Previously, I've had problems with Mathematica interpolating and plotting 3D lists, but I finally managed to do so by rescaling the x and y-axes with the help of the methods proposed here. Now my problem is with interpolating 2D lists.
I have a large 2D list that I'll call data of dimensions {4271,2} for which I need to find an interpolation. Using f = Interpolation[data] outputs an interpolating function without error messages or warnings. The problem arises first when comparing the curves produced by ListLinePlot[data] and Plot[f[s], {s, Min[data[[All, 1]]], Max[data[[All, 1]]]}] as shown below. The first plot looks like this:
and the second like this:
The first plot produces the expected curve whilst the second shows erratic behaviour between points. Evaluating the interpolating function offers only sensible result at points present in data and incoherent results elsewhere. I've tried sorting, cleaning, introducing noise into the data, but the interpolation always produces an erratic function.
I'll post an excerpt of the first 900 rows of the data below. Any help is much appreciated.
data[[1 ;; 900, All]] = {{1779.55, 9.9227*10^6}, {1784.38, 9.9225*10^6}, {1789.02,
9.92229*10^6}, {1793.49, 9.92208*10^6}, {1797.79,
9.92187*10^6}, {1808.57, 9.92165*10^6}, {1819.04,
9.92143*10^6}, {1829.07, 9.9212*10^6}, {1838.74,
9.92097*10^6}, {1848.07, 9.92074*10^6}, {1857.03,
9.9205*10^6}, {1865.69, 9.92026*10^6}, {1872.35,
9.92001*10^6}, {1875.87, 9.91976*10^6}, {1879.27,
9.91951*10^6}, {1882.56, 9.91925*10^6}, {1885.76,
9.91899*10^6}, {1888.86, 9.91872*10^6}, {1891.86,
9.91845*10^6}, {1896.6, 9.91818*10^6}, {1903.59,
9.9179*10^6}, {1910.38, 9.91762*10^6}, {1916.98,
9.91733*10^6}, {1923.36, 9.91704*10^6}, {1929.56,
9.91675*10^6}, {1935.6, 9.91645*10^6}, {1941.47,
9.91615*10^6}, {1947.16, 9.91584*10^6}, {1952.68,
9.91553*10^6}, {1958.05, 9.91522*10^6}, {1963.29,
9.9149*10^6}, {1968.4, 9.91458*10^6}, {1971.81,
9.91425*10^6}, {1974.01, 9.91392*10^6}, {1976.16,
9.91359*10^6}, {1978.26, 9.91325*10^6}, {1980.3,
9.91291*10^6}, {1982.3, 9.91256*10^6}, {1984.25,
9.91221*10^6}, {1986.15, 9.91186*10^6}, {1990.17,
9.9115*10^6}, {1994.44, 9.91114*10^6}, {1998.61,
9.91077*10^6}, {2002.69, 9.9104*10^6}, {2006.68,
9.91003*10^6}, {2010.59, 9.90965*10^6}, {2014.39,
9.90927*10^6}, {2018.11, 9.90888*10^6}, {2021.75,
9.90849*10^6}, {2025.31, 9.9081*10^6}, {2028.8,
9.9077*10^6}, {2032.23, 9.9073*10^6}, {2035.58,
9.90689*10^6}, {2038.86, 9.90648*10^6}, {2040.37,
9.90607*10^6}, {2041.84, 9.90565*10^6}, {2043.29,
9.90523*10^6}, {2044.7, 9.9048*10^6}, {2046.09,
9.90437*10^6}, {2047.45, 9.90394*10^6}, {2048.79,
9.9035*10^6}, {2050.1, 9.90306*10^6}, {2052.63,
