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Merge pull request #16 from altavir/dev

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Alexander Nozik 2018-10-12 11:18:54 +03:00 committed by GitHub
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1
.gitignore vendored
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@ -8,3 +8,4 @@
# Cache of project
.gradletasknamecache
gradle.properties

45
README.md
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@ -9,13 +9,27 @@ and `scipy` it is modular and has a lightweight core.
* Basic linear algebra operations (summs products, etc) backed by `Space` API.
* Complex numbers backed by `Field` API (meaning that they will be useable in any structures like vectors and NDArrays).
* [In progress] advanced linear algebra operations like matrix inversions.
* **Array-like structures** Full support of numpy-like ndarray including mixed ariphmetic operations and function operations
* **Array-like structures** Full support of numpy-like ndarray including mixed arithmetic operations and function operations
on arrays and numbers just like it works in python (with benefit of static type checking).
* **Expressions** Expressions are one of the ultimate goals of kmath. It is planned to be able to write some mathematical
expression once an then apply it to different types of objects by providing different context. Exception could be used
for a wide variety of purposes from high performance calculations to code generation.
## Planned features
* **Common mathematics** It is planned to gradually wrap most parts of [Apache commons-math](http://commons.apache.org/proper/commons-math/)
library in kotlin code and maybe rewrite some parts to better suite kotlin programming paradigm. There is no fixed priority list for that. Feel free
to submit a future request if you want something to be done first.
* **Messaging** A mathematical notation to support multi-language and multi-node communication for mathematical tasks.
## Multi-platform support
KMath is developed as a multi-platform library, which means that most of interfaces are declared in common module.
Implementation is also done in common module wherever it is possible. In some cases features are delegated to
platform even if they could be done in common module because of platform performance optimization.
Currently the main focus of development is the JVM platform, contribution of implementations for Kotlin - Native and
Kotlin - JS is welcome.
## Performance
The calculation performance is one of major goals of KMath in the future, but in some cases it is not possible to achieve
@ -25,8 +39,33 @@ but worse than optimized native/scipy (mostly due to boxing operations on primit
of optimized parts should be better than scipy.
## Releases
The project is currently in pre-release stage. Work builds could be obtained with
[![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath).
The project is currently in pre-release stage. Nightly builds could be used by adding additional repository to (groovy) gradle config:
```groovy
repositories {
maven { url = "http://npm.mipt.ru:8081/artifactory/gradle-dev" }
mavenCentral()
}
```
or for kotlin gradle dsl:
```kotlin
repositories {
maven { setUrl("http://npm.mipt.ru:8081/artifactory/gradle-dev") }
mavenCentral()
}
```
Then use regular dependency like
```groovy
compile(group: 'scientifik', name: 'kmath-core-jvm', version: '0.0.1-SNAPSHOT')
```
or in kotlin
```kotlin
compile(group = "scientifik", name = "kmath-core-jvm", version = "0.0.1-SNAPSHOT")
```
Work builds could be obtained with [![](https://jitpack.io/v/altavir/kmath.svg)](https://jitpack.io/#altavir/kmath).
## Contributing
The project requires a lot of additional work. Please fill free to contribute in any way and propose new features.

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build.gradle
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buildscript {
ext.kotlin_version = '1.2.60'
ext.kotlin_version = '1.3.0-rc-146'
repositories {
mavenCentral()
jcenter()
maven {
url = "http://dl.bintray.com/kotlin/kotlin-eap"
}
}
dependencies {
classpath "org.jetbrains.kotlin:kotlin-gradle-plugin:$kotlin_version"
classpath "org.jfrog.buildinfo:build-info-extractor-gradle:4+"
}
}
allprojects {
apply plugin: 'maven-publish'
apply plugin: "com.jfrog.artifactory"
group = 'scientifik'
version = '0.1 - SNAPSHOT'
group = 'scientifik'
version = '0.0.1-SNAPSHOT'
}
artifactory {
contextUrl = "${artifactory_contextUrl}" //The base Artifactory URL if not overridden by the publisher/resolver
publish {
repository {
repoKey = 'gradle-dev-local'
username = "${artifactory_user}"
password = "${artifactory_password}"
}
defaults {
publications('jvm', 'js', 'kotlinMultiplatform', 'metadata')
publishBuildInfo = false
publishArtifacts = true
publishPom = true
publishIvy = false
}
}
resolve {
repository {
repoKey = 'gradle-dev'
username = "${artifactory_user}"
password = "${artifactory_password}"
}
}
}

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kmath-common/build.gradle
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@ -1,14 +0,0 @@
description = "Platform-independent interfaces for kotlin maths"
apply plugin: 'kotlin-platform-common'
repositories {
mavenCentral()
}
dependencies {
compile "org.jetbrains.kotlin:kotlin-stdlib-common:$kotlin_version"
testCompile "org.jetbrains.kotlin:kotlin-test-annotations-common:$kotlin_version"
testCompile "org.jetbrains.kotlin:kotlin-test-common:$kotlin_version"
}

144
kmath-common/src/main/kotlin/scientifik/kmath/structures/LinearAlgrebra.kt
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@ -1,144 +0,0 @@
package scientifik.kmath.structures
import scientifik.kmath.operations.DoubleField
import scientifik.kmath.operations.Field
import scientifik.kmath.operations.Space
import scientifik.kmath.operations.SpaceElement
/**
* The space for linear elements. Supports scalar product alongside with standard linear operations.
* @param T type of individual element of the vector or matrix
* @param V the type of vector space element
*/
abstract class LinearSpace<T : Any, V : LinearStructure<out T>>(val rows: Int, val columns: Int, val field: Field<T>) : Space<V> {
/**
* Produce the element of this space
*/
abstract fun produce(initializer: (Int, Int) -> T): V
/**
* Produce new linear space with given dimensions
*/
abstract fun produceSpace(rows: Int, columns: Int): LinearSpace<T, V>
override val zero: V by lazy {
produce { _, _ -> field.zero }
}
override fun add(a: V, b: V): V {
return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
}
override fun multiply(a: V, k: Double): V {
//TODO it is possible to implement scalable linear elements which normed values and adjustable scale to save memory and processing poser
return produce { i, j -> with(field) { a[i, j] * k } }
}
/**
* Dot product
*/
fun multiply(a: V, b: V): V {
if (a.rows != b.columns) {
//TODO replace by specific exception
error("Dimension mismatch in vector dot product")
}
return produceSpace(a.rows, b.columns).produce { i, j ->
(0..a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
}
}
infix fun V.dot(b: V): V = multiply(this, b)
}
/**
* A matrix-like structure that is not dependent on specific space implementation
*/
interface LinearStructure<T : Any> {
val rows: Int
val columns: Int
operator fun get(i: Int, j: Int): T
fun transpose(): LinearStructure<T> {
return object : LinearStructure<T> {
override val rows: Int = this@LinearStructure.columns
override val columns: Int = this@LinearStructure.rows
override fun get(i: Int, j: Int): T = this@LinearStructure.get(j, i)
}
}
}
interface Vector<T : Any> : LinearStructure<T> {
override val columns: Int
get() = 1
operator fun get(i: Int) = get(i, 0)
}
/**
* DoubleArray-based implementation of vector space
*/
class ArraySpace<T : Any>(rows: Int, columns: Int, field: Field<T>) : LinearSpace<T, LinearStructure<out T>>(rows, columns, field) {
override fun produce(initializer: (Int, Int) -> T): LinearStructure<T> = ArrayMatrix<T>(this, initializer)
override fun produceSpace(rows: Int, columns: Int): LinearSpace<T, LinearStructure<out T>> {
return ArraySpace(rows, columns, field)
}
}
/**
* Member of [ArraySpace] which wraps 2-D array
*/
class ArrayMatrix<T : Any>(override val context: ArraySpace<T>, initializer: (Int, Int) -> T) : LinearStructure<T>, SpaceElement<LinearStructure<out T>, ArraySpace<T>> {
val list: List<List<T>> = (0 until rows).map { i -> (0 until columns).map { j -> initializer(i, j) } }
override val rows: Int get() = context.rows
override val columns: Int get() = context.columns
override fun get(i: Int, j: Int): T {
return list[i][j]
}
override val self: ArrayMatrix<T> get() = this
}
class ArrayVector<T : Any>(override val context: ArraySpace<T>, initializer: (Int) -> T) : Vector<T>, SpaceElement<LinearStructure<out T>, ArraySpace<T>> {
init {
if (context.columns != 1) {
error("Vector must have single column")
}
}
val list: List<T> = (0 until context.rows).map(initializer)
override val rows: Int get() = context.rows
override val columns: Int = 1
override fun get(i: Int, j: Int): T {
return list[i]
}
override val self: ArrayVector<T> get() = this
}
fun <T : Any> vector(size: Int, field: Field<T>, initializer: (Int) -> T) = ArrayVector(ArraySpace(size, 1, field), initializer)
//TODO replace by primitive array version
fun realVector(size: Int, initializer: (Int) -> Double) = vector(size, DoubleField, initializer)
fun <T : Any> Array<T>.asVector(field: Field<T>) = vector(size, field) { this[it] }
//TODO add inferred field from field element
fun DoubleArray.asVector() = realVector(this.size) { this[it] }
fun <T : Any> matrix(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) = ArrayMatrix<T>(ArraySpace(rows, columns, field), initializer)
fun realMatrix(rows: Int, columns: Int, initializer: (Int, Int) -> Double) = matrix(rows, columns, DoubleField, initializer)

