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/*
* (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
*
* Created on 17.06.2017
*/
package net.finmath.montecarlo.automaticdifferentiation.backward;
import java.io.IOException;
import java.io.Serializable;
import java.lang.reflect.Field;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.TreeMap;
import java.util.concurrent.atomic.AtomicLong;
import java.util.function.DoubleBinaryOperator;
import java.util.function.DoubleUnaryOperator;
import java.util.function.IntToDoubleFunction;
import java.util.stream.Collectors;
import java.util.stream.DoubleStream;
import net.finmath.functions.DoubleTernaryOperator;
import net.finmath.montecarlo.RandomVariableFromDoubleArray;
import net.finmath.montecarlo.automaticdifferentiation.RandomVariableDifferentiable;
import net.finmath.montecarlo.automaticdifferentiation.backward.RandomVariableDifferentiableAADFactory.DiracDeltaApproximationMethod;
import net.finmath.montecarlo.conditionalexpectation.LinearRegression;
import net.finmath.stochastic.ConditionalExpectationEstimator;
import net.finmath.stochastic.RandomVariable;
import net.finmath.stochastic.Scalar;
/**
* Implementation of RandomVariableDifferentiable using
* the backward algorithmic differentiation (adjoint algorithmic differentiation, AAD).
*
* This class implements the optimized stochastic ADD as it is described in
* ssrn.com/abstract=2995695.
*
* The class implements the special treatment of the conditional expectation operator as it is described in
* ssrn.com/abstract=3000822.
*
* The class implements the special treatment of indicator functions as it is described in
* ssrn.com/abstract=3282667.
*
* For details see http://christianfries.com/finmath/stochasticautodiff/.
*
* The class is serializable. Upon de-serialization the value of {@link #getID()} may be changed to ensure unique IDs in de-serialization context.
*
* @author Christian Fries
* @author Stefan Sedlmair
* @version 1.1
*/
public class RandomVariableDifferentiableAAD implements RandomVariableDifferentiable {
private static final long serialVersionUID = 2459373647785530657L;
private static final int typePriorityDefault = 3;
private static final RandomVariable one = new Scalar(1.0);
private final int typePriority;
private static AtomicLong indexOfNextRandomVariable = new AtomicLong(0);
private enum OperatorType {
ADD, MULT, DIV, SUB, SQUARED, SQRT, LOG, SIN, COS, EXP, INVERT, CAP, FLOOR, ABS,
ADDPRODUCT, ADDRATIO, SUBRATIO, CHOOSE, DISCOUNT, ACCRUE, POW, MIN, MAX, AVERAGE, VARIANCE,
STDEV, STDERROR, SVARIANCE, AVERAGE2, VARIANCE2,
STDEV2, STDERROR2, CONDITIONAL_EXPECTATION
}
/**
* A node in the operator tree. It
* stores an id (the index m), the operator (the function f_m), and the arguments.
* It also stores reference to the argument values, if required.
*
* @author Christian Fries
*/
private static class OperatorTreeNode implements Serializable {
private static final long serialVersionUID = -8428352552169568990L;
private final Long id;
private final OperatorType operatorType;
private final List arguments;
private final List argumentValues;
private final Object operator;
private final RandomVariableDifferentiableAADFactory factory;
private static final RandomVariable zero = new Scalar(0.0);
private static final RandomVariable one = new Scalar(1.0);
private static final RandomVariable minusOne = new Scalar(-1.0);
OperatorTreeNode(final OperatorType operatorType, final List arguments, List argumentValues, final Object operator, final RandomVariableDifferentiableAADFactory factory) {
super();
id = indexOfNextRandomVariable.getAndIncrement();
this.operatorType = operatorType;
this.arguments = arguments;
this.operator = operator;
this.factory = factory;
/*
* This is the simple modification which reduces memory requirements.
*/
if(operatorType != null && (operatorType.equals(OperatorType.ADD) || operatorType.equals(OperatorType.SUB))) {
// Addition does not need to retain arguments
argumentValues = null;
}
else if(operatorType != null && operatorType.equals(OperatorType.AVERAGE)) {
// Average does not need to retain arguments
argumentValues = null;
}
else if(operatorType != null && operatorType.equals(OperatorType.MULT)) {
// Product only needs to retain factors on differentiables
if(arguments.get(0) == null) {
argumentValues.set(1, null);
}
if(arguments.get(1) == null) {
argumentValues.set(0, null);
}
}
else if(operatorType != null && operatorType.equals(OperatorType.DIV)) {
// Division only needs to retain numerator if denominator is differentiable
if(arguments.get(1) == null) {
argumentValues.set(0, null);
}
}
else if(operatorType != null && operatorType.equals(OperatorType.ADDPRODUCT)) {
// Addition does not need to retain arguments
argumentValues.set(0, null);
// Addition of product only needs to retain factors on differentiables
if(arguments.get(1) == null) {
argumentValues.set(2, null);
}
if(arguments.get(2) == null) {
argumentValues.set(1, null);
}
}
else if(operatorType != null && operatorType.equals(OperatorType.ACCRUE)) {
// Addition of product only needs to retain factors on differentiables
if(arguments.get(1) == null && arguments.get(2) == null) {
argumentValues.set(0, null);
}
if(arguments.get(0) == null && arguments.get(1) == null) {
argumentValues.set(1, null);
}
if(arguments.get(0) == null && arguments.get(2) == null) {
argumentValues.set(2, null);
}
}
else if(operatorType != null && operatorType.equals(OperatorType.CHOOSE)) {
if(arguments.get(0) == null) {
argumentValues.set(1, null);
argumentValues.set(2, null);
}
}
this.argumentValues = argumentValues;
}
/*
* This implements the update rule D_i = D_i + Dm * d fm/dxi where i are the arguments of this node and m is this node.
