验5：数据预处理（2）
一：实验目的与要求
1：熟悉和掌握数据预处理，学习数据清洗、数据集成、数据变换、数据规约、R语言中主要数据预处理函数。
二：实验知识点总结
1：数据集成是将多个数据源合并存放在一个一致的数据存储中的过程，且多个数据源的表达形式不一定匹配。主要分为实体识别和冗余属性识别两个大类。
2：实体识别的任务是检测和解决同名异义、异名同义、单位不统一的冲突。
3：冗余属性识别的任务是检测同一属性多次出现、同一属性命名不一致导致重复的情况。
4：数据变换是对数据进行规范化的操作。主要方法有：简单函数变换、规范化、连续属性离散化、属性构造、小波变换。
5：简单函数变换是对原始诗句进行某些数学函数变换。常用方法包括：平方、开方、对数、差分运算。
6：规范化是消除指标之间的量纲和大小不一的影响。常用方法包括：最小-最大规范化、零-均值规范化、小数定标规范化。
7：连续属性离散化是将连续属性变换成分类属性。常用方法包括：等宽法、等频法、基于聚类分析的方法。
8：属性构造是利用已有的属性集构造出新的属性，并加入到现有的属性集合中。
9：数据规约是将海量数据进行规约，规约之后的数据仍接近于保持原数据的完整性，但数据量小得多。数据规约主要分为属性规约和数值规约。
10：属性规约的常用方法包括：合并属性、逐步向前选择、逐步向后删除、决策树归纳、主成分分析。
11：数值规约的常用方法包括：直方图、用聚类数据表示实际数据、抽样（采样）、参数回归法。
三：遇到的问题和解决方法
问题1：载入csv文件时，如果header有中文字符，则无法正确读入。
解决1：设置read.csv函数中的fileEncoding规则为GB2312。
四：课堂练习
【练习2：数据变换】PPT-07第24页——通过对一矩阵使用最小-最大规范化、零-均值规范化、小数定标规范化对其处理，对比结果
第一步：设置文件读取路径
| setwd("C:/Users/86158/Desktop") getwd() |
第二步：读取数据文件
| data <- read.csv('normalization_data.csv',header=F) data |
第三步：最小-最大规范化
| (b1 <- (data[, 1] - min(data[, 1])) / (max(data[, 1]) - min(data[, 1]))) (b2 <- (data[, 2] - min(data[, 2])) / (max(data[, 2]) - min(data[, 2]))) (b3 <- (data[, 3] - min(data[, 3])) / (max(data[, 3]) - min(data[, 3]))) (b4 <- (data[, 4] - min(data[, 4])) / (max(data[, 4]) - min(data[, 4]))) (data_scatter <- cbind(b1, b2, b3, b4)) |
第四步：零-均值规范化
| (data_zscore <- scale(data)) |
第五步：小数定标规范化
| (i1 <- ceiling(log(max(abs(data[, 1])), 10))) # 小数定标的指数 c1 <- data[, 1] / 10 ^ i1 i2 <- ceiling(log(max(abs(data[, 2])), 10)) c2 <- data[, 2] / 10 ^ i2 i3 <- ceiling(log(max(abs(data[, 3])), 10)) c3 <- data[, 3] / 10 ^ i3 i4 <- ceiling(log(max(abs(data[, 4])), 10)) c4 <- data[, 4] / 10 ^ i4 data_dot <- cbind(c1, c2, c3, c4) c1 i2 c2 i3 c3 i4 c4 data_dot |
第六步：归纳打印
| options(digits = 4) # 控制输出结果的有效位数 data data_scatter data_zscore data_dot |
【练习3：连续属性离散化】PPT-07第26页——通过“医学中中医证型相关数据” 进行连续属性离散化处理
第一步：读取数据文件，提取标题行
| data <- read.csv('discretization_data.csv', header = T,fileEncoding = "GB2312") data |
第二步：等宽离散化
| v1 <- ceiling(data[, 1] * 10) v1 |
第三步：等频离散化
| names(data) <- 'f' # 变量重命名 attach(data) seq(0, length(f), length(f) / 6) # 等频划分为6组 v <- sort(f) # 按大小排序作为离散化依据 v2 <- rep(0, 930) # 定义新变量 for (i in 1:930) { v2[i] <- ifelse (f[i] <= v[155], 1, ifelse (f[i] <= v[310], 2, ifelse (f[i] <= v[465], 3, ifelse (f[i] <= v[620], 4, ifelse (f[i] <= v[775], 5, 6))))) } detach(data) v2 |
第四步：聚类离散化
| result <- kmeans(data, 6) result v3 <- result$cluster v3 |
第五步：图示结果
| plot(data[, 1], v1, xlab = '肝气郁结证型系数') plot(data[, 1], v2, xlab = '肝气郁结证型系数') plot(data[, 1], v3, xlab = '肝气郁结证型系数') |
V1可视化
V2可视化
V3可视化
【练习4：属性构造】PPT-07第28页——通过“线损率属性构造” 进行数据处理
第一步：数据读取
| inputfile <- read.csv('electricity_data.csv', header = T,fileEncoding = "GB2312") inputfile |
第二步：构造属性
| loss <- 100 * (inputfile[, 1] - inputfile[, 2]) / inputfile[, 1] loss |
第三步：保存结果
| outputfile <- data.frame(inputfile, '线损率(%)' = loss) # 变量重命名，存入数据 outputfile |
【练习5：小波变换】
第一步：数据生成，信号模拟
| N <- 1024; k <- 6 # 参数赋值 x <- ((1:N) - N/2 ) * 2 * pi * k / N y <- ifelse(x > 0, sin(x), sin(3 * x) ) # 划分低频波动段和高频波动段 signal <- y + rnorm(N) / 10 # 添加扰动项，生成信号变量 N x y signal |
第二步：调用函数包
| install.packages("waveslim") library(waveslim) |
第三步：对信号z进行小波分解
| d <- dwt(signal, n.levels = 4) d |
第四步：输出各层小波系数
| data.frame(d$d1, d$d2, d$d3, d$d4) |
【练习6：主成分分析】PPT-07第40页——通过“主成分分析降维” 进行数据处理
第一步：数据读取
| inputfile <- read.csv('principal_component.csv', header = F) inputfile |
第二步：主成分分析
| PCA <- princomp(inputfile, cor = FALSE) names(PCA) # 查看输出项 |
第三步：查看主成分特征根
| (PCA$sdev) ^ 2 # 主成分特征根 |
第四步：查看主成分贡献率
| summary(PCA) # 主成分贡献率 |
第五步：查看主成分载荷
| PCA$loadings # 主成分载荷 |
第六步：查看主成分得分
| PCA$scores # 主成分得分 |
APPENDIX
【1】练习3数据的完整读入情况：