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kmath-core/build.gradle Normal file
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plugins {
id 'kotlin-multiplatform'// version '1.3.0-rc-116'
id "me.champeau.gradle.jmh" version "0.4.5"
}
repositories {
maven { url = 'http://dl.bintray.com/kotlin/kotlin-eap' }
mavenCentral()
}
kotlin {
targets {
fromPreset(presets.jvm, 'jvm')
fromPreset(presets.js, 'js')
// For ARM, preset should be changed to presets.iosArm32 or presets.iosArm64
// For Linux, preset should be changed to e.g. presets.linuxX64
// For MacOS, preset should be changed to e.g. presets.macosX64
//fromPreset(presets.mingwX64, 'mingw')
}
sourceSets {
commonMain {
dependencies {
implementation 'org.jetbrains.kotlin:kotlin-stdlib-common'
}
}
commonTest {
dependencies {
implementation 'org.jetbrains.kotlin:kotlin-test-common'
implementation 'org.jetbrains.kotlin:kotlin-test-annotations-common'
}
}
jvmMain {
dependencies {
implementation 'org.jetbrains.kotlin:kotlin-stdlib-jdk8'
}
}
jvmTest {
dependencies {
implementation 'org.jetbrains.kotlin:kotlin-test'
implementation 'org.jetbrains.kotlin:kotlin-test-junit'
}
}
jsMain {
dependencies {
implementation 'org.jetbrains.kotlin:kotlin-stdlib-js'
}
}
jsTest {
dependencies {
implementation 'org.jetbrains.kotlin:kotlin-test-js'
}
}
// mingwMain {
// }
// mingwTest {
// }
}
}

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kmath-core/src/commonMain/kotlin/scientifik/kmath/expressions/Expression.kt Normal file
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@ -0,0 +1,62 @@
package scientifik.kmath.expressions
import scientifik.kmath.operations.Field
import scientifik.kmath.operations.Space
interface Expression<T> {
operator fun invoke(arguments: Map<String, T>): T
}
operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T = invoke(mapOf(*pairs))
interface ExpressionContext<T> {
fun variable(name: String, default: T? = null): Expression<T>
fun const(value: T): Expression<T>
}
internal class VariableExpression<T>(val name: String, val default: T? = null) : Expression<T> {
override fun invoke(arguments: Map<String, T>): T {
return arguments[name] ?: default ?: error("The parameter not found: $name")
}
}
internal class ConstantExpression<T>(val value: T) : Expression<T> {
override fun invoke(arguments: Map<String, T>): T = value
}
internal class SumExpression<T>(val context: Space<T>, val first: Expression<T>, val second: Expression<T>) : Expression<T> {
override fun invoke(arguments: Map<String, T>): T = context.add(first.invoke(arguments), second.invoke(arguments))
}
internal class ProductExpression<T>(val context: Field<T>, val first: Expression<T>, val second: Expression<T>) : Expression<T> {
override fun invoke(arguments: Map<String, T>): T = context.multiply(first.invoke(arguments), second.invoke(arguments))
}
internal class ConstProductExpession<T>(val context: Field<T>, val expr: Expression<T>, val const: Double) : Expression<T> {
override fun invoke(arguments: Map<String, T>): T = context.multiply(expr.invoke(arguments), const)
}
internal class DivExpession<T>(val context: Field<T>, val expr: Expression<T>, val second: Expression<T>) : Expression<T> {
override fun invoke(arguments: Map<String, T>): T = context.divide(expr.invoke(arguments), second.invoke(arguments))
}
class FieldExpressionContext<T>(val field: Field<T>) : Field<Expression<T>>, ExpressionContext<T> {
override val zero: Expression<T> = ConstantExpression(field.zero)
override val one: Expression<T> = ConstantExpression(field.one)
override fun const(value: T): Expression<T> = ConstantExpression(value)
override fun variable(name: String, default: T?): Expression<T> = VariableExpression(name, default)
override fun add(a: Expression<T>, b: Expression<T>): Expression<T> = SumExpression(field, a, b)
override fun multiply(a: Expression<T>, k: Double): Expression<T> = ConstProductExpession(field, a, k)
override fun multiply(a: Expression<T>, b: Expression<T>): Expression<T> = ProductExpression(field, a, b)
override fun divide(a: Expression<T>, b: Expression<T>): Expression<T> = DivExpession(field, a, b)
}

