API

`err` at the REPL / top level

Julia's REPL defines its own global variable err (the last thrown error, the companion of ans) in Base.MainInclude. At the REPL prompt, in julia -e scripts, or at the top level of an included file, this variable shadows the err function exported by ADerrors, producing an UndefVarError. Inside functions and user modules bare err(...) always works. At the top level of a script or at the REPL, use the qualified form ADerrors.err(...).

Observables: creating `uwreal` values

ADerrors.uwreal — Type

uwreal(x::Float64)
uwreal([value::Float64, error::Float64], mcid)
uwreal(data::Vector{Float64}, mcid[, replica::Vector{Int64}])
uwreal(data::Vector{Float64}, mcid[, replica::Vector{Int64}], idm::Vector{Int64}, nms::Int64)

Returns an uwreal data type. Depending on the first argument, the uwreal stores the following information:

Input is a single Float64. In this case the variable acts in exactly the same way as a real number. This is understood as a quantity with zero error.
Input is a 2 element Vector of Float64 [value, error]. In this case the data is understood as value +/- error.
Input is a Vector of Float64 of length larger than 4. In this case the data is understood as consecutive measurements of an observable in a Monte Carlo (MC) simulation.

In the last two cases, an ensemble ID is required as input. Data with the same ID are considered as correlated (i.e. fully correlated for the case of a value +/- error observables measured on the same sample for the case of data from a MC simulation). The preferred way to input the ensemble tag is via a String that uniquely identifies the ensemble, but an integer is also supported for legacy reasons. Note that the legacy integer interface is deprecated and a warning is issued on each use; also note that a String name that parses as an integer (e.g. "100") is mapped to the same internal ID as the legacy integer 100, so the two interfaces share the ID space and such names should be avoided. For example:

using ADerrors # hide
a = uwreal([1.2, 0.2], "Simple var with error")   # a = 1.2 +/- 0.2
b = uwreal([1.2, 0.2], "Simple var with error")   # b = 1.2 +/- 0.2
c = uwreal([1.2, 0.2], "Another var with error")  # c = 1.2 +/- 0.2

d = a-b
uwerr(d)
println("d has zero error because a and b are correlated", d)

e = a-c
uwerr(e)
println("e has non zero error because a and c are independent", e)

Replica

data can contain measurements in several replica (i.e. independent simulations with the same physical and algorithmic parameters). How many measurements correspond to each replica are specified by an optional replica vector argument replica. Note that length(replica) is the number of replica (i.e. independent simulations), and that sum(replica) must match length(data)

using ADerrors # hide
# 1000 measurements in three replica of lengths
# 500, 100 and 400
a = uwreal(rand(1000), "Ensemble with three replica", [500, 100, 400])

Gaps in the measurements

In some situations an observable is not measured in every configuration. In this case two additional arguments are needed to define the observable

idm. Type Vector{Int64}. idm[n] labels the configuration where data[n]is measured.
nms. Type Int64. The total number of measurements in the ensemble

using ADerrors # hide
# Observable measured on the odd configurations 
# 1, 3, 5, ..., 999 on an emsemble of length 1000
a = uwreal(rand(500), "Observable with gaps", collect(1:2:999), 1000)

# Observable measured on the first 900 configurations 
# on the same emsemble
b = uwreal(rand(900), "Observable with gaps", collect(1:900), 1000)

Note that in this case, if the ensemble has different replica, sum(replica) must match nms

using ADerrors # hide
# Observable measured on the even configurations 
# 2, 4, 6, ..., 200 on an emsemble of length 200
# with two replica of lengths 75, 125
a = uwreal(data_a[1:500], "Observable with gaps in an ensemble with replica", [75, 125], collect(2:2:200), 200)