HDTenEightyP/NetNews huggingface dataset:
From: schultz@halley.est.3m.com (John C. Schultz)
Subject: Re: 100 digit integer division?
In-reply-to: jonathan@chpc.utexas.edu's message of Wed, 26 Aug 92 23:14:35 GMT
Organization: 3M Company, 3M Center, Minnesota, USA
	<1992Aug26.231435.5785@chpc.utexas.edu>
Date: Sat, 29 Aug 92 19:14:46 GMT

In article <1992Aug26.231435.5785@chpc.utexas.edu> jonathan@chpc.utexas.edu (Jonathan Thornburg) writes:
   ...
   Any decent symbolic algebra system should be able to do this.
   For example:

   % maple
       |\^/|      MAPLE V
   ._|\|   |/|_.  Copyright (c) 1981-1990 by the University of Waterloo.
    \  MAPLE  /   All rights reserved.  MAPLE is a registered trademark of
    <____ ____>   Waterloo Maple Software.
	 |        Type ? for help.
   ...

Is maple free? anon ftp sites?  All I could find asking ARCHIE was
maple DOS demo programs.

Also, not to start a flame war, but why use MAPLE V vs Mathematica if
they both cost money.  Mathematica seems to be the most widely used
from my viewpoint in a hole :-).

--
   John C. Schultz   +1 (612) 733-4047   schultz@halley.serc.3m.com
   How to include the taste of Glendronach in a multi-media system?
Organization: Penn State University
Date: Thu, 3 Sep 1992 09:18:26 EDT
From: Jack W. Sharer <J0S@psuvm.psu.edu>
Newsgroups: sci.math.num-analysis
Subject: Oscillatory Integration?

I'm having to evaluate this integral:

          /\ 0.5
         /           N
        /      f(x) D (2 pi x + phi) dx
       /
     \/ -0.5

                       N
for N ~ 500 and where D (x) is the N-point Dirichlet kernel:


               iNx
       N      e    - 1
      D (x) = --------,  i = sqrt(-1)   (highly oscilatory for large N)
                ix
               e  - 1

I'm successfully using a 2000-point Simpson integration, but I cannot
begin to evaluate all the needed cases (limited by computer resources).

Could you suggest a change of variable or another technique which
would dramatically improve the integration speed?

Thanks, Jack Sharer, Penn State, j0s@psuvm.psu.edu
From: hrubin@pop.stat.purdue.edu (Herman Rubin)
Newsgroups: sci.math.num-analysis
Subject: Re: Integration of Step function algorithm/code any?
Date: 28 Aug 92 19:59:31 GMT
Organization: Purdue University Statistics Department

In article <1992Aug28.011918.22579@harlow.harvard.edu> job@head-cfa.harvard.edu (Jeffrey Oliver Breen) writes:
>In article <1992Aug14.040957.16304@Princeton.EDU> muyu@burn.Princeton.EDU (Muyu Guo) writes:
>>I am having trouble doing the integral using either qtrap
>>or qsimp from Numerical Recipes:

>>    b
>>    /
>>    | f(x)dx,      	with a < 1, b > 2
>>    /
>>    a
>>   			and f(x) = 1 (1 <= x <= 2)
>>				 = 0  otherwise

>>For example a=0, b=4 or the like the results were nonsense.

>>Does anyone know if there is a good way to get thru this?
>>Thanks a million for your attention.

>Since f(x) will be one from x=1 to x=2, and this range is included by
>the a<1 and b>2 guarantee, and the function is zero everywhere else,
>then the integral just becomes:

>  2
> /
> | 1 dx, otherwise known as 1.  Is there a reason you were trying to
> /
> 1

>solve this numerically?

THIS function can be done that way, but what if things are more complicated?
It is not too difficult to handle discontinuous functions, or functions with
discontinuous derivatives, if one knows where the discontinuities are, and
the programmer breaks up the range.  For infinities, the problem is worse,
and for unknown discontinuities, still worse.  

Some integrators will attempt to handle this, but most assume that the 
function is sufficiently smooth that this problem does not arise.

