import sys, os
import numpyas np
sys.path.append(os.pardir)
from dataset.mnistimport load_mnist
import matplotlib.pyplotas plt
from PILimport Image
import pickle
#圖片預覽
# def img_show(img):
#? ? pil_img = Image.fromarray(np.uint8(img)) #將numpy數組的圖像數據轉換為PIL的數據對象
#? ? pil_img.show()
# img = x_train[0]
# label = t_train[0]
# print(label)
# print(img.shape)
# img = img.reshape(28, 28)
# print(img.shape)
# img_show(img)
# def sigmoid(z):
#? ? return 1 / (1 + np.exp(-z))
def softmax(a):
c = np.max(a)
exp_a = np.exp(a-c)
exp_sum = np.sum(exp_a)
return exp_a / exp_sum
#數據準備
def get_data():
(x_train, t_train), (x_test, t_test) = load_mnist(normalize=True,? flatten=True, one_hot_label=False)
return x_train, t_train
#
# def init_network():
#? ? with open('sample_weight.pkl', 'rb') as f : #讀取二進制文件，注意文件是否過大決定讀取方式，此處讀取不到該文件
#? ? ? ? network = pickle.load(f)
#? ? return network
# def predict(network, x):
#? ? W1, W2, W3 = network['W1'], network['W2'], network['W3']
#? ? b1, b2, b3 = network['b1'], network['b1'], network['b1']
#? ? z1 = np.dot(x, W1) + b1
#? ? a1 = sigmoid(z1)
#? ? z2 = np.dot(a1, W2) + b2
#? ? a2 = sigmoid(z2)
#? ? z3 = np.dot(a2, W3) + b3
#? ? y = softmax(z3)
#? ? return y
# x, t = get_data()
# network = init_network()
# accuracy_cnt = 0
# for i in range(len(x)):
#? ? y = predict(network, x)
#? ? p = np.argmax(y)
#? ? if p == t[i]:
#? ? ? ? accuracy_cnt += 1
# print('accuracy:'+ str(float(accuracy_cnt) / len(x)))
#批處理,加快運算速度
# x, t = get_data()
# network = init_network()
# batch_size = 100
# accuracy_cnt = 0
# for i in range(0, len(x), batch_size):
#? ? x_batch = x[i:i+batch_size]
#? ? y_batch = predict(network, x_batch)
#? ? p = np.argmax(y_batch, axis=1) #矩陣的第0維是列方向，第1維是行方向
#? ? accuracy_cnt += np.sum(p == t[i:i+batch_size])
# print('accuracy:'+ str(float(accuracy_cnt) / len(x)))
#第4章
#均方誤差
# def mean_squared_error(y, t):
#? ? return 0.5 * np.sum((y-t)**2)
# t = np.array([0, 0, 1, 0, 0, 0, 0, 0, 0, 0])
# y = np.array([0.1, 0.05, 0.6, 0.0, 0.05, 0.1, 0.0, 0.1, 0.0, 0.0])
# print(mean_squared_error(y, t))
#交叉熵誤差
# def cross_entropy_error(y, t):
#? ? delta = 1e-7
#? ? return -np.sum(t * np.log(y + delta))
# t = np.array([0, 0, 1, 0, 0, 0, 0, 0, 0, 0])
# y = np.array([0.1, 0.05, 0.6, 0.0, 0.05, 0.1, 0.0, 0.1, 0.0, 0.0])
# print(cross_entropy_error(y, t))
#隨機抽取
# x_train, t_train = get_data()
# train_size = x_train.shape[0]
# batch_size = 10
# batch_mask = np.random.choice(train_size, batch_size)
# x_batch = x_train[batch_mask]
# t_batch = t_train[batch_mask]
# print(batch_mask)
# print(x_train)
#交叉熵誤差，支持單個和批量數據
# def cross_entropy_error(y, t):
#? ? if y.ndim == 1:
#? ? ? ? t = t.reshape(1,t. size)
#? ? ? ? y = y.reshape(1, y.size)
#? ? batch_size = y.shape[0]
#? ? return -np.sum(t * np.log(y + 1e-7)) / batch_size
# #如果監督數據是標簽形式，計算交叉熵誤差
def cross_entrory_error(y, t):
if y.ndim ==1:
t = t.reshape(1, t.size)
y = y.reshape(1, y.size)
batch_size = y.shape[0]
return -np.sum(np.log(y[np.arange(batch_size), t] +1e-7)) / batch_size
#數值微分
def function_1(x):
return 0.01*x**2 +0.1*x
# # x = np.arange(0, 20, 0.1)
# # y = function_1(x)
# # plt.xlabel('x')
# # plt.ylabel('y')
# # plt.plot(x, y)
# # plt.show()
# def numerical_diff(f, x):
#? ? h = 1e-4
#? ? return (f(x+h) - f(x-h)) / (2*h)
# print(numerical_diff(function_1, 5))
#計算給定x的偏導數，例如（x1,x2,x3），會計算出三個偏導數
def numerical_gradient_nobatch(f, x):
h =1e-4
? ? grad = np.zeros_like(x)
for idxin range(x.size):
val = x[idx]
#f1(x)
? ? ? ? x[idx] = val + h
fxh1 = f(x)
#f2(x)
? ? ? ? x[idx] = val - h
fxh2 = f(x)
grad[idx] = (fxh1 - fxh2) / (2*h)
x[idx] = val
return grad
#包裝上述偏導計算函數，如果維度大于1維，通過enumerate每行取x for循環計算
def numerical_gradient(f, X):
if X.ndim ==1:
return numerical_gradient_nobatch(f, X)
else:
grad = np.zeros_like(X)
for idx, xin enumerate(X):
grad[idx] = numerical_gradient_nobatch(f, x)
return grad
def function_2(x):
return x[0]**2 + x[1]**2
#g = numerical_gradient(function_2, np.array([3.0, 4.0])) #沒有加小數點，導致結果差距很大
#使用梯度下降法求最小值
def gradient_decent(f, init_x, lr =0.01, step_num =100):
x = init_x
for iin range(step_num):
grad = numerical_gradient(f, x)
x -=lr * grad
return x
# init_x = np.array([-3.0, 4.0])
# g = gradient_decent(function_2, init_x, lr=0.1, step_num=100)
# print(g)
#神經網絡的類
class simpleNet:
def __init__(self):
self.W = np.random.randn(2,3)
def predict(self, x):
return np.dot(x, self.W)
def loss(self, x, t):
z =self.predict(x)
y = softmax(z)
loss = cross_entrory_error(y, t)
return loss
net = simpleNet()
print(net.W)
x = np.array([0.6, 0.9])
p = net.predict(x)
print(p)
print(np.argmax(p))
t = np.array([0, 0, 1])
print(net.loss(x, t))
#偏導計算函數的輸入變量，函數+自變量權重
f =lambda w : net.loss(x, t)
dW = numerical_gradient(f, net.W)
print(dW)
