Fast Training Algorithms for Deep Convolutional Fuzzy Systems With Application to Stock Index Prediction论文及代码
类似深度卷积神经网络DCNN，模糊系统领域有个深度卷积模糊系统 deep convolutional fuzzy system (DCFS)，每一层都是一个模糊系统，上一层的输出是下一层的输入。
这篇论文目的是加速DCFS的计算速度，解决可解释性
1990年提出，也用反向传播训练
DCFS受困于低维度小数据集，大数据量时计算负担太重。模糊系统的参数有物理意义，用Wang–Mendel加速计算（作者的成名作）。
Section II, 介绍DCFS结构细节
输入高维，输出标量(每层都是标量，最终也是个标量) （多输出的DCFS可能设计成多个单输出的DCFS）
低维输入（x）通过卷积窗口(长为m，比如3,4或5)挑选给集合（比如挑3个x进入I,I里有三个输入），I再输入给FS
输入进入FS后，FS中有q个模糊集和对应的隶属函数A，还有模糊规则if then，如果输入x得到对应的A，那A经过if then 得到最终输出y，FC的唯一的系数c就是要训练的
所以对DCFS的解释就是：输入x1,x2，x3等等，得到一个系数c，每个FC都能看作一个系统，这样就能轻松排查问题（讲完第三部分会具体讲怎么排查）
作者给出了FS的计算公式
降低DCFS计算量和存储量的方法是参数共享，同一层的FS完全相同。
Section III, DCFS的四种训练算法
如何离线训练DCFS，让输入输出对能匹配上。
隶属函数A要根据所有输入对的所有x的最值设置，以确保能包住
离线训练时参数共享咋用 共享的方式没原始方法准确率高
如何在线训练DCFS
在线训练时参数共享咋用 在线训练也是共享方法不行
Section IV, 用DCFS模型和它的训练算法取预测股票指数
下一刻预测值r(t)，当前时刻是t-1，过去的值是r(t-1)，r(t-2)...r(t-n)，用过去这n个值，代入DCFS，预测r(t) 这就是输入输出对
过去的r就是过去每天的收盘价。
训练集共3000个数据，前2000训练，后1000预测
每次放11个值进DCFS，3个组成一个I给FS，DCFS共5层，每层FS个数分别为9（11-3,11个数分成9组了）、7、5、3、1
我们尝试不同的模糊集个数，发现20个模糊集用Wang–Mendel算法速度快，错误率低，而用反向传播算法慢10倍，错误率高20%
用恒生指数发现q=10效果最好，但整体更难预测
交易策略：DCFS预测的r(t)>0，说明明天要涨，今天t-1买。 小于0则卖
作者说的两个value我用不着，是用来预测指数实际值和指数净值的
为了优化策略，创建了个两层网络，用一个指数和4个权重股，一起输入给顶层FS做预测
训练算法的代码MATLAB实现了
1 import numpy as np 2 import pickle 3 import matplotlib.pyplot as plt 4 5 6 # 定义 meb2 函数，用于计算隶属度 7 def meb2(n, i, x, xmin, xmax): 8 h = (xmax - xmin) / (n - 1) 9 res = 0 10 11 if i == 1: 12 if x < xmin: 13 res = 1 14 elif xmin <= x < xmin + h: 15 res = (xmin - x + h) / h 16 elif x >= xmin + h: 17 res = 0 18 elif 1 < i < n: 19 if x < xmin + (i - 2) * h or x > xmin + i * h: 20 res = 0 21 elif xmin + (i - 2) * h <= x < xmin + (i - 1) * h: 22 res = (x - xmin - (i - 2) * h) / h 23 elif xmin + (i - 1) * h <= x < xmin + i * h: 24 res = (-x + xmin + i * h) / h 25 elif i == n: 26 if x < xmax - h: 27 res = 0 28 elif xmax - h <= x < xmax: 29 res = (-xmax + x + h) / h 30 elif x >= xmax: 31 res = 1 32 33 return res 34 35 36 def wmdeepyy(mm, zb, ranges, xx): 37 # 计算模糊系统输出 38 numSamples, m = xx.shape 39 numInput = m 40 fnCounts = np.full(numInput, mm) 41 activFns = np.zeros((numInput, 2), dtype=int) 42 activGrades = np.zeros((numInput, 2)) 43 baseCount = np.zeros(numInput + 1, dtype=int) 44 baseCount[0] = 1 45 ma = np.zeros((2 ** numInput, numInput), dtype=int) 46 47 for i in range(1, numInput): 48 