Returns an `uwreal` data type. Depending on the first argument, the `uwreal` stores the following information:
Returns an `uwreal` data type. Depending on the first argument, the `uwreal` stores the following information:
- 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 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.
- A 2 element Vector of `Float64` `[value, error]`. In this case the data is understood as `value +/- error`.
- Input is a 2 element Vector of `Float64` `[value, error]`. In this case the data is understood as `value +/- error`.
- A Vector of `Float64` of length larger than 2. In this case the data is understood as consecutive measurements of an observable in a Monte Carlo (MC) simulation.
- 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). For example:
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). For example:
In some situations an observable is not measured in every configuration. In this case two additional arguments aree needed to define the observable
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.
- `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
- `nms`. Type `Int64`. The total number of measurements in the ensemble
```@example
```@example
using ADerrors # hide
using ADerrors # hide
...
@@ -694,17 +703,17 @@ b = sin(2.0*a)
...
@@ -694,17 +703,17 @@ b = sin(2.0*a)
uwerr(b)
uwerr(b)
println("LookhowIpropagateerrors:", b)
println("LookhowIpropagateerrors:", b)
c = 1.0 + b - 2.0*sin(a)*cos(a)
c = 1.0 + b - 2.0*sin(a)*cos(a)
uwerr(b)
uwerr(c)
println("LookhowgoodIamatthis(zeroerror!):", c)
println("LookhowgoodIamatthis(zeroerror!):", c)
```
```
### Optimal window
### Optimal window
Error in data coming from a Monte Carlo ensemble is performed by summing the autocorrelation function ``\Gamma_{\rm ID}(t)`` of the data for each ensemble ID. In practice this sum is truncated up to a window ``W_{\rm ID}``.
Error in data coming from a Monte Carlo ensemble is determined by summing the autocorrelation function ``\Gamma_{\rm ID}(t)`` of the data for each ensemble ID. In practice this sum is truncated up to a window ``W_{\rm ID}``.
By default, the summation window is determined as [proposed by U. Wolff](https://inspirehep.net/literature/621085) with a parameter ``S_{\tau} = 4``, but other methods are avilable via the optional argument `wpm`.
By default, the summation window is determined as [proposed by U. Wolff](https://inspirehep.net/literature/621085) with a parameter ``S_{\tau} = 4``, but other methods are avilable via the optional argument `wpm`.
For each ensemble `ID` one has to pass a vector of `Float64` of length 4. The first three components of the vector specify the criteria to determine the summation window:
For each ensemble `ID` one can pass a vector of `Float64` of length 4. The first three components of the vector specify the criteria to determine the summation window:
- `vp[1]`: The autocorrelation function is summed up to `t = round(vp[1])`.
- `vp[1]`: The autocorrelation function is summed up to `t = round(vp[1])`.
- `vp[2]`: The sumation window is determined [using U. Wolff poposal](https://inspirehep.net/literature/621085) with ``S_{\tau} = {\rm vp[2]}``.
- `vp[2]`: The sumation window is determined [using U. Wolff poposal](https://inspirehep.net/literature/621085) with ``S_{\tau} = {\rm vp[2]}``.
- `vp[3]`: The autocorrelation function ``\Gamma(t)`` is summed up a point where its error ``\delta\Gamma(t)`` is a factor `vp[3]` times larger than the signal.
- `vp[3]`: The autocorrelation function ``\Gamma(t)`` is summed up a point where its error ``\delta\Gamma(t)`` is a factor `vp[3]` times larger than the signal.
...
@@ -716,44 +725,80 @@ Note that:
...
@@ -716,44 +725,80 @@ Note that:
- One, and only one, of the components `vp[1:3]` has to be positive. This chooses your criteria to determine the summation window.
- One, and only one, of the components `vp[1:3]` has to be positive. This chooses your criteria to determine the summation window.
