Re: Beginner: List Indexing and Assignment
- To: mathgroup at smc.vnet.net
- Subject: [mg94534] Re: Beginner: List Indexing and Assignment
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Mon, 15 Dec 2008 07:49:38 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <gi2ut4$a5h$1@smc.vnet.net>
C Rose wrote:
> 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).
>
> 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?
>
> Another way (in the other system) is to create a logical array:
>
> logical = a>2
>
> resulting in
>
> [0 0 1]
> [1 1 1]
>
> and I could then do
>
> a(logical) = -1
>
> again resulting in
>
> [ 1 2 -1]
> [-1 -1 -1]
>
> I have been able to approximate this in Mathematica as
>
> logical = a /. x_ /; x > 2 -> True
> (* Note, unlike above, logical contains values of True and other integers. *)
>
> ReplacePart[a, Position[logical, x_ /; x == True] -> -1]
>
> Is there a more elegant method in Mathematica? (Of course, 'elegant' is a subjective quality; perhaps 'brevity' is a better word :-)
>
> Many thanks in advance
>
> Chris
You can apply transformation rules directly to the matrices. For
instance, a = a /. x_ /; x > 2 -> -1
In[1]:= a = {{1, 2, 3}, {4, 5, 6}}
Out[1]= {{1, 2, 3}, {4, 5, 6}}
In[2]:= MatrixForm[a]
Out[2]//MatrixForm=
1 2 3
4 5 6
In[3]:= a = a /. x_ /; x > 2 -> -1
Out[3]= {{1, 2, -1}, {-1, -1, -1}}
Regards,
-- Jean-Marc