| 肝气郁结证型系数 1 0.056 2 0.488 3 0.107 4 0.322 5 0.242 6 0.389 7 0.246 8 0.330 9 0.257 10 0.205 11 0.330 12 0.235 13 0.267 14 0.281 15 0.184 16 0.271 17 0.100 18 0.173 19 0.302 20 0.176 21 0.172 22 0.195 23 0.281 24 0.245 25 0.156 26 0.168 27 0.211 28 0.255 29 0.279 30 0.341 31 0.230 32 0.266 33 0.252 34 0.227 35 0.277 36 0.329 37 0.320 38 0.053 39 0.152 40 0.269 41 0.042 42 0.179 43 0.239 44 0.167 45 0.209 46 0.432 47 0.354 48 0.247 49 0.328 50 0.215 51 0.433 52 0.294 53 0.237 54 0.244 55 0.199 56 0.286 57 0.219 58 0.261 59 0.316 60 0.221 61 0.326 62 0.284 63 0.242 64 0.268 65 0.257 66 0.174 67 0.251 68 0.237 69 0.298 70 0.288 71 0.263 72 0.273 73 0.233 74 0.243 75 0.299 76 0.202 77 0.229 78 0.348 79 0.369 80 0.186 81 0.270 82 0.302 83 0.216 84 0.320 85 0.167 86 0.228 87 0.108 88 0.253 89 0.303 90 0.274 91 0.225 92 0.180 93 0.195 94 0.219 95 0.169 96 0.234 97 0.279 98 0.114 99 0.225 100 0.169 101 0.175 102 0.170 103 0.223 104 0.166 105 0.217 106 0.256 107 0.252 108 0.299 109 0.247 110 0.344 111 0.272 112 0.159 113 0.219 114 0.240 115 0.187 116 0.278 117 0.227 118 0.280 119 0.285 120 0.388 121 0.134 122 0.230 123 0.195 124 0.220 125 0.448 126 0.323 127 0.104 128 0.102 129 0.196 130 0.176 131 0.229 132 0.199 133 0.278 134 0.241 135 0.207 136 0.163 137 0.253 138 0.222 139 0.277 140 0.290 141 0.211 142 0.186 143 0.418 144 0.175 145 0.238 146 0.160 147 0.198 148 0.329 149 0.180 150 0.242 151 0.287 152 0.216 153 0.318 154 0.308 155 0.211 156 0.129 157 0.285 158 0.139 159 0.218 160 0.177 161 0.209 162 0.386 163 0.137 164 0.193 165 0.302 166 0.350 167 0.323 168 0.102 169 0.198 170 0.110 171 0.173 172 0.417 173 0.123 174 0.109 175 0.111 176 0.166 177 0.303 178 0.128 179 0.157 180 0.134 181 0.314 182 0.288 183 0.107 184 0.295 185 0.300 186 0.171 187 0.057 188 0.504 189 0.102 190 0.316 191 0.251 192 0.383 193 0.243 194 0.323 195 0.271 196 0.200 197 0.346 198 0.251 199 0.266 200 0.295 201 0.200 202 0.267 203 0.100 204 0.184 205 0.294 206 0.174 207 0.188 208 0.193 209 0.291 210 0.264 211 0.168 212 0.169 213 0.208 214 0.267 215 0.295 216 0.346 217 0.235 218 0.269 219 0.259 220 0.228 221 0.287 222 0.339 223 0.324 224 0.054 225 0.159 226 0.273 227 0.055 228 0.181 229 0.238 230 0.164 231 0.210 232 0.432 233 0.363 234 0.247 235 0.330 236 0.211 237 0.427 238 0.296 239 0.247 240 0.257 241 0.212 242 0.285 243 0.216 244 0.271 245 0.328 246 0.219 247 0.332 248 0.294 249 0.246 250 0.282 251 0.272 252 0.173 253 0.250 254 0.242 255 0.313 256 0.296 257 0.274 258 0.281 259 0.237 260 0.249 261 0.303 262 0.193 263 0.227 264 0.347 265 0.373 266 0.197 267 0.276 268 0.304 269 0.235 270 0.325 271 0.166 272 0.226 273 0.115 274 0.253 275 0.306 276 0.277 277 0.223 278 0.176 279 0.205 280 0.238 281 0.173 282 0.243 283 0.292 284 0.122 285 0.224 286 0.177 287 0.176 288 0.183 289 0.229 290 0.158 291 0.221 292 0.250 293 0.252 294 0.308 295 0.247 296 0.355 297 0.282 298 0.155 299 0.226 300 0.247 301 0.190 302 0.282 303 0.228 304 0.288 305 0.296 306 0.389 307 0.140 308 0.231 309 0.198 310 0.235 311 0.456 312 0.322 313 0.108 314 0.110 315 0.205 316 0.179 317 0.245 318 0.206 319 0.287 320 0.254 321 0.215 322 0.155 323 0.254 324 0.227 325 0.280 326 0.305 327 0.214 328 0.188 329 0.420 330 0.177 331 0.254 332 0.169 333 0.193 334 0.345 335 0.174 336 0.253 337 0.289 338 0.232 339 0.324 340 0.318 341 0.216 342 0.142 343 0.281 344 0.144 345 0.217 346 0.183 347 0.217 348 0.400 349 0.147 350 0.191 351 0.309 352 0.345 353 0.319 354 0.110 355 0.210 356 0.115 357 0.185 358 0.435 359 0.138 360 0.119 361 0.111 362 0.173 363 0.310 364 0.132 365 0.168 366 0.134 367 0.329 368 0.303 369 0.104 370 0.300 371 0.298 372 0.187 373 0.034 374 0.474 375 0.085 376 0.304 377 0.231 378 0.377 379 0.226 380 0.304 381 0.247 382 0.184 383 0.325 384 0.218 385 0.258 386 0.273 387 0.181 388 0.263 389 0.083 390 0.169 391 0.288 392 0.158 393 0.161 394 0.186 395 0.258 396 0.233 397 0.146 398 0.149 399 0.195 400 0.247 401 0.275 402 0.326 403 0.213 404 0.251 405 0.233 406 0.209 407 0.253 408 0.308 409 0.303 410 0.042 411 0.135 412 0.253 413 0.026 414 0.158 415 0.229 416 0.158 417 0.198 418 0.411 419 0.337 420 0.226 421 0.312 422 0.191 423 0.417 424 0.283 425 0.219 426 0.239 427 0.191 428 0.275 429 0.204 430 0.247 431 0.312 432 0.208 433 0.318 434 0.270 435 0.229 436 0.251 437 0.250 438 0.155 439 0.228 440 0.219 441 0.293 442 0.270 443 0.243 444 0.265 445 0.214 446 0.230 447 0.277 448 0.182 449 0.215 450 0.341 451 0.366 452 0.170 453 0.251 454 0.274 455 0.216 456 0.305 457 0.161 458 0.212 459 0.091 460 0.235 461 0.279 462 0.250 463 0.199 464 0.169 465 0.186 466 0.210 467 0.149 468 0.214 469 0.254 470 0.106 471 0.213 472 0.157 473 0.166 474 0.163 475 0.202 476 0.144 477 0.207 478 0.240 479 0.232 480 0.290 481 0.226 482 0.328 483 0.245 484 0.140 485 0.198 486 0.232 487 0.166 488 0.257 489 0.202 490 0.266 491 0.266 492 0.366 493 0.126 494 0.206 495 0.175 496 