Today, Swift AD has two separate transforms that produce forward mode derivatives (JVPs) and reverse mode derivatives (VJPs).
We can generalize this to a single transform that produces a single "derivative function" that can evaluate derivatives in both modes.
The "derivative function" is generic over a "derivative type" that determines the derivative mode.
The advantages over the existing system are:
Only non-stiff ODE solvers are tested since torchdiffeq does not have methods for stiff ODEs. The ODEs are chosen to be representative of models seen in physics and model-informed drug development (MIDD) studies (quantiative systems pharmacology) in order to capture the performance on realistic scenarios.
Below are the timings relative to the fastest method (lower is better). For approximately 1 million ODEs and less, torchdiffeq was more than an order of magnitude slower than DifferentialEquations.jl
| str = """ | |
| using Base.Test | |
| @testset "ts1" begin | |
| x=1 | |
| x==1 | |
| end | |
| @testset "ts2" begin | |
| x=2 | |
| x==1 |
| # To ensure correct alignment (e.g. for an 80-bit type) | |
| struct StrWrap{T} | |
| value::T | |
| end | |
| function unsafe_reinterpret(T, a::A) where {A} | |
| if sizeof(T) <= sizeof(A) | |
| r = Ref(a) | |
| Base.@gc_preserve r begin | |
| u = convert(Ptr{T}, Base.unsafe_convert(Ptr{A}, r)) |
| # credits: @TotalVerb, @oxinabox, @musm @mbauman @quinnj | |
| julia --compile=no --precompiled=no | |
| (x->@inbounds(x+=[0][x])+x)(9^9^9) | |
| [@inbounds([][x])for x=9^9^9] | |
| run(`1`) |
| class TableCell(object): | |
| bg_colour = None | |
| def __init__(self, value, header=False, bg_colour=None, text_colour=None): | |
| self.value = value | |
| self.header = header | |
| self.bg_colour = bg_colour | |
| self.text_colour = text_colour | |
| def _make_css(self): |
