Counting number of points in each grid?

Question

I would like to count the number of points in each cell. I have tried https://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram2d.html but the out isn't appropriate. Does anybody know how I can get the output properly?

XA_ = [269142.68863031495,
 269304.695760036,
 269466.0264386978,
 392942.21775866585,
 392942.1996439248,
 392942.18152918364,
 254311.33475757603,
 254755.19249382117,
 255185.41421253807,
 492148.2779438756,
 492148.25401910784,
 492149.2251416461,
 553489.7091844846,
 550809.3067433595,
 548052.5477973885,
 519079.7628172271,
 519079.76481877314,
 519079.7654325806,
 490406.2223452815,
 490405.9016914209,
 490405.80859746644,
 494940.3091149014,
 494940.5800286697,
 494940.8509424379,
 546707.1663319349,
 546707.1306325911,
 546707.0949332472,
 772902.3863664756,
 770096.23941861,
 767309.362644247,
 435988.6088680159,
 435987.50805015286,
 435987.8836906329,
 380576.07212457457,
 380576.07212457457,
 380576.07212457457,
 562355.5408083306,
 562082.6254618462,
 561634.2589078951,
 519593.2248320134,
 520163.14482233016,
 520488.3862171857,
 280709.43500114995,
 282667.54256107233,
 284629.027003666,
 470095.25384248036,
 470097.9496341577,
 470100.0199537931,
 498019.63516434917,
 498019.636166123,
 498019.71342578344,
 545429.26374282,
 545429.4701223552,
 545429.6765018903,
 560256.948519165,
 560256.9606162632,
 560256.9727133614,
 558056.8350144841,
 558056.6628962351,
 558056.4907779862,
 467082.92585511395,
 466337.26696158113,
 466122.5451118541,
 500312.4931377756,
 500551.29173690686,
 500822.4915701299,
 488320.8881096475,
 488320.8881096475,
 488320.8881096475,
 234959.4216230074,
 236845.74740121586,
 238718.82347044855,
 363174.86611545534,
 364935.9064735326,
 366706.2106342295,
 497033.57866991305,
 497034.0968566288,
 497034.61504334444,
 293350.87277344253,
 295267.91084818705,
 297205.4022341429,
 281289.02387468005,
 283835.4214070084,
 286407.3507544949,
 280238.8325805849,
 281953.0134381577,
 283686.984369215,
 557866.4127702332,
 557767.2853572157,
 557455.4201240427,
 544276.0818856795,
 544277.1213996302,
 544278.160913581,
 560196.4346866631,
 559906.2555994007,
 559172.798667107,
 553310.5854939698,
 553312.2779971804,
 553311.6820767054,
 551348.8430010471,
 551349.4377773844,
 551348.8386734851,
 541249.4470653739,
 541900.7794716425,
 541224.3467305955,
 554234.8757064611,
 554234.8483127754,
 554234.8209190895,
 545745.6891595804,
 545745.5111079012,
 545745.3330562222,
 484873.02436431707,
 484003.1661958206,
 483398.14173198934,
 493168.4175602927,
 493389.0097356766,
 493077.69151527993,
 465367.8596565175,
 467844.8061345208,
 470322.080322923,
 542718.2282091405,
 542719.3318877186,
 542720.4355662968,
 501776.6308987725,
 500612.92108499294,
 498837.2422073845,
 774472.767904973,
 772926.2774970894,
 771366.855492034,
 537081.1411321913,
 537081.1003055439,
 537081.0594788966,
 375647.9072125684,
 373962.44197150605,
 372269.5267818782,
 339410.01580095495,
 339722.0521972096,
 340034.08859346434,
 528523.2346622795,
 529138.3610987444,
 529858.6496138738,
 528863.0461216161,
 529027.9678429372,
 529772.1385178919,
 544459.4872846468,
 544459.1089965965,
 544458.7307085461,
 280433.304815039,
 282248.8618037564,
 284050.50736230274]