-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)
Newsgroups: sci.math.num-analysis
From: mcgrant@rascals.stanford.edu (Michael C. Grant)
Subject: Re: Advice wanted for using C++ in Numerical Analysis
Organization: Information Systems Laboratory, Stanford University
Date: 26 Aug 92 11:29:31

In article <BtKpKz.M3F@netnews.jhuapl.edu>
pwm@netnews.jhuapl.edu (Miller Phil F1E x8335 ) writes:

    Also I would like some advice on the best way to learn
   C++ and object oriented programming with numerical
   simulation in mind.

I see that other posters have recommended books for learning C++, so I
won't repeat them here.

I wanted to tell you, however, that I've been using C++ to design an
object-oriented approach to constrained optimziation and it's been working
beautifully. I can write a class to exploit the special structure of a
particular constraint function, and my optimization engine doesn't have to
change one bit, because the internal stucture of the constraint is hidden
from it. On the other hand, I can write different classes to exploit
different optimization techniques, and similarly the constraint code does
not need to change.

My code is extremely modular, easy to maintain, and optimized for speed
all at the same time (if I do say so myself :-)

Of course, object-oriented programming is not a complete solution to
numerical programming. As a matter of fact, I use the FORTRAN LAPACK
functions for my matrix algebra, because it suits my particular
application. There are some excellent matrix classes out there, though, as
others have recommended. I have tried out M++ from Dyad, for example, and
it's quite nice.

Mike
From: job@head-cfa.harvard.edu (Jeffrey Oliver Breen)
Newsgroups: sci.math.num-analysis
Subject: Re: Integration of Step function algorithm/code any?
Summary: The answer is 1!
Date: 28 Aug 92 01:19:18 GMT
Organization: Smithsonian Astrophysical Observatory, Cambridge, MA,  USA

In article <1992Aug14.040957.16304@Princeton.EDU> muyu@burn.Princeton.EDU (Muyu Guo) writes:
>I am having trouble doing the integral using either qtrap
>or qsimp from Numerical Recipes:
>
>    b
>    /
>    | f(x)dx,      	with a < 1, b > 2
>    /
>    a
>   			and f(x) = 1 (1 <= x <= 2)
>				 = 0  otherwise
>
>For example a=0, b=4 or the like the results were nonsense.
>
>Does anyone know if there is a good way to get thru this?
>Thanks a million for your attention.

Since f(x) will be one from x=1 to x=2, and this range is included by
the a<1 and b>2 guarantee, and the function is zero everywhere else,
then the integral just becomes:

  2
 /
 | 1 dx, otherwise known as 1.  Is there a reason you were trying to
 /
 1

solve this numerically?
-- 
+-----------
| Jeffrey Oliver Breen   Harvard-Smithsonian Center for Astrophysics,
| (617) 495-7252         60 Garden St., Room B-340, MS 6, Cambridge, MA  02138
|
Xref: sparky sci.math.num-analysis:2533 sci.math.stat:1751
From: hougen@uirvlh.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math.num-analysis,sci.math.stat
Subject: Least Squares with Inequality Constraints?
Keywords: least squares, inequality constraints
Date: 25 Aug 92 18:03:43 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: uirvlh.csl.uiuc.edu

I would like to find some code, preferably free and preferably in C,
that solves the general problem of linear least squares with
linear inequality constraints.  

I would also like to find a version of the conjugate gradient
algorithm that incorporates linear inequality constraints.

Actually, I really only need to be able to tell the program that some,
but not all, of the variables are constrained to be positive.

Is such code available?  I will post a summary of packages available,
if any.

Thanks in advance.

Darrell
Newsgroups: sci.math.num-analysis
From: uchpcjv@Msu.oscs.montana.edu
Subject: Re: predictor corrector methods for ODE's
Reply-To: uchpcjv@Msu.oscs.montana.edu
Organization: Montana State University
Date: Fri, 28 Aug 1992 11:44:10 GMT

]In article <1992Aug27.090322.8532@vax.oxford.ac.uk>, nagrwb@vax.oxford.ac.uk writes:
>In article <26AUG199218380252@robin.rp.csiro.au>, awhichel@robin.rp.csiro.au (Adrian Whichello) writes:
>> Dear Netters
>> 
>> 	I just read in Numerical Recipes that predictor-corrector methods for
>> solving initial value ODE's are dead, or at least on their way out. This
>> strikes me as rather strong, but I would like some other opinions. What do you
>> think? 
>> 					Adrian P. Whichello
OPINION.  IMHO, Milne method is conceputally quite useful.  It is practically
useless.  Okay.
Newsgroups: sci.math.num-analysis
From: emc@doe.carleton.ca (Eli Chiprout)
Subject: "Super (?)" Generalized Eigenvalues
Organization: Dept. of Electronics, Carleton University
Date: Fri, 28 Aug 1992 13:35:58 GMT

The eigenvalue problem is the solution to s in
det|sI-A|=0 where A is a matrix and I is the identity matrix.

