polylabel 1.0.2

A Rust implementation of the Polylabel algorithm
Documentation
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
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import geopandas as gp\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.collections import PatchCollection\n",
    "from matplotlib import rc\n",
    "from shapely.geometry import LineString, Polygon, Point, box, shape\n",
    "from shapely.ops import cascaded_union\n",
    "from fiona.crs import from_epsg\n",
    "from rtree import index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def nearest_postcode_distance(df, df2, sindex):\n",
    "    \"\"\"\n",
    "    Find nearest neighbour to df in df2 spatial index\n",
    "    Then, calculate distance between nearest neighbour geometry and df geometry\n",
    "    Return distance and postcode\n",
    "    Note: distance between adjacent postcodes is 0.0\n",
    "    \"\"\"\n",
    "    idx_pos = sindex.nearest(df.geometry.bounds, 1).next()\n",
    "    return df.geometry.distance(df2.iloc[idx_pos].geometry) / 1000., df2.iloc[idx_pos]['POSTCODE']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# CRS has been converted from 27700 to 25832 (ETRS89) for Euclidean distance measurement\n",
    "merged = gp.GeoDataFrame.from_file(\"merged_postcodes_centroids.shp\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Distance P</th>\n",
       "      <th>Minimum Di</th>\n",
       "      <th>PC_AREA</th>\n",
       "      <th>POSTCODE</th>\n",
       "      <th>UPP</th>\n",
       "      <th>geometry</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AB10 1AN</td>\n",
       "      <td>0.08436385277905387</td>\n",
       "      <td>AB</td>\n",
       "      <td>AB10 1AB</td>\n",
       "      <td>00000000000000000002</td>\n",
       "      <td>POLYGON ((-169708.694024045 6388795.9234469, -...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AB10 1AN</td>\n",
       "      <td>0</td>\n",
       "      <td>AB</td>\n",
       "      <td>AB10 1AL</td>\n",
       "      <td>00000000000000000003</td>\n",
       "      <td>POLYGON ((-169614.706281362 6388752.870788309,...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>AB10 1AN</td>\n",
       "      <td>0</td>\n",
       "      <td>AB</td>\n",
       "      <td>AB10 1AN</td>\n",
       "      <td>00000000000000000004</td>\n",
       "      <td>POLYGON ((-169546.2997755085 6388773.476457709...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>AB10 1AN</td>\n",
       "      <td>0.0233134882466831</td>\n",
       "      <td>AB</td>\n",
       "      <td>AB10 1AP</td>\n",
       "      <td>00000000000000000005</td>\n",
       "      <td>POLYGON ((-169690.3220984091 6388713.581593464...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>AB10 1AN</td>\n",
       "      <td>0.1438272018464478</td>\n",
       "      <td>AB</td>\n",
       "      <td>AB10 1AS</td>\n",
       "      <td>00000000000000000006</td>\n",
       "      <td>POLYGON ((-169779.7872413595 6388697.504694026...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Distance P           Minimum Di PC_AREA  POSTCODE                   UPP  \\\n",
       "0   AB10 1AN  0.08436385277905387      AB  AB10 1AB  00000000000000000002   \n",
       "1   AB10 1AN                    0      AB  AB10 1AL  00000000000000000003   \n",
       "2   AB10 1AN                    0      AB  AB10 1AN  00000000000000000004   \n",
       "3   AB10 1AN   0.0233134882466831      AB  AB10 1AP  00000000000000000005   \n",
       "4   AB10 1AN   0.1438272018464478      AB  AB10 1AS  00000000000000000006   \n",
       "\n",
       "                                            geometry  \n",
       "0  POLYGON ((-169708.694024045 6388795.9234469, -...  \n",
       "1  POLYGON ((-169614.706281362 6388752.870788309,...  \n",
       "2  POLYGON ((-169546.2997755085 6388773.476457709...  \n",
       "3  POLYGON ((-169690.3220984091 6388713.581593464...  \n",
       "4  POLYGON ((-169779.7872413595 6388697.504694026...  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create \"funded\" dataframe from CR-supplied data, and create a spatial index for it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df_funded = pd.read_excel(\"/Users/sth/Downloads/cr_funded.xlsx\")\n",
    "df_funded_geo = merged[merged['POSTCODE'].isin(list(df_funded['Grants Project Postcode']))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "merged.sort_index(inplace=True)\n",
