||
|
|
||||||
|
return eigenvalues to eigenvectors
|
||||||
|
}
|
||||||
|
|
||||||
|
private fun MutableStructure2D<Double>.jacobiHelper(
|
||||||
|
maxIteration: Int,
|
||||||
|
epsilon: Double
|
||||||
|
): Pair<Structure1D<Double>, Structure2D<Double>> {
|
||||||
|
val n = this.shape[0]
|
||||||
|
val A_ = this.copy()
|
||||||
|
val V = eye(n)
|
||||||
|
val D = DoubleTensor(intArrayOf(n), (0 until this.rowNum).map { this[it, it] }.toDoubleArray()).as1D()
|
||||||
|
val B = DoubleTensor(intArrayOf(n), (0 until this.rowNum).map { this[it, it] }.toDoubleArray()).as1D()
|
||||||
|
val Z = zeros(intArrayOf(n)).as1D()
|
||||||
|
|
||||||
|
// assume that buffered tensor is square matrix
|
||||||
|
operator fun BufferedTensor<Double>.get(i: Int, j: Int): Double {
|
||||||
|
return this.mutableBuffer.array()[bufferStart + i * this.shape[0] + j]
|
||||||
|
}
|
||||||
|
|
||||||
|
operator fun BufferedTensor<Double>.set(i: Int, j: Int, value: Double) {
|
||||||
|
this.mutableBuffer.array()[bufferStart + i * this.shape[0] + j] = value
|
||||||
|
}
|
||||||
|
|
||||||
|
fun maxOffDiagonal(matrix: BufferedTensor<Double>): Double {
|
||||||
|
var maxOffDiagonalElement = 0.0
|
||||||
|
for (i in 0 until n - 1) {
|
||||||
|
for (j in i + 1 until n) {
|
||||||
|
maxOffDiagonalElement = max(maxOffDiagonalElement, abs(matrix[i, j]))
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return maxOffDiagonalElement
|
||||||
|
}
|
||||||
|
|
||||||
|
fun rotate(a: BufferedTensor<Double>, s: Double, tau: Double, i: Int, j: Int, k: Int, l: Int) {
|
||||||
|
val g = a[i, j]
|
||||||
|
val h = a[k, l]
|
||||||
|
a[i, j] = g - s * (h + g * tau)
|
||||||
|
a[k, l] = h + s * (g - h * tau)
|
||||||
|
}
|
||||||
|
|
||||||
|
fun jacobiIteration(
|
||||||
|
a: BufferedTensor<Double>,
|
||||||
|
v: BufferedTensor<Double>,
|
||||||
|
d: MutableStructure1D<Double>,
|
||||||
|
z: MutableStructure1D<Double>,
|
||||||
|
) {
|
||||||
|
for (ip in 0 until n - 1) {
|
||||||
|
for (iq in ip + 1 until n) {
|
||||||
|
val g = 100.0 * abs(a[ip, iq])
|
||||||
|
|
||||||
|
if (g <= epsilon * abs(d[ip]) && g <= epsilon * abs(d[iq])) {
|
||||||
|
a[ip, iq] = 0.0
|
||||||
|
continue
|
||||||
|
}
|
||||||
|
|
||||||
|
var h = d[iq] - d[ip]
|
||||||
|
val t = when {
|
||||||
|
g <= epsilon * abs(h) -> (a[ip, iq]) / h
|
||||||
|
else -> {
|
||||||
|
val theta = 0.5 * h / (a[ip, iq])
|
||||||
|
val denominator = abs(theta) + sqrt(1.0 + theta * theta)
|
||||||
|
if (theta < 0.0) -1.0 / denominator else 1.0 / denominator
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
val c = 1.0 / sqrt(1 + t * t)
|
||||||
|
val s = t * c
|
||||||
|
val tau = s / (1.0 + c)
|
||||||
|
h = t * a[ip, iq]
|
||||||
|
z[ip] -= h
|
||||||
|
z[iq] += h
|
||||||
|
d[ip] -= h
|
||||||
|
d[iq] += h
|
||||||
|
a[ip, iq] = 0.0
|
||||||
|
|
||||||
|
for (j in 0 until ip) {
|
||||||
|
rotate(a, s, tau, j, ip, j, iq)
|
||||||
|
}
|
||||||
|
for (j in (ip + 1) until iq) {
|
||||||
|
rotate(a, s, tau, ip, j, j, iq)
|
||||||
|
}
|
||||||
|
for (j in (iq + 1) until n) {
|
||||||
|
rotate(a, s, tau, ip, j, iq, j)
|
||||||
|
}
|
||||||
|
for (j in 0 until n) {
|
||||||
|
rotate(v, s, tau, j, ip, j, iq)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fun updateDiagonal(
|
||||||
|
d: MutableStructure1D<Double>,
|
||||||
|
z: MutableStructure1D<Double>,
|
||||||
|
b: MutableStructure1D<Double>,
|
||||||
|
) {
|
||||||
|
for (ip in 0 until d.size) {
|
||||||
|
b[ip] += z[ip]
|
||||||
|
d[ip] = b[ip]
|
||||||
|
z[ip] = 0.0
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
var sm = maxOffDiagonal(A_)
|
||||||
|
for (iteration in 0 until maxIteration) {
|
||||||
|
if (sm < epsilon) {
|
||||||
|
break
|
||||||
|
}
|
||||||
|
|
||||||
|
jacobiIteration(A_, V, D, Z)
|
||||||
|
updateDiagonal(D, Z, B)
|
||||||
|
sm = maxOffDiagonal(A_)
|
||||||
|
}
|
||||||
|
|
||||||
|
// TODO sort eigenvalues
|
||||||
|
return D to V.as2D()
|
||||||
|
}
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Computes the determinant of a square matrix input, or of each square matrix in a batched input
|
* Computes the determinant of a square matrix input, or of each square matrix in a batched input
|
||||||
* using LU factorization algorithm.
|
* using LU factorization algorithm.
|
||||||
@ -997,5 +1139,6 @@ public open class DoubleTensorAlgebra :
|
|||||||
}
|
}
|
||||||
|
|
||||||
public val Double.Companion.tensorAlgebra: DoubleTensorAlgebra.Companion get() = DoubleTensorAlgebra
|
public val Double.Companion.tensorAlgebra: DoubleTensorAlgebra.Companion get() = DoubleTensorAlgebra
|
||||||
|
public val DoubleField.tensorAlgebra: DoubleTensorAlgebra.Companion get() = DoubleTensorAlgebra
|
||||||
|
|
||||||
|
|
||||||
|
File diff suppressed because it is too large
Load Diff
Loading…
Reference in New Issue
Block a user