The generalized eigenvalue problem is the solution to s in
det|sA+B| where A,B are matrices.

What is the name of the general problem

det|F(s)|=0 where F(s) is a matrix function of s?
Are there any known algorithms for solving this problem
partially or fully?  Any references?

I could find nothing in my extensive library search.
Some have tried to solve the problem
det|A+sB+(s^2)B|=0 but not the general problem mentioned.


--
Eli Chiprout
Dept. of Electronics, Carleton University
Ottawa, Ontario, Canada
emc@doe.carleton.ca
From: chr09tk@vmsa.technion.ac.il
Newsgroups: sci.math.num-analysis
Subject: A Tailor's Problem
Date: 1 Sep 92 17:07:30 GMT
Organization: Technion, Israel Institute of Technology

Hello!

I would be grateful for any refferences concerning the following problem:

We are given a roll of cloth of a given width and unlimited length. We are also
given a finite set of polygons (pieces of clothing). We want to cut out the
polygons using a minimal length of the cloth. Devise an algorithm that will get
us as close as possible to the minimum (within reasonable time). 

Thanks in advance,
Haggai Katriel
From: smith@minerva.harvard.edu (Steven Smith)
Newsgroups: sci.math.num-analysis
Subject: Re: Roots of equations Was: Newton Raphsons iteration method
Date: 3 Sep 92 15:49:11 GMT
Article-I.D.: minerva.SMITH.92Sep3104911
	<SMITH.92Sep1154327@minerva.harvard.edu>
	<alex.715433129@pv3448.vincent.iastate.edu>
	<SMITH.92Sep2103757@minerva.harvard.edu>
	<alex.715525035@pv3448.vincent.iastate.edu>
Organization: Harvard Robotics Lab, Harvard University

alex@iastate.edu (Roger Alexander) writes:

> >			[...]  The example x -> sin x works too.
> 
> This function is not an example because the derivative has a zero.

I don't understand what you mean.  The zero set of sin x is the
integers multiplied by pi.  The derivative of sin x at these points is
+- unity.  Newton's method works like a dream this instance.

Steven Smith
From: takriti@engin.umich.edu (samer Takriti)
Newsgroups: sci.math.num-analysis
Subject: Re: REQUEST: constrained optimization of positive definite quadratic form
Date: 1 Sep 92 14:11:52 GMT
Organization: University of Michigan Engineering, Ann Arbor

In article <BtvrIE.IB8@research.canon.oz.au> enzo@research.canon.oz.au (Enzo Liguori) writes:
>I'd like suggestions on how to minimize a positive definite quadratic form with
>the variable constrained to be within an interval like:
>A<=Xi<=B
>with A,B constants and Xi any variable of the quadratic form.
>If there's a faster algorithm that works with simpler constraints like:
>Xi<=0
>Xj>=0
>Xk unconstrained
>that'll probably do.
>Thanks in advance.
>
>        Enzo
>
>Enzo Liguori - Canon Information Systems Research Australia

This problem is well known and has a systematic method for solving it.
The more general problem can also be solved (i.e., linear constraints
on the variable: a11x1+a12x2+...= b1 and so on).
You can refer to any non-linear programming book and look under "quadratic
programming". There is a book by K. G. Murty, "Linear complementarity, 
linear and nonlinear programming". Another book is "Nonlinear Programming
theory and algorithms" by Bazraa and Shetty.
By the way if the problem is uconstrained, write the system in the form
X^t.Q.X (t indicates transpose), then solve the system of equatios, 
Q.x = 0 ==> x=0 as a unique solution since Q is positive definite.
-Samer
.
From: bardo@ief-paris-sud.fr (Bardo Muller)
Newsgroups: sci.math.num-analysis
Subject: Large Sparce Positive Definite Systems
Keywords: Large Sparce Positive Definite
Date: 2 Sep 92 14:46:35 GMT
Reply-To: bardo@ief-paris-sud.fr
Followup-To: sci.math.num-analysis
Organization: Universite de Paris

Dear newsgroup,

I'm looking for the source code described in 

J. A. George and J. W. H. Liu "Computer Solution of Large
Sparce Positive Definite Systems", Prentice Hall.

Code and/or authors e-mail adress welcome.