*/
private void propagateDerivativesFromResultToArgument(final Map derivatives) {
if(arguments == null) {
// The node has no arguments (it is a leaf node the tree). Do nothing.
return;
}
for(int argumentIndex = 0; argumentIndex < arguments.size(); argumentIndex++) {
final OperatorTreeNode argument = arguments.get(argumentIndex);
if(argument != null) {
final Long argumentID = argument.id;
final RandomVariable partialDerivative = getPartialDerivative(argument, argumentIndex);
RandomVariable derivative = derivatives.get(id);
RandomVariable argumentDerivative = derivatives.get(argumentID);
/*
* Special treatment of some stochastic operators
*/
switch(operatorType) {
case AVERAGE:
// Implementation of AVERAGE (see https://ssrn.com/abstract=2995695 for details).
derivative = derivative.average();
break;
case CONDITIONAL_EXPECTATION:
// Implementation of CONDITIONAL_EXPECTATION (see https://ssrn.com/abstract=2995695 for details).
final ConditionalExpectationEstimator estimator = (ConditionalExpectationEstimator)operator;
derivative = estimator.getConditionalExpectation(derivative);
break;
case CHOOSE:
// Implementation of CHOOSE (INDICATOR_FUNCTION)
if(argumentIndex == 0 && (factory.getDiracDeltaApproximationMethod() == DiracDeltaApproximationMethod.REGRESSION_ON_DENSITY || factory.getDiracDeltaApproximationMethod() == DiracDeltaApproximationMethod.REGRESSION_ON_DISTRIBUITON)) {
derivative = getDiracDeltaRegression(derivative, argumentValues.get(0));
}
break;
default:
// Ordinary operator - nothing to do
break;
}
/*
* Add the product of current nodes derivative and the vertex partialDerivative to the argument derivative
*/
if(argumentDerivative == null) {
// argumentDerivative is zero. Initialize value
argumentDerivative = derivative.mult(partialDerivative);
}
else {
// Add product to given value
argumentDerivative = argumentDerivative.addProduct(partialDerivative, derivative);
}
derivatives.put(argumentID, argumentDerivative);
}
}
}
/**
* Calculate the partial derivative of this node with respect to an argument node.
* Since a function f may use an argument node X in multiple arguments, say f(X,X), we need to provide index
* of the argument with respect to which the differentiation is performed (thanks to Vincent E. for pointing to this).
*
* @param differential The node of the argument.
* @param differentialIndex The index of the argument in the functions argument list.
* @return The value of the partial derivative.
*/
private RandomVariable getPartialDerivative(final OperatorTreeNode differential, final int differentialIndex) {
if(!arguments.contains(differential)) {
return zero;
}
final RandomVariable X = arguments.size() > 0 && argumentValues != null ? argumentValues.get(0) : null;
final RandomVariable Y = arguments.size() > 1 && argumentValues != null ? argumentValues.get(1) : null;
final RandomVariable Z = arguments.size() > 2 && argumentValues != null ? argumentValues.get(2) : null;
RandomVariable derivative;
switch(operatorType) {
/* functions with one argument */
case SQUARED:
derivative = X.mult(2.0);
break;
case SQRT:
derivative = X.sqrt().invert().mult(0.5);
break;
case EXP:
derivative = X.exp();
break;
case LOG:
derivative = X.invert();
break;
case SIN:
derivative = X.cos();
break;
case COS:
derivative = X.sin().mult(-1.0);
break;
case INVERT:
derivative = X.invert().squared().mult(-1);
break;
case AVERAGE:
derivative = one;
break;
case CONDITIONAL_EXPECTATION:
derivative = one;
break;
case VARIANCE:
derivative = X.sub(X.getAverage()*(2.0*X.size()-1.0)/X.size()).mult(2.0/X.size());
break;
case STDEV:
derivative = X.sub(X.getAverage()*(2.0*X.size()-1.0)/X.size()).mult(2.0/X.size()).mult(0.5).div(Math.sqrt(X.getVariance()));