0.215 497 0.429 498 0.298 499 0.094 500 0.087 501 0.180 502 0.155 503 0.216 504 0.175 505 0.267 506 0.233 507 0.193 508 0.151 509 0.238 510 0.198 511 0.258 512 0.270 513 0.188 514 0.173 515 0.397 516 0.166 517 0.217 518 0.145 519 0.178 520 0.326 521 0.173 522 0.239 523 0.277 524 0.216 525 0.298 526 0.294 527 0.190 528 0.122 529 0.273 530 0.125 531 0.203 532 0.162 533 0.204 534 0.368 535 0.118 536 0.165 537 0.289 538 0.324 539 0.312 540 0.092 541 0.195 542 0.089 543 0.161 544 0.400 545 0.118 546 0.101 547 0.095 548 0.164 549 0.288 550 0.124 551 0.147 552 0.122 553 0.306 554 0.284 555 0.087 556 0.272 557 0.286 558 0.151 559 0.045 560 0.487 561 0.089 562 0.304 563 0.232 564 0.375 565 0.229 566 0.317 567 0.248 568 0.193 569 0.317 570 0.226 571 0.254 572 0.277 573 0.184 574 0.263 575 0.089 576 0.169 577 0.290 578 0.165 579 0.163 580 0.180 581 0.268 582 0.240 583 0.150 584 0.154 585 0.205 586 0.252 587 0.270 588 0.328 589 0.215 590 0.254 591 0.243 592 0.211 593 0.269 594 0.319 595 0.308 596 0.045 597 0.144 598 0.262 599 0.033 600 0.173 601 0.229 602 0.158 603 0.202 604 0.417 605 0.342 606 0.236 607 0.317 608 0.206 609 0.424 610 0.279 611 0.233 612 0.241 613 0.193 614 0.276 615 0.207 616 0.252 617 0.304 618 0.216 619 0.314 620 0.264 621 0.228 622 0.263 623 0.249 624 0.163 625 0.242 626 0.223 627 0.289 628 0.278 629 0.260 630 0.260 631 0.224 632 0.232 633 0.292 634 0.191 635 0.212 636 0.333 637 0.362 638 0.173 639 0.263 640 0.291 641 0.214 642 0.312 643 0.156 644 0.210 645 0.105 646 0.238 647 0.289 648 0.264 649 0.208 650 0.165 651 0.179 652 0.218 653 0.155 654 0.228 655 0.266 656 0.105 657 0.210 658 0.163 659 0.159 660 0.163 661 0.214 662 0.151 663 0.215 664 0.238 665 0.245 666 0.292 667 0.243 668 0.337 669 0.262 670 0.147 671 0.211 672 0.234 673 0.177 674 0.272 675 0.210 676 0.265 677 0.269 678 0.375 679 0.125 680 0.218 681 0.183 682 0.212 683 0.432 684 0.311 685 0.094 686 0.092 687 0.188 688 0.157 689 0.217 690 0.191 691 0.270 692 0.238 693 0.198 694 0.144 695 0.237 696 0.209 697 0.271 698 0.285 699 0.206 700 0.179 701 0.411 702 0.165 703 0.232 704 0.143 705 0.184 706 0.326 707 0.166 708 0.233 709 0.275 710 0.216 711 0.309 712 0.299 713 0.197 714 0.120 715 0.268 716 0.129 717 0.211 718 0.166 719 0.200 720 0.383 721 0.134 722 0.175 723 0.292 724 0.337 725 0.314 726 0.093 727 0.195 728 0.097 729 0.162 730 0.408 731 0.117 732 0.099 733 0.098 734 0.162 735 0.294 736 0.126 737 0.145 738 0.130 739 0.304 740 0.283 741 0.103 742 0.283 743 0.287 744 0.161 745 0.049 746 0.488 747 0.098 748 0.313 749 0.237 750 0.381 751 0.239 752 0.323 753 0.254 754 0.195 755 0.326 756 0.233 757 0.259 758 0.277 759 0.184 760 0.266 761 0.098 762 0.171 763 0.293 764 0.171 765 0.171 766 0.188 767 0.276 768 0.244 769 0.153 770 0.164 771 0.208 772 0.253 773 0.277 774 0.336 775 0.221 776 0.256 777 0.247 778 0.217 779 0.273 780 0.327 781 0.317 782 0.049 783 0.146 784 0.268 785 0.041 786 0.177 787 0.232 788 0.163 789 0.202 790 0.426 791 0.344 792 0.243 793 0.322 794 0.207 795 0.425 796 0.284 797 0.236 798 0.242 799 0.193 800 0.283 801 0.213 802 0.256 803 0.313 804 0.217 805 0.323 806 0.274 807 0.236 808 0.264 809 0.254 810 0.167 811 0.246 812 0.233 813 0.293 814 0.285 815 0.263 816 0.267 817 0.225 818 0.237 819 0.294 820 0.192 821 0.219 822 0.341 823 0.366 824 0.178 825 0.264 826 0.293 827 0.216 828 0.317 829 0.163 830 0.219 831 0.106 832 0.247 833 0.297 834 0.268 835 0.217 836 0.172 837 0.188 838 0.218 839 0.163 840 0.231 841 0.272 842 0.107 843 0.217 844 0.166 845 0.167 846 0.166 847 0.217 848 0.156 849 0.217 850 0.248 851 0.247 852 0.293 853 0.244 854 0.341 855 0.264 856 0.153 857 0.216 858 0.236 859 0.183 860 0.277 861 0.220 862 0.273 863 0.277 864 0.383 865 0.133 866 0.226 867 0.193 868 0.218 869 0.439 870 0.317 871 0.098 872 0.098 873 0.192 874 0.166 875 0.227 876 0.194 877 0.278 878 0.238 879 0.205 880 0.153 881 0.247 882 0.216 883 0.273 884 0.289 885 0.207 886 0.183 887 0.415 888 0.171 889 0.237 890 0.152 891 0.192 892 0.327 893 0.173 894 0.239 895 0.284 896 0.216 897 0.311 898 0.302 899 0.206 900 0.127 901 0.277 902 0.135 903 0.214 904 0.173 905 0.205 906 0.384 907 0.134 908 0.184 909 0.294 910 0.341 911 0.317 912 0.098 913 0.195 914 0.102 915 0.172 916 0.415 917 0.122 918 0.106 919 0.107 920 0.165 921 0.302 922 0.127 923 0.152 924 0.131 925 0.311 926 0.284 927 0.103 928 0.287 929 0.296 930 0.169 |
