RBM代码注释c++

这代码各种看不懂，各种给跪，当工具用吧。。

主函数：

main.cpp

  1 #include "rbmpredictdata.h"
  2 #include "rbmdata.h"
  3 #include "rbm.h"
  4 #include "rbmparallel.h"
  5 #include <fstream>
  6 #include <string>
  7 #include <cstdlib>
  8 #include <deque>
  9 
 10 int main(int argc, char* argv[]) {
 11     parseArgs(argc, argv);   //第1步、这一步取得三个值 Hidden层数、trainfilename、testfilename
 12     srand(seed);
 13     printConfig();                  //第2步、打印初始化的数据
 14 
 15     RbmPredictData predictData;     //构造出对象
 16     safeLoad(predictData, testFilename);    //第3步、预测数据化成矩阵形式
 17     cout << "Done loading test data" << flush;
 18 
 19     RbmData data;
 20     safeLoad(data, trainFilename);            //步骤和第3步完全一样，这是训练集
 21     cout << "\rDone loading data.     " << endl;
 22 
 23     Rbm* r = NULL; 
 24     if (parallel) 
 25         r = new RbmParallel(nThreads, data, nHidden);   
 26     else
 27         r = new Rbm(data, nHidden);          //第4步、构造rbm，初始化各种W，hb，vb。查看rbm.cpp
 28     r->momentum = initialMomentum;
 29     r->hBiasLearnRate = hLearn;
 30     r->vBiasLearnRate = vLearn;
 31     r->WlearnRate = wLearn;
 32     r->weightDecay = wCost;
 33 
 34     for (int i = 1; i <= nEpochs; i++) {
 35         int increment = extractIncrements(i);    //浮云
 36         if (increment) {
 37             r->T += increment;
 38             cout << "\tT = " << r->T << endl;
 39         }
 40         if (i == finalMomentumStart)
 41             r->momentum = finalMomentum;
 42 
 43         r->performEpoch(data);        //第5步、最关键的步骤，查看rbm.cpp
 44 
 45         if (!epochsToSaveAt.empty() && epochsToSaveAt.front() == i) {
 46             epochsToSaveAt.pop_front();
 47             stringstream t;
 48             t << savePrefix << i;
 49             double d = r->predict(data, predictData, t.str());
 50             cout << i << ": saving to " << t.str() << "(" << d << ")" << endl;
 51         } else if (predictAlways) {
 52             double d = r->predict(data, predictData);            //第6步、预测，查看rbm.cpp
 53             cout << i << ": " << d << endl;
 54         } else {
 55             cout << i << ": omitting prediction" << endl;
 56         }
 57     }
 58 
 59     return 0;
 60 }
 61 
 62 //第1步、取参数
 63 void parseArgs(int argc, char* argv[]) {
 64     int current = 1;
 65     // TODO: make more user friendly in terms of error handling.
 66     //       and coding style leaves something to be desired...
 67     while (current < argc) {
 68         if (strcmp("-h", argv[current]) == 0) {
 69             printf(helpString, argv[0]);
 70             exit(0);
 71         } else if (strcmp("-d", argv[current]) == 0) {
 72             cout << "Defaults: " << endl;
 73             printConfig();
 74             exit(0);
 75         } else if (strcmp("-v", argv[current]) == 0) {
 76             vLearn = atof(argv[current + 1]);
 77             current += 1;
 78         } else if (strcmp("-H", argv[current]) == 0) {
 79             hLearn = atof(argv[current + 1]);
 80             current += 1;
 81         } else if (strcmp("-w", argv[current]) == 0) {
 82             wLearn = atof(argv[current + 1]);
 83             current += 1;
 84         } else if (strcmp("-n", argv[current]) == 0) {
 85             nHidden = atoi(argv[current + 1]);
 86             current += 1;
 87         } else if (strcmp("-i", argv[current]) == 0) {
 88             initialMomentum = atof(argv[current + 1]);
 89             current += 1;
 90         } else if (strcmp("-m", argv[current]) == 0) {
 91             finalMomentum = atof(argv[current + 1]);
 92             finalMomentumStart = atoi(argv[current + 2]);
 93             current += 2;
 94         } else if (strcmp("-e", argv[current]) == 0) {
 95             nEpochs = atoi(argv[current + 1]);
 96             current += 1;
 97         } else if (strcmp("-c", argv[current]) == 0) {
 98             wCost = atof(argv[current + 1]);
 99             current += 1;
100         } else if (strcmp("-t", argv[current]) == 0) {
101             do {
102                 current += 1;
103                 tIncrements.push_back(atoi(argv[current]));
104             } while (current + 1 < argc && 
105                     '0' <= argv[current + 1][0] && argv[current + 1][0] <= '9');
106         } else if (strcmp("-s", argv[current]) == 0) {
107             current += 1;
108             seed = atoi(argv[current]);
109         } else if (strcmp("--save", argv[current]) == 0) {
110             current += 1;
111             savePrefix = argv[current];
112             do {
113                 current += 1;
114                 epochsToSaveAt.push_back(atoi(argv[current]));
115             } while (current + 1 < argc && 
