This is a small perl script for transforming lanhep/calchep files to increase
performance by substituting excessively long "Lorentz" parts in lgrng.mdl
files with placeholders and evaluating these parts in func.mdl instead.
The way this script works is fairly simple:
- Lines are read in from the lgrng.mdl file.
- The lines are passed to Mathematica for collation and extraction of terms
proportional to (real,imaginary)x(scalar,G5,G(3),p_mu,m_i).
- A placeholder for each of these collections of terms in the form of A01,
B01 etc is made, where the numeral corresponds to the original line in the
lgrng.mdl file.
- The long expression in the lgrng.mdl file is replaced by, e.g., A01+B01*i
- The func.mdl file is expanded to include the placeholders and the long
expressions they stand for.
- In lines proportional to only a single Lorentz factor the placeholder A##
is moved into the "Factor" part of lgrng.mdl
The reason for doing this is that objects in func.mdl are evaluated only once
and the ensuing simplification in the calculation of the amplitudes from
the vertices in lgrng.mdl speeds up the overall calculation of more complex
models significantly.
The formatting required by the func.mdl file places some restrictions on this
operation:
1) The "Expression" field is truncated at around 2000 characters. This may
be simply a convention which could be changed in the source code of
calchep. In any case we work around it by simply splitting up longer
substitutions.
2) The "Name" field is exactly 7 characters long. Using the file line number
and upper case letters to uniquely identify a substitution means that
we can only accomodate
- 999.999 lines at lengths < ~50000 characters (26*1950) or
- 99.999 lines at lengths < ~1.3M characters (26^2*1950)
Even if it were the case that these are not simply the result of a coding
convention in calchep, it does not seem likely for either of these limits to
apply.
In addition to the above "limitations" there are a couple of caveats:
1) This script uses Mathematica, so problems with incompatible versions
may appear. This script was developed and tested using Mathematica 7
but it should run on older versions since we are not doing anything
fancy.
2) If the lanhep/calchep files contain negative exponents e.g. X**-2 or X^-2
this script will malfunction. I may get around to fixing this but as it
is a very unlikely occurrence (X*Y**-2 is written as X/Y**2) the added
complexity is not worth it right now.
3) For some reason Mathematica in some instances leaves parentheses in place
after ComplexExpand. If these are in of form (X*Y*Z) they are removed,
but if they are of form (X+Y) this script will abort.
4) You can overwrite Your files with this script. Default behavior is to
avoid and always check, but for convenience if e.g. both input and output
files are given it is assumed that overwriting is intended.
Substitution of ** --> ^ is performed on the input lgrng.mdl file's Lorentz
part to avoid confusion with Mathematica's NonCommutativeMultiply. In fact,
by default, this script also parses all other parts of the lgrng and func
files and makes that substitution.
With respect to the coding: It is very easy to make perl code completely
unreadable, but faced with either learning pyhton or just commenting a lot
and trying to keep things simple, I chose the latter. If you want this script
without the metric ton of comments use perltidy --dsc or run something like
cat lag2func.pl | sed -E 's/[ ]+(\# |\(\*).+//g.
If You do release modified / new code based on this work I'd love know!
Needless to say, if you find bugs or think of specific improvements,
please don't hesitate to contact me.
++Timo Ruppell