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kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LUDecomposition.kt Normal file
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package scientifik.kmath.linear
import scientifik.kmath.structures.MutableNDArray
import scientifik.kmath.structures.NDArray
import scientifik.kmath.structures.NDArrays
import kotlin.math.absoluteValue
/**
* Implementation copier from Apache common-maths
*/
abstract class LUDecomposition<T : Comparable<T>>(val matrix: Matrix<T>) {
private val field get() = matrix.context.field
/** Entries of LU decomposition. */
internal val lu: NDArray<T>
/** Pivot permutation associated with LU decomposition. */
internal val pivot: IntArray
/** Parity of the permutation associated with the LU decomposition. */
private var even: Boolean = false
init {
val pair = calculateLU()
lu = pair.first
pivot = pair.second
}
/**
* Returns the matrix L of the decomposition.
*
* L is a lower-triangular matrix
* @return the L matrix (or null if decomposed matrix is singular)
*/
val l: Matrix<out T> by lazy {
matrix.context.produce { i, j ->
when {
j < i -> lu[i, j]
j == i -> matrix.context.field.one
else -> matrix.context.field.zero
}
}
}
/**
* Returns the matrix U of the decomposition.
*
* U is an upper-triangular matrix
* @return the U matrix (or null if decomposed matrix is singular)
*/
val u: Matrix<out T> by lazy {
matrix.context.produce { i, j ->
if (j >= i) lu[i, j] else field.zero
}
}
/**
* Returns the P rows permutation matrix.
*
* P is a sparse matrix with exactly one element set to 1.0 in
* each row and each column, all other elements being set to 0.0.
*
* The positions of the 1 elements are given by the [ pivot permutation vector][.getPivot].
* @return the P rows permutation matrix (or null if decomposed matrix is singular)
* @see .getPivot
*/
val p: Matrix<out T> by lazy {
matrix.context.produce { i, j ->
//TODO ineffective. Need sparse matrix for that
if (j == pivot[i]) field.one else field.zero
}
}
/**
* Return the determinant of the matrix
* @return determinant of the matrix
*/
val determinant: T
get() {
with(matrix.context.field) {
var determinant = if (even) one else -one
for (i in 0 until matrix.rows) {
determinant *= lu[i, i]
}
return determinant
}
}
// /**
// * Get a solver for finding the A X = B solution in exact linear
// * sense.
// * @return a solver
// */
// val solver: DecompositionSolver
// get() = Solver(lu, pivot, singular)
/**
* In-place transformation for [MutableNDArray], using given transformation for each element
*/
operator fun <T> MutableNDArray<T>.set(i: Int, j: Int, value: T) {
this[listOf(i, j)] = value
}
abstract fun isSingular(value: T): Boolean
private fun abs(value: T) = if (value > matrix.context.field.zero) value else with(matrix.context.field) { -value }
private fun calculateLU(): Pair<NDArray<T>, IntArray> {
if (matrix.rows != matrix.columns) {
error("LU decomposition supports only square matrices")
}
val m = matrix.columns
val pivot = IntArray(matrix.rows)
//TODO fix performance
val lu: MutableNDArray<T> = NDArrays.createMutable(matrix.context.field, listOf(matrix.rows, matrix.columns)) { index -> matrix[index[0], index[1]] }
with(matrix.context.field) {
// Initialize permutation array and parity
for (row in 0 until m) {
pivot[row] = row
}
even = true
// Loop over columns
for (col in 0 until m) {
// upper
for (row in 0 until col) {
var sum = lu[row, col]
for (i in 0 until row) {
sum -= lu[row, i] * lu[i, col]
}
lu[row, col] = sum
}
// lower
val max = (col until m).maxBy { row ->
var sum = lu[row, col]
for (i in 0 until col) {
sum -= lu[row, i] * lu[i, col]
}
//luRow[col] = sum
lu[row, col] = sum
abs(sum)
} ?: col
// Singularity check
if (isSingular(lu[max, col])) {
error("Singular matrix")
}
// Pivot if necessary
if (max != col) {
//var tmp = zero
//val luMax = lu[max]
//val luCol = lu[col]
for (i in 0 until m) {
lu[max, i] = lu[col, i]
lu[col, i] = lu[max, i]
}
val temp = pivot[max]
pivot[max] = pivot[col]
pivot[col] = temp
even = !even
}
// Divide the lower elements by the "winning" diagonal elt.
val luDiag = lu[col, col]
for (row in col + 1 until m) {
lu[row, col] = lu[row, col] / luDiag
// lu[row, col] /= luDiag
}
}
}
return Pair(lu, pivot)
}
/**
* Returns the pivot permutation vector.
* @return the pivot permutation vector
* @see .getP
*/
fun getPivot(): IntArray {
return pivot.copyOf()
}
}
class RealLUDecomposition(matrix: Matrix<Double>, private val singularityThreshold: Double = DEFAULT_TOO_SMALL) : LUDecomposition<Double>(matrix) {
override fun isSingular(value: Double): Boolean {
return value.absoluteValue < singularityThreshold
}
companion object {
/** Default bound to determine effective singularity in LU decomposition. */
private const val DEFAULT_TOO_SMALL = 1e-11
}
}
/** Specialized solver. */
object RealLUSolver : LinearSolver<Double> {
//
// /** {@inheritDoc} */
// override fun solve(b: RealVector): RealVector {
// val m = pivot.size
// if (b.getDimension() != m) {
// throw DimensionMismatchException(b.getDimension(), m)
// }
// if (singular) {
// throw SingularMatrixException()
// }
//
// val bp = DoubleArray(m)
//
// // Apply permutations to b
// for (row in 0 until m) {
// bp[row] = b.getEntry(pivot[row])
// }
//
// // Solve LY = b
// for (col in 0 until m) {
// val bpCol = bp[col]
// for (i in col + 1 until m) {
// bp[i] -= bpCol * lu[i][col]
// }
// }
//
// // Solve UX = Y
// for (col in m - 1 downTo 0) {
// bp[col] /= lu[col][col]
// val bpCol = bp[col]
// for (i in 0 until col) {
// bp[i] -= bpCol * lu[i][col]
// }
// }
//
// return ArrayRealVector(bp, false)
// }
fun decompose(mat: Matrix<Double>, threshold: Double = 1e-11): RealLUDecomposition = RealLUDecomposition(mat, threshold)
override fun solve(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
val decomposition = decompose(a, a.context.field.zero)
if (b.rows != a.rows) {
error("Matrix dimension mismatch expected ${a.rows}, but got ${b.rows}")
}
// Apply permutations to b
val bp = Array(a.rows) { DoubleArray(b.columns) }
for (row in 0 until a.rows) {
val bpRow = bp[row]
val pRow = decomposition.pivot[row]
for (col in 0 until b.columns) {
bpRow[col] = b[pRow, col]
}
}
// Solve LY = b
for (col in 0 until a.rows) {
val bpCol = bp[col]
for (i in col + 1 until a.rows) {
val bpI = bp[i]
val luICol = decomposition.lu[i, col]
for (j in 0 until b.columns) {
bpI[j] -= bpCol[j] * luICol
}
}
}
// Solve UX = Y
for (col in a.rows - 1 downTo 0) {
val bpCol = bp[col]
val luDiag = decomposition.lu[col, col]
for (j in 0 until b.columns) {
bpCol[j] /= luDiag
}
for (i in 0 until col) {
val bpI = bp[i]
val luICol = decomposition.lu[i, col]
for (j in 0 until b.columns) {
bpI[j] -= bpCol[j] * luICol
}
}
}
return a.context.produce { i, j -> bp[i][j] }
}
}

