finMath lib documentation
net.finmath.montecarlo.automaticdifferentiation.backward

• java.lang.Object
• ### Method Detail

• #### getValues

public RandomVariable getValues()
Returns the underlying values.
Specified by:
getValues in interface RandomVariable
Returns:
The underling values.

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.
Specified by:
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:
• #### getTangents

public Map<Long,RandomVariable> getTangents(Set<Long> dependentIDs)
Description copied from interface: RandomVariableDifferentiable
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.
Specified by:
getTangents in interface RandomVariableDifferentiable
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.
• #### equals

public boolean equals(RandomVariable randomVariable)
Description copied from interface: RandomVariable
Compare this random variable with a given one
Specified by:
equals in interface RandomVariable
Parameters:
randomVariable - Random variable to compare with.
Returns:
True if this random variable and the given one are equal, otherwise false
• #### getFiltrationTime

public double getFiltrationTime()
Description copied from interface: RandomVariable
Returns the filtration time.
Specified by:
getFiltrationTime in interface RandomVariable
Returns:
The filtration time.
• #### get

public double get(int pathOrState)
Description copied from interface: RandomVariable
Evaluate at a given path or state.
Specified by:
get in interface RandomVariable
Parameters:
pathOrState - Index of the path or state.
Returns:
Value of this random variable at the given path or state.
• #### size

public int size()
Description copied from interface: RandomVariable
Returns the number of paths or states.
Specified by:
size in interface RandomVariable
Returns:
Number of paths or states.
• #### isDeterministic

public boolean isDeterministic()
Description copied from interface: RandomVariable
Check if this random variable is deterministic in the sense that it is represented by a single double value. Note that the methods returns false, if the random variable is represented by a vector where each element has the same value.
Specified by:
isDeterministic in interface RandomVariable
Returns:
True if this random variable is deterministic.
• #### getRealizations

public double[] getRealizations()
Description copied from interface: RandomVariable
Returns a vector representing the realization of this random variable. This method is merely useful for analysis. Its interpretation depends on the context (Monte-Carlo or lattice). The method does not expose an internal data model.
Specified by:
getRealizations in interface RandomVariable
Returns:
Vector of realizations of this random variable.
• #### getMin

public double getMin()
Description copied from interface: RandomVariable
Returns the minimum value attained by this random variable.
Specified by:
getMin in interface RandomVariable
Returns:
The minimum value.
• #### getMax

public double getMax()
Description copied from interface: RandomVariable
Returns the maximum value attained by this random variable.
Specified by:
getMax in interface RandomVariable
Returns:
The maximum value.
• #### getAverage

public double getAverage()
Description copied from interface: RandomVariable
Returns the expectation of this random variable. The result of this method has to agrees with average().doubleValue().
Specified by:
getAverage in interface RandomVariable
Returns:
The average assuming equi-distribution.
• #### getAverage

public double getAverage(RandomVariable probabilities)
Description copied from interface: RandomVariable
Returns the expectation of this random variable for a given probability measure (weight). The result of this method is (mathematically) equivalent to
this.mult(probabilities).getAverage() / probabilities.getAverage()
while the internal implementation may differ, e.g. being more efficient by performing multiplication and summation in the same loop.
Specified by:
getAverage in interface RandomVariable
Parameters:
probabilities - The probability weights.
Returns:
The average assuming the given probability weights.
• #### getVariance

public double getVariance()
Description copied from interface: RandomVariable
Returns the variance of this random variable, i.e., V where V = ((X-m)^2).getAverage() and X = this and m = X.getAverage().
Specified by:
getVariance in interface RandomVariable
Returns:
The average assuming equi-distribution.
• #### getVariance

public double getVariance(RandomVariable probabilities)
Description copied from interface: RandomVariable
Returns the variance of this random variable, i.e., V where V = ((X-m)^2).getAverage(probabilities) and X = this and m = X.getAverage(probabilities).
Specified by:
getVariance in interface RandomVariable
Parameters:
probabilities - The probability weights.
Returns:
The average assuming the given probability weights.
• #### getSampleVariance