【2】练习5数据的完整输出结果
X变量：
| [1] -18.81274 -18.77592 -18.73911 -18.70229 -18.66548 -18.62866 -18.59185 -18.55503 [9] -18.51822 -18.48140 -18.44458 -18.40777 -18.37095 -18.33414 -18.29732 -18.26051 [17] -18.22369 -18.18688 -18.15006 -18.11325 -18.07643 -18.03961 -18.00280 -17.96598 [25] -17.92917 -17.89235 -17.85554 -17.81872 -17.78191 -17.74509 -17.70827 -17.67146 [33] -17.63464 -17.59783 -17.56101 -17.52420 -17.48738 -17.45057 -17.41375 -17.37693 [41] -17.34012 -17.30330 -17.26649 -17.22967 -17.19286 -17.15604 -17.11923 -17.08241 [49] -17.04559 -17.00878 -16.97196 -16.93515 -16.89833 -16.86152 -16.82470 -16.78789 [57] -16.75107 -16.71425 -16.67744 -16.64062 -16.60381 -16.56699 -16.53018 -16.49336 [65] -16.45655 -16.41973 -16.38291 -16.34610 -16.30928 -16.27247 -16.23565 -16.19884 [73] -16.16202 -16.12521 -16.08839 -16.05157 -16.01476 -15.97794 -15.94113 -15.90431 [81] -15.86750 -15.83068 -15.79387 -15.75705 -15.72024 -15.68342 -15.64660 -15.60979 [89] -15.57297 -15.53616 -15.49934 -15.46253 -15.42571 -15.38890 -15.35208 -15.31526 [97] -15.27845 -15.24163 -15.20482 -15.16800 -15.13119 -15.09437 -15.05756 -15.02074 [105] -14.98392 -14.94711 -14.91029 -14.87348 -14.83666 -14.79985 -14.76303 -14.72622 [113] -14.68940 -14.65258 -14.61577 -14.57895 -14.54214 -14.50532 -14.46851 -14.43169 [121] -14.39488 -14.35806 -14.32124 -14.28443 -14.24761 -14.21080 -14.17398 -14.13717 [129] -14.10035 -14.06354 -14.02672 -13.98990 -13.95309 -13.91627 -13.87946 -13.84264 [137] -13.80583 -13.76901 -13.73220 -13.69538 -13.65856 -13.62175 -13.58493 -13.54812 [145] -13.51130 -13.47449 -13.43767 -13.40086 -13.36404 -13.32723 -13.29041 -13.25359 [153] -13.21678 -13.17996 -13.14315 -13.10633 -13.06952 -13.03270 -12.99589 -12.95907 [161] -12.92225 -12.88544 -12.84862 -12.81181 -12.77499 -12.73818 -12.70136 -12.66455 [169] -12.62773 -12.59091 -12.55410 -12.51728 -12.48047 -12.44365 -12.40684 -12.37002 [177] -12.33321 -12.29639 -12.25957 -12.22276 -12.18594 -12.14913 -12.11231 -12.07550 [185] -12.03868 -12.00187 -11.96505 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Y变量：
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7.572e-01 7.807e-01 [708] 8.032e-01 8.246e-01 8.449e-01 8.640e-01 8.819e-01 8.987e-01 9.142e-01 [715] 9.285e-01 9.415e-01 9.533e-01 9.638e-01 9.729e-01 9.808e-01 9.873e-01 [722] 9.925e-01 9.963e-01 9.988e-01 9.999e-01 9.997e-01 9.981e-01 9.952e-01 [729] 9.909e-01 9.853e-01 9.783e-01 9.700e-01 9.604e-01 9.495e-01 9.373e-01 [736] 9.239e-01 9.092e-01 8.932e-01 8.761e-01 8.577e-01 8.382e-01 8.176e-01 [743] 7.958e-01 7.730e-01 7.491e-01 7.242e-01 6.984e-01 6.716e-01 6.438e-01 [750] 6.152e-01 5.858e-01 5.556e-01 5.246e-01 4.929e-01 4.605e-01 4.276e-01 [757] 3.940e-01 3.599e-01 3.253e-01 2.903e-01 2.549e-01 2.191e-01 1.830e-01 [764] 1.467e-01 1.102e-01 7.356e-02 3.681e-02 3.674e-16 -3.681e-02 -7.356e-02 [771] -1.102e-01 -1.467e-01 -1.830e-01 -2.191e-01 -2.549e-01 -2.903e-01 -3.253e-01 [778] -3.599e-01 -3.940e-01 -4.276e-01 -4.605e-01 -4.929e-01 -5.246e-01 -5.556e-01 [785] -5.858e-01 -6.152e-01 -6.438e-01 -6.716e-01 -6.984e-01 -7.242e-01 -7.491e-01 [792] -7.730e-01 -7.958e-01 -8.176e-01 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8.701e-01 [883] 8.876e-01 9.040e-01 9.191e-01 9.330e-01 9.456e-01 9.569e-01 9.670e-01 [890] 9.757e-01 9.831e-01 9.892e-01 9.939e-01 9.973e-01 9.993e-01 1.000e+00 [897] 9.993e-01 9.973e-01 9.939e-01 9.892e-01 9.831e-01 9.757e-01 9.670e-01 [904] 9.569e-01 9.456e-01 9.330e-01 9.191e-01 9.040e-01 8.876e-01 8.701e-01 [911] 8.514e-01 8.315e-01 8.105e-01 7.883e-01 7.652e-01 7.410e-01 7.157e-01 [918] 6.895e-01 6.624e-01 6.344e-01 6.055e-01 5.758e-01 5.453e-01 5.141e-01 [925] 4.822e-01 4.496e-01 4.164e-01 3.827e-01 3.484e-01 3.137e-01 2.785e-01 [932] 2.430e-01 2.071e-01 1.710e-01 1.346e-01 9.802e-02 6.132e-02 2.454e-02 [939] -1.227e-02 -4.907e-02 -8.580e-02 -1.224e-01 -1.589e-01 -1.951e-01 -2.311e-01 [946] -2.667e-01 -3.020e-01 -3.369e-01 -3.713e-01 -4.052e-01 -4.386e-01 -4.714e-01 [953] -5.035e-01 -5.350e-01 -5.657e-01 -5.957e-01 -6.249e-01 -6.532e-01 -6.806e-01 [960] -7.071e-01 -7.327e-01 -7.572e-01 -7.807e-01 -8.032e-01 -8.246e-01 -8.449e-01 [967] -8.640e-01 -8.819e-01 -8.987e-01 -9.142e-01 -9.285e-01 -9.415e-01 -9.533e-01 [974] -9.638e-01 -9.729e-01 -9.808e-01 -9.873e-01 -9.925e-01 -9.963e-01 -9.988e-01 [981] -9.999e-01 -9.997e-01 -9.981e-01 -9.952e-01 -9.909e-01 -9.853e-01 -9.783e-01 [988] -9.700e-01 -9.604e-01 -9.495e-01 -9.373e-01 -9.239e-01 -9.092e-01 -8.932e-01 [995] -8.761e-01 -8.577e-01 -8.382e-01 -8.176e-01 -7.958e-01 -7.730e-01 [ reached getOption("max.print") -- omitted 24 entries ] |