    "df_funded_geo.sort_index(inplace=True)\n",
    "df_funded_geo['Funded Project Postcode'] = df_funded_geo[u'POSTCODE']\n",
    "df_funded_geo.rename(columns={'Grants Project Postcode': u'POSTCODE'}, inplace=True)\n",
    "sindex = df_funded_geo.sindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([              u'Distance P',               u'Minimum Di',\n",
       "                        u'PC_AREA',                 u'POSTCODE',\n",
       "                            u'UPP',                 u'geometry',\n",
       "               u'Minimum Distance', u'Nearest Project Postcode',\n",
       "        u'Funded Project Postcode'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_funded_geo.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate minimum distance in `km` and post code  \n",
    "This will result in distances of 0.0 for postcodes adjacent to postcodes in which a project has been funded. **CAUTION**: this will take a long time (20 - 45 minutes, depending on processor speed), and will use a lot of memory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "merged['Minimum Distance'], merged['Nearest Project Postcode'] = zip(*merged.apply(\n",
    "    nearest_postcode_distance, axis=1, args=(df_funded_geo, sindex)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([                 u'PC_AREA',                 u'POSTCODE',\n",
       "                            u'UPP',                 u'geometry',\n",
       "               u'Minimum Distance', u'Nearest Project Postcode'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([u'PC_AREA', u'POSTCODE', u'UPP', u'geometry',\n",
       "       u'Funded Project Postcode'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_funded_geo.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Join the funded projects DataFrame to the postcode DataFrame  \n",
    "This is an intermediate step -- we'll be using the new geometry column to calculate\n",
    "centroid distance between the nearest postcodes\n",
    "\n",
    "Duplicate columns from the funded projects df have the `_funded` suffix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "joined = merged.join(\n",
    "    df_funded_geo.set_index(u'POSTCODE'),\n",
    "    on = \"Nearest Project Postcode\",\n",
    "    rsuffix=u'_funded'\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index([                 u'PC_AREA',                 u'POSTCODE',\n",
       "                            u'UPP',                 u'geometry',\n",
       "               u'Minimum Distance', u'Nearest Project Postcode',\n",
       "                 u'PC_AREA_funded',               u'UPP_funded',\n",
       "                u'geometry_funded',  u'Funded Project Postcode'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the [centroid](https://en.wikipedia.org/wiki/Centroid) distance in `km` between each UK postcode, and the nearest postcode in which Comic Relief have funded a project.  \n",
    "\n",
    "See the accompanying image for an explanation of the difference between the two measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "joined['Minimum Distance Centroid'] = joined.apply(lambda df:\n",
    "    df.geometry.centroid.distance(df[u'geometry_funded'].centroid) / 1000., axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PC_AREA                    AB\n",
       "POSTCODE             AB11 5QH\n",
       "UPP                       469\n",
       "geometry                  foo\n",
       "Minimum Distance            1\n",
       "Distance Postcode    AB10 1AN\n",
       "Name: 721, dtype: object"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fix AB11 5QH -- its polygon is wrong\n",
    "# merged.iloc[721]['Minimum Distance'] = 1.0\n",
    "# merged.iloc[721]['Distance Postcode'] = 'AB10 1AN'\n",
    "# merged.iloc[721]\n",
    "\n",
    "# AB11 5QH HAS BEEN REMOVED DUE TO AN INVALID POLYGON."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the 20 post codes which are located the furthest from a post code in which Comic Relief have funded a project. The distance in this case is **polygon distance**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>POSTCODE</th>\n",
       "      <th>Minimum Distance</th>\n",
       "      <th>Nearest Project Postcode</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>689983</th>\n",