break;
case MIN:
final double min = X.getMin();
derivative = X.apply(new DoubleUnaryOperator() {
@Override
public double applyAsDouble(final double x) {
return (x == min) ? 1.0 : 0.0;
}
});
break;
case MAX:
final double max = X.getMax();
derivative = X.apply(new DoubleUnaryOperator() {
@Override
public double applyAsDouble(final double x) {
return (x == max) ? 1.0 : 0.0;
}
});
break;
case ABS:
derivative = X.choose(one, minusOne);
break;
case STDERROR:
derivative = X.sub(X.getAverage()*(2.0*X.size()-1.0)/X.size()).mult(2.0/X.size()).mult(0.5).div(Math.sqrt(X.getVariance() * X.size()));
break;
case SVARIANCE:
derivative = X.sub(X.getAverage()*(2.0*X.size()-1.0)/X.size()).mult(2.0/(X.size()-1));
break;
case ADD:
derivative = one;
break;
case SUB:
derivative = differentialIndex == 0 ? one : minusOne;
break;
case MULT:
derivative = differentialIndex == 0 ? Y : X;
break;
case DIV:
derivative = differentialIndex == 0 ? Y.invert() : X.div(Y.squared()).mult(-1);
break;
case CAP:
if(differentialIndex == 0) {
derivative = X.sub(Y).choose(zero, one);
}
else {
derivative = X.sub(Y).choose(one, zero);
}
break;
case FLOOR:
if(differentialIndex == 0) {
derivative = X.sub(Y).choose(one, zero);
}
else {
derivative = X.sub(Y).choose(zero, one);
}
break;
case AVERAGE2:
derivative = differentialIndex == 0 ? Y : X;
break;
case VARIANCE2:
derivative = differentialIndex == 0 ? Y.mult(2.0).mult(X.mult(Y.add(X.getAverage(Y)*(X.size()-1)).sub(X.getAverage(Y)))) :
X.mult(2.0).mult(Y.mult(X.add(Y.getAverage(X)*(X.size()-1)).sub(Y.getAverage(X))));
break;
case STDEV2:
derivative = differentialIndex == 0 ? Y.mult(2.0).mult(X.mult(Y.add(X.getAverage(Y)*(X.size()-1)).sub(X.getAverage(Y)))).div(Math.sqrt(X.getVariance(Y))) :
X.mult(2.0).mult(Y.mult(X.add(Y.getAverage(X)*(X.size()-1)).sub(Y.getAverage(X)))).div(Math.sqrt(Y.getVariance(X)));
break;
case STDERROR2:
derivative = differentialIndex == 0 ? Y.mult(2.0).mult(X.mult(Y.add(X.getAverage(Y)*(X.size()-1)).sub(X.getAverage(Y)))).div(Math.sqrt(X.getVariance(Y) * X.size())) :
X.mult(2.0).mult(Y.mult(X.add(Y.getAverage(X)*(X.size()-1)).sub(Y.getAverage(X)))).div(Math.sqrt(Y.getVariance(X) * Y.size()));
break;
case POW:
// second argument will always be deterministic and constant (currently pow does not exist with a random variable exponent)
derivative = (differentialIndex == 0) ? X.pow(Y.doubleValue() - 1.0).mult(Y) : zero;
break;
case ADDPRODUCT:
if(differentialIndex == 0) {
derivative = one;
} else if(differentialIndex == 1) {
derivative = Z;
} else {
derivative = Y;
}
break;
case ADDRATIO:
if(differentialIndex == 0) {
derivative = one;
} else if(differentialIndex == 1) {
derivative = Z.invert();
} else {
derivative = Y.div(Z.squared()).mult(-1.0);
}
break;
case SUBRATIO:
if(differentialIndex == 0) {
derivative = one;
} else if(differentialIndex == 1) {
derivative = Z.invert().mult(-1.0);
} else {
derivative = Y.div(Z.squared());
}
break;
case ACCRUE:
if(differentialIndex == 0) {
derivative = Y.mult(Z).add(1.0);
} else if(differentialIndex == 1) {
derivative = X.mult(Z);
} else {
derivative = X.mult(Y);
}
break;
case DISCOUNT:
if(differentialIndex == 0) {
derivative = Y.mult(Z).add(1.0).invert();
} else if(differentialIndex == 1) {
derivative = X.mult(Z).div(Y.mult(Z).add(1.0).squared()).mult(-1.0);
} else {
derivative = X.mult(Y).div(Y.mult(Z).add(1.0).squared()).mult(-1.0);
}
break;
case CHOOSE:
if(differentialIndex == 0) {
switch(factory.getDiracDeltaApproximationMethod()) {
case ONE:
{
derivative = Y.sub(Z);
break;
}
case ZERO:
{
derivative = zero;
break;
}
case DISCRETE_DELTA:
{
/*
* Approximation via local finite difference
* (see https://ssrn.com/abstract=2995695 for details).