116                     '0' <= argv[current + 1][0] && argv[current + 1][0] <= '9');
117         } else if (strcmp("--never", argv[current]) == 0) {
118             predictAlways = false;
119         } else if (argc - current == 2) {
120             trainFilename = argv[current];
121         } else if (argc - current == 1) {
122             testFilename = argv[current];
123         } else {
124             cerr << "ERROR: Unknown option: " << argv[current] << endl
125                  << "Exiting now." << endl;
126             exit(1);
127         }
128         current += 1;
129     }
130 }
131 
132 //第2步、打印参数
133 void printConfig() {
134     cout << "Learning rates:" << endl
135          << "  visible        " << vLearn << endl
136          << "  hidden         " << hLearn << endl
137          << "  weights        " << wLearn << endl
138          << "  cost           " << wCost << endl;
139     cout << "Hidden nodes:    " << nHidden << endl;
140     if (initialMomentum != 0.0 && finalMomentum != 0.0) {
141         cout << "Momentum:        " << endl
142              << "  initial        " << initialMomentum << endl
143              << "  final          " << finalMomentum << endl
144              << "  start          " << finalMomentumStart << endl;
145     }
146     if (tIncrements.size() > 0) {
147         cout << "T-increment on:  ";
148         for (unsigned i = 0; i < tIncrements.size(); i++) {
149             cout << tIncrements[i] << ' ';
150         }
151         cout << endl;
152     }
153     if (epochsToSaveAt.size() > 0) {
154         cout << "Saving at epochs:";
155         for (unsigned i = 0; i < epochsToSaveAt.size(); i++) {
156             cout << epochsToSaveAt[i] << ' ';
157         }
158         cout << endl;
159         cout << "Save prefix:     " << savePrefix << endl;
160     }
161     cout << "Datasets:      " << endl
162          << "  train          " << trainFilename << endl
163          << "  test           " << testFilename << endl;
164     cout << "Epochs:          " << nEpochs << endl;
165     cout << "Random seed:     " << seed << endl;
166     cout << "Predict always:  " << (predictAlways? "yes" : "no") << endl;
167     cout << endl;
168 }
169 
170 //第3步、这会调用rbmpredictdata.cpp的safeLoad函数，步骤3.1。
171 void safeLoad(RbmData& p, const string& fname) {
172     ifstream f(fname.c_str());
173     if (!f) {
174         cerr << "ERROR: " << fname << " could not be opened." << endl;
175         cerr << "Exiting now." << endl;
176         exit(1);
177     }
178     p.loadTsv(f);
179     f.close();
180 }
181 
182 char helpString[] =
183     "Usage: %s [arguments] <trainfile> <testfile>\n"
184     "\n"
185     "Arguments:\n"
186     "  -h                    Print Help (this message) and exit\n"
187     "  -v <float>            Set visible bias learning rate to <float>\n"
188     "  -H <float>            Set hidden bias learning rate to <float>\n"
189     "  -w <float>            Set weight learning rate to <float>\n"
190     "  -c <float>            Set weight-cost coefficient to <float>\n"
191     "  -n <uint>             Use <uint> hidden nodes\n"
192     "  -i <float>            Set initial momentum to <float>\n"
193     "  -m <float> <uint>     Set final momentum to <float> at epoch <uint>\n"
194     "  -e <uint>             Perform <uint> epochs\n"
195     "  -t <uint> [<uint>...] Increase T by one at epoch <uint>, <uint> ...\n"
196     "  -d                    Print the defaults and exit\n"
197     "  -s <uint>             Set the random seed to <uint>\n"
198     "  --save <string>       Save the predictions of the model after epoch\n"
199     "         <uint> [...]        <uint> to file: <string>+<uint>.dat\n"
200     "  --never               Do not predict, unless specified to save.\n"
201     "\n"
202     "Example usage:\n"
203     "  ./rbm -t 5 5 7 train.dat test.dat\n"
204     "     Set T to 3 at epoch 5, and to 4 at epoch 7.\n"
205     "  ./rbm --never --save mypredfile 10 20 train.dat test.dat\n"
206     "     Generates two files: mypredfile10.dat and mypredfile20.dat\n";
207 
208 string trainFilename, testFilename, savePrefix;
209 float vLearn = 0.005, hLearn = 0.005, wLearn = 0.005, wCost = 0.005;
210 int nHidden = 100, nEpochs = 40;
211 float finalMomentum = 0.0, initialMomentum = 0.0;
212 int finalMomentumStart = 5;
213 deque<int> tIncrements;
214 deque<int> epochsToSaveAt;
215 int seed = 1;
216 bool predictAlways = true;
217 bool parallel = false;
218 int nThreads = 32;
219 
220 int extractIncrements(int i) {
221     int increment = 0;
222     while (tIncrements.size() != 0 && tIncrements.front() == i) {
223         increment += 1;
224         tIncrements.pop_front();
225     }
226     return increment;
227 }

