def sigmoid_ prime(2) :sigmoid的导数”””
时间: 2024-02-09 09:08:36 浏览: 35
sigmoid函数的导数可以用sigmoid函数本身来表示,即:
sigmoid'(x) = sigmoid(x) * (1 - sigmoid(x))
下面是使用sigmoid函数计算其导数的示例代码(Python实现):
```python
import numpy as np
def sigmoid(x):
"""
sigmoid函数的实现
"""
return 1 / (1 + np.exp(-x))
def sigmoid_prime(x):
"""
sigmoid函数的导数的实现
"""
return sigmoid(x) * (1 - sigmoid(x))
# 测试sigmoid函数的导数
x = np.array([1, 2, 3])
print(sigmoid_prime(x))
```
输出结果:
```
[0.19661193 0.10499359 0.04517666]
```
其中,`sigmoid_prime`函数的实现使用了`sigmoid`函数本身来计算导数,可以对输入的向量或矩阵进行快速计算。在输出结果中,可以看到输入向量中每个元素的sigmoid函数的导数值。
相关问题
def sigmoid_prime(self, z): return self.sigmoid(z) * (1 - self.sigmoid(z))
这是一个神经网络中常用的sigmoid函数的导数,也称为sigmoid函数的导函数,用于计算反向传播中的梯度。其中,sigmoid函数本身是一个S形曲线,将输入值映射到0到1之间的输出值。其导数则是根据链式法则计算得到的,可以表示为sigmoid函数输出值关于输入值的导数,即sigmoid函数的输出值乘以1减去该输出值。
class BPNeuralNetwork:
BPNeuralNetwork 是一个基于反向传播算法的神经网络类,用于解决分类、回归等问题。下面是一个简单的实现示例:
``` python
import numpy as np
class BPNeuralNetwork:
def __init__(self, sizes):
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:])]
def sigmoid(self, z):
return 1.0 / (1.0 + np.exp(-z))
def sigmoid_prime(self, z):
return self.sigmoid(z) * (1 - self.sigmoid(z))
def feedforward(self, a):
for b, w in zip(self.biases, self.weights):
a = self.sigmoid(np.dot(w, a) + b)
return a
def train(self, training_data, epochs, mini_batch_size, eta, test_data=None):
if test_data:
n_test = len(test_data)
n = len(training_data)
for j in range(epochs):
np.random.shuffle(training_data)
mini_batches = [training_data[k:k+mini_batch_size] for k in range(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)
if test_data:
print("Epoch {0}: {1} / {2}".format(j, self.evaluate(test_data), n_test))
else:
print("Epoch {0} complete".format(j))
def update_mini_batch(self, mini_batch, eta):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)]
def backprop(self, x, y):
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
activation = x
activations = [x]
zs = []
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation) + b
zs.append(z)
activation = self.sigmoid(z)
activations.append(activation)
delta = self.cost_derivative(activations[-1], y) * self.sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
for l in range(2, self.num_layers):
z = zs[-l]
sp = self.sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def cost_derivative(self, output_activations, y):
return (output_activations-y)
def evaluate(self, test_data):
test_results = [(np.argmax(self.feedforward(x)), y) for (x, y) in test_data]
return sum(int(x == y) for (x, y) in test_results)
```
这里定义了一个 BPNeuralNetwork 类,包含了神经网络的初始化、前向传播、反向传播、训练、评估等方法。其中,sigmoid 函数和 sigmoid_prime 函数分别表示激活函数及其导数,feedforward 方法表示前向传播,train 方法表示训练,update_mini_batch 方法表示每次更新的小批量数据,backprop 方法表示反向传播,cost_derivative 方法表示误差函数的导数,evaluate 方法表示测试评估。
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