baseCount[i] = np.prod(fnCounts[numInput - i:numInput]) # 计算所有元素的乘积 49 50 for j in range(numInput): 51 for i1 in range(1, 2 ** (j + 1)): 52 for i2 in range(1, 2 ** (numInput - j) + 1): 53 ma[i2 + (i1 - 1) * 2 ** (numInput - j), j] = (i1 - 1) % 2 + 1 54 55 yy = np.zeros(numSamples) 56 for k in range(numSamples): 57 for i in range(numInput): 58 numFns = fnCounts[i] 59 nthActive = 0 60 for nthFn in range(1, numFns + 1): 61 grade = meb2(numFns, nthFn, xx[k, i], ranges[i, 0], ranges[i, 1]) 62 if grade > 0: 63 activFns[i, nthActive] = nthFn 64 activGrades[i, nthActive] = grade 65 nthActive += 1 66 67 for i in range(numInput): 68 nn = np.zeros(2, dtype=int) 69 nn[0] = activFns[i, 0] 70 nn[1] = nn[0] + 1 71 if nn[0] == fnCounts[i]: 72 nn[1] = nn[0] 73 74 a, b = 0, 0 75 for i in range(1, 2 ** numInput + 1): 76 indexcell = 1 77 grade = 1 78 for j in range(numInput): 79 grade *= activGrades[j, ma[i - 1, j]] 80 indexcell += (nn[numInput - j, ma[i - 1, numInput - j]] - 1) * baseCount[j] 81 a += zb[indexcell - 1] * grade 82 b += grade 83 84 yy[k] = a / b 85 86 return yy 87 88 89 def wmdeepzb(mm, xx, y): 90 extra = np.concatenate((xx, y.reshape(-1, 1)), axis=1) 91 num_samples, m = extra.shape 92 num_input = m - 1 93 fn_counts = np.full(num_input, mm, dtype=int) 94 ranges = np.zeros((num_input, 2)) 95 activ_fns = np.zeros((num_input, 2), dtype=int) 96 activ_grades = np.zeros((num_input, 2)) 97 search_path = np.zeros((num_input, 2), dtype=int) 98 num_cells = 1 # number of regions (cells) 99 100 # Calculate ranges and numCells 101 for i in range(num_input): 102 ranges[i] = [np.min(extra[:, i]), np.max(extra[:, i])] 103 num_cells *= fn_counts[i] 104 105 base_count = np.cumprod(fn_counts[::-1])[::-1] 106 base_count = base_count - 1 107 zb = np.zeros(num_cells) 108 ym = np.zeros(num_cells) 109 110 # Generate rules for cells covered by data 111 for k in range(num_samples): 112 for i in range(num_input): 113 num_fns = fn_counts[i] 114 nth_active = 0 115 for nth_fn in range(1, num_fns + 1): 116 grade = meb2(num_fns, nth_fn, extra[k, i], ranges[i][0], ranges[i][1]) 117 if grade > 0: 118 activ_fns[i, nth_active] = nth_fn 119 activ_grades[i, nth_active] = grade 120 nth_active += 1 121 122 for i in range(num_input): 123 if activ_grades[i, 0] >= activ_grades[i, 1]: 124 search_path[i] = [activ_fns[i, 0], activ_grades[i, 0]] 125 else: 126 