       "      <td>IV27 4XD</td>\n",
       "      <td>102.243906</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689981</th>\n",
       "      <td>IV27 4XA</td>\n",
       "      <td>102.193813</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689982</th>\n",
       "      <td>IV27 4XB</td>\n",
       "      <td>102.186633</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689984</th>\n",
       "      <td>IV27 4XE</td>\n",
       "      <td>102.154803</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689986</th>\n",
       "      <td>IV27 4XG</td>\n",
       "      <td>102.145813</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689992</th>\n",
       "      <td>IV27 4XQ</td>\n",
       "      <td>101.753515</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689989</th>\n",
       "      <td>IV27 4XL</td>\n",
       "      <td>101.681902</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689985</th>\n",
       "      <td>IV27 4XF</td>\n",
       "      <td>101.569011</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689987</th>\n",
       "      <td>IV27 4XH</td>\n",
       "      <td>100.444232</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689929</th>\n",
       "      <td>IV27 4QE</td>\n",
       "      <td>100.420907</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>690001</th>\n",
       "      <td>IV27 4YR</td>\n",
       "      <td>100.302919</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689932</th>\n",
       "      <td>IV27 4QH</td>\n",
       "      <td>100.149834</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>690000</th>\n",
       "      <td>IV27 4YQ</td>\n",
       "      <td>99.836299</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>690004</th>\n",
       "      <td>IV27 4YU</td>\n",
       "      <td>99.698467</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>693656</th>\n",
       "      <td>VIV00223</td>\n",
       "      <td>99.570614</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>693659</th>\n",
       "      <td>VIV00226</td>\n",
       "      <td>99.554083</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689924</th>\n",
       "      <td>IV27 4PY</td>\n",
       "      <td>99.537784</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689918</th>\n",
       "      <td>IV27 4PR</td>\n",
       "      <td>99.480622</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>690002</th>\n",
       "      <td>IV27 4YS</td>\n",
       "      <td>99.442818</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689919</th>\n",
       "      <td>IV27 4PS</td>\n",
       "      <td>99.378948</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        POSTCODE  Minimum Distance Nearest Project Postcode\n",
       "689983  IV27 4XD        102.243906                 KW15 1JD\n",
       "689981  IV27 4XA        102.193813                 KW15 1JD\n",
       "689982  IV27 4XB        102.186633                 KW15 1JD\n",
       "689984  IV27 4XE        102.154803                 IV30 5XF\n",
       "689986  IV27 4XG        102.145813                 IV30 5XF\n",
       "689992  IV27 4XQ        101.753515                 IV30 5XF\n",
       "689989  IV27 4XL        101.681902                 KW15 1JD\n",
       "689985  IV27 4XF        101.569011                 IV30 5XF\n",
       "689987  IV27 4XH        100.444232                 KW15 1JD\n",
       "689929  IV27 4QE        100.420907                  HS2 0BB\n",
       "690001  IV27 4YR        100.302919                 KW15 1JD\n",
       "689932  IV27 4QH        100.149834                  HS2 0BB\n",
       "690000  IV27 4YQ         99.836299                 KW15 1JD\n",
       "690004  IV27 4YU         99.698467                 KW15 1JD\n",
       "693656  VIV00223         99.570614                  HS2 0BB\n",
       "693659  VIV00226         99.554083                 KW15 1JD\n",
       "689924  IV27 4PY         99.537784                  HS2 0BB\n",
       "689918  IV27 4PR         99.480622                  HS2 0BB\n",
       "690002  IV27 4YS         99.442818                 KW15 1JD\n",
       "689919  IV27 4PS         99.378948                  HS2 0BB"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "merged[['POSTCODE', 'Minimum Distance', 'Nearest Project Postcode']].sort_values(\n",
