Mathematica 教學：對遺失資料做線性插值

datatemp={
{-818.2106,-6755.208,207.9009},{0,0,0},{0,0,0},{0,0,0},
{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},
{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},
{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},
{0,0,0},{0,0,0},{-767.4377,-6709.237,251.7202},
{-768.7812,-6700.438,253.0015},{-768.6588,-6701.238,252.8851},
{-767.7062,-6697.338,254.8504},{-765.7729,-6696.207,257.0257},
{-766.2335,-6689.349,259.0551},{-761.753,-6693.4,261.8711},
{-762.6193,-6685.736,264.3021},{-757.8909,-6690.449,267.0908},
{-754.3521,-6692.645,269.7541},{-752.003,-6692.321,272.2921},
{-750.8434,-6689.48,274.7048},{-750.8735,-6684.12,276.9922},
{-749.6801,-6681.277,279.5483},{-748.7109,-6677.929,282.1369},
{-747.9661,-6674.078,284.7577},{-747.4456,-6669.722,287.4109},
{-747.1495,-6664.861,290.0965},{-744.986,-6667.709,291.8721},
{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},
{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},
{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},{0,0,0},
{-714.5345,-6624.671,368.8935}
}

mytrans[datatemp_List]:=Block[{data,zeroindex},

(*先將讀入資料加進流水號*)

data=Flatten[{#,datatemp[[#]]}]&/@Range[Length@datatemp];

(*列出斷點*)

zeroindex=Split[Select[data,#[[2]]==0&][[All,1]],#2-#1==1&];

(*斷點內線性插值*)

test[z_]:=Block[{incr},

(*找出斷點前後的資料*)

data[[#]]&/@{zeroindex[[z,1]]-1,zeroindex[[z,-1]]+1};

(*計算插值並替換資料*)

incr=MapThread[#2-#1&,data[[#]]&/@{zeroindex[[z,1]]-1,
zeroindex[[z,-1]]+1}];
Map[(data[[#]]=data[[#-1]]+incr/incr[[1]])&,zeroindex[[z]]]];

(*計算所有斷點插值*)

test[#]&/@Range[Length@zeroindex];
data
]


With[{dd=mytrans[datatemp]},
GraphicsGrid@
Transpose@{ListPlot[datatemp[[All,#]],PlotRange->All]&/@{1,2,3},
ListPlot[dd[[All,#]],PlotRange->All]&/@{2,3,4}}]

Tags: Mathematica 教學

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