A generalized Transpose?

*To*: mathgroup at smc.vnet.net*Subject*: [mg9097] A generalized Transpose?*From*: Tom Burton <tburton at cts.com>*Date*: Mon, 13 Oct 1997 23:33:12 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Consider first the nested list In[16]:= ys1={{{a1,b1},{c1,d1}},{{a2,b2},{c2,d2}}}; It's easy to make the slowest index vary the fastest: In[21]:= Transpose[ys1,RotateRight[Range[Depth[ys1]-1]]] Out[21]= {{{a1,a2},{b1,b2}},{{c1,c2},{d1,d2}}} MY QUESTION: What I have is a list of structures of identical form, but each structure is not rectangular. An example with only two structures is ys={{a1,{b1,{c1,d1}}},{a2,{b2,{c2,d2}}}}; My question is, How can I make the similar change to this list, to obtain: ysT={{a1,a2},{{b1,b2},{{c1,c2},{d1,d2}}}}; MY MOTIVE FOR THE QUESTION: ys is a list of evaluations of a data structure at a list of values of an independent variable, say x: xs = {x1,x2} Given ysT, it's relatively easy to set up the {x,y} pairs: In[33]:= xys=Map[Transpose[{xs,#}]&,ysT,{-2}] Out[33]= {{{x1,a1},{x2,a2}},{{{x1,b1},{x2,b2}}, {{{x1,c1},{x2,c2}},{{x1,d1},{x2,d2}}}}} and then convert these to a structure of interpolations, In[34]:= Map[Interpolation,xys,{-3}] Out[34]= {Interpolation[{{x1,a1},{x2,a2}}], {Interpolation[{{x1,b1},{x2,b2}}], {Interpolation[{{x1,c1},{x2,c2}}], Interpolation[{{x1,d1},{x2,d2}}]}}} that matches the structure of my data. This generalization of Interpolation to structured data would be quite handy, but I am stumped by the first step in the process. Do you see how to do this step or how to reach the goal another way? Thanks for taking the time to read this. Thomas E. Burton 353 Sanford Road Brahea Consulting Encinitas CA 92024-1508 tburton at cts.com 619/436-7436