Finding local maxima in a grid

[Justin Niakamal]

Greetings everyone,

I'm interested in finding local maxima in a grid and haven't had any luck finding any material for doing so. The data below are coordinates (lat & lon) with density in a Census block.
Does anyone have any thoughts?

* Example generated by -dataex-. To install: ssc install dataex
clear
input str15 block_group double(latitude longitude ln_density)
"060590011011007" 33.9434681 -117.9524872  5.135222991690706
"060590011011009" 33.9426257 -117.9573157  6.835520232230146
"060590011011012" 33.9427533 -117.9551851  6.644436884918015
"060590011011013" 33.9427081 -117.9524832   4.46011340032976
"060590011011015" 33.9406193 -117.9513001  5.539835668679419
"060590011011016" 33.9401233 -117.9542428  8.459236258852162
"060590011011018"  33.939388 -117.9514234  8.597155114813228
"060590011012000" 33.9450803 -117.9732471 7.3089891868144825
"060590011012002" 33.9448772 -117.9742605   5.09649187215927
"060590011012006" 33.9426837 -117.9753973  5.955720608938407
"060590011012013" 33.9409248 -117.9721216  7.383450886265405
"060590011012015"  33.940325 -117.9760798  8.123953391754107
"060590011012017" 33.9401223 -117.9741911  9.670100630497895
"060590011012018" 33.9402502 -117.9714704    8.1007164966442
"060590011013003"  33.941427 -117.9614521   7.25995106610566
"060590011013007" 33.9425663 -117.9596719  7.169349890741607
"060590011013012" 33.9426864 -117.9642606  5.356662406785988
"060590011013020" 33.9398029 -117.9581037  8.589252557171747
"060590011014003" 33.9426845 -117.9684398  8.056539647149982
"060590011014005" 33.9436205 -117.9692948  6.110992034986769
"060590011014007" 33.9453006 -117.9693048  4.814600863501736
"060590011014008" 33.9458537 -117.9693632  6.146873104264652
"060590011014009" 33.9426228 -117.9698516  7.631225513518022
"060590011014011" 33.9423275  -117.966866  5.074397732463981
"060590011014014" 33.9414966 -117.9668138  5.460786693511332
"060590011014016"  33.940304 -117.9672266  7.539767479188758
"060590011021000" 33.9387185 -117.9688583   8.63816530727287
"060590011021001" 33.9393499 -117.9703444  7.285984209179809
"060590011021003" 33.9380985 -117.9723207  7.506867562045194
"060590011021004" 33.9393618 -117.9745767  7.472786954395636
"060590011021007" 33.9373803 -117.9755463  4.257395453610045
"060590011021009" 33.9370577 -117.9737302  5.834115676093456
"060590011021010" 33.9378978 -117.9712357  5.874003424949078
"060590011021013" 33.9370571 -117.9685726  5.554825879045601
"060590011022000" 33.9340999 -117.9701465  8.331081875194275
"060590011022002" 33.9342231 -117.9729718  4.681813582754534
"060590011022003" 33.9338535 -117.9736338  5.801669989040742
"060590011022007" 33.9337663 -117.9749678 6.4313901692496716
"060590011022009" 33.9324707 -117.9755643  7.861638731490633
"060590011023000" 33.9309823 -117.9688854   8.38465912113754
"060590011023001" 33.9291068 -117.9700995  4.273490140523255
"060590011023002" 33.9299584 -117.9745086  4.991112424458013
"060590011023008" 33.9302173 -117.9702333  6.234360214754072
"060590011031000" 33.9362313  -117.965508   6.50199921457729
"060590011031001" 33.9373815 -117.9665195  6.620841525611885
"060590011031002" 33.9382346  -117.967978 11.471327387680127
"060590011031004" 33.9346013 -117.9654764   5.19282912640733
"060590011031009" 33.9329882 -117.9651555  7.134669358036097
"060590011032001" 33.9311245 -117.9625063  4.054770754606315
"060590011032002" 33.9311803 -117.9660608   9.42103400132476
"060590011032003" 33.9304381 -117.9674894  8.021045940303441
"060590011032006" 33.9296139 -117.9678922  7.991798162748065
"060590011032008" 33.9288215 -117.9646909  6.015267914607325
"060590011032009" 33.9299527 -117.9654219   5.77137941583595
"060590011032011" 33.9297226 -117.9625118 5.6620955124275945
"060590011032013" 33.9287436 -117.9599904 4.9628342726815475
"060590011033000" 33.9379315 -117.9524642   8.11991161429057
"060590011033001" 33.9372933 -117.9570186  7.849143099579075
"060590011033002" 33.9363958 -117.9612607  8.027999492600122
"060590011033006" 33.9337007 -117.9615667  4.964860765149345
"060590011033009" 33.9357101 -117.9518561  6.520075202445931
"060590011033011" 33.9368418 -117.9537605  4.853627365295327
"060590012011001" 33.9352616 -117.9518526  6.556632101317803
"060590012011002" 33.9347752 -117.9545154  5.050518458674039
"060590012011006" 33.9347477  -117.958745  5.280860202210691
"060590012011008" 33.9329328 -117.9578704  5.595980596909468
"060590012011009" 33.9329391 -117.9561469  5.599226986636189
"060590012011010" 33.9341154 -117.9529452  5.669740651863973
"060590012011012" 33.9341211  -117.950758  6.930794493139333
"060590012012002" 33.9362321 -117.9492566  9.710435575231852
"060590012012003" 33.9343049 -117.9490173  4.633544295536558
"060590012012006" 33.9345805  -117.946952  9.553621300147421
"060590012012007" 33.9334458 -117.9469403  4.726439682843243
"060590012012008" 33.9325262 -117.9469341  5.797876853566051
"060590012012009" 33.9325251 -117.9485273  6.552428420302155
"060590012012010"  33.932525 -117.9498894  6.141296045642563
"060590012012011" 33.9325298 -117.9512748  6.543805354205198
"060590012012012" 33.9332114  -117.952458  6.181789186215849
"060590012012013"  33.933189 -117.9543664  5.715467975147872
"060590012012017" 33.9320774 -117.9512722  8.692765256421541
"060590012012018" 33.9320731 -117.9498865  9.084529755345171
"060590012012019" 33.9320735 -117.9485243  9.006257035788826
"060590012012020"  33.932075 -117.9469334  5.879235434681153
"060590012012021" 33.9320803 -117.9532577  7.184595500830879
"060590012013000" 33.9313696 -117.9518166 10.727702848354465
"060590012013001" 33.9297379 -117.9529581 6.7204211069319655
"060590012013003" 33.9300257 -117.9570014   7.41120985499027
"060590012021003" 33.9365482 -117.9404778  6.018700623742401
"060590012021005" 33.9347842 -117.9412616  5.194892775623838
"060590012021006" 33.9341549 -117.9396232  5.137143622641845
"060590012021010" 33.9323286 -117.9396011  7.593110153074182
"060590012021012" 33.9320768 -117.9412231  9.291328513848486
"060590012021013" 33.9321061 -117.9379581   9.54969547499974
"060590012022000" 33.9383831 -117.9429746  8.268228760057069
"060590012022001" 33.9363436   -117.94288 3.7913741652705797
"060590012022002" 33.9372469 -117.9450698  4.975614354389193
"060590012022004" 33.9354895 -117.9450397  6.798548003088426
"060590012022005" 33.9345663  -117.945075  6.423324949079913
"060590012022007" 33.9334671 -117.9428714  4.479673596339496
"060590012022008" 33.9334352 -117.9450208  5.166607784362848
end