search_path[i] = [activ_fns[i, 1], activ_grades[i, 1]] 127 128 index_cell = 1 129 grade = 1 130 for i in range(num_input): 131 grade *= search_path[i][1] 132 index_cell += (search_path[num_input - i - 1][0] - 1) * base_count[i] 133 134 if 0 <= int(index_cell) < len(ym): 135 ym[int(index_cell)] += grade 136 zb[int(index_cell)] += extra[k, -1] * grade 137 else: 138 print(f"Warning: index_cell value {index_cell} is out of bounds.") 139 140 141 # Normalize zb 142 for j in range(num_cells): 143 if ym[j] != 0: 144 zb[j] /= ym[j] 145 146 # Extrapolate the rules to all the cells 147 zbb = np.zeros(num_cells) 148 ymm = np.zeros(num_cells) 149 ct = 1 150 while ct > 0: 151 ct = 0 152 for s in range(num_cells): 153 if ym[s] == 0: 154 ct += 1 155 156 for s in range(num_cells): 157 if ym[s] == 0: 158 s1 = s 159 index = np.ones(num_input, dtype=int) 160 for i in range(num_input - 1, -1, -1): 161 while s1 > base_count[i]: 162 s1 -= base_count[i] 163 index[i] += 1 164 165 index[num_input - 1] = s1 166 zbnum = 0 167 168 for i in range(num_input - 1): 169 if index[i] > 1: 170 zbb[s] += zb[s - base_count[i]] 171 ymm[s] += ym[s - base_count[i]] 172 zbnum += np.sign(ym[s - base_count[i]]) 173 174 if index[i] < fn_counts[i]: 175 zbb[s] += zb[s + base_count[i]] 176 ymm[s] += ym[s + base_count[i]] 177 zbnum += np.sign(ym[s + base_count[i]]) 178 179 if index[num_input - 1] > 1: 180 zbb[s] += zb[s - 1] 181 ymm[s] += ym[s - 1] 182 zbnum += np.sign(ym[s - 1]) 183 184 if index[num_input - 1] < fn_counts[num_input - 1]: 185 zbb[s] += zb[s + 1] 186 ymm[s] += ym[s + 1] 187 zbnum += np.sign(ym[s + 1]) 188 189 if zbnum >= 1: 190 zbb[s] /= zbnum 191 ymm[s] /= zbnum 192 193 # Update zb and ym for cells without data 194 for s in range(num_cells): 195 if ym[s] == 0 and ymm[s] != 0: 196 zb[s] = zbb[s] 197 ym[s] = ymm[s] 198 199 return zb, ranges 200 201 202 def load_data(): 203 # 设置随机种子以获得可重复的结果 204 np.random.seed(0) 205 206 # 初始化时间序列的初始条件 207 p0 = np.zeros(3150) 208 for k in range(1, 51): 209 p0[k-1] = 0.04 * (k - 1) 210 211 for k in range(51, 3150): 212 p0[k-1] = 0.9 * p0[k-2] + 0.2 * p0[k-51] / (1 + p0[k-51]**10) 213 214 # 生成带有噪声的时间序列数据 215 r0 = np.zeros(3100) 216 for k in range(50, 3150): 217 r0[k-50] = np.log(p0[k-1] / p0[k-2]) + 0.0001 * np.random.randn() 218 219 # 重新排列数据以创建数据矩阵xx 220 xx = np.zeros((3000, 12)) 221 for i in range(3000): 222 for j in range(12): 223 xx[i, j] = r0[i + j] 224 225 # 保存数据集xx到磁盘（如果需要） 226 # np.save('xx.npy', xx) 227 return xx 228 229 ''' 230 代码段用于加载数据集xx，该数据集是一个N×12的矩阵，其中前11列是输入数据，最后一列是输出数据。 