master
/ miniconda3 / envs / poem / lib / python3.10 / site-packages / matplotlib / dates.py

dates.py @a8e0244

41a0142
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   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
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
"""
Matplotlib provides sophisticated date plotting capabilities, standing on the
shoulders of python :mod:`datetime` and the add-on module dateutil_.

By default, Matplotlib uses the units machinery described in
`~matplotlib.units` to convert `datetime.datetime`, and `numpy.datetime64`
objects when plotted on an x- or y-axis. The user does not
need to do anything for dates to be formatted, but dates often have strict
formatting needs, so this module provides many axis locators and formatters.
A basic example using `numpy.datetime64` is::

    import numpy as np

    times = np.arange(np.datetime64('2001-01-02'),
                      np.datetime64('2002-02-03'), np.timedelta64(75, 'm'))
    y = np.random.randn(len(times))

    fig, ax = plt.subplots()
    ax.plot(times, y)

.. seealso::

    - :doc:`/gallery/text_labels_and_annotations/date`
    - :doc:`/gallery/ticks/date_concise_formatter`
    - :doc:`/gallery/ticks/date_demo_convert`

.. _date-format:

Matplotlib date format
----------------------

Matplotlib represents dates using floating point numbers specifying the number
of days since a default epoch of 1970-01-01 UTC; for example,
1970-01-01, 06:00 is the floating point number 0.25. The formatters and
locators require the use of `datetime.datetime` objects, so only dates between
year 0001 and 9999 can be represented.  Microsecond precision
is achievable for (approximately) 70 years on either side of the epoch, and
20 microseconds for the rest of the allowable range of dates (year 0001 to
9999). The epoch can be changed at import time via `.dates.set_epoch` or
:rc:`dates.epoch` to other dates if necessary; see
:doc:`/gallery/ticks/date_precision_and_epochs` for a discussion.

.. note::

   Before Matplotlib 3.3, the epoch was 0000-12-31 which lost modern
   microsecond precision and also made the default axis limit of 0 an invalid
   datetime.  In 3.3 the epoch was changed as above.  To convert old
   ordinal floats to the new epoch, users can do::

     new_ordinal = old_ordinal + mdates.date2num(np.datetime64('0000-12-31'))


There are a number of helper functions to convert between :mod:`datetime`
objects and Matplotlib dates:

.. currentmodule:: matplotlib.dates

.. autosummary::
   :nosignatures:

   datestr2num
   date2num
   num2date
   num2timedelta
   drange
   set_epoch
   get_epoch

.. note::

   Like Python's `datetime.datetime`, Matplotlib uses the Gregorian calendar
   for all conversions between dates and floating point numbers. This practice
   is not universal, and calendar differences can cause confusing
   differences between what Python and Matplotlib give as the number of days
   since 0001-01-01 and what other software and databases yield.  For
   example, the US Naval Observatory uses a calendar that switches
   from Julian to Gregorian in October, 1582.  Hence, using their
   calculator, the number of days between 0001-01-01 and 2006-04-01 is
   732403, whereas using the Gregorian calendar via the datetime
   module we find::

     In [1]: date(2006, 4, 1).toordinal() - date(1, 1, 1).toordinal()
     Out[1]: 732401

All the Matplotlib date converters, tickers and formatters are timezone aware.
If no explicit timezone is provided, :rc:`timezone` is assumed, provided as a
string.  If you want to use a different timezone, pass the *tz* keyword
argument of `num2date` to any date tickers or locators you create.  This can
be either a `datetime.tzinfo` instance or a string with the timezone name that
can be parsed by `~dateutil.tz.gettz`.

A wide range of specific and general purpose date tick locators and
formatters are provided in this module.  See
:mod:`matplotlib.ticker` for general information on tick locators
and formatters.  These are described below.

The dateutil_ module provides additional code to handle date ticking, making it
easy to place ticks on any kinds of dates.  See examples below.

.. _dateutil: https://dateutil.readthedocs.io

Date tickers
------------

Most of the date tickers can locate single or multiple values.  For example::

    # import constants for the days of the week
    from matplotlib.dates import MO, TU, WE, TH, FR, SA, SU

    # tick on Mondays every week
    loc = WeekdayLocator(byweekday=MO, tz=tz)

    # tick on Mondays and Saturdays
    loc = WeekdayLocator(byweekday=(MO, SA))

In addition, most of the constructors take an interval argument::

    # tick on Mondays every second week
    loc = WeekdayLocator(byweekday=MO, interval=2)

The rrule locator allows completely general date ticking::

    # tick every 5th easter
    rule = rrulewrapper(YEARLY, byeaster=1, interval=5)
    loc = RRuleLocator(rule)

The available date tickers are:

* `MicrosecondLocator`: Locate microseconds.

* `SecondLocator`: Locate seconds.

* `MinuteLocator`: Locate minutes.

* `HourLocator`: Locate hours.

* `DayLocator`: Locate specified days of the month.

* `WeekdayLocator`: Locate days of the week, e.g., MO, TU.

* `MonthLocator`: Locate months, e.g., 7 for July.

* `YearLocator`: Locate years that are multiples of base.

* `RRuleLocator`: Locate using a `rrulewrapper`.
  `rrulewrapper` is a simple wrapper around dateutil_'s `dateutil.rrule`
  which allow almost arbitrary date tick specifications.
  See :doc:`rrule example </gallery/ticks/date_demo_rrule>`.

* `AutoDateLocator`: On autoscale, this class picks the best `DateLocator`
  (e.g., `RRuleLocator`) to set the view limits and the tick locations.  If
  called with ``interval_multiples=True`` it will make ticks line up with
  sensible multiples of the tick intervals.  For example, if the interval is
  4 hours, it will pick hours 0, 4, 8, etc. as ticks.  This behaviour is not
  guaranteed by default.

Date formatters
---------------

The available date formatters are:

* `AutoDateFormatter`: attempts to figure out the best format to use.  This is
  most useful when used with the `AutoDateLocator`.

* `ConciseDateFormatter`: also attempts to figure out the best format to use,
  and to make the format as compact as possible while still having complete
  date information.  This is most useful when used with the `AutoDateLocator`.

* `DateFormatter`: use `~datetime.datetime.strftime` format strings.
"""

import datetime
import functools
import logging
import math
import re

from dateutil.rrule import (rrule, MO, TU, WE, TH, FR, SA, SU, YEARLY,
                            MONTHLY, WEEKLY, DAILY, HOURLY, MINUTELY,
                            SECONDLY)
from dateutil.relativedelta import relativedelta
import dateutil.parser
import dateutil.tz
import numpy as np

import matplotlib as mpl
from matplotlib import _api, cbook, ticker, units

__all__ = ('datestr2num', 'date2num', 'num2date', 'num2timedelta', 'drange',
           'set_epoch', 'get_epoch', 'DateFormatter', 'ConciseDateFormatter',
           'AutoDateFormatter', 'DateLocator', 'RRuleLocator',
           'AutoDateLocator', 'YearLocator', 'MonthLocator', 'WeekdayLocator',
           'DayLocator', 'HourLocator', 'MinuteLocator',
           'SecondLocator', 'MicrosecondLocator',
           'rrule', 'MO', 'TU', 'WE', 'TH', 'FR', 'SA', 'SU',
           'YEARLY', 'MONTHLY', 'WEEKLY', 'DAILY',
           'HOURLY', 'MINUTELY', 'SECONDLY', 'MICROSECONDLY', 'relativedelta',
           'DateConverter', 'ConciseDateConverter', 'rrulewrapper')


_log = logging.getLogger(__name__)
UTC = datetime.timezone.utc


@_api.caching_module_getattr
class __getattr__:
    JULIAN_OFFSET = _api.deprecated("3.7")(property(lambda self: 1721424.5))
    # Julian date at 0000-12-31
    # note that the Julian day epoch is achievable w/
    # np.datetime64('-4713-11-24T12:00:00'); datetime64 is proleptic
    # Gregorian and BC has a one-year offset.  So
    # np.datetime64('0000-12-31') - np.datetime64('-4713-11-24T12:00') =
    # 1721424.5
    # Ref: https://en.wikipedia.org/wiki/Julian_day


def _get_tzinfo(tz=None):
    """
    Generate `~datetime.tzinfo` from a string or return `~datetime.tzinfo`.
    If None, retrieve the preferred timezone from the rcParams dictionary.
    """
    if tz is None:
        tz = mpl.rcParams['timezone']
        if tz == 'UTC':
            return UTC
    if isinstance(tz, str):
        tzinfo = dateutil.tz.gettz(tz)
        if tzinfo is None:
            raise ValueError(f"{tz} is not a valid timezone as parsed by"
                             " dateutil.tz.gettz.")
        return tzinfo
    if isinstance(tz, datetime.tzinfo):
        return tz
    raise TypeError("tz must be string or tzinfo subclass.")