```@example
```@example
using ADerrors # hide
using ADerrors # hide
a = uwreal(rand(2000), 1233)
# Generate some correlated data
eta = randn(1000)
x = Vector{Float64}(undef, 1000)
x[1] = 0.0
for i in 2:1000
x[i] = x[i-1] + eta[i]
if abs(x[i]) > 1.0
x[i] = x[i-1]
end
end
# Load the data in a uwreal
a = uwreal(x.^2, 1233)
wpm = Dict{Int64,Vector{Float64}}()
wpm = Dict{Int64,Vector{Float64}}()
# Use default analysis (stau = 4.0)
# Use default analysis (stau = 4.0)
uwerr(a)
uwerr(a)
println(a)
println("default:", a, "(tauint=", taui(a, 1233), ")")
# This will still do default analysis because
# This will still do default analysis because
# a does not depend on emsemble 300
# a does not depend on emsemble 300
wpm[300] = [-1.0, 8.0, -1.0, 145.0]
wpm[300] = [-1.0, 8.0, -1.0, 145.0]
uwerr(a, wpm)
uwerr(a, wpm)
println(a)
println("default:", a, "(tauint=", taui(a, 1233), ")")
# Fix the summation window to 1 (i.e. uncorrelated data)
# Fix the summation window to 1 (i.e. uncorrelated data)
wpm[1233] = [1.0, -1.0, -1.0, -1.0]
wpm[1233] = [1.0, -1.0, -1.0, -1.0]
uwerr(a, wpm)
uwerr(a, wpm)
println(a)
println("uncorrelated:", a, "(tauint=", taui(a, 1233), ")")
# Use stau = 1.5
# Use stau = 1.5
wpm[1233] = [-1.0, 1.5, -1.0, -1.0]
wpm[1233] = [-1.0, 1.5, -1.0, -1.0]
uwerr(a, wpm)
uwerr(a, wpm)
println(a)
println("stau=1.5:", a, "(tauint=", taui(a, 1233), ")")
# Use fixed window 15 and add tail with texp = 100.0
# Use fixed window 15 and add tail with texp = 100.0
wpm[1233] = [15.0, -1.0, -1.0, 100.0]
wpm[1233] = [15.0, -1.0, -1.0, 100.0]
uwerr(a, wpm)
uwerr(a, wpm)
println(a)
println("Fixedwindow15,texp=100:", a, "(tauint=", taui(a, 1233), ")")
# Sum up to the point that the signal in Gamma is
# Sum up to the point that the signal in Gamma is
# 1.5 times the error and add a tail with texp = 30.0
# 1.5 times the error and add a tail with texp = 30.0
wpm[1233] = [-1.0, -1.0, 1.5, 30.0]
wpm[1233] = [-1.0, -1.0, 1.5, 30.0]
uwerr(a, wpm)
uwerr(a, wpm)
println(a)
println("signal/noise=1.5,texp=30:", a, "(tauint=", taui(a, 1233), ")")
An optional parameter `wpm` can be used to choose the summation window for the relevant autocorrelation functions. The situation is completely analogous to the case of error analysis of single variables.
@@ -11,53 +11,214 @@ function find_mcid(a::uwreal, mcid::Int64)
...
@@ -11,53 +11,214 @@ function find_mcid(a::uwreal, mcid::Int64)
end
end
end
end
return0
returnnothing
end
end
err(a::uwreal)=a.err
"""
err(a::uwreal)
Returns the error of the `uwreal` variable `a`. It is assumed that `uwerr` has been run on the variable so that an error is available. Otherwise an error message is printed.
```@example
using ADerrors # hide
a = uwreal([1.2, 0.2], 12) # a = 1.2 +/- 0.2
uwerr(a)
println("ahaserror:", err(a))
```
"""
function err(a::uwreal)
if(length(a.cfd)==0)
error("No error available... maybe run uwerr")
end
returna.err
end
"""
value(a::uwreal)
Returns the (mean) value of the `uwreal` variable `a`
```@example
using ADerrors # hide
a = uwreal([1.2, 0.2], 12) # a = 1.2 +/- 0.2
uwerr(a)
println("ahascentralvalue:", value(a))
```
"""
value(a::uwreal)=a.mean
value(a::uwreal)=a.mean
derror(a::uwreal)=a.derr
"""
derror(a::uwreal)
Returns an estimate of teh error of the error of the `uwreal` variable `a`. It is assumed that `uwerr` has been run on the variable so that an error is available. Otherwise an error message is printed.
```@example
using ADerrors # hide
a = uwreal([1.2, 0.2], 12) # a = 1.2 +/- 0.2
uwerr(a)
println("ahaserroroftheerror:", derror(a))
```
"""
function derror(a::uwreal)
if(length(a.cfd)==0)
error("No error available... maybe run uwerr")
end
returna.derr
end
"""
taui(a::uwreal, id::Int64)
Returns the value of tauint for the ensemble `id`. It is assumed that `uwerr` has been run on the variable and that `id` contributes to the observable `a`. Otherwise an error message is printed.
```@example
using ADerrors # hide
# Generate some correlated data
eta = randn(1000)
x = Vector{Float64}(undef, 1000)
x[1] = 0.0
for i in 2:1000
x[i] = x[i-1] + eta[i]
if abs(x[i]) > 1.0
x[i] = x[i-1]
end
end
a = uwreal(x.^2, 666)
uwerr(a)
println("Erroranalysisresult:", a, "(tauint=", taui(a, 666), ")")
```
"""
function taui(a::uwreal,mcid::Int64)
function taui(a::uwreal,mcid::Int64)
idx=find_mcid(a,mcid)
idx=find_mcid(a,mcid)
if(idx==0)
if(idx==nothing)
return0.5
error("No error available... maybe run uwerr")
else
else
returna.cfd[idx].taui
returna.cfd[idx].taui
end
end
end
end
"""
dtaui(a::uwreal, id::Int64)
Returns an estimate on the error of tauint for the ensemble `id`. It is assumed that `uwerr` has been run on the variable and that `id` contributes to the observable `a`. Otherwise an error message is printed.
Returns the summation window for the ensemble `id`. It is assumed that `uwerr` has been run on the variable and that `id` contributes to the observable `a`. Otherwise an error message is printed.
