def test_find_discretization_on_real_acyclic_matching(matches, filtration,
delta, expected_matches):
from dmt.matching import Matching
from dmt.binning import find_discretization
from dmt.binning import ceil
matching = Matching(matches=matches)
bins = find_discretization(matching, filtration, delta)
ceiled_filtration = ceil(filtration, bins)
assert np.all(ceiled_filtration >= filtration)
assert ceiled_filtration.delta <= delta
assert len(
matching.induce_filtered_matching(ceil(
filtration, bins)).matches) == expected_matches
def test_ceil():
from dmt.binning import ceil
filtration = np.array([5, 3, 7, 2, 43, 7, 3, 1, 5, -2])
bins = np.array([0, 2, 5, 10])
assert np.all(
ceil(filtration, bins) ==
[5., 5., 10., 2., np.inf, 10., 5., 2., 5., 0.])
def morse_approx_induced_matching(morse_complex,
delta,
return_matching=False,
deltatrick=True):
""" Creates an approximative Morse reduction with the induced matching approach
The induced matching approach tries to create an unfiltered acyclic matching with small filtration differences
and solves a minimal cut problem on this matching to get an induced filtered acyclic matching.
Setting delta=0 results in the same algorithm as morse_reduce_nanda from MN[13]
:param morse_complex: MorseComplex to reduce
:param delta: Approximation parameter for the filtration and the persistence module
:param return_matching: Return a tuple of the reduced complex and the matching used to reduce it
:param deltatrick: Use 2*delta approximation from below and shift it down by delta. This allows more reductions.
:returns Reduced complex, optionally also the filtered acyclic matching
"""
delta = 2 * delta if deltatrick else delta
global_acyclic_matching = construct_acyclic_matching(morse_complex, delta)
bins_aposteriori = find_discretization(global_acyclic_matching,
morse_complex.filtration, delta)
discrete_filtration = ceil(morse_complex.filtration,
bins_aposteriori) - (deltatrick * delta / 2)
filtered_acyclic_matching = global_acyclic_matching.induce_filtered_matching(
discrete_filtration)
reduced_cplx = reduce_by_acyclic_matching(filtered_acyclic_matching)
if return_matching:
return reduced_cplx, filtered_acyclic_matching
return reduced_cplx
def plot_partial_sol(matching, filtration, partial_sol, delta, ax=None, plot_xticks=False, xlim=None):
points, intervals = partial_sol
ceiled_filtration = ceil(filtration, points)
ax = ax or plt.gca()
ax.set_aspect(.3)
height = .2*(max(filtration) - min(filtration)) / len(matching)
for h, match in zip(range(len(matching)), matching):
s, e = match
begin, end = filtration[s], filtration[e]
is_seen = begin <= points[-1]
is_cut = is_seen and ceiled_filtration[s] != ceiled_filtration[e]
linestyle = "solid" if is_seen else "dashed"
color = "red" if is_cut else "k"
ax.plot([begin, end], [h * height, h * height],
linestyle=linestyle, c=color, linewidth=1)
for point in points[:-1]:
ax.axvline(point, linestyle="--", c="grey")
ax.axvline(points[-1], linestyle="--", c="k")
ax.set_ylabel("%s" % len(intervals))
ax.set_ylim([-height, (len(matching) + .5) * height])
ax.set_yticks([])
ax.set_xticks([])
if plot_xticks:
xticks = np.arange(0, (max(filtration) + delta) / delta, 1)
ax.set_xticks(xticks * delta)
ax.set_xticklabels(["%i$\delta$" % i for i in xticks])
if xlim:
ax.set_xlim(xlim)
def test_find_discretization(filtration, delta):
from dmt.filtration import Filtration
from dmt.binning import find_discretization, ceil
filtr_len = len(filtration)
assert filtr_len % 2 == 0, "Filtration should give pairwise matches, thus has to have an even length"
acyclic_matching = list(
zip(range(0, filtr_len + 1, 2), range(1, filtr_len + 1,
2))) # Match neighboring pairs
filtration = Filtration(filtration)
bins = find_discretization(acyclic_matching, filtration, delta)
ceiled_filtration = ceil(filtration, bins)
assert np.all(ceiled_filtration >= filtration)
assert ceiled_filtration.delta <= delta
def test_find_discretization_is_good():
from dmt.matching import Matching
from dmt.binning import find_discretization
from dmt.binning import ceil
acyclic_matching = Matching(matches=[(0, 1), (2, 3), (4, 5)])
filtration = np.array([0, 1, 1, 2, 1, 2])
delta = 1.2
bins = find_discretization(acyclic_matching, filtration, delta)
# For a good binning of the given matching the following should hold
assert len(bins) >= 2
assert bins[0] <= 1
assert bins[-1] >= 2
assert len(
acyclic_matching.induce_filtered_matching(ceil(filtration,
bins)).matches) == 2
def test_ceil_equal():
from dmt.binning import ceil
filtration = np.array([5, 3, 7, 2, 43, 7, 3, 1, 5, -2])
bins = np.unique(filtration)
assert np.all(ceil(filtration, bins) == filtration)