Support correlation between variables

[giordano]

Currently,

using Measurements
x = 5.2 ± 0.4
x-x != zero(x)
x*x != x^2
tan(x) != sin(x)/cos(x)

because the package doesn't support correlation between variables.

I don't really know how the covariance matrix should be calculated in this case, where there are two single measurements, not two elements of a population. Any hint on this is appreciated.

After looking at the user guide of the Python package uncertainties, I think that the Measurement type should be extended to have two extra fields: a unique tag to identify each measurement (so that two measurement with the same value and uncertainty are equal), and the list of derivatives of variables constituting the object. For example:

# Definition.  The Measurement type is composed by the following fields:
#   * val: the nominal value of the measurement
#   * err: the uncertainty, assumed to be standard deviation
#   * tag: a (hopefully) unique identifier, it is used to identify a specific
#     measurement in the list of derivatives.
#   * der: the list of derivates.  It is a dictionary, whose keys are the tags
#     of the quantities with which the measurement has been derived, and the
#     corresponding value is the derivative of the new measurement with respect
#     to that measurement.  This dictionary is useful to trace the contribution
#     of each measurement.
immutable Measurement{T<:Real} <: Real
    val::T
    err::T
    tag::Float64
    der::Dict{Float64, T}
end

# Constructor
function Measurement(val::Real, err::Real)
    val, err, der = promote(val, err, one(val))
    tag = rand()
    return Measurement(val, err, tag, Dict(tag=>der))
end

This change, necessary to make the package fully work, will definitely degrade performance, so it needs to be thought carefully. Input is very welcome.

[giordano]

This has been implemented in commits 6f8fb48...590d423 (from 6f8fb48 Move @uncertain to math.jl file to 590d423 10x improvement for "result" function for more than one argument; see 6f8fb48...590d423)