kmath-core/space.kscience.kmath.expressions

Package-level declarations

Types

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fun interface AutoDiffProcessor<T, I, out A : Algebra<I>>

A factory that converts an expression in autodiff variables to a DifferentiableExpression

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open class AutoDiffValue<out T>(val value: T)
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class DerivationResult<T : Any>(val value: T, derivativeValues: Map<String, T>, val context: Field<T>)

Represents result of simpleAutoDiff call.

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@UnstableKMathAPI
class DerivativeStructureRingExpression<T, A : Ring<T>, ScaleOperations<T>, NumericAlgebra<T>>(val algebra: A, val elementBufferFactory: MutableBufferFactory<T> = algebra.bufferFactory, val function: DSRing<T, A>.() -> DS<T, A>) : DifferentiableExpression<T>
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interface DifferentiableExpression<T> : Expression<T>

Represents expression, which structure can be differentiated.

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@UnstableKMathAPI
interface DoubleExpression : Expression<Double>

Specialization of Expression for Double allowing better performance because of using array.

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@UnstableKMathAPI
interface DS<T, A : Ring<T>>

Class representing both the value and the differentials of a function.

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@UnstableKMathAPI
abstract class DSAlgebra<T, A : Ring<T>>(val algebra: A, val order: Int, bindings: Map<Symbol, T>) : ExpressionAlgebra<T, DS<T, A>> , SymbolIndexer
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class DSCompiler<T, out A : Algebra<T>>

Class holding "compiled" computation rules for derivative structures.

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@UnstableKMathAPI
class DSField<T, A : ExtendedField<T>>(algebra: A, order: Int, bindings: Map<Symbol, T>) : DSRing<T, A> , ExtendedField<DS<T, A>>

A field over DS.

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@UnstableKMathAPI
class DSFieldExpression<T, A : ExtendedField<T>>(val algebra: A, val function: DSField<T, A>.() -> DS<T, A>) : DifferentiableExpression<T>
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@UnstableKMathAPI
open class DSRing<T, A : Ring<T>, NumericAlgebra<T>, ScaleOperations<T>>(algebra: A, order: Int, bindings: Map<Symbol, T>) : DSAlgebra<T, A> , Ring<DS<T, A>> , ScaleOperations<DS<T, A>> , NumericAlgebra<DS<T, A>> , NumbersAddOps<DS<T, A>>

A ring over DS.

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fun interface Expression<T>

An elementary function that could be invoked on a map of arguments.

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interface ExpressionAlgebra<in T, E> : Algebra<E>

A context for expression construction

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class ExpressionWithDefault<T>(origin: Expression<T>, defaultArgs: Map<Symbol, T>) : Expression<T>
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abstract class FirstDerivativeExpression<T> : DifferentiableExpression<T>

A DifferentiableExpression that defines only first derivatives

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abstract class FunctionalExpressionAlgebra<T, out A : Algebra<T>>(val algebra: A) : ExpressionAlgebra<T, Expression<T>>

A context class for Expression construction.

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open class FunctionalExpressionGroup<T, out A : Group<T>>(algebra: A) : FunctionalExpressionAlgebra<T, A> , Group<Expression<T>>

A context class for Expression construction for Ring algebras.

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open class FunctionalExpressionRing<T, out A : Ring<T>>(algebra: A) : FunctionalExpressionGroup<T, A> , Ring<Expression<T>>
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@UnstableKMathAPI
interface IntExpression : Expression<Int>

Specialization of Expression for Int allowing better performance because of using array.

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@UnstableKMathAPI
interface LongExpression : Expression<Long>

Specialization of Expression for Long allowing better performance because of using array.

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interface MST

A Mathematical Syntax Tree (MST) node for mathematical expressions.

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@UnstableKMathAPI
object MstLogicAlgebra : LogicAlgebra<MST>

Logic algebra for MST

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object MstRing : Ring<MST> , NumbersAddOps<MST> , ScaleOperations<MST>

Ring over MST nodes.

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class NamedMatrix<T>(val values: Matrix<T>, val indexer: SymbolIndexer) : Structure2D<T>
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class SimpleAutoDiffExpression<T : Any, F : Field<T>>(val field: F, val function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>) : FirstDerivativeExpression<T>

A constructs that creates a derivative structure with required order on-demand

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open class SimpleAutoDiffField<T : Any, F : Field<T>>(val context: F, bindings: Map<Symbol, T>) : Field<AutoDiffValue<T>> , ExpressionAlgebra<T, AutoDiffValue<T>> , NumbersAddOps<AutoDiffValue<T>>

Represents field in context of which functions can be derived.

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interface SpecialDifferentiableExpression<T, out R : Expression<T>> : DifferentiableExpression<T>

A special type of DifferentiableExpression which returns typed expressions as derivatives.

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interface Symbol : MST

A marker interface for a symbol. A symbol must have an identity with equality relation based on it. Other properties are to store additional, transient data only.

