Exception "Not a mode, as quality is too high"

[paul019]

In the luigi config, one specifies the parameter ModeSearchConfig.quality_threshold; usually in the range of 1e-6 to 1e-4. This parameters is used at two points in the overall code:

1. Both FindPassiveModes and FindThresholdModes call the function refine_mode_brownian_ratchet, where quality_threshold is a parameter that tells the algorithm when to stop the search.
2. Later on, in ComputeModeCompetitionMatrix, the function mode_on_nodes is called (see below). In there, some mode quality is calculated and compared against quality_threshold. If it exceeds the threshold, an exception is thrown.

For some runs, I get the exception mentioned in point 2. I initially tried those runs with ModeSearchConfig.quality_threshold = 1e-6 and got the exception that my quality was slightly above that – usually just by a factor not greater than 1.5 (which is quite small considering we are speaking about orders of magnitude here). Then I increased ModeSearchConfig.quality_threshold to 1e-5, but still get an exception:

Not a mode, as quality is too high: 1.0717457667280263e-05 > 1e-05, mode: (6.873399477319817-0.0033058189568381364j)

It seems that (for some reason) the actual quality always exceeds the target quality by a tiny bit. The easy solution would be to compare the actual quality in the function mode_on_nodes (see below) against 2 * quality_threshold . This way, all exceptions that I get would be removed.

However, to be honest, I don't understand the code deeply enough (yet) to judge whether this solution would be reasonable. This is why I would be glad about an opinion from the code authors here.

netSALT/netsalt/modes.py

Lines 265 to 282 in 7729c76

	def mode_on_nodes(mode, graph):
	"""Compute the mode solution on the nodes of the graph."""
	laplacian = construct_laplacian(to_complex(mode), graph)
	min_eigenvalue, node_solution = sc.sparse.linalg.eigs(
	laplacian, k=1, sigma=0, v0=np.ones(len(graph)), which="LM"
	)
	quality_thresh = graph.graph["params"].get("quality_threshold", 1e-4)
	if abs(min_eigenvalue[0]) > quality_thresh:
	raise Exception(
	"Not a mode, as quality is too high: "
	+ str(abs(min_eigenvalue[0]))
	+ " > "
	+ str(quality_thresh)
	+ ", mode: "
	+ str(mode)
	)
	return node_solution[:, 0]