Taylor Coefficients for multivariate Functions

[LeanderK]

Hi, i wonder whether I can use this to compute the taylor coefficients for multivariate function up to a certain order. Right now, it takes a direction-parameter so it's really just univariate taylor coefficients as far as I understand. For my use-case, I am interested in all the combinations as I need it over all parameters. Thanks!

[tansongchen]

TaylorDiff.jl is in principle nestable, which means that you can do this:

using TaylorDiff

f(x, y) = exp(x) * exp(y)
x0, y0 = 0., 0.
x_dx = TaylorScalar{2}(x0, one(x0))
x_dxdy = TaylorScalar{2}(x_dx, zero(x_dx))
y_dx = TaylorScalar{2}(y0, zero(y_0))
y_dxdy = TaylorScalar{2}(y_dx, one(y_dx))
result = f(x_dxdy, y_dxdy)

which gives you

TaylorScalar{TaylorScalar{Float64, 2}, 2}(TaylorScalar{Float64, 2}(1.0, (1.0, 0.5)), (TaylorScalar{Float64, 2}(1.0, (1.0, 0.5)), TaylorScalar{Float64, 2}(0.5, (0.5, 0.25))))

and if you run this

map(TaylorDiff.flatten, TaylorDiff.flatten(result))

you can conveniently get all the normalized coefficients of

((1.0, 1.0, 0.5), (1.0, 1.0, 0.5), (0.5, 0.5, 0.25))

which correspond to ((f, dfdx, dfdx2), (dfdy, dfdxy, dfdx2y), ...)

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That being said, nested calculations are not tested rigorously, so some bugs might be there. Welcome any feedbacks!