    "    by='Minimum Distance', ascending=False).head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show the 20 post codes which are located the furthest from a post code in which Comic Relief have funded a project. The distance in this case is **centroid distance**, which is greater than polygon distance (see for instance the top result: the minimum polygon distance between `HS6 5DL` and `IV51 9DT` is 79.094 km, but the centroid distance is 111.73 km) but is a subjectively better measure of distances between adjacent post codes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>POSTCODE</th>\n",
       "      <th>Minimum Distance</th>\n",
       "      <th>Minimum Distance Centroid</th>\n",
       "      <th>Nearest Project Postcode</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>642866</th>\n",
       "      <td>HS6 5DL</td>\n",
       "      <td>79.094774</td>\n",
       "      <td>111.729833</td>\n",
       "      <td>IV51 9DT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>643062</th>\n",
       "      <td>HS9 5YW</td>\n",
       "      <td>97.247336</td>\n",
       "      <td>105.578325</td>\n",
       "      <td>IV51 9DT</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689929</th>\n",
       "      <td>IV27 4QE</td>\n",
       "      <td>100.420907</td>\n",
       "      <td>103.728483</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689985</th>\n",
       "      <td>IV27 4XF</td>\n",
       "      <td>101.569011</td>\n",
       "      <td>103.334439</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>690003</th>\n",
       "      <td>IV27 4YT</td>\n",
       "      <td>97.668976</td>\n",
       "      <td>103.241990</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>690001</th>\n",
       "      <td>IV27 4YR</td>\n",
       "      <td>100.302919</td>\n",
       "      <td>102.885857</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689986</th>\n",
       "      <td>IV27 4XG</td>\n",
       "      <td>102.145813</td>\n",
       "      <td>102.855545</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689984</th>\n",
       "      <td>IV27 4XE</td>\n",
       "      <td>102.154803</td>\n",
       "      <td>102.510731</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>720099</th>\n",
       "      <td>KW14 7TJ</td>\n",
       "      <td>79.766687</td>\n",
       "      <td>102.389255</td>\n",
       "      <td>KW17 2PU</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689992</th>\n",
       "      <td>IV27 4XQ</td>\n",
       "      <td>101.753515</td>\n",
       "      <td>102.341355</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689983</th>\n",
       "      <td>IV27 4XD</td>\n",
       "      <td>102.243906</td>\n",
       "      <td>102.335801</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689981</th>\n",
       "      <td>IV27 4XA</td>\n",
       "      <td>102.193813</td>\n",
       "      <td>102.306455</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689982</th>\n",
       "      <td>IV27 4XB</td>\n",
       "      <td>102.186633</td>\n",
       "      <td>102.300491</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689928</th>\n",
       "      <td>IV27 4QD</td>\n",
       "      <td>98.620823</td>\n",
       "      <td>102.085076</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689989</th>\n",
       "      <td>IV27 4XL</td>\n",
       "      <td>101.681902</td>\n",
       "      <td>102.012712</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689987</th>\n",
       "      <td>IV27 4XH</td>\n",
       "      <td>100.444232</td>\n",
       "      <td>101.951465</td>\n",
       "      <td>KW15 1JD</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689932</th>\n",
       "      <td>IV27 4QH</td>\n",
       "      <td>100.149834</td>\n",
       "      <td>101.847465</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689926</th>\n",
       "      <td>IV27 4QA</td>\n",
       "      <td>99.207035</td>\n",
       "      <td>101.726996</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689998</th>\n",
       "      <td>IV27 4YL</td>\n",
       "      <td>94.432503</td>\n",
       "      <td>101.615775</td>\n",
       "      <td>IV30 5XF</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>689927</th>\n",
       "      <td>IV27 4QB</td>\n",
       "      <td>98.351980</td>\n",
       "      <td>101.505845</td>\n",