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kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt Normal file
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package scientifik.kmath.linear
import scientifik.kmath.operations.DoubleField
import scientifik.kmath.operations.Field
import scientifik.kmath.operations.Space
import scientifik.kmath.operations.SpaceElement
import scientifik.kmath.structures.NDArray
import scientifik.kmath.structures.NDArrays.createFactory
import scientifik.kmath.structures.NDFieldFactory
import scientifik.kmath.structures.realNDFieldFactory
/**
* The space for linear elements. Supports scalar product alongside with standard linear operations.
* @param T type of individual element of the vector or matrix
* @param V the type of vector space element
*/
abstract class MatrixSpace<T : Any>(val rows: Int, val columns: Int, val field: Field<T>) : Space<Matrix<T>> {
/**
* Produce the element of this space
*/
abstract fun produce(initializer: (Int, Int) -> T): Matrix<T>
/**
* Produce new matrix space with given dimensions. The space produced could be raised from cache since [MatrixSpace] does not have mutable elements
*/
abstract fun produceSpace(rows: Int, columns: Int): MatrixSpace<T>
override val zero: Matrix<T> by lazy {
produce { _, _ -> field.zero }
}
// val one: Matrix<T> by lazy {
// produce { i, j -> if (i == j) field.one else field.zero }
// }
override fun add(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
return produce { i, j -> with(field) { a[i, j] + b[i, j] } }
}
override fun multiply(a: Matrix<T>, k: Double): Matrix<T> {
//TODO it is possible to implement scalable linear elements which normed values and adjustable scale to save memory and processing poser
return produce { i, j -> with(field) { a[i, j] * k } }
}
/**
* Dot product. Throws exception on dimension mismatch
*/
fun multiply(a: Matrix<T>, b: Matrix<T>): Matrix<T> {
if (a.rows != b.columns) {
//TODO replace by specific exception
error("Dimension mismatch in linear structure dot product: [${a.rows},${a.columns}]*[${b.rows},${b.columns}]")
}
return produceSpace(a.rows, b.columns).produce { i, j ->
(0 until a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
}
}
override fun equals(other: Any?): Boolean {
if (this === other) return true
if (other !is MatrixSpace<*>) return false
if (rows != other.rows) return false
if (columns != other.columns) return false
if (field != other.field) return false
return true
}
override fun hashCode(): Int {
var result = rows
result = 31 * result + columns
result = 31 * result + field.hashCode()
return result
}
}
infix fun <T : Any> Matrix<T>.dot(b: Matrix<T>): Matrix<T> = this.context.multiply(this, b)
/**
* A matrix-like structure
*/
interface Matrix<T : Any> : SpaceElement<Matrix<T>, MatrixSpace<T>> {
/**
* Number of rows
*/
val rows: Int
/**
* Number of columns
*/
val columns: Int
/**
* Get element in row [i] and column [j]. Throws error in case of call ounside structure dimensions
*/
operator fun get(i: Int, j: Int): T
override val self: Matrix<T>
get() = this
fun transpose(): Matrix<T> {
return object : Matrix<T> {
override val context: MatrixSpace<T> = this@Matrix.context
override val rows: Int = this@Matrix.columns
override val columns: Int = this@Matrix.rows
override fun get(i: Int, j: Int): T = this@Matrix[j, i]
}
}
companion object {
/**
* Create [ArrayMatrix] with custom field
*/
fun <T : Any> of(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) =
ArrayMatrix(ArrayMatrixSpace(rows, columns, field), initializer)
/**
* Create [ArrayMatrix] of doubles. The implementation in general should be faster than generic one due to boxing.
*/
fun ofReal(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
ArrayMatrix(ArrayMatrixSpace(rows, columns, DoubleField, realNDFieldFactory), initializer)
/**
* Create a diagonal value matrix. By default value equals [Field.one].
*/
fun <T : Any> diagonal(rows: Int, columns: Int, field: Field<T>, values: (Int) -> T = { field.one }): Matrix<T> {
return of(rows, columns, field) { i, j -> if (i == j) values(i) else field.zero }
}
/**
* Equality check on two generic matrices
*/
fun equals(mat1: Matrix<*>, mat2: Matrix<*>): Boolean {
if (mat1 === mat2) return true
if (mat1.context != mat2.context) return false
for (i in 0 until mat1.rows) {
for (j in 0 until mat2.columns) {
if (mat1[i, j] != mat2[i, j]) return false
}
}
return true
}
}
}
/**
* A linear space for vectors
*/
abstract class VectorSpace<T : Any>(val size: Int, val field: Field<T>) : Space<Vector<T>> {
abstract fun produce(initializer: (Int) -> T): Vector<T>
override val zero: Vector<T> by lazy { produce { field.zero } }
override fun add(a: Vector<T>, b: Vector<T>): Vector<T> = produce { with(field) { a[it] + b[it] } }
override fun multiply(a: Vector<T>, k: Double): Vector<T> = produce { with(field) { a[it] * k } }
}
interface Vector<T : Any> : SpaceElement<Vector<T>, VectorSpace<T>> {
val size: Int
get() = context.size
operator fun get(i: Int): T
companion object {
/**
* Create vector with custom field
*/
fun <T : Any> of(size: Int, field: Field<T>, initializer: (Int) -> T) =
ArrayVector(ArrayVectorSpace(size, field), initializer)
/**
* Create vector of [Double]
*/
fun ofReal(size: Int, initializer: (Int) -> Double) =
ArrayVector(ArrayVectorSpace(size, DoubleField, realNDFieldFactory), initializer)
fun equals(v1: Vector<*>, v2: Vector<*>): Boolean {
if (v1 === v2) return true
if (v1.context != v2.context) return false
for (i in 0 until v2.size) {
if (v1[i] != v2[i]) return false
}
return true
}
}
}
/**
* NDArray-based implementation of vector space. By default uses slow [SimpleNDField], but could be overridden with custom [NDField] factory.
*/
class ArrayMatrixSpace<T : Any>(
rows: Int,
columns: Int,
field: Field<T>,
val ndFactory: NDFieldFactory<T> = createFactory(field)
) : MatrixSpace<T>(rows, columns, field) {
val ndField by lazy {
ndFactory(listOf(rows, columns))
}
override fun produce(initializer: (Int, Int) -> T): Matrix<T> = ArrayMatrix(this, initializer)
override fun produceSpace(rows: Int, columns: Int): ArrayMatrixSpace<T> {
return ArrayMatrixSpace(rows, columns, field, ndFactory)
}
}
class ArrayVectorSpace<T : Any>(
size: Int,
field: Field<T>,
val ndFactory: NDFieldFactory<T> = createFactory(field)
) : VectorSpace<T>(size, field) {
val ndField by lazy {
ndFactory(listOf(size))
}
override fun produce(initializer: (Int) -> T): Vector<T> = ArrayVector(this, initializer)
}
/**
* Member of [ArrayMatrixSpace] which wraps 2-D array
*/
class ArrayMatrix<T : Any> internal constructor(override val context: ArrayMatrixSpace<T>, val array: NDArray<T>) : Matrix<T> {
constructor(context: ArrayMatrixSpace<T>, initializer: (Int, Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0], list[1]) })
override val rows: Int get() = context.rows
override val columns: Int get() = context.columns
override fun get(i: Int, j: Int): T {
return array[i, j]
}
override val self: ArrayMatrix<T> get() = this
}
class ArrayVector<T : Any> internal constructor(override val context: ArrayVectorSpace<T>, val array: NDArray<T>) : Vector<T> {
constructor(context: ArrayVectorSpace<T>, initializer: (Int) -> T) : this(context, context.ndField.produce { list -> initializer(list[0]) })
init {
if (context.size != array.shape[0]) {
error("Array dimension mismatch")
}
}
override fun get(i: Int): T {
return array[i]
}
override val self: ArrayVector<T> get() = this
}
/**
* A group of methods to resolve equation A dot X = B, where A and B are matrices or vectors
*/
interface LinearSolver<T : Any> {
fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T>
fun solve(a: Matrix<T>, b: Vector<T>): Vector<T> = solve(a, b.toMatrix()).toVector()
fun inverse(a: Matrix<T>): Matrix<T> = solve(a, Matrix.diagonal(a.rows, a.columns, a.context.field))
}
/**
* Convert vector to array (copying content of array)
*/
fun <T : Any> Array<T>.toVector(field: Field<T>) = Vector.of(size, field) { this[it] }
fun DoubleArray.toVector() = Vector.ofReal(this.size) { this[it] }
/**
* Convert matrix to vector if it is possible
*/
fun <T : Any> Matrix<T>.toVector(): Vector<T> {
return when {
this.columns == 1 -> {
// if (this is ArrayMatrix) {
// //Reuse existing underlying array
// ArrayVector(ArrayVectorSpace(rows, context.field, context.ndFactory), array)
// } else {
// //Generic vector
// vector(rows, context.field) { get(it, 0) }
// }
Vector.of(rows, context.field) { get(it, 0) }
}
else -> error("Can't convert matrix with more than one column to vector")
}
}
fun <T : Any> Vector<T>.toMatrix(): Matrix<T> {
// return if (this is ArrayVector) {
// //Reuse existing underlying array
// ArrayMatrix(ArrayMatrixSpace(size, 1, context.field, context.ndFactory), array)
// } else {
// //Generic vector
// matrix(size, 1, context.field) { i, j -> get(i) }
// }
return Matrix.of(size, 1, context.field) { i, j -> get(i) }
}