YA_ = [5132177.351959863,
 5132454.958881595,
 5132745.370623719,
 4799027.16964639,
 4799027.176172647,
 4799027.182698905,
 4715865.972909568,
 4713622.766967746,
 4711410.429097172,
 5457995.491064864,
 5457995.141018024,
 5457993.652179124,
 4186724.748168416,
 4192055.050270996,
 4196836.825863356,
 5055792.355154564,
 5055791.7003405765,
 5055791.499530954,
 5457761.110190328,
 5457760.810745233,
 5457760.905925446,
 5425090.107417448,
 5425089.945452439,
 5425089.783487429,
 5278376.892017033,
 5278376.926682054,
 5278376.961347076,
 3794053.371397486,
 3794709.5665947185,
 3795368.8242837745,
 5115530.463440255,
 5115531.452352677,
 5115530.8992273975,
 5358357.1023906255,
 5358357.1023906255,
 5358357.1023906255,
 4183098.247108328,
 4182948.827814135,
 4182885.9698557155,
 5407586.030581906,
 5406415.191339511,
 5405865.425063687,
 5375278.898674618,
 5375121.025397821,
 5374989.029128767,
 5116484.487521737,
 5116484.474359201,
 5116484.327957711,
 5460928.317758323,
 5460931.097035308,
 5460932.16597176,
 5275208.30780482,
 5275208.618292654,
 5275208.928780487,
 4191410.6479157065,
 4191410.6712179165,
 4191410.694520126,
 5316862.846383741,
 5316862.315750707,
 5316861.785117673,
 5330678.414959482,
 5330671.996565787,
 5330418.313207476,
 4163275.3309627674,
 4163226.6567090345,
 4163777.7841287856,
 5384017.101647103,
 5384017.101647103,
 5384017.101647103,
 4090311.256141706,
 4090693.785906165,
 4091058.6390411435,
 5370953.649420215,
 5370851.631358324,
 5370724.235093637,
 5460877.6502608415,
 5460877.121433894,
 5460876.592606948,
 5104032.844699361,
 5104258.580699895,
 5104481.703445772,
 5377703.767245022,
 5377314.848272017,
 5376930.082459292,
 5373566.998644971,
 5373499.640390588,
 5373424.392858532,
 5316718.793442256,
 5315880.204122022,
 5315034.313263214,
 5280653.029302435,
 5280653.093216645,
 5280653.157130855,
 4191298.0409879684,
 4191017.0872896235,
 4190645.2342315284,
 4183569.0872102487,
 4183569.1835233,
 4183569.649855316,
 4184723.109379307,
 4184722.3671754412,
 4184723.8510904764,
 5249410.077029127,
 5248611.795298904,
 5247698.280675454,
 4195846.819949482,
 4195846.808210647,
 4195846.796471813,
 5279541.718556855,
 5279541.628946132,
 5279541.539335408,
 5378985.391374318,
 5381918.20070081,
 5384888.530195987,
 5461865.454342501,
 5462165.871095877,
 5461872.279347949,
 3608063.7852862985,
 3607970.9720990215,
 3607876.5264585214,
 5233854.779060345,
 5233851.871695311,
 5233848.9643302765,
 5459987.914939486,
 5460436.0631904565,
 5460259.83089087,
 3793294.915596035,
 3793721.698014937,
 3794172.4687402523,
 5399204.188631518,
 5399204.188361312,
 5399204.188091108,
 5119433.976897289,
 5119442.723172148,
 5119502.80378085,
 5547685.238786915,
 5546913.531515202,
 5546141.824243488,
 5267654.5443007015,
 5267958.675113996,
 5268557.912623625,
 5373282.781331167,
 5373224.423177257,
 5373304.47750142,
 5281026.651830151,
 5281026.488362015,
 5281026.32489388,
 5373438.891298835,
 5373382.566426716,
 5373347.855447044]



gridx = np.linspace(300000, 800000, 5)
gridy = np.linspace(3700000, 5500000, 5)
grid, _, _ = np.histogram2d(XA_, YA_, bins=[gridx, gridy])
plt.figure()
plt.plot(XA_, YA_, 'ro')
plt.grid(True)
plt.figure()
plt.pcolormesh(gridx, gridy, grid)
plt.plot(XA_, YA_, 'ro')
plt.colorbar()
plt.show()

Could you please edit your post to include the code you used to create these graphs? — Aaron, Sep 22 '19 at 06:44

gene · Answer 1 · 2019-09-22T19:59:19.523

If it is a geospatial problem (points), use the geospatial python modules

1) With shapely and GeoPandas for example

The points

import geopandas as gpd
from shapely.geometry import Point
points = gpd.GeoDataFrame({"x":XA_,"y":YA_})
points['geometry'] = points.apply(lambda p: Point(p.x, p.y), axis=1)
print(points.head(2))
          x             y                            geometry
0  269142.68863  5132177.35196  POINT (269142.688630315 5132177.351959863)
1  269304.69576  5132454.95888  POINT (269304.695760036 5132454.958881595)

The grid (polygons -> look at numpy meshgrid to Shapely polygons)

from shapely.ops import polygonize
hlines = [((x1, yi), (x2, yi)) for x1, x2 in list(zip(gridx[:-1], gridx[1:])) for yi in gridy]
vlines = [((xi, y1), (xi, y2)) for y1, y2 in zip(gridy[:-1], gridy[1:]) for xi in gridx]
polys = list(polygonize(MultiLineString(hlines + vlines)))
id = [i for i in range(len(grids))]
grid = gpd.GeoDataFrame({"id":id,"geometry":polys})
print(grid.head(2))
   id                                           geometry
0   0  POLYGON ((425000 3700000, 300000 3700000, 300000 4150000, 425000 4150000, 425000 3700000))
1   1  POLYGON ((425000 4150000, 300000 4150000, 300000 4600000, 425000 4600000, 425000 4150000))

(you need to specify plt.axis('equal') or plt.axes().set_aspect('equal') to plot correctly your data)

Number of points in polygons (look at More Efficient Spatial join in Python without QGIS, ArcGIS, PostGIS, etc)

from geopandas.tools import sjoin
pointInPolys = sjoin(points, grid, how='left')
print(pointInPolys.groupby(['id']).size().reset_index(name='count'))
   id  count
0   2     3
1   3     9
2   5     4
3   7    72
4   9    20
5   11    6
6   12    6

2) You can also use Quadrat Based Statistical Method for Planar Point Patterns with pointpats: Point Pattern Analysis in PySAL for that.

Counting number of points in each grid?

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