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Re: Basic questions on list manipulation in the "Mathematica Way"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95628] Re: Basic questions on list manipulation in the "Mathematica Way"
  • From: dangerrity at gmail.com
  • Date: Fri, 23 Jan 2009 05:06:49 -0500 (EST)
  • References: <gl71s8$c41$1@smc.vnet.net> <gl9n7s$avr$1@smc.vnet.net>

On Jan 22, 4:02 am, "Sjoerd C. de Vries" <sjoerd.c.devr... at gmail.com>
wrote:
> An alternative to your field modification code... First, let's get us
> a data set in your style:
>
> In[79]:= ClearAll[data];
> data =
>   {
>    {"Thomas Jefferson" -> {val1 -> 12, val2 -> 34, val3 -> 56,
>       val4 -> 78}},
>    {"George Washington" -> {val1 -> 91, val2 -> 234, val3 -> 567,
>       val4 -> 893}},
>    {"John Kennedy" -> {val1 -> 21, val2 -> 33, val3 -> 444,
>       val4 -> 555}},
>    {"Barack Obama" -> {val1 -> 377, val2 -> 12, val3 -> 34,
>       val4 -> 5534}}
>    };
>
> Examining an entry:
>
> In[84]:= "Thomas Jefferson" /. Flatten[data]
>
> Out[84]= {val1 -> 12, val2 -> 34, val3 -> 56, val4 -> 78}
>
> I used Flatten because the rules are nested a level too deep. You
> could remove the {} around each individual.
>
> Getting to one of its fields:
>
> In[89]:= val1 /. ("Thomas Jefferson" /. Flatten[data])
>
> Out[89]= 12
>
> Modification of a field:
>
> In[87]:= data=data /.
>  HoldPattern[{"Thomas Jefferson" -> {a___, val2 -> x_,
>       b___}}] -> {"Thomas Jefferson" -> {a, val2 -> 4444, b}}
>
> Out[87]= {{"Thomas Jefferson" -> {val1 -> 12, val2 -> 4444,
>     val3 -> 56, val4 -> 78}}, {"George Washington" -> {val1 -> 91,
>     val2 -> 234, val3 -> 567,
>     val4 -> 893}}, {"John Kennedy" -> {val1 -> 21, val2 -> 33,
>     val3 -> 444, val4 -> 555}}, {"Barack Obama" -> {val1 -> 377,
>     val2 -> 12, val3 -> 34, val4 -> 5534}}}
>
> Note that since the data set consists of rules, using a rule for
> replacement needs some precausions otherwise the wrong rule is
> applied. The HoldPattern takes care of that.
>
> A slight modification prevents the necessity of providing the
> attribute name twice:
>
> data /. HoldPattern[{"Thomas Jefferson" -> {a___, y:val3 -> x_,
>       b___}}] -> {"Thomas Jefferson" -> {a, y -> 4444, b}}
>
> Now for other possible data structures:
>
> If the attribute types are the same for all individuals you could use
> a plain list like this:
>
> data =
>   {
>    {"Thomas Jefferson", 12, 34, 56, 78},
>    {"George Washington", 91, 234, 567, 893},
>    {"John Kennedy", 21, 33, 444, 555},
>    {"Barack Obama", 377, 12, 34, 5534}
>    };
>
> So, every column corresponds to a certain attribute.
> Modifications could be done like this:
>
> data = data /. {"Thomas Jefferson", x_, y_, z_,
>     w_} -> {"Thomas Jefferson", 4444, y, 1111, w}
>
> This code is easily readable and understandable, but modification in
> this simple way also means copying the whole database which may be a
> problem if it's huge. In that case, one should use indexes.
>
> An alternative would be the following, in which the database is a
> function:
>
> ClearAll[data];
> data["Thomas Jefferson"] = {12, 34, 56, 78};
> data["George Washington"] = {91, 234, 567, 893};
> data["John Kennedy"] = {21, 33, 444, 555};
> data["Barack Obama"] = {377, 12, 34, 5534};
>
> data["Thomas Jefferson"] =
>  data["Thomas Jefferson"] /. {x_, y_, z_, w_} -> {4444, y, 1111, w}
>
> This idea of a function as a database can be used even more:
>
> ClearAll[data];
> data["Thomas Jefferson", "val1"] = 12;
> data["Thomas Jefferson", "val2"] = 34;
> data["Thomas Jefferson", "val3"] = 56;
> data["Thomas Jefferson", "val4"] = 78;
> data["George Washington", "val1"] = 91;
> data["George Washington", "val2"] = 234;
> data["George Washington", "val3"] = 567;
> data["George Washington", "val4"] = 893;
> data["John Kennedy", "val1"] = 21; data["John Kennedy", "val2"] = 33;
> data["John Kennedy", "val3"] = 444; data["John Kennedy", "val4"] =
> 555;
> data["Barack Obama", "val1"] = 377; data["Barack Obama", "val2"] = 12=
;
> data["Barack Obama", "val3"] = 34;
> data["Barack Obama", "val4"] = 5534;
>
> Modification of a value is now simply a redefinition of the function:
>
> data["Thomas Jefferson", "val1"] = 4444;
>
> This has the disadvantage that it is difficult to collect all values
> of val1.
>
> Of course, you could also use external databases, see DatabaseLink/
> tutorial/Overview in the help centre.
>
> Cheers -- Sjoerd
>
> On Jan 21, 1:45 pm, dangerr... at gmail.com wrote:
>
> > Hello,
>
> > I have some basic questions about using lists in Mathematica.
> > Specifically I have a table that serves as sort of a database with the
> > following structure:
>
> > ct = {
> >           { sym1 -> {val1->20, val2->300, val3->1000, ... },
> >           { sym2 -> {val1->50, val2->500, val3->20000,...},
> >           ...
> >        }
>
> > sym1, sym2, ... are people and val1, val2 ... represent attributes of
> > each person.
>
> > Now I'm trying to go in and modify values.  I can do it, but I think
> > not well and I think with a "programming language" mindset instead of
> > a "Mathematica mindset."
>
> > Here is my specific question.  In order to change a specific value in
> > the list above (valxxx) for a given individual (symxxx), I created
> > this function:
>
> > changeVal[ who_, class_, amnt_ ] := (
> >     ct[[ Position[ ct, who ][[ 1, 1 ]], 2 ]] =
> >     ReplacePart[ ct[[ Position[ ct, who ][[ 1, 1 ]], 2 ]],
> >      Position[ ct[[ Position[ ct, who ][[ 1, 1 ]] ]], class ][[ 1=
,
> > 2 ]] -> (class -> amnt) ]
> > );
>
> > Now I know there is a better way than that using list manipulation and
> > patterns.  Can some of you experienced pros help me out?  I call th=
is
> > "write only" code because I don't know that I could explain it once
> > it's written.
>
> > Perhaps a more fundamental question: is this the right way to store
> > data in lists?  Or would it be better to just have the values and
> > reference them by index number?
>
> > Thanks for your patience with a simple question.

Thanks for yet another insight -- the structure being one level too
deep requiring Flatten all the time.


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