[R] Can you turn a string into a (working) symbol?

[andrewH]

Dear Greg—

You mean FAQ 7.21, not 7.22, correct? Though 7.12 also seems relevant.
Though I would say I was asking about turning a string into an expression
rather than a variable. At any rate, thanks for the pointer. I sure I would
benefit from rereading the FAQ on a monthly basis, until I actually know
most of what is in it.

As to your question about my question, I’ve wanted to do this exact thing
several times in different contexts. However, you are quite correct that I
am struggling with this problem in a particular context.  I have of a large,
multi-dimensional object containing count data. Currently this object is
implemented as a 26 dimensional (and growing) array with two to thirteen
dimnames per dimension, though I am thinking of switching it to a data frame
with dimensions as factors and dimname-equivilent factor levels.

I need to take a lot of complicated partitions of this object, mainly,
though not always, summing to the entire object. Most of the partitions are
subsets of --

– OK, now I have to digress to address a terminological uncertainty. Think
of a 4X4X4 cube. It has three dimensions, and each dimension has four of
what?  I’m going to call them levels right now, though I don’t think that is
right -- it would be confusing if there were factors in the picture. Also,
the dimnames do not name the dimensions, but the thing I am calling levels,
which is also confusing. --

Anyway, most of the partitions consist of two to four dimensions out of 24,
but sometimes with some levels omitted or summed, and occasionally the
partitions that are much more complicated (to deal with censored data,
mainly). I have to use each partition multiple times, doing a very different
thing each time (and then repeat the whole set many times) The next 4
paragraphs describe what I am actually doing with the partitions, but you
can skip over them and cut to the chase if you are not so interested.

I am summing over the dimensions in each partition, dividing a table of
“forcing totals” for that partition by those sums (element by element), and
then taking the resulting ratios and multiplying each of the terms in the
original, non-summed object by the corresponding ratio. 

This is easiest to understand by analogy to the two-dimensional case. You
take the row sums and divide them element by element by a vector of
pre-determined row “forcing totals,” to get a vector of forcing ratios. Then
you multiply each row by the corresponding forcing ratio, so that the row
sum will then match the forcing total. Then you do the same thing with the
columns. Repeat, alternating row and columns, to convergence. Each column
has a corresponding column forcing total, and each row has a corresponding
row forcing total. The elements of the matrix have two partitions that we
use, one into rows, and the other into columns.  This is sometimes called
RAS balancing, or biproportional matrix adjustment. It is an algorithm that
is used a lot to update big matrices in national income accounting and
input-output analysis.  

What I am doing is the same, but I have forcing totals in two to four
dimensional tables instead of a one dimensional vectors.  Each partition
divides the array into groups of elements that I want to sum to my forcing
totals. Again, you go around in a circle, doing forcing with each of the
(currently 18) tables, to convergence. On count data it should always
converge.

The thing is, I need to keep track of all these partitions, and then
multiply the forcing totals by the exact same elements of the array as I
previously summed.  I got up to five dimensions, coding by hand, and then
realized that 1: the amount of work in going from, e.g., 19 dimensions to 20
was going to very great, and 2. the likelihood that I would get all the
nesting and partition-matching right was vanishingly small. 

So I am looking for a way to encode the partitions that I use, that would
allow me to use the same encoding to represent both the subsets of the array
to sum over, crunching the array down to a set of totals corresponding to my
forcing totals, and also defining the subsets of the array that should be
multiplied by each forcing ratio.  And I thought, maybe I could do it with
strings of indexing commands, one per table of forcing totals. But this will
only work If I can sum the array over the subdivisions that the partition
defines, multiply all the elements in partition subdivisions by the
corresponding constants, and then assign the results back to the array, or
to a new array. Hence my question. 

I’m afraid that this explanation is too long for people to read, but hope
springs eternal.  I’d be remarkably pleased and eternally grateful if I got
a solution to the problem of keeping track of partitions that can be used in
the three ways described in the previous paragraph, even if it has nothing
to do with executing strings.

Warmest regards, 
andrewH




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