# AN ENROLMENT PROJECTION PROBLEM

Sun Jun 29 17:51:48 CEST 2003

```Ajith Prasad wrote:
> I would appreciate advice on how best to formulate the following
> problem in Python. I have originally posted the problem to the J
> Programming forum and received a one-line formulation ((#s)
> (|.s)&(+/@:*)\ I)! I was wondering what the equivalent Python
> formulation would be.

Wow! that one line formulation is dense.
Why do you *want* a compact answer?
I'm curious, if you put it down, do you have problems undestanding the
above program in a weeks time?
Or in a days time?

>
> The Problem:
>
> The enrolment E(n) of an institution at the beginning of year n is the
> sum of the intake for year n, I(n), and the survivors from the intakes
> of previous r years. Thus, if s(1) is the 1-year intake survival rate,
> s(2) is the 2-year survival rate, etc, we have:
>
> E(n)= I(n)+I(n-1)*s(1)+ I(n-2)*s(2)+...+I(n-r)*s(r)
> E(n+1)= I(n+1)+I(n)*s(1)+I(n-1)*s(2)+... +I(n-r-1)*s(r)
> .
> .
> .
> E(n+k)= I(n+k)+I(n+k-1)*s(1)+I(n+k-2)*s(2)+...+I(n+k-r)*s(r)
>
> Given:
> (a) the actual intakes for the current and previous r years, I(n),
> I(n-1),I(n-2),..,I(n-r), and the planned intakes for the next n+k
> years: I(n+1), I(n+2),..., I(n+k), we have the intake vector I =
> (I(n-r), I(n-r-1),...,I(n),I(n+1),..., I(n+k)); and
> (b) the survival rate vector, s = (1,s(1), s(2),...,s(r))
> Find:
> The  k*1 enrolment projection column vector, E =
> (E(n+1),E(n+2),...,E(n+k)) in terms of a k*(r+1) matrix P (derived
> from
> I) and the (r+1)*1 column vector, s.
>
> I = P*s
>
> Is there a compact Python representation of the relevant matrix P
> where:
>
> P = [I(n+1) I(n) I(n-1).. . I(n-r)
>      I(n+2) I(n+1) I(n)...  I(n-r-1)
>      .
>      .
>      I(n+k) I(n+k-1) I(n+k-2)... I(n+k-r)]
>
> Alternatively, a non-matrix formulation of the problem would be
> acceptable. Thanks in advance for any suggestions on how to proceeed.

```