public double getSampleVariance()
Description copied from interface: RandomVariable
Returns the sample variance of this random variable, i.e., V * size()/(size()-1) where V = getVariance().
Specified by:
getSampleVariance in interface RandomVariable
Returns:
The sample variance.
• #### getStandardDeviation

public double getStandardDeviation()
Description copied from interface: RandomVariable
Returns the standard deviation of this random variable, i.e., sqrt(V) where V = ((X-m)^2).getAverage() and X = this and m = X.getAverage().
Specified by:
getStandardDeviation in interface RandomVariable
Returns:
The standard deviation assuming equi-distribution.
• #### getStandardDeviation

public double getStandardDeviation(RandomVariable probabilities)
Description copied from interface: RandomVariable
Returns the standard deviation of this random variable, i.e., sqrt(V) where V = ((X-m)^2).getAverage(probabilities) and X = this and m = X.getAverage(probabilities).
Specified by:
getStandardDeviation in interface RandomVariable
Parameters:
probabilities - The probability weights.
Returns:
The standard error assuming the given probability weights.
• #### getStandardError

public double getStandardError()
Description copied from interface: RandomVariable
Returns the standard error (discretization error) of this random variable. For a Monte-Carlo simulation this is 1/Math.sqrt(n) * RandomVariable.getStandardDeviation().
Specified by:
getStandardError in interface RandomVariable
Returns:
The standard error assuming equi-distribution.
• #### getQuantile

public double getQuantile(double quantile)
Description copied from interface: RandomVariable
Returns the quantile value for this given random variable, i.e., the value x such that P(this < x) = quantile, where P denotes the probability measure. The method will consider picewise constant values (with constant extrapolation) in the random variable. That is getQuantile(0) wiil return the smallest value and getQuantile(1) will return the largest value.
Specified by:
getQuantile in interface RandomVariable
Parameters:
quantile - The quantile level.
Returns:
The quantile value assuming equi-distribution.
• #### getQuantile

public double getQuantile(double quantile,
RandomVariable probabilities)
Description copied from interface: RandomVariable
Returns the quantile value for this given random variable, i.e., the value x such that P(this < x) = quantile, where P denotes the probability measure.
Specified by:
getQuantile in interface RandomVariable
Parameters:
quantile - The quantile level.
probabilities - The probability weights.
Returns:
The quantile value assuming the given probability weights.
• #### getQuantileExpectation

public double getQuantileExpectation(double quantileStart,
double quantileEnd)
Description copied from interface: RandomVariable
Returns the expectation over a quantile for this given random variable. The method will consider picewise constant values (with constant extrapolation) in the random variable. For a ≤ b the method returns (Σa ≤ i ≤ b x[i]) / (b-a+1), where
• a = min(max((n+1) * quantileStart - 1, 0, 1);
• b = min(max((n+1) * quantileEnd - 1, 0, 1);
• n = this.size();
For quantileStart > quantileEnd the method returns getQuantileExpectation(quantileEnd, quantileStart).
Specified by:
getQuantileExpectation in interface RandomVariable
Parameters:
quantileStart - Lower bound of the integral.
quantileEnd - Upper bound of the integral.
Returns:
The (conditional) expectation of the values between two quantile levels assuming equi-distribution.
• #### getHistogram

public double[] getHistogram(double[] intervalPoints)
Description copied from interface: RandomVariable
Generates a Histogram based on the realizations stored in this random variable. The returned result array's length is intervalPoints.length+1.
• The value result[0] equals the relative frequency of values observed in the interval ( -infinity, intervalPoints[0] ].
• The value result[i] equals the relative frequency of values observed in the interval ( intervalPoints[i-1], intervalPoints[i] ].
• The value result[n] equals the relative frequency of values observed in the interval ( intervalPoints[n-1], infinity ).
where n = intervalPoints.length. Note that the intervals are open on the left, closed on the right, i.e., result[i] contains the number of elements x with intervalPoints[i-1] < x ≤ intervalPoints[i]. Thus, is you have a random variable which only takes values contained in the (sorted) array possibleValues, then result = getHistogram(possibleValues) returns an array where result[i] is the relative frequency of occurrence of possibleValues[i]. The sum of result[i] over all i is equal to 1, except for uninitialized random variables where all values are 0.
Specified by:
getHistogram in interface RandomVariable
Parameters:
intervalPoints - Array of ascending values defining the interval boundaries.
Returns:
A histogram with respect to a provided interval.
• #### getHistogram

