Added information on the use of PackageCompiler

README.md

@@ -37,5 +37,37 @@ julia> import Pkg
 
 It is better to start with the [Getting started](https://ific.uv.es/~alramos/docs/ADerrors/tutorial/) guide.
 
+# Alleviating time to first run
+
+`Julia` is well known for being slow the first time that you run some
+routines. On the first call to a function Julia not only runs the
+code, but also compiles it, making the first call slow.
+This problem can be alleviated in general with
+[PackageCompiler.jl](https://github.com/JuliaLang/PackageCompiler.jl). This
+is specially true for the case of `ADerrors` since most functions are
+type static. 
+
+As example, the file `extra/typical.jl` contains the most typical
+calls to `ADerrors`. One can execute this file telling julia to
+annotate the functions that are compiled
+```julia
+julia --trace-compile=precompile_aderrors.jl typical.jl
+```
+Now the functions annotated in `precompile_aderrors.jl` can be
+compiled and included in a `sysimage` that is autmatically loaded
+whenever you start Julia
+```julia
+julia> using PackageCompiler
+julia> PackageCompiler.create_sysimage(:ADerrors; precompile_statements_file="precompile_aderrors.jl", replace_default=true)
+```
+
+This will make `ADerrors` from the first call. Obviously you can tune
+the file `typical.jl` to your usage, or add other packages. Please
+note that packages included in the sysimage are locked to the versions
+of the sysimage. If you update `ADerrors` make sure to re-generate the
+sysimage. Probably is better to read [the documentation of
+PackageCompiler](https://julialang.github.io/PackageCompiler.jl/dev/sysimages/)
+in order to fully understand the drawbacks.
+
 
 

extra/typical.jl

+using ADerrors
+
+# Input of uwreal's
+a = uwreal(rand(1000), 1)
+b = uwreal([1.0, 0.1], 2)
+p = cobs([1.0, 2.0], [1.0 0.1;
+                      0.1 2.0], [3, 4])
+
+# Most common operations.
+# You might add something else if
+# you use it frequently
+for op in (:-, :sin, :cos, :log, :log10, :log2, :sqrt, :exp, :exp2, :exp10, :sinh, :cosh, :tanh)
+    @eval c = $op(a)
+end
+c = 1.0 + b
+c = 1.0 - b
+c = 1.0 * b
+c = 1.0 / b
+c = a + 2.0
+c = a - 2.0
+c = a * 2.0
+c = a / 2.0
+c = a ^ 3
+c = a + b
+c = a - b
+c = a * b
+c = a / b
+
+# Error analysis
+uwerr(c)
+cov([c, a, b])
+trcov([1.0 2.0 3.0;
+       2.0 1.0 0.4;
+       3.0 0.4 1.0], [c, a, b])
+details(c)
+
+# Error analysis of fit parameters
+npt = 12
+sig = zeros(npt, npt)
+dx  = zeros(npt)
+for i in 1:npt
+    dx[i]    = 0.01*i
+    sig[i,i] = dx[i]^2
+    for j in i+1:npt
+        sig[i,j] = 0.0001 - 0.000005*abs(i-j)
+        sig[j,i] = 0.0001 - 0.000005*abs(i-j)
+    end
+end
+y = [0.0802273592699947
+  0.09150837606934502
+  0.047923648239388834
+  0.024851583326401416
+  0.01635482325054799
+  0.13115281737744588
+  0.21013177679604178
+  0.002143355151617357
+  0.2292183950698425
+ -0.05174734852593241
+  0.1384913891139784
+ -0.05211234898997283]
+dt = cobs(y, sig, [100+n for n in 1:npt])
+chisq(p, d) = sum( (d .- p[1]) .^ 2 ./ dx .^2 )
+xp = [sum(value.(dt) ./ dx)/sum(1.0 ./ dx)]
+(fitp, csqexp) = fit_error(chisq, xp, dt)
+chiexp(chisq, xp, dt)
+