HDTenEightyP/NetNews huggingface dataset:
From: wjh@cbnewsl.cb.att.com (william.j.hery)
Subject: ftp sites for floating point benchmark suites?
Organization: AT&T Bell Laboratories
Distribution: usa
Date: Thu, 17 Dec 1992 21:43:25 GMT
Followup-To: comp.arch
Keywords: linpack, livermore loops, specmarks

Can anyone point me to an ftp site where I can get the source code
for standard flaoting point benchmarks, like LINPACK, the Livermore
loops, SPECKmarks, etc.?

I will summarize any email responses I receive.

Thanks,

Bill Hery
AT&T Bell Labs
201-386-2362
hery@att.COM
Newsgroups: sci.math.num-analysis
From: a722756@roper.mc.ti.com (W. Donald Rolph)
Subject: RE: finite element limitations??
Originator: a722756@roper.mc.ti.com
Organization: Texas Instruments / Attleboro Mass / USA
Date: Wed, 16 Dec 1992 21:50:59 GMT


In article <1992Dec16.095858.5370@dutrun2.tudelft.nl>, rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
|> In article <1992Dec15.092610@roper.mc.ti.com> W. Donald Rolph:
|> > You are indeed confused.
|> 
|> I am never confused about these things.
|> 
|> >  Any approximation procedure must have trial functions.
|> 
|> No, no.
|> 
|> > In traditional FEA they are called shape functions, choose the name you like
|> > but all FEA procedures must have some approximating function over the domain
|> > space.
|> 
|> *All* procedures?
|> 
|> Gee, how then could I calculate the temperature distribution in a sodium pump
|> by an direct FE method, WITHOUT ever needing such "approximating functions"?
|> (An accompanying article is called "Multimode Heat Transfer in Sodium Pumps".
|> It is found in the Proceedings of the 0Xth Conference on Numerical Methods
|> in Thermal, or whatever, Problems, Swansea U.K., 197X. Look it up ;-)
|> 
|> I also did some work on pure advection without shape functions. But who am I?
|> There exists CFD code named "FLOTRAN", which has a "streamline upwind" scheme
|> in it, derived directly without shape functions. It's all in my SUNA articles.
|> 
|> And almost any Finite Element book starts with the assembly of resistor-like
|> elements, without approximations. The element-matrix of an electrical resistor
|> is derived directly by applying the laws of Ohm and Kirchhoff, giving:
|> 
|>          | +1/R  -1/R |
|>          | -1/R  +1/R |
|> 
|> Just define the connectivity (no coordinates) of your resistor-network,
|> two voltages as a boundary condition, and go ...
|> -- 
|> * Han de Bruijn; Applications&Graphics | "A little bit of Physics * No
|> * TUD Computing Centre; P.O. Box 354   | would be NO idleness in  * Oil
|> * 2600 AJ  Delft; The Netherlands.     | Mathematics" (HdB).      * for
|> * E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood

When you defined your resistor network you assumed a trial function which is
linear between the nodes.  You also incidentally also assumed triangular elements
if you applied this over 2D surfaces (I assume tetrahedrals over 3D but I haven't
worked that problem out.).  In short just because you chose lumped elements did
not remove you from choosing a trial function, it just hid the trial function
from your observations!  Good luck I enjoy talking with you!!
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263
From: holland@geop.ubc.ca (Stephen Holland)
Newsgroups: sci.math.num-analysis
Subject: Fitting multi-Gaussians
Followup-To: sci.math.num-analysis
Date: 14 Dec 1992 18:11:19 GMT
Organization: Geophysics & Astronomy, U.B.C. Vancouver, Canada
Distribution: world
Reply-To: holland@geop.ubc.ca
NNTP-Posting-Host: iridium.astro.ubc.ca

Thanks to everyone who replied to my post last week.  Sorry that I didn't
word it as clearly as I could have.  Your help is greatly
appreciated.

steve holland
From: pa@verano.sba.ca.us (Pierre Asselin)
Newsgroups: sci.math.num-analysis
Subject: Re: Restatement of the Integration Problem
Date: 11 Dec 92 05:55:46 GMT
Distribution: usa
Organization: None.  Santa Barbara, CA

In <1992Dec09.171136.118661@zeus.calpoly.edu>
	mjohnson@zeus.calpoly.edu (Mark S. Johnson) writes:

>You might try adaptive quadrature. In my experience, Romberg is faster
>than adaptive quadrature (can anyone else back this up?)[...]