231 代码进一步划分了训练集和测试集，设置了模糊集合的数量mm，并准备了训练数据以供9个模糊系统使用。 232 最后，代码训练了这些模糊系统，并得到了每个系统的zb和rg参数。 233 ''' 234 # 假设xx已经被加载到NumPy数组中 235 # xx = np.load('xx.npy') 236 xx = load_data() 237 N = xx.shape[0] # 获取数据集的大小 238 ntrain = int(N * 2 / 3) # 划分训练数据和测试数据 239 mm = 20 # 设置模糊集合的数量 240 241 242 def train(xx): 243 # 初始化训练和测试数据集 244 x11 = np.zeros((ntrain, 3)) 245 x12 = np.zeros((ntrain, 3)) 246 x13 = np.zeros((ntrain, 3)) 247 x14 = np.zeros((ntrain, 3)) 248 x15 = np.zeros((ntrain, 3)) 249 x16 = np.zeros((ntrain, 3)) 250 x17 = np.zeros((ntrain, 3)) 251 x18 = np.zeros((ntrain, 3)) 252 x19 = np.zeros((ntrain, 3)) 253 y = np.zeros((ntrain, 1)) 254 255 # 填充训练数据集 256 for i in range(ntrain): 257 for j in range(3): # window size=3 258 x11[i, j] = xx[i, j] 259 x12[i, j] = xx[i, j+1] 260 x13[i, j] = xx[i, j+2] 261 x14[i, j] = xx[i, j+3] 262 x15[i, j] = xx[i, j+4] 263 x16[i, j] = xx[i, j+5] 264 x17[i, j] = xx[i, j+6] 265 x18[i, j] = xx[i, j+7] 266 x19[i, j] = xx[i, j+8] 267 y[i] = xx[i, 11] # 目标输出 268 269 # 训练9个模糊系统 270 zb11, rg11 = wmdeepzb(mm, x11, y) 271 zb12, rg12 = wmdeepzb(mm, x12, y) 272 zb13, rg13 = wmdeepzb(mm, x13, y) 273 zb14, rg14 = wmdeepzb(mm, x14, y) 274 zb15, rg15 = wmdeepzb(mm, x15, y) 275 zb16, rg16 = wmdeepzb(mm, x16, y) 276 zb17, rg17 = wmdeepzb(mm, x17, y) 277 zb18, rg18 = wmdeepzb(mm, x18, y) 278 zb19, rg19 = wmdeepzb(mm, x19, y) 279 280 print('Level 1 training done') 281 282 # 代码段用于计算第二层的输入数据x21到x27，这些数据是基于第一层9个模糊系统的输出以及部分输入数据生成的。接着，代码训练了第二层的7个模糊系统。 283 # 初始化第二层的输入数据 284 x21 = np.zeros((ntrain, 3)) 285 x22 = np.zeros((ntrain, 3)) 286 x23 = np.zeros((ntrain, 3)) 287 x24 = np.zeros((ntrain, 3)) 288 x25 = np.zeros((ntrain, 3)) 289 x26 = np.zeros((ntrain, 3)) 290 x27 = np.zeros((ntrain, 3)) 291 292 # 计算第二层的输入数据 293 x21[:, 0] = wmdeepyy(mm, zb11, rg11, x11) 294 x21[:, 1] = wmdeepyy(mm, zb12, rg12, x12) 295 x21[:, 2] = wmdeepyy(mm, zb13, rg13, x13) 296 297 x22[:, 0] = x21[:, 1] 298 x22[:, 1] = x21[:, 2] 299 x22[:, 2] = wmdeepyy(mm, zb14, rg14, x14) 300 301 x23[:, 0] = x21[:, 2] 302 x23[:, 1] = x22[:, 2] 303 x23[:, 2] = wmdeepyy(mm, zb15, rg15, x15) 304 305 x24[:, 0] = x22[:, 2] 306 x24[:, 1] = x23[:, 2] 307 x24[:, 2] = wmdeepyy(mm, zb16, rg16, x16) 308 309 