# Time-related constants.
EPOCH_OFFSET = float(datetime.datetime(1970, 1, 1).toordinal())
# EPOCH_OFFSET is not used by matplotlib
MICROSECONDLY = SECONDLY + 1
HOURS_PER_DAY = 24.
MIN_PER_HOUR = 60.
SEC_PER_MIN = 60.
MONTHS_PER_YEAR = 12.

DAYS_PER_WEEK = 7.
DAYS_PER_MONTH = 30.
DAYS_PER_YEAR = 365.0

MINUTES_PER_DAY = MIN_PER_HOUR * HOURS_PER_DAY

SEC_PER_HOUR = SEC_PER_MIN * MIN_PER_HOUR
SEC_PER_DAY = SEC_PER_HOUR * HOURS_PER_DAY
SEC_PER_WEEK = SEC_PER_DAY * DAYS_PER_WEEK

MUSECONDS_PER_DAY = 1e6 * SEC_PER_DAY

MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY, SUNDAY = (
    MO, TU, WE, TH, FR, SA, SU)
WEEKDAYS = (MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY, SUNDAY)

# default epoch: passed to np.datetime64...
_epoch = None


def _reset_epoch_test_example():
    """
    Reset the Matplotlib date epoch so it can be set again.

    Only for use in tests and examples.
    """
    global _epoch
    _epoch = None


def set_epoch(epoch):
    """
    Set the epoch (origin for dates) for datetime calculations.

    The default epoch is :rc:`dates.epoch` (by default 1970-01-01T00:00).

    If microsecond accuracy is desired, the date being plotted needs to be
    within approximately 70 years of the epoch. Matplotlib internally
    represents dates as days since the epoch, so floating point dynamic
    range needs to be within a factor of 2^52.

    `~.dates.set_epoch` must be called before any dates are converted
    (i.e. near the import section) or a RuntimeError will be raised.

    See also :doc:`/gallery/ticks/date_precision_and_epochs`.

    Parameters
    ----------
    epoch : str
        valid UTC date parsable by `numpy.datetime64` (do not include
        timezone).

    """
    global _epoch
    if _epoch is not None:
        raise RuntimeError('set_epoch must be called before dates plotted.')
    _epoch = epoch


def get_epoch():
    """
    Get the epoch used by `.dates`.

    Returns
    -------
    epoch : str
        String for the epoch (parsable by `numpy.datetime64`).
    """
    global _epoch

    if _epoch is None:
        _epoch = mpl.rcParams['date.epoch']
    return _epoch


def _dt64_to_ordinalf(d):
    """
    Convert `numpy.datetime64` or an `numpy.ndarray` of those types to
    Gregorian date as UTC float relative to the epoch (see `.get_epoch`).
    Roundoff is float64 precision.  Practically: microseconds for dates
    between 290301 BC, 294241 AD, milliseconds for larger dates
    (see `numpy.datetime64`).
    """

    # the "extra" ensures that we at least allow the dynamic range out to
    # seconds.  That should get out to +/-2e11 years.
    dseconds = d.astype('datetime64[s]')
    extra = (d - dseconds).astype('timedelta64[ns]')
    t0 = np.datetime64(get_epoch(), 's')
    dt = (dseconds - t0).astype(np.float64)
    dt += extra.astype(np.float64) / 1.0e9
    dt = dt / SEC_PER_DAY

    NaT_int = np.datetime64('NaT').astype(np.int64)
    d_int = d.astype(np.int64)
    dt[d_int == NaT_int] = np.nan
    return dt


def _from_ordinalf(x, tz=None):
    """
    Convert Gregorian float of the date, preserving hours, minutes,
    seconds and microseconds.  Return value is a `.datetime`.

    The input date *x* is a float in ordinal days at UTC, and the output will
    be the specified `.datetime` object corresponding to that time in
    timezone *tz*, or if *tz* is ``None``, in the timezone specified in
    :rc:`timezone`.
    """

    tz = _get_tzinfo(tz)

    dt = (np.datetime64(get_epoch()) +
          np.timedelta64(int(np.round(x * MUSECONDS_PER_DAY)), 'us'))
    if dt < np.datetime64('0001-01-01') or dt >= np.datetime64('10000-01-01'):
        raise ValueError(f'Date ordinal {x} converts to {dt} (using '
                         f'epoch {get_epoch()}), but Matplotlib dates must be '
                          'between year 0001 and 9999.')
    # convert from datetime64 to datetime:
    dt = dt.tolist()

    # datetime64 is always UTC:
    dt = dt.replace(tzinfo=dateutil.tz.gettz('UTC'))
    # but maybe we are working in a different timezone so move.
    dt = dt.astimezone(tz)
    # fix round off errors
    if np.abs(x) > 70 * 365:
        # if x is big, round off to nearest twenty microseconds.
        # This avoids floating point roundoff error
        ms = round(dt.microsecond / 20) * 20
        if ms == 1000000:
            dt = dt.replace(microsecond=0) + datetime.timedelta(seconds=1)
        else:
            dt = dt.replace(microsecond=ms)

    return dt


# a version of _from_ordinalf that can operate on numpy arrays
_from_ordinalf_np_vectorized = np.vectorize(_from_ordinalf, otypes="O")


# a version of dateutil.parser.parse that can operate on numpy arrays
_dateutil_parser_parse_np_vectorized = np.vectorize(dateutil.parser.parse)


def datestr2num(d, default=None):
    """
    Convert a date string to a datenum using `dateutil.parser.parse`.

    Parameters
    ----------
    d : str or sequence of str
        The dates to convert.

    default : datetime.datetime, optional
        The default date to use when fields are missing in *d*.
    """
    if isinstance(d, str):
        dt = dateutil.parser.parse(d, default=default)
        return date2num(dt)
    else:
        if default is not None:
            d = [date2num(dateutil.parser.parse(s, default=default))
                 for s in d]
            return np.asarray(d)
        d = np.asarray(d)
        if not d.size:
            return d
        return date2num(_dateutil_parser_parse_np_vectorized(d))


def date2num(d):
    """
    Convert datetime objects to Matplotlib dates.

    Parameters
    ----------
    d : `datetime.datetime` or `numpy.datetime64` or sequences of these

    Returns
    -------
    float or sequence of floats
        Number of days since the epoch.  See `.get_epoch` for the
        epoch, which can be changed by :rc:`date.epoch` or `.set_epoch`.  If
        the epoch is "1970-01-01T00:00:00" (default) then noon Jan 1 1970
        ("1970-01-01T12:00:00") returns 0.5.

    Notes
    -----
    The Gregorian calendar is assumed; this is not universal practice.
    For details see the module docstring.
    """
    # Unpack in case of e.g. Pandas or xarray object
    d = cbook._unpack_to_numpy(d)

    # make an iterable, but save state to unpack later:
    iterable = np.iterable(d)
    if not iterable:
        d = [d]

    masked = np.ma.is_masked(d)
    mask = np.ma.getmask(d)
    d = np.asarray(d)

    # convert to datetime64 arrays, if not already:
    if not np.issubdtype(d.dtype, np.datetime64):
        # datetime arrays
        if not d.size:
            # deals with an empty array...
            return d
        tzi = getattr(d[0], 'tzinfo', None)
        if tzi is not None:
            # make datetime naive:
            d = [dt.astimezone(UTC).replace(tzinfo=None) for dt in d]
            d = np.asarray(d)
        d = d.astype('datetime64[us]')

    d = np.ma.masked_array(d, mask=mask) if masked else d
    d = _dt64_to_ordinalf(d)

    return d if iterable else d[0]


@_api.deprecated("3.7")
def julian2num(j):
    """
    Convert a Julian date (or sequence) to a Matplotlib date (or sequence).

