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Re: Functional programming?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92016] Re: Functional programming?
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Wed, 17 Sep 2008 04:28:49 -0400 (EDT)
  • References: <200809130957.FAA03536@smc.vnet.net> <gal3dg$dql$1@smc.vnet.net> <gapf5u$nvq$1@smc.vnet.net>

Jean-Marc Gulliet wrote:
> peter lindsay wrote:
> 
>> as an old-timer myself - I'd be very interested in this too,
>> particularly - as you say - with reference to engineering problems.
>> I'm afraid my favorite construct was the REPEAT - UNTIL loop, which
>> should finally ruin any shreds of credibility that I may once have
>> had...
>> Peter
>>
>> 2008/9/13 AES <siegman at stanford.edu>:
>>> I suggest it might be instructive if some of the functional programming
>>> proponents on this group could provide us DO-looping old timers with a
>>> brief summary or tutorial as to what is really meant by, or involved in,
>>> "functional programming"?
>>>
>>> --- especially as this concept might relate to building programs to do
>>> calculations involving multi-stage real-world engineering or technical
>>> problems
>>>
>>> --- and especially as it might relate to programs that are going to be
>>> developed in an evolutionary process and that in the end, rather than
>>> being built into some long-term library, are maybe only going to be run
>>> or executed a few times before the person involved (e.g., an engineer,
>>> or scientist, or other real-world individual, not a "programmer") moves
>>> on to some other totally different task or assignment.
> 
> 
> Say we want to compute the mean (average) of all non-zero values for 
> each row of a two dimensional array. The code must not crash when fed 
> with data of incorrect format as well as it must handle nicely such 
> things like divisions by zero.
> 
> (* Functional / Pattern matching code *)
> 
> myMean2[array_?VectorQ] := Mean[Select[array, # != 0 &]]
> myMean2[array_?MatrixQ] := Map[myMean2, array]
> 
> 
> (* Procedural code *)
> 
> myMean1[array_] :=
>   Module[{iter, len, cnt, sum, mean},
>    sum = 0;
>    mean = 0;
>    cnt = 0;
>    len = Length[array];
>    If[len != 0,
>     For[iter = 1, iter <= len, iter = iter + 1,
>      If[array[[iter]] != 0, sum = sum + array[[iter]]; cnt = cnt + 1];
>      ];
>     If[cnt != 0,
>      mean = sum/cnt;
>      , mean = "NA";
>      ];
>     , mean = "NA";
>     ];
>    Return[mean]
>    ]
> 
> meanArray[array_] :=
>   Module[{res, len, dim},
>    res = {};
>    len = Length[array];
>    dim = Depth[array] - 1;
>    If[dim != 2,
>     Return["NA"]];
>    For[iter = 1, iter <= len, iter = iter + 1,
>     AppendTo[res, myMean1[array[[iter]]]
>       ];
>     ];
>    Return[res]
>    ]
> 
> 
> (* Some data and some tests *)
> 
> data = {{}, {1, 2, 3, 4, 5, 0, 0, 0}, {0, 0, 0}, {1, 2, -10,
>      3, 4}, {a, b, c}};
> 
> meanArray[{1, 2, 3, 4, 5, 0, 0, 0}]
> meanArray[{{1, 2, 3, 4, 5, 0, 0, 0}}]
> meanArray[data]
> meanArray[{{{1, 2, 3, 4}, {5, 0, 0, 0}}}]
> 
> (*
> Out[6]= "NA"
> 
> Out[7]= {3}
> 
> Out[8]= {"NA", 3, "NA", 0, "NA"}
> 
> Out[9]= "NA"
> *)
> 
> myMean2[{1, 2, 3, 4, 5, 0, 0, 0}]
> myMean2[{{1, 2, 3, 4, 5, 0, 0, 0}}]
> Map[myMean2, data]
> Map[myMean2, {{{1, 2, 3, 4}, {5, 0, 0, 0}}}]
> 
> (*
> Out[10]= 3
> 
> Out[11]= {3}
> 
> Out[12]= {Mean[{}], 3, Mean[{}], 0, Mean[{}]}
> 
> Out[13]= {{5/2, 5}}
> *)
> 
> 
> Regards,
> -- Jean-Marc
> 
I think you have chosen a rather favourable example here. Suppose 
instead that you need to remove every zero together with the preceding 
element (sweeping from left to right). Realistically, you also probably 
want to do something, rather than output Mean[{}] for myMean2[{0,0,0}].

I would say that users should not be scared away from using procedural 
code when faced with ad hoc problems of this sort.

David Bailey
http://www.dbaileyconsultancy.co.uk


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