public double[][] getHistogram(int numberOfPoints,
double standardDeviations)
Description copied from interface: RandomVariable
Generates a histogram based on the realizations stored in this random variable using interval points calculated from the arguments, see also RandomVariable.getHistogram(double[]). The interval points are set with equal distance over an the interval of the specified standard deviation. The interval points used are
x[i] = mean + alpha[i] * standardDeviations * sigma
where The methods result is an array of two vectors, where result[0] are the intervals center points ('anchor points') and result[1] contains the relative frequency for the interval. The 'anchor point' for the interval (-infinity, x[0]) is x[0] - 1/2 (x[1]-x[0]) and the 'anchor point' for the interval (x[n], infinity) is x[n] + 1/2 (x[n]-x[n-1]). Here n = numberOfPoints is the number of interval points.
Specified by:
getHistogram in interface RandomVariable
Parameters:
numberOfPoints - The number of interval points.
standardDeviations - The number of standard deviations defining the discretization radius.
Returns:
A histogram, given as double[2][], where result[0] are the center point of the intervals and result[1] is the value of RandomVariable.getHistogram(double[]) for the given the interval points. The length of result[0] and result[1] is numberOfPoints+1.
• #### cache

public RandomVariable cache()
Description copied from interface: RandomVariable
Return a cacheable version of this object (often a self-reference). This method should be called when you store the object for later use, i.e., assign it, or when the object is consumed in a function, but later used also in another function.
Specified by:
cache in interface RandomVariable
Returns:
A cacheable version of this object (often a self-reference).
• #### cap

public RandomVariable cap(double cap)
Description copied from interface: RandomVariable
Applies x → min(x,cap) to this random variable. It returns a new random variable with the result.
Specified by:
cap in interface RandomVariable
Parameters:
cap - The cap.
Returns:
New random variable with the result of the function.
• #### floor

public RandomVariable floor(double floor)
Description copied from interface: RandomVariable
Applies x → max(x,floor) to this random variable. It returns a new random variable with the result.
Specified by:
floor in interface RandomVariable
Parameters:
floor - The floor.
Returns:
New random variable with the result of the function.

Description copied from interface: RandomVariable
Applies x → x + value to this random variable. It returns a new random variable with the result.
Specified by:
Parameters:
value - The value to add.
Returns:
New random variable with the result of the function.
• #### sub

public RandomVariable sub(double value)
Description copied from interface: RandomVariable
Applies x → x - value to this random variable.
Specified by:
sub in interface RandomVariable
Parameters:
value - The value to subtract.
Returns:
New random variable with the result of the function.
• #### mult

public RandomVariable mult(double value)
Description copied from interface: RandomVariable
Applies x → x * value to this random variable.
Specified by:
mult in interface RandomVariable
Parameters:
value - The value to multiply.
Returns:
New random variable with the result of the function.
• #### div

public RandomVariable div(double value)
Description copied from interface: RandomVariable
Applies x → x / value to this random variable.
Specified by:
div in interface RandomVariable
Parameters:
value - The value to divide.
Returns:
New random variable with the result of the function.
• #### pow

public RandomVariable pow(double exponent)
Description copied from interface: RandomVariable
Applies x → pow(x,exponent) to this random variable.
Specified by:
pow in interface RandomVariable
Parameters:
exponent - The exponent.
Returns:
New random variable with the result of the function.
• #### average

public RandomVariable average()
Description copied from interface: RandomVariable
Returns a random variable which is deterministic and corresponds the expectation of this random variable.
Specified by:
average in interface RandomVariable
Returns:
New random variable being the expectation of this random variable.
• #### getConditionalExpectation