Thank you

Bardo

___________________________________________________________________________
| Bardo MULLER                          | phone  : [33] [1] 69 41 78 50    |
| Institut d'Electronique Fondamentale  | fax    : [33] [1] 60 19 25 93    |
| Bat. 220 Universite Paris Sud         | e-mail : bardo@ief-paris-sud.fr  |
| 91405 ORSAY CEDEX FRANCE              |             THE NET WORKS !      |
|_______________________________________|__________________________________|
From: jtien@venice.eng.uci.edu (Joe Tien)
Subject: CFD info
Newsgroups: sci.math.num-analysis
Reply-To: jtien@venice.eng.uci.edu (Joe Tien)
Organization: University of California, Irvine
Date: 3 Sep 92 20:09:04 GMT


Hi,

If this is not the right place for this question, sorry, and please point me
to the right one.

Does anybody know where I can get info on some Computational Fluid Dynamics
benchmark programs? (Things like: the equations it implements and the types of
inputs and outputs). 

The programs I am looking at are: unriem.xx, crale.xx, line.xx and nav.70xx

Please email me at jtien@balboa.eng.uci.edu

Thanks,

Joe Tien
From: smith@minerva.harvard.edu (Steven Smith)
Newsgroups: sci.math.num-analysis
Subject: Re: Roots of equations Was: Newton Raphsons iteration method
Date: 2 Sep 92 15:37:57 GMT
Article-I.D.: minerva.SMITH.92Sep2103757
	<SMITH.92Sep1154327@minerva.harvard.edu>
	<alex.715433129@pv3448.vincent.iastate.edu>
Organization: Harvard Robotics Lab, Harvard University

alex@iastate.edu (Roger Alexander) writes:

>          Not so.  The solutions of the equation are isolated (implicit
> function theorem) but there may be infinitely many.  Let
>
>          g(x,y) = (exp(x)cos(y)-1, exp(x) sin(y)).
>
> Then det g' = exp(2x) != 0 anywhere, but g(0,2*Pi*n) = 0 for every
> integer n.

Yes, I posted before I thought.  The example x -> sin x works too.
The zero set of an analytic function !==0 is at most countable.

Steven Smith
Newsgroups: sci.math.num-analysis
From: iwelch@agsm.ucla.edu (Ivo Welch)
Subject: Re: REQUEST: constrained optimization of positive definite quadratic form
Organization: UCLA, Anderson Graduate School Of Management
Date: 2 Sep 92 15:50:39 PDT

Could someone please post code which solves this quadratic programming
problem, or refer me to a free  source of such code?

Preference: C++, C, Fortran (in descending order).

Thanks.

/ivo welch
Newsgroups: sci.math.num-analysis
From: awhichel@robin.rp.csiro.au (Adrian Whichello)
Subject: Predictor-Corrector methods for ODE's - are they dead?
News-Software: VAX/VMS VNEWS 1.41    
Keywords:  ODE
Organization: CSIRO Division of Radiophysics/Australia Telescope National Faci
Date: Thu, 27 Aug 1992 08:37:00 GMT

Dear Netters,
	I read in Numerical Recipes that Predictor-Corrector methods for 
initial value ODE's are dead, or on their way out. This strikes me as rather 
strong, so I'm looking for other opinions: what do you think?
							Adrian Whichello.
From: mjfrisch vx.cis.umn.edu (Michael J. Frisch, CIS 612/625-5830)
Newsgroups: sci.math.num-analysis
Subject: Location of Archive for this News Group
Date: 28 Aug 92 19:43:00 GMT
Organization: University of Minnesota CIS
News-Software: VAX/VMS VNEWS 1.41

