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Tags:
Large Language Models
LLM Evaluation
Sequential Reasoning
Scaling Laws
Synthetic Benchmarks
Commonsense Reasoning
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File size: 28,374 Bytes
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import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import matplotlib.patches as patches
from matplotlib.patches import FancyArrowPatch, Rectangle
import numpy as np
from scipy.interpolate import splprep, splev
import math
def pretty_plot_maze(
maze_loader,
W=4,
H=4,
save_path=None,
model_solution=None,
ground_truth_solution=None,
mode="comparison",
):
"""
Display the maze using Matplotlib and optionally save to a file.
Args:
mode: Visualization mode
- "comparison": Side-by-side optimal vs model (default)
- "empty": Just maze structure
- "optimal": Maze + optimal path only
- "model": Maze + model path only
"""
plt.rcParams["font.size"] = 10
plt.rcParams["font.family"] = "sans-serif"
plt.rcParams["figure.dpi"] = 100
# Configure subplot layout based on mode
if mode == "comparison":
fig, (ax2, ax3) = plt.subplots(1, 2, figsize=(15, 8.5))
axes = [ax2, ax3]
elif mode == "empty":
# Special layout for empty maze with legend space
fig, ax = plt.subplots(1, 1, figsize=(14, 8.5))
axes = [ax]
else:
fig, ax = plt.subplots(1, 1, figsize=(10, 8.5))
axes = [ax]
# Draw the base maze on all plots
for ax in axes:
covered_cells = set()
for cell in maze_loader.connected_cells.keys():
for neighbor in maze_loader.connected_cells[cell]:
if (cell, neighbor) in covered_cells or (
neighbor,
cell,
) in covered_cells:
continue
covered_cells.add((cell, neighbor))
add_path_segment(
(cell[0] * W, cell[1] * H),
(neighbor[0] * W, neighbor[1] * H),
ax,
door=(cell, neighbor) in maze_loader.doors.keys(),
status=None
if (cell, neighbor) not in maze_loader.doors.keys()
else maze_loader.doors[(cell, neighbor)][0].split(" ")[0],
lock_status=(
None
if (cell, neighbor) not in maze_loader.doors.keys()
or maze_loader.doors[(cell, neighbor)][0] == "open"
else maze_loader.doors[(cell, neighbor)][0].split(" ")[-1]
),
)
# Add keys
for key_id, key_location in maze_loader.keys_locations.items():
door_locations = {
maze_loader.doors[(rA, rB)][1]: (
(rA[0] + rB[0]) * W / 2,
(rA[1] + rB[1]) * H / 2,
)
for (rA, rB) in maze_loader.doors.keys()
}
add_key(
key_location[0] * W,
key_location[1] * H,
ax,
door_location=door_locations.get(key_id, (0, 0)),
)
# Add start and end rooms
start = (
maze_loader.data["start_room"][0] * W,
maze_loader.data["start_room"][1] * H,
)
end = (maze_loader.data["end_room"][0] * W, maze_loader.data["end_room"][1] * H)
enhanced_mode = True # Use enhanced mode for all visualizations
add_start_and_end_room(start, end, ax, enhanced_mode=enhanced_mode)
# Create a mapping from room names to coordinates
room_name_to_coord = {}
for cell in maze_loader.connected_cells.keys():
room_name_to_coord[maze_loader.room_name[cell]] = cell
# Define colors for different action types
move_color_gt = "gold" # Yellow for regular movement (ground truth)
move_color_model = "mediumpurple" # Purple for regular movement (model)
start_color = "#FF7F0E" # Orange for start action
pickup_key_color = "#1E88E5" # Blue for key pickup