    Parameters
    ----------
    j : float or sequence of floats
        Julian dates (days relative to 4713 BC Jan 1, 12:00:00 Julian
        calendar or 4714 BC Nov 24, 12:00:00, proleptic Gregorian calendar).

    Returns
    -------
    float or sequence of floats
        Matplotlib dates (days relative to `.get_epoch`).
    """
    ep = np.datetime64(get_epoch(), 'h').astype(float) / 24.
    ep0 = np.datetime64('0000-12-31T00:00:00', 'h').astype(float) / 24.
    # Julian offset defined above is relative to 0000-12-31, but we need
    # relative to our current epoch:
    dt = __getattr__("JULIAN_OFFSET") - ep0 + ep
    return np.subtract(j, dt)  # Handles both scalar & nonscalar j.


@_api.deprecated("3.7")
def num2julian(n):
    """
    Convert a Matplotlib date (or sequence) to a Julian date (or sequence).

    Parameters
    ----------
    n : float or sequence of floats
        Matplotlib dates (days relative to `.get_epoch`).

    Returns
    -------
    float or sequence of floats
        Julian dates (days relative to 4713 BC Jan 1, 12:00:00).
    """
    ep = np.datetime64(get_epoch(), 'h').astype(float) / 24.
    ep0 = np.datetime64('0000-12-31T00:00:00', 'h').astype(float) / 24.
    # Julian offset defined above is relative to 0000-12-31, but we need
    # relative to our current epoch:
    dt = __getattr__("JULIAN_OFFSET") - ep0 + ep
    return np.add(n, dt)  # Handles both scalar & nonscalar j.


def num2date(x, tz=None):
    """
    Convert Matplotlib dates to `~datetime.datetime` objects.

    Parameters
    ----------
    x : float or sequence of floats
        Number of days (fraction part represents hours, minutes, seconds)
        since the epoch.  See `.get_epoch` for the
        epoch, which can be changed by :rc:`date.epoch` or `.set_epoch`.
    tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
        Timezone of *x*. If a string, *tz* is passed to `dateutil.tz`.

    Returns
    -------
    `~datetime.datetime` or sequence of `~datetime.datetime`
        Dates are returned in timezone *tz*.

        If *x* is a sequence, a sequence of `~datetime.datetime` objects will
        be returned.

    Notes
    -----
    The Gregorian calendar is assumed; this is not universal practice.
    For details, see the module docstring.
    """
    tz = _get_tzinfo(tz)
    return _from_ordinalf_np_vectorized(x, tz).tolist()


_ordinalf_to_timedelta_np_vectorized = np.vectorize(
    lambda x: datetime.timedelta(days=x), otypes="O")


def num2timedelta(x):
    """
    Convert number of days to a `~datetime.timedelta` object.

    If *x* is a sequence, a sequence of `~datetime.timedelta` objects will
    be returned.

    Parameters
    ----------
    x : float, sequence of floats
        Number of days. The fraction part represents hours, minutes, seconds.

    Returns
    -------
    `datetime.timedelta` or list[`datetime.timedelta`]
    """
    return _ordinalf_to_timedelta_np_vectorized(x).tolist()


def drange(dstart, dend, delta):
    """
    Return a sequence of equally spaced Matplotlib dates.

    The dates start at *dstart* and reach up to, but not including *dend*.
    They are spaced by *delta*.

    Parameters
    ----------
    dstart, dend : `~datetime.datetime`
        The date limits.
    delta : `datetime.timedelta`
        Spacing of the dates.

    Returns
    -------
    `numpy.array`
        A list floats representing Matplotlib dates.

    """
    f1 = date2num(dstart)
    f2 = date2num(dend)
    step = delta.total_seconds() / SEC_PER_DAY

    # calculate the difference between dend and dstart in times of delta
    num = int(np.ceil((f2 - f1) / step))

    # calculate end of the interval which will be generated
    dinterval_end = dstart + num * delta

    # ensure, that an half open interval will be generated [dstart, dend)
    if dinterval_end >= dend:
        # if the endpoint is greater than or equal to dend,
        # just subtract one delta
        dinterval_end -= delta
        num -= 1

    f2 = date2num(dinterval_end)  # new float-endpoint
    return np.linspace(f1, f2, num + 1)


def _wrap_in_tex(text):
    p = r'([a-zA-Z]+)'
    ret_text = re.sub(p, r'}$\1$\\mathdefault{', text)

    # Braces ensure symbols are not spaced like binary operators.
    ret_text = ret_text.replace('-', '{-}').replace(':', '{:}')
    # To not concatenate space between numbers.
    ret_text = ret_text.replace(' ', r'\;')
    ret_text = '$\\mathdefault{' + ret_text + '}$'
    ret_text = ret_text.replace('$\\mathdefault{}$', '')
    return ret_text


## date tickers and formatters ###


class DateFormatter(ticker.Formatter):
    """
    Format a tick (in days since the epoch) with a
    `~datetime.datetime.strftime` format string.
    """

    def __init__(self, fmt, tz=None, *, usetex=None):
        """
        Parameters
        ----------
        fmt : str
            `~datetime.datetime.strftime` format string
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        usetex : bool, default: :rc:`text.usetex`
            To enable/disable the use of TeX's math mode for rendering the
            results of the formatter.
        """
        self.tz = _get_tzinfo(tz)
        self.fmt = fmt
        self._usetex = (usetex if usetex is not None else
                        mpl.rcParams['text.usetex'])

    def __call__(self, x, pos=0):
        result = num2date(x, self.tz).strftime(self.fmt)
        return _wrap_in_tex(result) if self._usetex else result

    def set_tzinfo(self, tz):
        self.tz = _get_tzinfo(tz)


class ConciseDateFormatter(ticker.Formatter):
    """
    A `.Formatter` which attempts to figure out the best format to use for the
    date, and to make it as compact as possible, but still be complete. This is
    most useful when used with the `AutoDateLocator`::

    >>> locator = AutoDateLocator()
    >>> formatter = ConciseDateFormatter(locator)

    Parameters
    ----------
    locator : `.ticker.Locator`
        Locator that this axis is using.

    tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
        Ticks timezone, passed to `.dates.num2date`.

    formats : list of 6 strings, optional
        Format strings for 6 levels of tick labelling: mostly years,
        months, days, hours, minutes, and seconds.  Strings use
        the same format codes as `~datetime.datetime.strftime`.  Default is
        ``['%Y', '%b', '%d', '%H:%M', '%H:%M', '%S.%f']``

    zero_formats : list of 6 strings, optional
        Format strings for tick labels that are "zeros" for a given tick
        level.  For instance, if most ticks are months, ticks around 1 Jan 2005
        will be labeled "Dec", "2005", "Feb".  The default is
        ``['', '%Y', '%b', '%b-%d', '%H:%M', '%H:%M']``

    offset_formats : list of 6 strings, optional
        Format strings for the 6 levels that is applied to the "offset"
        string found on the right side of an x-axis, or top of a y-axis.
        Combined with the tick labels this should completely specify the
        date.  The default is::

            ['', '%Y', '%Y-%b', '%Y-%b-%d', '%Y-%b-%d', '%Y-%b-%d %H:%M']

    show_offset : bool, default: True
        Whether to show the offset or not.

    usetex : bool, default: :rc:`text.usetex`
        To enable/disable the use of TeX's math mode for rendering the results
        of the formatter.

