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MathGroup Archive 2000

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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 



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