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Johann Dreo 2017-06-10 23:00:17 +02:00
commit eadb161f34
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arshipery.py Normal file → Executable file
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@ -1,3 +1,5 @@
#!/usr/bin/env python3
# encoding: utf-8
# Playing battleships with archery.
# You fire two arrows, one for the column index and one for the line index.
@ -8,8 +10,15 @@
# – The arrow distribution on the target follow a normal law.
# – The drift on target is symetric in all direction. There is no covariance in the distribution.
# Questions:
# Statistics questions:
# – Given a player's precision, what are the cells with the minimal probability of hit?
# A: 10/10, you'd better place ships on the 10th line and column.
# – What if players have different levels?
# Game theory questions:
# – What if players have a limited number of arrows?
# – What are the optimal mixed strategy (for ship placement and aiming)?
import sys
import math
@ -84,72 +93,95 @@ if __name__ == "__main__":
d_radius = 10
dim = 2
nb_circles = 10
player_level = {"01-gold":1, "02-yellow":2,"04-red":5,"06-blue":9,"08-black":11,"10-white":14,"99-crap":20}
player_level = {"01-gold":1, "02-yellow":3,"04-red":5,"06-blue":9,"08-black":11,"10-white":15,"100-crap":25,"900-wtf":40}
print("levels=",sorted(player_level.keys()))
targets = make_target(nb_circles, d_radius)
print("targets=",targets)
# One line per player level, two subplots:
# on left, an example target, on right the density of probability.
fig, axarr = plt.subplots(len(player_level),3)
# One column per player level, two subplots:
# oup, an example target, down the density of probability.
fig1, axarr = plt.subplots(2, len(player_level))
for i,pl in enumerate(sorted(player_level.keys())):
print(i,"/",len(player_level),":",pl)
lvl_score = {}
for i,pl1 in enumerate(sorted(player_level.keys())):
print(i,"/",len(player_level),":",pl1)
sys.stdout.flush()
# DRAW TARGET
# Pastel
targets_colors = ["gold","lightcoral","lightblue","lightgrey","white",]
# targets_colors = ["gold","lightcoral","lightblue","lightgrey","white",]
# Official
# targets_colors = ["yellow","red","blue","black","white",]
targets_colors = ["yellow","red","blue","black","white",]
prev_r = 0
for t,(inf,sup) in enumerate(targets):
face = plt.Circle((0, 0), sup, color=targets_colors[(nb_circles-t-1)//2],zorder=2)
border = plt.Circle((0, 0), sup, color="grey", fill=False,zorder=2)
axarr[i,0].add_artist(face)
axarr[i,0].add_artist(border)
axarr[i,0].set_aspect("equal")
face = plt.Circle((0, 0), sup, color=targets_colors[(nb_circles-t-1)//2],zorder=1)
border = plt.Circle((0, 0), sup, color="grey", fill=False,zorder=3)
axarr[0,i].add_artist(face)
axarr[0,i].add_artist(border)
axarr[0,i].set_aspect("equal")
# DRAW ARROWS
# for i,k in enumerate(player_level.keys()):
# arrows = fire(nb_arrows, 10-i, player_level[k])
# axarr[0,0].scatter(*arrows, edgecolor=player_color[i], color="none", alpha=0.3, marker=".", zorder=100)
arrows, score = play(player_level[pl], player_level[pl], nb_circles, nb_arrows, dim)
arrows, score = play(player_level[pl1], player_level[pl1], nb_circles, nb_arrows, dim)
lvl_score[(player_level[pl1], player_level[pl1])] = score
# Plot arbitrary arrows.
aim_p1 = 1
aim_p2 = 1
max_points = 100
lim = 2 * (nb_circles * d_radius)
axarr[i,0].set_xlim((-lim,lim))
axarr[i,0].set_ylim((-lim,lim))
axarr[0,i].set_xlim((-lim,lim))
axarr[0,i].set_ylim((-lim,lim))
p1,p2 = 0,1
p1_arrows = arrows[aim_p1-1][aim_p2-1][p1][:,:max_points]
p2_arrows = arrows[aim_p1-1][aim_p2-1][p2][:,:max_points]
axarr[i,0].scatter(* p1_arrows , edgecolor="magenta", color="none", alpha=0.3, marker=".", zorder=100)
axarr[i,0].scatter(*(-1*p2_arrows), edgecolor="green" , color="none", alpha=0.3, marker=".", zorder=100)
axarr[0,i].scatter(* p1_arrows , edgecolor="magenta", color="none", alpha=0.5, marker=".", zorder=2)
axarr[0,i].scatter(*(-1*p2_arrows), edgecolor="green" , color="none", alpha=0.5, marker=".", zorder=2)
axarr[0,i].set_title(pl1.split("-")[1])
axarr[0,i].axes.get_yaxis().set_visible(False)
axarr[0,i].axes.get_xaxis().set_visible(False)
# Compute probabilities of hit
H,xe,ye = np.histogram2d(*score, bins=11, normed=True)
# Plot the full normalized histogram
axarr[i,1].imshow(H, interpolation='nearest', origin='low',
# extent=[xe[0],xe[-1],ye[0],ye[-1]]
# extent=[0,11,0,11]
)
# # Plot the full normalized histogram
# axarr[i,1].imshow(H, interpolation='nearest', origin='low',
# # extent=[xe[0],xe[-1],ye[0],ye[-1]]
# # extent=[0,11,0,11]
# )
# Plot the normalized histogram without out arrows.
axarr[i,2].imshow(H[1:,1:], interpolation='nearest', origin='low',
im = axarr[1,i].imshow(H[1:,1:], interpolation='nearest', origin='low', cmap="viridis",
# extent=[xe[0],xe[-1],ye[0],ye[-1]]
# extent=[1,11,1,11]
)
plt.show()
# fig1.colorbar(im, ax=axarr[1,i])
# Grid
minticks = [i-0.5 for i in range(nb_circles+1)]
axarr[1,i].set_xticks(minticks, minor=True)
axarr[1,i].set_yticks(minticks, minor=True)
axarr[1,i].grid(which="minor")
# Labels
majticks = [i for i in range(nb_circles)]
labels = [i+1 for i in range(nb_circles)]
axarr[1,i].set_xticks(majticks)
axarr[1,i].set_yticks(majticks)
axarr[1,i].set_xticklabels(labels)
axarr[1,i].set_yticklabels(labels)
# s = 1000
# h,w = s * 3, s * 4
# plt.savefig("target_eq-levels.png",dpi=300, figsize=(h,w))
plt.show()