use_key_color = "#43A047" # Green for using a key
unlock_color = "#9C27B0" # Purple for unlocking door
rescue_color = "#D81B60" # Pink for rescue
# Draw a path with numbered steps
def process_solution(solution, ax, base_color="gold"):
if not solution:
return
all_actions = []
current_room = None
last_position = None
# Parse solution into actions
for i, action in enumerate(solution):
if len(action) < 2:
continue
action_type, param = action[0], action[1]
step_number = i + 1 # Start numbering from 1
# Track the current room for each action
if action_type == "start":
current_room = param
# Mark start position specially
all_actions.append((current_room, step_number, action_type, None))
elif action_type == "move_to" and param in room_name_to_coord:
prev_room = current_room
current_room = param
# Store movement with both source and destination
all_actions.append((current_room, step_number, action_type, prev_room))
elif action_type in [
"pick_up_key",
"use_key",
"unlock_and_open_door_to",
"rescue",
]:
if current_room:
# Store special action with current room
all_actions.append((current_room, step_number, action_type, None))
used_positions = set()
# First draw all movement paths
for room, step_number, action_type, prev_room in all_actions:
if (
action_type == "move_to"
and prev_room
and room in room_name_to_coord
and prev_room in room_name_to_coord
):
start_cell = room_name_to_coord[prev_room]
end_cell = room_name_to_coord[room]
# Get coordinates
x1, y1 = start_cell[0] * W, start_cell[1] * H
x2, y2 = end_cell[0] * W, end_cell[1] * H
# Draw the path for movement
ax.plot(
[x1, x2], [y1, y2], "-", color=base_color, linewidth=2, zorder=10, alpha=0.5
)
# Add arrow near destination
arrow_pos = 0.9
arrow_x = x1 + (x2 - x1) * arrow_pos
arrow_y = y1 + (y2 - y1) * arrow_pos
dx = x2 - x1
dy = y2 - y1
length = math.sqrt(dx * dx + dy * dy)
if length > 0:
dx /= length
dy /= length
arrow = FancyArrowPatch(
(arrow_x - dx * 0.3, arrow_y - dy * 0.3),
(arrow_x + dx * 0.3, arrow_y + dy * 0.3),
arrowstyle="-|>",
mutation_scale=12,
color=base_color,
linewidth=2,
zorder=10,
alpha=0.4,
)
ax.add_patch(arrow)
# Then add step markers for each action
for action_idx, (room, step_number, action_type, prev_room) in enumerate(
all_actions
):
if room in room_name_to_coord:
room_cell = room_name_to_coord[room]
# Determine position and color based on action type
if (
action_type == "move_to"
and prev_room
and prev_room in room_name_to_coord
):
# For movement, place marker along the path
start_cell = room_name_to_coord[prev_room]
end_cell = room_name_to_coord[room]
x1, y1 = start_cell[0] * W, start_cell[1] * H
x2, y2 = end_cell[0] * W, end_cell[1] * H
pos_x = x1 + (x2 - x1) * 0.6
pos_y = y1 + (y2 - y1) * 0.6
# Add perpendicular offset to avoid placing directly on line
dx = x2 - x1
dy = y2 - y1
length = math.sqrt(dx * dx + dy * dy)
if length > 0:
perp_x = -dy / length * 0.7
perp_y = dx / length * 0.7
# Alternate sides for consecutive steps
if step_number % 2 == 0:
perp_x = -perp_x
perp_y = -perp_y
pos_x += perp_x
pos_y += perp_y
color = base_color
else:
# For non-movement actions, place at the room with offset
pos_x = room_cell[0] * W
pos_y = room_cell[1] * H
