I have the following 2D data set:
rrange = Range[1.5, 30, Abs[1.5 - 30]/9]; thetarange = Range[0.1, Pi - 0.1, (Pi - 0.2)/9]; coefflistupExpl = {{-135.14511024461106`, -491.0604985408635`, -881.9421291151137`,-1260.0984328238856`, -1513.9513638338296`, -1513.9513638338299`,-1260.0984328238856`, -881.9421291151135`, -491.06049854086405`,-135.1451102446111`}, {-1.5142531933295087`, -0.37232388448807263`,-0.2331372158847184`, -0.18715805003653702`, -0.17086515888649814`,-0.17086515888649814`, -0.187158050036537`, -0.23313721588471834`,-0.3723238844880723`, -1.514253193329507`}, {-0.5727476098161932`,-0.1395022760893628`, -0.08586657085967929`, -0.0677270725405478`,-0.06115525894956358`, -0.06115525894956358`, -0.06772707254054777`,-0.08586657085967928`, -0.1395022760893627`, -0.5727476098161925`},{-0.259039791853082`, -0.06288669153708114`, -0.038477816530581944`,-0.030163367358386196`, -0.027132279009877695`,-0.027132279009877695`, -0.030163367358386192`,-0.03847781653058193`, -0.06288669153708111`, -0.2590397918530817`},{-0.1292779426088209`, -0.03133326914673598`, -0.019114511395125464`,-0.01493815213757028`, -0.013411227032263872`,-0.013411227032263872`, -0.014938152137570276`,-0.01911451139512546`, -0.03133326914673597`, -0.12927794260882072`},{-0.06862807437799888`, -0.016617240479419433`,-0.010119133584897298`, -0.007893648637412628`,-0.007078629937110175`, -0.007078629937110175`,-0.007893648637412628`, -0.010119133584897294`,-0.016617240479419426`, -0.0686280743779988`},{-0.038026791744121956`, -0.009201614269998633`,-0.005596708070678661`, -0.004360468819581065`,-0.00390723960010555`, -0.00390723960010555`, -0.004360468819581064`,-0.0055967080706786606`, -0.009201614269998628`,-0.03802679174412191`}, {-0.021767232119110393`,-0.0052646932925957575`, -0.0031993992562647103`,-0.0024904749577585525`, -0.002230367642969974`,-0.002230367642969974`, -0.0024904749577585516`,-0.0031993992562647094`, -0.005264693292595755`,-0.02176723211911036`}, {-0.012804905748478031`,-0.0030959032771096778`, -0.0018801502157455158`,-0.001462531784991384`, -0.0013092141328043484`,-0.0013092141328043484`, -0.0014625317849913837`,-0.0018801502157455151`, -0.0030959032771096747`,-0.012804905748478014`}, {-0.007732194246853996`,-0.0018688756462285204`, -0.001134336349530597`,-0.0008818640583349311`, -0.0007891292257421068`,-0.0007891292257421068`, -0.0008818640583349306`,-0.001134336349530597`, -0.0018688756462285191`,-0.0077321942468539856`}}; And I want to generate an interpolating function matching the data. However, my naive attempt with the following code failed.
Flatten[Table[{{rrange[[k]], thetarange[[j]]}, coefflistupExpl[[k, j]]}, {k, 1, 10}, {j, 1, 10}], 1] // N; ff = Interpolation[%]; Plot3D[ff[r, th], {r, 2, 10}, {th, 10^-1, Pi - 10^-1}] Flatten[Table[{rrange[[k]], thetarange[[j]], coefflistupExpl[[k, j]]}, {k, 1, 10}, {j, 1, 10}], 1]; ListPlot3D[%] The interpolating function produced by the above code is
whereas the data looks like:
I suspect that Interpolation has problems with the diverging behavior of these data at 0 and Pi, but that's why I already cut out a large piece of the region close to 0 and Pi, though, as you can see, without success. Is there a way to construct a reliable interpolating function for the whole domain?