Not me.  Besides, you can have it both ways.  I remember a subprogram by
Carl de Boor called CADRE, for Cautious ADaptive Romberg Extrapolation.
I think I saw it in a book titled "Mathematical Software" dating from
the *early seventies*.  This is not a cutting edge problem, folks!

The code performs a Romberg integration over the given interval while
monitoring the convergence.  If it fails to reach the theoretical rate,
it divides the interval in two and resumes recursively in each half
(hoping that one of the halves has some sort of singularity but the
other is clean).  It is very effective at isolating sharp peaks, jump
discontinuities and certain endpoint singularities.  I remember passing
it a wrapper that would plot its (x,y) values before returning the
function value (x supplied by CADRE, y returned by some ugly test
function).  The plots were always judiciously graded in the tight spots.

>Adaptive quadrature is best (or at least most easily) implemented as a
>recursive function, so FORTRAN is out. I'm told it CAN be done in
>FORTRAN, but it ain't pretty.

The code in question is in Fortran.
-- 

--Pierre Asselin, Santa Barbara, California
  pa@verano.sba.ca.us
Newsgroups: sci.math.num-analysis
From: a722756@roper.mc.ti.com (W. Donald Rolph)
Subject: Re: Comparison between FEM and FDM/CVM for fluid flow modeling
Originator: a722756@roper.mc.ti.com
Organization: Texas Instruments / Attleboro Mass / USA
Date: Tue, 15 Dec 1992 14:22:13 GMT


There  is, however, no requirement that either FVM or FEA to either be
conservative or nonconservative (Oden has some nice mathematics describing
requirments for conservation in FEA fluid mechanics).  The issue remains the
shape or approximation functions.  Chooses identical shape funcitons and FVM and
FEA are identical.  Choose  bad ones,  and both fail.


Fundamentally all numerical procedures for PDE approximation have a basic
underlying comonality:  minimizing error in the approxiamtion funcitons with
respect to the actual solution.  We realy need to get away from these parochial
battles over differences in what are in fact identical procedures.
-- 

Regards.
 
Don Rolph  a722756@pan.mc.ti.com WD3 MS10-13 (508)-699-1263
Newsgroups: sci.math.num-analysis
From: mgh@hobbes.phys.ucalgary.ca (Mike Henderson)
Subject: Nonlinear systems of equations
Date: Thu, 17 Dec 92 17:44:19 GMT
Organization: Institute for Space Research

I am trying to solve a set of 8 nonlinear equations in 8 unknowns.
I have tried the Newton-Raphson technique given in NR (I know
roughly what the solution should be) but havent had much luck. Are
there any more robust methods to choose from?

Mike Henderson
Dept. of Physics and Astronomy
University of Calgary
mgh@hobbes.phys.ucalgary.ca
Organization: Doctoral student, Mechanical Engineering, Carnegie Mellon, Pittsburgh, PA
Newsgroups: sci.math.num-analysis
Date: Sun, 13 Dec 1992 16:34:02 -0500 
From: "Anand V. Lakshmikumaran" <al2c+@andrew.cmu.edu>
Subject: Determinants

I am interested in an efficient routine to compute the determinant of a matrix
of size n (n < 100), when only one of the terms of the determinant has been 
changed; in terms of the determinant of the original matrix.

To make it more clear,

Step 1: I have this matrix G and i need to compute its determinant
once. (this is quite easy since there are canned routines for this)

Step 2: But then i just change only of its elements and compute its
determinant.
(Let G' be the new matrix)

Step 2 is repeated quite a few times and each time G' differs from G at
just a single
element. So does any of you know about any public domain routine which could
perform step 2 more efficiently than just by computing the determinant? (like
finding the determinant of G' in terms of determinant of G and the
changed element).

I looked into different techniques of evaluating the determinant. One
method was
to expand the determinant into a sum of n! terms and just grouping the
(n-1)! terms corresponding to the changed term. But my feeling was this would
be more time consuming than computing the determinant itself (which is of
order n**3 if LU factorisation is used). Correct me if i am wrong and 
is there any simpler technique to compute the determinant in such a case?

Thanks

Anand
From: frost@sdsc.edu (Richard Frost)
Newsgroups: sci.math.num-analysis
Subject: Re: Num Recipies Source
Date: 17 Dec 92 23:08:58 GMT
Article-I.D.: network.1gr1aaINNe1b
Reply-To: frost@sdsc.edu
Distribution: world
Organization: San Diego Supercomputer Center @UCSD.
NNTP-Posting-Host: stimpy.sdsc.edu


In article <Byou7o.q3@world.std.com>, jbk@world.std.com (Jeffrey B Kane) writes:
|> Does anyone know where (if anywhere) source code and eratas are posted for the
|> numerical recipies series of books?
|>       Jeffrey


Cambridge University Press
510 North Avenue
New Rochelle, NY 10801
Newsgroups: sci.math.num-analysis
From: Berni@nw42.wiwi.uni-bielefeld.de (B. Strohmeier)
Subject: complex QR-decomposition question
Date: Thu, 17 Dec 1992 17:22:52 GMT
Organization: Fakultaet fuer Wirtschaftswissenschaften, Uni Bielefeld, Germany

Hello, I have a simple question.

