Elementary mathematical operations
Elementary mathematical operations (+, -, *, and /) between arbitrary uncertain values of different types and scalars are supported.
Syntax
Resampling is used to perform the mathematical operations. All mathematical operations return a vector containing the results of repeated element-wise operations (where each element is a resampled draw from the furnishing distribution(s) of the uncertain value(s)).
The default number of realizations is set to 10000. This allows calling uval1 + uval2 for two uncertain values uval1 and uval2. If you need to tune the number of resample draws to n, use the +(uval1, uval2, n) syntax.
Future improvements
In the future, elementary operations might be improved for certain combinations of uncertain values where exact expressions for error propagation are now, for example using the machinery in Measurements.jl for normally distributed values.
Supported operations
Addition
Base.:+ — MethodBase.:+(a::AbstractUncertainValue, b::AbstractUncertainValue) -> UncertainValueAddition operator for pairs of uncertain values.
Computes the element-wise sum between for a default of n = 10000 realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise sums.
Use the +(a, b, n) syntax to tune the number (n) of draws.
Base.:+ — MethodBase.:+(a::AbstractUncertainValue, b::AbstractUncertainValue, n::Int) -> UncertainValueAddition operator for pairs of uncertain values.
Computes the element-wise sum between a and b for n realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise sums.
Call this function using the +(a, b, n) syntax.
Base.:+ — MethodBase.:+(a::Real, b::AbstractUncertainValue) -> UncertainValueAddition operator for between scalars and uncertain values.
Computes the element-wise sum between a and b for a default of n = 10000 realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise sums.
Use the +(a, b, n) syntax to tune the number (n) of draws.
Base.:+ — MethodBase.:+(a::Real, b::AbstractUncertainValue, n::Int) -> UncertainValueAddition operator for scalar-uncertain value pairs.
Computes the element-wise sum between a and b for n realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise sums.
Call this function using the +(a, b, n) syntax.
Base.:+ — MethodBase.:+(a::AbstractUncertainValue, b::Real) -> UncertainValueAddition operator for between uncertain values and scalars.
Computes the element-wise sum between a and b for a default of n = 10000 realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise sums.
Use the +(a, b, n) syntax to tune the number (n) of draws.
Base.:+ — MethodBase.:+(a::AbstractUncertainValue, b::Real, n::Int) -> UncertainValueAddition operator for scalar-uncertain value pairs.
Computes the element-wise sum between a and b for n realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise sums.
Call this function using the +(a, b, n) syntax.
Subtraction
Base.:- — MethodBase.:-(a::AbstractUncertainValue, b::AbstractUncertainValue) -> UncertainValueSubtraction operator for pairs of uncertain values.
Computes the element-wise differences between for a default of n = 30000 realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise differences.
Use the -(a, b, n) syntax to tune the number (n) of draws.
Base.:- — MethodBase.:-(a::AbstractUncertainValue, b::AbstractUncertainValue, n::Int) -> UncertainValueSubtraction operator for pairs of uncertain values.
Computes the element-wise differences between a and b for n realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise differences.
Call this function using the -(a, b, n) syntax.
Base.:- — MethodBase.:-(a::Real, b::AbstractUncertainValue) -> UncertainValueSubtraction operator for between scalars and uncertain values.
Computes the element-wise differences between a and b for a default of n = 30000 realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise differences.
Use the -(a, b, n) syntax to tune the number (n) of draws.
Base.:- — MethodBase.:-(a::Real, b::AbstractUncertainValue, n::Int) -> UncertainValueSubtraction operator for scalar-uncertain value pairs.
Computes the element-wise differences between a and b for n realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise differences.
Call this function using the -(a, b, n) syntax.
Base.:- — MethodBase.:-(a::AbstractUncertainValue, b::Real) -> UncertainValueSubtraction operator for between uncertain values and scalars.
Computes the element-wise differences between a and b for a default of n = 30000 realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise differences.
Use the -(a, b, n) syntax to tune the number (n) of draws.
