File size: 80,183 Bytes
c61ccee
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
import types
import math
from torch import inf
from functools import wraps, partial
import warnings
import weakref
from collections import Counter
from bisect import bisect_right

from .optimizer import Optimizer

__all__ = ['LambdaLR', 'MultiplicativeLR', 'StepLR', 'MultiStepLR', 'ConstantLR', 'LinearLR',
           'ExponentialLR', 'SequentialLR', 'CosineAnnealingLR', 'ChainedScheduler', 'ReduceLROnPlateau',
           'CyclicLR', 'CosineAnnealingWarmRestarts', 'OneCycleLR', 'PolynomialLR', 'LRScheduler']

EPOCH_DEPRECATION_WARNING = (
    "The epoch parameter in `scheduler.step()` was not necessary and is being "
    "deprecated where possible. Please use `scheduler.step()` to step the "
    "scheduler. During the deprecation, if epoch is different from None, the "
    "closed form is used instead of the new chainable form, where available. "
    "Please open an issue if you are unable to replicate your use case: "
    "https://github.com/pytorch/pytorch/issues/new/choose."
)

def _check_verbose_deprecated_warning(verbose):
    """Raises a warning when verbose is not the default value."""
    if verbose != "deprecated":
        warnings.warn("The verbose parameter is deprecated. Please use get_last_lr() "
                      "to access the learning rate.", UserWarning)
        return verbose
    return False

class LRScheduler:

    def __init__(self, optimizer, last_epoch=-1, verbose="deprecated"):

        # Attach optimizer
        if not isinstance(optimizer, Optimizer):
            raise TypeError(f'{type(optimizer).__name__} is not an Optimizer')
        self.optimizer = optimizer

        # Initialize epoch and base learning rates
        if last_epoch == -1:
            for group in optimizer.param_groups:
                group.setdefault('initial_lr', group['lr'])
        else:
            for i, group in enumerate(optimizer.param_groups):
                if 'initial_lr' not in group:
                    raise KeyError("param 'initial_lr' is not specified "
                                   f"in param_groups[{i}] when resuming an optimizer")
        self.base_lrs = [group['initial_lr'] for group in optimizer.param_groups]
        self.last_epoch = last_epoch

        # Following https://github.com/pytorch/pytorch/issues/20124
        # We would like to ensure that `lr_scheduler.step()` is called after
        # `optimizer.step()`
        def with_counter(method):
            if getattr(method, '_with_counter', False):
                # `optimizer.step()` has already been replaced, return.
                return method

            # Keep a weak reference to the optimizer instance to prevent
            # cyclic references.
            instance_ref = weakref.ref(method.__self__)
            # Get the unbound method for the same purpose.
            func = method.__func__
            cls = instance_ref().__class__
            del method

            @wraps(func)
            def wrapper(*args, **kwargs):
                instance = instance_ref()
                instance._step_count += 1
                wrapped = func.__get__(instance, cls)
                return wrapped(*args, **kwargs)

            # Note that the returned function here is no longer a bound method,
            # so attributes like `__func__` and `__self__` no longer exist.
            wrapper._with_counter = True
            return wrapper

        self.optimizer.step = with_counter(self.optimizer.step)
        self.verbose = _check_verbose_deprecated_warning(verbose)

        self._initial_step()

    def _initial_step(self):
        """Initialize step counts and performs a step"""
        self.optimizer._step_count = 0
        self._step_count = 0
        self.step()

    def state_dict(self):
        """Returns the state of the scheduler as a :class:`dict`.



        It contains an entry for every variable in self.__dict__ which

        is not the optimizer.

        """
        return {key: value for key, value in self.__dict__.items() if key != 'optimizer'}

    def load_state_dict(self, state_dict):
        """Loads the schedulers state.



        Args:

            state_dict (dict): scheduler state. Should be an object returned

                from a call to :meth:`state_dict`.

        """
        self.__dict__.update(state_dict)

    def get_last_lr(self):
        """ Return last computed learning rate by current scheduler.

        """
        return self._last_lr

    def get_lr(self):
        # Compute learning rate using chainable form of the scheduler
        raise NotImplementedError

    def print_lr(self, is_verbose, group, lr, epoch=None):
        """Display the current learning rate.

        """
        if is_verbose:
            if epoch is None:
                print(f'Adjusting learning rate of group {group} to {lr:.4e}.')
            else:
                epoch_str = ("%.2f" if isinstance(epoch, float) else
                             "%.5d") % epoch
                print(f'Epoch {epoch_str}: adjusting learning rate of group {group} to {lr:.4e}.')


    def step(self, epoch=None):
        # Raise a warning if old pattern is detected
        # https://github.com/pytorch/pytorch/issues/20124
        if self._step_count == 1:
            if not hasattr(self.optimizer.step, "_with_counter"):
                warnings.warn("Seems like `optimizer.step()` has been overridden after learning rate scheduler "
                              "initialization. Please, make sure to call `optimizer.step()` before "
                              "`lr_scheduler.step()`. See more details at "
                              "https://pytorch.org/docs/stable/optim.html#how-to-adjust-learning-rate", UserWarning)

            # Just check if there were two first lr_scheduler.step() calls before optimizer.step()
            elif self.optimizer._step_count < 1:
                warnings.warn("Detected call of `lr_scheduler.step()` before `optimizer.step()`. "
                              "In PyTorch 1.1.0 and later, you should call them in the opposite order: "
                              "`optimizer.step()` before `lr_scheduler.step()`.  Failure to do this "
                              "will result in PyTorch skipping the first value of the learning rate schedule. "
                              "See more details at "
                              "https://pytorch.org/docs/stable/optim.html#how-to-adjust-learning-rate", UserWarning)
        self._step_count += 1

        with _enable_get_lr_call(self):
            if epoch is None:
                self.last_epoch += 1
                values = self.get_lr()
            else:
                warnings.warn(EPOCH_DEPRECATION_WARNING, UserWarning)
                self.last_epoch = epoch
                if hasattr(self, "_get_closed_form_lr"):
                    values = self._get_closed_form_lr()
                else:
                    values = self.get_lr()

        for i, data in enumerate(zip(self.optimizer.param_groups, values)):
            param_group, lr = data
            param_group['lr'] = lr

        self._last_lr = [group['lr'] for group in self.optimizer.param_groups]


# Including _LRScheduler for backwards compatibility
# Subclass instead of assign because we want __name__ of _LRScheduler to be _LRScheduler (assigning would make it LRScheduler).
class _LRScheduler(LRScheduler):
    pass


class _enable_get_lr_call:

    def __init__(self, o):
        self.o = o

    def __enter__(self):
        self.o._get_lr_called_within_step = True
        return self

    def __exit__(self, type, value, traceback):
        self.o._get_lr_called_within_step = False


class LambdaLR(LRScheduler):
    """Sets the learning rate of each parameter group to the initial lr

    times a given function. When last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        lr_lambda (function or list): A function which computes a multiplicative

            factor given an integer parameter epoch, or a list of such

            functions, one for each group in optimizer.param_groups.

        last_epoch (int): The index of last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> # Assuming optimizer has two groups.

        >>> lambda1 = lambda epoch: epoch // 30

        >>> lambda2 = lambda epoch: 0.95 ** epoch

        >>> scheduler = LambdaLR(optimizer, lr_lambda=[lambda1, lambda2])

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, optimizer, lr_lambda, last_epoch=-1, verbose="deprecated"):
        self.optimizer = optimizer

        if not isinstance(lr_lambda, list) and not isinstance(lr_lambda, tuple):
            self.lr_lambdas = [lr_lambda] * len(optimizer.param_groups)
        else:
            if len(lr_lambda) != len(optimizer.param_groups):
                raise ValueError(f"Expected {len(optimizer.param_groups)} lr_lambdas, but got {len(lr_lambda)}")
            self.lr_lambdas = list(lr_lambda)
        super().__init__(optimizer, last_epoch, verbose)

    def state_dict(self):
        """Returns the state of the scheduler as a :class:`dict`.



