.= Julia 中的运算符

Question

代码取自：https://tutorials.sciml.ai/html/models/01-classical_physics.html 如下所示：

# Simple Harmonic Oscillator Problem
using OrdinaryDiffEq, Plots

# Parameters
ω = 1

# Initial Conditions
x₀ = [0.0]
dx₀ = [π/2]
tspan = (0.0, 2π)

ϕ = atan((dx₀[1]/ω)/x₀[1])
A = √(x₀[1]^2 + dx₀[1]^2)

# Define the problem
function harmonicoscillator(ddu,du,u,ω,t)
    ddu .= -ω^2 * u
end

# Pass to solvers
prob = SecondOrderODEProblem(harmonicoscillator, dx₀, x₀, tspan, ω)
sol = solve(prob, DPRKN6())

# Plot
plot(sol, vars=[2,1], linewidth=2, title ="Simple Harmonic Oscillator", xaxis = "Time", yaxis = "Elongation", label = ["x" "dx"])
plot!(t->A*cos(ω*t-ϕ), lw=3, ls=:dash, label="Analytical Solution x")
plot!(t->-A*ω*sin(ω*t-ϕ), lw=3, ls=:dash, label="Analytical Solution dx")

我不明白 .= 运算符在谐波振荡器函数中的用法。使用 = 给我错误的答案。所以，我想知道 .= 与 = 有何不同？它没有向量化 ddu 因为 RHS 都是标量。

Answer 1

I don't understand the usage of .= operator in the function harmonicoscillator. [...] It is not vectorizing ddu because RHS is all scalar.

是； u、du 和 ddu 不是标量，它们是长度为 1 的向量。

你可以问 Julia .= 语法是什么意思：

julia> Meta.@lower a .= b
:($(Expr(:thunk, CodeInfo(
    @ none within `top-level scope'
1 ─ %1 = Base.broadcasted(Base.identity, b)
│   %2 = Base.materialize!(a, %1)
└──      return %2
))))

看起来有点复杂，但本质上是一个广播作业，类似于

for i in eachindex(a, b)
    a[i] = b[i]
end

Using = gives me the wrong answer.

是的，因为 DiffEq 库需要函数 harmonicoscillator 来修改输入。如果你只使用 = 你创建一个新的函数局部变量而不是修改输入向量，并且从外部是不可见的。

.= Julia 中的运算符

.= operator in Julia

julia

differentialequations.jl