# Interpolation on large 2D list results in erratic function

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,
9.34881*10^6}, {2295.66, 9.34666*10^6}, {2295.9,
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8.1605*10^6}, {2330.25, 8.15674*10^6}, {2330.16,
8.15297*10^6}, {2330.07, 8.1492*10^6}, {2329.98,
8.14543*10^6}, {2329.89, 8.14165*10^6}, {2329.79,
8.13787*10^6}, {2329.7, 8.13408*10^6}, {2329.6,
8.13029*10^6}, {2329.51, 8.1265*10^6}}

-

Your data does not represent a function. I believe you will need to parametrize, like this:

data2 = MapIndexed[{#2, #} &, data];

f = Interpolation[data2]

InterpolatingFunction[{{1.,900.}},<>]

ParametricPlot[Log @ f[x], {x, 1, 900}]


-
Good grief, you couldn't wait a couple of minutes? – Daniel Lichtblau Mar 10 '13 at 21:06
@Daniel Believe it or not, I did. :D – Mr.Wizard Mar 10 '13 at 21:07
@DanielLichtblau Rest assured, you're not alone :-( – Sjoerd C. de Vries Mar 10 '13 at 21:18
@Sjoerd you shouldn't let my terse answer stop you from posting your own. – Mr.Wizard Mar 10 '13 at 21:23
Actually yours has the advantage of correctly treating the repeated x coordinates. My deleting them really is not the right thing to do. I think I'll redelete my answer. – Daniel Lichtblau Mar 10 '13 at 21:28