        It contains an entry for every variable in self.__dict__ which

        is not the optimizer.

        The learning rate lambda functions will only be saved if they are callable objects

        and not if they are functions or lambdas.



        When saving or loading the scheduler, please make sure to also save or load the state of the optimizer.

        """

        state_dict = {key: value for key, value in self.__dict__.items() if key not in ('optimizer', 'lr_lambdas')}
        state_dict['lr_lambdas'] = [None] * len(self.lr_lambdas)

        for idx, fn in enumerate(self.lr_lambdas):
            if not isinstance(fn, types.FunctionType):
                state_dict['lr_lambdas'][idx] = fn.__dict__.copy()

        return state_dict

    def load_state_dict(self, state_dict):
        """Loads the schedulers state.



        When saving or loading the scheduler, please make sure to also save or load the state of the optimizer.



        Args:

            state_dict (dict): scheduler state. Should be an object returned

                from a call to :meth:`state_dict`.

        """

        lr_lambdas = state_dict.pop('lr_lambdas')
        self.__dict__.update(state_dict)
        # Restore state_dict keys in order to prevent side effects
        # https://github.com/pytorch/pytorch/issues/32756
        state_dict['lr_lambdas'] = lr_lambdas

        for idx, fn in enumerate(lr_lambdas):
            if fn is not None:
                self.lr_lambdas[idx].__dict__.update(fn)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.")

        return [base_lr * lmbda(self.last_epoch)
                for lmbda, base_lr in zip(self.lr_lambdas, self.base_lrs)]


class MultiplicativeLR(LRScheduler):
    """Multiply the learning rate of each parameter group by the factor given

    in the specified function. When last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        lr_lambda (function or list): A function which computes a multiplicative

            factor given an integer parameter epoch, or a list of such

            functions, one for each group in optimizer.param_groups.

        last_epoch (int): The index of last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> lmbda = lambda epoch: 0.95

        >>> scheduler = MultiplicativeLR(optimizer, lr_lambda=lmbda)

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, optimizer, lr_lambda, last_epoch=-1, verbose="deprecated"):
        self.optimizer = optimizer

        if not isinstance(lr_lambda, list) and not isinstance(lr_lambda, tuple):
            self.lr_lambdas = [lr_lambda] * len(optimizer.param_groups)
        else:
            if len(lr_lambda) != len(optimizer.param_groups):
                raise ValueError(f"Expected {len(optimizer.param_groups)} lr_lambdas, but got {len(lr_lambda)}")
            self.lr_lambdas = list(lr_lambda)
        super().__init__(optimizer, last_epoch, verbose)

    def state_dict(self):
        """Returns the state of the scheduler as a :class:`dict`.



        It contains an entry for every variable in self.__dict__ which

        is not the optimizer.

        The learning rate lambda functions will only be saved if they are callable objects

        and not if they are functions or lambdas.

        """
        state_dict = {key: value for key, value in self.__dict__.items() if key not in ('optimizer', 'lr_lambdas')}
        state_dict['lr_lambdas'] = [None] * len(self.lr_lambdas)

        for idx, fn in enumerate(self.lr_lambdas):
            if not isinstance(fn, types.FunctionType):
                state_dict['lr_lambdas'][idx] = fn.__dict__.copy()

        return state_dict

    def load_state_dict(self, state_dict):
        """Loads the schedulers state.



        Args:

            state_dict (dict): scheduler state. Should be an object returned

                from a call to :meth:`state_dict`.

        """
        lr_lambdas = state_dict.pop('lr_lambdas')
        self.__dict__.update(state_dict)
        # Restore state_dict keys in order to prevent side effects
        # https://github.com/pytorch/pytorch/issues/32756
        state_dict['lr_lambdas'] = lr_lambdas

        for idx, fn in enumerate(lr_lambdas):
            if fn is not None:
                self.lr_lambdas[idx].__dict__.update(fn)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if self.last_epoch > 0:
            return [group['lr'] * lmbda(self.last_epoch)
                    for lmbda, group in zip(self.lr_lambdas, self.optimizer.param_groups)]
        else:
            return [group['lr'] for group in self.optimizer.param_groups]


class StepLR(LRScheduler):
    """Decays the learning rate of each parameter group by gamma every

    step_size epochs. Notice that such decay can happen simultaneously with

    other changes to the learning rate from outside this scheduler. When

    last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        step_size (int): Period of learning rate decay.

        gamma (float): Multiplicative factor of learning rate decay.

            Default: 0.1.

        last_epoch (int): The index of last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> # Assuming optimizer uses lr = 0.05 for all groups

        >>> # lr = 0.05     if epoch < 30

        >>> # lr = 0.005    if 30 <= epoch < 60

        >>> # lr = 0.0005   if 60 <= epoch < 90

        >>> # ...

        >>> scheduler = StepLR(optimizer, step_size=30, gamma=0.1)

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, optimizer, step_size, gamma=0.1, last_epoch=-1, verbose="deprecated"):
        self.step_size = step_size
        self.gamma = gamma
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if (self.last_epoch == 0) or (self.last_epoch % self.step_size != 0):
            return [group['lr'] for group in self.optimizer.param_groups]
        return [group['lr'] * self.gamma
                for group in self.optimizer.param_groups]

    def _get_closed_form_lr(self):
        return [base_lr * self.gamma ** (self.last_epoch // self.step_size)
                for base_lr in self.base_lrs]


class MultiStepLR(LRScheduler):
    """Decays the learning rate of each parameter group by gamma once the

    number of epoch reaches one of the milestones. Notice that such decay can

    happen simultaneously with other changes to the learning rate from outside

    this scheduler. When last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        milestones (list): List of epoch indices. Must be increasing.

        gamma (float): Multiplicative factor of learning rate decay.

            Default: 0.1.

        last_epoch (int): The index of last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> # Assuming optimizer uses lr = 0.05 for all groups

        >>> # lr = 0.05     if epoch < 30

        >>> # lr = 0.005    if 30 <= epoch < 80

        >>> # lr = 0.0005   if epoch >= 80

        >>> scheduler = MultiStepLR(optimizer, milestones=[30,80], gamma=0.1)

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, optimizer, milestones, gamma=0.1, last_epoch=-1, verbose="deprecated"):
        self.milestones = Counter(milestones)
        self.gamma = gamma
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if self.last_epoch not in self.milestones:
            return [group['lr'] for group in self.optimizer.param_groups]
        return [group['lr'] * self.gamma ** self.milestones[self.last_epoch]
                for group in self.optimizer.param_groups]

    def _get_closed_form_lr(self):
        milestones = sorted(self.milestones.elements())
        return [base_lr * self.gamma ** bisect_right(milestones, self.last_epoch)
                for base_lr in self.base_lrs]


class ConstantLR(LRScheduler):
    """Multiply the learning rate of each parameter group by a small constant factor until the

    number of epoch reaches a pre-defined milestone: total_iters.

    Notice that such multiplication of the small constant factor can

    happen simultaneously with other changes to the learning rate from outside this scheduler.

    When last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        factor (float): The number we multiply learning rate until the milestone. Default: 1./3.

        total_iters (int): The number of steps that the scheduler multiplies the learning rate by the factor.

            Default: 5.

        last_epoch (int): The index of the last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> # Assuming optimizer uses lr = 0.05 for all groups

        >>> # lr = 0.025   if epoch == 0

        >>> # lr = 0.025   if epoch == 1

        >>> # lr = 0.025   if epoch == 2

        >>> # lr = 0.025   if epoch == 3

        >>> # lr = 0.05    if epoch >= 4

        >>> scheduler = ConstantLR(optimizer, factor=0.5, total_iters=4)

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, optimizer, factor=1.0 / 3, total_iters=5, last_epoch=-1, verbose="deprecated"):
        if factor > 1.0 or factor < 0:
            raise ValueError('Constant multiplicative factor expected to be between 0 and 1.')

        self.factor = factor
        self.total_iters = total_iters
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if self.last_epoch == 0:
            return [group['lr'] * self.factor for group in self.optimizer.param_groups]

        if self.last_epoch != self.total_iters:
            return [group['lr'] for group in self.optimizer.param_groups]

        return [group['lr'] * (1.0 / self.factor) for group in self.optimizer.param_groups]

    def _get_closed_form_lr(self):
        return [base_lr * (self.factor + (self.last_epoch >= self.total_iters) * (1 - self.factor))
                for base_lr in self.base_lrs]


class LinearLR(LRScheduler):
    """Decays the learning rate of each parameter group by linearly changing small

    multiplicative factor until the number of epoch reaches a pre-defined milestone: total_iters.