# Special case for door-related actions - place them near but not at the door
if action_type in ["use_key", "unlock_and_open_door_to"]:
door_cell1 = room_cell
door_cell2 = None
if action_type == "unlock_and_open_door_to":
# Find the destination room for the door
dest_room = param
if dest_room in room_name_to_coord:
door_cell2 = room_name_to_coord[dest_room]
elif prev_room in room_name_to_coord:
# For use_key, consider the previous room as second door cell
door_cell2 = room_name_to_coord[prev_room]
if door_cell2:
# Calculate door position (midpoint between rooms)
door_x = (door_cell1[0] + door_cell2[0]) * W / 2
door_y = (door_cell1[1] + door_cell2[1]) * H / 2
# Calculate vector from door to room (normalized)
dx = pos_x - door_x
dy = pos_y - door_y
dist = math.sqrt(dx * dx + dy * dy)
if dist > 0:
# Normalize vector
dx /= dist
dy /= dist
# Position marker at 2/3 distance from door to room
pos_x = (
door_x + dx * 1.5
) # Place partway from door toward room
pos_y = door_y + dy * 1.5
# Add small perpendicular offset to avoid direct overlap with path
perp_x = -dy * 0.5
perp_y = dx * 0.5
# Alternate sides for consecutive markers
if step_number % 2 == 0:
perp_x = -perp_x
perp_y = -perp_y
pos_x += perp_x
pos_y += perp_y
else:
# Fallback if rooms are at same location
offset_x = 0.7 * (1 if step_number % 2 == 0 else -1)
offset_y = 0.7 * (1 if step_number % 4 >= 2 else -1)
pos_x += offset_x
pos_y += offset_y
else:
# If second door cell not found, use standard offset from room
offset_x = 0.7 * (1 if step_number % 2 == 0 else -1)
offset_y = 0.7 * (1 if step_number % 4 >= 2 else -1)
pos_x += offset_x
pos_y += offset_y
else:
# Regular offset for other action types
if action_type == "start":
# Start marker at top-left of room
offset_x, offset_y = -0.7, -0.7
else:
# Other actions - different offsets for different action types
offset_multiplers = {
"pick_up_key": (0.7, 0.7),
"rescue": (-0.7, -0.7),
}
multiplier = offset_multiplers.get(action_type, (0, 0))
offset_x, offset_y = multiplier
# Further vary offsets for multiple actions in same room
same_room_actions = sum(
1
for r, _, a_type, _ in all_actions[:action_idx]
if r == room and a_type != "move_to"
)
if same_room_actions > 0:
offset_x *= 1 + 0.3 * same_room_actions
offset_y *= 1 + 0.3 * same_room_actions
pos_x += offset_x
pos_y += offset_y
# Determine color for special actions - now with distinct colors for all types
if action_type == "start":
color = start_color
elif action_type == "pick_up_key":
color = pickup_key_color
elif action_type == "use_key":
color = use_key_color
elif action_type == "unlock_and_open_door_to":
color = unlock_color
elif action_type == "rescue":
color = rescue_color
else:
color = base_color
# Avoid overlap with existing markers
while any(
(abs(pos_x - px) < 0.8 and abs(pos_y - py) < 0.8)
for px, py in used_positions
):
# Slightly adjust position
pos_x += 0.3 * (1 if step_number % 2 == 0 else -1)
pos_y += 0.3 * (1 if step_number % 4 >= 2 else -1)
# Add marker
# ax.text(
# pos_x,
# pos_y,
# f"{step_number}",
# color="white",
# fontsize=3,
# ha="center",
# va="center",
# bbox=dict(
# boxstyle="circle,pad=0.3",
# fc=color,
# ec="black",
# alpha=0.9,
# linewidth=1,
# ),
# zorder=20,
# )
# Remember this position
used_positions.add((pos_x, pos_y))