9.90261*10^6}, {2055.48, 9.90216*10^6}, {2058.28,
9.90171*10^6}, {2061.03, 9.90125*10^6}, {2063.73,
9.90079*10^6}, {2066.38, 9.90032*10^6}, {2068.99,
9.89985*10^6}, {2071.56, 9.89938*10^6}, {2074.08,
9.8989*10^6}, {2076.55, 9.89842*10^6}, {2078.97,
9.89793*10^6}, {2081.35, 9.89744*10^6}, {2083.68,
9.89695*10^6}, {2085.98, 9.89645*10^6}, {2088.25,
9.89595*10^6}, {2090.47, 9.89544*10^6}, {2092.66,
9.89493*10^6}, {2094.82, 9.89442*10^6}, {2096.94,
9.8939*10^6}, {2099.03, 9.89338*10^6}, {2101.08,
9.89285*10^6}, {2102.83, 9.89232*10^6}, {2103.77,
9.89179*10^6}, {2104.7, 9.89125*10^6}, {2105.62,
9.89071*10^6}, {2106.52, 9.89016*10^6}, {2107.41,
9.88961*10^6}, {2108.28, 9.88906*10^6}, {2109.14,
9.8885*10^6}, {2109.98, 9.88794*10^6}, {2111.38,
9.88737*10^6}, {2113.19, 9.8868*10^6}, {2114.98,
9.88623*10^6}, {2116.74, 9.88565*10^6}, {2118.47,
9.88507*10^6}, {2120.19, 9.88448*10^6}, {2121.87,
9.88389*10^6}, {2123.54, 9.8833*10^6}, {2125.18,
9.8827*10^6}, {2126.8, 9.8821*10^6}, {2128.39,
9.88149*10^6}, {2129.97, 9.88088*10^6}, {2131.52,
9.88027*10^6}, {2133.05, 9.87965*10^6}, {2134.56,
9.87903*10^6}, {2136.05, 9.8784*10^6}, {2137.5,
9.87777*10^6}, {2138.94, 9.87714*10^6}, {2140.36,
9.8765*10^6}, {2141.76, 9.87586*10^6}, {2143.14,
9.87521*10^6}, {2144.5, 9.87456*10^6}, {2145.84,
9.87391*10^6}, {2147.17, 9.87325*10^6}, {2148.48,
9.87259*10^6}, {2149.78, 9.87192*10^6}, {2151.06,
9.87125*10^6}, {2152.32, 9.87058*10^6}, {2153.56,
9.8699*10^6}, {2154.79, 9.86922*10^6}, {2156.01,
9.86853*10^6}, {2157.21, 9.86784*10^6}, {2158.39,
9.86715*10^6}, {2159.57, 9.86645*10^6}, {2160.72,
9.86575*10^6}, {2161.33, 9.86504*10^6}, {2161.86,
9.86433*10^6}, {2162.38, 9.86362*10^6}, {2162.9,
9.8629*10^6}, {2163.41, 9.86218*10^6}, {2163.91,
9.86145*10^6}, {2164.4, 9.86072*10^6}, {2164.89,
9.85999*10^6}, {2165.39, 9.85925*10^6}, {2166.46,
9.85851*10^6}, {2167.51, 9.85776*10^6}, {2168.55,
9.85701*10^6}, {2169.58, 9.85626*10^6}, {2170.6,
9.8555*10^6}, {2171.6, 9.85474*10^6}, {2172.6,
9.85397*10^6}, {2173.58, 9.8532*10^6}, {2174.55,
9.85243*10^6}, {2175.52, 9.85165*10^6}, {2176.47,
9.85087*10^6}, {2177.41, 9.85008*10^6}, {2178.34,
9.84929*10^6}, {2179.26, 9.8485*10^6}, {2180.16,
9.8477*10^6}, {2181.06, 9.8469*10^6}, {2181.95,
9.84609*10^6}, {2182.83, 9.84528*10^6}, {2183.7,
9.84447*10^6}, {2184.56, 9.84365*10^6}, {2185.41,
9.84283*10^6}, {2186.26, 9.842*10^6}, {2187.09,
9.84117*10^6}, {2187.91, 9.84034*10^6}, {2188.73,
9.8395*10^6}, {2189.53, 9.83866*10^6}, {2190.32,
9.83781*10^6}, {2191.11, 9.83696*10^6}, {2191.88,
9.83611*10^6}, {2192.65, 9.83525*10^6}, {2193.41,
9.83439*10^6}, {2194.16, 9.83352*10^6}, {2194.91,
