#目的：非線性迴歸
 
#（1）步驟1：載入AI函式庫：import tensorflow library（TensorFlow and keras）
import tensorflow as tf 

#（2）步驟2：建立神經網絡模型，單層神經，一個神經元units=1
model = tf.keras.Sequential()
model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation='relu'))
model.add(tf.keras.layers.Dense(units=8, activation='relu'))
model.add(tf.keras.layers.Dense(units=8, activation='relu'))
model.add(tf.keras.layers.Dense(units=8, activation='relu'))
model.add(tf.keras.layers.Dense(units=1, activation='relu'))

#（3）步驟3：建立目標函數，設定求解方法(最少需要設定兩個參數：A.損失函數loss，B.優化函數optimizer）
model.compile(
    optimizer = tf.keras.optimizers.Adam(),
    #optimizer = tf.keras.optimizers.SGD(),
    loss = tf.keras.losses.MeanSquaredError()
    
)

#（4）步驟4：設定輸入矩陣數據(x,y)，
import numpy as np
xs = np.array([-0.5, -0.44736842, -0.39473684, -0.34210526, -0.28947368, -0.23684211,
 -0.18421053, -0.13157895, -0.07894737, -0.02631579, 0.02631579, 0.07894737,
  0.13157895, 0.18421053, 0.23684211, 0.28947368, 0.34210526, 0.39473684,
  0.44736842,  0.5])
ys = np.array([0.24595018, 0.19992016, 0.11848622, 0.09924376, 0.08173275, 0.0596075,
  0.02737021, 0.01544445, 0.02764277, 0.00527432,-0.00814974,-0.01725386,
  0.0489, 0.02935983, 0.04428556, 0.08552249, 0.12389014, 0.15113714,
  0.20734122, 0.23009059])
    
#（5）步驟5：訓練模型：
model.fit(xs,ys,epochs=500)

#（6）步驟6：預測
yp = model.predict([1.0])

#（7）步驟畫圖：訓練+預測
import matplotlib.pyplot as plt
plt.plot(xs,ys,'ro')
plt.plot([1.0],yp,'bo')