Signal变量：
| [1] 0.103588 0.159229 0.257206 0.398181 0.394149 0.642875 0.807076 0.708578 [9] 0.822142 0.839928 1.079443 0.998710 0.948755 0.986902 1.038690 0.859163 [17] 0.966382 1.021463 0.798092 0.648737 0.677768 0.838383 0.439877 0.536021 [25] 0.479744 0.339455 0.213790 0.150643 -0.072786 -0.268040 -0.199418 -0.212463 [33] -0.633718 -0.485137 -0.714467 -0.509975 -0.734494 -0.703327 -0.946445 -0.991649 [41] -0.888877 -0.942271 -1.046716 -0.873494 -0.954240 -0.847401 -0.900906 -0.730416 [49] -0.815376 -0.794427 -0.608286 -0.374967 -0.420642 -0.473822 -0.264666 -0.194307 [57] -0.083374 0.101414 0.133346 0.351216 0.479044 0.557862 0.722336 0.687951 [65] 0.667976 1.037892 0.811187 0.916204 1.084028 1.007892 0.840116 1.059681 [73] 1.039480 1.045307 0.926264 0.747340 0.760684 0.675833 0.589906 0.813286 [81] 0.432571 0.350387 0.396386 0.252984 -0.000983 -0.037952 -0.027570 -0.170781 [89] -0.329537 -0.296620 -0.467449 -0.752044 -0.835210 -0.815107 -0.894349 -0.905307 [97] -0.906279 -1.009645 -0.985465 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0.933385 1.022160 [297] 1.061783 1.118468 0.827204 0.826592 0.967705 0.777801 0.814469 0.697698 [305] 0.593624 0.654701 0.648118 0.687699 0.401678 0.310857 0.135846 0.066787 [313] 0.063432 -0.135141 -0.269823 -0.167889 -0.280686 -0.457161 -0.653975 -0.816416 [321] -0.691397 -0.667434 -0.749241 -0.907055 -0.924575 -1.060746 -0.743248 -0.979182 [329] -1.032643 -1.049463 -1.064820 -0.722184 -0.826912 -0.879851 -0.600402 -0.485218 [337] -0.474649 -0.482563 -0.325446 -0.284252 -0.199437 0.324137 0.269291 0.227392 [345] 0.275366 0.554676 0.513212 0.678868 0.575117 0.800631 0.967619 0.985626 [353] 0.877983 1.130050 1.003327 1.031223 0.938600 0.894526 0.936131 0.921776 [361] 0.729839 0.741252 0.801042 0.452690 0.316212 0.463444 0.174150 0.180528 [369] 0.025572 -0.027861 -0.035183 -0.254118 -0.448403 -0.361562 -0.480372 -0.599570 [377] -0.716556 -0.978822 -0.868095 -0.899780 -0.889003 -1.212809 -0.936850 -0.914872 [385] -0.708651 -0.857610 -1.034849 -0.873827 -0.747812 -0.837841 -0.529324 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0.644127 0.752687 [881] 0.892045 0.830150 1.012149 0.736630 0.915056 1.010314 0.967470 1.074040 [889] 0.969929 1.052997 0.768429 0.987253 0.944919 0.926432 0.989354 1.088121 [897] 1.114191 0.956347 0.826919 0.860805 1.051662 1.046700 0.935175 1.055754 [905] 0.914179 1.071757 0.944316 0.904501 0.883572 0.896286 0.865604 0.914045 [913] 0.902010 0.762866 0.499185 0.607978 0.669228 0.950874 0.650704 0.680393 [921] 0.469986 0.733428 0.553503 0.489168 0.494667 0.335521 0.330488 0.213163 [929] 0.294541 0.193239 0.297200 0.279628 0.047234 0.133355 0.121910 0.131836 [937] -0.159546 0.215912 -0.024681 -0.154823 -0.268119 -0.016491 -0.242633 -0.293635 [945] -0.195649 -0.287497 -0.366917 -0.362930 -0.406867 -0.398483 -0.316419 -0.485540 [953] -0.522943 -0.565903 -0.549048 -0.451718 -0.539942 -0.674976 -0.605367 -0.648732 [961] -0.636346 -0.683019 -0.983954 -0.774175 -0.778645 -1.076530 -0.734000 -0.945962 [969] -0.963318 -1.030235 -1.108809 -0.946843 -0.997289 -0.789405 -0.980609 -0.979494 [977] -0.999809 -0.914506 -0.963061 -1.076397 -0.968043 -0.999039 -1.039874 -0.985952 [985] -1.026914 -1.090971 -1.091551 -0.797769 -0.726782 -0.932085 -0.951486 -0.879593 [993] -1.123251 -0.763735 -0.817981 -0.888878 -0.914471 -0.706287 -1.047424 -0.729106 [ reached getOption("max.print") -- omitted 24 entries ] |
D变量：