x25[:, 0] = x23[:, 2] 310 x25[:, 1] = x24[:, 2] 311 x25[:, 2] = wmdeepyy(mm, zb17, rg17, x17) 312 313 x26[:, 0] = x24[:, 2] 314 x26[:, 1] = x25[:, 2] 315 x26[:, 2] = wmdeepyy(mm, zb18, rg18, x18) 316 317 x27[:, 0] = x25[:, 2] 318 x27[:, 1] = x26[:, 2] 319 x27[:, 2] = wmdeepyy(mm, zb19, rg19, x19) 320 321 # 训练第二层的7个模糊系统 322 zb21, rg21 = wmdeepzb(mm, x21, y) 323 zb22, rg22 = wmdeepzb(mm, x22, y) 324 zb23, rg23 = wmdeepzb(mm, x23, y) 325 zb24, rg24 = wmdeepzb(mm, x24, y) 326 zb25, rg25 = wmdeepzb(mm, x25, y) 327 zb26, rg26 = wmdeepzb(mm, x26, y) 328 zb27, rg27 = wmdeepzb(mm, x27, y) 329 330 print('Level 2 training done') 331 332 # 代码段用于计算第三层的输入数据x31到x35，这些数据是基于第二层模糊系统的输出生成的。接着，代码训练了第三层的5个模糊系统。 333 # 初始化第三层的输入数据 334 x31 = np.zeros((ntrain, 3)) 335 x32 = np.zeros((ntrain, 3)) 336 x33 = np.zeros((ntrain, 3)) 337 x34 = np.zeros((ntrain, 3)) 338 x35 = np.zeros((ntrain, 3)) 339 340 # 计算第三层的输入数据 341 x31[:, 0] = wmdeepyy(mm, zb21, rg21, x21) 342 x31[:, 1] = wmdeepyy(mm, zb22, rg22, x22) 343 x31[:, 2] = wmdeepyy(mm, zb23, rg23, x23) 344 345 x32[:, 0] = x31[:, 1] 346 x32[:, 1] = x31[:, 2] 347 x32[:, 2] = wmdeepyy(mm, zb24, rg24, x24) 348 349 x33[:, 0] = x31[:, 2] 350 x33[:, 1] = x32[:, 2] 351 x33[:, 2] = wmdeepyy(mm, zb25, rg25, x25) 352 353 x34[:, 0] = x32[:, 2] 354 x34[:, 1] = x33[:, 2] 355 x34[:, 2] = wmdeepyy(mm, zb26, rg26, x26) 356 357 x35[:, 0] = x33[:, 2] 358 x35[:, 1] = x34[:, 2] 359 x35[:, 2] = wmdeepyy(mm, zb27, rg27, x27) 360 361 # 训练第三层的5个模糊系统 362 zb31, rg31 = wmdeepzb(mm, x31, y) 363 zb32, rg32 = wmdeepzb(mm, x32, y) 364 zb33, rg33 = wmdeepzb(mm, x33, y) 365 zb34, rg34 = wmdeepzb(mm, x34, y) 366 zb35, rg35 = wmdeepzb(mm, x35, y) 367 368 print('Level 3 training done') 369 370 # 代码段用于计算第四层的输入数据x41、x42和x43，这些数据是基于第三层模糊系统的输出生成的。接着，代码训练了第四层的3个模糊系统。 371 # 初始化第四层的输入数据 372 x41 = np.zeros((ntrain, 3)) 373 x42 = np.zeros((ntrain, 3)) 374 x43 = np.zeros((ntrain, 3)) 375 376 # 计算第四层的输入数据 377 x41[:, 0] = wmdeepyy(mm, zb31, rg31, x31) 378 x41[:, 1] = wmdeepyy(mm, zb32, rg32, x32) 379 x41[:, 2] = wmdeepyy(mm, zb33, rg33, x33) 380 381 x42[:, 0] = x41[:, 1] 382 x42[:, 1] = x41[:, 2] 383 x42[:, 2] = wmdeepyy(mm, zb34, rg34, x34) 384 385 x43[:, 0] = x41[:, 2] 386 x43[:, 1] = x42[:, 2] 387 x43[:, 2] = wmdeepyy(mm, zb35, rg35, x35) 388 389 # 训练第四层的3个模糊系统 390 zb41, rg41 = wmdeepzb(mm, x41, y) 391 zb42, rg42 = wmdeepzb(mm, x42, y) 392 zb43, rg43 = wmdeepzb(mm, x43, y) 393 394 print('Level 4 training done') 395 396 # 代码段用于计算第五层的输入数据x51，这些数据是基于第四层模糊系统的输出生成的。