public RandomVariable getConditionalExpectation(ConditionalExpectationEstimator estimator)
Description copied from interface: RandomVariable
Returns the conditional expectation using a given conditional expectation estimator.
Specified by:
getConditionalExpectation in interface RandomVariable
Parameters:
estimator - A given conditional expectation estimator.
Returns:
The conditional expectation of this random variable (as a random variable)
• #### squared

public RandomVariable squared()
Description copied from interface: RandomVariable
Applies x → x * x to this random variable.
Specified by:
squared in interface RandomVariable
Returns:
New random variable with the result of the function.
• #### sqrt

public RandomVariable sqrt()
Description copied from interface: RandomVariable
Applies x → sqrt(x) to this random variable.
Specified by:
sqrt in interface RandomVariable
Returns:
New random variable with the result of the function.
• #### exp

public RandomVariable exp()
Description copied from interface: RandomVariable
Applies x → exp(x) to this random variable.
Specified by:
exp in interface RandomVariable
Returns:
New random variable with the result of the function.
• #### log

public RandomVariable log()
Description copied from interface: RandomVariable
Applies x → log(x) to this random variable.
Specified by:
log in interface RandomVariable
Returns:
New random variable with the result of the function.
• #### sin

public RandomVariable sin()
Description copied from interface: RandomVariable
Applies x → sin(x) to this random variable.
Specified by:
sin in interface RandomVariable
Returns:
New random variable with the result of the function.
• #### cos

public RandomVariable cos()
Description copied from interface: RandomVariable
Applies x → cos(x) to this random variable.
Specified by:
cos in interface RandomVariable
Returns:
New random variable with the result of the function.

Description copied from interface: RandomVariable
Applies x → x+randomVariable to this random variable.
Specified by:
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### sub

public RandomVariable sub(RandomVariable randomVariable)
Description copied from interface: RandomVariable
Applies x → x-randomVariable to this random variable.
Specified by:
sub in interface RandomVariable
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### bus

public RandomVariable bus(RandomVariable randomVariable)
Description copied from interface: RandomVariable
Applies x → randomVariable-x to this random variable.
Specified by:
bus in interface RandomVariable
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### mult

public RandomVariable mult(RandomVariable randomVariable)
Description copied from interface: RandomVariable
Applies x → x*randomVariable to this random variable.
Specified by:
mult in interface RandomVariable
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### div

public RandomVariable div(RandomVariable randomVariable)
Description copied from interface: RandomVariable
Applies x → x/randomVariable to this random variable.
Specified by:
div in interface RandomVariable
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### vid

public RandomVariable vid(RandomVariable randomVariable)
Description copied from interface: RandomVariable
Applies x → randomVariable/x to this random variable.
Specified by:
vid in interface RandomVariable
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### cap

public RandomVariable cap(RandomVariable randomVariable)
Description copied from interface: RandomVariable
Applies x → min(x,cap) to this random variable.
Specified by:
cap in interface RandomVariable
Parameters:
randomVariable - The cap. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### floor

public RandomVariable floor(RandomVariable floor)
Description copied from interface: RandomVariable
Applies x → max(x,floor) to this random variable.
Specified by:
floor in interface RandomVariable
Parameters:
floor - The floor. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### accrue

public RandomVariable accrue(RandomVariable rate,
double periodLength)
Description copied from interface: RandomVariable
Applies x → x * (1.0 + rate * periodLength) to this random variable.
Specified by:
accrue in interface RandomVariable
Parameters:
rate - The accruing rate. A random variable (compatible with this random variable).
periodLength - The period length
Returns:
New random variable with the result of the function.
• #### discount

public RandomVariable discount(RandomVariable rate,
double periodLength)
Description copied from interface: RandomVariable
Applies x → x / (1.0 + rate * periodLength) to this random variable.
Specified by:
discount in interface RandomVariable
Parameters:
rate - The discounting rate. A random variable (compatible with this random variable).
periodLength - The period length
Returns:
New random variable with the result of the function.
• #### choose