```@example
using ADerrors # hide
# Generate some correlated data
eta = randn(1000)
x = Vector{Float64}(undef, 1000)
x[1] = 0.0
for i in 2:1000
x[i] = x[i-1] + eta[i]
if abs(x[i]) > 1.0
x[i] = x[i-1]
end
end
a = uwreal(x.^2, 666)
uwerr(a)
println("Erroranalysisresult:", a,
"(window=", window(a, 666), ")")
```
"""
function window(a::uwreal,mcid::Int64)
function window(a::uwreal,mcid::Int64)
idx=find_mcid(a,mcid)
idx=find_mcid(a,mcid)
if(idx==0)
if(idx==nothing)
return0
error("No error available... maybe run uwerr")
else
else
returna.cfd[idx].iw
returna.cfd[idx].iw
end
end
end
end
"""
rho(a::uwreal, id::Int64)
Returns the normalized autocorrelation function of `a` for the ensemble `id`. It is assumed that `uwerr` has been run on the variable and that `id` contributes to the observable `a`. Otherwise an error message is printed.
```@example
using ADerrors # hide
# Generate some correlated data
eta = randn(1000)
x = Vector{Float64}(undef, 1000)
x[1] = 0.0
for i in 2:1000
x[i] = x[i-1] + eta[i]
if abs(x[i]) > 1.0
x[i] = x[i-1]
end
end
a = uwreal(x.^2, 666)
uwerr(a)
v = rho(a, 666)
for i in 1:length(v)
println(i, "", v[i])
end
```
"""
function rho(a::uwreal,mcid::Int64)
function rho(a::uwreal,mcid::Int64)
idx=find_mcid(a,mcid)
idx=find_mcid(a,mcid)
if(idx==0)
if(idx==nothing)
return[1.0]
error("No error available... maybe run uwerr")
else
else
returna.cfd[idx].gamm./a.cfd[idx].gamm[1]
returna.cfd[idx].gamm./a.cfd[idx].gamm[1]
end
end
end
end
"""
rho(a::uwreal, id::Int64)
Returns an estimate of the error on the normalized autocorrelation function of `a` for the ensemble `id`. It is assumed that `uwerr` has been run on the variable and that `id` contributes to the observable `a`. Otherwise an error message is printed.
```@example
using ADerrors # hide
# Generate some correlated data
eta = randn(1000)
x = Vector{Float64}(undef, 1000)
x[1] = 0.0
for i in 2:1000
x[i] = x[i-1] + eta[i]
if abs(x[i]) > 1.0
x[i] = x[i-1]
end
end
a = uwreal(x.^2, 666)
uwerr(a)
v = rho(a, 666)
dv = drho(a, 666)
for i in 1:length(v)
println(i, "", v[i], "+/-", dv[i])
end
```
"""
function drho(a::uwreal,mcid::Int64)
function drho(a::uwreal,mcid::Int64)
idx=find_mcid(a,mcid)
if(idx==nothing)
if(idx==0)
error("No error available... maybe run uwerr")
return[0.0]
else
else
returna.cfd[idx].drho
returna.cfd[idx].drho
end
end
...
@@ -219,11 +380,11 @@ function details(a::uwreal, ws::wspace, io::IO=stdout, names::Dict{Int64, String
...
@@ -219,11 +380,11 @@ function details(a::uwreal, ws::wspace, io::IO=stdout, names::Dict{Int64, String
Returns a vector of `uwreal` such that their mean values are `avgs[:]` and their covariance is `Mcov[:,:]`. In order to construct these observables `n=length(avgs)` ensemble ID are used. These have to be specified in the vector `ids[:]`.
```@example
using ADerrors # hide
# Put some average values and covariance
avg = [16.26, 0.12, -0.0038]
Mcov = [0.478071 -0.176116 0.0135305
-0.176116 0.0696489 -0.00554431
0.0135305 -0.00554431 0.000454180]
# Produce observables with ensemble ID
# [1, 2001, 32]. Do error analysis
p = cobs(avg, Mcov, [1, 2001, 32])
uwerr.(p)
# Check central values are ok
avg2 = value.(p)
println("Betterbezero:", sum((avg.-avg2).^2))
# Check that the covariance is ok
Mcov2 = cov(p)
println("Betterbezero:", sum((Mcov.-Mcov2).^2))
```
"""
function cobs(avgs::Vector{Float64},cov::Array{Float64,2},ids::Vector{Int64})
function cobs(avgs::Vector{Float64},cov::Array{Float64,2},ids::Vector{Int64})
where the function ``f_i(p)`` is an arbitrary function of the fit parameters. In simple words, the function is assumed to be quadratic in the data.
- `xp`: A vector of `Float64`. The value of the fit parameters at the minima.
- `data`: A vector of `uwreal`. The data whose fluctuations enter in the evaluation of the `chisq`.
- `W`: A matrix. The weights that enter in the evaluation of the `chisq` function. If a vector is passed, the matrix is assumed to be diagonal (i.e. **uncorrelated** fit). If no weights are passed, the routines assumes that `W` is diagonal with entries given by the inverse errors squared of the data (i.w. the `chisq` is weighted with the errors of the data).
