Extra vertices reported by pmfe-parametrizer

[annakirkpatrick]

When generating a polytope from an RNA sequence, the software reports a few extra vertices which are actually interior to the edges. These vertices appear in the *.rnapoly files. As a result, the reported vertex and facet counts are incorrect. These counts are both reported as terminal output and written to the header of the *.rnapoly files.

A correct list of vertices, along with correct vertex and facet counts, can be attained from Sage, by reading the *.rnapoly file with rna_poly.py.

[annakirkpatrick]

Here is a sequence simple enough to generate a polytope where this issue can be seen easily.
aaaacaaaagaaaacaaaagaaaacaaaagaaaacaaaagaaaa

And the output rnapoly file:

# Points: 12
# Facets: 8

#	AAAACAAAAGAAAACAAAAGAAAACAAAAGAAAACAAAAGAAAA	m	u	h	w	e
1	...<(..................................)>...	0	0	0	473/100	0
2	...<(....(...<(....)....(....)>...)....)>...	1	12	3	73/10	-1
3	...<(...<(....)..............(....)>...)>...	1	22	3	11/2	-10
4	....(....)....(....)....(....)....(....)....	0	0	0	82/5	-1640/473
5	....(....)....(....(....)....(....)....)....	1	12	3	131/10	-111/82
6	...<(...<(....)...<(....)....(....)>...)>...	1	16	4	49/5	-1
7	........<(>..<(....)>..<(....)>..<)>........	1	12	3	3/2	-107/100
8	....(....(....)..............(....)....)....	1	22	3	9	-199/164
9	....(....(....)....(....)....(....)....)....	1	16	4	27/2	-201/164
10	...<(>..<(....)>..<(....)>..<(....)>..<)>...	1	16	4	43/10	-7/43
11	............................................	0	0	0	0	0
12	...<(>.......<(....)>..<(....)>.......<)>...	1	22	3	3/2	-4

[annakirkpatrick]

For the sake of documentation, I want to record that I have briefly discussed this bug with Andrew Gainer-Dewar over email.

Regarding the extra vertices, he stated

For the extra points, my guess would be that these are leftovers of the initialization stage of the algorithm, which I believe computes a few points with d=0 to bootstrap the process. It may be possible to tell CGAL to clean up the polytope before exporting it, in which case fixing this would be easy, but in any case, as you say, it's not really hurting anything as the software is currently used.

[maxieds]

@ceheitsch
I'm just browsing the past issues page. Now that things compile, is this something you want me to look at?

[ceheitsch]

In the example above, the vertices of the polytope are points 4,5,7-12.
Points 1-3,6 are output by pmfe-findmfe for nonzero parameter vectors [e.g. (1,0,0,0), (-1,0,0,0), (0,-1,0,0), (-1,0,-1,0) resp.]. But, according to pmfe-subopt, there are multiple other signatures with the same energy for these parameters. Hence, these rrnapoly points lie on a higher dimensional face of the polytope.
Because the beneath-and-beyond method builds the convex hull incrementally, it may be that the parameter vector being considered corresponds to a (new) 1d or higher face of the polytope.
The code will (correctly) identify that the corresponding signature lies on the boundary, and hence should be added to the convex hull, but will not know the dimension of the associated face.
To compute which points in the rnapoly file are vertices/0d faces of the polytope, use Sage.