Transpose[ InterpolatingFunction, { n1, n2, ...} ]

*To*: mathgroup at smc.vnet.net*Subject*: [mg81195] Transpose[ InterpolatingFunction, { n1, n2, ...} ]*From*: pdickof at scf.sk.ca*Date*: Sat, 15 Sep 2007 04:11:18 -0400 (EDT)

Suppose I have a table, grid lines, InterpolatingFunction, and order list as follows ... lens = {6, 5, 4} t = Table[i + j + k, {i,1, lens[[1]], 1}, {j, 10, 10lens[[2]], 10}, {k, 100, 100lens[[3]], 100}] g = {Range[lens[[1]]], 10Range[lens[[2]]], 100Range[lens[[3]]]} f = ListInterpolation[t, g] Evaluate that and everything makes sense. Note that Dimensions[t]==Map[Length,g] Now let me transpose as follows ... axisPosit = {3, 2, 1}; t2 = Transpose[t, axisPosit] g2 = Part[g, axisPosit] o2 = Part[o, axisPosit] f2 = ListInterpolation[t2, g2, InterpolationOrder -> o2] Again, no problems on evaluation. and Dimensions[t2]==Map[Length,g2] Trying all permutations of {1,2,3},... we see that the Dimensions and Lengths do not always agree (and the corresponding ListInterpolation must fail) Map[{#, Dimensions[t2 = Transpose[t, #]] == Map[Length, g2 = Part[g, #]], Head[ListInterpolation[t2, g2]] === InterpolatingFunction} &, Permutations[Range[3]]] // MatrixForm I think all of these cases should always be True. Is there a bug in Transpose or am I confused? I am trying to generalize Transpose to work on InterpolatingFunctions including those where an N1-D InterpolatingFunction has data for only N2-D dimensional hyperplanes where (0<=N2<=N1) (ie. where elements in the list lens above can be =1). The function would be myTranspose[ InterpolatingFunction, {n1, n2, ...} ] I intend to check that Sort[{n1, n2, ...}]==Range[N1] Does anyone have any advice on how to accomplish this? Thanks in advance!