       "      <td>HS2 0BB</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        POSTCODE  Minimum Distance  Minimum Distance Centroid  \\\n",
       "642866   HS6 5DL         79.094774                 111.729833   \n",
       "643062   HS9 5YW         97.247336                 105.578325   \n",
       "689929  IV27 4QE        100.420907                 103.728483   \n",
       "689985  IV27 4XF        101.569011                 103.334439   \n",
       "690003  IV27 4YT         97.668976                 103.241990   \n",
       "690001  IV27 4YR        100.302919                 102.885857   \n",
       "689986  IV27 4XG        102.145813                 102.855545   \n",
       "689984  IV27 4XE        102.154803                 102.510731   \n",
       "720099  KW14 7TJ         79.766687                 102.389255   \n",
       "689992  IV27 4XQ        101.753515                 102.341355   \n",
       "689983  IV27 4XD        102.243906                 102.335801   \n",
       "689981  IV27 4XA        102.193813                 102.306455   \n",
       "689982  IV27 4XB        102.186633                 102.300491   \n",
       "689928  IV27 4QD         98.620823                 102.085076   \n",
       "689989  IV27 4XL        101.681902                 102.012712   \n",
       "689987  IV27 4XH        100.444232                 101.951465   \n",
       "689932  IV27 4QH        100.149834                 101.847465   \n",
       "689926  IV27 4QA         99.207035                 101.726996   \n",
       "689998  IV27 4YL         94.432503                 101.615775   \n",
       "689927  IV27 4QB         98.351980                 101.505845   \n",
       "\n",
       "       Nearest Project Postcode  \n",
       "642866                 IV51 9DT  \n",
       "643062                 IV51 9DT  \n",
       "689929                  HS2 0BB  \n",
       "689985                 IV30 5XF  \n",
       "690003                 KW15 1JD  \n",
       "690001                 KW15 1JD  \n",
       "689986                 IV30 5XF  \n",
       "689984                 IV30 5XF  \n",
       "720099                 KW17 2PU  \n",
       "689992                 IV30 5XF  \n",
       "689983                 KW15 1JD  \n",
       "689981                 KW15 1JD  \n",
       "689982                 KW15 1JD  \n",
       "689928                  HS2 0BB  \n",
       "689989                 KW15 1JD  \n",
       "689987                 KW15 1JD  \n",
       "689932                  HS2 0BB  \n",
       "689926                  HS2 0BB  \n",
       "689998                 IV30 5XF  \n",
       "689927                  HS2 0BB  "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined[['POSTCODE', 'Minimum Distance', 'Minimum Distance Centroid', 'Nearest Project Postcode']].sort_values(\n",
    "    by='Minimum Distance Centroid', ascending=False).head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at some summary stats for both sets of distance calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.3708649416420808"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined['Minimum Distance'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.6501219489666115"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined['Minimum Distance Centroid'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3061707476917683"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined['Minimum Distance'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5462807258789875"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined['Minimum Distance Centroid'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    1.673695e+06\n",
       "mean     4.370865e+00\n",
       "std      5.529624e+00\n",
       "min      0.000000e+00\n",
       "25%      9.216085e-01\n",
       "50%      2.306171e+00\n",
       "75%      5.910296e+00\n",
       "max      1.022439e+02\n",
       "Name: Minimum Di, dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined['Minimum Distance'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    1.673695e+06\n",
       "mean     4.650122e+00\n",
       "std      5.663566e+00\n",
       "min      0.000000e+00\n",
       "25%      1.105992e+00\n",
       "50%      2.546281e+00\n",
       "75%      6.253126e+00\n",
       "max      1.117298e+02\n",
