def __init__(self, axes, musnus,
radius=0.01,
labels=None,
companions=None,
picker=10,
alpha_marker=0.5,
visible=True,
annotation_size=12,
show_annotation=True,
colors = {'mu':'b', 'nu':'g', 'elem':'r'},
bins = {'mu':10, 'nu':10}
):
self.axes = axes
self.labels = labels if (labels is not None) \
else list(range(len(musnus[0])))
self.companions = companions
self.companion = None
rang = 1
# rotation=None
xlinspace = np.linspace(0.0, rang, bins['mu']+1)
self.axes.set_xticks(xlinspace)
ylinspace = np.linspace(0.0, rang, bins['nu']+1)
self.axes.set_yticks(ylinspace)
plot_triangle(rang, self.axes, 'k')
self.axes.grid(True, linestyle='--')
for lin in self.axes.get_xgridlines():
lin.set_color(colors['mu'])
for lin in self.axes.get_ygridlines():
lin.set_color(colors['nu'])
self.axes.legend(loc='upper right')
self.holder = []
for label, mu, nu in zip(self.labels, *musnus):
obj = HolderCircle(axes, (mu,nu), radius,
label=str(label),
color=colors['elem'],
picker=picker)
self.holder.append(obj)
def __init(self, bins, colors):
rang = 1
# rotation=None
xlinspace = np.linspace(0.0, rang, bins['mu'] + 1)
self.axes.set_xticks(xlinspace)
ylinspace = np.linspace(0.0, rang, bins['nu'] + 1)
self.axes.set_yticks(ylinspace)
plot_triangle(rang, self.axes, 'k')
self.axes.grid(True, linestyle='--')
for lin in self.axes.get_xgridlines():
lin.set_color(colors['mu'])
for lin in self.axes.get_ygridlines():
lin.set_color(colors['nu'])
self.axes.legend(loc='upper right')
def plot_membership_3Dhistogram(ifs,
ax,
bins=None,
typs=['mu', 'nu'],
colors={
'mu': 'b',
'nu': 'g',
'elem': 'r'
},
alpha=0.3):
bins = ifs.get_range() if (bins is None) else bins
indices, mus, nus, pis = ifs.elements_split()
rang = ifs.get_range()
plot_triangle(rang, ax, plottyp='--', color='k')
# Plot scatter
ax.scatter(mus,
nus,
np.zeros(len(mus), dtype='float32'),
color=colors['elem'])
#//Plot scatter
hist2d, muEdges, nuEdges = np.histogram2d(mus,
nus,
bins=bins,
range=[[0, rang], [0, rang]])
plot_grid_triangular(ax, rang, muEdges[1:], nuEdges[1:], colors)
# Plot the nu histogram on the Nu axis
d = rang / bins # the length of a bin (area = length(bin)**2)
# In the 2d histograms (on the Nu and Mu axes), if b = number of bins
# The area of the k-th line is A_k = (b - k + 1/2) * d^2, where k = 1:b
# (b - k + 1/2) * d^2 should be proportional to the length of the
# square k-test line D_k
# D_k/D_1 = sqrt(A_k/A_1) = C and we want D_1 = d/2
# That is, D_k = D_1 * sqrt(A_k/A_1)
D1 = d / 2
C = np.sqrt([(bins - k + 0.5) / (bins - 1 + 0.5)
for k in range(1, bins + 1)])
dAx = D1 * C
#We suppose that the mu and nu bins have equal length!!!
#In the future this they may be different -> edgesMin should depend on that
edgesMid = muEdges[:-1] + (muEdges[1:] - muEdges[:-1] - dAx) * 0.5
zLimit = 0.0 # To be set in the plot_membership function
def plot_membership(typ):
assert (typ in ['mu', 'nu'])
# static variable to update the limit of the z-axes
if not hasattr(plot_membership, "zLimit"):
plot_membership.zLimit = 0.0
dMu = dAx if typ == 'mu' else 0.0
dNu = dAx if typ == 'nu' else 0.0
muEdgesMid = edgesMid if typ == 'mu' else -d * np.ones_like(edgesMid)
nuEdgesMid = edgesMid if typ == 'nu' else -d * np.ones_like(edgesMid)
dz = [sum(hist2d[:,i]) for i in range(len(hist2d))] if typ=='nu' \
else [sum(hist2d[i,:]) for i in range(len(hist2d))]
plot_membership.zLimit = max(plot_membership.zLimit, max(dz))
ax.bar3d(muEdgesMid,
nuEdgesMid,
np.zeros_like(edgesMid),
dMu,
dNu,
dz,
color=colors[typ],
alpha=alpha)
plot_membership('mu')
plot_membership('nu')
zLimit = plot_membership.zLimit
############
ax.set_xlabel('Membership', labelpad=20)
ax.set_xlim3d(-d, rang + d)
ax.set_xticks(muEdges, minor=False)
ax.tick_params(axis='x', colors=colors['mu'])
ax.set_ylabel('Non-membership', labelpad=20)
ax.set_ylim3d(-d, rang + d)
ax.set_yticks(nuEdges, minor=False)
ax.tick_params(axis='y', colors=colors['nu'])
rotate_axislabels(ax, angles={'x': -45, 'y': 45})
ax.set_zlabel('Number of occurences per area', labelpad=20)
###########
ax.set_zlim3d(0, zLimit + 0.5)
#Add a legend in 3D
elemMapsLabel = lines.Line2D([0], [0],
linestyle="none",
c=colors['elem'],
marker='o')
muHistBars = plt.Rectangle((0, 0), 1, 1, fc=colors['mu'])
nuHistBars = plt.Rectangle((0, 0), 1, 1, fc=colors['nu'])
ax.legend([muHistBars, nuHistBars, elemMapsLabel], [
'Membership histogram bins', 'Non-membership histogram bins',
'Map of the elements from the Universe'
],
numpoints=2)
def plot_3D_histogramm(ifs,
bins=None,
colors={
'mu': 'b',
'nu': 'g',
'hist': 'y',
'elem': 'r'
}):
'''
Plot a 3D histogram in the triangular representation
of an IFS.