59
kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Cumulative.kt Normal file
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@ -0,0 +1,59 @@
package scientifik.kmath.misc
import kotlin.jvm.JvmName
/**
* Generic cumulative operation on iterator
* @param T type of initial iterable
* @param R type of resulting iterable
* @param initial lazy evaluated
*/
fun <T, R> Iterator<T>.cumulative(initial: R, operation: (T, R) -> R): Iterator<R> = object : Iterator<R> {
var state: R = initial
override fun hasNext(): Boolean = this@cumulative.hasNext()
override fun next(): R {
state = operation.invoke(this@cumulative.next(), state)
return state
}
}
fun <T, R> Iterable<T>.cumulative(initial: R, operation: (T, R) -> R): Iterable<R> = object : Iterable<R> {
override fun iterator(): Iterator<R> = this@cumulative.iterator().cumulative(initial, operation)
}
fun <T, R> Sequence<T>.cumulative(initial: R, operation: (T, R) -> R): Sequence<R> = object : Sequence<R> {
override fun iterator(): Iterator<R> = this@cumulative.iterator().cumulative(initial, operation)
}
fun <T, R> List<T>.cumulative(initial: R, operation: (T, R) -> R): List<R> = this.iterator().cumulative(initial, operation).asSequence().toList()
//Cumulative sum
@JvmName("cumulativeSumOfDouble")
fun Iterable<Double>.cumulativeSum() = this.cumulative(0.0){ element, sum -> sum + element}
@JvmName("cumulativeSumOfInt")
fun Iterable<Int>.cumulativeSum() = this.cumulative(0){ element, sum -> sum + element}
@JvmName("cumulativeSumOfLong")
fun Iterable<Long>.cumulativeSum() = this.cumulative(0L){ element, sum -> sum + element}
@JvmName("cumulativeSumOfDouble")
fun Sequence<Double>.cumulativeSum() = this.cumulative(0.0){ element, sum -> sum + element}
@JvmName("cumulativeSumOfInt")
fun Sequence<Int>.cumulativeSum() = this.cumulative(0){ element, sum -> sum + element}
@JvmName("cumulativeSumOfLong")
fun Sequence<Long>.cumulativeSum() = this.cumulative(0L){ element, sum -> sum + element}
@JvmName("cumulativeSumOfDouble")
fun List<Double>.cumulativeSum() = this.cumulative(0.0){ element, sum -> sum + element}
@JvmName("cumulativeSumOfInt")
fun List<Int>.cumulativeSum() = this.cumulative(0){ element, sum -> sum + element}
@JvmName("cumulativeSumOfLong")
fun List<Long>.cumulativeSum() = this.cumulative(0L){ element, sum -> sum + element}

37
kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/Grids.kt Normal file
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@ -0,0 +1,37 @@
package scientifik.kmath.misc
/**
* Convert double range to sequence.
*
* If the step is positive, than the sequence starts with the lower boundary and increments by [step] until current value is lower than upper boundary.
* The boundary itself is not necessary included.
*
* If step is negative, the same goes from upper boundary downwards
*/
fun ClosedFloatingPointRange<Double>.toSequence(step: Double): Sequence<Double> {
return when {
step == 0.0 -> error("Zero step in double progression")
step > 0 -> sequence {
var current = start
while (current <= endInclusive) {
yield(current)
current += step
}
}
else -> sequence {
var current = endInclusive
while (current >= start) {
yield(current)
current += step
}
}
}
}
/**
* Convert double range to array of evenly spaced doubles, where the size of array equals [numPoints]
*/
fun ClosedFloatingPointRange<Double>.toGrid(numPoints: Int): DoubleArray {
if (numPoints < 2) error("Can't create grid with less than two points")
return DoubleArray(numPoints) { i -> start + (endInclusive - start) / (numPoints - 1) * i }
}

23
kmath-common/src/main/kotlin/scientifik/kmath/operations/Algebra.kt → kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Algebra.kt
View File

@ -3,8 +3,15 @@ package scientifik.kmath.operations
/**
* The generic mathematics elements which is able to store its context
* @param T the self type of the element
* @param S the type of mathematical context for this element
*/
interface MathElement<T, S>{
interface MathElement<T, S> {
/**
* Self value. Needed for static type checking.
*/
val self: T
/**
* The context this element belongs to
*/
@ -51,13 +58,7 @@ interface Space<T> {
* @param T self type of the element. Needed for static type checking
* @param S the type of space
*/
interface SpaceElement<T, S : Space<T>>: MathElement<T,S> {
/**
* Self value. Needed for static type checking. Needed to avoid type erasure on JVM.
*/
val self: T
interface SpaceElement<T, S : Space<T>> : MathElement<T, S> {
operator fun plus(b: T): T = context.add(self, b)
operator fun minus(b: T): T = context.add(self, context.multiply(b, -1.0))
operator fun times(k: Number): T = context.multiply(self, k.toDouble())
@ -99,6 +100,12 @@ interface Field<T> : Ring<T> {
operator fun T.div(b: T): T = divide(this, b)
operator fun Number.div(b: T) = this * divide(one, b)
operator fun T.plus(b: Number) = this.plus(b * one)
operator fun Number.plus(b: T) = b + this
operator fun T.minus(b: Number) = this.minus(b * one)
operator fun Number.minus(b: T) = -b + this
}
/**

41
kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Complex.kt Normal file
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@ -0,0 +1,41 @@
package scientifik.kmath.operations
/**
* A field for complex numbers
*/
object ComplexField : Field<Complex> {
override val zero: Complex = Complex(0.0, 0.0)
override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
override fun multiply(a: Complex, k: Double): Complex = Complex(a.re * k, a.im * k)
override val one: Complex = Complex(1.0, 0.0)
override fun multiply(a: Complex, b: Complex): Complex = Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square
}
/**
* Complex number class
*/
data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
override val self: Complex get() = this
override val context: ComplexField
get() = ComplexField
/**
* A complex conjugate
*/
val conjugate: Complex
get() = Complex(re, -im)
val square: Double
get() = re * re + im * im
val abs: Double
get() = kotlin.math.sqrt(square)
}

54
kmath-common/src/main/kotlin/scientifik/kmath/operations/Fields.kt → kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/Fields.kt
View File

@ -1,7 +1,6 @@
package scientifik.kmath.operations
import kotlin.math.pow
import kotlin.math.sqrt
/**
* Field for real values
@ -29,7 +28,7 @@ object RealField : Field<Real>, TrigonometricOperations<Real>, PowerOperations<R
*
* TODO could be replaced by inline class in kotlin 1.3 if it would allow to avoid boxing
*/
class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
data class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
/*
* The class uses composition instead of inheritance since Double is final
*/
@ -51,53 +50,22 @@ class Real(val value: Double) : Number(), FieldElement<Real, RealField> {
}
/**
* A field for complex numbers
*/
object ComplexField : Field<Complex> {
override val zero: Complex = Complex(0.0, 0.0)
override fun add(a: Complex, b: Complex): Complex = Complex(a.re + b.re, a.im + b.im)
override fun multiply(a: Complex, k: Double): Complex = Complex(a.re * k, a.im * k)
override val one: Complex = Complex(1.0, 0.0)
override fun multiply(a: Complex, b: Complex): Complex = Complex(a.re * b.re - a.im * b.im, a.re * b.im + a.im * b.re)
override fun divide(a: Complex, b: Complex): Complex = Complex(a.re * b.re + a.im * b.im, a.re * b.im - a.im * b.re) / b.square
}
/**
* Complex number class
*/
data class Complex(val re: Double, val im: Double) : FieldElement<Complex, ComplexField> {
override val self: Complex get() = this
override val context: ComplexField
get() = ComplexField
/**
* A complex conjugate
*/
val conjugate: Complex
get() = Complex(re, -im)
val square: Double
get() = re * re + im * im
val module: Double
get() = sqrt(square)
}
/**
* A field for double without boxing. Does not produce appropriate field element
*/
object DoubleField : Field<Double> {
object DoubleField : Field<Double>, TrigonometricOperations<Double>, PowerOperations<Double>, ExponentialOperations<Double> {
override val zero: Double = 0.0
override fun add(a: Double, b: Double): Double = a + b
override fun multiply(a: Double, @Suppress("PARAMETER_NAME_CHANGED_ON_OVERRIDE") b: Double): Double = a * b
override val one: Double = 1.0
override fun divide(a: Double, b: Double): Double = a / b
override fun sin(arg: Double): Double = kotlin.math.sin(arg)
override fun cos(arg: Double): Double = kotlin.math.cos(arg)
override fun power(arg: Double, pow: Double): Double = arg.pow(pow)
override fun exp(arg: Double): Double =kotlin.math.exp(arg)
override fun ln(arg: Double): Double = kotlin.math.ln(arg)
}

