Re: Beginner: List Indexing and Assignment
- To: mathgroup at smc.vnet.net
- Subject: [mg94515] Re: Beginner: List Indexing and Assignment
- From: Albert Retey <awnl at gmx-topmail.de>
- Date: Mon, 15 Dec 2008 07:46:11 -0500 (EST)
- References: <gi2ut4$a5h$1@smc.vnet.net>
Hi,
> I am moving from another system to Mathematica and have a few simple
> questions about indexing and altering lists. I've been able to find
> Mathematica equivalents to some of the other system's idioms, but
> as a Mathematica neophyte they're not very elegant. I'd be very
> grateful if someone could tell me the Mathematica equivalents---or
> point me to a suitable Rosetta stone (Google didn't easily turn one up).
The heart and strongest part of the other system is handling numeric
matrices and manipulating these. If you compare Mathematica with the
other system in exactly that field, you will not always, but often be
disappointed. At the heart of Mathematica is pattern matching and
functional programming, and if you want elegant (or brief, or efficient)
solutions, you will need to take advantage of the strong parts of
Mathematica.
> In the other system, I would create a 2x3 matrix using
>
> a = [1 2 3; 4 5 6]
>
> resulting in
>
> [1 2 3]
> [4 5 6]
>
> and then assign any element of the matrix whose value is greater than 2 the value -1 using
>
> a(a>2) = -1
>
> resulting in
>
> [ 1 2 -1]
> [-1 -1 -1]
>
> I can do this in Mathematica by:
>
> a = ReplacePart[a, Position[a, x_ /; x > 2] -> -1]
>
> but is there a more elegant method?
You have asked for list indexing, but your example does only address a
list indexing problem when thinking in terms of the other system. What I
see is that you want to change all entries of a matrix that are larger
than 2 to be -1. This is what probably comes to a Mathematica users mind
first:
mat = {{1,2,Pi},{4,5,6}}
mat = mat /. n_ /; n>2 -> -1
What it does is this: replace ( /. is short for ReplaceAll) everything
within mat with minus one, provided that (/; is short for Condition) it
is larger than 2 and reassign the result to mat. Looking at your
original solution, you have not been far away, it was just your prior
experience that did make you think that you would need to somehow create
indices, but that is not necessary when using patterns.
Of course the above way of doing things has disadvantages: pattern
matching is very general and powerful, but for simple tasks like this
usually has too much overhead and thus is not very fast. The above code
will also make a copy of a, so for large matrices the above will not be
a good solution. There are many possibilities to do this more
efficiently also in Mathematica, but most of these would be more
elaborate. Here is a try that is short and should be reasonable fast
even for larger matrices (as long as a copy fits in memory):
a = Clip[a, {0, 2}, {0, -1}]
Oh, and it could be changed to handle cases with negative entries also:
a = Clip[a, {-Infinity, 2}, {-Infinity, -1}]
That approach will still make a copy of a and is not as short as in the
other system, but probably you see that with a slightly different kind
of thinking you can get your problems solved with Mathematica without
too much effort.
All in all for this very special task the other system wins in many
respects, but of course there are many other tasks, where the outcome
will be (very) different. It really depends on what you plan to do and
of course how you think about your problems and how you formulate
possible solutions. If operations on numerical matrices is all you are
doing, all you will be doing in the future and all you can think of
(that should by no means be interpreted that I suggest you couldn't
:-)), a move to Mathematica will probably not pay off...
hth,
albert
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