Package space.kscience.kmath.expressions

Types

AutoDiffProcessor

common

fun fun interface AutoDiffProcessor<T : Any, I : Any, A : ExpressionAlgebra<T, I>, out R : Expression<T>>

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

AutoDiffValue

common

open class AutoDiffValue<out T>(value: T)

DerivationResult

common

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

Represents result of simpleAutoDiff call.

DifferentiableExpression

common

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

Represents expression which structure can be differentiated.

Expression

common

fun fun interface Expression<T>

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

ExpressionAlgebra

common

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

A context for expression construction

FirstDerivativeExpression

common

abstract class FirstDerivativeExpression<T, R : Expression<T>> : DifferentiableExpression<T, R>

A DifferentiableExpression that defines only first derivatives

FunctionalExpressionAlgebra

common

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

A context class for Expression construction.

FunctionalExpressionExtendedField

common

open class FunctionalExpressionExtendedField<T, A : ExtendedField<T>>(algebra: A) : FunctionalExpressionField<T, A> , ExtendedField<Expression<T>>

FunctionalExpressionField

common

open class FunctionalExpressionField<T, A : Field<T>>(algebra: A) : FunctionalExpressionRing<T, A> , Field<Expression<T>> , ScaleOperations<Expression<T>>

FunctionalExpressionGroup

common

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

A context class for Expression construction for Ring algebras.

FunctionalExpressionRing

common

open class FunctionalExpressionRing<T, A : Ring<T>>(algebra: A) : FunctionalExpressionGroup<T, A> , Ring<Expression<T>>

MST

common

sealed class MST

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

MstAlgebra

common

object MstAlgebra : NumericAlgebra<MST>

Algebra over MST nodes.

MstExtendedField

common

object MstExtendedField : ExtendedField<MST> , NumericAlgebra<MST>

ExtendedField over MST nodes.

MstField

common

object MstField : Field<MST> , NumbersAddOperations<MST> , ScaleOperations<MST>

Field over MST nodes.

MstGroup

common

object MstGroup : Group<MST> , NumericAlgebra<MST> , ScaleOperations<MST>

Group over MST nodes.

MstRing

common

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

Ring over MST nodes.

SimpleAutoDiffExpression

common

class SimpleAutoDiffExpression<T : Any, F : Field<T>>(field: F, function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>) : FirstDerivativeExpression<T, Expression<T>>

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

SimpleAutoDiffExtendedField

common

class SimpleAutoDiffExtendedField<T : Any, F : ExtendedField<T>>(context: F, bindings: Map<Symbol, T>) : SimpleAutoDiffField<T, F> , ExtendedField<AutoDiffValue<T>> , ScaleOperations<AutoDiffValue<T>>

SimpleAutoDiffField

common

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

Represents field in context of which functions can be derived.

SimpleSymbolIndexer

common

@JvmInline()

class SimpleSymbolIndexer(symbols: List<Symbol>) : SymbolIndexer

SymbolIndexer

common

interface SymbolIndexer

An environment to easy transform indexed variables to symbols and back.

Functions

acos

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.acos(x: AutoDiffValue<T>): AutoDiffValue<T>

acosh

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.acosh(x: AutoDiffValue<T>): AutoDiffValue<T>

asin

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.asin(x: AutoDiffValue<T>): AutoDiffValue<T>

asinh

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.asinh(x: AutoDiffValue<T>): AutoDiffValue<T>

atan

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.atan(x: AutoDiffValue<T>): AutoDiffValue<T>

atanh

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.atanh(x: AutoDiffValue<T>): AutoDiffValue<T>

binding

common

fun <T, E> ExpressionAlgebra<T, E>.binding(): ReadOnlyProperty<Any?, E>

Bind a symbol by name inside the ExpressionAlgebra

cos

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.cos(x: AutoDiffValue<T>): AutoDiffValue<T>

cosh

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.cosh(x: AutoDiffValue<T>): AutoDiffValue<T>

derivative

common

fun <T, R : Expression<T>> DifferentiableExpression<T, R>.derivative(vararg symbols: Symbol): R

fun <T, R : Expression<T>> DifferentiableExpression<T, R>.derivative(name: String): R

fun <T, R : Expression<T>> DifferentiableExpression<T, R>.derivative(symbols: List<Symbol>): R

evaluate

common

fun <T> Algebra<T>.evaluate(node: MST): T

Interprets the MST node with this Algebra.

exp

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.exp(x: AutoDiffValue<T>): AutoDiffValue<T>

expressionInExtendedField

common

inline fun <T, A : ExtendedField<T>> A.expressionInExtendedField(block: FunctionalExpressionExtendedField<T, A>.() -> Expression<T>): Expression<T>

expressionInField

common

inline fun <T, A : Field<T>> A.expressionInField(block: FunctionalExpressionField<T, A>.() -> Expression<T>): Expression<T>

expressionInRing

common

inline fun <T, A : Ring<T>> A.expressionInRing(block: FunctionalExpressionRing<T, A>.() -> Expression<T>): Expression<T>

expressionInSpace

common

inline fun <T, A : Ring<T>> A.expressionInSpace(block: FunctionalExpressionGroup<T, A>.() -> Expression<T>): Expression<T>

grad

common

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

Computes the gradient for variables in given order.

interpret

common

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

Interprets the MST node with this Algebra and optional arguments

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

Interprets the MST node with this Algebra and optional arguments

invoke

common

operator fun <T> Expression<T>.invoke(): T

Calls this expression without providing any arguments.

@JvmName(name = callByString)

operator fun <T> Expression<T>.invoke(vararg pairs: Pair<String, T>): T

Calls this expression from arguments.

@JvmName(name = callBySymbol)

operator fun <T> Expression<T>.invoke(vararg pairs: Pair<Symbol, T>): T

Calls this expression from arguments.

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.ln(x: AutoDiffValue<T>): AutoDiffValue<T>

pow

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.pow(x: AutoDiffValue<T>, y: Double): AutoDiffValue<T>

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.pow(x: AutoDiffValue<T>, y: Int): AutoDiffValue<T>

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.pow(x: AutoDiffValue<T>, y: AutoDiffValue<T>): AutoDiffValue<T>

simpleAutoDiff

common

fun <T : Any, F : Field<T>> simpleAutoDiff(field: F): AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>, Expression<T>>

Generate AutoDiffProcessor for SimpleAutoDiffExpression

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.

sin

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.sin(x: AutoDiffValue<T>): AutoDiffValue<T>

sinh

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.sinh(x: AutoDiffValue<T>): AutoDiffValue<T>

sqr

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.sqr(x: AutoDiffValue<T>): AutoDiffValue<T>

sqrt

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.sqrt(x: AutoDiffValue<T>): AutoDiffValue<T>

tan

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.tan(x: AutoDiffValue<T>): AutoDiffValue<T>

tanh

common

fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.tanh(x: AutoDiffValue<T>): AutoDiffValue<T>

toExpression

common

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

Interpret this MST as expression.

withSymbols

common

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

Execute the block with symbol indexer based on given symbol order

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