    Notice that such decay can happen simultaneously with other changes to the learning rate

    from outside this scheduler. When last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        start_factor (float): The number we multiply learning rate in the first epoch.

            The multiplication factor changes towards end_factor in the following epochs.

            Default: 1./3.

        end_factor (float): The number we multiply learning rate at the end of linear changing

            process. Default: 1.0.

        total_iters (int): The number of iterations that multiplicative factor reaches to 1.

            Default: 5.

        last_epoch (int): The index of the last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> # Assuming optimizer uses lr = 0.05 for all groups

        >>> # lr = 0.025    if epoch == 0

        >>> # lr = 0.03125  if epoch == 1

        >>> # lr = 0.0375   if epoch == 2

        >>> # lr = 0.04375  if epoch == 3

        >>> # lr = 0.05    if epoch >= 4

        >>> scheduler = LinearLR(optimizer, start_factor=0.5, total_iters=4)

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, optimizer, start_factor=1.0 / 3, end_factor=1.0, total_iters=5, last_epoch=-1,

                 verbose="deprecated"):
        if start_factor > 1.0 or start_factor <= 0:
            raise ValueError('Starting multiplicative factor expected to be greater than 0 and less or equal to 1.')

        if end_factor > 1.0 or end_factor < 0:
            raise ValueError('Ending multiplicative factor expected to be between 0 and 1.')

        self.start_factor = start_factor
        self.end_factor = end_factor
        self.total_iters = total_iters
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if self.last_epoch == 0:
            return [group['lr'] * self.start_factor for group in self.optimizer.param_groups]

        if self.last_epoch > self.total_iters:
            return [group['lr'] for group in self.optimizer.param_groups]

        return [group['lr'] * (1. + (self.end_factor - self.start_factor) /
                (self.total_iters * self.start_factor + (self.last_epoch - 1) * (self.end_factor - self.start_factor)))
                for group in self.optimizer.param_groups]

    def _get_closed_form_lr(self):
        return [base_lr * (self.start_factor +
                (self.end_factor - self.start_factor) * min(self.total_iters, self.last_epoch) / self.total_iters)
                for base_lr in self.base_lrs]


class ExponentialLR(LRScheduler):
    """Decays the learning rate of each parameter group by gamma every epoch.

    When last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        gamma (float): Multiplicative factor of learning rate decay.

        last_epoch (int): The index of last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.

    """

    def __init__(self, optimizer, gamma, last_epoch=-1, verbose="deprecated"):
        self.gamma = gamma
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if self.last_epoch == 0:
            return [group['lr'] for group in self.optimizer.param_groups]
        return [group['lr'] * self.gamma
                for group in self.optimizer.param_groups]

    def _get_closed_form_lr(self):
        return [base_lr * self.gamma ** self.last_epoch
                for base_lr in self.base_lrs]


class SequentialLR(LRScheduler):
    """Receives the list of schedulers that is expected to be called sequentially during

    optimization process and milestone points that provides exact intervals to reflect

    which scheduler is supposed to be called at a given epoch.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        schedulers (list): List of chained schedulers.

        milestones (list): List of integers that reflects milestone points.

        last_epoch (int): The index of last epoch. Default: -1.

        verbose (bool): Does nothing.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> # Assuming optimizer uses lr = 1. for all groups

        >>> # lr = 0.1     if epoch == 0

        >>> # lr = 0.1     if epoch == 1

        >>> # lr = 0.9     if epoch == 2

        >>> # lr = 0.81    if epoch == 3

        >>> # lr = 0.729   if epoch == 4

        >>> scheduler1 = ConstantLR(optimizer, factor=0.1, total_iters=2)

        >>> scheduler2 = ExponentialLR(optimizer, gamma=0.9)

        >>> scheduler = SequentialLR(optimizer, schedulers=[scheduler1, scheduler2], milestones=[2])

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, optimizer, schedulers, milestones, last_epoch=-1, verbose="deprecated"):
        for scheduler_idx in range(len(schedulers)):
            if schedulers[scheduler_idx].optimizer != optimizer:
                raise ValueError(
                    "Sequential Schedulers expects all schedulers to belong to the same optimizer, but "
                    f"got schedulers at index {scheduler_idx} to be different than the optimizer passed in."
                )

            if (schedulers[scheduler_idx].optimizer != schedulers[0].optimizer):
                raise ValueError(
                    "Sequential Schedulers expects all schedulers to belong to the same optimizer, but "
                    f"got schedulers at index {0} and {scheduler_idx} to be different."
                )
        if (len(milestones) != len(schedulers) - 1):
            raise ValueError(
                "Sequential Schedulers expects number of schedulers provided to be one more "
                f"than the number of milestone points, but got number of schedulers {len(schedulers)} and the "
                f"number of milestones to be equal to {len(milestones)}"
            )
        _check_verbose_deprecated_warning(verbose)
        self._schedulers = schedulers
        self._milestones = milestones
        self.last_epoch = last_epoch + 1
        self.optimizer = optimizer

        # Reset learning rates back to initial values
        for group in self.optimizer.param_groups:
            group["lr"] = group["initial_lr"]

        # "Undo" the step performed by other schedulers
        for scheduler in self._schedulers:
            scheduler.last_epoch -= 1

        # Perform the initial step for only the first scheduler
        self._schedulers[0]._initial_step()

        self._last_lr = schedulers[0].get_last_lr()

    def step(self):
        self.last_epoch += 1
        idx = bisect_right(self._milestones, self.last_epoch)
        scheduler = self._schedulers[idx]
        if idx > 0 and self._milestones[idx - 1] == self.last_epoch:
            scheduler.step(0)
        else:
            scheduler.step()

        self._last_lr = scheduler.get_last_lr()

    def state_dict(self):
        """Returns the state of the scheduler as a :class:`dict`.



        It contains an entry for every variable in self.__dict__ which

        is not the optimizer.

        The wrapped scheduler states will also be saved.

        """
        state_dict = {key: value for key, value in self.__dict__.items() if key not in ('optimizer', '_schedulers')}
        state_dict['_schedulers'] = [None] * len(self._schedulers)

        for idx, s in enumerate(self._schedulers):
            state_dict['_schedulers'][idx] = s.state_dict()

        return state_dict

    def load_state_dict(self, state_dict):
        """Loads the schedulers state.



        Args:

            state_dict (dict): scheduler state. Should be an object returned

                from a call to :meth:`state_dict`.

        """
        _schedulers = state_dict.pop('_schedulers')
        self.__dict__.update(state_dict)
        # Restore state_dict keys in order to prevent side effects
        # https://github.com/pytorch/pytorch/issues/32756
        state_dict['_schedulers'] = _schedulers

        for idx, s in enumerate(_schedulers):
            self._schedulers[idx].load_state_dict(s)


class PolynomialLR(LRScheduler):
    """Decays the learning rate of each parameter group using a polynomial function

    in the given total_iters. When last_epoch=-1, sets initial lr as lr.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        total_iters (int): The number of steps that the scheduler decays the learning rate. Default: 5.

        power (float): The power of the polynomial. Default: 1.0.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP("undefined vars")

        >>> # Assuming optimizer uses lr = 0.001 for all groups

        >>> # lr = 0.001     if epoch == 0

        >>> # lr = 0.00075   if epoch == 1

        >>> # lr = 0.00050   if epoch == 2

        >>> # lr = 0.00025   if epoch == 3

        >>> # lr = 0.0       if epoch >= 4

        >>> scheduler = PolynomialLR(optimizer, total_iters=4, power=1.0)

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """
    def __init__(self, optimizer, total_iters=5, power=1.0, last_epoch=-1, verbose="deprecated"):
        self.total_iters = total_iters
        self.power = power
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if self.last_epoch == 0 or self.last_epoch > self.total_iters:
            return [group["lr"] for group in self.optimizer.param_groups]

        decay_factor = ((1.0 - self.last_epoch / self.total_iters) / (1.0 - (self.last_epoch - 1) / self.total_iters)) ** self.power
        return [group["lr"] * decay_factor for group in self.optimizer.param_groups]

    def _get_closed_form_lr(self):
        return [
            (
                base_lr * (1.0 - min(self.total_iters, self.last_epoch) / self.total_iters) ** self.power
            )
            for base_lr in self.base_lrs
        ]


class CosineAnnealingLR(LRScheduler):
    r"""Set the learning rate of each parameter group using a cosine annealing

    schedule, where :math:`\eta_{max}` is set to the initial lr and

    :math:`T_{cur}` is the number of epochs since the last restart in SGDR:



    .. math::

        \begin{aligned}

            \eta_t & = \eta_{min} + \frac{1}{2}(\eta_{max} - \eta_{min})\left(1

            + \cos\left(\frac{T_{cur}}{T_{max}}\pi\right)\right),

            & T_{cur} \neq (2k+1)T_{max}; \\

            \eta_{t+1} & = \eta_{t} + \frac{1}{2}(\eta_{max} - \eta_{min})

            \left(1 - \cos\left(\frac{1}{T_{max}}\pi\right)\right),

            & T_{cur} = (2k+1)T_{max}.

        \end{aligned}



    When last_epoch=-1, sets initial lr as lr. Notice that because the schedule

    is defined recursively, the learning rate can be simultaneously modified

    outside this scheduler by other operators. If the learning rate is set

    solely by this scheduler, the learning rate at each step becomes:



    .. math::

        \eta_t = \eta_{min} + \frac{1}{2}(\eta_{max} - \eta_{min})\left(1 +

        \cos\left(\frac{T_{cur}}{T_{max}}\pi\right)\right)



    It has been proposed in

    `SGDR: Stochastic Gradient Descent with Warm Restarts`_. Note that this only

    implements the cosine annealing part of SGDR, and not the restarts.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        T_max (int): Maximum number of iterations.

        eta_min (float): Minimum learning rate. Default: 0.

        last_epoch (int): The index of last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    .. _SGDR\: Stochastic Gradient Descent with Warm Restarts:

        https://arxiv.org/abs/1608.03983

    """

    def __init__(self, optimizer, T_max, eta_min=0, last_epoch=-1, verbose="deprecated"):
        self.T_max = T_max
        self.eta_min = eta_min
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        if self.last_epoch == 0:
            return [group['lr'] for group in self.optimizer.param_groups]
        elif self._step_count == 1 and self.last_epoch > 0:
            return [self.eta_min + (base_lr - self.eta_min) *
                    (1 + math.cos((self.last_epoch) * math.pi / self.T_max)) / 2
                    for base_lr, group in
                    zip(self.base_lrs, self.optimizer.param_groups)]
        elif (self.last_epoch - 1 - self.T_max) % (2 * self.T_max) == 0:
            return [group['lr'] + (base_lr - self.eta_min) *
                    (1 - math.cos(math.pi / self.T_max)) / 2
                    for base_lr, group in
                    zip(self.base_lrs, self.optimizer.param_groups)]
        return [(1 + math.cos(math.pi * self.last_epoch / self.T_max)) /
                (1 + math.cos(math.pi * (self.last_epoch - 1) / self.T_max)) *
                (group['lr'] - self.eta_min) + self.eta_min
                for group in self.optimizer.param_groups]

    def _get_closed_form_lr(self):
        return [self.eta_min + (base_lr - self.eta_min) *
                (1 + math.cos(math.pi * self.last_epoch / self.T_max)) / 2
                for base_lr in self.base_lrs]


class ChainedScheduler(LRScheduler):
    """Chains list of learning rate schedulers. It takes a list of chainable learning

    rate schedulers and performs consecutive step() functions belonging to them by just

    one call.



    Args:

        schedulers (list): List of chained schedulers.



    Example:

        >>> # xdoctest: +SKIP

        >>> # Assuming optimizer uses lr = 1. for all groups

        >>> # lr = 0.09     if epoch == 0

        >>> # lr = 0.081    if epoch == 1

        >>> # lr = 0.729    if epoch == 2

        >>> # lr = 0.6561   if epoch == 3

        >>> # lr = 0.59049  if epoch >= 4

        >>> scheduler1 = ConstantLR(optimizer, factor=0.1, total_iters=2)

        >>> scheduler2 = ExponentialLR(optimizer, gamma=0.9)

        >>> scheduler = ChainedScheduler([scheduler1, scheduler2])

        >>> for epoch in range(100):

        >>>     train(...)

        >>>     validate(...)

        >>>     scheduler.step()

    """

    def __init__(self, schedulers):
        for scheduler_idx in range(1, len(schedulers)):
            if (schedulers[scheduler_idx].optimizer != schedulers[0].optimizer):
                raise ValueError(
                    "ChainedScheduler expects all schedulers to belong to the same optimizer, but "
                    f"got schedulers at index {0} and {scheduler_idx} to be different"
                )
        self._schedulers = list(schedulers)
        self.optimizer = schedulers[0].optimizer
        self._last_lr = [group['lr'] for group in self._schedulers[-1].optimizer.param_groups]

    def step(self):
        for scheduler in self._schedulers:
            scheduler.step()
        self._last_lr = [group['lr'] for group in self._schedulers[-1].optimizer.param_groups]

    def state_dict(self):
        """Returns the state of the scheduler as a :class:`dict`.



        It contains an entry for every variable in self.__dict__ which

        is not the optimizer.

        The wrapped scheduler states will also be saved.

        """
        state_dict = {key: value for key, value in self.__dict__.items() if key not in ('optimizer', '_schedulers')}
        state_dict['_schedulers'] = [None] * len(self._schedulers)

        for idx, s in enumerate(self._schedulers):
            state_dict['_schedulers'][idx] = s.state_dict()

        return state_dict

    def load_state_dict(self, state_dict):
        """Loads the schedulers state.



        Args:

            state_dict (dict): scheduler state. Should be an object returned

                from a call to :meth:`state_dict`.

        """
        _schedulers = state_dict.pop('_schedulers')
        self.__dict__.update(state_dict)
        # Restore state_dict keys in order to prevent side effects
        # https://github.com/pytorch/pytorch/issues/32756
        state_dict['_schedulers'] = _schedulers

        for idx, s in enumerate(_schedulers):
            self._schedulers[idx].load_state_dict(s)


class ReduceLROnPlateau(LRScheduler):
    """Reduce learning rate when a metric has stopped improving.

    Models often benefit from reducing the learning rate by a factor

    of 2-10 once learning stagnates. This scheduler reads a metrics

    quantity and if no improvement is seen for a 'patience' number

    of epochs, the learning rate is reduced.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        mode (str): One of `min`, `max`. In `min` mode, lr will

            be reduced when the quantity monitored has stopped

            decreasing; in `max` mode it will be reduced when the

            quantity monitored has stopped increasing. Default: 'min'.

        factor (float): Factor by which the learning rate will be

            reduced. new_lr = lr * factor. Default: 0.1.

        patience (int): The number of allowed epochs with no improvement after

            which the learning rate will be reduced.

            For example, consider the case of having no patience (`patience = 0`).

            In the first epoch, a baseline is established and is always considered good as there's no previous baseline.

            In the second epoch, if the performance is worse than the baseline,

            we have what is considered an intolerable epoch.

