From 303bf558b5c995834643e5e89a773de37cbc0050 Mon Sep 17 00:00:00 2001
From: hppeng <hppeng>
Date: Sun, 6 Feb 2022 00:04:01 -0800
Subject: [PATCH] Scripts for analyzing mana steal and mana regen using markov
 chains

---
 .gitignore           |  1 +
 testing/ms_linalg.py | 48 +++++++++++++++++++++++++++++++++++
 testing/ms_sslow.py  | 60 ++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 109 insertions(+)
 create mode 100644 testing/ms_linalg.py
 create mode 100644 testing/ms_sslow.py

diff --git a/.gitignore b/.gitignore
index ce62501..91acd82 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,3 +4,4 @@ sets/
 
 .idea/
 *.iml
+.editor_log.txt
diff --git a/testing/ms_linalg.py b/testing/ms_linalg.py
new file mode 100644
index 0000000..c3436f6
--- /dev/null
+++ b/testing/ms_linalg.py
@@ -0,0 +1,48 @@
+import numpy as np
+import numpy.linalg as la
+import matplotlib.pyplot as plt
+
+# Attack speed independent. Fast speed losses not accounted for
+mana_consumption = 3
+mana_steal = 10     # /3s
+mana_regen = 0      # /5s
+#mana_steal = 5     # /3s
+#mana_regen = 5      # /5s
+natural_regen = 1
+
+weight_natural = 8/15   # 4/5 * 2/3
+weight_mr = 2/15        # 1/5 * 2/3
+weight_ms = 4/15        # 4/5 * 1/3
+weight_mr_ms = 1/15     # 1/5 * 1/3
+
+MAX_MANA = 20
+transition_matrix = np.zeros((MAX_MANA, MAX_MANA))
+for i in range(MAX_MANA):
+    natural_state = max(0, i - mana_consumption + natural_regen)
+    mr_state = min(19, natural_state + mana_regen)
+    ms_state = min(19, natural_state + mana_steal)
+    mr_ms_state = min(19, natural_state + mana_regen + mana_steal)
+    transition_matrix[natural_state, i] = weight_natural
+    transition_matrix[mr_state, i] += weight_mr
+    transition_matrix[ms_state, i] += weight_ms
+    transition_matrix[mr_ms_state, i] += weight_mr_ms
+
+eigval, eigvec = la.eig(transition_matrix)
+print(eigval)
+eps = 0.00001
+ind = np.argwhere(abs(eigval - 1) < eps)
+steady_state = abs(eigvec[:, ind])
+steady_state /= np.sum(steady_state)
+cumulative = np.cumsum(steady_state)
+print("mana\tprob cumsum")
+for i in range(MAX_MANA):
+    print(f"{i+1}\t{cumulative[i]}")
+
+plt.figure()
+plt.scatter(range(len(steady_state)), steady_state)
+plt.xlim(0, 19)
+plt.ylim(0, 0.2)
+plt.xlabel("Mana Value")
+plt.ylabel("Probability at t=infty")
+plt.title(f"Build={mana_regen}mr,{mana_steal}ms,{mana_consumption}mana/sec")
+plt.show()
diff --git a/testing/ms_sslow.py b/testing/ms_sslow.py
new file mode 100644
index 0000000..3cd068b
--- /dev/null
+++ b/testing/ms_sslow.py
@@ -0,0 +1,60 @@
+import numpy as np
+import numpy.linalg as la
+import matplotlib.pyplot as plt
+
+# Super slow attack speed. (Idealized to 1 hit/2s, 2/3 chance of proc
+mana_consumption = 3
+mana_steal = 5      # /3s
+mana_regen = 4      # /5s
+#mana_steal = 5      # /3s
+#mana_regen = 5      # /5s
+natural_regen = 1
+
+ms_period = 2
+ms_chance = ms_period / 3
+no_ms_chance = 1 - ms_chance
+
+MAX_MANA = 20
+TIME_CYCLE = 10
+transition_matrix = np.zeros((MAX_MANA * TIME_CYCLE, MAX_MANA * TIME_CYCLE))
+for j in range(TIME_CYCLE):
+    for i in range(MAX_MANA):
+        natural_state = max(0, i - mana_consumption + natural_regen)
+        if j % 5 == 0:  # mr activation
+            natural_state = min(19, natural_state + mana_regen)
+        next_ind = ((j+1) % TIME_CYCLE) * MAX_MANA
+        if j % ms_period == 0:  # ms activation
+            ms_state = min(19, natural_state + mana_steal)
+            transition_matrix[next_ind + natural_state, i+j*MAX_MANA] = no_ms_chance
+            transition_matrix[next_ind + ms_state, i+j*MAX_MANA] += ms_chance
+        else:
+            transition_matrix[next_ind + natural_state, i+j*MAX_MANA] = 1
+
+eigval, eigvec = la.eig(transition_matrix)
+print(eigval)
+eps = 0.00001
+ind = np.argwhere(abs(eigval - 1) < eps)
+steady_state = np.sum(abs(eigvec[:, ind]).reshape((TIME_CYCLE, MAX_MANA)), axis=0)
+steady_state /= np.sum(steady_state)
+cumulative = np.cumsum(steady_state)
+print("mana\tcumulative probability")
+for i in range(MAX_MANA):
+    print(f"{i+1}\t{cumulative[i]}")
+
+x_ticks = list(range(len(steady_state)))
+plt.figure()
+plt.scatter(x_ticks, steady_state, label="mana values")
+plt.xlim(0, 19)
+plt.ylim(0, 0.3)
+plt.axvline(x=6+mana_consumption)
+plt.xlabel("Mana Value")
+plt.xticks(x_ticks)
+plt.ylabel("Probability at t=infty")
+plt.legend()
+ax2 = plt.gca().twinx()
+ax2.plot(x_ticks, cumulative, label="cumulative probability")
+ax2.set_ylim(0, 1)
+ax2.set_ylabel("Cumulative probability at t=infty")
+plt.title(f"Build={mana_regen}mr,{mana_steal}ms,{mana_consumption}mana/sec")
+plt.legend()
+plt.show()