    Examples
    --------
    See :doc:`/gallery/ticks/date_concise_formatter`

    .. plot::

        import datetime
        import matplotlib.dates as mdates

        base = datetime.datetime(2005, 2, 1)
        dates = np.array([base + datetime.timedelta(hours=(2 * i))
                          for i in range(732)])
        N = len(dates)
        np.random.seed(19680801)
        y = np.cumsum(np.random.randn(N))

        fig, ax = plt.subplots(constrained_layout=True)
        locator = mdates.AutoDateLocator()
        formatter = mdates.ConciseDateFormatter(locator)
        ax.xaxis.set_major_locator(locator)
        ax.xaxis.set_major_formatter(formatter)

        ax.plot(dates, y)
        ax.set_title('Concise Date Formatter')

    """

    def __init__(self, locator, tz=None, formats=None, offset_formats=None,
                 zero_formats=None, show_offset=True, *, usetex=None):
        """
        Autoformat the date labels.  The default format is used to form an
        initial string, and then redundant elements are removed.
        """
        self._locator = locator
        self._tz = tz
        self.defaultfmt = '%Y'
        # there are 6 levels with each level getting a specific format
        # 0: mostly years,  1: months,  2: days,
        # 3: hours, 4: minutes, 5: seconds
        if formats:
            if len(formats) != 6:
                raise ValueError('formats argument must be a list of '
                                 '6 format strings (or None)')
            self.formats = formats
        else:
            self.formats = ['%Y',  # ticks are mostly years
                            '%b',          # ticks are mostly months
                            '%d',          # ticks are mostly days
                            '%H:%M',       # hrs
                            '%H:%M',       # min
                            '%S.%f',       # secs
                            ]
        # fmt for zeros ticks at this level.  These are
        # ticks that should be labeled w/ info the level above.
        # like 1 Jan can just be labelled "Jan".  02:02:00 can
        # just be labeled 02:02.
        if zero_formats:
            if len(zero_formats) != 6:
                raise ValueError('zero_formats argument must be a list of '
                                 '6 format strings (or None)')
            self.zero_formats = zero_formats
        elif formats:
            # use the users formats for the zero tick formats
            self.zero_formats = [''] + self.formats[:-1]
        else:
            # make the defaults a bit nicer:
            self.zero_formats = [''] + self.formats[:-1]
            self.zero_formats[3] = '%b-%d'

        if offset_formats:
            if len(offset_formats) != 6:
                raise ValueError('offset_formats argument must be a list of '
                                 '6 format strings (or None)')
            self.offset_formats = offset_formats
        else:
            self.offset_formats = ['',
                                   '%Y',
                                   '%Y-%b',
                                   '%Y-%b-%d',
                                   '%Y-%b-%d',
                                   '%Y-%b-%d %H:%M']
        self.offset_string = ''
        self.show_offset = show_offset
        self._usetex = (usetex if usetex is not None else
                        mpl.rcParams['text.usetex'])

    def __call__(self, x, pos=None):
        formatter = DateFormatter(self.defaultfmt, self._tz,
                                  usetex=self._usetex)
        return formatter(x, pos=pos)

    def format_ticks(self, values):
        tickdatetime = [num2date(value, tz=self._tz) for value in values]
        tickdate = np.array([tdt.timetuple()[:6] for tdt in tickdatetime])

        # basic algorithm:
        # 1) only display a part of the date if it changes over the ticks.
        # 2) don't display the smaller part of the date if:
        #    it is always the same or if it is the start of the
        #    year, month, day etc.
        # fmt for most ticks at this level
        fmts = self.formats
        # format beginnings of days, months, years, etc.
        zerofmts = self.zero_formats
        # offset fmt are for the offset in the upper left of the
        # or lower right of the axis.
        offsetfmts = self.offset_formats
        show_offset = self.show_offset

        # determine the level we will label at:
        # mostly 0: years,  1: months,  2: days,
        # 3: hours, 4: minutes, 5: seconds, 6: microseconds
        for level in range(5, -1, -1):
            unique = np.unique(tickdate[:, level])
            if len(unique) > 1:
                # if 1 is included in unique, the year is shown in ticks
                if level < 2 and np.any(unique == 1):
                    show_offset = False
                break
            elif level == 0:
                # all tickdate are the same, so only micros might be different
                # set to the most precise (6: microseconds doesn't exist...)
                level = 5

        # level is the basic level we will label at.
        # now loop through and decide the actual ticklabels
        zerovals = [0, 1, 1, 0, 0, 0, 0]
        labels = [''] * len(tickdate)
        for nn in range(len(tickdate)):
            if level < 5:
                if tickdate[nn][level] == zerovals[level]:
                    fmt = zerofmts[level]
                else:
                    fmt = fmts[level]
            else:
                # special handling for seconds + microseconds
                if (tickdatetime[nn].second == tickdatetime[nn].microsecond
                        == 0):
                    fmt = zerofmts[level]
                else:
                    fmt = fmts[level]
            labels[nn] = tickdatetime[nn].strftime(fmt)

        # special handling of seconds and microseconds:
        # strip extra zeros and decimal if possible.
        # this is complicated by two factors.  1) we have some level-4 strings
        # here (i.e. 03:00, '0.50000', '1.000') 2) we would like to have the
        # same number of decimals for each string (i.e. 0.5 and 1.0).
        if level >= 5:
            trailing_zeros = min(
                (len(s) - len(s.rstrip('0')) for s in labels if '.' in s),
                default=None)
            if trailing_zeros:
                for nn in range(len(labels)):
                    if '.' in labels[nn]:
                        labels[nn] = labels[nn][:-trailing_zeros].rstrip('.')

        if show_offset:
            # set the offset string:
            self.offset_string = tickdatetime[-1].strftime(offsetfmts[level])
            if self._usetex:
                self.offset_string = _wrap_in_tex(self.offset_string)
        else:
            self.offset_string = ''

        if self._usetex:
            return [_wrap_in_tex(l) for l in labels]
        else:
            return labels

    def get_offset(self):
        return self.offset_string

    def format_data_short(self, value):
        return num2date(value, tz=self._tz).strftime('%Y-%m-%d %H:%M:%S')


class AutoDateFormatter(ticker.Formatter):
    """
    A `.Formatter` which attempts to figure out the best format to use.  This
    is most useful when used with the `AutoDateLocator`.

    `.AutoDateFormatter` has a ``.scale`` dictionary that maps tick scales (the
    interval in days between one major tick) to format strings; this dictionary
    defaults to ::

        self.scaled = {
            DAYS_PER_YEAR: rcParams['date.autoformatter.year'],
            DAYS_PER_MONTH: rcParams['date.autoformatter.month'],
            1: rcParams['date.autoformatter.day'],
            1 / HOURS_PER_DAY: rcParams['date.autoformatter.hour'],
            1 / MINUTES_PER_DAY: rcParams['date.autoformatter.minute'],
            1 / SEC_PER_DAY: rcParams['date.autoformatter.second'],
            1 / MUSECONDS_PER_DAY: rcParams['date.autoformatter.microsecond'],
        }

    The formatter uses the format string corresponding to the lowest key in
    the dictionary that is greater or equal to the current scale.  Dictionary
    entries can be customized::

        locator = AutoDateLocator()
        formatter = AutoDateFormatter(locator)
        formatter.scaled[1/(24*60)] = '%M:%S' # only show min and sec

    Custom callables can also be used instead of format strings.  The following
    example shows how to use a custom format function to strip trailing zeros
    from decimal seconds and adds the date to the first ticklabel::

        def my_format_function(x, pos=None):
            x = matplotlib.dates.num2date(x)
            if pos == 0:
                fmt = '%D %H:%M:%S.%f'
            else:
                fmt = '%H:%M:%S.%f'
            label = x.strftime(fmt)
            label = label.rstrip("0")
            label = label.rstrip(".")
            return label

        formatter.scaled[1/(24*60)] = my_format_function
    """

    # This can be improved by providing some user-level direction on
    # how to choose the best format (precedence, etc.).

    # Perhaps a 'struct' that has a field for each time-type where a
    # zero would indicate "don't show" and a number would indicate
    # "show" with some sort of priority.  Same priorities could mean
    # show all with the same priority.

    # Or more simply, perhaps just a format string for each
    # possibility...

    def __init__(self, locator, tz=None, defaultfmt='%Y-%m-%d', *,
                 usetex=None):
        """
        Autoformat the date labels.

        Parameters
        ----------
        locator : `.ticker.Locator`
            Locator that this axis is using.

