def Von_Luxburg_approximations(t):
ones = np.ones_like(t)
n = t.shape[0]
# d_v is the in-degree, which is the column sum. this
# multiplication does the right thing
d_v = np.sum(t, axis=0) * ones
# transpose to get d_u
d_u = d_v.T
# vol(G) is sum of degrees, which we interpret in the directed
# case as sum of out-degrees (which is anyway equal to sum of
# in-degrees); because weights are transition probabilities, each
# out-degree = 1; so vol(G) = n.
vol_G = float(n)
mfpt_vla = vol_G * 1.0 / d_v
set_self_transition_zero(mfpt_vla)
ct_vla = vol_G * (1.0 / d_u + 1.0 / d_v)
set_self_transition_zero(ct_vla)
return mfpt_vla, ct_vla
def compare_MFPT_estimate_RW_v_exact(dirname):
def get_indices_of_common_entries(a, b):
result = []
for i in b:
try:
j = a.index(i)
result.append(j)
except ValueError:
pass
assert len(result) == len(b)
return result
filename = dirname + "/MFPT.dat"
mfpt = np.genfromtxt(filename)
filename = dirname + "/compare_MFPT_estimate_RW_v_exact.tex"
f = open(filename, "w")
if "depth_2" in dirname:
lengths = [1298, 12980, 129800]
elif "depth_1" in dirname:
# NB with 18, too few values to run correlation
lengths = [180, 1800, 18000]
for length in lengths:
# mfpte: read, mask nan, mask len < 5 (100x100)
filename = dirname + "/estimate_MFPT_using_RW_" + str(
length) + "/MFPT.dat"
mfpte = np.genfromtxt(filename, usemask=True, missing_values="NaN,nan")
filename = dirname + "/estimate_MFPT_using_RW_" + str(
length) + "/MFPT_len.dat"
mfpte_len = np.genfromtxt(filename)
min_vals = 5 # an attempt at reliability
print("%d of %d values of length < 5" %
(np.sum(mfpte_len < min_vals), len(mfpte_len)**2))
mfpte[mfpte_len < min_vals] = np.ma.masked
# mfpt: copy, select sampled only to make it 100x100
mfpt_tmp = mfpt.copy()
# need to restrict mfpt_tmp to the 100x100 entries which are
# indicated by the trees_sampled.dat file
filename = dirname + "/estimate_MFPT_using_RW_" + str(
length) + "/trees_sampled.dat"
trees_sampled = open(filename).read().strip().split("\n")
filename = dirname + "/all_trees.dat"
all_trees = open(filename).read().strip().split("\n")
indices = get_indices_of_common_entries(all_trees, trees_sampled)
# the selected indices are into both the rows and columns
mfpt_tmp = mfpt_tmp[indices][:, indices]
# mfpte will contain the self-hitting time on the diagonal: we
# want zero there for true comparison.
set_self_transition_zero(mfpte)
# reshape both
mfpte = mfpte.reshape(len(mfpte)**2)
mfpt_tmp = mfpt_tmp.reshape(len(mfpt_tmp)**2)
# correlate using mask
f.write("Number of samples: " + str(length) + "\n")
corr, p = get_pearson_r(mfpt_tmp, mfpte)
f.write("Pearson R correlation " + str(corr) + "; ")
f.write("p-value " + str(p) + ". ")
corr, p = get_spearman_rho(mfpt_tmp, mfpte)
f.write("Spearman rho correlation " + str(corr) + "; ")
f.write("p-value " + str(p) + ". ")
if len(mfpte) < 1000:
corr, p = get_kendall_tau(mfpt_tmp, mfpte)
f.write("Kendall tau correlation " + str(corr) + "; ")
f.write("p-value " + str(p) + ". ")
else:
f.write(
"Omitting Kendall tau because it is infeasible for large matrices. "
)
f.write("\n")
f.close()
def compare_MFPT_estimate_RW_v_exact(dirname):
def get_indices_of_common_entries(a, b):
result = []
for i in b:
try:
j = a.index(i)
result.append(j)
except ValueError:
pass
assert len(result) == len(b)
return result
filename = dirname + "/MFPT.dat"
mfpt = np.genfromtxt(filename)
filename = dirname + "/compare_MFPT_estimate_RW_v_exact.tex"
f = open(filename, "w")
if "depth_2" in dirname:
lengths = [1298, 12980, 129800]
elif "depth_1" in dirname:
# NB with 18, too few values to run correlation
lengths = [180, 1800, 18000]
for length in lengths:
# mfpte: read, mask nan, mask len < 5 (100x100)
filename = dirname + "/estimate_MFPT_using_RW_" + str(length) + "/MFPT.dat"
mfpte = np.genfromtxt(filename, usemask=True, missing_values="NaN,nan")
filename = dirname + "/estimate_MFPT_using_RW_" + str(length) + "/MFPT_len.dat"
mfpte_len = np.genfromtxt(filename)
min_vals = 5 # an attempt at reliability
print("%d of %d values of length < 5" % (np.sum(mfpte_len < min_vals), len(mfpte_len)**2))
mfpte[mfpte_len < min_vals] = np.ma.masked
# mfpt: copy, select sampled only to make it 100x100
mfpt_tmp = mfpt.copy()
# need to restrict mfpt_tmp to the 100x100 entries which are
# indicated by the trees_sampled.dat file
filename = dirname + "/estimate_MFPT_using_RW_" + str(length) + "/trees_sampled.dat"
trees_sampled = open(filename).read().strip().split("\n")
filename = dirname + "/all_trees.dat"
all_trees = open(filename).read().strip().split("\n")
indices = get_indices_of_common_entries(all_trees, trees_sampled)
# the selected indices are into both the rows and columns
mfpt_tmp = mfpt_tmp[indices][:,indices]
# mfpte will contain the self-hitting time on the diagonal: we
# want zero there for true comparison.
set_self_transition_zero(mfpte)
# reshape both
mfpte = mfpte.reshape(len(mfpte)**2)
mfpt_tmp = mfpt_tmp.reshape(len(mfpt_tmp)**2)
# correlate using mask
f.write("Number of samples: " + str(length) + "\n")
corr, p = get_pearson_r(mfpt_tmp, mfpte)
f.write("Pearson R correlation " + str(corr) + "; ")
f.write("p-value " + str(p) + ". ")
corr, p = get_spearman_rho(mfpt_tmp, mfpte)
f.write("Spearman rho correlation " + str(corr) + "; ")
f.write("p-value " + str(p) + ". ")
if len(mfpte) < 1000:
corr, p = get_kendall_tau(mfpt_tmp, mfpte)
f.write("Kendall tau correlation " + str(corr) + "; ")
f.write("p-value " + str(p) + ". ")
else:
f.write("Omitting Kendall tau because it is infeasible for large matrices. ")
f.write("\n")
f.close()