public RandomVariable choose(RandomVariable valueIfTriggerNonNegative,
RandomVariable valueIfTriggerNegative)
Description copied from interface: RandomVariable
Applies x → (x ≥ 0 ? valueIfTriggerNonNegative : valueIfTriggerNegative)
Specified by:
choose in interface RandomVariable
Parameters:
valueIfTriggerNonNegative - The value used if this is greater or equal 0
valueIfTriggerNegative - The value used if the this is less than 0
Returns:
New random variable with the result of the function.
• #### invert

public RandomVariable invert()
Description copied from interface: RandomVariable
Applies x → 1/x to this random variable.
Specified by:
invert in interface RandomVariable
Returns:
New random variable with the result of the function.
• #### abs

public RandomVariable abs()
Description copied from interface: RandomVariable
Applies x → Math.abs(x), i.e. x → |x| to this random variable.
Specified by:
abs in interface RandomVariable
Returns:
New random variable with the result of the function.

double factor2)
Description copied from interface: RandomVariable
Applies x → x + factor1 * factor2
Specified by:
Parameters:
factor1 - The factor 1. A random variable (compatible with this random variable).
factor2 - The factor 2.
Returns:
New random variable with the result of the function.

RandomVariable factor2)
Description copied from interface: RandomVariable
Applies x → x + factor1 * factor2
Specified by:
Parameters:
factor1 - The factor 1. A random variable (compatible with this random variable).
factor2 - The factor 2. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.

RandomVariable denominator)
Description copied from interface: RandomVariable
Applies x → x + numerator / denominator
Specified by:
Parameters:
numerator - The numerator of the ratio to add. A random variable (compatible with this random variable).
denominator - The denominator of the ratio to add. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### subRatio

public RandomVariable subRatio(RandomVariable numerator,
RandomVariable denominator)
Description copied from interface: RandomVariable
Applies x → x - numerator / denominator
Specified by:
subRatio in interface RandomVariable
Parameters:
numerator - The numerator of the ratio to sub. A random variable (compatible with this random variable).
denominator - The denominator of the ratio to sub. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• #### isNaN

public RandomVariable isNaN()
Description copied from interface: RandomVariable
Applies x → (Double.isNaN(x) ? 1.0 : 0.0)
Specified by:
isNaN in interface RandomVariable
Returns:
A random variable which is 1.0 for all states that are NaN, otherwise 0.0.
• #### getOperator

public IntToDoubleFunction getOperator()
Description copied from interface: RandomVariable
Returns the operator path → this.get(path) corresponding to this random variable.
Specified by:
getOperator in interface RandomVariable
Returns:
The operator path → this.get(path) corresponding to this random variable.
• #### getRealizationsStream

public DoubleStream getRealizationsStream()
Description copied from interface: RandomVariable
Returns a stream of doubles corresponding to the realizations of this random variable.
Specified by:
getRealizationsStream in interface RandomVariable
Returns:
A stream of doubles corresponding to the realizations of this random variable.
• #### apply

public RandomVariable apply(DoubleUnaryOperator operator)
Description copied from interface: RandomVariable
Applies x → operator(x) to this random variable. It returns a new random variable with the result.
Specified by:
apply in interface RandomVariable
Parameters:
operator - An unary operator/function, mapping double to double.
Returns:
New random variable with the result of the function.
• #### apply

public RandomVariable apply(DoubleBinaryOperator operator,
RandomVariable argument)
Description copied from interface: RandomVariable
Applies x → operator(x,y) to this random variable, where x is this random variable and y is a given random variable. It returns a new random variable with the result.
Specified by:
apply in interface RandomVariable
Parameters:
operator - A binary operator/function, mapping (double,double) to double.
argument - A random variable.
Returns:
New random variable with the result of the function.
• #### apply

public RandomVariable apply(DoubleTernaryOperator operator,
RandomVariable argument1,
RandomVariable argument2)
Description copied from interface: RandomVariable
Applies x → operator(x,y,z) to this random variable, where x is this random variable and y and z are given random variable. It returns a new random variable with the result.
Specified by:
apply in interface RandomVariable
Parameters:
operator - A ternary operator/function, mapping (double,double,double) to double.
argument1 - A random variable representing y.
argument2 - A random variable representing z.
Returns:
New random variable with the result of the function.