大头来了

rbm.h

 1 #ifndef RBM_H
 2 #define RBM_H
 3 
 4 #include "rbmdata.h"
 5 #include "rbmpredictdata.h"
 6 #include <Eigen/Dense>
 7 #include <vector>
 8 #include <thread>
 9 
10 using namespace Eigen;
11 using namespace std;
12 
13 typedef Matrix<bool, 1, Dynamic> RowVectorXb;
14 
15 class Rbm {
16 public:
17     Rbm(const RbmData& data, int nHidden);
18 
19     virtual void performEpoch(const RbmData& data);
20 
21     virtual double predict(
22             const RbmData& data, 
23             const RbmPredictData& predictData, 
24             const string& filename);
25 
26     virtual double predict(
27             const RbmData& data,
28             const RbmPredictData& predictData);
29 
30     virtual double predict(
31             const RbmData& data,
32             const RbmPredictData& predictData,
33             ostream& predictStream);
34 
35     static float hBiasLearnRate;
36     static float vBiasLearnRate;
37     static float WlearnRate;
38     static float weightDecay;
39     static float momentum;
40     static int T;
41 private:
42     Rbm();
43 
44     void negActivation(const RowVectorXf& h0states);
45 
46     void gibbsSample();
47 
48     void normalizedNegActivation(const RowVectorXf& h0states);
49     void softmax(const RowVectorXf& h0states);
50 
51     void initVisibleBias(const RbmData& data);
52 
53     void applyMomentum(const RbmData& data, int user);
54     void selectWeights(const RbmData& data, int rangeStart, int rangeEnd);
55 
56 public: // These are public so RbmParallel can use them
57     MatrixXf W, Wsel, Wmomentum;
58     RowVectorXf vBias, vBiasSel, vBiasMomentum, hBias, hBiasMomentum;
59 
60     void performEpoch(const RbmData& data, int userStart, int userEnd);
61 
62 private:
63     RowVectorXf h0probs, hTProbs;
64     RowVectorXb h0states;
65 
66     RowVectorXf negData;
67 
68     MatrixXf posProds, negProds;
69 
70     int nHidden;
71     int nClasses;
72 };
73 
74 #endif