*/
final double epsilon = factory.getDiracDeltaApproximationWidthPerStdDev()*X.getStandardDeviation();
if(Double.isInfinite(epsilon)) {
derivative = Y.sub(Z);
}
else if(epsilon > 0) {
derivative = Y.sub(Z);
derivative = derivative.mult(X.add(epsilon/2).choose(one, zero));
derivative = derivative.mult(X.sub(epsilon/2).choose(zero, one));
derivative = derivative.div(epsilon);
}
else {
derivative = zero;
}
break;
}
case REGRESSION_ON_DENSITY:
case REGRESSION_ON_DISTRIBUITON:
{
derivative = Y.sub(Z);
break;
}
default:
{
throw new UnsupportedOperationException("Diract Delta Approximation Method " + factory.getDiracDeltaApproximationMethod().name() + " not supported.");
}
}
} else if(differentialIndex == 1) {
derivative = X.choose(one, zero);
} else {
derivative = X.choose(zero, one);
}
break;
default:
throw new IllegalArgumentException("Operation " + operatorType.name() + " not supported in differentiation.");
}
return derivative;
}
private RandomVariable getDiracDeltaRegression(RandomVariable derivative, final RandomVariable indicator) {
final double diracDeltaApproximationWidthPerStdDev = factory.getDiracDeltaApproximationWidthPerStdDev();
final double epsilon = diracDeltaApproximationWidthPerStdDev*indicator.getStandardDeviation();
final RandomVariable localizedOne = (indicator.add(epsilon/2).choose(one, zero)).mult(indicator.sub(epsilon/2).choose(zero, one));
final boolean isDirectDeltaRegressionUseRegressionOnAdjointDerivative = false; // currently disabled, was used in experiments
if(isDirectDeltaRegressionUseRegressionOnAdjointDerivative) {
final RandomVariable localizedValue = indicator.mult(localizedOne);
final RandomVariable[] regressionBasisFunctions = new RandomVariable[] {
localizedOne,
localizedValue,
localizedValue.squared()
};
derivative = localizedOne.mult((new LinearRegression(regressionBasisFunctions)).getRegressionCoefficients(derivative)[0]).div(localizedOne.getAverage());
}
else {
derivative = derivative.mult(localizedOne).div(localizedOne.getAverage());
}
return derivative.mult(getDensityRegression(indicator));
}
private double getDensityRegression(final RandomVariable indicator) {
final double diracDeltaApproximationDensityRegressionWidthPerStdDev = factory.getDiracDeltaApproximationDensityRegressionWidthPerStdDev();
/*
* Density regression
*/
final double underlyingStdDev = indicator.getStandardDeviation();
final int numberOfSamplePointsHalf = 50; // @TODO numberOfSamplePoints should become a parameter.
final double sampleIntervalWidthHalf = diracDeltaApproximationDensityRegressionWidthPerStdDev/2 * underlyingStdDev / numberOfSamplePointsHalf;
final double[] samplePointX = new double[numberOfSamplePointsHalf*2];
final double[] samplePointY = new double[numberOfSamplePointsHalf*2];
double sampleInterval = sampleIntervalWidthHalf;
final RandomVariable indicatorPositiveValues = indicator.choose(new Scalar(1.0), new Scalar(0.0));
final RandomVariable indicatorNegativeValues = indicator.choose(new Scalar(0.0), new Scalar(1.0));
switch(factory.getDiracDeltaApproximationMethod()) {
case REGRESSION_ON_DENSITY:
{
for(int i=0; i extractOperatorTreeNodes(final List arguments) {
return arguments != null ? arguments.stream().map( OperatorTreeNode::of ).collect(Collectors.toList()) : null;
}
private static List extractOperatorValues(final List arguments) {
return arguments != null ? arguments.stream().map( OperatorTreeNode::getValue ).collect(Collectors.toList()) : null;
}
private void readObject(final java.io.ObjectInputStream stream) throws IOException, ClassNotFoundException {
stream.defaultReadObject();
// Reassign id
try {
final Field idField = this.getClass().getDeclaredField("id");
idField.setAccessible(true);
idField.set(this, indexOfNextRandomVariable.getAndIncrement());
idField.setAccessible(false);
} catch (NoSuchFieldException | SecurityException | IllegalArgumentException | IllegalAccessException e) {
throw new RuntimeException("Unable to re-assing id of " + this.getClass().getSimpleName() + ".", e);
}
}
}
/*
* Data model. We maintain the underlying values and a link to the node in the operator tree.
