Re: Need to speed up a matrix calculation
- To: mathgroup at smc.vnet.net
- Subject: [mg105714] Re: Need to speed up a matrix calculation
- From: Bill Rowe <readnews at sbcglobal.net>
- Date: Wed, 16 Dec 2009 06:19:22 -0500 (EST)
On 12/15/09 at 7:26 AM, warsaw95826 at mypacks.net (Garapata) wrote:
>I have a calculation, which I want to do in a more direct, elegant,
>and faster calculating way.
>Start with 3 variables and 2 matrices:
>intervals = 10; samples = 5; measurements = 3;
>p = Array[a, {intervals -1, samples, measurements}];
>m = Array[b, {samples, intervals}];
>mMost = Drop[w, None, -1];
>This also shortens the length the next line, the one I need help
>with.
>composition = (Transpose[p[[#]]] . mMost[[All, #]] ) * 5 /
>Total[mMost [[All, #]]] & /@ Range[Length[p]]
>This works, but will likely get quite slow as I increase the number
>of intervals, samples, and measurements. I'd like a more direct way
>to do this. The above seems bit like making map like an iterative
>loop, kind of cheating at functional programing.
This last can be made more efficient using:
In[53]:= compA =
MapThread[#1.#2 &, {Transpose[p, {1, 3, 2}],
Most@Transpose[m]}] 5/
Total[mMost];
In[54]:= compA == composition
Out[54]= True
Also, mMost is not needed in your code since you explicitly
select only the first p columns of mMost which are also the
first p columns of m. That is:
In[56]:= compB = (Transpose[p[[#]]].m[[All, #]])*5/
Total[m[[All, #]]] & /@ Range[Length[p]];
In[57]:= compB == composition
Out[57]= True