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1.304786e-01 2.762620e-02 [411] 1.567903e-01 4.306310e-03 -2.653859e-01 1.356271e-01 9.487137e-02 [416] 1.027860e-01 -5.654236e-02 -1.005861e-01 2.344388e-02 4.027134e-02 [421] -4.017445e-02 1.801772e-02 -1.033892e-01 3.475513e-02 1.701408e-01 [426] -5.128172e-02 -1.634238e-01 1.023643e-01 1.610590e-01 -2.666249e-02 [431] -3.390945e-02 -6.147060e-02 6.827609e-02 -3.709758e-02 -8.660077e-02 [436] -6.589333e-02 5.301064e-02 -3.108457e-02 3.272870e-01 6.961218e-02 [441] -1.336410e-01 -1.632624e-01 -5.787381e-02 2.346349e-01 1.937084e-02 [446] 1.094779e-01 1.791053e-02 3.144318e-02 7.846193e-02 -4.332928e-02 [451] 6.038778e-03 4.713937e-02 6.835427e-02 1.366163e-01 -7.951419e-02 [456] 4.288790e-02 1.120584e-01 1.005783e-01 9.374808e-02 -3.576727e-02 [461] -1.598757e-02 2.283697e-02 8.280369e-02 -2.372313e-03 1.216407e-02 [466] -3.021822e-02 1.514331e-01 1.903270e-02 -1.064367e-02 1.928754e-01 [471] 6.785994e-02 -1.244777e-01 1.317947e-01 -1.171187e-01 3.931856e-02 [476] 9.019697e-02 -4.441719e-02 -6.104842e-02 -3.640358e-02 7.882929e-02 [481] -5.318993e-02 1.421117e-01 6.545700e-02 8.262534e-02 -3.699463e-02 [486] -3.386248e-02 2.312457e-01 1.040194e-01 -7.197747e-02 -1.740371e-01 [491] -1.578724e-01 5.741980e-02 7.140914e-02 4.161671e-02 -5.373970e-02 [496] 4.912161e-02 4.140521e-03 9.916405e-02 8.978955e-02 -3.305709e-05 [501] 1.456247e-01 4.839027e-02 1.023188e-01 -3.866172e-02 7.193397e-02 [506] 1.065479e-01 3.960089e-03 7.780404e-02 4.384112e-02 -1.531487e-01 [511] -8.491370e-02 -1.392553e-01 $d2 [1] 0.0477415175 0.0386860237 -0.0880180584 -0.1273590685 0.0820961028 [6] -0.0099549886 -0.0576645096 0.0719677011 -0.1349857780 0.0483447854 [11] 0.0198023454 -0.1625738646 0.0012492982 -0.0114267648 0.1062209740 [16] 0.1225359478 0.1621114460 -0.0819737310 -0.0470522901 0.0288799246 [21] 0.0095044147 0.1985927003 -0.0962438778 0.0290258862 -0.0191859619 [26] -0.1249148882 0.2365673088 0.0628095216 0.0065759230 -0.0153927927 [31] -0.0928051488 0.1154848084 0.0888687911 -0.0794056203 0.1816490395 [36] 0.0767207068 -0.0858592489 -0.0488393606 -0.0535103078 0.1837119461 [41] -0.0857210424 -0.0308452663 0.2299246363 0.0599722999 0.1778349902 [46] -0.1041062532 0.1191709186 -0.0758875679 0.1917888846 0.0194966446 [51] -0.1110304701 0.0435657941 0.0922149147 -0.0606493936 -0.0804396003 [56] -0.0597893524 -0.1375142765 -0.0785028405 -0.2226820637 0.0253285685 [61] 0.0198333767 -0.2805424467 0.0255316937 0.0779806932 0.1364085786 [66] 0.0231378520 0.2248131662 0.0395414885 0.0446881456 0.1722869937 [71] -0.0623234816 -0.1200950687 0.0943626462 0.0776778947 0.2009390328 [76] 0.0319308393 -0.0001729663 0.0008060633 -0.0494284961 -0.0466142040 [81] 0.0437450651 0.0385805468 0.1076882717 0.2472838005 -0.0863816240 [86] 0.0271969655 -0.0112372412 -0.1414973696 0.0346497059 0.0011235349 [91] -0.0258176639 -0.1335981315 0.0359020637 0.0076360118 0.1522175624 [96] -0.0363469404 0.0271721027 0.1155142370 -0.0146568642 0.0211151526 [101] 0.0456204310 -0.0266485226 -0.1470250416 -0.0025980108 0.0478021277 [106] -0.1270506587 0.1313414469 -0.0362298265 0.2528658761 0.0630928129 [111] 0.0355616805 -0.1939586234 0.1079921097 0.2069690412 -0.1181696478 [116] -0.0313431886 0.2403763224 -0.1672908287 -0.1341294876 0.1291571384 [121] 0.0168236003 0.0026481452 -0.0119424459 0.0453285361 -0.1193224160 [126] -0.0119321332 -0.0595710207 -0.1324543622 0.0078046128 -0.0448876319 [131] 0.2034459679 -0.1057942814 -0.0523800888 -0.0425325815 0.0470114274 [136] -0.0069023238 0.0248426591 0.0544460327 0.0294856211 -0.1841367065 [141] 0.0733933092 0.0031328733 0.0345915128 -0.1731352516 -0.0965073029 [146] -0.0351071274 0.0512506393 0.0787737193 0.1353583562 0.0169377006 [151] 0.1172650475 -0.0139035989 -0.0764296038 -0.1104911716 0.1679525157 [156] -0.0371104228 0.0255856212 -0.0464027719 -0.1227051836 -0.0704117005 [161] -0.0146294235 0.0688463208 0.1261616071 -0.0778333288 -0.0504608283 [166] 0.1003143350 0.0210210450 -0.0129175849 -0.1223036013 -0.0153003295 [171] 0.0831506057 0.0386362826 -0.2609239460 0.1402546455 0.0357319085 [176] -0.0092282253 0.1561504285 -0.0317440170 0.0605509585 -0.0654513162 [181] -0.1395881165 0.2002132522 0.0193468607 -0.0116902221 0.1377578744 [186] 0.0519928748 0.0470585640 0.1328185327 -0.1221004174 0.0580031349 [191] 0.0350528088 0.0306593530 -0.0102386232 0.1238545905 -0.0010789261 [196] 0.1629325007 0.0733950054 -0.0199836552 0.0780897673 0.1189446950 [201] 0.0042110265 0.0246922714 0.0697183541 -0.1052124508 -0.1130703698 [206] -0.1110017660 0.0299187862 -0.1199064510 -0.0041414431 -0.0122250799 [211] -0.1280119431 0.1352246188 0.0449188214 -0.0428061780 -0.0250432350 [216] -0.0830307506 0.1261875376 0.1040855563 -0.0613883780 -0.0866996946 [221] 0.1751533187 -0.2364051526 -0.0782113397 0.0010994396 -0.0070537710 [226] 0.0620828022 0.0888070921 -0.0244400613 -0.0073183750 0.1134787856 [231] -0.0243725714 -0.0246565048 0.0610445778 -0.1136923543 -0.1056802534 [236] -0.0733613696 0.0633739918 -0.0948063338 -0.0482743502 0.1483978760 [241] 0.0890776799 0.0450893094 0.1819614619 -0.0076922720 0.2529053334 [246] -0.1173956872 0.0031411391 -0.0931795054 0.1785810254 0.0458929706 [251] -0.0309783764 -0.1866673727 -0.0300618520 0.1215138929 0.0229725697 [256] 0.1449466755 $d3 [1] 0.1299838141 0.1089680249 -0.3127672146 0.0481466523 -0.0888467600 [6] 0.1562313904 -0.1908710832 -0.3033155240 -0.1222808661 0.0322125234 [11] 0.0229952877 0.0669679844 0.2237622306 -0.0787838895 -0.0267621537 [16] -0.0969776935 -0.1695522284 0.0369876324 0.2404078567 -0.0403642119 [21] 0.0627580422 -0.0859388992 -0.1903929032 -0.0059325338 -0.0007156265 [26] 0.0650327300 -0.0043767107 -0.0815173443 -0.0400316680 -0.1763469852 [31] -0.0138245507 0.1383217609 0.0650518349 -0.0073258823 0.0433624892 [36] 0.0198461149 -0.0638578289 0.0175504991 -0.0204348798 -0.0826227531 [41] -0.0648849652 0.0610952839 -0.1801559769 -0.1819935454 0.0237705816 [46] 0.1628199414 0.0635609283 -0.0255278889 0.0558713259 -0.0744493123 [51] 0.0191462957 0.0473246008 -0.0222018468 0.1177359940 0.0803584539 [56] -0.1302090375 -0.1292357383 0.0952704147 -0.1295563591 -0.0892188522 [61] -0.0599015012 0.0621573896 -0.2618992631 0.0645141551 0.2655573431 [66] -0.1091623369 0.2925373067 -0.1378004978 -0.0496998275 0.0690813920 [71] 0.0043105611 0.1584173444 0.1231505058 0.0063173269 -0.1288328014 [76] 0.1410048794 -0.1609059294 0.0291054717 -0.3181426654 0.0837769455 [81] -0.0331038068 0.2126994765 -0.1247288420 -0.0836999869 0.1782949054 [86] 0.1967440932 -0.0138124646 -0.0544567703 -0.0786022324 0.2135341106 [91] -0.0933760658 0.1521777205 -0.0597633222 0.0508069394 -0.0487722257 [96] -0.1313573535 0.0673635172 0.0114777995 0.1027654663 0.1177810921 [101] 0.1662206531 0.1436401255 0.0351757649 0.0525750263 -0.1348657961 [106] -0.1001415453 -0.0346436709 -0.0157721845 -0.0012472132 -0.1750315293 [111] 0.0778586577 -0.0101349384 0.0177433775 -0.0556005704 -0.1996858505 [116] -0.0300386525 -0.1458708739 -0.0341674267 0.0106776128 -0.0475409947 [121] 0.0138519938 -0.2074502652 -0.0221322765 -0.0362328522 0.1926670271 [126] -0.0369443325 0.0654158859 0.0531361233 $d4 [1] -0.013706814 0.083205500 -0.436098138 0.748750948 0.031082055 -0.647853568 [7] 0.193783145 0.535064173 -0.524363472 -0.200105847 0.560054839 0.109039213 [13] -0.613186609 0.258317873 0.569685259 -0.255253348 -0.415464008 0.462639222 [19] -0.002885610 -0.554408916 0.142259452 0.590980862 -0.320522385 -0.530692369 [25] 0.519074341 0.361603639 -0.692111284 -0.251946618 0.648129387 -0.123200637 [31] -0.665204582 0.374033750 0.427336071 -0.415394810 0.216555790 -0.104709670 [37] 0.314255095 0.059258208 0.107447897 0.055690174 -0.092667680 0.093127863 [43] 0.011887406 -0.153625601 -0.004977462 -0.037125752 -0.209230574 -0.012898640 [49] 0.199461798 -0.104300508 0.081104867 -0.021290449 -0.057351872 -0.145716871 [55] -0.061499352 -0.083656790 -0.080509829 0.053697754 0.002387073 0.013453628 [61] 0.113542443 -0.012187531 0.116696778 -0.017691859 $s4 [1] -3.4722572 -2.0230791 2.1312363 3.0313748 -3.1886782 -1.8769653 3.8609396 [8] 0.3692460 -3.9269093 1.2550543 3.3990462 -2.5395725 -2.6368951 3.5394799 [15] 1.1655239 -3.9154605 0.2589406 3.8258573 -2.0884422 -3.0027849 3.0707279 [22] 1.8661781 -3.6896876 -0.2920342 3.7842825 -1.2446800 -3.5866580 2.4560273 [29] 2.5294180 -3.4709250 -1.0268054 3.9604570 -0.5075112 -3.7096894 0.7170155 [36] 2.5413230 3.7654851 3.7723801 2.3751474 0.1896060 -2.0719965 -3.7651670 [43] -3.9120780 -3.0520953 -1.1660656 1.1197533 3.1523068 4.0416039 3.4889039 [50] 1.8377618 -0.6473579 -2.5435719 -3.7788224 -3.8954183 -2.4976928 -0.5124875 [57] 1.9409717 3.6199176 3.8569644 3.0533129 1.2656010 -1.3482865 -2.9613589 [64] -4.0511120 attr(,"class") [1] "dwt" attr(,"wavelet") [1] "la8" attr(,"boundary") [1] "periodic" |