rbm.cpp

  1 #include "rbm.h"
  2 #include <iomanip>
  3 #include <numeric>
  4 #include <thread>
  5 #include <cmath>
  6 #include <fstream>
  7 
  8 float Rbm::hBiasLearnRate = 0.001;
  9 float Rbm::vBiasLearnRate = 0.008;
 10 float Rbm::WlearnRate = 0.0006;
 11 float Rbm::weightDecay = 0.0001;
 12 float Rbm::momentum = 0.5;
 13 int Rbm::T = 1;
 14 
 15 
 16 //第4步、初始化w，hb，vb
 17 //W = N(movie) * K(评分类数) * M(隐层节点数)
 18 //vb = N(movie) * K(评分类数)
 19 //hb = M(隐层节点数)
 20 Rbm::Rbm(const RbmData& data, int nHidden) 
 21         : nHidden(nHidden), nClasses(data.nClasses)
 22 {
 23     W.setRandom(data.nMovies * nClasses, nHidden);
 24     W.array() *= 0.01;
 25     vBias.setZero(data.nMovies * nClasses);
 26     initVisibleBias(data);                    //可见层的bias初始化。
 27     hBias.setZero(nHidden);
 28 }
 29 
 30 
 31 //4.1所建立的movies和ratings根据用户id进行匹配
 32 
 33 void Rbm::initVisibleBias(const RbmData& data) {
 34     MatrixXi totals = MatrixXi::Zero(1, data.nMovies);
 35     int nUsers = data.range.size() - 1;
 36     for (int i = 0; i < nUsers; i++) {
 37         
 38 //segment根据data.range(i), data.range(i + 1)也就是每行的userid数建立矩阵        
 39         const auto& movies = data.movies.segment(
 40                 data.range(i), data.range(i + 1) - data.range(i));
 41         const auto& ratings = data.ratings.segment(
 42                 data.range(i), data.range(i + 1) - data.range(i));
 43                 
 44 //表示userid=0有多少个 1有多少。。。且和每行的movies、ratings相等                
 45         int amountOfRatings = data.range(i + 1) - data.range(i);     
 46         for (int r = 0; r < amountOfRatings; r++) {
 47             vBias(movies(r)) += ratings(r);
 48             int exactMovie = movies(r) / nClasses;
 49             totals(exactMovie) += ratings(r);
 50         }
 51     }
 52     for (int m = 0; m < totals.size(); m++) {
 53         for (int c = 0; c < nClasses; c++) {
 54             if (vBias(m * nClasses + c) != 0) {
 55                 vBias(m * nClasses + c) /= totals(m);
 56                 vBias(m * nClasses + c) = 
 57                     log(vBias(m * nClasses + c));
 58             }
 59         }
 60     }
 61 }
 62 
 63 
 64 //第5步、坑爹的又调用下面的
 65 void Rbm::performEpoch(const RbmData& data) {
 66     performEpoch(data, 0, data.range.size() - 1);
 67 }
 68 
 69 //第5.1步、开刀
 70 void Rbm::performEpoch(const RbmData& data, int userStart, int userEnd) {
 71     vector<int> randomizedIds(userEnd - userStart, 0);       //定义了End-Start个0元素
 72     for (int i = userStart; i < userEnd; i++) 
 73         randomizedIds[i - userStart] = i;                                            //根据传进来的值知道这个相当是userid个数
 74     random_shuffle(randomizedIds.begin(), randomizedIds.end());    //打乱顺序
 75 
 76     for (unsigned i = 0; i < randomizedIds.size(); i++) {
 77         int rangeStart = data.range(randomizedIds[i]);
 78         int rangeEnd = data.range(randomizedIds[i] + 1); // end is exclusive
 79         int rangeLength = rangeEnd - rangeStart;                //用户id为i的那一行有几个电影评分了*5；
 80         
 81         selectWeights(data, rangeStart, rangeEnd);            //寻找和userid匹配的W
 82         const auto& visData = data.ratings.segment(rangeStart, rangeLength);   //这个userid矩阵化
 83 
 84         h0probs = 1 / (1 + (-visData*Wsel - hBias).array().exp());        //h0
 85         h0states = h0probs.array() > 
 86             (h0probs.Random(h0probs.size()).array() + 1) / 2;           //？
 87         negActivation(h0states.cast<float>());                                                    //？
 88 
 89         hTProbs = 1 / (1 + (-negData*Wsel - hBias).array().exp());      //h1
 90         for (int t = 1; t < T; t++)
 91             gibbsSample();                                                                                            //gibbs
 92 
 93         posProds.noalias() = visData.transpose() * h0probs;
 94         negProds.noalias() = negData.transpose() * hTProbs; 
 95 
 96         if (i > 0)
 97             applyMomentum(data, randomizedIds[i - 1]);                        //userid>0
 98 
 99 
100 //下面各种更新参数
101         hBiasMomentum.noalias() = hBiasLearnRate * (h0probs - hTProbs);
102         hBias.noalias() += hBiasMomentum;
103         vBiasMomentum.noalias() = vBiasLearnRate * (visData - negData);
104         for (int r = rangeStart; r < rangeEnd; r++)
105             vBias(data.movies(r)) += vBiasMomentum(r - rangeStart);
106 
107         Wmomentum.noalias() = posProds - negProds;
