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Speeding up Replacement Rules

• To: mathgroup at smc.vnet.net
• Subject: [mg24527] Speeding up Replacement Rules
• From: "Johannes Ludsteck" <ludsteck at zew.de>
• Date: Mon, 24 Jul 2000 03:04:08 -0400 (EDT)
• Organization: Zentr. f. Europ. Wirtschaftsforsch
• Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup Members,
I use Mathematica to compute the hessian of a complicated 
function of a vector of about 50 variables. My problem with the job 
is that I need the mean of the hessian for about 50000 sets of 
vector values.

Of course, it is simpe to compute a symbolic expression of the 
hessian in two steps:
g=Map[D[f[args],#]&,args];
h=Map[D[g,#]&,args];
and to use this to compute the mean by defining a list of 500000 
replacement rules, and to replace the stuff with
(Plus@@(h/.rules))/50000;

This works fine but very sloooooooow. Since I have to redo the 
computation of the mean some hundred times, I nead a drastic 
gain in speed. I think that the main reason for the poor performance 
of my strategy is that the replacement operation is slow. I think it 
should be possible to generate a Compiled function object which is 
much faster. Since I expect that this will require some time, I would 
like to know whether the increase in speed will compensate me for 
the pains of the implementation.
Of course, if someone has Mathematica code which takes a vector 
valued function and generates a Compiled gradient or hessian 
function, I will accept it gratefully.
The simple advice to compute the hessian by hand and to put this 
in a Compiled function is worthless for me, since I have to apply 
the mean hessian computation to a variety of different functions.


Thank you,
	Johannes Ludsteck



Johannes Ludsteck
Centre for European Economic Research (ZEW)
Department of Labour Economics,
Human Resources and Social Policy
Phone (+49)(0)621/1235-157
Fax (+49)(0)621/1235-225

P.O.Box 103443
D-68034 Mannheim
GERMANY

Email: ludsteck at zew.de