I want to calculate the QR-decomposition of a complex matrix with
only real and positive elements at the main diagonal.

Is this possible using the householder method?

Thanks in advance.

B.Strohmeier
email: bstrohm@erasmus.hrz.uni-bielefeld.de
From: xm9@sdcc12.ucsd.edu (richard g. adair)
Newsgroups: sci.math.num-analysis
Subject: Re: Band Matrix Multiplication
Keywords: Matrix Vector
Date: 16 Dec 92 06:24:00 GMT
Organization: University of California, San Diego

In article <1992Dec15.145457@is.morgan.com> robt@is.morgan.com (Rob Torop) writes:
>
>I have some code, the core of which is a loop that computes the transformation of a
>vector by a band matrix multiple times:
>
>	x <-- Bx    where  B  =    b c 0 . . . 0
>			           a b c . . . 0
>				   . . .
>		                   0 0 0 . a b c
>
>Right now, I'm basically doing the obvious thing, looping over the vector.  I have this nagging feeling that there is something brilliant and very different that can be done.  I'm running on Sun Sparcs (2 and 10), in case that makes a difference.  Any advice?
>
>
>-- Rob Torop

Yes, you're right about there being other ways to do this.  Your
banded matrix has special structure - it is a Toeplitz matrix, that
is, the diagonals have constant entries.  Multiplication of a vector
by a Toeplitz matrix can be done by convolution - consult Numerical
Recipes, for example, for an explanation of convolution.    However,
there is an even easier way in the case of your compact, tridiagonal
matrix.

Think of your matrix B as the sum aI(-) + bI + cI(+), where I is the
identity matrix, I(-) is a matrix of all ones along the first
sub-diagonal, and I(+) is all ones along the first super-diagonal.
The effect of multiplication by I(-) is to shift a vector forward by
one entry, with the first entry replaced by zero.  Thus,
I(-)*[1,2,3] = [0,1,2]; I intend my vector notation to denote a
column vector.  

Similarly, multiplication by I(+) shifts
the entries back one, replacing the last entry by zero: 
I(+)*[1,2,3]=[2,3,0].  I, of course, simply returns the orginal
vector.

If you put this all together, our example would be
	Bx = a*[0,1,2] + b*[1,2,3] + c*[2,3,0] 

The generalization to your problem is straightforward.  This is done
in 3*(n-1) + 1 flops, whereas general matrix-vector multiplication
requries n^2 flops, where n is the length of the vector. If your
matrix is Toeplitz, but more of the diagonals are filled out, you
can use Fast Fourier transforms to do the equivalent convolutions,
which could be done in order n*log2(n) operations.  In practice, the
speed of the FFT approach depends a lot on implementation details,
and so your effort wouldn't be repayed except at large n (~ 512 or
greater, in my experience).
intermdediate to . 
Newsgroups: sci.math.num-analysis,sci.math.stat,sci.math.symbolic
From: andersh@maths.lth.se (Anders Holtsberg)
Subject: Re: mathematica stepwise regression package
Keywords: mathematica stepwise regression
Organization: Lund Institute of Technology, Sweden
Date: Tue, 15 Dec 1992 08:32:58 GMT


gary mcclelland mcclella@yertle.colorado.edu:
>Stepwise regression is a tool of the devil. Anyone smart enough
>to be using Mathematica ought to be able to decide which
>questions he or she wants to ask of the data rather than letting
>a demonstrably suboptimal stepwise algorithm decide which
>questions to ask.  One day there may be good AI programs for
>doing statistical analysis, but stepwise regression won't be
>among them.

You mean what is bad? Let's say we want to make predictions.
Is the idea of using a subset of the predictors that is bad or
do you mean the stepwise way to pick them? If the latter: do
you know any better way (except trying all combinations)?

Anders Holtsberg
From: holland@geop.ubc.ca (Stephen Holland)
Newsgroups: sci.math.num-analysis
Subject: Fitting Multiple Gaussians
Date: 15 Dec 92 20:12:14 GMT
Reply-To: holland@geop.ubc.ca
Followup-To: sci.math.num-analysis
Organization: Geophysics & Astronomy, U.B.C. Vancouver, Canada
NNTP-Posting-Host: crisium.astro.ubc.ca

As requested here is a brief summary of the various replies
I received over the last week.

