matrix weights1, weights2, weights3; // 权重矩阵
matrix output1, output2, result; // 神经层输出矩阵
input int layer1 = 200; // 第一个隐藏层的大小
input int layer2 = 200; // 第二个隐藏层的大小
input int Epochs = 20000; // 训练世代的数量
input double lr = 3e-6; // 学习率
input ENUM_ACTIVATION_FUNCTION ac_func = AF_SWISH; // 激活函数
//+------------------------------------------------------------------+
//| 脚本程序 start 函数 |
//+------------------------------------------------------------------+
void OnStart()
{
//---
int train = 1000; // 训练样本大小
int test = 10; // 测试样本大小
matrix m_data, m_target;
//--- 生成训练样本
if(!CreateData(m_data, m_target, train))
return;
//--- 训练模型
if(!Train(m_data, m_target, Epochs))
return;
//--- 生成测试样本
if(!CreateData(m_data, m_target, test))
return;
//--- 测试模型
Test(m_data, m_target);
}
//+------------------------------------------------------------------+
//| 样本生成方法 |
//+------------------------------------------------------------------+
bool CreateData(matrix &data, matrix &target, const int count)
{
//--- 初始化初始数据和结果矩阵
if(!data.Init(count, 3) || !target.Init(count, 1))
return false;
//--- 用随机值填充初始数据矩阵
data.Random(-10, 10);
//--- 计算训练样本的目标值
vector X1 = MathPow(data.Col(0) + data.Col(1) + data.Col(1), 2);
vector X2 = MathPow(data.Col(0), 2) + MathPow(data.Col(1), 2) + MathPow(data.Col(2), 2);
if(!target.Col(X1 / X2, 0))
return false;
//--- 返回结果
return true;
}
//+------------------------------------------------------------------+
//| 模型训练方法 |
//+------------------------------------------------------------------+
bool Train(matrix &data, matrix &target, const int epochs = 10000)
{
//--- 创建模型
if(!CreateNet())
return false;
//--- 训练模型
for(int ep = 0; ep < epochs; ep++)
{
//--- 前向验算
if(!FeedForward(data))
return false;
PrintFormat("Epoch %d, loss %.5f", ep, result.Loss(target, LOSS_MSE));
//--- 权重矩阵的反向传播与更新
if(!Backprop(data, target))
return false;
}
//--- 返回结果
return true;
}
//+------------------------------------------------------------------+
//| 模型创建方法 |
//+------------------------------------------------------------------+
bool CreateNet()
{
//--- 初始化权重矩阵
if(!weights1.Init(4, layer1) || !weights2.Init(layer1 + 1, layer2) || !weights3.Init(layer2 + 1, 1))
return false;
//--- 用随机值填充权重矩阵
weights1.Random(-0.1, 0.1);
weights2.Random(-0.1, 0.1);
weights3.Random(-0.1, 0.1);
//--- 返回结果
return true;
}
//+------------------------------------------------------------------+
//| 前向验算方法 |
//+------------------------------------------------------------------+
bool FeedForward(matrix &data)
{
//--- 检查初始数据大小
if(data.Cols() != weights1.Rows() - 1)
return false;
//--- 计算第一个神经层
matrix temp = data;
if(!temp.Resize(temp.Rows(), weights1.Rows()) ||
!temp.Col(vector::Ones(temp.Rows()), weights1.Rows() - 1))
return false;
output1 = temp.MatMul(weights1);
//--- 计算激活函数
if(!output1.Activation(temp, ac_func))
return false;
//--- 计算第二个神经层
if(!temp.Resize(temp.Rows(), weights2.Rows()) ||
!temp.Col(vector::Ones(temp.Rows()), weights2.Rows() - 1))
return false;
output2 = temp.MatMul(weights2);
//--- 计算激活函数
if(!output2.Activation(temp, ac_func))
return false;
//--- 计算第三个神经层
if(!temp.Resize(temp.Rows(), weights3.Rows()) ||
!temp.Col(vector::Ones(temp.Rows()), weights3.Rows() - 1))
return false;
result = temp.MatMul(weights3);
//--- 返回结果
return true;
}
//+------------------------------------------------------------------+
//| 反向传播法 |
//+------------------------------------------------------------------+
bool Backprop(matrix &data, matrix &target)
{
//--- 检查目标值矩阵的大小
if(target.Rows() != result.Rows() ||
target.Cols() != result.Cols())
return false;
//--- 检测计算值与目标的偏差
matrix loss = (target - result) * 2;
//--- 将梯度传播到上一层
matrix gradient = loss.MatMul(weights3.Transpose());
//--- 更新最后一层的权重矩阵
matrix temp;
if(!output2.Activation(temp, ac_func))
return false;
if(!temp.Resize(temp.Rows(), weights3.Rows()) ||
!temp.Col(vector::Ones(temp.Rows()), weights3.Rows() - 1))
return false;
weights3 = weights3 + temp.Transpose().MatMul(loss) * lr;
//--- 依据激活函数的导数调整误差梯度
if(!output2.Derivative(temp, ac_func))
return false;
if(!gradient.Resize(gradient.Rows(), gradient.Cols() - 1))
return false;
loss = gradient * temp;
//--- 将梯度传播到更低一层
gradient = loss.MatMul(weights2.Transpose());
//--- 更新第二隐藏层的权重矩阵
if(!output1.Activation(temp, ac_func))
return false;
if(!temp.Resize(temp.Rows(), weights2.Rows()) ||
!temp.Col(vector::Ones(temp.Rows()), weights2.Rows() - 1))
return false;
weights2 = weights2 + temp.Transpose().MatMul(loss) * lr;
//--- 依据激活函数的导数调整误差梯度
if(!output1.Derivative(temp, ac_func))
return false;
if(!gradient.Resize(gradient.Rows(), gradient.Cols() - 1))
return false;
loss = gradient * temp;
//--- 更新第一隐藏层的权重矩阵
temp = data;
if(!temp.Resize(temp.Rows(), weights1.Rows()) ||
!temp.Col(vector::Ones(temp.Rows()), weights1.Rows() - 1))
return false;
weights1 = weights1 + temp.Transpose().MatMul(loss) * lr;
//--- 返回结果
return true;
}
//+------------------------------------------------------------------+
//| 模型测试方法 |
//+------------------------------------------------------------------+
bool Test(matrix &data, matrix &target)
{
//--- 前向测试数据
if(!FeedForward(data))
return false;
//--- 记录模型计算结果和真实值
PrintFormat("Test loss %.5f", result.Loss(target, LOSS_MSE));
ulong total = data.Rows();
for(ulong i = 0; i < total; i++)
PrintFormat("(%.2f + %.2f + %.2f)^2 / (%.2f^2 + %.2f^2 + %.2f^2) = Net %.2f, Target %.2f", data[i, 0], data[i, 1], data[i, 2],
data[i, 0], data[i, 1], data[i, 2], result[i, 0], target[i, 0]);
//--- 返回结果
return true;
}
//+------------------------------------------------------------------+
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