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MathGroup Archive 1998

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splines and interpolation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14779] splines and interpolation
  • From: Napoleon J Leoni <Napoleon.Leoni at worldnet.att.net>
  • Date: Sat, 14 Nov 1998 03:08:09 -0500
  • Organization: AT&T WorldNet Services
  • Sender: owner-wri-mathgroup at wolfram.com

Is the fit through splines in Mathematica limited to 1-d data? Also, for
the Interpolation function must the data be ordered in a grid or will
it work for scattered data? I tried to generate an Interpolation fit
for the following data points:

data:={{0,0,50},{0,0,100},{0,0,200},{0,0,300},{0.5,3,53.3},{0.5,3,104.8},{0.
5,3,
   
156.04},{0.5,3,202.62},{0.5,3,250.06},{1.5,2,51.4},{1.5,2,102},{1.5,2,

152.7},{1.5,2,203},{1.5,2,304},{1.5,2,404},{1.5,4.3,22.3},{1.5,4.3,42.7},{
    1.5,4.3,109.6},{1.5,4.3,214.3},{1.5,4.3,261.7},{1.5,4.3,307},{1.5,6,

61.8},{1.5,6,117.4},{1.5,6,167.2},{1.5,6,210.5},{1.5,6,254},{1.5,6,297},{
   
1.5,6,333},{1.1,6,62.1},{1.1,6,117.6},{1.1,6,170},{1.1,6,212},{1.1,6,

253},{1.1,6,288},{0.5,6,20.26},{0.5,6,62.29},{0.5,6,92.26},{0.5,6,113.8},{

0.5,6,130},{0.5,6,150},{0,6,29.8},{0,6,56.5},{0,6,138},{0,6,212.12},{0,6,
   
253.4},{0,6,303.9},{0,6,351.5},{0.9,4.8,23.5},{0.9,4.8,111.7},{0.9,4.8,
    164.7},{0.9,4.8,213},{0.9,4.8,259}}

with response values at each point given by

f:={0.48,0.24,0.12,0.08,0.422402839,0.218518734,0.147853162,0.116916718,
  0.095953937,0.454208239,0.230680507,0.15439187,0.11647941,0.077908587,
 
0.058817763,0.904904583,0.491419357,0.199797538,0.104519397,0.087608008,
 
0.076393383,0.314198636,0.174130581,0.128774524,0.10832708,0.093000186,
 
0.081624324,0.07574764,0.311170233,0.173538803,0.124567474,0.106799573,
 
0.093736818,0.086805556,0.779598682,0.309274835,0.253736777,0.222386266,
 
0.213017751,0.213333333,0.506733931,0.283185841,0.126023945,0.080009078,
 
0.074752895,0.064966557,0.05827494,0.814848348,0.192355627,0.132713561,
  0.105799114,0.089444105}

So I generated a table of the form {{x1,y1,z1,f1},....,{xn,yn,zn,fn}}
and I get an error message:

Interpolation::"inddp":
    "The point \!\(0\) in dimension \!\(2\) is duplicated."


Napoleon leoni

leoni+ at andrew.cmu.edu



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