Due to my vacation and our two-week limit on News Group messages, I missed
messages sent from Aug. 3 - Aug. 10.  I used archie to check for archive sites
but they all seem to be Frequently Asked Questions.  Can someone send me the
messages from that period or tell me where I can get them?  Thanks very much.
From: jonathan@chpc.utexas.edu (Jonathan Thornburg)
Newsgroups: sci.math.num-analysis
Subject: Re: predictor corrector methods for ODE's
Summary: PC methods are *not* obselete, many *excellent* codes use them
Keywords: predictor corrector ODE integrate LSODE Hindmarsh DE/STEP Shampine Gordon
Date: 26 Aug 92 18:42:46 GMT
Organization: U of Texas at Austin / Physics Dept / Center for Relativity

In article <26AUG199218380252@robin.rp.csiro.au>
awhichel@robin.rp.csiro.au (Adrian Whichello) writes:
>	I just read in Numerical Recipes that predictor-corrector methods for
>solving initial value ODE's are dead, or at least on their way out. This
>strikes me as rather strong, but I would like some other opinions. What do you
>think? 

Numerical Recipes is (very) wrong here.  Predictor-Corrector (PC)
methods for non-stiff initial value ODE integration are alive and
well.  ODE experts (which I'm not) recommend them as being robust
and efficient for a wide range of problems.  See, for example, the
review and discussion in:
\mybibitem{Gear, C. W.}{1981}
        ``Numerical Solution of Ordinary Differential Equations:
          Is There Anything Left to Do?''
        SIAM Review {\bf 23}(1), 10--24.

Indeed, of the current high quality "black box" ODE codes, a large
fraction use PC methods.  Notable examples include Hindmarsh's LSODE
suite, and the Shampine & Gordon DE/STEP package.

PC methods are also "culturally similar" to the backwards
differentiation multistep methods which seem to be the current
favorites for stiff ODEs, which makes it easier to combine both in
a single general purpose code or code suite.  (For example, LSODE
does this.)

- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}
From: jtien@venice.eng.uci.edu (Joe Tien)
Subject: need math functions
Newsgroups: sci.math.num-analysis
Reply-To: jtien@venice.eng.uci.edu (Joe Tien)
Organization: University of California, Irvine
Date: 3 Sep 92 20:05:04 GMT


Hello everyone,

Does anybody know where I can get the software for computing math functions
such as bessel, erf, and matrix inversions. FTP sites would be okay too. 

Please send email to jtien@balboa.eng.uci.edu.

Thanks much,

Joe Tien

Xref: sparky sci.math.num-analysis:2604 comp.lang.fortran:3321
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math.num-analysis,comp.lang.fortran
Subject: Re: The importance of high-performance computing
Date: 31 Aug 92 01:04:42 GMT
Followup-To: sci.math.num-analysis
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <l9p02vINNorv@almaak.usc.edu> ajayshah@almaak.usc.edu (Ajay Shah) writes:
>... I know
>exactly one person who uses parallel hardware.  Every single person I
>know who does scientific computation uses single-CPUs.

This just means you don't know people with big enough problems.

>Parallel hardware is obviously a way to get revolutionary gains in
>compute power, but Bill Joy's law suggests that single CPUs will give
>tremendous gains without paying any software irritations (they
>certainly have done great in the last five years).

There is a limit. Have you noticed that all the screaming "uniprocessors" are
going superscalar? SPARCs are already starting down the multiprocessing road.

Now I'm not trying to tell you that most scientific computing is parallel, or
anything similarly off-planet. But don't think that parallel computing is
going to go away anytime soon. Eventually, you hit the Boltzmann limit and then
the _only_ performance gain is parallelization. Your enthusiasm for single
CPU performance gains just means that you'll hit this wall sooner, rather than
later.
>
> I suspect most
>scientific computation out there does not know or care about parallel
>hardware.

You aren't talking about the major leaguers here, are you? In my experience,
places with graduate programs specializing in scientific computation are also
hotbeds of parallelization research and cross-fertilization.

