Axis points order

[Noloben]

Thank you for your module, it's very useful for my computations. Though, I need a clarification on certain issue.

Repeating your first example ("Computation of a circle") I used axis grids as follows:

ax_x = Axis([-5, 0, 5], "x"); 
ax_y = Axis([-5, 0, 5], "y"); 

and everything worked well. But when I performed

f(x,y)=x^2+y^2-9
ax_x=Axis([0, -5, 5], "x")
ax_y=Axis([0, -5, 5], "y")
mymdbm=MDBM_Problem(f, [ax_x, ax_y])
solve!(mymdbm, 5)
x_sol,y_sol=getinterpolatedsolution(mymdbm)
scatter(x_sol, y_sol)

only bottom-left quarter was calculated. Is it important that axis grid is sorted?

Right now I'm going to use MDBM to find intersection of an arbitrary surface with known minima points with a horizontal surface (i. e. solutions of f(x, y)-f0, and we know where minima of f(x, y) are located). I was going to set x-axis grid points as [absoluteLeft, Minimum1x, Minimum2x, ..., absoluteRight] and similar with y-axis. Will it be possible of there will be some problems?

Do I need to sort x-axis and y-axis points ascending? If so, is it OK that x-axis and y-axis points do not coincide for each given minimum? For example, will intersection of 2nd x-axis point and 5th y-axis point be considered?

[bachrathyd]

Hi! Theoretically, it is possible to use unsorted vectors as a grid (however, it is pointless). In this case, the initial grid is like a folded paper and there will be overlapping regions. In your example, there are two initial segments for both axes: [0,-5] and [-5,5] which will be divided later. The first segment is ok (there are proper sign changes), but the second is too large so the solution is lost.

So I suggest sorting the axes (ascending or descending)! The repeated points should not be a problem.

See the test for unsorted axes with repeated points:

using MDBM
using Plots
f(x,y)=x^2+y^2-9
ax_x=Axis([0, -5, -5, 0,0,0, 5], "x")
ax_y=Axis([0, -5, -5, 0,0,0, 5], "y")
mymdbm=MDBM_Problem(f, [ax_x, ax_y])
solve!(mymdbm,5)
x_sol,y_sol=getinterpolatedsolution(mymdbm)
scatter(x_sol, y_sol)