Hi Michele, I'll reply to this in ApproxFun's Gitter, which is is a better forum for ApproxFun specific questions.
Cheers, Sheehan On Tuesday, May 3, 2016 at 6:55:07 PM UTC+10, Michele Zaffalon wrote: > > Hello, > > I am confused by `ApproxFun.TensorSpace`. I understand the following. > > dom1, dom2 = Fourier(), Chebyshev() > dom = dom1 ⊗ dom2 > @assert TensorSpace(Fourier(), Chebyshev()) == dom1 ⊗ dom2 > d1, d2 = Derivative(dom1), Derivative(dom2) > @assert Derivative(dom1, 1) == Derivative(dom1) > > > Here are the parts I do not understand: > > 1) Why doesn't the following evaluate to either error or 0? `dom1` is a > single variable space > > Derivative(dom1, 2) * Fun([0,0,1], dom1) > > 2) Why isn't this statement true? `d1` is the partial derivative with > respect to the first variable of `dom` > > Derivative(dom1) ⊗ I == Derivative(dom, 1) # --> false > > 3) Sorry for the dumb question but what is `Derivative(dom)`? Is > `Derivative(dom)==Derivative(dom, 1)`? It looks like the following is true > for all `f` > > (Derivative(dom1) ⊗ I) * f == Derivative(dom) * f == Derivative(dom, 1) * > f # --> true > > whose first part seems to contradict 2). > > > It looks like negation of derivative for the tensor space is not defined: > > (-Derivative(dom1)) * Fun([0,0,1],dom1) # valid expression for single > variable function > (-Derivative(dom)) * Fun([0,0,1],dom) # invalid expression for the tensor > space > > Also, I would like to define the divergence and I expect div rot = 0 > identically. I fail to define \partial_1\partial_2 but \partial_2\partial_1 > works > > stream_fun = Fun(randn(5), dom) > jϕ = Derivative(dom, 2) * stream_fun > jz = Derivative(dom, 1) * stream_fun > #Derivative(dom, 1) * jϕ # ∂_1∂_2(stream_fun) --> error > Derivative(dom, 2) * jz # ∂_2∂_1(stream_fun) --> OK > > > Last: `ApproxFun.transform(dom, y)` changes the values of `y` invalidating > the convention about functions modifying its arguments. > > > michele >