9.83265*10^6}, {2195.64, 9.83178*10^6}, {2196.37,
9.8309*10^6}, {2197.09, 9.83002*10^6}, {2197.8,
9.82913*10^6}, {2198.51, 9.82824*10^6}, {2199.21,
9.82735*10^6}, {2199.9, 9.82645*10^6}, {2200.58,
9.82555*10^6}, {2201.26, 9.82464*10^6}, {2201.93,
9.82373*10^6}, {2202.6, 9.82282*10^6}, {2203.25,
9.8219*10^6}, {2203.9, 9.82098*10^6}, {2204.55,
9.82005*10^6}, {2205.18, 9.81912*10^6}, {2205.82,
9.81819*10^6}, {2206.44, 9.81725*10^6}, {2207.06,
9.81631*10^6}, {2207.67, 9.81536*10^6}, {2208.28,
9.81441*10^6}, {2208.88, 9.81346*10^6}, {2209.47,
9.8125*10^6}, {2210.06, 9.81154*10^6}, {2210.64,
9.81057*10^6}, {2211.22, 9.8096*10^6}, {2211.6,
9.80863*10^6}, {2211.83, 9.80765*10^6}, {2212.05,
9.80667*10^6}, {2212.28, 9.80568*10^6}, {2212.5,
9.80469*10^6}, {2212.71, 9.8037*10^6}, {2212.93,
9.8027*10^6}, {2213.14, 9.8017*10^6}, {2213.61,
9.80069*10^6}, {2214.15, 9.79968*10^6}, {2214.69,
9.79867*10^6}, {2215.22, 9.79765*10^6}, {2215.74,
9.79663*10^6}, {2216.26, 9.7956*10^6}, {2216.77,
9.79457*10^6}, {2217.28, 9.79354*10^6}, {2217.78,
9.7925*10^6}, {2218.28, 9.79146*10^6}, {2218.78,
9.79041*10^6}, {2219.27, 9.78936*10^6}, {2219.75,
9.78831*10^6}, {2220.23, 9.78725*10^6}, {2220.71,
9.78619*10^6}, {2221.18, 9.78512*10^6}, {2221.64,
9.78405*10^6}, {2222.1, 9.78298*10^6}, {2222.56,
9.7819*10^6}, {2223.02, 9.78082*10^6}, {2223.46,
9.77973*10^6}, {2223.91, 9.77864*10^6}, {2224.35,
9.77755*10^6}, {2224.79, 9.77645*10^6}, {2225.22,
9.77535*10^6}, {2225.65, 9.77424*10^6}, {2226.07,
9.77313*10^6}, {2226.49, 9.77202*10^6}, {2226.91,
9.7709*10^6}, {2227.32, 9.76978*10^6}, {2227.73,
9.76865*10^6}, {2228.13, 9.76752*10^6}, {2228.53,
9.76639*10^6}, {2228.93, 9.76525*10^6}, {2229.32,
9.76411*10^6}, {2229.71, 9.76296*10^6}, {2230.1,
9.76181*10^6}, {2230.48, 9.76066*10^6}, {2230.86,
9.7595*10^6}, {2231.23, 9.75834*10^6}, {2231.6,
9.75717*10^6}, {2231.97, 9.756*10^6}, {2232.34,
9.75483*10^6}, {2232.69, 9.75365*10^6}, {2233.05,
9.75247*10^6}, {2233.4, 9.75128*10^6}, {2233.74,
9.75009*10^6}, {2234.09, 9.7489*10^6}, {2234.43,
9.7477*10^6}, {2234.77, 9.7465*10^6}, {2235.1,
9.74529*10^6}, {2235.43, 9.74408*10^6}, {2235.76,
9.74287*10^6}, {2236.08, 9.74165*10^6}, {2236.41,
9.74043*10^6}, {2236.72, 9.7392*10^6}, {2237.04,
9.73797*10^6}, {2237.35, 9.73674*10^6}, {2237.66,
9.7355*10^6}, {2237.97, 9.73426*10^6}, {2238.27,
9.73301*10^6}, {2238.57, 9.73176*10^6}, {2238.87,
9.73051*10^6}, {2239.17, 9.72925*10^6}, {2239.46,
9.72799*10^6}, {2239.75, 9.72672*10^6}, {2240.03,
9.72545*10^6}, {2240.32, 9.72418*10^6}, {2240.6,
9.7229*10^6}, {2240.88, 9.72162*10^6}, {2241.15,
9.72033*10^6}, {2241.43, 9.71904*10^6}, {2241.7,
9.71775*10^6}, {2241.96, 9.71645*10^6}, {2242.23,