接着，代码训练了第五层的模糊系统。 397 # 初始化第五层的输入数据 398 x51 = np.zeros((ntrain, 3)) 399 400 # 计算第五层的输入数据 401 x51[:, 0] = wmdeepyy(mm, zb41, rg41, x41) 402 x51[:, 1] = wmdeepyy(mm, zb42, rg42, x42) 403 x51[:, 2] = wmdeepyy(mm, zb43, rg43, x43) 404 405 # 训练第五层的模糊系统 406 zb51, rg51 = wmdeepzb(mm, x51, y) 407 408 print('Level 5 training done') 409 print('Training done') 410 411 # 创建一个字典来保存所有的系数 412 coefficients = { 413 'zb11': zb11, 'rg11': rg11, 414 'zb12': zb12, 'rg12': rg12, 415 'zb13': zb13, 'rg13': rg13, 416 'zb14': zb14, 'rg14': rg14, 417 'zb15': zb15, 'rg15': rg15, 418 'zb16': zb16, 'rg16': rg16, 419 'zb17': zb17, 'rg17': rg17, 420 'zb18': zb18, 'rg18': rg18, 421 'zb19': zb19, 'rg19': rg19, 422 'zb21': zb21, 'rg21': rg21, 423 'zb22': zb22, 'rg22': rg22, 424 'zb23': zb23, 'rg23': rg23, 425 'zb24': zb24, 'rg24': rg24, 426 'zb25': zb25, 'rg25': rg25, 427 'zb26': zb26, 'rg26': rg26, 428 'zb27': zb27, 'rg27': rg27, 429 'zb31': zb31, 'rg31': rg31, 430 'zb32': zb32, 'rg32': rg32, 431 'zb33': zb33, 'rg33': rg33, 432 'zb34': zb34, 'rg34': rg34, 433 'zb35': zb35, 'rg35': rg35, 434 'zb41': zb41, 'rg41': rg41, 435 'zb42': zb42, 'rg42': rg42, 436 'zb43': zb43, 'rg43': rg43, 437 'zb51': zb51, 'rg51': rg51 438 } 439 440 # 将字典保存到文件 441 with open('fuzzy_system_coefficients.pkl', 'wb') as file: 442 pickle.dump(coefficients, file) 443 444 print('Coefficients have been saved to fuzzy_system_coefficients.pkl') 445 446 return y 447 448 449 def predict(): 450 # 加载系数 451 with open('fuzzy_system_coefficients.pkl', 'rb') as file: 452 coefficients = pickle.load(file) 453 # 现在可以访问每个系数，例如： 454 zb11 = coefficients['zb11'] 455 rg11 = coefficients['rg11'] 456 zb12 = coefficients['zb12'] 457 rg12 = coefficients['rg12'] 458 zb13 = coefficients['zb13'] 459 rg13 = coefficients['rg13'] 460 zb14 = coefficients['zb14'] 461 rg14 = coefficients['rg14'] 462 zb15 = coefficients['zb15'] 463 rg15 = coefficients['rg15'] 464 zb16 = coefficients['zb16'] 465 rg16 = coefficients['rg16'] 466 zb17 = coefficients['zb17'] 467 rg17 = coefficients['rg17'] 468 zb18 = coefficients['zb18'] 469 rg18 = coefficients['rg18'] 470 zb19 = coefficients['zb19'] 471 rg19 = coefficients['rg19'] 472 zb21 = coefficients['zb21'] 473 rg21 = coefficients['rg21'] 474 zb22 = coefficients['zb22'] 475 rg22 = coefficients['rg22'] 476 zb23 = coefficients['zb23'] 477 rg23 = coefficients['rg23'] 478 zb24 = coefficients['zb24'] 479 rg24 = coefficients['rg24'] 480 zb25 = coefficients['zb25'] 481 rg25 = coefficients['rg25'] 482 zb26 = coefficients['zb26'] 483 rg26 = coefficients['rg26'] 484 zb27 = coefficients['zb27'] 485 rg27 = coefficients['rg27'] 486 zb31 = coefficients['zb31'] 487 rg31 = coefficients['rg31'] 488 zb32 = coefficients['zb32'] 489 rg32 = coefficients['rg32'] 490 zb33 = coefficients['zb33'] 491 rg33 = coefficients['rg33'] 492 zb34 = coefficients['zb34'] 493 rg34 = coefficients['rg34'] 494 zb35 = coefficients['zb35'] 495 rg35 = coefficients['rg35'] 496 zb41 = coefficients['zb41'] 497 rg41 = coefficients['rg41'] 498 zb42 = coefficients['zb42'] 499 rg42 = coefficients['rg42'] 500 zb43 = coefficients['zb43'] 501 rg43 = coefficients['rg43'] 502 zb51 = coefficients['zb51'] 503 rg51 = coefficients['rg51'] 504 505 mm = 20 # 设置模糊集合的数量 506 507 # 初始化各级的输入输出数据 508 N = xx.shape[0] 509 x11 = np.zeros((N, 3)) 510 x12 = np.zeros((N, 3)) 511 x13 = np.zeros((N, 3)) 512 x14 = np.zeros((N, 3)) 513 x15 = np.zeros((N, 3)) 514 x16 = np.zeros((N, 3)) 515 x17 = np.zeros((N, 3)) 516 x18 = np.zeros((N, 3)) 517 x19 = np.zeros((N, 3)) 518 y = np.zeros((N, 1)) 519 520 # 填充第一层输入数据 521 for i in range(N): 522 for j in range(3): 523 x11[i, j] = xx[i, j] 524 x12[i, j] = xx[i, j+1] 525 x13[i, j] = xx[i, j+2] 526 x14[i, j] = xx[i, j+3] 527 x15[i, j] = xx[i, j+4] 528 x16[i, j] = xx[i, j+5] 529 x17[i, j] = xx[i, j+6] 530 x18[i, j] = xx[i, j+7] 531 x19[i, j] = xx[i, j+8] 532 y[i] = xx[i, 12] # 目标输出 533 534 print('Level 1 computing done') 535 536 # 计算第一层输出 537 x21 = np.zeros((N, 3)) 538 x22 = np.zeros((N, 3)) 539 x23 = np.zeros((N, 3)) 540 x24 = np.zeros((N, 3)) 541 x25 = np.zeros((N, 3)) 542 x26 = np.zeros((N, 3)) 543 x27 = np.zeros((N, 3)) 544 545 x21[:, 0] = wmdeepyy(mm, zb11, rg11, x11) 546 x21[:, 1] = wmdeepyy(mm, zb12, rg12, x12) 547 x21[:, 2] = wmdeepyy(mm, zb13, rg13, x13) 548 x22[:, 0] = x21[:, 1] 549 x22[:, 1] = x21[:, 2] 550 x22[:, 2] = wmdeepyy(mm, zb14, rg14, x14) 551 x23[:, 0] = x21[:, 2] 552 x23[:, 1] = x22[:, 2] 553 x23[:, 2] = wmdeepyy(mm, zb15, rg15, x15) 554 x24[:, 0] = x22[:, 2] 555 x24[:, 1] = x23[:, 2] 556 x24[:, 2] = wmdeepyy(mm, zb16, rg16, x16) 557 x25[:, 0] = x23[:, 2] 558 x25[:, 1] = x24[:, 2] 559 