8
kmath-common/src/main/kotlin/scientifik/kmath/operations/OptionalOperations.kt → kmath-core/src/commonMain/kotlin/scientifik/kmath/operations/OptionalOperations.kt
View File

@ -10,7 +10,7 @@ package scientifik.kmath.operations
* It also allows to override behavior for optional operations
*
*/
interface TrigonometricOperations<T>: Field<T> {
interface TrigonometricOperations<T> : Field<T> {
fun sin(arg: T): T
fun cos(arg: T): T
@ -39,10 +39,10 @@ fun <T : MathElement<T, out PowerOperations<T>>> sqr(arg: T): T = arg pow 2.0
/* Exponential */
interface ExponentialOperations<T>{
interface ExponentialOperations<T> {
fun exp(arg: T): T
fun ln(arg: T): T
}
fun <T: MathElement<T, out ExponentialOperations<T>>> exp(arg:T): T = arg.context.exp(arg)
fun <T: MathElement<T, out ExponentialOperations<T>>> ln(arg:T): T = arg.context.ln(arg)
fun <T : MathElement<T, out ExponentialOperations<T>>> exp(arg: T): T = arg.context.exp(arg)
fun <T : MathElement<T, out ExponentialOperations<T>>> ln(arg: T): T = arg.context.ln(arg)

112
kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/BufferNDField.kt Normal file
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@ -0,0 +1,112 @@
package scientifik.kmath.structures
import scientifik.kmath.operations.Field
/**
* A generic buffer for both primitives and objects
*/
interface Buffer<T> {
operator fun get(index: Int): T
operator fun set(index: Int, value: T)
/**
* A shallow copy of the buffer
*/
fun copy(): Buffer<T>
}
/**
* Generic implementation of NDField based on continuous buffer
*/
abstract class BufferNDField<T>(shape: List<Int>, field: Field<T>) : NDField<T>(shape, field) {
/**
* Strides for memory access
*/
private val strides: List<Int> by lazy {
ArrayList<Int>(shape.size).apply {
var current = 1
add(1)
shape.forEach {
current *= it
add(current)
}
}
}
protected fun offset(index: List<Int>): Int {
return index.mapIndexed { i, value ->
if (value < 0 || value >= shape[i]) {
throw RuntimeException("Index out of shape bounds: ($i,$value)")
}
value * strides[i]
}.sum()
}
//TODO introduce a fast way to calculate index of the next element?
protected fun index(offset: Int): List<Int> {
return sequence {
var current = offset
var strideIndex = strides.size - 2
while (strideIndex >= 0) {
yield(current / strides[strideIndex])
current %= strides[strideIndex]
strideIndex--
}
}.toList().reversed()
}
private val capacity: Int
get() = strides[shape.size]
protected abstract fun createBuffer(capacity: Int, initializer: (Int) -> T): Buffer<T>
override fun produce(initializer: (List<Int>) -> T): NDArray<T> {
val buffer = createBuffer(capacity) { initializer(index(it)) }
return BufferNDArray(this, buffer)
}
/**
* Produce mutable NDArray instance
*/
fun produceMutable(initializer: (List<Int>) -> T): MutableNDArray<T> {
val buffer = createBuffer(capacity) { initializer(index(it)) }
return MutableBufferedNDArray(this, buffer)
}
private open class BufferNDArray<T>(override val context: BufferNDField<T>, val data: Buffer<T>) : NDArray<T> {
override fun get(vararg index: Int): T {
return data[context.offset(index.asList())]
}
override fun equals(other: Any?): Boolean {
if (this === other) return true
if (other !is BufferNDArray<*>) return false
if (context != other.context) return false
if (data != other.data) return false
return true
}
override fun hashCode(): Int {
var result = context.hashCode()
result = 31 * result + data.hashCode()
return result
}
override val self: NDArray<T> get() = this
}
private class MutableBufferedNDArray<T>(context: BufferNDField<T>, data: Buffer<T>): BufferNDArray<T>(context,data), MutableNDArray<T>{
override operator fun set(index: List<Int>, value: T){
data[context.offset(index)] = value
}
}
}

46
kmath-common/src/main/kotlin/scientifik/kmath/structures/NDArray.kt → kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDArray.kt
View File

@ -73,7 +73,9 @@ abstract class NDField<T>(val shape: List<Int>, val field: Field<T>) : Field<NDA
}
}
/**
* Many-dimensional array
*/
interface NDArray<T> : FieldElement<NDArray<T>, NDField<T>> {
/**
@ -125,6 +127,22 @@ interface NDArray<T> : FieldElement<NDArray<T>, NDField<T>> {
}
}
/**
* In-place mutable [NDArray]
*/
interface MutableNDArray<T> : NDArray<T> {
operator fun set(index: List<Int>, value: T)
}
/**
* In-place transformation for [MutableNDArray], using given transformation for each element
*/
fun <T> MutableNDArray<T>.transformInPlace(action: (List<Int>, T) -> T) {
for ((index, oldValue) in this) {
this[index] = action(index, oldValue)
}
}
/**
* Element by element application of any operation on elements to the whole array. Just like in numpy
*/
@ -136,7 +154,7 @@ operator fun <T> Function1<T, T>.invoke(ndArray: NDArray<T>): NDArray<T> = ndArr
* Summation operation for [NDArray] and single element
*/
operator fun <T> NDArray<T>.plus(arg: T): NDArray<T> = transform { _, value ->
with(context.field){
with(context.field) {
arg + value
}
}
@ -150,7 +168,7 @@ operator fun <T> T.plus(arg: NDArray<T>): NDArray<T> = arg + this
* Subtraction operation between [NDArray] and single element
*/
operator fun <T> NDArray<T>.minus(arg: T): NDArray<T> = transform { _, value ->
with(context.field){
with(context.field) {
arg - value
}
}
@ -159,7 +177,7 @@ operator fun <T> NDArray<T>.minus(arg: T): NDArray<T> = transform { _, value ->
* Reverse minus operation
*/
operator fun <T> T.minus(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
with(arg.context.field){
with(arg.context.field) {
this@minus - value
}
}
@ -170,7 +188,7 @@ operator fun <T> T.minus(arg: NDArray<T>): NDArray<T> = arg.transform { _, value
* Product operation for [NDArray] and single element
*/
operator fun <T> NDArray<T>.times(arg: T): NDArray<T> = transform { _, value ->
with(context.field){
with(context.field) {
arg * value
}
}
@ -184,7 +202,7 @@ operator fun <T> T.times(arg: NDArray<T>): NDArray<T> = arg * this
* Division operation between [NDArray] and single element
*/
operator fun <T> NDArray<T>.div(arg: T): NDArray<T> = transform { _, value ->
with(context.field){
with(context.field) {
arg / value
}
}
@ -193,20 +211,8 @@ operator fun <T> NDArray<T>.div(arg: T): NDArray<T> = transform { _, value ->
* Reverse division operation
*/
operator fun <T> T.div(arg: NDArray<T>): NDArray<T> = arg.transform { _, value ->
with(arg.context.field){
this@div/ value
with(arg.context.field) {
this@div / value
}
}
/**
* Create a platform-specific NDArray of doubles
*/
expect fun realNDArray(shape: List<Int>, initializer: (List<Int>) -> Double = { 0.0 }): NDArray<Double>
fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDArray<Double> {
return realNDArray(listOf(dim1, dim2)) { initializer(it[0], it[1]) }
}
fun real3DArray(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDArray<Double> {
return realNDArray(listOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
}