Base.:- — MethodBase.:-(a::AbstractUncertainValue, b::Real, n::Int) -> UncertainValueSubtraction operator for scalar-uncertain value pairs.
Computes the element-wise differences between a and b for n realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise differences.
Call this function using the -(a, b, n) syntax.
Multiplication
Base.:* — MethodBase.:*(a::AbstractUncertainValue, b::AbstractUncertainValue) -> UncertainValueMultiplication operator for pairs of uncertain values.
Computes the element-wise products between for a default of n = 10000 realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise products.
Use the *(a, b, n) syntax to tune the number (n) of draws.
Base.:* — MethodBase.:*(a::AbstractUncertainValue, b::AbstractUncertainValue, n::Int) -> UncertainValueMultiplication operator for pairs of uncertain values.
Computes the element-wise products between a and b for n realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise products.
Call this function using the *(a, b, n) syntax.
Base.:* — MethodBase.:*(a::Real, b::AbstractUncertainValue) -> UncertainValueMultiplication operator for between scalars and uncertain values.
Computes the element-wise products between a and b for a default of n = 10000 realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise products.
Use the *(a, b, n) syntax to tune the number (n) of draws.
Base.:* — MethodBase.:*(a::Real, b::AbstractUncertainValue, n::Int) -> UncertainValueMultiplication operator for scalar-uncertain value pairs.
Computes the element-wise products between a and b for n realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise products.
Call this function using the *(a, b, n) syntax.
Base.:* — MethodBase.:*(a::AbstractUncertainValue, b::Real) -> UncertainValueMultiplication operator for between uncertain values and scalars.
Computes the element-wise products between a and b for a default of n = 10000 realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise products.
Use the *(a, b, n) syntax to tune the number (n) of draws.
Base.:* — MethodBase.:*(a::AbstractUncertainValue, b::Real, n::Int) -> UncertainValueMultiplication operator for scalar-uncertain value pairs.
Computes the element-wise products between a and b for n realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise products.
Call this function using the *(a, b, n) syntax.
Division
Base.:/ — MethodBase.:/(a::AbstractUncertainValue, b::AbstractUncertainValue) -> UncertainValueDivision operator for pairs of uncertain values.
Computes the element-wise quotients between for a default of n = 10000 realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise quotients.
Use the /(a, b, n) syntax to tune the number (n) of draws.
Base.:/ — MethodBase.:/(a::AbstractUncertainValue, b::AbstractUncertainValue, n::Int) -> UncertainValueDivision operator for pairs of uncertain values.
Computes the element-wise quotients between a and b for n realizations of a and b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise quotients.
Call this function using the /(a, b, n) syntax.
Base.:/ — MethodBase.:/(a::Real, b::AbstractUncertainValue) -> UncertainValueDivision operator for between scalars and uncertain values.
Computes the element-wise quotients between a and b for a default of n = 10000 realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise quotients.
Use the /(a, b, n) syntax to tune the number (n) of draws.
Base.:/ — MethodBase.:/(a::Real, b::AbstractUncertainValue, n::Int) -> UncertainValueDivision operator for scalar-uncertain value pairs.
Computes the element-wise quotients between a and b for n realizations of b, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise quotients.
Call this function using the /(a, b, n) syntax.
Base.:/ — MethodBase.:/(a::AbstractUncertainValue, b::Real) -> UncertainValueDivision operator for between uncertain values and scalars.
Computes the element-wise quotients between a and b for a default of n = 10000 realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise quotients.
Use the /(a, b, n) syntax to tune the number (n) of draws.
Base.:/ — MethodBase.:/(a::AbstractUncertainValue, b::Real, n::Int) -> UncertainValueDivision operator for scalar-uncertain value pairs.
Computes the element-wise quotients between a and b for n realizations of a, then returns an uncertain value based on a kernel density estimate to the distribution of the element-wise quotients.
Call this function using the /(a, b, n) syntax.
Special cases
CertainValues
Performing elementary operations with CertainValues behaves as for scalars.