Build matrices iteratively with functional constructs
- To: mathgroup at smc.vnet.net
- Subject: [mg105438] Build matrices iteratively with functional constructs
- From: Garapata <warsaw95826 at mypacks.net>
- Date: Wed, 2 Dec 2009 06:28:29 -0500 (EST)
I try to keep learning about functional programing constructs (with
lots of help from reading through posts on this forum), but now I've
gotten stuck as I've tried to apply such approaches to nested lists
and matrices.
I need to construct three matrices whose successive values depend on
earlier values in matrices (i.e. earlier in a time series). This can
get a bit confusing so let's start with as much as I've got working so
far, then see if I can describe the problem clearly enough for someone
to help.
Initialize some variables:
intervals = 10; measurements = 3; samples = 5;
Build 2 nested lists:
pList = Array[p, {intervals, measures}]; sList = Array[s,
{measurements, samples}];
I typically look at them in MatrixForm:
pList // MatrixForm
sList // MatrixForm
pList represents a time series of intervals with associated
measurement values. In the field we'll take 5 samples these
measurements during any time period.
I create a ratio of each row of pList to its corresponding elements in
sList with the following:
spRatio = sList / # & /@ pList;
spRatio // MatrixForm
This gives me a nested list of the following dimensions:
Dimensions[spRatio]
{10, 3, 5}
Now I need some help. I can do the following a step at a time, but
I'd like a way to apply this all at once in a functional style for
speed and simplicity.
step 0: Initialize an vector
w0 = Array[1, samples]
w0 // MatrixForm
Start a loop
Step 1: The following takes a part of spRatio, the first row in the
matrix:
spRatio1 = spRatio[[1, 1 ;; 3, All]]; spRatio1 // MatrixForm
Step 2:
pos1 = Transpose[w0*Transpose[spRatio1]]; pos1 // MatrixForm
Step 3a:
comp1 = (pos1 . w0)* numOfSamples/Total[w0]; comp1 // MatrixForm
Step 3b:
w1 = pList[[1]].pos1;
Repeat loop for interval - 1 steps incrementing some appropriate
index (w0, w1, w2, ...; pos1, pos2, pos3, ...; comp1, comp2,
comp3 ...;
spRatio1 = spRatio[[1, 1 ;; 3, All]], spRatio2 = spRatio[[2, 1 ;; 3,
All]] ).
I could put this kind of thing in a Do loop and use Append to build
the various matrices, but there must be a better way.
At the end of this process I want 3 matrices with the following
dimensions, let's designate them:
matrix dimensions
-----------------------------------
w {5, 10}
pos {9, 5, 3}
comp {9, 3}
The 9s corresponding to intervals -1.
I don't need to preserve w and pos I really only need comp as output
so that may affect the efficiency of a solution.
I've tried to figure out ways of using Map, MapThread, Fold, and
FoldList to do this, but haven't made headway.
The specific calculations of each the above steps aside, I really need
a way build nested lists and matrices from earlier parts of one or
more matrices.
Thanks to all.