'''
bins = ifs.get_range() if (bins is None) else bins
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
indices, mus, nus, pis = ifs.elements_split()
# print(ifs.get_range())
rang = ifs.get_range()
plot_triangle(rang, ax, plottyp='--', color='k')
# Plot scatter
ax.scatter(mus,
nus,
np.zeros(len(mus), dtype='float32'),
color=colors['elem'])
#//Plot scatter
hist2d, mEdges, nEdges = np.histogram2d(mus,
nus,
bins=bins,
range=[[0, rang], [0, rang]])
plot_grid_triangular(ax, rang, mEdges[1:], nEdges[1:], colors)
# print(mEdges)
# print(nEdges)
lhist = len(hist2d)
for i in range(lhist):
hist2d[i, lhist - 1 - i] *= 2
mEdgesMid = mEdges[:-1] + (mEdges[1:] - mEdges[:-1]) * 0.375
nEdgesMid = nEdges[:-1] + (nEdges[1:] - nEdges[:-1]) * 0.375
muPos = np.zeros(bins * (bins + 1) // 2, dtype='float32')
nuPos = np.zeros_like(muPos)
dz = np.zeros_like(muPos)
S = lambda k: k * (k + 1) // 2 # = 1+2+...+k
l = len(mEdgesMid)
for i, pos in enumerate(mEdgesMid):
start = S(l) - S(l - i) # = l+(l-1)+...+(l-i+1)
end = S(l) - S(l - (i + 1)) # = l+(l-1)+...+(l-i+1)+(l-i)
dz[start:end] = hist2d[i, :l - i]
muPos[start:end] = pos
nuPos[start:end] = nEdgesMid[:l - i]
# The diagonal bins are triangular (half), fix them
# muPos[end-1] = mEdges[i] + (mEdges[i+1] - mEdges[i])*0.25
# nuPos[end-1] = nEdges[l-i-1] + (mEdges[l-i] - mEdges[l-i-1])*0.25
dmu = (mEdges[1] - mEdges[0]) * 0.25 * np.ones_like(muPos)
dnu = (nEdges[1] - nEdges[0]) * 0.25 * np.ones_like(nuPos)
for i, _ in enumerate(mEdgesMid):
diag_pos = S(l) - S(l - (i + 1))
dmu[diag_pos - 1] = (mEdges[i + 1] - mEdges[i]) * 0.125
dnu[diag_pos - 1] = (mEdges[l - i] - mEdges[l - i - 1]) * 0.125
ax.bar3d(muPos,
nuPos,
np.zeros_like(muPos),
dmu,
dnu,
dz,
color=colors['hist'],
alpha=0.3)
# # zsort='average')
d = rang / bins # the length of a bin (area = length(bin)**2)
ax.set_xlabel('Membership', labelpad=20)
ax.set_xlim3d(-d, rang + d)
ax.set_xticks(mEdges, minor=False)
ax.tick_params(axis='x', colors=colors['mu'])
ax.set_ylabel('Non-membership', labelpad=20)
ax.set_ylim3d(-d, rang + d)
ax.set_yticks(nEdges, minor=False)
ax.tick_params(axis='y', colors=colors['nu'])
rotate_axislabels(ax, angles={'x': -45, 'y': 45})
ax.set_zlabel('Number of occurences per area (square)', labelpad=20)
ax.set_zlim3d(0, max(dz) + 0.5)
#Add a legend in 3D
muBinsLabel = lines.Line2D([0], [0],
linestyle="none",
c=colors['mu'],
marker=0)
nuBinsLabel = lines.Line2D([0], [0],
linestyle="none",
c=colors['nu'],
marker=0)
elemMapsLabel = lines.Line2D([0], [0],
linestyle="none",
c=colors['elem'],
marker='o')
histBars = plt.Rectangle((0, 0), 1, 1, fc=colors['hist'])
ax.legend([muBinsLabel, nuBinsLabel, histBars, elemMapsLabel], [
'Membership degree grid', 'Non-membership degree grid',
"Histogram bars", "Map of the elements from the Universe"
],
numpoints=2)
