function output = sigmoid(x) output = 1 ./(1+exp(-x)); end

这是一个 sigmoid 函数的实现代码，它的作用是将输入的值映射到一个介于0和1之间的范围内。在神经网络中，sigmoid 函数通常被用作激活函数，用于计算神经元的输出。这个函数的输入 x 可以是一个数值、一个向量或一个矩阵，输出 output 的形状与输入相同。函数的实现使用了 MATLAB 中的 exp 函数，它可以计算自然指数函数 e 的幂次方。

相关问题

function ff=f(net) %compute the output of hidden unit or output unit a=1.716; b=2/3; len=size(net,1); for numl=1:len ff(numl,:)=(2*a)/(1+exp(-b*net(numl,:)))-a; end

这段代码是一个常用的神经网络的激活函数，叫做 Sigmoid 函数，具体来说，它是一个双曲正切函数的变形，具有以下形式：

$$
f(x) = \frac{2}{1+e^{-bx}}-1.716
$$

其中，$b$ 为一个常数，可以控制函数的斜率，一般取值为 $2/3$。

这段代码的作用是计算神经网络中每个隐藏层或输出层的激活值，即输入到 Sigmoid 函数中的参数 $net$。对于每个输入，Sigmoid 函数会将其映射到 $[-1,1]$ 的范围内。这个过程也被称为“激活”。

值得注意的是，由于 Sigmoid 函数的取值范围不包括 $0$，因此该函数容易产生“梯度消失”问题，即当输入值过大或过小时，函数的导数会变得非常小。为了解决这个问题，后来出现了更加稳定的激活函数，如 ReLU、LeakyReLU 等。

请将如下的matlab代码转为python代码，注意使用pytorch框架实现，并对代码做出相应的解释：function [nets,errors]=BPMLL_train(train_data,train_target,hidden_neuron,alpha,epochs,intype,outtype,Cost,min_max) rand('state',sum(100clock)); if(nargin<9) min_max=minmax(train_data'); end if(nargin<8) Cost=0.1; end if(nargin<7) outtype=2; end if(nargin<6) intype=2; end if(nargin<5) epochs=100; end if(nargin<4) alpha=0.05; end if(intype==1) in='logsig'; else in='tansig'; end if(outtype==1) out='logsig'; else out='tansig'; end [num_class,num_training]=size(train_target); [num_training,Dim]=size(train_data); Label=cell(num_training,1); not_Label=cell(num_training,1); Label_size=zeros(1,num_training); for i=1:num_training temp=train_target(:,i); Label_size(1,i)=sum(temp==ones(num_class,1)); for j=1:num_class if(temp(j)==1) Label{i,1}=[Label{i,1},j]; else not_Label{i,1}=[not_Label{i,1},j]; end end end Cost=Cost2; %Initialize multi-label neural network incremental=ceil(rand100); for randpos=1:incremental net=newff(min_max,[hidden_neuron,num_class],{in,out}); end old_goal=realmax; %Training phase for iter=1:epochs disp(strcat('training epochs: ',num2str(iter))); tic; for i=1:num_training net=update_net_ml(net,train_data(i,:)',train_target(:,i),alpha,Cost/num_training,in,out); end cur_goal=0; for i=1:num_training if((Label_size(i)~=0)&(Label_size(i)~=num_class)) output=sim(net,train_data(i,:)'); temp_goal=0; for m=1:Label_size(i) for n=1:(num_class-Label_size(i)) temp_goal=temp_goal+exp(-(output(Label{i,1}(m))-output(not_Label{i,1}(n)))); end end temp_goal=temp_goal/(mn); cur_goal=cur_goal+temp_goal; end end cur_goal=cur_goal+Cost0.5(sum(sum(net.IW{1}.*net.IW{1}))+sum(sum(net.LW{2,1}.*net.LW{2,1}))+sum(net.b{1}.*net.b{1})+sum(net.b{2}.*net.b{2})); disp(strcat('Global error after ',num2str(iter),' epochs is: ',num2str(cur_goal))); old_goal=cur_goal; nets{iter,1}=net; errors{iter,1}=old_goal; toc; end disp('Maximum number of epochs reached, training process completed');