x25[:, 2] = wmdeepyy(mm, zb17, rg17, x17) 560 x26[:, 0] = x24[:, 2] 561 x26[:, 1] = x25[:, 2] 562 x26[:, 2] = wmdeepyy(mm, zb18, rg18, x18) 563 x27[:, 0] = x25[:, 2] 564 x27[:, 1] = x26[:, 2] 565 x27[:, 2] = wmdeepyy(mm, zb19, rg19, x19) 566 567 print('Level 2 computing done') 568 569 # 计算第二层输出 570 x31 = np.zeros((N, 3)) 571 x32 = np.zeros((N, 3)) 572 x33 = np.zeros((N, 3)) 573 x34 = np.zeros((N, 3)) 574 x35 = np.zeros((N, 3)) 575 576 x31[:, 0] = wmdeepyy(mm, zb21, rg21, x21) 577 x31[:, 1] = wmdeepyy(mm, zb22, rg22, x22) 578 x31[:, 2] = wmdeepyy(mm, zb23, rg23, x23) 579 x32[:, 0] = x31[:, 1] 580 x32[:, 1] = x31[:, 2] 581 x32[:, 2] = wmdeepyy(mm, zb24, rg24, x24) 582 x33[:, 0] = x31[:, 2] 583 x33[:, 1] = x32[:, 2] 584 x33[:, 2] = wmdeepyy(mm, zb25, rg25, x25) 585 x34[:, 0] = x32[:, 2] 586 x34[:, 1] = x33[:, 2] 587 x34[:, 2] = wmdeepyy(mm, zb26, rg26, x26) 588 x35[:, 0] = x33[:, 2] 589 x35[:, 1] = x34[:, 2] 590 x35[:, 2] = wmdeepyy(mm, zb27, rg27, x27) 591 592 print('Level 3 computing done') 593 594 # 计算第三层输出 595 x41 = np.zeros((N, 3)) 596 x42 = np.zeros((N, 3)) 597 x43 = np.zeros((N, 3)) 598 599 x41[:, 0] = wmdeepyy(mm, zb31, rg31, x31) 600 x41[:, 1] = wmdeepyy(mm, zb32, rg32, x32) 601 x41[:, 2] = wmdeepyy(mm, zb33, rg33, x33) 602 x42[:, 0] = x41[:, 1] 603 x42[:, 1] = x41[:, 2] 604 x42[:, 2] = wmdeepyy(mm, zb34, rg34, x34) 605 x43[:, 0] = x41[:, 2] 606 x43[:, 1] = x42[:, 2] 607 x43[:, 2] = wmdeepyy(mm, zb35, rg35, x35) 608 609 print('Level 4 computing done') 610 611 # 计算第四层输出 612 x51 = np.zeros((N, 3)) 613 614 x51[:, 0] = wmdeepyy(mm, zb41, rg41, x41) 615 x51[:, 1] = wmdeepyy(mm, zb42, rg42, x42) 616 x51[:, 2] = wmdeepyy(mm, zb43, rg43, x43) 617 618 print('Level 5 computing done') 619 620 # 计算DCFS的最终输出 621 yy = np.zeros((N, 1)) 622 yy = wmdeepyy(mm, zb51, rg51, x51) 623 624 return yy 625 626 627 y = train(xx) # 训练好的参数保存到本地，训练集的输出 628 yy = predict() # 预测集的输出 629 # 计算所有点的误差 630 e = y - yy 631 632 # 计算训练误差 633 err_train = np.sqrt(np.sum(e[:ntrain] ** 2) / ntrain) 634 635 # 计算测试误差 636 err_test = np.sqrt(np.sum(e[ntrain:] ** 2) / (N - ntrain)) 637 638 # 绘制误差曲线 639 plt.figure(figsize=(10, 6)) 640 plt.plot(e, label='DCFS Error') 641 plt.title(f'DCFS: Training error = {err_train:.4f}, Testing error = {err_test:.4f}') 642 plt.xlabel('Data Point') 643 plt.ylabel('Error') 644 plt.legend() 645 plt.grid(True) 646 plt.show()