*/
private RandomVariable values;
private final OperatorTreeNode operatorTreeNode;
private final RandomVariableDifferentiableAADFactory factory;
public RandomVariableDifferentiableAAD(final RandomVariable values, final List argumentOperatorTreeNodes, final List argumentValues, final ConditionalExpectationEstimator estimator, final OperatorType operator, final RandomVariableDifferentiableAADFactory factory, final int methodArgumentTypePriority) {
super();
this.values = values;
operatorTreeNode = new OperatorTreeNode(operator, argumentOperatorTreeNodes, argumentValues, estimator, factory);
this.factory = factory != null ? factory : new RandomVariableDifferentiableAADFactory();
typePriority = methodArgumentTypePriority;
}
public static RandomVariableDifferentiableAAD of(final double value) {
return new RandomVariableDifferentiableAAD(value);
}
public static RandomVariableDifferentiableAAD of(final RandomVariable randomVariable) {
return new RandomVariableDifferentiableAAD(randomVariable);
}
public RandomVariableDifferentiableAAD(final double value) {
this(new Scalar(value), null, null, null);
}
public RandomVariableDifferentiableAAD(final RandomVariable randomVariable) {
this(randomVariable, null, null, randomVariable instanceof RandomVariableDifferentiableAAD ? ((RandomVariableDifferentiableAAD)randomVariable).getFactory() : null);
}
public RandomVariableDifferentiableAAD(final RandomVariable values, final RandomVariableDifferentiableAADFactory factory) {
this(values, null, null, factory);
}
private RandomVariableDifferentiableAAD(final RandomVariable values, final List arguments, final OperatorType operator, final RandomVariableDifferentiableAADFactory factory) {
this(values, arguments, null, operator, factory);
}
public RandomVariableDifferentiableAAD(final RandomVariable values, final List arguments, final ConditionalExpectationEstimator estimator, final OperatorType operator, final RandomVariableDifferentiableAADFactory factory) {
this(values, arguments, estimator, operator, factory, typePriorityDefault);
}
public RandomVariableDifferentiableAAD(final RandomVariable values, final List arguments, final ConditionalExpectationEstimator estimator, final OperatorType operator, final RandomVariableDifferentiableAADFactory factory, final int methodArgumentTypePriority) {
this(values, OperatorTreeNode.extractOperatorTreeNodes(arguments), OperatorTreeNode.extractOperatorValues(arguments), estimator, operator, factory, methodArgumentTypePriority);
}
public OperatorTreeNode getOperatorTreeNode() {
return operatorTreeNode;
}
/**
* Returns the underlying values.
*
* @return The underling values.
*/
@Override
public RandomVariable getValues(){
return values;
}
public RandomVariableDifferentiableAADFactory getFactory() {
return factory;
}
@Override
public Long getID(){
return getOperatorTreeNode().id;
}
/**
* Returns the gradient of this random variable with respect to all its leaf nodes.
* The method calculated the map \( v \mapsto \frac{d u}{d v} \) where \( u \) denotes this.
*
* Performs a backward automatic differentiation.
*
* @return The gradient map.
*/
@Override
public Map getGradient(final Set independentIDs) {
// The map maintaining the derivatives id -> derivative
final Map derivatives = new HashMap<>();
// Put derivative of this node w.r.t. itself
derivatives.put(getID(), one);
// The set maintaining the independents. Note: TreeMap is maintaining a sorting on the keys.
final TreeMap independents = new TreeMap<>();
// Initialize with root node
independents.put(getID(), getOperatorTreeNode());
while(independents.size() > 0) {
// Get and remove node with the highest id in independents
final Map.Entry independentEntry = independents.pollLastEntry();
final Long id = independentEntry.getKey();
final OperatorTreeNode independent = independentEntry.getValue();
// Process this node (node with highest id in independents)
final List arguments = independent.arguments;
if(arguments != null && arguments.size() > 0) {
// Node has arguments: Propagate derivative to arguments.
independent.propagateDerivativesFromResultToArgument(derivatives);
// Remove id of this node from derivatives - keep only leaf nodes.
if(isGradientRetainsLeafNodesOnly()) {
derivatives.remove(id);
}
// Add all non leaf node arguments to the list of independents
for(final OperatorTreeNode argument : arguments) {
// If an argument is null, it is a (non-differentiable) constant.
if(argument != null) {
independents.put(argument.id, argument);
}
}
}
if(independentIDs != null && independentIDs.contains(id)) {
derivatives.remove(id);
}
}
return derivatives;
}
private boolean isGradientRetainsLeafNodesOnly() {
return getFactory() != null && getFactory().isGradientRetainsLeafNodesOnly();
}
@Override
public Map getTangents(final Set dependentIDs) {
throw new UnsupportedOperationException();
}
/*
* The following methods are end points since they return double values.
* You cannot differentiate these results.
*/
@Override
public boolean equals(final RandomVariable randomVariable) {
return getValues().equals(randomVariable);
}
@Override
public double getFiltrationTime() {
return getValues().getFiltrationTime();
}
@Override
public int getTypePriority() {
return typePriority;
}
@Override
public double get(final int pathOrState) {
return getValues().get(pathOrState);
}
@Override
public int size() {
return getValues().size();
}
@Override
public boolean isDeterministic() {
return getValues().isDeterministic();
}
@Override
public double[] getRealizations() {
return getValues().getRealizations();
}
@Override
public Double doubleValue() {
return getValues().doubleValue();
}
@Override
public double getMin() {
return getValues().getMin();
}
@Override
public double getMax() {
return getValues().getMax();
}
@Override
public double getAverage() {
return getValues().getAverage();
}
@Override
public double getAverage(final RandomVariable probabilities) {
return getValues().getAverage(probabilities);
}
@Override
public double getVariance() {
return getValues().getVariance();
}
@Override
public double getVariance(final RandomVariable probabilities) {
return getValues().getVariance(probabilities);
}
@Override
public double getSampleVariance() {
return getValues().getSampleVariance();
}
@Override
public double getStandardDeviation() {
return getValues().getStandardDeviation();
}
@Override
public double getStandardDeviation(final RandomVariable probabilities) {
return getValues().getStandardDeviation(probabilities);
}
@Override
public double getStandardError() {
return getValues().getStandardError();
}
@Override
public double getStandardError(final RandomVariable probabilities) {
return getValues().getStandardError(probabilities);
}
@Override
public double getQuantile(final double quantile) {
return getValues().getQuantile(quantile);
}
@Override
public double getQuantile(final double quantile, final RandomVariable probabilities) {
return getValues().getQuantile(quantile, probabilities);
}
@Override
public double getQuantileExpectation(final double quantileStart, final double quantileEnd) {
return getValues().getQuantileExpectation(quantileStart, quantileEnd);
}
@Override
public double[] getHistogram(final double[] intervalPoints) {
return getValues().getHistogram(intervalPoints);
}
@Override
public double[][] getHistogram(final int numberOfPoints, final double standardDeviations) {
return getValues().getHistogram(numberOfPoints, standardDeviations);
}
/*
* The following methods are differentiable operations.