108         for (int r = 0; r < rangeLength; r++)
109             W.row(data.movies(r + rangeStart)).noalias() += 
110                 WlearnRate * (Wmomentum.row(r) - weightDecay*Wsel.row(r));
111     }
112 }
113 
114 void Rbm::negActivation(const RowVectorXf& h0states) {
115     softmax(h0states);
116 }
117 
118 void Rbm::gibbsSample() {
119     h0states = 
120         hTProbs.array() > (hTProbs.Random(hTProbs.size()).array() + 1) / 2;
121     negActivation(h0states.cast<float>());
122     hTProbs = 1 / (1 + (-negData*Wsel - hBias).array().exp());
123 }
124 
125 void Rbm::normalizedNegActivation(const RowVectorXf& h0states) {
126     softmax(h0states);
127 }
128 
129 void Rbm::softmax(const RowVectorXf& h0states) {
130     negData = (h0states*Wsel.transpose() + vBiasSel);
131     for (int m = 0; m < negData.size(); m += nClasses) {
132         negData.segment(m, nClasses).array() -=
133             negData.segment(m, nClasses).maxCoeff();           //userid=i那行减去其最大值
134     }
135     negData.array() = negData.array().exp();
136     for (int m = 0; m < negData.size(); m += nClasses) {
137         negData.segment(m, nClasses).array() /=
138             negData.segment(m, nClasses).sum();                     //userid=i那行减去其最大值，不知何用意?
139     }
140 }
141 
142 void Rbm::selectWeights(const RbmData& data, int rangeStart, int rangeEnd) {
143     int rangeLength = rangeEnd - rangeStart;
144     Wsel.resize(rangeLength, nHidden);
145     vBiasSel.resize(rangeLength);
146     for (int r = rangeStart; r < rangeEnd; r++) {
147         Wsel.row(r - rangeStart).noalias() = W.row(data.movies(r));
148         vBiasSel(r - rangeStart) = vBias(data.movies(r));
149     }
150 }
151 
152 void Rbm::applyMomentum(const RbmData& data, int user) {
153     if (momentum == 0.0) return;
154     int rangeStart = data.range(user);
155     int rangeEnd = data.range(user + 1); // end is exclusive
156     int rangeLength = rangeEnd - rangeStart;
157 
158     hBias.noalias() += momentum * hBiasMomentum;
159     for (int r = rangeStart; r < rangeEnd; r++)
160         vBias(data.movies(r)) += momentum * vBiasMomentum(r - rangeStart);
161 
162     for (int r = 0; r < rangeLength; r++) {
163         W.row(data.movies(r + rangeStart)).noalias() += 
164             momentum * Wmomentum.row(r);
165     }
166 }
167 
168 double Rbm::predict(const RbmData& data, const RbmPredictData& predictData,
169         const string& fname) {
170     ofstream out(fname.c_str());
171     double d = predict(data, predictData, out);
172     out.close();
173     return d;
174 }
175 
176 //第6步、又特么调用下面的
177 double Rbm::predict(const RbmData& data, const RbmPredictData& predictData) {
178     stringstream dontcare;        //输入流，传入参数和目标对象类型自动推导
179     return predict(data, predictData, dontcare);
180 }
181 
182 //第6.1步。主要思想如下
183 //由之前训练重构的数据和预测数据相减算rmse
184 double Rbm::predict(const RbmData& data, const RbmPredictData& predictData,
185         ostream& predictStream) {
186     double rmse = 0.0;
187     int predictCount = 0;
188     for (unsigned i = 0; i < predictData.userIds.size(); i++) {
189         int userId = predictData.userIds[i];
190         int rangeStart = data.range(userId);
191         int rangeEnd = data.range(userId + 1); // end is exclusive
192         selectWeights(data, rangeStart, rangeEnd);
193         const auto& visData = 
194             data.ratings.segment(rangeStart, rangeEnd - rangeStart);
195         h0probs = 1 / (1 + (-visData*Wsel - hBias).array().exp());       //这里又不知道在干嘛。
196 
197         rangeStart = predictData.range(i);
198         rangeEnd = predictData.range(i + 1);
199         selectWeights(predictData, rangeStart, rangeEnd);
200         normalizedNegActivation(h0probs);
201         const auto& actualData = 
202             predictData.ratings.segment(rangeStart, rangeEnd - rangeStart);    //预测集ratings矩阵化
203 
204         for (int r = 0; r < actualData.size(); r += nClasses) {
205             float actual = 0;
206             float predicted = 0;
207             for (int c = 0; c < nClasses; c++) {
208                 actual += actualData(r + c) * (c + 1);          //把5维的0 1 转化成评分数1~k
209                 predicted += negData(r + c) * (c + 1);                
210             }
211             predictStream << predicted << endl;
212             float t = actual - predicted;
213             rmse += t * t;
214         }
215         predictCount += actualData.size() / nClasses;
216     }
217     return sqrt(rmse / predictCount);
218 }

