感知器

 1: import numpy as np
 2: 
 3: def step_function(x):
 4:     return np.array(x >= 0, int)
 5: 
 6: def OR(x1, x2):
 7:     x = np.array([x1, x2])
 8:     w = np.array([1, 1])
 9:     b = -0.5
10:     y = np.sum(w*x) + b
11:     return step_function(y)
12: 
13: print("0 OR 0 -> ", OR(0,0))
14: print("0 OR 1 -> ", OR(0,1))
15: print("1 OR 0 -> ", OR(1,0))
16: print("1 OR 1 -> ", OR(1,1))

 1: import numpy as np
 2: 
 3: def step_function(x):
 4:     return np.array(x >= 0, dtype=int)
 5: 
 6: def AND(x1, x2):
 7:     x = np.array([x1, x2])
 8:     w = np.array([___, ___])  # 請填入權重
 9:     b = ___                     # 請填入偏移值
10:     y = np.sum(w*x) + b
11:     return step_function(y)
12: 
13: print("0 AND 0 -> ", AND(0,0))
14: print("0 AND 1 -> ", AND(0,1))
15: print("1 AND 0 -> ", AND(1,0))
16: print("1 AND 1 -> ", AND(1,1))

 1: import numpy as np
 2: 
 3: def step_function(x):
 4:     return np.array(x >= 0, dtype=int)
 5: 
 6: def NAND(x1, x2):
 7:     x = np.array([x1, x2])
 8:     w = np.array([___, ___])  # 請填入權重
 9:     b = ___
10:     y = np.sum(w*x) + b
11:     return step_function(y)
12: 
13: print("0 NAND 0 -> ", NAND(0,0))
14: print("0 NAND 1 -> ", NAND(0,1))
15: print("1 NAND 0 -> ", NAND(1,0))
16: print("1 NAND 1 -> ", NAND(1,1))

 1: #python code for XOR gate simulation
 2: import numpy as np
 3: 
 4: def step_function(x):
 5:     return np.array(x >= 0, dtype=int)
 6: 
 7: def AND(x1, x2):
 8:     x = np.array([x1, x2])
 9:     w = np.array([0.5, 0.5])
10:     b = -0.7
11:     return step_function(np.sum(w*x) + b)
12: 
13: def OR(x1, x2):
14:     x = np.array([x1, x2])
15:     w = np.array([0.5, 0.5])
16:     b = -0.2
17:     return step_function(np.sum(w*x) + b)
18: 
19: def NAND(x1, x2):
20:     x = np.array([x1, x2])
21:     w = np.array([-0.5, -0.5])
22:     b = 0.7
23:     return step_function(np.sum(w*x) + b)
24: 
25: def XOR(x1, x2):
26:     s1 = NAND(x1, x2)
27:     s2 = OR(x1, x2)
28:     y = AND(s1, s2)
29:     return y
30: 
31: print("XOR(0,0): ", XOR(0,0))
32: print("XOR(0,1): ", XOR(0,1))
33: print("XOR(1,0): ", XOR(1,0))
34: print("XOR(1,1): ", XOR(1,1))

 1: import numpy as np
 2: 
 3: def step_function(x):
 4:     return np.array(x >= 0, dtype=int)
 5: 
 6: # 同學資料 [昨晚睡幾小時, 今天咖啡幾杯]
 7: X = np.array([[8,2], [4,0], [7,1], [3,1],
 8:               [6,2], [5,0], [4,2], [3,0]])
 9: # 標籤: 清醒=1, 睡著=0
10: y = np.array([1, 0, 1, 0, 1, 0, 1, 0])
11: names = ['阿明','小美','大雄','胖虎','靜香','小夫','阿福','魯夫']
12: 
13: # 只看睡眠（w2=0 表示完全忽略咖啡）
14: w = np.array([1, 0])
15: b = -5.5  # 門檻 = 5.5 小時
16: 
17: print("預測結果（只看睡眠時數）:")
18: for i in range(len(X)):
19:     pred = step_function(np.dot(w, X[i]) + b)
20:     label = '清醒' if pred == 1 else '睡著'
21:     correct = '○' if pred == y[i] else '×'
22:     print(f"  {names[i]}（睡{X[i][0]}hr, 咖啡{X[i][1]}杯）→ {label} {correct}")

 1: import numpy as np
 2: import matplotlib.pyplot as plt
 3: 
 4: def step_function(x):
 5:     return np.array(x >= 0, dtype=int)
 6: 
 7: # 同學資料 [昨晚睡幾小時, 今天咖啡幾杯]
 8: X = np.array([[8,2], [4,0], [7,1], [3,1],
 9:               [6,2], [5,0], [4,2], [3,0]])
10: # 標籤: 清醒=1, 睡著=0
11: y = np.array([1, 0, 1, 0, 1, 0, 1, 0])
12: names = ['阿明','小美','大雄','胖虎','靜香','小夫','阿福','魯夫']
13: 
14: # TODO: 修改 w 和 b，同時考慮睡眠和咖啡，讓 8 個人全部分對
15: w = np.array([___, ___])  # [睡眠權重, 咖啡權重]
16: b = ___
17: 
18: # 測試感知器
19: print("預測結果:")
20: for i in range(len(X)):
21:     pred = step_function(np.dot(w, X[i]) + b)
22:     label = '清醒' if pred == 1 else '睡著'
23:     correct = '○' if pred == y[i] else '×'
24:     print(f"  {names[i]}（睡{X[i][0]}hr, 咖啡{X[i][1]}杯）→ {label} {correct}")
25: 
26: # 繪製散佈圖與決策邊界
27: plt.figure(figsize=(6, 5))
28: awake = y == 1
29: asleep = y == 0
30: plt.scatter(X[awake, 0], X[awake, 1], c='green', marker='o', s=100, label='清醒')
31: plt.scatter(X[asleep, 0], X[asleep, 1], c='red', marker='x', s=100, label='睡著')
32: for i, name in enumerate(names):
33:     plt.annotate(name, (X[i,0]+0.1, X[i,1]+0.1))
34: 
35: # 決策邊界: w1*x1 + w2*x2 + b = 0 → x2 = -(w1*x1 + b)/w2
36: x1_line = np.linspace(2, 9, 100)
37: x2_line = -(w[0] * x1_line + b) / w[1]
38: plt.plot(x1_line, x2_line, 'b--', linewidth=2, label='決策邊界')
39: 
40: plt.xlabel('昨晚睡幾小時')
41: plt.ylabel('今天咖啡幾杯')
42: plt.title('感知器預測：你會不會睡著？')
43: plt.legend()
44: plt.grid(True)
45: plt.savefig("images/perceptron-sleep.png", dpi=300)