*/
@Override
public RandomVariable cache() {
values = values.cache();
return this;
}
@Override
public RandomVariable cap(final double cap) {
return new RandomVariableDifferentiableAAD(
getValues().cap(cap),
Arrays.asList(this.getOperatorTreeNode(), null),
Arrays.asList(this.getValues(), new Scalar(cap)),
null,
OperatorType.CAP,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable floor(final double floor) {
return new RandomVariableDifferentiableAAD(
getValues().floor(floor),
Arrays.asList(this.getOperatorTreeNode(), null),
Arrays.asList(this.getValues(), new Scalar(floor)),
null,
OperatorType.FLOOR,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable add(final double value) {
return new RandomVariableDifferentiableAAD(
getValues().add(value),
Arrays.asList(this.getOperatorTreeNode(), null),
Arrays.asList(null /* this */, null /* new RandomVariableFromDoubleArray(value) */), // For ADD we do not need all arguments to evaluate the differential
null,
OperatorType.ADD,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable sub(final double value) {
return new RandomVariableDifferentiableAAD(
getValues().sub(value),
Arrays.asList(this.getOperatorTreeNode(), null),
Arrays.asList(null /* this */, null /* new RandomVariableFromDoubleArray(value) */), // For SUB we do not need all arguments to evaluate the differential
null,
OperatorType.SUB,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable mult(final double value) {
return new RandomVariableDifferentiableAAD(
getValues().mult(value),
Arrays.asList(this.getOperatorTreeNode(), null),
Arrays.asList(null, new Scalar(value)), // For MULT with constant we do not need all arguments to evaluate the differential
null,
OperatorType.MULT,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable div(final double value) {
return new RandomVariableDifferentiableAAD(
getValues().div(value),
Arrays.asList(this.getOperatorTreeNode(), null),
Arrays.asList(null, new Scalar(value)), // For DIV with constant we do not need all arguments to evaluate the differential
null,
OperatorType.DIV,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable pow(final double exponent) {
return new RandomVariableDifferentiableAAD(
getValues().pow(exponent),
Arrays.asList(this, new Scalar(exponent)),
OperatorType.POW,
getFactory());
}
@Override
public RandomVariable average() {
return new RandomVariableDifferentiableAAD(
getValues().average(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.AVERAGE,
getFactory());
}
@Override
public RandomVariable getConditionalExpectation(final ConditionalExpectationEstimator estimator) {
return new RandomVariableDifferentiableAAD(
getValues().getConditionalExpectation(estimator),
Arrays.asList(new RandomVariable[]{ this }),
estimator,
OperatorType.CONDITIONAL_EXPECTATION,
getFactory());
}
@Override
public RandomVariable squared() {
return new RandomVariableDifferentiableAAD(
getValues().squared(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.SQUARED,
getFactory());
}
@Override
public RandomVariable sqrt() {
return new RandomVariableDifferentiableAAD(
getValues().sqrt(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.SQRT,
getFactory());
}
@Override
public RandomVariable exp() {
return new RandomVariableDifferentiableAAD(
getValues().exp(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.EXP,
getFactory());
}
@Override
public RandomVariable log() {
return new RandomVariableDifferentiableAAD(
getValues().log(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.LOG,
getFactory());
}
@Override
public RandomVariable sin() {
return new RandomVariableDifferentiableAAD(
getValues().sin(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.SIN,
getFactory());
}
@Override
public RandomVariable cos() {
return new RandomVariableDifferentiableAAD(
getValues().cos(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.COS,
getFactory());
}
/*
* Binary operators: checking for return type priority.
