Re: interpolating f(x,y) from evaluation

*To*: mathgroup at smc.vnet.net*Subject*: [mg8658] Re: [mg8599] interpolating f(x,y) from evaluation*From*: Allan Hayes <hay at haystack.demon.co.uk>*Date*: Fri, 12 Sep 1997 04:11:09 -0400*Sender*: owner-wri-mathgroup at wolfram.com

"K. Nikolaj Berntsen" <knb at _nospam_bkm.dtu.dk> [mg8599] interpolating f(x,y) from evaluation writes > I want to generate an interpolatingfunction-like object for a > complicated function of several variables .... > I tried: > > Interpolation[Table[{f[i,j].i.j},{i,3},{j,3}]] > > but it did not work. Nikolaj: I may not be understanding your quastion but 1. the dots in f[i,j].i.j seem odd. 2. assuming that you want to interpolate data giving values f[i,j] at i,j with i and j ranging over 1 to 3 then you need to supply the data in the form {{1,1,f[1,1]},{1,2,f[1,2]}, ..} (the order of main list is unimportant, {{1,2,f[1,2]},{1,1,f[1,1]}, ..} will do just as well) However with Table get In[1]:= Table[{i,j,f[i,j]},{i,3},{j,3}] Out[1]= {{{1,1,f[1,1]},{1,2,f[1,2]},{1,3,f[1,3]}},{{2,1,f[2,1]},{2,2,f[2,2]}, {2,3,f[2,3]}},{{3,1,f[3,1]},{3,2,f[3,2]},{3,3,f[3,3]}}} which is not of form expected. We need to remove some of the brackets. In[2]:= data = Flatten[%,1] (* the 1 stops the flattening at level 1*) Out[2]= {{1,1,f[1,1]},{1,2,f[1,2]},{1,3,f[1,3]},{2,1,f[2,1]},{2,2,f[2,2]},{2,3,f[2,3]},{3,1,f[3,1]},{3,2,f[3,2]},{3,3,f[3,3]}} Now define f. In[3]:= f[i_,j_]:= i-j The values of f are now numeric. In[4]:= data Out[4]= {{1,1,0},{1,2,-1},{1,3,-2},{2,1,1},{2,2,0},{2,3,-1},{3,1,2},{3,2,1}, {3,3,0}} Do the interpolation In[5]:= intf = Interpolation[data] Interpolation::"inhr": "Requested order is too high; order has been reduced to {2,2}." Out[5]= InterpolatingFunction[{{1,3},{1,3}},"<>"] The message simply says that with only 3 data points each way, it cannot do an order {3,3} interpolation (the default), and has instead done an order {2,2} one (you can set this order via the option InterpolationOrder). The intf works as expected You can find information online via the help browser: menu Help/Help Allan Hayes hay at haystack.demon.co.uk http://www.haystack.demon.co.uk/training.html voice:+44 (0)116 2714198 fax: +44 (0)116 2718642 Leicester, UK