Implementation of linear algebra for ArrayPartition  #105

using NLsolve
using RecursiveArrayTools

function mymodel(F, vars)
    for i in 1:2
        x = vars.x[i]    
        F.x[i][1,1] = (x[1,1]+3)*(x[1,2]^3-7)+18.0
        F.x[i][1,2] = sin(x[1,2]*exp(x[1,1])-1)
        F.x[i][2,1] = (x[2,1]+3)*(x[2,2]^3-7)+19.0
        F.x[i][2,2] = sin(x[2,2]*exp(x[2,1])-3)
    end
end

# To show that the function works
F = ArrayPartition([0.0 0.0; 0.0 0.0],[0.0 0.0; 0.0 0.0])
u0= ArrayPartition([0.1 1.2; 0.1 1.2], [0.1 1.2; 0.1 1.2])
result = mymodel(F, u0) 
vec(u0)

# To show the NLsolve error that results with ArrayPartition: 
nlsolve(mymodel, u0)