RE: A Functional Programming Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg24746] RE: [mg24705] A Functional Programming Question*From*: Wolf Hartmut <hwolf at debis.com>*Date*: Wed, 9 Aug 2000 02:31:54 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

> -----Original Message----- > From: David Park [SMTP:djmp at earthlink.net] To: mathgroup at smc.vnet.net > Sent: Saturday, August 05, 2000 1:02 AM > To: BobHanlon at aol.com; andrzej at tuins.ac.jp; Johannes Ludsteck; Allan > Hayes; Hartmut Wolf; MathGroup; Paul J. Hinton; linsuain+ at andrew.cmu.edu > Subject: RE: [mg24705] A Functional Programming Question > > Thanks everybody for the replies. > > I zeroed in on two of them, the one by Johannes Ludsteck and the one by > Allan Hayes because they seemed to be adaptable to a more general parallel > manipulation of equations. > > Here is a somewhat more general set of parallel equations: > > eqns = {(a1 x + b1)/c1 == 0, (a2 y + b2)/c2 == 0, (a3 z + b3)/c3 == 0}; > > Suppose that we wish to solve for the square roots of x, y and z. > > Here is a routine which is an adaptation of Johannes method: > > parallelmap[eqns_, op_, parms_] := > MapThread[ > Function[parm, Function[eq, op[#, parm] & /@ eq]][#2][#1] &, {eqns, > parms}] > > We can now manipulate the equations in parallel, step-by-step. > > parallelmap[eqns, #1#2 &, {c1, c2, c3}] > parallelmap[%, #1 - #2 &, {b1, b2, b3}] > parallelmap[%, #1/#2 &, {a1, a2, a3}] > parallelmap[%, Sqrt[#] &, {d, d, d}] > > {b1 + a1 x == 0, b2 + a2 y == 0, b3 + a3 z == 0} > {a1 x == -b1, a2 y == -b2, a3 z == -b3} > {x == -(b1/a1), y == -(b2/a2), z == -(b3/a3)} > {Sqrt[x] == Sqrt[-(b1/a1)], Sqrt[y] == Sqrt[-(b2/a2)], > Sqrt[z] == Sqrt[-(b3/a3)]} > > The last step works because the function only looks for one argument and > we > can just put in dummy values for the second argument. Using Sqrt instead > of > Sqrt[#]& will not work. > > Working with Allan Hayes method, I came up with this routine: > > parallelmap2[eqns_, op_, parms_] := > Equal @@@ op[List @@@ eqns, parms] > > parallelmap2[eqns2, #1*#2 & , {c1, c2, c3}] > parallelmap2[%, #1 - #2 & , {b1, b2, b3}] > parallelmap2[%, #1/#2 & , {a1, a2, a3}] > parallelmap2[%, Sqrt[#1] & , {d, d, d}] > > gives the same answers. > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > > [Hartmut Wolf] Hello David, I'd like to give you yet an alternative for parallelmap which, I think, is clear and easy readable: parallelmap3[eqns_, op_, parms_] := MapThread[Thread[op[##], Equal] &, {eqns, parms}] Kind regards, Hartmut