        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.

        defaultfmt : str
            The default format to use if none of the values in ``self.scaled``
            are greater than the unit returned by ``locator._get_unit()``.

        usetex : bool, default: :rc:`text.usetex`
            To enable/disable the use of TeX's math mode for rendering the
            results of the formatter. If any entries in ``self.scaled`` are set
            as functions, then it is up to the customized function to enable or
            disable TeX's math mode itself.
        """
        self._locator = locator
        self._tz = tz
        self.defaultfmt = defaultfmt
        self._formatter = DateFormatter(self.defaultfmt, tz)
        rcParams = mpl.rcParams
        self._usetex = (usetex if usetex is not None else
                        mpl.rcParams['text.usetex'])
        self.scaled = {
            DAYS_PER_YEAR: rcParams['date.autoformatter.year'],
            DAYS_PER_MONTH: rcParams['date.autoformatter.month'],
            1: rcParams['date.autoformatter.day'],
            1 / HOURS_PER_DAY: rcParams['date.autoformatter.hour'],
            1 / MINUTES_PER_DAY: rcParams['date.autoformatter.minute'],
            1 / SEC_PER_DAY: rcParams['date.autoformatter.second'],
            1 / MUSECONDS_PER_DAY: rcParams['date.autoformatter.microsecond']
        }

    def _set_locator(self, locator):
        self._locator = locator

    def __call__(self, x, pos=None):
        try:
            locator_unit_scale = float(self._locator._get_unit())
        except AttributeError:
            locator_unit_scale = 1
        # Pick the first scale which is greater than the locator unit.
        fmt = next((fmt for scale, fmt in sorted(self.scaled.items())
                    if scale >= locator_unit_scale),
                   self.defaultfmt)

        if isinstance(fmt, str):
            self._formatter = DateFormatter(fmt, self._tz, usetex=self._usetex)
            result = self._formatter(x, pos)
        elif callable(fmt):
            result = fmt(x, pos)
        else:
            raise TypeError('Unexpected type passed to {0!r}.'.format(self))

        return result


class rrulewrapper:
    """
    A simple wrapper around a `dateutil.rrule` allowing flexible
    date tick specifications.
    """
    def __init__(self, freq, tzinfo=None, **kwargs):
        """
        Parameters
        ----------
        freq : {YEARLY, MONTHLY, WEEKLY, DAILY, HOURLY, MINUTELY, SECONDLY}
            Tick frequency. These constants are defined in `dateutil.rrule`,
            but they are accessible from `matplotlib.dates` as well.
        tzinfo : `datetime.tzinfo`, optional
            Time zone information. The default is None.
        **kwargs
            Additional keyword arguments are passed to the `dateutil.rrule`.
        """
        kwargs['freq'] = freq
        self._base_tzinfo = tzinfo

        self._update_rrule(**kwargs)

    def set(self, **kwargs):
        """Set parameters for an existing wrapper."""
        self._construct.update(kwargs)

        self._update_rrule(**self._construct)

    def _update_rrule(self, **kwargs):
        tzinfo = self._base_tzinfo

        # rrule does not play nicely with timezones - especially pytz time
        # zones, it's best to use naive zones and attach timezones once the
        # datetimes are returned
        if 'dtstart' in kwargs:
            dtstart = kwargs['dtstart']
            if dtstart.tzinfo is not None:
                if tzinfo is None:
                    tzinfo = dtstart.tzinfo
                else:
                    dtstart = dtstart.astimezone(tzinfo)

                kwargs['dtstart'] = dtstart.replace(tzinfo=None)

        if 'until' in kwargs:
            until = kwargs['until']
            if until.tzinfo is not None:
                if tzinfo is not None:
                    until = until.astimezone(tzinfo)
                else:
                    raise ValueError('until cannot be aware if dtstart '
                                     'is naive and tzinfo is None')

                kwargs['until'] = until.replace(tzinfo=None)

        self._construct = kwargs.copy()
        self._tzinfo = tzinfo
        self._rrule = rrule(**self._construct)

    def _attach_tzinfo(self, dt, tzinfo):
        # pytz zones are attached by "localizing" the datetime
        if hasattr(tzinfo, 'localize'):
            return tzinfo.localize(dt, is_dst=True)

        return dt.replace(tzinfo=tzinfo)

    def _aware_return_wrapper(self, f, returns_list=False):
        """Decorator function that allows rrule methods to handle tzinfo."""
        # This is only necessary if we're actually attaching a tzinfo
        if self._tzinfo is None:
            return f

        # All datetime arguments must be naive. If they are not naive, they are
        # converted to the _tzinfo zone before dropping the zone.
        def normalize_arg(arg):
            if isinstance(arg, datetime.datetime) and arg.tzinfo is not None:
                if arg.tzinfo is not self._tzinfo:
                    arg = arg.astimezone(self._tzinfo)

                return arg.replace(tzinfo=None)

            return arg

        def normalize_args(args, kwargs):
            args = tuple(normalize_arg(arg) for arg in args)
            kwargs = {kw: normalize_arg(arg) for kw, arg in kwargs.items()}

            return args, kwargs

        # There are two kinds of functions we care about - ones that return
        # dates and ones that return lists of dates.
        if not returns_list:
            def inner_func(*args, **kwargs):
                args, kwargs = normalize_args(args, kwargs)
                dt = f(*args, **kwargs)
                return self._attach_tzinfo(dt, self._tzinfo)
        else:
            def inner_func(*args, **kwargs):
                args, kwargs = normalize_args(args, kwargs)
                dts = f(*args, **kwargs)
                return [self._attach_tzinfo(dt, self._tzinfo) for dt in dts]

        return functools.wraps(f)(inner_func)

    def __getattr__(self, name):
        if name in self.__dict__:
            return self.__dict__[name]

        f = getattr(self._rrule, name)

        if name in {'after', 'before'}:
            return self._aware_return_wrapper(f)
        elif name in {'xafter', 'xbefore', 'between'}:
            return self._aware_return_wrapper(f, returns_list=True)
        else:
            return f

    def __setstate__(self, state):
        self.__dict__.update(state)


class DateLocator(ticker.Locator):
    """
    Determines the tick locations when plotting dates.

    This class is subclassed by other Locators and
    is not meant to be used on its own.
    """
    hms0d = {'byhour': 0, 'byminute': 0, 'bysecond': 0}

    def __init__(self, tz=None):
        """
        Parameters
        ----------
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        self.tz = _get_tzinfo(tz)

    def set_tzinfo(self, tz):
        """
        Set timezone info.

        Parameters
        ----------
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        self.tz = _get_tzinfo(tz)

    def datalim_to_dt(self):
        """Convert axis data interval to datetime objects."""
        dmin, dmax = self.axis.get_data_interval()
        if dmin > dmax:
            dmin, dmax = dmax, dmin

        return num2date(dmin, self.tz), num2date(dmax, self.tz)

    def viewlim_to_dt(self):
        """Convert the view interval to datetime objects."""
        vmin, vmax = self.axis.get_view_interval()
        if vmin > vmax:
            vmin, vmax = vmax, vmin
        return num2date(vmin, self.tz), num2date(vmax, self.tz)

    def _get_unit(self):
        """
        Return how many days a unit of the locator is; used for
        intelligent autoscaling.
        """
        return 1

    def _get_interval(self):
        """
        Return the number of units for each tick.
        """
        return 1

    def nonsingular(self, vmin, vmax):
        """
        Given the proposed upper and lower extent, adjust the range
        if it is too close to being singular (i.e. a range of ~0).
        """
        if not np.isfinite(vmin) or not np.isfinite(vmax):
            # Except if there is no data, then use 1970 as default.
            return (date2num(datetime.date(1970, 1, 1)),
                    date2num(datetime.date(1970, 1, 2)))
        if vmax < vmin:
            vmin, vmax = vmax, vmin
        unit = self._get_unit()
        interval = self._get_interval()
        if abs(vmax - vmin) < 1e-6:
            vmin -= 2 * unit * interval
            vmax += 2 * unit * interval
        return vmin, vmax


class RRuleLocator(DateLocator):
    # use the dateutil rrule instance

    def __init__(self, o, tz=None):
        super().__init__(tz)
        self.rule = o

    def __call__(self):
        # if no data have been set, this will tank with a ValueError
        try:
            dmin, dmax = self.viewlim_to_dt()
        except ValueError:
            return []

        return self.tick_values(dmin, dmax)

    def tick_values(self, vmin, vmax):
        start, stop = self._create_rrule(vmin, vmax)
        dates = self.rule.between(start, stop, True)
        if len(dates) == 0:
            return date2num([vmin, vmax])
        return self.raise_if_exceeds(date2num(dates))

    def _create_rrule(self, vmin, vmax):
        # set appropriate rrule dtstart and until and return
        # start and end
        delta = relativedelta(vmax, vmin)

        # We need to cap at the endpoints of valid datetime
        try:
            start = vmin - delta
        except (ValueError, OverflowError):
            # cap
            start = datetime.datetime(1, 1, 1, 0, 0, 0,
                                      tzinfo=datetime.timezone.utc)

        try:
            stop = vmax + delta
        except (ValueError, OverflowError):
            # cap
            stop = datetime.datetime(9999, 12, 31, 23, 59, 59,
                                     tzinfo=datetime.timezone.utc)

        self.rule.set(dtstart=start, until=stop)

        return vmin, vmax

    def _get_unit(self):
        # docstring inherited
        freq = self.rule._rrule._freq
        return self.get_unit_generic(freq)

    @staticmethod
    def get_unit_generic(freq):
        if freq == YEARLY:
            return DAYS_PER_YEAR
        elif freq == MONTHLY:
            return DAYS_PER_MONTH
        elif freq == WEEKLY:
            return DAYS_PER_WEEK
        elif freq == DAILY:
            return 1.0
        elif freq == HOURLY:
            return 1.0 / HOURS_PER_DAY
        elif freq == MINUTELY:
            return 1.0 / MINUTES_PER_DAY
        elif freq == SECONDLY:
            return 1.0 / SEC_PER_DAY
        else:
            # error
            return -1  # or should this just return '1'?

    def _get_interval(self):
        return self.rule._rrule._interval


class AutoDateLocator(DateLocator):
    """
    On autoscale, this class picks the best `DateLocator` to set the view
    limits and the tick locations.

    Attributes
    ----------
    intervald : dict

        Mapping of tick frequencies to multiples allowed for that ticking.
        The default is ::

            self.intervald = {
                YEARLY  : [1, 2, 4, 5, 10, 20, 40, 50, 100, 200, 400, 500,
                           1000, 2000, 4000, 5000, 10000],
                MONTHLY : [1, 2, 3, 4, 6],
                DAILY   : [1, 2, 3, 7, 14, 21],
                HOURLY  : [1, 2, 3, 4, 6, 12],
                MINUTELY: [1, 5, 10, 15, 30],
                SECONDLY: [1, 5, 10, 15, 30],
                MICROSECONDLY: [1, 2, 5, 10, 20, 50, 100, 200, 500,
                                1000, 2000, 5000, 10000, 20000, 50000,
                                100000, 200000, 500000, 1000000],
            }

        where the keys are defined in `dateutil.rrule`.

        The interval is used to specify multiples that are appropriate for
        the frequency of ticking. For instance, every 7 days is sensible
        for daily ticks, but for minutes/seconds, 15 or 30 make sense.

        When customizing, you should only modify the values for the existing
        keys. You should not add or delete entries.

        Example for forcing ticks every 3 hours::

            locator = AutoDateLocator()
            locator.intervald[HOURLY] = [3]  # only show every 3 hours
    """

    def __init__(self, tz=None, minticks=5, maxticks=None,
                 interval_multiples=True):
        """
        Parameters
        ----------
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        minticks : int
            The minimum number of ticks desired; controls whether ticks occur
            yearly, monthly, etc.
        maxticks : int
            The maximum number of ticks desired; controls the interval between
            ticks (ticking every other, every 3, etc.).  For fine-grained
            control, this can be a dictionary mapping individual rrule
            frequency constants (YEARLY, MONTHLY, etc.) to their own maximum
            number of ticks.  This can be used to keep the number of ticks
            appropriate to the format chosen in `AutoDateFormatter`. Any
            frequency not specified in this dictionary is given a default
            value.
        interval_multiples : bool, default: True
            Whether ticks should be chosen to be multiple of the interval,
            locking them to 'nicer' locations.  For example, this will force
            the ticks to be at hours 0, 6, 12, 18 when hourly ticking is done
            at 6 hour intervals.
        """
        super().__init__(tz=tz)
        self._freq = YEARLY
        self._freqs = [YEARLY, MONTHLY, DAILY, HOURLY, MINUTELY,
                       SECONDLY, MICROSECONDLY]
        self.minticks = minticks

        self.maxticks = {YEARLY: 11, MONTHLY: 12, DAILY: 11, HOURLY: 12,
                         MINUTELY: 11, SECONDLY: 11, MICROSECONDLY: 8}
        if maxticks is not None:
            try:
                self.maxticks.update(maxticks)
            except TypeError:
                # Assume we were given an integer. Use this as the maximum
                # number of ticks for every frequency and create a
                # dictionary for this
                self.maxticks = dict.fromkeys(self._freqs, maxticks)
        self.interval_multiples = interval_multiples
        self.intervald = {
            YEARLY:   [1, 2, 4, 5, 10, 20, 40, 50, 100, 200, 400, 500,
                       1000, 2000, 4000, 5000, 10000],
            MONTHLY:  [1, 2, 3, 4, 6],
            DAILY:    [1, 2, 3, 7, 14, 21],
            HOURLY:   [1, 2, 3, 4, 6, 12],
            MINUTELY: [1, 5, 10, 15, 30],
            SECONDLY: [1, 5, 10, 15, 30],
            MICROSECONDLY: [1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000,
                            5000, 10000, 20000, 50000, 100000, 200000, 500000,
                            1000000],
                            }
        if interval_multiples:
            # Swap "3" for "4" in the DAILY list; If we use 3 we get bad
            # tick loc for months w/ 31 days: 1, 4, ..., 28, 31, 1
            # If we use 4 then we get: 1, 5, ... 25, 29, 1
            self.intervald[DAILY] = [1, 2, 4, 7, 14]

        self._byranges = [None, range(1, 13), range(1, 32),
                          range(0, 24), range(0, 60), range(0, 60), None]

    def __call__(self):
        # docstring inherited
        dmin, dmax = self.viewlim_to_dt()
        locator = self.get_locator(dmin, dmax)
        return locator()

    def tick_values(self, vmin, vmax):
        return self.get_locator(vmin, vmax).tick_values(vmin, vmax)

    def nonsingular(self, vmin, vmax):
        # whatever is thrown at us, we can scale the unit.
        # But default nonsingular date plots at an ~4 year period.
        if not np.isfinite(vmin) or not np.isfinite(vmax):
            # Except if there is no data, then use 1970 as default.
            return (date2num(datetime.date(1970, 1, 1)),
                    date2num(datetime.date(1970, 1, 2)))
        if vmax < vmin:
            vmin, vmax = vmax, vmin
        if vmin == vmax:
            vmin = vmin - DAYS_PER_YEAR * 2
            vmax = vmax + DAYS_PER_YEAR * 2
        return vmin, vmax

    def _get_unit(self):
        if self._freq in [MICROSECONDLY]:
            return 1. / MUSECONDS_PER_DAY
        else:
            return RRuleLocator.get_unit_generic(self._freq)

    def get_locator(self, dmin, dmax):
        """Pick the best locator based on a distance."""
        delta = relativedelta(dmax, dmin)
        tdelta = dmax - dmin

        # take absolute difference
        if dmin > dmax:
            delta = -delta
            tdelta = -tdelta
        # The following uses a mix of calls to relativedelta and timedelta
        # methods because there is incomplete overlap in the functionality of
        # these similar functions, and it's best to avoid doing our own math
        # whenever possible.
        numYears = float(delta.years)
        numMonths = numYears * MONTHS_PER_YEAR + delta.months
        numDays = tdelta.days  # Avoids estimates of days/month, days/year.
        numHours = numDays * HOURS_PER_DAY + delta.hours
        numMinutes = numHours * MIN_PER_HOUR + delta.minutes
        numSeconds = np.floor(tdelta.total_seconds())
        numMicroseconds = np.floor(tdelta.total_seconds() * 1e6)

        nums = [numYears, numMonths, numDays, numHours, numMinutes,
                numSeconds, numMicroseconds]

        use_rrule_locator = [True] * 6 + [False]