9.71515*10^6}, {2242.49, 9.71384*10^6}, {2242.75,
9.71253*10^6}, {2243.01, 9.71122*10^6}, {2243.26,
9.7099*10^6}, {2243.51, 9.70858*10^6}, {2243.76,
9.70725*10^6}, {2244.01, 9.70592*10^6}, {2244.26,
9.70459*10^6}, {2244.5, 9.70325*10^6}, {2244.74,
9.70191*10^6}, {2244.98, 9.70056*10^6}, {2245.21,
9.69921*10^6}, {2245.44, 9.69786*10^6}, {2245.67,
9.6965*10^6}, {2245.9, 9.69514*10^6}, {2246.13,
9.69377*10^6}, {2246.35, 9.6924*10^6}, {2246.57,
9.69103*10^6}, {2246.79, 9.68965*10^6}, {2247.01,
9.68827*10^6}, {2247.22, 9.68688*10^6}, {2247.44,
9.68549*10^6}, {2247.65, 9.6841*10^6}, {2247.76,
9.6827*10^6}, {2247.78, 9.6813*10^6}, {2247.79,
9.67989*10^6}, {2247.8, 9.67848*10^6}, {2247.95,
9.67707*10^6}, {2248.16, 9.67565*10^6}, {2248.36,
9.67423*10^6}, {2248.56, 9.6728*10^6}, {2248.76,
9.67137*10^6}, {2248.96, 9.66994*10^6}, {2249.15,
9.6685*10^6}, {2249.34, 9.66706*10^6}, {2249.53,
9.66561*10^6}, {2249.72, 9.66416*10^6}, {2249.91,
9.66271*10^6}, {2250.09, 9.66125*10^6}, {2250.27,
9.65979*10^6}, {2250.45, 9.65832*10^6}, {2250.63,
9.65685*10^6}, {2250.81, 9.65538*10^6}, {2250.98,
9.6539*10^6}, {2251.16, 9.65242*10^6}, {2251.33,
9.65093*10^6}, {2251.5, 9.64944*10^6}, {2251.66,
9.64795*10^6}, {2251.83, 9.64645*10^6}, {2251.99,
9.64495*10^6}, {2252.15, 9.64344*10^6}, {2252.31,
9.64193*10^6}, {2252.47, 9.64042*10^6}, {2252.62,
9.6389*10^6}, {2252.78, 9.63738*10^6}, {2252.93,
9.63585*10^6}, {2253.08, 9.63432*10^6}, {2253.23,
9.63279*10^6}, {2253.38, 9.63125*10^6}, {2253.52,
9.62971*10^6}, {2253.67, 9.62816*10^6}, {2253.81,
9.62661*10^6}, {2253.95, 9.62506*10^6}, {2254.09,
9.6235*10^6}, {2254.22, 9.62194*10^6}, {2254.36,
9.62037*10^6}, {2254.49, 9.6188*10^6}, {2254.62,
9.61723*10^6}, {2254.75, 9.61565*10^6}, {2254.88,
9.61407*10^6}, {2255.01, 9.61248*10^6}, {2255.13,
9.61089*10^6}, {2255.26, 9.6093*10^6}, {2255.38,
9.6077*10^6}, {2255.5, 9.6061*10^6}, {2255.62,
9.60449*10^6}, {2255.74, 9.60288*10^6}, {2255.85,
9.60127*10^6}, {2255.97, 9.59965*10^6}, {2256.08,
9.59803*10^6}, {2256.19, 9.5964*10^6}, {2256.3,
9.59477*10^6}, {2256.41, 9.59314*10^6}, {2256.51,
9.5915*10^6}, {2256.62, 9.58986*10^6}, {2256.72,
9.58821*10^6}, {2256.82, 9.58656*10^6}, {2256.92,
9.58491*10^6}, {2257.02, 9.58325*10^6}, {2257.12,
9.58159*10^6}, {2257.22, 9.57992*10^6}, {2257.31,
9.57825*10^6}, {2257.4, 9.57658*10^6}, {2257.5,
9.5749*10^6}, {2257.58, 9.57322*10^6}, {2257.67,
9.57153*10^6}, {2257.75, 9.56984*10^6}, {2257.84,
9.56815*10^6}, {2257.92, 9.56645*10^6}, {2258.,
9.56475*10^6}, {2258.08, 9.56304*10^6}, {2258.16,
9.56133*10^6}, {2258.23, 9.55962*10^6}, {2258.39,
9.5579*10^6}, {2258.82, 9.55618*10^6}, {2259.26,