     ----------------

1) Suggested algorithms:
    -Simplex and Marquardt-Levenberg from Numerical Recipes, adpated to
     the problem at hand
    -Using a maximum liklihood method
    -A few people mailed me lists of source code avaliable from 
     various archives, NetLib, and where-ever.  Since many of these
     have been posted, or pointers to them posted, I won't repost them.

2) Several people said that this sort of fitting is sensitive to 
   the initial guesses at the parameters so their initial values
   and search regions should close to the "true" values.

3) Don't try to fit too many Gaussians to the data.

4) Subjective "chi-by-eye" type fitting is subjective.  Just because
   one fit "looks" better than another doesn't mean that it actually is
   better.  

     ------------------

Again, thanks to those who responded.

steve
From: frederik@pollux.acs.uci.edu (M. Donald Frederick)
Subject: Re: Request - Fast Exp/Log C routines
Newsgroups: sci.math.num-analysis
Reply-To: frederik@pollux.acs.uci.edu (M. Donald Frederick)
Organization: University of California, Irvine
Keywords: exp, log, fast, C
Date: 11 Dec 92 22:49:22 GMT

In article <1992Dec7.034240.27779@trl.oz.au>, peter@gort.trl.OZ.AU (Peter K. Campbell) writes:
|> Hello out there.  We have a C program here which the profiler tells us
|> is making extensive use of exp & log functions.  Seeing as it takes
|> several days to run on a Sun Sparcstation & several hours on a Cray
|> Y-MP, we are looking for a quicker implementation of the general
|> exp/log algorithm than cc or gcc provides.
|> 
|> So, would anyone out there know of any C implementation of a fast,
|> general purpose exp/log (e.g. table lookup with a few iterations for
|> fine tuning), available publicly or in a book?  Or perhaps a
|> description of a general algorithm that I can implement in C without
|> too many problems?
|> 
|> Thanks in advance.
|> 
|> Peter K. Campbell
|> p.campbell@trl.oz.au

Take a look at "Table-Driven implementation of the exponential function for
IEEE floating-point arithmetic", Ping Tak Peter Tang, ACM Trans. Math. Softw.,
Vol. 15, No. 2 ( June 1989) pp144-157.

------------------------------------------------------------------------
        Donald Frederick       |      Office of Academic Computing
        frederik@uci.edu       |      University of California, Irvine
        frederik@UCI.BITNET    |      Irvine, CA  92717
        (714) 725-3200         |      FAX (714) 725-2069
-----------------------------------------------------------------------
From: borchers@nmt.edu (Brian Borchers)
Newsgroups: sci.math.num-analysis
Subject: Re: Determinants
Date: 13 Dec 92 23:29:56 GMT
Article-I.D.: nmt.1992Dec13.232956.29606
Organization: New Mexico Tech

The original poster wants to know how to update his calculation of the 
determinant of a matrix after a very slight change to the matrix.  
 
You might take a look at section 12.6 of the second edition of Matrix
Computations by Golub and Van Loan.  This section discusses methods for
updating the QR factorization of a matrix after such a change, and has
pointers to the literature on updating LU and other factorizations.  You 
could use these techniques to update your LU factorization and then 
recompute the determinant from the updated factorization.  
 
On the other hand, calculating the determinant from an LU factorization
is notoriously unstable.  Are you sure that you can't avoid the computation
of the determinant?  Can you live with an inaccurate answer?  
 
Brian Borchers                                                Borchers@nmt.edu
Department of Mathematics
New Mexico Tech
Socorro, NM 87801
  
Newsgroups: sci.math.num-analysis,sci.math.stat,sci.math.symbolic
From: dclason@dante.nmsu.edu (Dennis Clason)
Subject: Re: mathematica stepwise regression package
Keywords: mathematica stepwise regression
Organization: New Mexico State University, Las Cruces, NM
Date: Wed, 16 Dec 1992 21:30:59 GMT

In article <1992Dec15.083258.1474@lth.se> andersh@maths.lth.se (Anders Holtsberg) writes:
>
>gary mcclelland mcclella@yertle.colorado.edu:
>>Stepwise regression is a tool of the devil. Anyone smart enough
>>to be using Mathematica ought to be able to decide which
>>questions he or she wants to ask of the data rather than letting
>>a demonstrably suboptimal stepwise algorithm decide which
>>questions to ask.  One day there may be good AI programs for
>>doing statistical analysis, but stepwise regression won't be
>>among them.
>
>You mean what is bad? Let's say we want to make predictions.
>Is the idea of using a subset of the predictors that is bad or
>do you mean the stepwise way to pick them? If the latter: do
>you know any better way (except trying all combinations)?
>