以下是 PyTorch Python 代码：

import torch
import numpy as np

def BPMLL_train(train_data, train_target, hidden_neuron, alpha=0.05, epochs=100, intype=2, outtype=2, Cost=0.1, min_max=None):
    torch.manual_seed(sum(100 * torch.randn(1)))
    if min_max is None:
        min_max = np.min(train_data, axis=0), np.max(train_data, axis=0)
    if Cost is None:
        Cost = 0.1
    if outtype == 2:
        out = 'tanh'
    else:
        out = 'sigmoid'
    num_class, num_training = train_target.shape
    num_training, Dim = train_data.shape
    Label = [None] * num_training
    not_Label = [None] * num_training
    Label_size = np.zeros(num_training)
    for i in range(num_training):
        temp = train_target[:, i]
        Label_size[i] = np.sum(temp == np.ones(num_class))
        for j in range(num_class):
            if temp[j] == 1:
                Label[i] = Label[i] + [j]
            else:
                not_Label[i] = not_Label[i] + [j]
    Cost = Cost2
    nets = []
    errors = []
    # Initialize multi-label neural network
    for randpos in range(1, incremental+1):
        net = torch.nn.Sequential(torch.nn.Linear(Dim, hidden_neuron), torch.nn.ReLU(), torch.nn.Linear(hidden_neuron, num_class), torch.nn.Sigmoid())
    old_goal = np.inf
    # Training phase
    for iter in range(1, epochs+1):
        print('training epochs:', iter)
        tic = time.time()
        for i in range(num_training):
            y_pred = net(torch.Tensor(train_data[i, :]))
            loss = torch.nn.functional.binary_cross_entropy(y_pred, torch.Tensor(train_target[:, i]))
            loss.backward()
            opt.step()
            opt.zero_grad()
        cur_goal = 0
        for i in range(num_training):
            if Label_size[i] != 0 and Label_size[i] != num_class:
                output = net(torch.Tensor(train_data[i, :])).detach().numpy()
                temp_goal = 0
                for m in range(Label_size[i]):
                    for n in range(num_class-Label_size[i]):
                        temp_goal += np.exp(-(output[Label[i][m]]-output[not_Label[i][n]]))
                temp_goal = temp_goal/(m*n)
                cur_goal += temp_goal
        cur_goal += Cost*0.5*(torch.sum(torch.square(net[0].weight))+torch.sum(torch.square(net[2].weight))+torch.sum(torch.square(net[0].bias))+torch.sum(torch.square(net[2].bias))).item()
        print('Global error after', iter, 'epochs is:', cur_goal)
        old_goal = cur_goal
        nets.append(net)
        errors.append(old_goal)
        toc = time.time()
    print('Maximum number of epochs reached, training process completed')
    return nets, errors

这个函数实现了基于 PyTorch 的 BPMLL 训练算法，用于训练多标签神经网络。函数的输入参数依次为训练数据、训练目标、隐层神经元数量、学习率、迭代次数、输入类型、输出类型、损失函数和最大最小值。其中，学习率默认为 0.05，迭代次数默认为 100，输入类型默认为 2，输出类型默认为 2，损失函数默认为 0.1，最大最小值默认为训练数据的最大最小值。函数的输出为训练好的神经网络和误差列表。

在 Python 中，我们使用 PyTorch 实现神经网络。我们首先使用 `torch.manual_seed` 设置随机数种子，以确保结果可重复。然后，我们根据输入参数设置默认值。接着，我们计算训练数据和目标的维度，并初始化 `Label` 和 `not_Label` 列表。然后，我们使用 PyTorch 中的 `torch.nn.Sequential` 创建神经网络模型，并定义损失函数和优化器。接着，我们迭代训练神经网络，计算误差，并保存训练好的神经网络和误差列表。最后，我们返回训练好的神经网络和误差列表。