rbmparallel.h

 1 #ifndef RBM_PARALLEL_H
 2 #define RBM_PARALLEL_H
 3 #include "rbm.h"
 4 #include "rbmdata.h"
 5 
 6 class RbmParallel : public Rbm {
 7 public:
 8     RbmParallel(int nThreads, const RbmData& data, int nHidden);
 9 
10     void performEpoch(const RbmData& data);
11 
12 private:
13     RbmParallel();
14 
15     void startEpochs(const RbmData& data, int batchStart, int batchSize);
16     void joinExecution();
17     void updateWeights();
18     void synchronizeWeights();
19 
20     static void performEpochInThread(
21             Rbm& r, const RbmData& data, int userStart, int userEnd);
22 
23     int nThreads;
24     int nUsers;
25     vector<Rbm> subRbms;
26     vector<thread> threads;
27 };
28 
29 #endif

rbmparallel.cpp

 1 #include "rbmparallel.h"
 2 
 3 RbmParallel::RbmParallel(int nThreads, const RbmData& data, int nHidden) : 
 4     Rbm(data, nHidden), 
 5     nThreads(nThreads), 
 6     nUsers(data.range.size() - 1),
 7     subRbms(nThreads - 1, Rbm(data, nHidden))
 8 {
 9     synchronizeWeights();
10 }
11 
12 void RbmParallel::performEpoch(const RbmData& data) {
13     int batchSize = nUsers;
14     for (int batchStart = 0; batchStart < nUsers; batchStart += batchSize) {
15         startEpochs(data, batchStart, batchSize);
16         joinExecution();
17         updateWeights();
18     }
19 }
20 
21 void RbmParallel::startEpochs(
22         const RbmData& data, int batchStart, int batchSize) {
23     threads.clear();
24     int usersPerStep = batchSize / nThreads;
25     int userStart = batchStart;
26     for (int i = 0; i < nThreads - 1; i++) {
27         threads.push_back(
28                 thread(&RbmParallel::performEpochInThread, 
29                     ref(subRbms[i]), ref(data), 
30                     userStart, userStart + usersPerStep));
31         userStart += usersPerStep;
32     }
33     Rbm::performEpoch(data, userStart, nUsers);
34 }
35 
36 void RbmParallel::performEpochInThread(
37         Rbm& r, const RbmData& data, int userStart, int userEnd) {
38     r.performEpoch(data, userStart, userEnd);
39 }
40 
41 void RbmParallel::joinExecution() {
42     for (auto it = threads.begin(); it != threads.end(); it++) {
43         it->join();
44     }
45 }
46 
47 void RbmParallel::updateWeights() {
48     float updateFactor = 1.0 / nThreads;
49     W *= updateFactor;
50     vBias *= updateFactor;
51     hBias *= updateFactor;
52     for (auto it = subRbms.begin(); it != subRbms.end(); it++) {
53         W += it->W * updateFactor;
54         vBias += it->vBias * updateFactor;
55         hBias += it->hBias * updateFactor;
56     }
57     synchronizeWeights();
58 }
59 
60 void RbmParallel::synchronizeWeights() {
61     for (auto it = subRbms.begin(); it != subRbms.end(); it++) {
62         it->W = W;
63         it->hBias = hBias;
64         it->vBias = vBias;
65     }
66 }

基础太差，看了一个星期，还是看不懂，伤不起。