9.55445*10^6}, {2259.69, 9.55272*10^6}, {2260.13,
9.55099*10^6}, {2260.55, 9.54925*10^6}, {2260.98,
9.54751*10^6}, {2261.4, 9.54576*10^6}, {2261.82,
9.54401*10^6}, {2262.24, 9.54226*10^6}, {2262.65,
9.5405*10^6}, {2263.06, 9.53874*10^6}, {2263.47,
9.53697*10^6}, {2263.87, 9.5352*10^6}, {2264.28,
9.53343*10^6}, {2264.68, 9.53165*10^6}, {2265.07,
9.52987*10^6}, {2265.47, 9.52808*10^6}, {2265.86,
9.52629*10^6}, {2266.25, 9.5245*10^6}, {2266.63,
9.5227*10^6}, {2267.02, 9.5209*10^6}, {2267.4,
9.51909*10^6}, {2267.78, 9.51728*10^6}, {2268.17,
9.51547*10^6}, {2268.56, 9.51365*10^6}, {2268.94,
9.51183*10^6}, {2269.33, 9.51*10^6}, {2269.71,
9.50817*10^6}, {2270.09, 9.50634*10^6}, {2270.47,
9.5045*10^6}, {2270.84, 9.50266*10^6}, {2271.21,
9.50081*10^6}, {2271.58, 9.49896*10^6}, {2271.95,
9.49711*10^6}, {2272.31, 9.49525*10^6}, {2272.67,
9.49339*10^6}, {2273.03, 9.49152*10^6}, {2273.39,
9.48965*10^6}, {2273.74, 9.48778*10^6}, {2274.09,
9.4859*10^6}, {2274.44, 9.48402*10^6}, {2274.78,
9.48213*10^6}, {2275.13, 9.48024*10^6}, {2275.47,
9.47835*10^6}, {2275.81, 9.47645*10^6}, {2276.14,
9.47455*10^6}, {2276.48, 9.47264*10^6}, {2276.81,
9.47073*10^6}, {2277.14, 9.46882*10^6}, {2277.5,
9.4669*10^6}, {2277.93, 9.46498*10^6}, {2278.35,
9.46305*10^6}, {2278.77, 9.46112*10^6}, {2279.19,
9.45919*10^6}, {2279.61, 9.45725*10^6}, {2280.02,
9.45531*10^6}, {2280.4, 9.45336*10^6}, {2280.75,
9.45141*10^6}, {2281.1, 9.44946*10^6}, {2281.44,
9.4475*10^6}, {2281.79, 9.44554*10^6}, {2282.13,
9.44357*10^6}, {2282.47, 9.4416*10^6}, {2282.81,
9.43963*10^6}, {2283.14, 9.43765*10^6}, {2283.47,
9.43567*10^6}, {2283.8, 9.43368*10^6}, {2284.13,
9.43169*10^6}, {2284.46, 9.4297*10^6}, {2284.78,
9.4277*10^6}, {2285.1, 9.4257*10^6}, {2285.42,
9.42369*10^6}, {2285.73, 9.42168*10^6}, {2286.05,
9.41967*10^6}, {2286.36, 9.41765*10^6}, {2286.67,
9.41563*10^6}, {2286.97, 9.4136*10^6}, {2287.28,
9.41157*10^6}, {2287.58, 9.40954*10^6}, {2287.88,
9.4075*10^6}, {2288.18, 9.40546*10^6}, {2288.47,
9.40341*10^6}, {2288.77, 9.40136*10^6}, {2289.06,
9.39931*10^6}, {2289.35, 9.39725*10^6}, {2289.63,
9.39519*10^6}, {2289.92, 9.39312*10^6}, {2290.2,
9.39105*10^6}, {2290.48, 9.38898*10^6}, {2290.76,
9.3869*10^6}, {2291.04, 9.38482*10^6}, {2291.31,
9.38273*10^6}, {2291.58, 9.38064*10^6}, {2291.85,
9.37855*10^6}, {2292.12, 9.37645*10^6}, {2292.39,
9.37435*10^6}, {2292.65, 9.37224*10^6}, {2292.91,
9.37013*10^6}, {2293.17, 9.36802*10^6}, {2293.43,
9.3659*10^6}, {2293.68, 9.36378*10^6}, {2293.94,
9.36165*10^6}, {2294.19, 9.35952*10^6}, {2294.44,
9.35739*10^6}, {2294.69, 9.35525*10^6}, {2294.93,
9.35311*10^6}, {2295.18, 9.35096*10^6}, {2295.42,
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