各层小波系数：
| d.d1 d.d2 d.d3 d.d4 1 0.0799620248 0.0477415175 0.1299838141 -0.013706814 2 -0.0109157951 0.0386860237 0.1089680249 0.083205500 3 0.1973640717 -0.0880180584 -0.3127672146 -0.436098138 4 -0.0025093363 -0.1273590685 0.0481466523 0.748750948 5 0.2133998899 0.0820961028 -0.0888467600 0.031082055 6 -0.1491369736 -0.0099549886 0.1562313904 -0.647853568 7 0.0399566833 -0.0576645096 -0.1908710832 0.193783145 8 -0.0566613361 0.0719677011 -0.3033155240 0.535064173 9 0.1654646116 -0.1349857780 -0.1222808661 -0.524363472 10 0.0424894059 0.0483447854 0.0322125234 -0.200105847 11 0.0268006328 0.0198023454 0.0229952877 0.560054839 12 -0.0490529955 -0.1625738646 0.0669679844 0.109039213 13 0.1759637615 0.0012492982 0.2237622306 -0.613186609 14 0.0101228911 -0.0114267648 -0.0787838895 0.258317873 15 0.0088279894 0.1062209740 -0.0267621537 0.569685259 16 -0.1185913747 0.1225359478 -0.0969776935 -0.255253348 17 0.1104620504 0.1621114460 -0.1695522284 -0.415464008 18 0.0616272809 -0.0819737310 0.0369876324 0.462639222 19 -0.1002050896 -0.0470522901 0.2404078567 -0.002885610 20 -0.0404193378 0.0288799246 -0.0403642119 -0.554408916 21 -0.0500386287 0.0095044147 0.0627580422 0.142259452 22 -0.1247158921 0.1985927003 -0.0859388992 0.590980862 23 0.0113025864 -0.0962438778 -0.1903929032 -0.320522385 24 -0.0226769293 0.0290258862 -0.0059325338 -0.530692369 25 -0.0409669485 -0.0191859619 -0.0007156265 0.519074341 26 0.1480968913 -0.1249148882 0.0650327300 0.361603639 27 -0.0053637151 0.2365673088 -0.0043767107 -0.692111284 28 -0.0527050856 0.0628095216 -0.0815173443 -0.251946618 29 -0.1395580917 0.0065759230 -0.0400316680 0.648129387 30 0.0072704396 -0.0153927927 -0.1763469852 -0.123200637 31 -0.0645710830 -0.0928051488 -0.0138245507 -0.665204582 32 -0.0104084646 0.1154848084 0.1383217609 0.374033750 33 0.0799550208 0.0888687911 0.0650518349 0.427336071 34 0.0054125143 -0.0794056203 -0.0073258823 -0.415394810 35 0.0489524379 0.1816490395 0.0433624892 0.216555790 36 0.1408812386 0.0767207068 0.0198461149 -0.104709670 37 0.1605731513 -0.0858592489 -0.0638578289 0.314255095 38 0.0197814217 -0.0488393606 0.0175504991 0.059258208 39 -0.0103766645 -0.0535103078 -0.0204348798 0.107447897 40 0.0411444575 0.1837119461 -0.0826227531 0.055690174 41 0.0886923151 -0.0857210424 -0.0648849652 -0.092667680 42 -0.1071197524 -0.0308452663 0.0610952839 0.093127863 43 0.1605157206 0.2299246363 -0.1801559769 0.011887406 44 -0.0488377713 0.0599722999 -0.1819935454 -0.153625601 45 0.0773904510 0.1778349902 0.0237705816 -0.004977462 46 0.0136003270 -0.1041062532 0.1628199414 -0.037125752 47 -0.0235173510 0.1191709186 0.0635609283 -0.209230574 48 0.2187629991 -0.0758875679 -0.0255278889 -0.012898640 49 0.0853201288 0.1917888846 0.0558713259 0.199461798 50 0.0021347741 0.0194966446 -0.0744493123 -0.104300508 51 0.0018867451 -0.1110304701 0.0191462957 0.081104867 52 0.0552811143 0.0435657941 0.0473246008 -0.021290449 53 -0.0237662735 0.0922149147 -0.0222018468 -0.057351872 54 -0.1080351333 -0.0606493936 0.1177359940 -0.145716871 55 0.0400917079 -0.0804396003 0.0803584539 -0.061499352 56 0.1426342572 -0.0597893524 -0.1302090375 -0.083656790 57 -0.0948758199 -0.1375142765 -0.1292357383 -0.080509829 58 -0.0124793425 -0.0785028405 0.0952704147 0.053697754 59 0.0219722332 -0.2226820637 -0.1295563591 0.002387073 60 -0.0173276924 0.0253285685 -0.0892188522 0.013453628 61 -0.0448573818 0.0198333767 -0.0599015012 0.113542443 62 0.0315960312 -0.2805424467 0.0621573896 -0.012187531 63 -0.0580308210 0.0255316937 -0.2618992631 0.116696778 64 0.0323421000 0.0779806932 0.0645141551 -0.017691859 65 -0.0620520346 0.1364085786 0.2655573431 -0.013706814 66 -0.0224765056 0.0231378520 -0.1091623369 0.083205500 67 0.2326436241 0.2248131662 0.2925373067 -0.436098138 68 0.0903618017 0.0395414885 -0.1378004978 0.748750948 69 0.1240559485 0.0446881456 -0.0496998275 0.031082055 70 0.0408376853 0.1722869937 0.0690813920 -0.647853568 71 -0.0302644614 -0.0623234816 0.0043105611 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![[寿司力扣DP对于应用]712. 两个字符串的最小ASCII删除和【详细图解】](https://img-blog.csdnimg.cn/direct/c170f043b2f84215877b2eb59d98c3d8.png)
