# 用TensorFlow實現線性回歸算法
#----------------------------------
#
# This function shows how to use TensorFlow to
# solve linear regression.
# y = Ax + b
#
# We will use the iris data, specifically:
# y = Sepal Length
# x = Petal Width

import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from sklearn import datasets
from tensorflow.python.framework import ops
ops.reset_default_graph()

# Create graph
sess = tf.Session()

# Load the data
# iris.data = [(Sepal Length, Sepal Width, Petal Length, Petal Width)]
iris = datasets.load_iris()
x_vals = np.array([x[3] for x in iris.data])
y_vals = np.array([y[0] for y in iris.data])

# 批量大小
batch_size = 25

# Initialize 占位符
x_data = tf.placeholder(shape=[None, 1], dtype=tf.float32)
y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)

# 模型變量
A = tf.Variable(tf.random_normal(shape=[1,1]))
b = tf.Variable(tf.random_normal(shape=[1,1]))

# 增加線性模型，y=Ax+b
model_output = tf.add(tf.matmul(x_data, A), b)

# 聲明L2損失函數，其為批量損失的平均值。
loss = tf.reduce_mean(tf.square(y_target - model_output))

# 聲明優化器 學習率設為0.05
my_opt = tf.train.GradientDescentOptimizer(0.05)
train_step = my_opt.minimize(loss)

# 初始化變量
init = tf.global_variables_initializer()
sess.run(init)

# 批量訓練遍歷迭代
# 迭代100次，每25次迭代輸出變量值和損失值
loss_vec = []
for i in range(100):
  rand_index = np.random.choice(len(x_vals), size=batch_size)
  rand_x = np.transpose([x_vals[rand_index]])
  rand_y = np.transpose([y_vals[rand_index]])
  sess.run(train_step, feed_dict={x_data: rand_x, y_target: rand_y})
  temp_loss = sess.run(loss, feed_dict={x_data: rand_x, y_target: rand_y})
  loss_vec.append(temp_loss)
  if (i+1)%25==0:
    print('Step #' + str(i+1) + ' A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b)))
    print('Loss = ' + str(temp_loss))

# 抽取系數
[slope] = sess.run(A)
[y_intercept] = sess.run(b)

# 創建最佳擬合直線
best_fit = []
for i in x_vals:
 best_fit.append(slope*i+y_intercept)

# 繪制兩幅圖
# 擬合的直線
plt.plot(x_vals, y_vals, 'o', label='Data Points')
plt.plot(x_vals, best_fit, 'r-', label='Best fit line', linewidth=3)
plt.legend(loc='upper left')
plt.title('Sepal Length vs Pedal Width')
plt.xlabel('Pedal Width')
plt.ylabel('Sepal Length')
plt.show()

# Plot loss over time
# 迭代100次的L2正則損失函數
plt.plot(loss_vec, 'k-')
plt.title('L2 Loss per Generation')
plt.xlabel('Generation')
plt.ylabel('L2 Loss')
plt.show()

Step #25 A = [[ 1.93474162]] b = [[ 3.11190438]]
Loss = 1.21364
Step #50 A = [[ 1.48641717]] b = [[ 3.81004381]]
Loss = 0.945256
Step #75 A = [[ 1.26089203]] b = [[ 4.221035]]
Loss = 0.254756
Step #100 A = [[ 1.1693294]] b = [[ 4.47258472]]
Loss = 0.281654