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Re: Functional programming?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91992] Re: Functional programming?
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 16 Sep 2008 19:23:51 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <200809130957.FAA03536@smc.vnet.net> <gal3dg$dql$1@smc.vnet.net>

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


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