title_props = dict(fontsize=12, fontweight="bold")
# Set titles and process solutions based on mode
if mode == "comparison":
axes[0].set_title("Optimal Path", **title_props)
axes[1].set_title("Model Path", **title_props)
if ground_truth_solution:
process_solution(ground_truth_solution, axes[0], base_color=move_color_gt)
if model_solution:
process_solution(model_solution, axes[1], base_color=move_color_model)
elif mode == "empty":
axes[0].set_title("Maze Layout", **title_props)
# No paths to process for empty maze
elif mode == "optimal":
axes[0].set_title("Optimal Path", **title_props)
if ground_truth_solution:
process_solution(ground_truth_solution, axes[0], base_color=move_color_gt)
elif mode == "model":
axes[0].set_title("Model Path", **title_props)
if model_solution:
process_solution(model_solution, axes[0], base_color=move_color_model)
for ax in axes:
ax.set_xticks([])
ax.set_yticks([])
ax.axis("off")
current_xlim = ax.get_xlim()
current_ylim = ax.get_ylim()
ax.set_xlim(current_xlim[0] - 1, current_xlim[1] + 1)
ax.set_ylim(current_ylim[0] - 3, current_ylim[1] + 1)
# Add legend for empty maze mode (enhanced for LLM interpretability)
if mode == "empty":
# Clean, simple title
axes[0].set_title("Maze Navigation: Find path from START (green) to GOAL (red)",
fontsize=12, fontweight='bold', pad=20)
legend_elements = [
plt.Line2D([0], [0], marker='o', color='w', markerfacecolor='limegreen',
markersize=12, markeredgecolor='darkgreen', markeredgewidth=2, label='START'),
plt.Line2D([0], [0], marker='o', color='w', markerfacecolor='red',
markersize=12, markeredgecolor='darkred', markeredgewidth=2, label='GOAL'),
plt.Rectangle((0, 0), 1, 1, facecolor='red', alpha=0.8, label='locked door'),
plt.Line2D([0], [0], marker='o', color='w', markerfacecolor='yellow',
markersize=10, markeredgecolor='orange', markeredgewidth=2, label='key'),
]
axes[0].legend(handles=legend_elements, loc='center left', bbox_to_anchor=(0.95, 0.5),
frameon=True, fancybox=True, shadow=False, fontsize=9)
# Only add path legend for non-empty modes
if mode != "empty":
legend_items = [
("Start", start_color),
("Move", move_color_gt if ground_truth_solution else move_color_model),
("Key pickup", pickup_key_color),
("Use key", use_key_color),
("Unlock door", unlock_color),
("Rescue", rescue_color),
]
legend_patches = [
plt.Rectangle((0, 0), 1, 1, fc=color, ec="black", alpha=0.9)
for _, color in legend_items
]
# fig.legend(
# legend_patches,
# [text for text, _ in legend_items],
# loc="lower center",
# bbox_to_anchor=(0.5, 0.02),
# ncol=len(legend_items),
# frameon=True,
# fancybox=True,
# shadow=True,
# fontsize=10,
# )
# Handle layout based on mode
if mode == "empty":
plt.tight_layout()
# Adjust layout to accommodate legend with less gap
plt.subplots_adjust(right=0.90)
else:
plt.tight_layout()
if save_path is not None:
try:
plt.savefig(save_path, dpi=400, bbox_inches="tight", format="png")
except Exception as e:
print(f"Error saving plot: {e}")
plt.close(fig)
def draw_path_with_arrow(
point1,
point2,
ax,
color="red",
linewidth=1.5,
alpha=0.8,
arrow_size=5,
arrow_color=None,
):
"""Draw a path between two points with a smaller, more subtle directional arrow."""
if arrow_color is None:
arrow_color = color
# Calculate the midpoint for the arrow position - shift slightly toward destination
# to avoid overlap with nodes
midpoint_x = point1[0] + (point2[0] - point1[0]) * 0.6
midpoint_y = point1[1] + (point2[1] - point1[1]) * 0.6
# Draw the line
line = ax.plot(
[point1[0], point2[0]],
[point1[1], point2[1]],
color=color,
linewidth=linewidth,
alpha=alpha,
)[0]
# Calculate the direction vector
dx = point2[0] - point1[0]
dy = point2[1] - point1[1]
# Normalize the direction vector
length = np.sqrt(dx**2 + dy**2)
if length > 0:
dx /= length
dy /= length
# Add a small arrow
ax.arrow(
midpoint_x,
midpoint_y,
dx * arrow_size / 3,
dy * arrow_size / 3,
head_width=arrow_size * 0.8,
head_length=arrow_size * 0.8,
fc=arrow_color,
ec=arrow_color,
alpha=alpha,
length_includes_head=True,
)
return line
def add_arc_between_points(point1, point2, ax, alpha=0.2):
# Use spline of degree 2 (since m = 3)
tck, _ = splprep(
[
[point1[0], (point1[0] + point2[0]) / 2.0 - alpha, point2[0]],
[point1[1], (point1[1] + point2[1]) / 2.0 + alpha, point2[1]],
],
s=0,
k=2,
)
t = np.linspace(0, 1, 100)
x_spline, y_spline = splev(t, tck)
# Plot
ax.plot(x_spline, y_spline, label="Spline curve", linestyle="--")
def add_door(
x_center, y_center, ax, status="closed", door_color="black", door_location=(0, 0)
):
# make a hallow rectangle
x1 = x_center - 0.2
x2 = x_center + 0.2
y1 = y_center - 0.4
y2 = y_center + 0.4
if status == "open":
# make the fill color transparent
rect = patches.Polygon(
[[x1, y1], [x2, y1], [x2, y2], [x1, y2]],
closed=True,
edgecolor="black",
facecolor="none",
)
else:
rect = patches.Polygon(
[[x1, y1], [x2, y1], [x2, y2], [x1, y2]], closed=True, facecolor=door_color
)
ax.add_patch(rect)
def h_link(
x1,
x2,
y,
ax,
door=False,
status="closed",
lock_status="unlocked",
line_color="#76b5c5",
):
# make sure it is brought to the front of all other patches z_order = 100
ax.add_patch(patches.Circle((x1, y), 0.3, facecolor="black", zorder=100000))
ax.add_patch(patches.Circle((x2, y), 0.3, facecolor="black", zorder=100000))
x1 = x1 - 0.05
x2 = x2 + 0.05
y = y - 0.05
rect = patches.Polygon(
[[x1, y], [x2, y], [x2, y + 0.1], [x1, y + 0.1]],
closed=True,
facecolor=line_color,
)
ax.add_patch(rect)
x_center = (x1 + x2) / 2.0 + 0.05
if door:
if status == "open":
add_door(x_center, y + 0.05, ax, status="open")
else:
if lock_status == "locked":
door_color = "red"
else:
door_color = "green"
add_door(x_center, y + 0.05, ax, status="closed", door_color=door_color)
# add circles at both ends of the line
def v_link(
x,
y1,
y2,
ax,
door=False,
status="closed",
lock_status="locked",
line_color="#76b5c5",
):
# make sure it is brought to the front of all other patches z_order = 100
ax.add_patch(patches.Circle((x, y1), 0.3, facecolor="black", zorder=100000))
ax.add_patch(patches.Circle((x, y2), 0.3, facecolor="black", zorder=100000))
y1 = y1 - 0.05
y2 = y2 + 0.05
x = x - 0.05
triangle = patches.Polygon(
[[x, y1], [x, y2], [x + 0.1, y2], [x + 0.1, y1]],
closed=True,
facecolor=line_color,
)
ax.add_patch(triangle)
y_center = (y1 + y2) / 2.0
if door:
if status == "open":
add_door(x + 0.05, y_center, ax, status="open")
else:
if lock_status == "locked":
door_color = "red"
else:
door_color = "green"
add_door(x + 0.05, y_center, ax, status="closed", door_color=door_color)
# add circles at both ends of the line
def add_start_and_end_room(start_room, end_room, ax, size=0.6, enhanced_mode=False):
if enhanced_mode:
# Enhanced mode for LLM interpretability - clean colored circles only
x, y = start_room
# Start room: Large green circle (no text)
ax.add_patch(patches.Circle((x, y), size*1.5, facecolor="limegreen", edgecolor="darkgreen", linewidth=3, zorder=100000))
x, y = end_room
# End room: Large red circle (no text)
ax.add_patch(patches.Circle((x, y), size*1.5, facecolor="red", edgecolor="darkred", linewidth=3, zorder=100000))
else:
# Original mode: black triangles
x, y = start_room
ax.add_patch(
patches.Polygon(
[[x - size, y - size], [x + size, y - size], [x, y + size]],
closed=True,
facecolor="black",
edgecolor="black",
zorder=100000,
)
)
x, y = end_room
ax.add_patch(
patches.Polygon(
[[x - size, y + size], [x + size, y + size], [x, y - size]],
closed=True,
facecolor="black",
edgecolor="black",
zorder=100000,
)
)
def add_path_segment(
point1, point2, ax, door=False, status="closed", lock_status="locked"
):
if point1[0] == point2[0]:
v_link(point1[0], point1[1], point2[1], ax, door, status, lock_status)
else:
h_link(point1[0], point2[0], point1[1], ax, door, status, lock_status)
def add_key(x, y, ax, door_location=(0, 0)):
# Enhanced key visualization - yellow circle
ax.add_patch(
patches.Circle((x, y), 0.4, facecolor="yellow", edgecolor="orange", linewidth=2, zorder=100000)
)
add_arc_between_points((x, y), door_location, ax)
if __name__ == "__main__":
# Create a plot
fig, ax = plt.subplots()
add_path_segment((1, 1), (1, 4), ax, door=True, status="open")
add_key(1, 4, ax, door_location=(2.5, 4))
add_path_segment(
(1, 4), (4, 4), ax, door=True, status="closed", lock_status="locked"
)
add_path_segment((4, 4), (4, 7), ax, door=False)
add_path_segment(
(4, 7), (1, 7), ax, door=True, status="closed", lock_status="unlocked"
)
ax.set_aspect("equal")
ax.axis("off")
ax.set_xlim(0, 10)
ax.set_ylim(0, 10)
plt.show()
def pretty_plot_maze_vs_noise(
maze_loader,
W=4,
H=4,
save_path=None,
ground_truth_solution=None,
problem_description=None
):
"""
Display the maze using Matplotlib and optionally save to a file.
Shows three plots: Maze Layout, Ground Truth Path, and Model Path.
"""
plt.rcParams["font.size"] = 10
plt.rcParams["font.family"] = "sans-serif"
plt.rcParams["figure.dpi"] = 100
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(20, 8.5))
# Draw the base maze on all three plots
for ax in [ax1, ax2, ax3]:
covered_cells = set()
for cell in maze_loader.connected_cells.keys():
for neighbor in maze_loader.connected_cells[cell]:
if (cell, neighbor) in covered_cells or (
neighbor,
cell,
) in covered_cells:
continue
covered_cells.add((cell, neighbor))
add_path_segment(
(cell[0] * W, cell[1] * H),
(neighbor[0] * W, neighbor[1] * H),
ax,
door=(cell, neighbor) in maze_loader.doors.keys(),
status=None
if (cell, neighbor) not in maze_loader.doors.keys()
else maze_loader.doors[(cell, neighbor)][0].split(" ")[0],
lock_status=(
None
if (cell, neighbor) not in maze_loader.doors.keys()
or maze_loader.doors[(cell, neighbor)][0] == "open"
else maze_loader.doors[(cell, neighbor)][0].split(" ")[-1]
),
)
# Add keys
for key_id, key_location in maze_loader.keys_locations.items():
door_locations = {
maze_loader.doors[(rA, rB)][1]: (
(rA[0] + rB[0]) * W / 2,
(rA[1] + rB[1]) * H / 2,
)
for (rA, rB) in maze_loader.doors.keys()
}
add_key(
key_location[0] * W,
key_location[1] * H,
ax,
door_location=door_locations.get(key_id, (0, 0)),
)
# Add start and end rooms
start = (
maze_loader.data["start_room"][0] * W,
maze_loader.data["start_room"][1] * H,
)
end = (maze_loader.data["end_room"][0] * W, maze_loader.data["end_room"][1] * H)
add_start_and_end_room(start, end, ax)
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