*/
@Override
public RandomVariable add(final RandomVariable randomVariable) {
if(randomVariable.getTypePriority() > this.getTypePriority()) {
// Check type priority
return randomVariable.add(this);
}
return new RandomVariableDifferentiableAAD(
getValues().add(randomVariable.getValues()),
Arrays.asList(this.getOperatorTreeNode(), OperatorTreeNode.of(randomVariable)),
Arrays.asList(null /* this.getValues() */, null /* randomVariable.getValues() */), // For ADD we do not need all arguments to evaluate the differential
null,
OperatorType.ADD,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable sub(final RandomVariable randomVariable) {
if(randomVariable.getTypePriority() > this.getTypePriority()) {
// Check type priority
return randomVariable.bus(this);
}
return new RandomVariableDifferentiableAAD(
getValues().sub(randomVariable.getValues()),
Arrays.asList(this.getOperatorTreeNode(), OperatorTreeNode.of(randomVariable)),
Arrays.asList(null /* this.getValues() */, null /* randomVariable.getValues() */), // For SUB we do not need all arguments to evaluate the differential
null,
OperatorType.SUB,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable bus(final RandomVariable randomVariable) {
if(randomVariable.getTypePriority() > this.getTypePriority()) {
// Check type priority
return randomVariable.sub(this);
}
return new RandomVariableDifferentiableAAD(
getValues().bus(randomVariable.getValues()),
Arrays.asList(OperatorTreeNode.of(randomVariable), this.getOperatorTreeNode()), // SUB with swapped arguments
Arrays.asList(null, null), // For SUB we do not need all arguments to evaluate the differential
null,
OperatorType.SUB,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable mult(final RandomVariable randomVariable) {
if(randomVariable.getTypePriority() > this.getTypePriority()) {
// Check type priority
return randomVariable.mult(this);
}
return new RandomVariableDifferentiableAAD(
getValues().mult(randomVariable.getValues()),
Arrays.asList(this.getOperatorTreeNode(), OperatorTreeNode.of(randomVariable)),
Arrays.asList(this.getValues(), randomVariable.getValues()),
null,
OperatorType.MULT,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable div(final RandomVariable randomVariable) {
if(randomVariable.getTypePriority() > this.getTypePriority()) {
// Check type priority
return randomVariable.vid(this);
}
return new RandomVariableDifferentiableAAD(
getValues().div(randomVariable.getValues()),
Arrays.asList(this.getOperatorTreeNode(), OperatorTreeNode.of(randomVariable)),
Arrays.asList(this.getValues(), randomVariable.getValues()),
null,
OperatorType.DIV,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable vid(final RandomVariable randomVariable) {
if(randomVariable.getTypePriority() > this.getTypePriority()) {
// Check type priority
return randomVariable.div(this);
}
return new RandomVariableDifferentiableAAD(
getValues().vid(randomVariable.getValues()),
Arrays.asList(OperatorTreeNode.of(randomVariable), this.getOperatorTreeNode()), // DIV with swapped arguments
Arrays.asList(randomVariable.getValues(), this.getValues()), // DIV with swapped arguments
null,
OperatorType.DIV,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable cap(final RandomVariable randomVariable) {
if(randomVariable.getTypePriority() > this.getTypePriority()) {
// Check type priority
return randomVariable.cap(this);
}
return new RandomVariableDifferentiableAAD(
getValues().cap(randomVariable.getValues()),
Arrays.asList(this, randomVariable),
OperatorType.CAP,
getFactory());
}
@Override
public RandomVariable floor(final RandomVariable floor) {
if(floor.getTypePriority() > this.getTypePriority()) {
// Check type priority
return floor.floor(this);
}
return new RandomVariableDifferentiableAAD(
getValues().floor(floor.getValues()),
Arrays.asList(this, floor),
OperatorType.FLOOR,
getFactory());
}
@Override
public RandomVariable accrue(final RandomVariable rate, final double periodLength) {
if(rate.getTypePriority() > this.getTypePriority()) {
// Check type priority
return rate.mult(periodLength).add(1.0).mult(this);
}
return new RandomVariableDifferentiableAAD(
getValues().accrue(rate.getValues(), periodLength),
Arrays.asList(this, rate, new RandomVariableFromDoubleArray(periodLength)),
OperatorType.ACCRUE,
getFactory());
}
@Override
public RandomVariable discount(final RandomVariable rate, final double periodLength) {
if(rate.getTypePriority() > this.getTypePriority()) {
// Check type priority
return rate.mult(periodLength).add(1.0).invert().mult(this);
}
return new RandomVariableDifferentiableAAD(
getValues().discount(rate.getValues(), periodLength),
Arrays.asList(this, rate, new RandomVariableFromDoubleArray(periodLength)),
OperatorType.DISCOUNT,
getFactory());
}
@Override
public RandomVariable choose(final RandomVariable valueIfTriggerNonNegative, final RandomVariable valueIfTriggerNegative) {
return new RandomVariableDifferentiableAAD(
getValues().choose(valueIfTriggerNonNegative.getValues(), valueIfTriggerNegative.getValues()),
Arrays.asList(this.getOperatorTreeNode(), OperatorTreeNode.of(valueIfTriggerNonNegative), OperatorTreeNode.of(valueIfTriggerNegative)),
Arrays.asList(this.getValues(), valueIfTriggerNonNegative.getValues(), valueIfTriggerNegative.getValues()),
null,
OperatorType.CHOOSE,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable invert() {
