Delaunay interpolator patch: support grid whose width or height is 1

The current implementation of Delaunay interpolator returns NaN for grids whose x or y has dimension 1 (i.e. when you try to interpolate along a horizontal/vertical line, or in a single point). See example below.

By looking at the code, it seems that this can be fixed by simple rearrangement of calculations.
Suggested patch provided here: https://github.com/AmitAronovitch/matplotlib/commit/f312d864da9c72681eb3db3b5920ae64793c713e (let me know if you want a pull request).

The suggested implementation is almost identical. It might actually perform faster in some cases (there is one less multiplication op in the inner loop). There might be some differences in accuracy, but I believe they should only become observable in cases where the grid size is very large (which would probably cause memory problems anyway).

Example (before suggested patch):

from matplotlib.delaunay import Triangulation
tri = Triangulation([0,10,10,0],[0,0,10,10])
lin = tri.linear_interpolator([1,10,5,2.0])

2x2 grid works fine

lin[3:6:2j,1:4:2j]
array([[ 1.6, 3.1],
[ 1.9, 2.8]])

but not when 1x2, 2x1, 1x1:

lin[3:6:2j,1:1:1j]
array([[ nan],

   [ nan]])

lin[3:3:1j,1:1:1j]
array([[ nan]])

After suggested patch:

from matplotlib.delaunay import Triangulation

tri = Triangulation([0,10,10,0],[0,0,10,10])

lin = tri.linear_interpolator([1,10,5,2.0])

2x2 grid: same same

lin[3:6:2j,1:4:2j]

array([[ 1.6, 3.1],

   [ 1.9,  2.8]])

but these work now

lin[3:6:2j,1:1:1j]

array([[ 1.6],

   [ 1.9]])

lin[3:3:1j,1:1:1j]

array([[ 1.6]])

···

I am always a fan of people who test and design their methods against edge cases like these, so my hat is off to you. I would suggest putting together a pull request so that we can properly test the potential impact such a change could have.

Thanks!
Ben Root

···

On Sat, Jul 7, 2012 at 7:30 PM, Amit Aronovitch <aronovitch@…149…> wrote:

The current implementation of Delaunay interpolator returns NaN for grids whose x or y has dimension 1 (i.e. when you try to interpolate along a horizontal/vertical line, or in a single point). See example below.

By looking at the code, it seems that this can be fixed by simple rearrangement of calculations.
Suggested patch provided here: https://github.com/AmitAronovitch/matplotlib/commit/f312d864da9c72681eb3db3b5920ae64793c713e (let me know if you want a pull request).

The suggested implementation is almost identical. It might actually perform faster in some cases (there is one less multiplication op in the inner loop). There might be some differences in accuracy, but I believe they should only become observable in cases where the grid size is very large (which would probably cause memory problems anyway).

Example (before suggested patch):

from matplotlib.delaunay import Triangulation
tri = Triangulation([0,10,10,0],[0,0,10,10])
lin = tri.linear_interpolator([1,10,5,2.0])

2x2 grid works fine

lin[3:6:2j,1:4:2j]
array([[ 1.6, 3.1],
[ 1.9, 2.8]])

but not when 1x2, 2x1, 1x1:

lin[3:6:2j,1:1:1j]
array([[ nan],

   [ nan]])

lin[3:3:1j,1:1:1j]
array([[ nan]])

After suggested patch:

from matplotlib.delaunay import Triangulation

tri = Triangulation([0,10,10,0],[0,0,10,10])

lin = tri.linear_interpolator([1,10,5,2.0])

2x2 grid: same same

lin[3:6:2j,1:4:2j]

array([[ 1.6, 3.1],

   [ 1.9,  2.8]])

but these work now

lin[3:6:2j,1:1:1j]

array([[ 1.6],

   [ 1.9]])

lin[3:3:1j,1:1:1j]

array([[ 1.6]])

<-- snipped (sent as issue #997) -->

I am always a fan of people who test and design their methods against edge cases like these, so my hat is off to you.

FTR: this was not a case of testing, but of hacking:
I had some code using scipy’s delaunay interpolator, and I had to provide fallback functionality for a machine that does not have a recent scipy installed (luckily, it had matplotlib :slight_smile: ).

Since the sample set was irregular (not a grid) - the easiest (though inefficient) fix was to loop over the set and use 1x1 grids. At this point I hit this issue…

I would suggest putting together a pull request so that we can properly test the potential impact such a change could have.

Done.
thanks,

Amit

···

On Mon, Jul 9, 2012 at 4:34 PM, Benjamin Root <ben.root@…553…> wrote:

On Sat, Jul 7, 2012 at 7:30 PM, Amit Aronovitch <aronovitch@…149…> wrote: