Posts

Benchmarking Solutions to Mrode (4th Ed.): BLUPF90, R, and Julia

The publication of the 4th edition of Linear Models for the Prediction of the Genetic Merit of Animals by R. A. Mrode and I. Pocrnic (2023, CABI) provides a comprehensive pedagogical reference for linear mixed models in quantitative genetics and animal breeding. Accompanying the text are three open-source companion solution repositories implementing the worked examples across the textbook:

  1. BLUPF90 Suite (Examples_BLUPF90): Parameter and data setups for the legacy Fortran 90 binaries developed by Ignacy Misztal and colleagues at the University of Georgia.
  2. R Scripts (Examples_R): Educational scripts using standard R packages (Matrix, pedigreemm, lme4, and the tidyverse).
  3. Julia Package (Mrode4edExamples.jl / Examples-Julia): A native, type-stable implementation built on the domain-specific libraries RelationshipMatrices.jl and Breeding.jl.

Below is an empirical benchmark and architectural evaluation comparing the computational paradigms, execution performance, numerical reliability, and algorithmic scaling of these three solution suites.

read more
Posts

Some interesting Julia codes

Julia is fast, composable, dynamic, general, reproducible and open source. The codes below were taken from https://julialang.org. I found it very illustrating.

Multiple dispatch

struct Dog end
struct Cat end

dog, cat = Dog(), Cat()
meet(a::Dog, b::Dog) = "The dogs play together"
meet(a::Dog, b::Cat) = "The dog chases the cat"
meet(a::Cat, b::Dog) = "The cat hisses at the dog"
meet(a::Cat, b::Cat) = "The cats ignore each other"

meet(dog, cat)
meet(dog, dog)
meet(cat, cat)

Display customization

struct Nutshell{T}
	contents::T
end
Base.show(io::IO, n::Nutshell) = print(io, "🥜 ", n.contents, " 🥜")
Nutshell("Julia")

Unicode and math

α, β = .5, .3
f(x) = α * x + β
Σ(v) = reduce(+, v)
Σ(f.(1:5))

Comprehensions

[x^2 for x in 1:5]

Broadcasting

A = [1 2; 3 4]
sin.(A) .+ 1
Dict(c => i for (i, c) in enumerate("julia")

Piping and composition

1:5 |> sum |> sqrt
(sqrt ∘ sum)(1:5) # equiv. above
map(exp ∘ abs, [-1, 2, -3])

Destructuring

(a, b, c) = 1:3
a, c # => (1, 3)
head, tail... = ["first", "second", "third"]
head, tail # => ("first", ["second", "third"])

Metaprogramming

ex = :(1 + 2 * 3)
typeof(ex) # => Expr
eval(ex)   # => 7

Easy package install

using DataFrames
# if not installed, prompted for installation, after 'y' answer
df = DataFrame(name = ["Alice", "Bob"], age = [25, 30])

Defaults and keywords args

function greet(name, greeting = "Hello"; punctuation = "!")
	"$greeting, $name$puctuation"
end
greet("Julia")  # "Hello, Julia!"
greet("world", "Hi"; puctuation = ".") # "Hi, world."

Multi-threading

function fib(n)
	n < 2 && return n
	t = Threads.@spawn fib(n-2)
	return fib(n-1) + fetch(t)
end
fib(10)
Threads.nthreads() # => threads assigned to Julia

Build-in REPL modes

# Default Julia mode, backspace from other modes
# Press ] for package mode
# Press ; for shell mode
# Press ? for helps
# Press $ for R mode, if RCall.jl is installed

Code introspection (simplified)

f(x, y) = x + y
@code_warntype f(1, 2)
@code_llvm f(1, 2)
@code_native f(1, 2)
read more