            Since the count of intolerable epochs (1) is greater than the patience level (0),

            the learning rate is reduced at the end of this epoch.

            From the third epoch onwards, the learning rate continues to be reduced at the end of each epoch

            if the performance is worse than the baseline. If the performance improves or remains the same,

            the learning rate is not adjusted.

            Default: 10.

        threshold (float): Threshold for measuring the new optimum,

            to only focus on significant changes. Default: 1e-4.

        threshold_mode (str): One of `rel`, `abs`. In `rel` mode,

            dynamic_threshold = best * ( 1 + threshold ) in 'max'

            mode or best * ( 1 - threshold ) in `min` mode.

            In `abs` mode, dynamic_threshold = best + threshold in

            `max` mode or best - threshold in `min` mode. Default: 'rel'.

        cooldown (int): Number of epochs to wait before resuming

            normal operation after lr has been reduced. Default: 0.

        min_lr (float or list): A scalar or a list of scalars. A

            lower bound on the learning rate of all param groups

            or each group respectively. Default: 0.

        eps (float): Minimal decay applied to lr. If the difference

            between new and old lr is smaller than eps, the update is

            ignored. Default: 1e-8.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)

        >>> scheduler = ReduceLROnPlateau(optimizer, 'min')

        >>> for epoch in range(10):

        >>>     train(...)

        >>>     val_loss = validate(...)

        >>>     # Note that step should be called after validate()

        >>>     scheduler.step(val_loss)

    """

    def __init__(self, optimizer, mode='min', factor=0.1, patience=10,

                 threshold=1e-4, threshold_mode='rel', cooldown=0,

                 min_lr=0, eps=1e-8, verbose="deprecated"):

        if factor >= 1.0:
            raise ValueError('Factor should be < 1.0.')
        self.factor = factor

        # Attach optimizer
        if not isinstance(optimizer, Optimizer):
            raise TypeError(f'{type(optimizer).__name__} is not an Optimizer')
        self.optimizer = optimizer

        if isinstance(min_lr, (list, tuple)):
            if len(min_lr) != len(optimizer.param_groups):
                raise ValueError(f"expected {len(optimizer.param_groups)} min_lrs, got {len(min_lr)}")
            self.min_lrs = list(min_lr)
        else:
            self.min_lrs = [min_lr] * len(optimizer.param_groups)

        self.patience = patience

        self.verbose = _check_verbose_deprecated_warning(verbose)
        self.cooldown = cooldown
        self.cooldown_counter = 0
        self.mode = mode
        self.threshold = threshold
        self.threshold_mode = threshold_mode
        self.best = None
        self.num_bad_epochs = None
        self.mode_worse = None  # the worse value for the chosen mode
        self.eps = eps
        self.last_epoch = 0
        self._last_lr = [group['lr'] for group in self.optimizer.param_groups]
        self._init_is_better(mode=mode, threshold=threshold,
                             threshold_mode=threshold_mode)
        self._reset()

    def _reset(self):
        """Resets num_bad_epochs counter and cooldown counter."""
        self.best = self.mode_worse
        self.cooldown_counter = 0
        self.num_bad_epochs = 0

    def step(self, metrics, epoch=None):
        # convert `metrics` to float, in case it's a zero-dim Tensor
        current = float(metrics)
        if epoch is None:
            epoch = self.last_epoch + 1
        else:
            warnings.warn(EPOCH_DEPRECATION_WARNING, UserWarning)
        self.last_epoch = epoch

        if self.is_better(current, self.best):
            self.best = current
            self.num_bad_epochs = 0
        else:
            self.num_bad_epochs += 1

        if self.in_cooldown:
            self.cooldown_counter -= 1
            self.num_bad_epochs = 0  # ignore any bad epochs in cooldown

        if self.num_bad_epochs > self.patience:
            self._reduce_lr(epoch)
            self.cooldown_counter = self.cooldown
            self.num_bad_epochs = 0

        self._last_lr = [group['lr'] for group in self.optimizer.param_groups]

    def _reduce_lr(self, epoch):
        for i, param_group in enumerate(self.optimizer.param_groups):
            old_lr = float(param_group['lr'])
            new_lr = max(old_lr * self.factor, self.min_lrs[i])
            if old_lr - new_lr > self.eps:
                param_group['lr'] = new_lr

    @property
    def in_cooldown(self):
        return self.cooldown_counter > 0

    def is_better(self, a, best):
        if self.mode == 'min' and self.threshold_mode == 'rel':
            rel_epsilon = 1. - self.threshold
            return a < best * rel_epsilon

        elif self.mode == 'min' and self.threshold_mode == 'abs':
            return a < best - self.threshold

        elif self.mode == 'max' and self.threshold_mode == 'rel':
            rel_epsilon = self.threshold + 1.
            return a > best * rel_epsilon

        else:  # mode == 'max' and epsilon_mode == 'abs':
            return a > best + self.threshold

    def _init_is_better(self, mode, threshold, threshold_mode):
        if mode not in {'min', 'max'}:
            raise ValueError('mode ' + mode + ' is unknown!')
        if threshold_mode not in {'rel', 'abs'}:
            raise ValueError('threshold mode ' + threshold_mode + ' is unknown!')

        if mode == 'min':
            self.mode_worse = inf
        else:  # mode == 'max':
            self.mode_worse = -inf

        self.mode = mode
        self.threshold = threshold
        self.threshold_mode = threshold_mode

    def state_dict(self):
        return {key: value for key, value in self.__dict__.items() if key != 'optimizer'}

    def load_state_dict(self, state_dict):
        self.__dict__.update(state_dict)
        self._init_is_better(mode=self.mode, threshold=self.threshold, threshold_mode=self.threshold_mode)


class CyclicLR(LRScheduler):
    r"""Sets the learning rate of each parameter group according to

    cyclical learning rate policy (CLR). The policy cycles the learning

    rate between two boundaries with a constant frequency, as detailed in

    the paper `Cyclical Learning Rates for Training Neural Networks`_.

    The distance between the two boundaries can be scaled on a per-iteration

    or per-cycle basis.



    Cyclical learning rate policy changes the learning rate after every batch.

    `step` should be called after a batch has been used for training.



    This class has three built-in policies, as put forth in the paper:



    * "triangular": A basic triangular cycle without amplitude scaling.

    * "triangular2": A basic triangular cycle that scales initial amplitude by half each cycle.

    * "exp_range": A cycle that scales initial amplitude by :math:`\text{gamma}^{\text{cycle iterations}}`

      at each cycle iteration.



    This implementation was adapted from the github repo: `bckenstler/CLR`_



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        base_lr (float or list): Initial learning rate which is the

            lower boundary in the cycle for each parameter group.

        max_lr (float or list): Upper learning rate boundaries in the cycle

            for each parameter group. Functionally,

            it defines the cycle amplitude (max_lr - base_lr).

            The lr at any cycle is the sum of base_lr

            and some scaling of the amplitude; therefore

            max_lr may not actually be reached depending on

            scaling function.

        step_size_up (int): Number of training iterations in the

            increasing half of a cycle. Default: 2000

        step_size_down (int): Number of training iterations in the

            decreasing half of a cycle. If step_size_down is None,

            it is set to step_size_up. Default: None

        mode (str): One of {triangular, triangular2, exp_range}.

            Values correspond to policies detailed above.

            If scale_fn is not None, this argument is ignored.

            Default: 'triangular'

        gamma (float): Constant in 'exp_range' scaling function:

            gamma**(cycle iterations)

            Default: 1.0

        scale_fn (function): Custom scaling policy defined by a single

            argument lambda function, where

            0 <= scale_fn(x) <= 1 for all x >= 0.

            If specified, then 'mode' is ignored.

            Default: None

        scale_mode (str): {'cycle', 'iterations'}.

            Defines whether scale_fn is evaluated on

            cycle number or cycle iterations (training

            iterations since start of cycle).

