On Sep 24, 2010, at 9:20 AM, Nicholas Kinar wrote:
> Hello,
>
> Suppose that I have an expression such as the one given below:
>
> M = Indexed('M')
> var('A B C')
> i,j,n = symbols('i j n', integer = True)
>
> expr = A*M(1,2)**n + B*M(-2,1)**n + C*M(-1,-1)**n
>
> Is there a way to iterate through this expression and apply the following
> sequence of operations?
>
> (1) In each term, take the indexed variable M(i,j) and replace it with
> another variable in M_i_j_n format. Thus, for expr given above,
>
> ( M(1,2)**n ) in the first term would be replaced with another non-indexed
> variable M_1_2_n
> ( M(-2,1)**n) in the second term would be replaced with another non-indexed
> variable M_neg2_1_n
> ( M(-1,-1)**n) in the third term would be replaced with another non-indexed
> variable M_neg1_neg1_n
>
There's no need to iterate through the expression to do this. Just use subs,
i.e., expr.subs({M(1, 2)**n: Symbol('M_1_2_n'), M(-2, 1)**n:
Symbol('M_neg2_1_n'), …})
Of course, if you want to generate the Symbols automatically, that would
require you to be a little more clever.
> (2) For every replacement, a list (or similar data structure) is created with
> the names of the variables [M_1_2_n, M_neg2_1_n, M_neg1_neg1_n]. The list
> contains the names of unique variables, such that if the variable name is
> already in the list, it is not added. Is it possible to make this a list of
> strings?
So it sounds like that is what you want to do. I guess you need to combine the
expr.atoms(IndexedElement) with str() or .args and some regular expression
replacement. Something like '_'.join([str(t) for t in
index.args]).replace('-', 'neg'), where index is a M(1, 2, …) element (again a
very GOOD reason to make n an element of M and not an exponent; it is much
easier to code that way.
>
> The following sequence of operations can be used to convert an expression
> with indexed elements into a format where the ccode() function can then be
> used to output the expression in C/C++ form.
>
> Nicholas
Hmm. To me, it seems like ccode() should be able to do this on its own. Maybe
you could submit it as a patch to ccode(). Or maybe it really can and neither
of us know about it. Øyvind (or anyone)?
Aaron Meurer
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