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@UnstableKMathAPI
interface SymbolIndexer

An environment to easy transform indexed variables to symbols and back. TODO requires multi-receivers to be beautiful

Functions

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inline fun <T : Any, F : Field<T>> SimpleAutoDiffField<T, F>.const(block: F.() -> T): AutoDiffValue<T>
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@UnstableKMathAPI
fun <T, A : Ring<T>> DS<T, A>.derivative(vararg symbols: Symbol): T
@UnstableKMathAPI
fun <T, A : Ring<T>> DS<T, A>.derivative(symbols: List<Symbol>): T

Provide a partial derivative with given symbols. On symbol could me mentioned multiple times

fun <T> DifferentiableExpression<T>.derivative(vararg symbols: Symbol): Expression<T>
fun <T> DifferentiableExpression<T>.derivative(name: String): Expression<T>
fun <T> DifferentiableExpression<T>.derivative(symbols: List<Symbol>): Expression<T>
fun <T, R : Expression<T>> SpecialDifferentiableExpression<T, R>.derivative(vararg symbols: Symbol): R
fun <T, R : Expression<T>> SpecialDifferentiableExpression<T, R>.derivative(name: String): R
fun <T, R : Expression<T>> SpecialDifferentiableExpression<T, R>.derivative(symbols: List<Symbol>): R
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inline fun <T, A : Field<T>> A.expressionInField(block: FunctionalExpressionField<T, A>.() -> Expression<T>): Expression<T>
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inline fun <T, A : Group<T>> A.expressionInGroup(block: FunctionalExpressionGroup<T, A>.() -> Expression<T>): Expression<T>
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inline fun <T, A : Ring<T>> A.expressionInRing(block: FunctionalExpressionRing<T, A>.() -> Expression<T>): Expression<T>
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operator fun <T> Map<String, T>.get(symbol: Symbol): T?

Ger a value from a String-keyed map by a Symbol

operator fun <T> Map<Symbol, T>.get(string: String): T?

Get a value from a Symbol-keyed map by a String

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fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T>

Computes the gradient for variables in given order.

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fun <T> MST.interpret(algebra: Algebra<T>, vararg arguments: Pair<Symbol, T>): T
fun <T> MST.interpret(algebra: Algebra<T>, arguments: Map<Symbol, T>): T

Interprets the MST node with this Algebra and optional arguments

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@UnstableKMathAPI
operator fun DoubleExpression.invoke(): Double
operator fun <T> Expression<T>.invoke(): T
@UnstableKMathAPI
operator fun IntExpression.invoke(): Int
@UnstableKMathAPI
operator fun LongExpression.invoke(): Long

Calls this expression without providing any arguments.

@UnstableKMathAPI
operator fun DoubleExpression.invoke(vararg arguments: Double): Double
@JvmName(name = "callByString")
operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T
@JvmName(name = "callBySymbol")
operator fun <T> Expression<T>.invoke(vararg pairs: Pair<Symbol, T>): T
@UnstableKMathAPI
operator fun IntExpression.invoke(vararg arguments: Int): Int
@UnstableKMathAPI
operator fun LongExpression.invoke(vararg arguments: Long): Long

Calls this expression from arguments.

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fun <T> Matrix<T>.named(symbols: List<Symbol>): NamedMatrix<T>
fun <T> Matrix<T>.named(indexer: SymbolIndexer): NamedMatrix<T>
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operator fun <T> MutableMap<String, T>.set(symbol: Symbol, value: T)
operator fun <T> MutableMap<Symbol, T>.set(string: String, value: T)

Set a value of String-keyed map by a Symbol

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fun <T : Any, F : Field<T>> F.simpleAutoDiff(vararg bindings: Pair<Symbol, T>, body: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T>

fun <T : Any, F : Field<T>> F.simpleAutoDiff(bindings: Map<Symbol, T>, body: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T>

Runs differentiation and establishes SimpleAutoDiffField context inside the block of code.

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fun Symbol(identity: String): Symbol

Create s Symbols with a string identity

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fun <T : Any> MST.toExpression(algebra: Algebra<T>): Expression<T>

Interpret this MST as expression.

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@UnstableKMathAPI
inline fun <R> withSymbols(vararg symbols: Symbol, block: SymbolIndexer.() -> R): R

Execute the block with symbol indexer based on given symbol order

@UnstableKMathAPI
inline fun <R> withSymbols(symbols: Collection<Symbol>, block: SymbolIndexer.() -> R): R

Properties

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val <T, E> ExpressionAlgebra<T, E>.binding: ReadOnlyProperty<Any?, E>

Bind a symbol by name inside the ExpressionAlgebra

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val symbol: ReadOnlyProperty<Any?, Symbol>

A delegate to create a symbol with a string identity in this scope

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@UnstableKMathAPI
val <T, A : Ring<T>> DS<T, A>.value: T

The value part of the derivative structure.