            Default: 'cycle'

        cycle_momentum (bool): If ``True``, momentum is cycled inversely

            to learning rate between 'base_momentum' and 'max_momentum'.

            Default: True

        base_momentum (float or list): Lower momentum boundaries in the cycle

            for each parameter group. Note that momentum is cycled inversely

            to learning rate; at the peak of a cycle, momentum is

            'base_momentum' and learning rate is 'max_lr'.

            Default: 0.8

        max_momentum (float or list): Upper momentum boundaries in the cycle

            for each parameter group. Functionally,

            it defines the cycle amplitude (max_momentum - base_momentum).

            The momentum at any cycle is the difference of max_momentum

            and some scaling of the amplitude; therefore

            base_momentum may not actually be reached depending on

            scaling function. Note that momentum is cycled inversely

            to learning rate; at the start of a cycle, momentum is 'max_momentum'

            and learning rate is 'base_lr'

            Default: 0.9

        last_epoch (int): The index of the last batch. This parameter is used when

            resuming a training job. Since `step()` should be invoked after each

            batch instead of after each epoch, this number represents the total

            number of *batches* computed, not the total number of epochs computed.

            When last_epoch=-1, the schedule is started from the beginning.

            Default: -1

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)

        >>> scheduler = torch.optim.lr_scheduler.CyclicLR(optimizer, base_lr=0.01, max_lr=0.1)

        >>> data_loader = torch.utils.data.DataLoader(...)

        >>> for epoch in range(10):

        >>>     for batch in data_loader:

        >>>         train_batch(...)

        >>>         scheduler.step()





    .. _Cyclical Learning Rates for Training Neural Networks: https://arxiv.org/abs/1506.01186

    .. _bckenstler/CLR: https://github.com/bckenstler/CLR

    """

    def __init__(self,

                 optimizer,

                 base_lr,

                 max_lr,

                 step_size_up=2000,

                 step_size_down=None,

                 mode='triangular',

                 gamma=1.,

                 scale_fn=None,

                 scale_mode='cycle',

                 cycle_momentum=True,

                 base_momentum=0.8,

                 max_momentum=0.9,

                 last_epoch=-1,

                 verbose="deprecated"):

        # Attach optimizer
        if not isinstance(optimizer, Optimizer):
            raise TypeError(f'{type(optimizer).__name__} is not an Optimizer')
        self.optimizer = optimizer

        base_lrs = self._format_param('base_lr', optimizer, base_lr)
        if last_epoch == -1:
            for lr, group in zip(base_lrs, optimizer.param_groups):
                group['lr'] = lr

        self.max_lrs = self._format_param('max_lr', optimizer, max_lr)

        step_size_up = float(step_size_up)
        step_size_down = float(step_size_down) if step_size_down is not None else step_size_up
        self.total_size = step_size_up + step_size_down
        self.step_ratio = step_size_up / self.total_size

        if mode not in ['triangular', 'triangular2', 'exp_range'] \
                and scale_fn is None:
            raise ValueError('mode is invalid and scale_fn is None')

        self.mode = mode
        self.gamma = gamma

        self._scale_fn_ref = None
        self._scale_fn_custom = scale_fn
        self.scale_mode = scale_mode
        self._init_scale_fn()

        self.cycle_momentum = cycle_momentum
        if cycle_momentum:
            if 'momentum' not in optimizer.defaults and 'betas' not in optimizer.defaults:
                raise ValueError('optimizer must support momentum or beta1 with `cycle_momentum` option enabled')

            self.use_beta1 = 'betas' in self.optimizer.defaults
            self.base_momentums = self._format_param('base_momentum', optimizer, base_momentum)
            self.max_momentums = self._format_param('max_momentum', optimizer, max_momentum)
            if last_epoch == -1:
                for m_momentum, b_momentum, group in zip(self.max_momentums, self.base_momentums, optimizer.param_groups):
                    if self.use_beta1:
                        group['betas'] = (m_momentum, *group['betas'][1:])
                    else:
                        group['momentum'] = m_momentum
                    group['max_momentum'] = m_momentum
                    group['base_momentum'] = b_momentum

        super().__init__(optimizer, last_epoch, verbose)
        self.base_lrs = base_lrs

    def _init_scale_fn(self):
        if self._scale_fn_custom is not None:
            return
        if self.mode == 'triangular':
            self._scale_fn_ref = self._triangular_scale_fn
            self.scale_mode = 'cycle'
        elif self.mode == 'triangular2':
            self._scale_fn_ref = self._triangular2_scale_fn
            self.scale_mode = 'cycle'
        elif self.mode == 'exp_range':
            self._scale_fn_ref = partial(self._exp_range_scale_fn, self.gamma)
            self.scale_mode = 'iterations'

    def _format_param(self, name, optimizer, param):
        """Return correctly formatted lr/momentum for each param group."""
        if isinstance(param, (list, tuple)):
            if len(param) != len(optimizer.param_groups):
                raise ValueError(f"expected {len(optimizer.param_groups)} values for {name}, got {len(param)}")
            return param
        else:
            return [param] * len(optimizer.param_groups)

    def scale_fn(self, x):
        if self._scale_fn_custom is not None:
            return self._scale_fn_custom(x)
        else:
            return self._scale_fn_ref(x)  # static method

    @staticmethod
    def _triangular_scale_fn(x):
        return 1.

    @staticmethod
    def _triangular2_scale_fn(x):
        return 1 / (2. ** (x - 1))

    @staticmethod
    def _exp_range_scale_fn(gamma, x):
        return gamma ** x

    def get_lr(self):
        """Calculates the learning rate at batch index. This function treats

        `self.last_epoch` as the last batch index.



        If `self.cycle_momentum` is ``True``, this function has a side effect of

        updating the optimizer's momentum.

        """

        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        cycle = math.floor(1 + self.last_epoch / self.total_size)
        x = 1. + self.last_epoch / self.total_size - cycle
        if x <= self.step_ratio:
            scale_factor = x / self.step_ratio
        else:
            scale_factor = (x - 1) / (self.step_ratio - 1)

        lrs = []
        for base_lr, max_lr in zip(self.base_lrs, self.max_lrs):
            base_height = (max_lr - base_lr) * scale_factor
            if self.scale_mode == 'cycle':
                lr = base_lr + base_height * self.scale_fn(cycle)
            else:
                lr = base_lr + base_height * self.scale_fn(self.last_epoch)
            lrs.append(lr)

        if self.cycle_momentum:
            momentums = []
            for base_momentum, max_momentum in zip(self.base_momentums, self.max_momentums):
                base_height = (max_momentum - base_momentum) * scale_factor
                if self.scale_mode == 'cycle':
                    momentum = max_momentum - base_height * self.scale_fn(cycle)
                else:
                    momentum = max_momentum - base_height * self.scale_fn(self.last_epoch)
                momentums.append(momentum)
            for param_group, momentum in zip(self.optimizer.param_groups, momentums):
                if self.use_beta1:
                    param_group['betas'] = (momentum, *param_group['betas'][1:])
                else:
                    param_group['momentum'] = momentum

        return lrs

    def state_dict(self):
        state = super().state_dict()
        # We are dropping the `_scale_fn_ref` attribute because it is a
        # `weakref.WeakMethod` and can't be pickled.
        state.pop('_scale_fn_ref')
        fn = state.pop('_scale_fn_custom')
        state['_scale_fn_custom'] = None
        if fn is not None and not isinstance(fn, types.FunctionType):
            # The _scale_fn_custom will only be saved if it is a callable object
            # and not if it is a function or lambda.
            state['_scale_fn_custom'] = fn.__dict__.copy()

        return state

    def load_state_dict(self, state_dict):
        fn = state_dict.pop('_scale_fn_custom')
        super().load_state_dict(state_dict)
        if fn is not None:
            self._scale_fn_custom.__dict__.update(fn)
        self._init_scale_fn()


class CosineAnnealingWarmRestarts(LRScheduler):
    r"""Set the learning rate of each parameter group using a cosine annealing

    schedule, where :math:`\eta_{max}` is set to the initial lr, :math:`T_{cur}`

    is the number of epochs since the last restart and :math:`T_{i}` is the number

    of epochs between two warm restarts in SGDR:



    .. math::

        \eta_t = \eta_{min} + \frac{1}{2}(\eta_{max} - \eta_{min})\left(1 +

        \cos\left(\frac{T_{cur}}{T_{i}}\pi\right)\right)



    When :math:`T_{cur}=T_{i}`, set :math:`\eta_t = \eta_{min}`.