72
kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/NDArrays.kt Normal file
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@ -0,0 +1,72 @@
package scientifik.kmath.structures
import scientifik.kmath.operations.Field
typealias NDFieldFactory<T> = (shape: List<Int>) -> NDField<T>
/**
* The factory class for fast platform-dependent implementation of NDField of doubles
*/
expect val realNDFieldFactory: NDFieldFactory<Double>
class SimpleNDField<T : Any>(field: Field<T>, shape: List<Int>) : BufferNDField<T>(shape, field) {
override fun createBuffer(capacity: Int, initializer: (Int) -> T): Buffer<T> {
val array = ArrayList<T>(capacity)
(0 until capacity).forEach {
array.add(initializer(it))
}
return BufferOfObjects(array)
}
private class BufferOfObjects<T>(val array: ArrayList<T>) : Buffer<T> {
override fun get(index: Int): T = array[index]
override fun set(index: Int, value: T) {
array[index] = value
}
override fun copy(): Buffer<T> = BufferOfObjects(ArrayList(array))
}
}
object NDArrays {
/**
* Create a platform-optimized NDArray of doubles
*/
fun realNDArray(shape: List<Int>, initializer: (List<Int>) -> Double = { 0.0 }): NDArray<Double> {
return realNDFieldFactory(shape).produce(initializer)
}
fun real1DArray(dim: Int, initializer: (Int) -> Double = { _ -> 0.0 }): NDArray<Double> {
return realNDArray(listOf(dim)) { initializer(it[0]) }
}
fun real2DArray(dim1: Int, dim2: Int, initializer: (Int, Int) -> Double = { _, _ -> 0.0 }): NDArray<Double> {
return realNDArray(listOf(dim1, dim2)) { initializer(it[0], it[1]) }
}
fun real3DArray(dim1: Int, dim2: Int, dim3: Int, initializer: (Int, Int, Int) -> Double = { _, _, _ -> 0.0 }): NDArray<Double> {
return realNDArray(listOf(dim1, dim2, dim3)) { initializer(it[0], it[1], it[2]) }
}
/**
* Simple boxing NDField
*/
fun <T : Any> createFactory(field: Field<T>): NDFieldFactory<T> = { shape -> SimpleNDField(field, shape) }
/**
* Simple boxing NDArray
*/
fun <T : Any> create(field: Field<T>, shape: List<Int>, initializer: (List<Int>) -> T): NDArray<T> {
return SimpleNDField(field, shape).produce { initializer(it) }
}
/**
* Mutable boxing NDArray
*/
fun <T : Any> createMutable(field: Field<T>, shape: List<Int>, initializer: (List<Int>) -> T): MutableNDArray<T> {
return SimpleNDField(field, shape).produceMutable { initializer(it) }
}
}

42
kmath-core/src/commonTest/kotlin/scientifik/kmath/expressions/FieldExpressionContextTest.kt Normal file
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@ -0,0 +1,42 @@
package scientifik.kmath.expressions
import scientifik.kmath.operations.Complex
import scientifik.kmath.operations.ComplexField
import scientifik.kmath.operations.DoubleField
import kotlin.test.Test
import kotlin.test.assertEquals
class FieldExpressionContextTest {
@Test
fun testExpression() {
val context = FieldExpressionContext(DoubleField)
val expression = with(context) {
val x = variable("x", 2.0)
x * x + 2 * x + 1.0
}
assertEquals(expression("x" to 1.0), 4.0)
assertEquals(expression(), 9.0)
}
@Test
fun testComplex() {
val context = FieldExpressionContext(ComplexField)
val expression = with(context) {
val x = variable("x", Complex(2.0, 0.0))
x * x + 2 * x + 1.0
}
assertEquals(expression("x" to Complex(1.0, 0.0)), Complex(4.0, 0.0))
assertEquals(expression(), Complex(9.0, 0.0))
}
@Test
fun separateContext() {
fun <T> FieldExpressionContext<T>.expression(): Expression<T>{
val x = variable("x")
return x * x + 2 * x + 1.0
}
val expression = FieldExpressionContext(DoubleField).expression()
assertEquals(expression("x" to 1.0), 4.0)
}
}

34
kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/ArrayMatrixTest.kt Normal file
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@ -0,0 +1,34 @@
package scientifik.kmath.linear
import kotlin.test.Test
import kotlin.test.assertEquals
class ArrayMatrixTest {
@Test
fun testSum() {
val vector1 = realVector(5) { it.toDouble() }
val vector2 = realVector(5) { 5 - it.toDouble() }
val sum = vector1 + vector2
assertEquals(5.0, sum[2])
}
@Test
fun testVectorToMatrix() {
val vector = realVector(5) { it.toDouble() }
val matrix = vector.toMatrix()
assertEquals(4.0, matrix[4, 0])
}
@Test
fun testDot() {
val vector1 = realVector(5) { it.toDouble() }
val vector2 = realVector(5) { 5 - it.toDouble() }
val product = vector1.toMatrix() dot (vector2.toMatrix().transpose())
assertEquals(5.0, product[1, 0])
assertEquals(6.0, product[2, 2])
}
}

21
kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt Normal file
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@ -0,0 +1,21 @@
package scientifik.kmath.linear
import scientifik.kmath.operations.DoubleField
import kotlin.test.Test
import kotlin.test.assertTrue
class RealLUSolverTest {
@Test
fun testInvertOne() {
val matrix = Matrix.diagonal(2, 2, DoubleField)
val inverted = RealLUSolver.inverse(matrix)
assertTrue { Matrix.equals(matrix,inverted) }
}
// @Test
// fun testInvert() {
// val matrix = realMatrix(2,2){}
// val inverted = RealLUSolver.inverse(matrix)
// assertTrue { Matrix.equals(matrix,inverted) }
// }
}

13
kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/CumulativeKtTest.kt Normal file
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@ -0,0 +1,13 @@
package scientifik.kmath.misc
import kotlin.test.Test
import kotlin.test.assertEquals
class CumulativeKtTest {
@Test
fun testCumulativeSum() {
val initial = listOf(-1.0, 2.0, 1.0, 1.0)
val cumulative = initial.cumulativeSum()
assertEquals(listOf(-1.0, 1.0, 2.0, 3.0), cumulative)
}
}

0
kmath-common/src/test/kotlin/scientifik/kmath/operations/RealFieldTest.kt → kmath-core/src/commonTest/kotlin/scientifik/kmath/operations/RealFieldTest.kt
View File

11
kmath-jvm/src/test/kotlin/scientifik/kmath/structures/RealNDFieldTest.kt → kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/RealNDFieldTest.kt
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@ -1,8 +1,9 @@
package scientifik.kmath.structures
import org.junit.Assert.assertEquals
import scientifik.kmath.structures.NDArrays.real2DArray
import kotlin.math.pow
import kotlin.test.Test
import kotlin.test.assertEquals
class RealNDFieldTest {
val array1 = real2DArray(3, 3) { i, j -> (i + j).toDouble() }
@ -11,13 +12,13 @@ class RealNDFieldTest {
@Test
fun testSum() {
val sum = array1 + array2
assertEquals(4.0, sum[2, 2], 0.1)
assertEquals(4.0, sum[2, 2])
}
@Test
fun testProduct() {
val product = array1 * array2
assertEquals(0.0, product[2, 2], 0.1)
assertEquals(0.0, product[2, 2])
}
@Test
@ -28,7 +29,7 @@ class RealNDFieldTest {
for (i in 0..2) {
for (j in 0..2) {
val expected = (i * 10 + j).toDouble()
assertEquals("Error at index [$i, $j]", expected, array[i, j], 0.1)
assertEquals(expected, array[i, j],"Error at index [$i, $j]")
}
}
}
@ -37,6 +38,6 @@ class RealNDFieldTest {
fun testExternalFunction() {
val function: (Double) -> Double = { x -> x.pow(2) + 2 * x + 1 }
val result = function(array1) + 1.0
assertEquals(10.0, result[1,1],0.01)
assertEquals(10.0, result[1,1])
}
}