Later,
Andrew Mullhaupt
Newsgroups: sci.math.num-analysis
From: alex@iastate.edu (Roger Alexander)
Subject: Re: Roots of equations Was: Newton Raphsons iteration method
Organization: Iowa State University, Ames IA
Date: Thu, 3 Sep 1992 12:57:15 GMT

In <SMITH.92Sep2103757@minerva.harvard.edu> smith@minerva.harvard.edu (Steven Smith) writes:

>alex@iastate.edu (Roger Alexander) writes:

>>          Not so.  The solutions of the equation are isolated (implicit
>> function theorem) but there may be infinitely many.  Let
>>
>>          g(x,y) = (exp(x)cos(y)-1, exp(x) sin(y)).
>>
>> Then det g' = exp(2x) != 0 anywhere, but g(0,2*Pi*n) = 0 for every
>> integer n.

>			[...]  The example x -> sin x works too.

This function is not an example because the derivative has a zero.
-- 
*_________________*  "Faculty members encourage the free pursuit of       
 Roger Alexander  | learning in their students and protect academic          
 alex@iastate.edu | freedom of students." --ISU Faculty Handbook
*_________________* [official statement of policies & procedures]
Newsgroups: sci.math.num-analysis
From: rairan@ecf.toronto.edu (RAI Ranjan)
Subject: Re: *moan*beg*: HELP : sob,snif "forlorn looks", much suffering....
Keywords: COMMUNICATION BREAKDOWN ...
Organization: University of Toronto, Engineering Computing Facility
Distribution: usa
Date: Mon, 24 Aug 1992 03:49:10 GMT

In article <1992Aug23.113011.816@ecst.csuchico.edu> madams@ecst.csuchico.edu (Michael E. Adams) writes:
>Given:  p, n, b, & f = 0;  How do you solve for 'i'?
>
>                            -n                       -n
>     100 p  1 - (1 + i/100)^   +  b = -f (1 + i/100)^
>            ---------------
>                   i


   To all the guys who responded to this original posting:  Mike DIDN'T mean
 p = n = b = f = 0.  Only f = 0.  You would think the guy from Stanford would
 have figured that out :)  

   Anyway, there is no general `formula' for `i' in terms of the other 
 quantities, but you can make some considerable simplifications to the given
 equation: 
                                        -n                   
                        1 - (1 + i/100)^               
                   100p ---------------    + b = 0  
                              i
   let y = 1 + i/100 and after some manipulation you get the much nicer eqn.
           (b/p)*y^(n+1) + (1-b/p)*y^(n) = 1, which is a polynomial.

   Now use whatever root-finding code you may have (remember i !=0 ).

-- 
---
Ranjan Rai                             <rairan@ecf.toronto.edu> 
Engineering Science 9T3                <rairan@eecg.toronto.edu>
University of Toronto                      
Newsgroups: sci.math.num-analysis
From: tab@piis10.joanneum.ac.at (Behnam TABATABAI)
Subject: Bug in Numerical Recipes? (ludcmp)
Organization: Joanneum Research, Graz, Austria
X-Newsreader: Tin 1.1 PL5
Date: Mon, 31 Aug 92 12:51:42 GMT

Hi!

It seems that the function `ludcmp' for LU-decomposition does not work
well. After decomposition of a matrix in the form
  ( 0   0   2 )
  | 0   3   0 |
  ( 1   0   0 )
the content of the indx-vector is (3,2,3) instead of (3,2,1). The following
is the code for this example:

#include <stdio.h>
main()
{
  float **a, d;
  int n, *indx;

  extern float **matrix();
  extern int   *ivector();
  extern void  ludcmp();

  a = matrix( 1, 3, 1, 3 );
  indx = ivector( 1, 3 );

  a[1][1] = 0.0; a[1][2] = 0.0; a[1][3] = 2.0;
  a[2][1] = 0.0; a[2][2] = 3.0; a[2][3] = 0.0;
  a[3][1] = 1.0; a[3][2] = 0.0; a[3][3] = 0.0;

  ludcmp( a, 3, indx, &d );
  for ( n = 1; n <= 3;  n++ ) printf( "indx[%d] = %d\n", n, indx[n] );
}

Do I make a mistake? Does anybody has an idea?
Thanks in advance!
Behnam
--
Behnam Tabatabai,                 | e-mail: tab@piis10.joanneum.ac.at
Joanneum Research, Graz, Austria  |         tabatabai@joanneum.ada.at
Newsgroups: sci.math.num-analysis