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gen_methods_figures.py
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import numpy as np
from sklearn.datasets import make_blobs
from scipy.spatial.distance import pdist, squareform
from mi_density import *
import matplotlib.pyplot as plt
plt.style.use("ggplot")
plt.rcParams["font.size"] = 10
plt.rcParams["font.family"] = "monospace"
# set a custom color cycle
plt.rcParams["axes.prop_cycle"] = plt.cycler(
color=["#348ABD", "#A60628", "#7A68A6", "#467821", "#D95204", "#D982BA"]
)
SAVE = True
FIGSIZE = (3.5, 3.5)
POS = [0.17, 0.17, 0.8, 0.8]
# Plot the Dummy Data ##################################################################
# Define the parameters for each blob
blob_params = [
{"center": [0, 0], "std": 0.1, "random_state": 10},
{"center": [1, 1], "std": 0.3, "random_state": 5},
{"center": [2, 2], "std": 0.5, "random_state": 6},
{"center": [2, 1], "std": 0.1, "random_state": 11},
]
# Generate all blobs and concatenate
X = np.vstack(
[
make_blobs(
n_samples=20,
centers=[params["center"]],
cluster_std=params["std"],
random_state=params["random_state"],
)[0]
for params in blob_params
]
)
X_dm = squareform(pdist(X, metric="euclidean"))
fig, ax = plt.subplots(figsize=FIGSIZE, dpi=500, layout="constrained")
ax.set_position(POS, which="both")
plt.scatter(X[:, 0], X[:, 1], c="k", marker=".", s=85)
plt.scatter(X[50, 0], X[50, 1], c="C0", marker=".", s=95, ec="k")
plt.scatter(X[56, 0], X[56, 1], c="C1", marker=".", s=95, ec="k")
plt.scatter(X[47, 0], X[47, 1], c="C2", marker=".", s=95, ec="k")
# annotate those points of interest A, B, C
plt.annotate(
"A", (X[50, 0] + 0.05, X[50, 1] + 0.05), color="k", fontsize=8, weight="bold"
)
plt.annotate(
"B", (X[56, 0] + 0.05, X[56, 1] + 0.05), color="k", fontsize=8, weight="bold"
)
plt.annotate(
"C", (X[47, 0] + 0.05, X[47, 1] + 0.05), color="k", fontsize=8, weight="bold"
)
plt.yticks([0.0, 1.0, 2.0, 3.0], ["0.0", "1.0", "2.0", "3.0"])
plt.xticks([0.0, 1.0, 2.0, 3.0], ["0.0", "1.0", "2.0", "3.0"])
plt.xlim(-0.5, 3.5)
plt.ylim(-0.5, 3.25)
plt.xlabel("X$_1$ [a.u.]")
plt.ylabel("X$_2$ [a.u.]")
if SAVE:
plt.savefig("figures/dummydata.png", dpi=500)
else:
plt.show(block=False)
# Plot the Cummulative #################################################################
fig, ax = plt.subplots(1, 1, figsize=FIGSIZE, dpi=500, layout="constrained")
ax.set_position(POS, which="both")
for i, row in enumerate(X_dm):
count = np.ones(row.shape[0])
cs = np.cumsum(count) / np.sum(count)
# add annotations above the lines
if i in [50, 56, 47]:
label = "A" if i == 50 else "B" if i == 56 else "C"
plt.text(
x=np.sort(row)[-1],
y=cs[-1] + 0.005,
s=f"{label}",
color="k",
fontsize=8,
ha="center",
zorder=100,
weight="bold",
)
# Correct line color assignment using proper elif structure
line_color = "C0" if i == 50 else "C1" if i == 56 else "C2" if i == 47 else "k"
# Correct line alpha using proper comparison
line_alpha = 1.0 if i in [50, 56, 47] else 0.1
# Correct line zorder
line_zorder = 2 if i in [50, 56, 47] else 1
# correct the lw
lw = 2 if i in [50, 56, 47] else 1
ax.step(
np.sort(row),
cs,
color=line_color,
alpha=line_alpha,
zorder=line_zorder,
lw=lw,
where="post",
)
plt.xlim(0, None)
plt.ylim(0, 1)
plt.xlabel("Distance [a.u.]")