    When :math:`T_{cur}=0` after restart, set :math:`\eta_t=\eta_{max}`.



    It has been proposed in

    `SGDR: Stochastic Gradient Descent with Warm Restarts`_.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        T_0 (int): Number of iterations for the first restart.

        T_mult (int, optional): A factor increases :math:`T_{i}` after a restart. Default: 1.

        eta_min (float, optional): Minimum learning rate. Default: 0.

        last_epoch (int, optional): The index of last epoch. Default: -1.

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    .. _SGDR\: Stochastic Gradient Descent with Warm Restarts:

        https://arxiv.org/abs/1608.03983

    """

    def __init__(self, optimizer, T_0, T_mult=1, eta_min=0, last_epoch=-1, verbose="deprecated"):
        if T_0 <= 0 or not isinstance(T_0, int):
            raise ValueError(f"Expected positive integer T_0, but got {T_0}")
        if T_mult < 1 or not isinstance(T_mult, int):
            raise ValueError(f"Expected integer T_mult >= 1, but got {T_mult}")
        if not isinstance(eta_min, (float, int)):
            raise ValueError(f"Expected float or int eta_min, but got {eta_min} of type {type(eta_min)}")
        self.T_0 = T_0
        self.T_i = T_0
        self.T_mult = T_mult
        self.eta_min = eta_min
        self.T_cur = last_epoch
        super().__init__(optimizer, last_epoch, verbose)

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        return [self.eta_min + (base_lr - self.eta_min) * (1 + math.cos(math.pi * self.T_cur / self.T_i)) / 2
                for base_lr in self.base_lrs]

    def step(self, epoch=None):
        """Step could be called after every batch update



        Example:

            >>> # xdoctest: +SKIP("Undefined vars")

            >>> scheduler = CosineAnnealingWarmRestarts(optimizer, T_0, T_mult)

            >>> iters = len(dataloader)

            >>> for epoch in range(20):

            >>>     for i, sample in enumerate(dataloader):

            >>>         inputs, labels = sample['inputs'], sample['labels']

            >>>         optimizer.zero_grad()

            >>>         outputs = net(inputs)

            >>>         loss = criterion(outputs, labels)

            >>>         loss.backward()

            >>>         optimizer.step()

            >>>         scheduler.step(epoch + i / iters)



        This function can be called in an interleaved way.



        Example:

            >>> # xdoctest: +SKIP("Undefined vars")

            >>> scheduler = CosineAnnealingWarmRestarts(optimizer, T_0, T_mult)

            >>> for epoch in range(20):

            >>>     scheduler.step()

            >>> scheduler.step(26)

            >>> scheduler.step() # scheduler.step(27), instead of scheduler(20)

        """

        if epoch is None and self.last_epoch < 0:
            epoch = 0

        if epoch is None:
            epoch = self.last_epoch + 1
            self.T_cur = self.T_cur + 1
            if self.T_cur >= self.T_i:
                self.T_cur = self.T_cur - self.T_i
                self.T_i = self.T_i * self.T_mult
        else:
            if epoch < 0:
                raise ValueError(f"Expected non-negative epoch, but got {epoch}")
            if epoch >= self.T_0:
                if self.T_mult == 1:
                    self.T_cur = epoch % self.T_0
                else:
                    n = int(math.log((epoch / self.T_0 * (self.T_mult - 1) + 1), self.T_mult))
                    self.T_cur = epoch - self.T_0 * (self.T_mult ** n - 1) / (self.T_mult - 1)
                    self.T_i = self.T_0 * self.T_mult ** (n)
            else:
                self.T_i = self.T_0
                self.T_cur = epoch
        self.last_epoch = math.floor(epoch)

        class _enable_get_lr_call:

            def __init__(self, o):
                self.o = o

            def __enter__(self):
                self.o._get_lr_called_within_step = True
                return self

            def __exit__(self, type, value, traceback):
                self.o._get_lr_called_within_step = False
                return self

        with _enable_get_lr_call(self):
            for i, data in enumerate(zip(self.optimizer.param_groups, self.get_lr())):
                param_group, lr = data
                param_group['lr'] = lr

        self._last_lr = [group['lr'] for group in self.optimizer.param_groups]


class OneCycleLR(LRScheduler):
    r"""Sets the learning rate of each parameter group according to the

    1cycle learning rate policy. The 1cycle policy anneals the learning

    rate from an initial learning rate to some maximum learning rate and then

    from that maximum learning rate to some minimum learning rate much lower

    than the initial learning rate.

    This policy was initially described in the paper `Super-Convergence:

    Very Fast Training of Neural Networks Using Large Learning Rates`_.



    The 1cycle learning rate policy changes the learning rate after every batch.

    `step` should be called after a batch has been used for training.



    This scheduler is not chainable.



    Note also that the total number of steps in the cycle can be determined in one

    of two ways (listed in order of precedence):



    #. A value for total_steps is explicitly provided.

    #. A number of epochs (epochs) and a number of steps per epoch

       (steps_per_epoch) are provided.

       In this case, the number of total steps is inferred by

       total_steps = epochs * steps_per_epoch



    You must either provide a value for total_steps or provide a value for both

    epochs and steps_per_epoch.



    The default behaviour of this scheduler follows the fastai implementation of 1cycle, which

    claims that "unpublished work has shown even better results by using only two phases". To

    mimic the behaviour of the original paper instead, set ``three_phase=True``.



    Args:

        optimizer (Optimizer): Wrapped optimizer.

        max_lr (float or list): Upper learning rate boundaries in the cycle

            for each parameter group.

        total_steps (int): The total number of steps in the cycle. Note that

            if a value is not provided here, then it must be inferred by providing

            a value for epochs and steps_per_epoch.

            Default: None

        epochs (int): The number of epochs to train for. This is used along

            with steps_per_epoch in order to infer the total number of steps in the cycle

            if a value for total_steps is not provided.

            Default: None

        steps_per_epoch (int): The number of steps per epoch to train for. This is

            used along with epochs in order to infer the total number of steps in the

            cycle if a value for total_steps is not provided.

            Default: None

        pct_start (float): The percentage of the cycle (in number of steps) spent

            increasing the learning rate.

            Default: 0.3

        anneal_strategy (str): {'cos', 'linear'}

            Specifies the annealing strategy: "cos" for cosine annealing, "linear" for

            linear annealing.

            Default: 'cos'

        cycle_momentum (bool): If ``True``, momentum is cycled inversely

            to learning rate between 'base_momentum' and 'max_momentum'.

            Default: True

        base_momentum (float or list): Lower momentum boundaries in the cycle

            for each parameter group. Note that momentum is cycled inversely

            to learning rate; at the peak of a cycle, momentum is

            'base_momentum' and learning rate is 'max_lr'.

            Default: 0.85

        max_momentum (float or list): Upper momentum boundaries in the cycle

            for each parameter group. Functionally,

            it defines the cycle amplitude (max_momentum - base_momentum).

            Note that momentum is cycled inversely

            to learning rate; at the start of a cycle, momentum is 'max_momentum'

            and learning rate is 'base_lr'

            Default: 0.95

        div_factor (float): Determines the initial learning rate via

            initial_lr = max_lr/div_factor

            Default: 25

        final_div_factor (float): Determines the minimum learning rate via

            min_lr = initial_lr/final_div_factor

            Default: 1e4

        three_phase (bool): If ``True``, use a third phase of the schedule to annihilate the

            learning rate according to 'final_div_factor' instead of modifying the second

            phase (the first two phases will be symmetrical about the step indicated by

            'pct_start').

        last_epoch (int): The index of the last batch. This parameter is used when

            resuming a training job. Since `step()` should be invoked after each

            batch instead of after each epoch, this number represents the total

            number of *batches* computed, not the total number of epochs computed.

