commit 1c2df2e866091377fa6454a21341727abc098517
parent 50f8e9bf1997a1bd3f076046a1bae16ad610dd41
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date: Tue, 8 Aug 2023 20:13:41 +0200
Added multiplicity stats
Diffstat:
3 files changed, 75 insertions(+), 23 deletions(-)
diff --git a/__pycache__/billiard3d.cpython-311.pyc b/__pycache__/billiard3d.cpython-311.pyc
Binary files differ.
diff --git a/billiard3d.py b/billiard3d.py
@@ -54,11 +54,7 @@ def is_double(path):
return False
-def print_multiplicities(n, sizes, r):
- print("")
- print("Points with multiplicity > 1:")
- print("")
-
+def get_multiplicities(n, sizes, r):
d = dict()
path = [tuple(x) for x in get_path(n, sizes, r)]
@@ -72,6 +68,15 @@ def print_multiplicities(n, sizes, r):
for p in d:
d[p] //= 2
+ return d
+
+def print_multiplicities(n, sizes, r):
+ d = get_multiplicities(n, sizes, r)
+
+ print("")
+ print("Points with multiplicity > 1:")
+ print("")
+
for i in range(2, max(d.values())+1):
L = []
for point in d:
@@ -259,21 +264,22 @@ def user_input():
# Main routine below
###############################################################################
-# You can choose to write your input here or to get it interactively
-#sizes, r, pic = [15, 9, 7], [2, 0, 0], "p"
-#sizes, r, pic = [2, 3, 4], [0, 0, 0], "3"
-sizes, r, pic = user_input()
-
-print("---------------------------------")
-print_multiplicities(len(sizes), sizes, r)
-print("---------------------------------")
-print_points_on_edges(sizes, r)
-print("---------------------------------")
-
-if pic == "p":
- draw_3d_projections(sizes, r)
-elif pic == "3":
- draw_3d_picture(sizes, r)
-else:
- draw_3d_projections(sizes, r)
- draw_3d_picture(sizes, r)
+if __name__ == '__main__':
+ # You can choose to write your input here or to get it interactively
+ #sizes, r, pic = [15, 9, 7], [2, 0, 0], "p"
+ #sizes, r, pic = [2, 3, 4], [0, 0, 0], "3"
+ sizes, r, pic = user_input()
+
+ print("---------------------------------")
+ print_multiplicities(len(sizes), sizes, r)
+ print("---------------------------------")
+ print_points_on_edges(sizes, r)
+ print("---------------------------------")
+
+ if pic == "p":
+ draw_3d_projections(sizes, r)
+ elif pic == "3":
+ draw_3d_picture(sizes, r)
+ else:
+ draw_3d_projections(sizes, r)
+ draw_3d_picture(sizes, r)
diff --git a/multiplicity_stats.py b/multiplicity_stats.py
@@ -0,0 +1,46 @@
+import billiard3d
+import sys
+
+def get_stats(i, j, k, mult):
+ for r1 in range(i+1):
+ for r2 in range(j+1):
+ for r3 in range(k+1):
+ d = billiard3d.get_multiplicities(3, [i, j, k], [r1, r2, r3])
+ for key in d:
+ mult[d[key]] += 1
+
+def print_stats(N):
+ mult = [0] * 10
+ for i in range(1, N+1):
+ for j in range(i, N+1):
+ for k in range(j, N+1):
+ get_stats(i, j, k, mult)
+
+ print("Statistics for paths with 0 < a <= b <= c <= {0}".format(N))
+ print("Considering all paths starting from any possible point")
+ for i in range(1, 10):
+ if mult[i] != 0:
+ print("Multiplicity {0}: {1} points".format(i, mult[i]))
+ print("There are no points of positive multiplicity different from those listed above")
+
+def print_stats_single(a, b, c):
+ mult = [0] * 10
+ get_stats(a, b, c, mult)
+
+ print("Statistics for paths with a={0}, b={1} and c={2}".format(a, b, c))
+ print("Considering all paths starting from any possible point")
+ for i in range(1, 10):
+ if mult[i] != 0:
+ print("Multiplicity {0}: {1} points".format(i, mult[i]))
+ print("There are no points of positive multiplicity different from those listed above")
+
+if len(sys.argv) == 2:
+ N = int(sys.argv[1])
+ print_stats(N)
+elif len(sys.argv) == 4:
+ a, b, c = int(sys.argv[1]), int(sys.argv[2]), int(sys.argv[3])
+ print_stats_single(a, b, c)
+else:
+ print("Use one of the following options:")
+ print("\tpython multiplicity_stats.py N\t\t # For all possible sizes up to N")
+ print("\tpython multiplicity_stats.py a b c\t # For all starting points for the single 3d box (a,b,c)")