Efroymson's stepwise algorithms are bad for any of
a number of reasons.  First, the statistic labelled
"F" is generally a pseudo-F statistic, whose value
CANNOT be reasonably compared to the central F
distribution.  Second, the method tends to converge
to wrong models, and often the model selected
omits important regressors.  In fact, the algorithms
may never even consider the appropriate model (
whatever THAT is.)

There are better subset regression algorithms
available.  The most efficient known algorithm
is Furnival and Wilson's Leaps and Bounds, implemented
in BMDP 9R and in the new SAS PROC REG (v. 6.07).
Ron Hocking and Lynn LaMotte did a lot of work in
this area during the 70s.  Hocking's review papers
in Biometrics (around '80 or so) and Tech (around '85?)
are the best starting place for self study in this
area.

As a statistical consultant I dread it when a
collaborator comes into my office and says "I've
been running PROC STEPWISE and I've got this
nice regression model. . ."  The only reason
not to run all possible subsets is that it
takes too much resources.  Smart algorithms
cut way down on the resources needed to get
the effect of all possible subsets.  You ought
to use them.

Dennis

---
Dennis L. Clason                          dclason@nmsu.edu
Dept of Experimental Statistics             ESTATX08@NMSUVM1.NMSU.EDU
New Mexico State University
Las Cruces, NM 88001


Newsgroups: sci.math.num-analysis
From: dbailey@wk49.nas.nasa.gov (David H. Bailey)
Subject: FFT for odd n and other problems
Organization: NAS, NASA Ames Research Center, Moffett Field, California
Date: Fri, 11 Dec 92 21:18:41 GMT

There is in fact a general algorithm to rapidly compute the DFT of a
sequence n points, for any n, odd, even, prime, or other.  This method
is variously known as the "chirp-z transform" or the "fractional
Fourier transform".  It is only about four times more expensive than a
conventional FFT (comparing the cost for n near a power of two).  In
fact this method employs an FFT in a key step.

This technique has a number of other applications, including computing
DFTs of sparse (i.e. mostly zero) sequences, analyzing sequences with
non-integer periodicities, performing high-resolution trigonometric
interpolation, detecting lines in noisy images and detecting signals
with linearly drifting frequencies.

Excuse my immodesty, but a good writeup of this method is the article
"The Fractional Fourier Transform and Applications", by myself and P.
N. Swarztrauber, SIAM Review, Sept. 1991.

David H. Bailey
From: pa@verano.sba.ca.us (Pierre Asselin)
Newsgroups: sci.math.num-analysis
Subject: Re: Does this product converge ???
Date: 19 Dec 92 19:24:31 GMT
Distribution: na
Organization: None.  Santa Barbara, CA

In <4526@winnie.fit.edu>
	rma93758@zach.fit.edu ( Pavlos Kairis /ADVISOR-Gary Howell) writes:

>Does the following product converge;
>     Product(k=3,infinity,cos(pi/k))

It converges, because...  Hmmm...  This isn't a homework, is it?

>if so what is the limit ?

For a numerical value, take the log;  directly sum a dozen terms
or so;  finish off with Euler-MacLaurin.
-- 

--Pierre Asselin, Santa Barbara, California
  pa@verano.sba.ca.us
Newsgroups: sci.math.num-analysis
From: walsteyn@fys.ruu.nl (Fred Walsteijn)
Subject: Re: finite element limitations??
Organization: Physics Department, University of Utrecht, The Netherlands
Date: Mon, 14 Dec 1992 23:20:57 GMT

In <1992Dec14.133530.24703@dutrun2.tudelft.nl> rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:

>In article <1992Dec11.184635@roper.mc.ti.com> Don Rolph:
>> Excellent response - so long as one chooses appropriate shape function
>> (ah now there's the rub!!) FEA methods dont "fail"!

>Sorry Don. The gist of an FEA method is definitely _not_ in an appropriate
>choice of the shape functions. There exist many working FEM methods which
>do not even refer to something like a shape function, yet are successfull.

                                 ^^^^^^^  huh ????

Try to get good results from a linear standard FEM method applied
to the inviscid Burgers' equation.
In this case other basis functions should be used...

Fred -- walsteyn@fys.ruu.nl

Newsgroups: sci.math.num-analysis