return new RandomVariableDifferentiableAAD(
getValues().invert(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.INVERT,
getFactory());
}
@Override
public RandomVariable abs() {
return new RandomVariableDifferentiableAAD(
getValues().abs(),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.ABS,
getFactory());
}
@Override
public RandomVariable addProduct(final RandomVariable factor1, final double factor2) {
if(factor1.getTypePriority() > this.getTypePriority()) {
// Check type priority
return factor1.mult(factor2).add(this);
}
return new RandomVariableDifferentiableAAD(
getValues().addProduct(factor1.getValues(), factor2),
Arrays.asList(this.getOperatorTreeNode(), OperatorTreeNode.of(factor1), null),
Arrays.asList(this.getValues(), factor1.getValues(), new Scalar(factor2)),
null,
OperatorType.ADDPRODUCT,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable addProduct(final RandomVariable factor1, final RandomVariable factor2) {
if(factor1.getTypePriority() > this.getTypePriority() || factor2.getTypePriority() > this.getTypePriority()) {
// Check type priority
return factor1.mult(factor2).add(this);
}
return new RandomVariableDifferentiableAAD(
getValues().addProduct(factor1.getValues(), factor2.getValues()),
Arrays.asList(this.getOperatorTreeNode(), OperatorTreeNode.of(factor1), OperatorTreeNode.of(factor2)),
Arrays.asList(this.getValues(), factor1.getValues(), factor2.getValues()),
null,
OperatorType.ADDPRODUCT,
getFactory(),
typePriorityDefault);
}
@Override
public RandomVariable addRatio(final RandomVariable numerator, final RandomVariable denominator) {
if(numerator.getTypePriority() > this.getTypePriority() || denominator.getTypePriority() > this.getTypePriority()) {
// Check type priority
return numerator.div(denominator).add(this);
}
return new RandomVariableDifferentiableAAD(
getValues().addRatio(numerator.getValues(), denominator.getValues()),
Arrays.asList(this, numerator, denominator),
OperatorType.ADDRATIO,
getFactory());
}
@Override
public RandomVariable subRatio(final RandomVariable numerator, final RandomVariable denominator) {
if(numerator.getTypePriority() > this.getTypePriority() || denominator.getTypePriority() > this.getTypePriority()) {
// Check type priority
return numerator.div(denominator).mult(-1).add(this);
}
return new RandomVariableDifferentiableAAD(
getValues().subRatio(numerator.getValues(), denominator.getValues()),
Arrays.asList(this, numerator, denominator),
OperatorType.SUBRATIO,
getFactory());
}
/*
* The following methods are end points, the result is not differentiable.
*/
@Override
public RandomVariable isNaN() {
return getValues().isNaN();
}
@Override
public IntToDoubleFunction getOperator() {
return getValues().getOperator();
}
@Override
public DoubleStream getRealizationsStream() {
return getValues().getRealizationsStream();
}
@Override
public RandomVariable apply(final DoubleUnaryOperator operator) {
throw new UnsupportedOperationException("Applying functions is not supported.");
}
@Override
public RandomVariable apply(final DoubleBinaryOperator operator, final RandomVariable argument) {
throw new UnsupportedOperationException("Applying functions is not supported.");
}
@Override
public RandomVariable apply(final DoubleTernaryOperator operator, final RandomVariable argument1, final RandomVariable argument2) {
throw new UnsupportedOperationException("Applying functions is not supported.");
}
public RandomVariable getVarianceAsRandomVariableAAD(){
/*returns deterministic AAD random variable */
return new RandomVariableDifferentiableAAD(
new RandomVariableFromDoubleArray(getVariance()),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.VARIANCE,
getFactory());
}
public RandomVariable getSampleVarianceAsRandomVariableAAD() {
/*returns deterministic AAD random variable */
return new RandomVariableDifferentiableAAD(
new RandomVariableFromDoubleArray(getSampleVariance()),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.SVARIANCE,
getFactory());
}
public RandomVariable getStandardDeviationAsRandomVariableAAD(){
/*returns deterministic AAD random variable */
return new RandomVariableDifferentiableAAD(
new RandomVariableFromDoubleArray(getStandardDeviation()),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.STDEV,
getFactory());
}
public RandomVariable getStandardErrorAsRandomVariableAAD(){
/*returns deterministic AAD random variable */
return new RandomVariableDifferentiableAAD(
new RandomVariableFromDoubleArray(getStandardError()),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.STDERROR,
getFactory());
}
public RandomVariable getMinAsRandomVariableAAD(){
/*returns deterministic AAD random variable */
return new RandomVariableDifferentiableAAD(
new RandomVariableFromDoubleArray(getMin()),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.MIN,
getFactory());
}
public RandomVariable getMaxAsRandomVariableAAD(){
/*returns deterministic AAD random variable */
return new RandomVariableDifferentiableAAD(
new RandomVariableFromDoubleArray(getMax()),
Arrays.asList(new RandomVariable[]{ this }),
OperatorType.MAX,
getFactory());
}
@Override
public String toString() {
return "RandomVariableDifferentiableAAD [values=" + values + ",\n ID=" + getID() + "]";
}
@Override
public RandomVariableDifferentiable getCloneIndependent() {
return new RandomVariableDifferentiableAAD(this.getValues());
}
}