        # Default setting of bymonth, etc. to pass to rrule
        # [unused (for year), bymonth, bymonthday, byhour, byminute,
        #  bysecond, unused (for microseconds)]
        byranges = [None, 1, 1, 0, 0, 0, None]

        # Loop over all the frequencies and try to find one that gives at
        # least a minticks tick positions.  Once this is found, look for
        # an interval from a list specific to that frequency that gives no
        # more than maxticks tick positions. Also, set up some ranges
        # (bymonth, etc.) as appropriate to be passed to rrulewrapper.
        for i, (freq, num) in enumerate(zip(self._freqs, nums)):
            # If this particular frequency doesn't give enough ticks, continue
            if num < self.minticks:
                # Since we're not using this particular frequency, set
                # the corresponding by_ to None so the rrule can act as
                # appropriate
                byranges[i] = None
                continue

            # Find the first available interval that doesn't give too many
            # ticks
            for interval in self.intervald[freq]:
                if num <= interval * (self.maxticks[freq] - 1):
                    break
            else:
                if not (self.interval_multiples and freq == DAILY):
                    _api.warn_external(
                        f"AutoDateLocator was unable to pick an appropriate "
                        f"interval for this date range. It may be necessary "
                        f"to add an interval value to the AutoDateLocator's "
                        f"intervald dictionary. Defaulting to {interval}.")

            # Set some parameters as appropriate
            self._freq = freq

            if self._byranges[i] and self.interval_multiples:
                byranges[i] = self._byranges[i][::interval]
                if i in (DAILY, WEEKLY):
                    if interval == 14:
                        # just make first and 15th.  Avoids 30th.
                        byranges[i] = [1, 15]
                    elif interval == 7:
                        byranges[i] = [1, 8, 15, 22]

                interval = 1
            else:
                byranges[i] = self._byranges[i]
            break
        else:
            interval = 1

        if (freq == YEARLY) and self.interval_multiples:
            locator = YearLocator(interval, tz=self.tz)
        elif use_rrule_locator[i]:
            _, bymonth, bymonthday, byhour, byminute, bysecond, _ = byranges
            rrule = rrulewrapper(self._freq, interval=interval,
                                 dtstart=dmin, until=dmax,
                                 bymonth=bymonth, bymonthday=bymonthday,
                                 byhour=byhour, byminute=byminute,
                                 bysecond=bysecond)

            locator = RRuleLocator(rrule, tz=self.tz)
        else:
            locator = MicrosecondLocator(interval, tz=self.tz)
            if date2num(dmin) > 70 * 365 and interval < 1000:
                _api.warn_external(
                    'Plotting microsecond time intervals for dates far from '
                    f'the epoch (time origin: {get_epoch()}) is not well-'
                    'supported. See matplotlib.dates.set_epoch to change the '
                    'epoch.')

        locator.set_axis(self.axis)
        return locator


class YearLocator(RRuleLocator):
    """
    Make ticks on a given day of each year that is a multiple of base.

    Examples::

      # Tick every year on Jan 1st
      locator = YearLocator()

      # Tick every 5 years on July 4th
      locator = YearLocator(5, month=7, day=4)
    """
    def __init__(self, base=1, month=1, day=1, tz=None):
        """
        Parameters
        ----------
        base : int, default: 1
            Mark ticks every *base* years.
        month : int, default: 1
            The month on which to place the ticks, starting from 1. Default is
            January.
        day : int, default: 1
            The day on which to place the ticks.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        rule = rrulewrapper(YEARLY, interval=base, bymonth=month,
                            bymonthday=day, **self.hms0d)
        super().__init__(rule, tz=tz)
        self.base = ticker._Edge_integer(base, 0)

    def _create_rrule(self, vmin, vmax):
        # 'start' needs to be a multiple of the interval to create ticks on
        # interval multiples when the tick frequency is YEARLY
        ymin = max(self.base.le(vmin.year) * self.base.step, 1)
        ymax = min(self.base.ge(vmax.year) * self.base.step, 9999)

        c = self.rule._construct
        replace = {'year': ymin,
                   'month': c.get('bymonth', 1),
                   'day': c.get('bymonthday', 1),
                   'hour': 0, 'minute': 0, 'second': 0}

        start = vmin.replace(**replace)
        stop = start.replace(year=ymax)
        self.rule.set(dtstart=start, until=stop)

        return start, stop


class MonthLocator(RRuleLocator):
    """
    Make ticks on occurrences of each month, e.g., 1, 3, 12.
    """
    def __init__(self, bymonth=None, bymonthday=1, interval=1, tz=None):
        """
        Parameters
        ----------
        bymonth : int or list of int, default: all months
            Ticks will be placed on every month in *bymonth*. Default is
            ``range(1, 13)``, i.e. every month.
        bymonthday : int, default: 1
            The day on which to place the ticks.
        interval : int, default: 1
            The interval between each iteration. For example, if
            ``interval=2``, mark every second occurrence.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        if bymonth is None:
            bymonth = range(1, 13)

        rule = rrulewrapper(MONTHLY, bymonth=bymonth, bymonthday=bymonthday,
                            interval=interval, **self.hms0d)
        super().__init__(rule, tz=tz)


class WeekdayLocator(RRuleLocator):
    """
    Make ticks on occurrences of each weekday.
    """

    def __init__(self, byweekday=1, interval=1, tz=None):
        """
        Parameters
        ----------
        byweekday : int or list of int, default: all days
            Ticks will be placed on every weekday in *byweekday*. Default is
            every day.

            Elements of *byweekday* must be one of MO, TU, WE, TH, FR, SA,
            SU, the constants from :mod:`dateutil.rrule`, which have been
            imported into the :mod:`matplotlib.dates` namespace.
        interval : int, default: 1
            The interval between each iteration. For example, if
            ``interval=2``, mark every second occurrence.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        rule = rrulewrapper(DAILY, byweekday=byweekday,
                            interval=interval, **self.hms0d)
        super().__init__(rule, tz=tz)


class DayLocator(RRuleLocator):
    """
    Make ticks on occurrences of each day of the month.  For example,
    1, 15, 30.
    """
    def __init__(self, bymonthday=None, interval=1, tz=None):
        """
        Parameters
        ----------
        bymonthday : int or list of int, default: all days
            Ticks will be placed on every day in *bymonthday*. Default is
            ``bymonthday=range(1, 32)``, i.e., every day of the month.
        interval : int, default: 1
            The interval between each iteration. For example, if
            ``interval=2``, mark every second occurrence.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        if interval != int(interval) or interval < 1:
            raise ValueError("interval must be an integer greater than 0")
        if bymonthday is None:
            bymonthday = range(1, 32)

        rule = rrulewrapper(DAILY, bymonthday=bymonthday,
                            interval=interval, **self.hms0d)
        super().__init__(rule, tz=tz)


class HourLocator(RRuleLocator):
    """
    Make ticks on occurrences of each hour.
    """
    def __init__(self, byhour=None, interval=1, tz=None):
        """
        Parameters
        ----------
        byhour : int or list of int, default: all hours
            Ticks will be placed on every hour in *byhour*. Default is
            ``byhour=range(24)``, i.e., every hour.
        interval : int, default: 1
            The interval between each iteration. For example, if
            ``interval=2``, mark every second occurrence.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        if byhour is None:
            byhour = range(24)

        rule = rrulewrapper(HOURLY, byhour=byhour, interval=interval,
                            byminute=0, bysecond=0)
        super().__init__(rule, tz=tz)


class MinuteLocator(RRuleLocator):
    """
    Make ticks on occurrences of each minute.
    """
    def __init__(self, byminute=None, interval=1, tz=None):
        """
        Parameters
        ----------
        byminute : int or list of int, default: all minutes
            Ticks will be placed on every minute in *byminute*. Default is
            ``byminute=range(60)``, i.e., every minute.
        interval : int, default: 1
            The interval between each iteration. For example, if
            ``interval=2``, mark every second occurrence.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        if byminute is None:
            byminute = range(60)

        rule = rrulewrapper(MINUTELY, byminute=byminute, interval=interval,
                            bysecond=0)
        super().__init__(rule, tz=tz)


class SecondLocator(RRuleLocator):
    """
    Make ticks on occurrences of each second.
    """
    def __init__(self, bysecond=None, interval=1, tz=None):
        """
        Parameters
        ----------
        bysecond : int or list of int, default: all seconds
            Ticks will be placed on every second in *bysecond*. Default is
            ``bysecond = range(60)``, i.e., every second.
        interval : int, default: 1
            The interval between each iteration. For example, if
            ``interval=2``, mark every second occurrence.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        if bysecond is None:
            bysecond = range(60)

        rule = rrulewrapper(SECONDLY, bysecond=bysecond, interval=interval)
        super().__init__(rule, tz=tz)


class MicrosecondLocator(DateLocator):
    """
    Make ticks on regular intervals of one or more microsecond(s).