            When last_epoch=-1, the schedule is started from the beginning.

            Default: -1

        verbose (bool): If ``True``, prints a message to stdout for

            each update. Default: ``False``.



            .. deprecated:: 2.2

                ``verbose`` is deprecated. Please use ``get_last_lr()`` to access the

                learning rate.



    Example:

        >>> # xdoctest: +SKIP

        >>> data_loader = torch.utils.data.DataLoader(...)

        >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)

        >>> scheduler = torch.optim.lr_scheduler.OneCycleLR(optimizer, max_lr=0.01, steps_per_epoch=len(data_loader), epochs=10)

        >>> for epoch in range(10):

        >>>     for batch in data_loader:

        >>>         train_batch(...)

        >>>         optimizer.step()

        >>>         scheduler.step()





    .. _Super-Convergence\: Very Fast Training of Neural Networks Using Large Learning Rates:

        https://arxiv.org/abs/1708.07120

    """
    def __init__(self,

                 optimizer,

                 max_lr,

                 total_steps=None,

                 epochs=None,

                 steps_per_epoch=None,

                 pct_start=0.3,

                 anneal_strategy='cos',

                 cycle_momentum=True,

                 base_momentum=0.85,

                 max_momentum=0.95,

                 div_factor=25.,

                 final_div_factor=1e4,

                 three_phase=False,

                 last_epoch=-1,

                 verbose="deprecated"):

        # Validate optimizer
        if not isinstance(optimizer, Optimizer):
            raise TypeError(f'{type(optimizer).__name__} is not an Optimizer')
        self.optimizer = optimizer

        # Validate total_steps
        if total_steps is None and epochs is None and steps_per_epoch is None:
            raise ValueError("You must define either total_steps OR (epochs AND steps_per_epoch)")
        elif total_steps is not None:
            if total_steps <= 0 or not isinstance(total_steps, int):
                raise ValueError(f"Expected positive integer total_steps, but got {total_steps}")
            self.total_steps = total_steps
        else:
            if epochs <= 0 or not isinstance(epochs, int):
                raise ValueError(f"Expected positive integer epochs, but got {epochs}")
            if steps_per_epoch <= 0 or not isinstance(steps_per_epoch, int):
                raise ValueError(f"Expected positive integer steps_per_epoch, but got {steps_per_epoch}")
            self.total_steps = epochs * steps_per_epoch

        if three_phase:
            self._schedule_phases = [
                {
                    'end_step': float(pct_start * self.total_steps) - 1,
                    'start_lr': 'initial_lr',
                    'end_lr': 'max_lr',
                    'start_momentum': 'max_momentum',
                    'end_momentum': 'base_momentum',
                },
                {
                    'end_step': float(2 * pct_start * self.total_steps) - 2,
                    'start_lr': 'max_lr',
                    'end_lr': 'initial_lr',
                    'start_momentum': 'base_momentum',
                    'end_momentum': 'max_momentum',
                },
                {
                    'end_step': self.total_steps - 1,
                    'start_lr': 'initial_lr',
                    'end_lr': 'min_lr',
                    'start_momentum': 'max_momentum',
                    'end_momentum': 'max_momentum',
                },
            ]
        else:
            self._schedule_phases = [
                {
                    'end_step': float(pct_start * self.total_steps) - 1,
                    'start_lr': 'initial_lr',
                    'end_lr': 'max_lr',
                    'start_momentum': 'max_momentum',
                    'end_momentum': 'base_momentum',
                },
                {
                    'end_step': self.total_steps - 1,
                    'start_lr': 'max_lr',
                    'end_lr': 'min_lr',
                    'start_momentum': 'base_momentum',
                    'end_momentum': 'max_momentum',
                },
            ]

        # Validate pct_start
        if pct_start < 0 or pct_start > 1 or not isinstance(pct_start, float):
            raise ValueError(f"Expected float between 0 and 1 pct_start, but got {pct_start}")

        # Validate anneal_strategy
        if anneal_strategy not in ['cos', 'linear']:
            raise ValueError(f"anneal_strategy must by one of 'cos' or 'linear', instead got {anneal_strategy}")
        elif anneal_strategy == 'cos':
            self.anneal_func = self._annealing_cos
        elif anneal_strategy == 'linear':
            self.anneal_func = self._annealing_linear

        # Initialize learning rate variables
        max_lrs = self._format_param('max_lr', self.optimizer, max_lr)
        if last_epoch == -1:
            for idx, group in enumerate(self.optimizer.param_groups):
                group['initial_lr'] = max_lrs[idx] / div_factor
                group['max_lr'] = max_lrs[idx]
                group['min_lr'] = group['initial_lr'] / final_div_factor

        # Initialize momentum variables
        self.cycle_momentum = cycle_momentum
        if self.cycle_momentum:
            if 'momentum' not in self.optimizer.defaults and 'betas' not in self.optimizer.defaults:
                raise ValueError('optimizer must support momentum or beta1 with `cycle_momentum` option enabled')
            self.use_beta1 = 'betas' in self.optimizer.defaults
            max_momentums = self._format_param('max_momentum', optimizer, max_momentum)
            base_momentums = self._format_param('base_momentum', optimizer, base_momentum)
            if last_epoch == -1:
                for m_momentum, b_momentum, group in zip(max_momentums, base_momentums, optimizer.param_groups):
                    if self.use_beta1:
                        group['betas'] = (m_momentum, *group['betas'][1:])
                    else:
                        group['momentum'] = m_momentum
                    group['max_momentum'] = m_momentum
                    group['base_momentum'] = b_momentum

        super().__init__(optimizer, last_epoch, verbose)

    def _format_param(self, name, optimizer, param):
        """Return correctly formatted lr/momentum for each param group."""
        if isinstance(param, (list, tuple)):
            if len(param) != len(optimizer.param_groups):
                raise ValueError(f"expected {len(optimizer.param_groups)} values for {name}, got {len(param)}")
            return param
        else:
            return [param] * len(optimizer.param_groups)

    @staticmethod
    def _annealing_cos(start, end, pct):
        "Cosine anneal from `start` to `end` as pct goes from 0.0 to 1.0."
        cos_out = math.cos(math.pi * pct) + 1
        return end + (start - end) / 2.0 * cos_out

    @staticmethod
    def _annealing_linear(start, end, pct):
        "Linearly anneal from `start` to `end` as pct goes from 0.0 to 1.0."
        return (end - start) * pct + start

    def get_lr(self):
        if not self._get_lr_called_within_step:
            warnings.warn("To get the last learning rate computed by the scheduler, "
                          "please use `get_last_lr()`.", UserWarning)

        lrs = []
        step_num = self.last_epoch

        if step_num > self.total_steps:
            raise ValueError("Tried to step {} times. The specified number of total steps is {}"
                             .format(step_num, self.total_steps))

        for group in self.optimizer.param_groups:
            start_step = 0
            for i, phase in enumerate(self._schedule_phases):
                end_step = phase['end_step']
                if step_num <= end_step or i == len(self._schedule_phases) - 1:
                    pct = (step_num - start_step) / (end_step - start_step)
                    computed_lr = self.anneal_func(group[phase['start_lr']], group[phase['end_lr']], pct)
                    if self.cycle_momentum:
                        computed_momentum = self.anneal_func(group[phase['start_momentum']], group[phase['end_momentum']], pct)
                    break
                start_step = phase['end_step']

            lrs.append(computed_lr)
            if self.cycle_momentum:
                if self.use_beta1:
                    group['betas'] = (computed_momentum, *group['betas'][1:])
                else:
                    group['momentum'] = computed_momentum

        return lrs