16
kmath-core/src/commonTest/kotlin/scientifik/kmath/structures/SimpleNDFieldTest.kt Normal file
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@ -0,0 +1,16 @@
package scientifik.kmath.structures
import scientifik.kmath.operations.DoubleField
import scientifik.kmath.structures.NDArrays.create
import kotlin.test.Test
import kotlin.test.assertEquals
class SimpleNDFieldTest{
@Test
fun testStrides(){
val ndArray = create(DoubleField, listOf(10,10)){(it[0]+it[1]).toDouble()}
assertEquals(ndArray[5,5], 10.0)
}
}

53
kmath-core/src/jmh/kotlin/scietifik/kmath/structures/ArrayBenchmark.kt Normal file
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@ -0,0 +1,53 @@
package scietifik.kmath.structures
import org.openjdk.jmh.annotations.*
import java.nio.IntBuffer
@Fork(1)
@Warmup(iterations = 2)
@Measurement(iterations = 50)
@State(Scope.Benchmark)
open class ArrayBenchmark {
lateinit var array: IntArray
lateinit var arrayBuffer: IntBuffer
lateinit var nativeBuffer: IntBuffer
@Setup
fun setup() {
array = IntArray(10000) { it }
arrayBuffer = IntBuffer.wrap(array)
nativeBuffer = IntBuffer.allocate(10000)
for (i in 0 until 10000) {
nativeBuffer.put(i,i)
}
}
@Benchmark
fun benchmarkArrayRead() {
var res = 0
for (i in 1..10000) {
res += array[10000 - i]
}
print(res)
}
@Benchmark
fun benchmarkBufferRead() {
var res = 0
for (i in 1..10000) {
res += arrayBuffer.get(10000 - i)
}
print(res)
}
@Benchmark
fun nativeBufferRead() {
var res = 0
for (i in 1..10000) {
res += nativeBuffer.get(10000 - i)
}
print(res)
}
}

8
kmath-core/src/jsMain/kotlin/scientifik/kmath/structures/_NDArrays.kt Normal file
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@ -0,0 +1,8 @@
package scientifik.kmath.structures
import scientifik.kmath.operations.DoubleField
/**
* Using boxing implementation for js
*/
actual val realNDFieldFactory: NDFieldFactory<Double> = NDArrays.createFactory(DoubleField)

26
kmath-core/src/jvmMain/kotlin/scientifik/kmath/structures/_NDArrays.kt Normal file
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@ -0,0 +1,26 @@
package scientifik.kmath.structures
import scientifik.kmath.operations.DoubleField
import java.nio.DoubleBuffer
private class RealNDField(shape: List<Int>) : BufferNDField<Double>(shape, DoubleField) {
override fun createBuffer(capacity: Int, initializer: (Int) -> Double): Buffer<Double> {
val array = DoubleArray(capacity, initializer)
val buffer = DoubleBuffer.wrap(array)
return BufferOfDoubles(buffer)
}
private class BufferOfDoubles(val buffer: DoubleBuffer): Buffer<Double>{
override fun get(index: Int): Double = buffer.get(index)
override fun set(index: Int, value: Double) {
buffer.put(index, value)
}
override fun copy(): Buffer<Double> {
return BufferOfDoubles(buffer)
}
}
}
actual val realNDFieldFactory: NDFieldFactory<Double> = { shape -> RealNDField(shape) }

21
kmath-jvm/build.gradle
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@ -1,21 +0,0 @@
apply plugin: 'kotlin-platform-jvm'
repositories {
mavenCentral()
}
dependencies {
expectedBy project(":kmath-common")
compile "org.jetbrains.kotlin:kotlin-stdlib-jdk8:$kotlin_version"
testCompile "junit:junit:4.12"
testCompile "org.jetbrains.kotlin:kotlin-test-junit:$kotlin_version"
testCompile "org.jetbrains.kotlin:kotlin-test:$kotlin_version"
}
compileKotlin {
kotlinOptions.jvmTarget = "1.8"
}
compileTestKotlin {
kotlinOptions.jvmTarget = "1.8"
}
sourceCompatibility = "1.8"

80
kmath-jvm/src/main/kotlin/scientifik/kmath/structures/RealNDArray.kt
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@ -1,80 +0,0 @@
package scientifik.kmath.structures
import scientifik.kmath.operations.DoubleField
import java.nio.DoubleBuffer
private class RealNDField(shape: List<Int>) : NDField<Double>(shape, DoubleField) {
/**
* Strides for memory access
*/
private val strides: List<Int> by lazy {
ArrayList<Int>(shape.size).apply {
var current = 1
add(1)
shape.forEach {
current *= it
add(current)
}
}
}
fun offset(index: List<Int>): Int {
return index.mapIndexed { i, value ->
if (value < 0 || value >= shape[i]) {
throw RuntimeException("Index out of shape bounds: ($i,$value)")
}
value * strides[i]
}.sum()
}
val capacity: Int
get() = strides[shape.size]
override fun produce(initializer: (List<Int>) -> Double): NDArray<Double> {
//TODO use sparse arrays for large capacities
val buffer = DoubleBuffer.allocate(capacity)
//FIXME there could be performance degradation due to iteration procedure. Replace by straight iteration
NDArray.iterateIndexes(shape).forEach {
buffer.put(offset(it), initializer(it))
}
return RealNDArray(this, buffer)
}
class RealNDArray(override val context: RealNDField, val data: DoubleBuffer) : NDArray<Double> {
override fun get(vararg index: Int): Double {
return data.get(context.offset(index.asList()))
}
override fun equals(other: Any?): Boolean {
if (this === other) return true
if (javaClass != other?.javaClass) return false
other as RealNDArray
if (context.shape != other.context.shape) return false
if (data != other.data) return false
return true
}
override fun hashCode(): Int {
var result = context.shape.hashCode()
result = 31 * result + data.hashCode()
return result
}
//TODO generate fixed hash code for quick comparison?
override val self: NDArray<Double> get() = this
}
}
actual fun realNDArray(shape: List<Int>, initializer: (List<Int>) -> Double): NDArray<Double> {
//TODO cache fields?
return RealNDField(shape).produce { initializer(it) }
}

26
kmath-jvm/src/test/kotlin/scientifik/kmath/structures/ArrayMatrixTest.kt
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@ -1,26 +0,0 @@
package scientifik.kmath.structures
import org.junit.Assert.assertEquals
import org.junit.Test
class ArrayMatrixTest {
@Test
fun testSum() {
val vector1 = realVector(5) { it.toDouble() }
val vector2 = realVector(5) { 5 - it.toDouble() }
val sum = vector1 + vector2
assertEquals(5.0, sum[2, 0], 0.1)
}
@Test
fun testDot() {
val vector1 = realVector(5) { it.toDouble() }
val vector2 = realVector(5) { 5 - it.toDouble() }
val product = with(vector1.context) {
vector1 dot (vector2.transpose())
}
assertEquals(10.0, product[1, 0], 0.1)
}
}

15
settings.gradle
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@ -1,4 +1,13 @@
rootProject.name = 'kmath'
include 'kmath-common'
include 'kmath-jvm'
pluginManagement {
repositories {
maven { url = 'http://dl.bintray.com/kotlin/kotlin-eap' }
mavenCentral()
maven { url = 'https://plugins.gradle.org/m2/' }
}
}
enableFeaturePreview('GRADLE_METADATA')
rootProject.name = 'kmath'
include ':kmath-core'