    .. note::

        By default, Matplotlib uses a floating point representation of time in
        days since the epoch, so plotting data with
        microsecond time resolution does not work well for
        dates that are far (about 70 years) from the epoch (check with
        `~.dates.get_epoch`).

        If you want sub-microsecond resolution time plots, it is strongly
        recommended to use floating point seconds, not datetime-like
        time representation.

        If you really must use datetime.datetime() or similar and still
        need microsecond precision, change the time origin via
        `.dates.set_epoch` to something closer to the dates being plotted.
        See :doc:`/gallery/ticks/date_precision_and_epochs`.

    """
    def __init__(self, interval=1, tz=None):
        """
        Parameters
        ----------
        interval : int, default: 1
            The interval between each iteration. For example, if
            ``interval=2``, mark every second occurrence.
        tz : str or `~datetime.tzinfo`, default: :rc:`timezone`
            Ticks timezone. If a string, *tz* is passed to `dateutil.tz`.
        """
        super().__init__(tz=tz)
        self._interval = interval
        self._wrapped_locator = ticker.MultipleLocator(interval)

    def set_axis(self, axis):
        self._wrapped_locator.set_axis(axis)
        return super().set_axis(axis)

    def __call__(self):
        # if no data have been set, this will tank with a ValueError
        try:
            dmin, dmax = self.viewlim_to_dt()
        except ValueError:
            return []

        return self.tick_values(dmin, dmax)

    def tick_values(self, vmin, vmax):
        nmin, nmax = date2num((vmin, vmax))
        t0 = np.floor(nmin)
        nmax = nmax - t0
        nmin = nmin - t0
        nmin *= MUSECONDS_PER_DAY
        nmax *= MUSECONDS_PER_DAY

        ticks = self._wrapped_locator.tick_values(nmin, nmax)

        ticks = ticks / MUSECONDS_PER_DAY + t0
        return ticks

    def _get_unit(self):
        # docstring inherited
        return 1. / MUSECONDS_PER_DAY

    def _get_interval(self):
        # docstring inherited
        return self._interval


@_api.deprecated("3.6", alternative="`AutoDateLocator` and `AutoDateFormatter`"
                 " or vendor the code")
def date_ticker_factory(span, tz=None, numticks=5):
    """
    Create a date locator with *numticks* (approx) and a date formatter
    for *span* in days.  Return value is (locator, formatter).
    """

    if span == 0:
        span = 1 / HOURS_PER_DAY

    mins = span * MINUTES_PER_DAY
    hrs = span * HOURS_PER_DAY
    days = span
    wks = span / DAYS_PER_WEEK
    months = span / DAYS_PER_MONTH      # Approx
    years = span / DAYS_PER_YEAR        # Approx

    if years > numticks:
        locator = YearLocator(int(years / numticks), tz=tz)  # define
        fmt = '%Y'
    elif months > numticks:
        locator = MonthLocator(tz=tz)
        fmt = '%b %Y'
    elif wks > numticks:
        locator = WeekdayLocator(tz=tz)
        fmt = '%a, %b %d'
    elif days > numticks:
        locator = DayLocator(interval=math.ceil(days / numticks), tz=tz)
        fmt = '%b %d'
    elif hrs > numticks:
        locator = HourLocator(interval=math.ceil(hrs / numticks), tz=tz)
        fmt = '%H:%M\n%b %d'
    elif mins > numticks:
        locator = MinuteLocator(interval=math.ceil(mins / numticks), tz=tz)
        fmt = '%H:%M:%S'
    else:
        locator = MinuteLocator(tz=tz)
        fmt = '%H:%M:%S'

    formatter = DateFormatter(fmt, tz=tz)
    return locator, formatter


class DateConverter(units.ConversionInterface):
    """
    Converter for `datetime.date` and `datetime.datetime` data, or for
    date/time data represented as it would be converted by `date2num`.

    The 'unit' tag for such data is None or a `~datetime.tzinfo` instance.
    """

    def __init__(self, *, interval_multiples=True):
        self._interval_multiples = interval_multiples
        super().__init__()

    def axisinfo(self, unit, axis):
        """
        Return the `~matplotlib.units.AxisInfo` for *unit*.

        *unit* is a `~datetime.tzinfo` instance or None.
        The *axis* argument is required but not used.
        """
        tz = unit

        majloc = AutoDateLocator(tz=tz,
                                 interval_multiples=self._interval_multiples)
        majfmt = AutoDateFormatter(majloc, tz=tz)
        datemin = datetime.date(1970, 1, 1)
        datemax = datetime.date(1970, 1, 2)

        return units.AxisInfo(majloc=majloc, majfmt=majfmt, label='',
                              default_limits=(datemin, datemax))

    @staticmethod
    def convert(value, unit, axis):
        """
        If *value* is not already a number or sequence of numbers, convert it
        with `date2num`.

        The *unit* and *axis* arguments are not used.
        """
        return date2num(value)

    @staticmethod
    def default_units(x, axis):
        """
        Return the `~datetime.tzinfo` instance of *x* or of its first element,
        or None
        """
        if isinstance(x, np.ndarray):
            x = x.ravel()

        try:
            x = cbook._safe_first_finite(x)
        except (TypeError, StopIteration):
            pass

        try:
            return x.tzinfo
        except AttributeError:
            pass
        return None


class ConciseDateConverter(DateConverter):
    # docstring inherited

    def __init__(self, formats=None, zero_formats=None, offset_formats=None,
                 show_offset=True, *, interval_multiples=True):
        self._formats = formats
        self._zero_formats = zero_formats
        self._offset_formats = offset_formats
        self._show_offset = show_offset
        self._interval_multiples = interval_multiples
        super().__init__()

    def axisinfo(self, unit, axis):
        # docstring inherited
        tz = unit
        majloc = AutoDateLocator(tz=tz,
                                 interval_multiples=self._interval_multiples)
        majfmt = ConciseDateFormatter(majloc, tz=tz, formats=self._formats,
                                      zero_formats=self._zero_formats,
                                      offset_formats=self._offset_formats,
                                      show_offset=self._show_offset)
        datemin = datetime.date(1970, 1, 1)
        datemax = datetime.date(1970, 1, 2)
        return units.AxisInfo(majloc=majloc, majfmt=majfmt, label='',
                              default_limits=(datemin, datemax))


class _SwitchableDateConverter:
    """
    Helper converter-like object that generates and dispatches to
    temporary ConciseDateConverter or DateConverter instances based on
    :rc:`date.converter` and :rc:`date.interval_multiples`.
    """

    @staticmethod
    def _get_converter():
        converter_cls = {
            "concise": ConciseDateConverter, "auto": DateConverter}[
                mpl.rcParams["date.converter"]]
        interval_multiples = mpl.rcParams["date.interval_multiples"]
        return converter_cls(interval_multiples=interval_multiples)

    def axisinfo(self, *args, **kwargs):
        return self._get_converter().axisinfo(*args, **kwargs)

    def default_units(self, *args, **kwargs):
        return self._get_converter().default_units(*args, **kwargs)

    def convert(self, *args, **kwargs):
        return self._get_converter().convert(*args, **kwargs)


units.registry[np.datetime64] = \
    units.registry[datetime.date] = \
    units.registry[datetime.datetime] = \
    _SwitchableDateConverter()