Add jacobian!

[PerezHz]

Related to TaylorIntegration's PR #18. For performance reasons, it would be good to have an in-place evaluation version of jacobian in TaylorSeries. My proposal is something like this:

function jacobian!{T<:Number}(jjac::Array{T,2}, vf::Array{TaylorN{T},1})
    numVars = get_numvars()
    @assert length(vf) == numVars

    for comp = 1:numVars
        jjac[comp,:] = vf[comp].coeffs[2].coeffs[1:end]
    end

    nothing
end

As far as I've tested it, this change improves memory use on TaylorIntegration Lyapunov spectrum methods, in particular stabilitymatrix!, where jacobian is currently used.. Perhaps this could be included in #87 ?

[PerezHz]

This version is even faster:

function jacobian!{T<:Number}(jjac::Array{T,2}, vf::Array{TaylorN{T},1})
    numVars = get_numvars()
    @assert length(vf) == numVars

    for comp2 = 1:numVars
        for comp1 = 1:numVars
            jjac[comp1,comp2] = vf[comp1].coeffs[2].coeffs[comp2]
        end
    end

    nothing
end

Edit: I was messing with the indices, now it should work fine

[lbenet]

Can you send a PR, with tests? I'm actually spending some time in this kind of tricks...

[lbenet]

Regarding #87, if you are in a hurry, just send it using the current master.

[PerezHz]

PR #91 is an attempt to implement inplace evaluation versions of jacobian and hessian 😄

[PerezHz]

Closed by PR #91

[lbenet]

Done it, though not in a clean way; you'll have to git pull -f...

[lbenet]

... on that branch