net.finmath.montecarlo.automaticdifferentiation

Interface RandomVariableDifferentiableInterface

All Superinterfaces:

RandomVariableInterface, Serializable

All Known Implementing Classes:

RandomVariableDifferentiableAAD, RandomVariableDifferentiableAD

public interface RandomVariableDifferentiableInterface
extends RandomVariableInterface

Interface providing additional methods for random variable implementing RandomVariableInterface allowing automatic differentiation. The interface will introduce three additional methods: Long getID() and Map<Long, RandomVariableInterface> getGradient() and Map<Long, RandomVariableInterface> getTangents(). The method getGradient will return a map providing the first order differentiation of the given random variable (this) with respect to all its input RandomVariableDifferentiableInterfaces. The method getTangents will return a map providing the first order differentiation of all dependent random variables with respect to the given random variable (this). To get the differentiation dY/dX of Y with respect to a specific object X using backward mode (getGradient) use Map gradient = Y.getGradient(); RandomVariableInterface derivative = Y.get(X.getID()); To get the differentiation dY/dX of Y with respect to a specific object X using forward mode (getTanget) use Map tangent = X.getTangent(); RandomVariableInterface derivative = X.get(Y.getID()); Note: Some implementations may allow limit the result of the gradient to leave nodes or the result of the tangent to terminal nodes.

Version:

1.0

Author:

Christian Fries

Method Summary

Modifier and Type	Method and Description
default RandomVariableDifferentiableInterface	getCloneIndependent() Returns a clone of this differentiable random variable with a new ID.
default Map<Long,RandomVariableInterface>	getGradient() Returns the gradient of this random variable with respect to all its leaf nodes.
Map<Long,RandomVariableInterface>	getGradient(Set<Long> independentIDs) Returns the gradient of this random variable with respect to the given IDs.
Long	getID() A unique id for this random variable.
default Map<Long,RandomVariableInterface>	getTangents() Returns the tangents of this random variable with respect to all its dependent nodes.
Map<Long,RandomVariableInterface>	getTangents(Set<Long> dependentIDs) Returns the tangents of this random variable with respect to the given dependent node IDs (if dependent).

Methods inherited from interface net.finmath.stochastic.RandomVariableInterface

abs, accrue, add, add, addProduct, addProduct, addRatio, addSumProduct, apply, apply, apply, average, barrier, barrier, bus, cache, cap, cap, choose, cos, discount, div, div, doubleValue, equals, exp, floor, floor, get, getAverage, getAverage, getConditionalExpectation, getFiltrationTime, getHistogram, getHistogram, getMax, getMin, getOperator, getQuantile, getQuantile, getQuantileExpectation, getRealizations, getRealizationsStream, getSampleVariance, getStandardDeviation, getStandardDeviation, getStandardError, getStandardError, getTypePriority, getValues, getVariance, getVariance, invert, isDeterministic, isNaN, log, mult, mult, pow, sin, size, sqrt, squared, sub, sub, subRatio, vid

Method Detail

getID

Long getID()

A unique id for this random variable. Will be used in getGradient.

Returns:

The id for this random variable.

getGradient

default Map<Long,RandomVariableInterface> getGradient()

Returns the gradient of this random variable with respect to all its leaf nodes. The method calculates the map \( v \mapsto \frac{d u}{d v} \) where \( u \) denotes this.

Returns:

The gradient map.

getGradient

Map<Long,RandomVariableInterface> getGradient(Set<Long> independentIDs)

Returns the gradient of this random variable with respect to the given IDs. The method calculates the map \( v \mapsto \frac{d u}{d v} \) where \( u \) denotes this.

Parameters:

independentIDs - Set of IDs of random variables \( v \) with respect to which the gradients \( \frac{d u}{d v} \) will be calculated. If null, derivatives w.r.t. all known independents are returned.

Returns:

The gradient map.

getTangents

default Map<Long,RandomVariableInterface> getTangents()

Returns the tangents of this random variable with respect to all its dependent nodes. The method calculated the map \( u \mapsto \frac{d u}{d v} \) where \( v \) denotes this.

Returns:

The map of all tangents .

getTangents

Map<Long,RandomVariableInterface> getTangents(Set<Long> dependentIDs)

Returns the tangents of this random variable with respect to the given dependent node IDs (if dependent). The method calculated the map \( u \mapsto \frac{d u}{d v} \) where \( v \) denotes this.

Parameters:

dependentIDs - Set of IDs of random variables \( u \) with respect to which the differentials \( \frac{d u}{d v} \) will be calculated. If null, derivatives w.r.t. all known dependents are returned.

Returns:

The map of differentials.

getCloneIndependent

default RandomVariableDifferentiableInterface getCloneIndependent()

Returns a clone of this differentiable random variable with a new ID. This implies that the random variable is a leaf node and independent from all previous calculations.

Returns:

A clone of this differentiable random variable with a new ID.