       "Name: Minimum Distance Centroid, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined['Minimum Distance Centroid'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are Matplotlib parameters -- you can ignore this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rc('font', **{'family':'sans-serif',\n",
    "    'sans-serif':['Helvetica'],\n",
    "    'monospace': ['Inconsolata'],\n",
    "    'serif': ['Adobe Garamamond Pro']}\n",
    ")\n",
    "\n",
    "rc('text', **{'usetex': True})\n",
    "rc('text', **{'latex.preamble': '\\usepackage{sfmath}'})\n",
    "\n",
    "save_args = {\n",
    "    \"format\": \"png\",\n",
    "    \"bbox_inches\": 'tight',\n",
    "    \"alpha\": True,\n",
    "    \"transparent\": True,\n",
    "    \"dpi\": 200\n",
    "}\n",
    "fontsize = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot a histogram of both sets of distance measurements. Use a log scale for the `y` axis, in order to stop it being gigantic, due to the fact that so many (75%) postcodes are within ~16km of a project."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEiCAYAAAD5+KUgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJBICACAgIQAAJJEQAAABCQEAIEn6f3go3Ap7mNr3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x147f7c2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "fig = plt.figure(1, figsize=(7., 10.), dpi=100)\n",
    "ax = fig.add_subplot(121)\n",
    "h = ax.hist(joined['Minimum Di'], 10, log=True, ec='#333333')\n",
    "\n",
    "ax.grid(b=False)\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.set_xlabel(u'Polygon-to-Polygon (km)', fontsize=fontsize)\n",
    "ax.set_ylabel('Number of post codes (log)', fontsize=fontsize)\n",
    "\n",
    "\n",
    "ax2 = fig.add_subplot(122, sharey=ax)\n",
    "h2 = ax2.hist(joined['Minimum Distance Centroid'], 10, log=True, ec='#333333')\n",
    "\n",
    "ax2.grid(b=False)\n",
    "ax2.spines['top'].set_visible(False)\n",
    "ax2.spines['right'].set_visible(False)\n",
    "ax2.spines['left'].set_visible(False)\n",
    "ax2.set_xlabel(u'Centroid-to-Centroid (km)', fontsize=fontsize)\n",
    "\n",
    "ax2.tick_params(\n",
    "    axis='y',          # changes apply to the x-axis\n",
    "    which='both',      # both major and minor ticks are affected\n",
    "    left='off')\n",
    "ax2.yaxis.set_tick_params(size=0)\n",
    "ax2.yaxis.set_visible(False)\n",
    "\n",
    "\n",
    "plt.suptitle(\"Post Code Distances, 1673814 Post Codes\", fontsize=fontsize)\n",
    "plt.savefig(\"postcodes.png\", **save_args)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "joined.to_file(\"joined_postcodes_centroids.shp\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use [Chebyshev's theorem](http://www.philender.com/courses/intro/notes3/chebyshev.html) to calculate distributions:\n",
    "\n",
    "Mean: `4.650122`  \n",
    "Standard deviation: `5.663566`  \n",
    "Chebyshev: $1 - (1/k^2)$  \n",
    "where `k` is the number of standard deviations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def chebyshev(mu, sigma, stddev):\n",
    "    \"\"\"\n",
    "    Use Chebyshev's theorem to calculate distributions\n",
    "    mu: mean\n",
    "    sigma: the standard deviation\n",
    "    stddev: the number of standard deviations you wish to calculate\n",
    "    \n",
    "    In this case, we can't have a distance less than 0.0, so it's\n",
    "    not mu +/- (sigma * stddev), just mu + (sigma * stddev)\n",
    "    \n",
    "    Returns a tuple:\n",
    "    the percentage of the distribution, and the distance, in this case.\n",
    "    \n",
    "    \"\"\"\n",
    "    return (1. - (1. / stddev ** 2)), mu + (sigma * stddev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0.75, 15.977254), (0.8888888888888888, 21.64082), (0.9375, 27.304386))"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get 75%, 88%, and 93.75% values\n",
    "chebyshev(4.650122, 5.663566, 2),\\\n",
    "chebyshev(4.650122, 5.663566, 3),\\\n",
    "chebyshev(4.650122, 5.663566, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore:\n",
    "- 75% of post codes (2 standard deviations) lie within **15.97 km**\n",
    "- 88% of post codes (3 standard deviations) lie within **21.64 km**\n",
    "- 93.75% of post codes (4 standard deviations) lie within **27.30 km**\n",
    "\n",
    "of a funded project, measured by **centroid distance**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert km to miles: multiply by 0.621371"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}