plt.ylabel("Cumulative Probability")
if SAVE:
plt.savefig("figures/cumulativeprob.png", dpi=500)
else:
plt.show(block=False)
# Cutoff Distance and Decay ############################################################
def get_sigma_for_decay(cutoff, target_decay):
"""Calculate sigma needed to achieve target decay value at cutoff."""
return cutoff / np.sqrt(-2 * np.log(target_decay))
cutoff, mi_profile = get_MI_profile(X_dm, 200)
fig, ax = plt.subplots(1, 1, figsize=FIGSIZE, dpi=500, layout="constrained")
ax.set_position(POS, which="both")
for i, row in enumerate(X_dm):
count = np.ones(row.shape[0])
cs = np.cumsum(count) / np.sum(count)
ax.step(np.sort(row), cs, color="k", alpha=0.15, zorder=1, lw=1, where="post")
x = np.linspace(0, 1.75, 500)
x = np.linspace(np.min(X_dm), np.max(X_dm), 200)
mi_decay = 1 - mi_profile / np.max(mi_profile)
mi_decay = mi_decay[x < cutoff]
x = x[x < cutoff]
ax.plot(x, mi_decay, color="C1", lw=2)
ax.axvline(cutoff, color="C1", linestyle="--", lw=2)
# put the word "cutoff" above the line
plt.text(
x=cutoff - 0.05,
y=1.015,
s="CUTOFF",
color="k",
fontsize=8,
ha="left",
va="center",
weight="bold",
)
ax.set_ylim(0, 1.0)
ax.set_xlim(0, np.max(X_dm))
ax.set_xlabel("Distance [a.u.]")
ax.set_ylabel("Decay Factor / Probability")
if SAVE:
plt.savefig("figures/decayfunc.png", dpi=500)
else:
plt.show(block=False)
# Compute Dummy Density ################################################################
cutoff = 1.3522078158872688 # computed elsewhere
# dens = compute_gaussian_density(X_dm, cutoff, end_decay=0.01)
cutoff, mi_profile = get_MI_profile(X_dm, 200)
dens = compute_mi_density(X_dm, cutoff, mi_profile)
fig, ax = plt.subplots(figsize=FIGSIZE, dpi=500)
ax.set_position(POS, which="both")
ax.scatter(X[:, 0], X[:, 1], c=dens, marker=".", s=95, cmap="rainbow", ec="k")
# annotate the lowest 5 densities with the lowest starting at 1
for i, d in enumerate(np.argsort(dens)[:5]):
plt.annotate(
f"{i+1}", (X[d, 0] + 0.05, X[d, 1] + 0.05), color="k", fontsize=8, weight="bold"
)
# draw a circle around the 50th point with a radius of the cutoff
ax.add_artist(plt.Circle((X[50, 0], X[50, 1]), cutoff, color="k", fill=False, ls=":"))
ax.add_artist(plt.Circle((X[50, 0], X[50, 1]), 0.115, color="k", fill=False, ls=":"))
ax.add_artist(plt.Circle((X[50, 0], X[50, 1]), 0.236, color="k", fill=False, ls=":"))
ax.add_artist(plt.Circle((X[50, 0], X[50, 1]), 0.645, color="k", fill=False, ls=":"))
# add cbar and make it short and put it within the plot
cax = ax.inset_axes([0.6, 0.2, 0.3, 0.05]) # [x, y, width, height] in axes coordinates
cbar = plt.colorbar(ax.collections[0], cax=cax, orientation="horizontal", pad=0.1)
cax.set_facecolor("white") # Set background color
cbar.set_label("Density")
ax.add_artist(
plt.Rectangle(
(0.59, 0.03), # Match inset_axes x,y
0.32, # Match inset_axes width
0.23, # Match inset_axes height
fc="white",
ec="k",
transform=ax.transAxes,
zorder=1,
)
)
plt.yticks([0.0, 1.0, 2.0, 3.0], ["0.0", "1.0", "2.0", "3.0"])
plt.xticks([0.0, 1.0, 2.0, 3.0], ["0.0", "1.0", "2.0", "3.0"])
plt.xlim(-0.5, 3.5)
plt.ylim(-0.5, 3.25)
plt.xlabel("X$_1$ [a.u.]")
plt.ylabel("X$_2$ [a.u.]")
if SAVE:
plt.savefig("figures/dummydensity.png", dpi=500)
else:
plt.show(block=True)