 1: import numpy as np
 2: 
 3: def step_function(x):
 4:     return np.array(x >= 0, dtype=int)
 5: 
 6: # 訓練資料 [每週滑手機hr, 每週讀書hr]
 7: X = np.array([[30,2], [5,25], [25,5], [10,20], [20,10], [15,15]])
 8: y = np.array([0, 1, 0, 1, 0, 1])  # 0=被當, 1=存活
 9: names = ['小明', '學霸', '阿宅', '認真妹', '社畜', '覺醒者']
10: 
11: # 初始化
12: w = np.zeros(2)
13: b = 0.0
14: eta = 0.01   # 學習率
15: 
16: # 訓練
17: print(f"初始狀態: w=[{w[0]:.3f}, {w[1]:.3f}], b={b:.3f}")
18: for epoch in range(50):
19:     w_before, b_before = w.copy(), b  # 記錄 epoch 開始前的狀態
20:     errors = 0
21:     for xi, yi in zip(X, y):
22:         y_pred = step_function(np.dot(w, xi) + b)
23:         error = yi - y_pred
24:         if error != 0:
25:             w = w + eta * error * xi  # 權重更新
26:             b = b + eta * error        # 偏移值更新
27:             errors += 1
28:     if epoch < 5 or errors == 0:
29:         changed = "（權重已更新）" if (not np.array_equal(w, w_before) or b != b_before) else "（無變化）"
30:         print(f"Epoch {epoch+1:2d}: w=[{w[0]:.3f}, {w[1]:.3f}], b={b:.3f}, 錯誤數={errors} {changed}")
31:     if errors == 0:
32:         print("訓練完成！導師的 AI 預警系統上線了。")
33:         break
34: 
35: # 測試
36: print("\n=== 預測結果 ===")
37: for i in range(len(X)):
38:     pred = step_function(np.dot(w, X[i]) + b)
39:     result = '存活' if pred == 1 else '被當'
40:     correct = '○' if pred == y[i] else '×'
41:     print(f"  {names[i]}: 滑手機{X[i][0]}hr 讀書{X[i][1]}hr → {result} {correct}")

 1: # （接續上方程式碼，請貼在最後面一起執行）
 2: 
 3: # 預測新同學
 4: new_students = [
 5:     ("邊緣人", [18, 12]),   # 滑手機略多於讀書
 6:     ("佛系仔", [15, 16]),   # 幾乎一半一半，讀書只多 1 小時
 7:     ("手遊王", [35, 1]),    # 不用預測你也知道
 8: ]
 9: print("\n=== 導師的黑名單預測 ===")
10: for name, data in new_students:
11:     x = np.array(data)
12:     score = np.dot(w, x) + b
13:     pred = step_function(score)
14:     status = '存活' if pred == 1 else '被當'
15:     emoji = '安全過關' if pred == 1 else '準備叫家長'
16:     print(f"  {name}: 滑{data[0]}hr 讀{data[1]}hr → 分數={score:.2f} → {status}（{emoji}）")

 1: # （接續任務 A 程式碼，請貼在最後面一起執行）
 2: 
 3: import matplotlib.pyplot as plt
 4: 
 5: plt.figure(figsize=(7, 6))
 6: survived = y == 1
 7: failed = y == 0
 8: plt.scatter(X[survived, 0], X[survived, 1], c='green', marker='o', s=120, label='存活', zorder=5)
 9: plt.scatter(X[failed, 0], X[failed, 1], c='red', marker='x', s=120, linewidths=2, label='被當', zorder=5)
10: 
11: for i, name in enumerate(names):
12:     plt.annotate(name, (X[i,0]+0.5, X[i,1]+0.5), fontsize=10)
13: 
14: # 決策邊界
15: x1_line = np.linspace(0, 40, 100)
16: if w[1] != 0:
17:     x2_line = -(w[0] * x1_line + b) / w[1]
18:     plt.plot(x1_line, x2_line, 'b--', linewidth=2, label='決策邊界（生死線）')
19: 
20: plt.xlabel('每週滑手機時數')
21: plt.ylabel('每週讀書時數')
22: plt.title('導師的 AI 預警系統：期末生死分界線')
23: plt.legend()
24: plt.grid(True, alpha=0.3)
25: plt.xlim(0, 40)
26: plt.ylim(0, 30)
27: plt.savefig("images/perceptron-flunk.png", dpi=300)
28: print("決策邊界圖已儲存！")
29: print(f"生死線方程式: {w[0]:.3f} × 滑手機 + {w[1]:.3f} × 讀書 + {b:.3f} = 0")