Re: How to copy pattern from one expression to another?

*To*: mathgroup at smc.vnet.net*Subject*: [mg45357] Re: How to copy pattern from one expression to another?*From*: drbob at bigfoot.com (Bobby R. Treat)*Date*: Fri, 2 Jan 2004 04:23:46 -0500 (EST)*References*: <bsbn05$lri$1@smc.vnet.net> <bsrhq7$qj7$1@smc.vnet.net> <bsu1cf$8gr$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Here's a different solution that may be useful: ClearAll@linear Solve[a + b #[[1]] == #[[2]] & /@ {{x1, y1}, {x2, y2}}, {a, b}] // Simplify; linear[{{x1_?AtomQ, y1_?AtomQ}, {x2_?AtomQ, y2_? AtomQ}}] = a + b #1 & /. First@%; linear[{a__}] := linear /@ {a} atom1 = {{a61, y61}, {a62, y62}}; atom2 = {{1, 2}, {3, 4}}; xx = {atom1, atom2}; linear[atom1] linear[atom2] linear[xx] linear[{atom1, xx, atom2}] The result at lowest level is a pure function, symbolic input is OK, and Solve is called only once. (Versus using Fit many times.) Bobby drbob at bigfoot.com (Bobby R. Treat) wrote in message news:<bsu1cf$8gr$1 at smc.vnet.net>... > Fit is defined only for numeric data, so... assuming that other kinds > of data leads to evaluation of some function "g" which you can define, > here's a solution: > > ClearAll[f] > f[x:{{_?NumericQ, > _?NumericQ}, > {_?NumericQ, > _?NumericQ}}] := > Block[{y}, Fit[x, {1, y}, > y]] > f[x:{{_?AtomQ, _?AtomQ}, > {_?AtomQ, _?AtomQ}}] := g[x] > f[{a__}] := f /@ {a} > > Testing: > > atom1 = {{a61, y61}, > {a62, y62}}; > atom2 = {{1, 2}, {3, 4}}; > xx = {atom1, atom2}; > f[atom1] > f[atom2] > f[xx] > f[{atom1, xx, atom2}] > g[{{a61, y61}, {a62, y62}}] > 0.9999999999999988 + > 1.0000000000000002*y > {g[{{a61, y61}, {a62, y62}}], > 0.9999999999999988 + > 1.0000000000000002*y} > {g[{{a61, y61}, {a62, y62}}], > {g[{{a61, y61}, {a62, > y62}}], > 0.9999999999999988 + > 1.0000000000000002*y}, > 0.9999999999999988 + > 1.0000000000000002*y} > > Bobby > > "Nico" <pipponep at hotmail.com> wrote in message news:<bsrhq7$qj7$1 at smc.vnet.net>... > > Thanks you all for your replies. > > Indeed, what you suggested only solves my partially my issue. I guess I > > should get deeped into the problem... > > Each xi I wrote in the previous messages represents of couple of (x,y) > > coordinates in the form {{a1,y1},{a2,y2}} which represents the points to > > which I have to apply function Fit[]. > > > > I.e. xx={{x11,x12,x13},x2,x3,x4,{x51,x52},x6,{x71,x72},x8}= > > {...,{{a61,y61},{a62,y62}},...} > > > > Now, if I set Fit[] to Listable, then I would get > > > > Fit[xx,{1,x},x]={...,{{Fit[a61,{1,x},x],Fit[y61,{1,x},x]},{Fit[a62,{1,x},x], > > Fit[y62,{1,x},x]}},...} > > > > which obviously something meaningless. > > I would therefore need something that "flattens" xx down to a list so that > > only tokens like {{a1,y1},{a2,y2}} appear. I would then apply Fit[] in the > > correct way, and then I would like to construct a list with the same pattern > > that xx had... > > Is it confusing? It is to me... > > > > Please, let me know if you need further explanations. Thanks you all for > > your help! > > Nicola