Subject: Re: CLAPACK
From: Konrad Hinsen
Date: 26 Nov 1996 10:40:15 +0100
dave becker writes:
> I'm solving the problem Ax = (lambda)Bx with
> dsygv. The routine re-orders the eigensolutions
> in ascending order. Is there a way to trace that
> re-ordering? In other words, how can I find out
> which degee of freedom in the original matrices corresponds to
> which degee of freedom in the eigenvector?
There is no such correspondence. Since you write about "degrees of
freedom", I suppose you are dealing with something like a normal mode
calculation in mechanics. In that case, component i of each
eigenvector indicates the weight of degree of freedom i in the
original matrix.
--
-------------------------------------------------------------------------------
Konrad Hinsen | E-Mail: hinsen@ibs.ibs.fr
Laboratoire de Dynamique Moleculaire | Tel.: +33-4.76.88.99.28
Institut de Biologie Structurale | Fax: +33-4.76.88.54.94
41, av. des Martyrs | Deutsch/Esperanto/English/
38027 Grenoble Cedex 1, France | Nederlands/Francais
-------------------------------------------------------------------------------
Subject: PARADOXE
From: Jeanfaivre Laurent
Date: Tue, 26 Nov 1996 12:54:31 +0100
Bonjour a tous,
Je recherche des paradoxes scientifiques ! Je m'explique : la science
permet souvent d'etablir des resultats qui defient completement le sens
physique voire le bon sens commun. Par exemple, quel non scientifique
irait s'imaginer qu'un avion est plus petit en vol qu'au sol ?
Par consequent, quel que soit votre domaine, si vous connaissez de pres
ou de loin, des "phenomenes", quels qu'ils soient, qui peuvent paraitre
surprenants au commun des mortels, je vous remercie de me les decrire.
Je recherche d'autre part des pieds-de-nez scientifiques, du type de la
demonstration mathematique (truquee heureusement) de 2=1.
N'hesitez pas a m'envoyer vos suggestions, tout m'interesse ...
Merci d'avance.
Subject: Compiling DGESVD code from NAG
From: dlundin@aol.com
Date: 26 Nov 1996 13:40:45 GMT
Gentlemen,
I am attempting to use the SVD code from www.netlib.org for CLAPACK, the C
language version of LAPACK.
I have discovered that several calls are made to routines which I do not
have and did not find any directions that would suggest I need to download
any other libraries.
The routines (so far) are:
dcopy, dgemm_, dgemv_, dlamc1_, dlamc3_, dlamc4_, dlamc5_, dlarfg_,
dlarf_, dlasq2_, dlasrt_, dlam2r_, dorml2_, drot_, dscal_, dswap_, dtrmm_,
dtrmv_, d_sign, pow_dd, pow_di, s_cat, s_cmp, s_copy.
Are there any gurus out there who can assist?
Regards
Subject: Re: Transpose of a Complex Matrix
From: hbaker@netcom.com (Henry Baker)
Date: Tue, 26 Nov 1996 14:16:11 GMT
In article , Bala
wrote:
> Do u have to take the Conjugate of the elements while finding the
> Transpose of a Complex Matrix.?
>
> I find this so confusing as MATLAB gives a conjugated transpose while
> MAPLE does not!!!
Technically, the transpose does not conjugate, while the 'tranjugate'
(some authors) does conjugate. The people who developed MATLAB know
this, and there is no confusion since they (and most others) found that
when working with complex matrices the 'tranjugate' is more common and
more useful than the simple transpose. Therefore, they made the prime
symbol (') mean conjugated transpose.
I actually consider this an advance, since I've often thought that
linear algebra books made things _more_ confusing by not presenting
the conjugated transpose immediately, and then motivating this with
a number of complex examples. I guess this is another example of the
discrimination against complex numbers still found in many texts.
Subject: PARADOXE
From: Jeanfaivre Laurent
Date: Tue, 26 Nov 1996 15:07:36 +0100
Bonjour a tous,
Je recherche des paradoxes scientifiques ! Je m'explique : la science
permet souvent d'etablir des resultats qui defient completement le sens
physique voire le bon sens commun. Par exemple, quel non scientifique
irait s'imaginer qu'un avion est plus petit en vol qu'au sol ?
Par consequent, quel que soit votre domaine, si vous connaissez de pres
ou de loin, des "phenomenes", quels qu'ils soient, qui peuvent paraitre
surprenants au commun des mortels, je vous remercie de me les decrire.
Je recherche d'autre part des pieds-de-nez scientifiques, du type de la
demonstration mathematique (truquee heureusement) de 2=1.
N'hesitez pas a m'envoyer vos suggestions, tout m'interesse ...
Merci d'avance.
Subject: bicubic spline 3D fitting algorithm
From: wimg@azuur.tn.tudelft.nl (Wim van Geloven)
Date: 26 Nov 1996 14:16:44 GMT
Hi,
I'm looking for a routine that can create a cubic spline fit from an
arbitrary set of points in 3 dimensions, represented by $(x,y,z,v)_i$
(preferrably in a weighted least squares sense).
For 2 dimensions (i.e. for surfaces with points $(x,y,v)_i$ )these
routines already exist. For example such a routine is given by NAGs
E02DAF.
Secondly, has anybody experience with these kind of representations.
Thanks in advance !
Wim van Geloven
Laboratory of Seismics and Acoustics
Delft University of Technology
Subject: Re: Numerov Algorithm
From: michael@amo (Michael Courtney)
Date: 26 Nov 1996 14:28:24 GMT
Lupo LeBoucher (ix@io.com) wrote:
: I'm writing code which, at one point, solves several stiff, coupled, 2nd
: order, complex differential equations. Historically, this part has been
: solved using the Numerov method in Fortran, as Numerov is much more
: efficient than, say Runge-Kutta. I was wondering if there was a freely
: distributable Numerov solver (perhaps with adaptive stepsize) out there
: somewhere which I could use, rather than reinventing the wheel.
: If not, perhaps some people familliar with Numerov algorithm could give me
: some advice? For example; perhaps Numerov is a terribly outdated way of
: doing things and I should be using predictor-corrector methods like
: everyone else?
Numerov is a good choice. I've never code for applying it generally,
but I've coded several specific applications of it myself. It is quite
easy to code it for a specific application, probably even easier than
figuring out how to use someone else's more general code.
--
Michael Courtney, Ph. D.
michael@amo.mit.edu
Subject: Re: Compiling DGESVD code from NAG
From: Hans D Mittelmann
Date: Tue, 26 Nov 1996 07:41:38 -0700
dlundin@aol.com wrote:
>
> Gentlemen,
>
> I am attempting to use the SVD code from www.netlib.org for CLAPACK, the C
> language version of LAPACK.
>
> I have discovered that several calls are made to routines which I do not
> have and did not find any directions that would suggest I need to download
> any other libraries.
>
> The routines (so far) are:
> dcopy, dgemm_, dgemv_, dlamc1_, dlamc3_, dlamc4_, dlamc5_, dlarfg_,
> dlarf_, dlasq2_, dlasrt_, dlam2r_, dorml2_, drot_, dscal_, dswap_, dtrmm_,
> dtrmv_, d_sign, pow_dd, pow_di, s_cat, s_cmp, s_copy.
>
> Are there any gurus out there who can assist?
>
> Regards
Hi,
the key word here is "dependencies"! Go to
http://www.netlib.org
go under browse then clapack then under clapack/double and then
click not on dgesvd but on dgesvd with dependencies. You have to check
if that includes the BLAS (dcopy, dgemm), if not get them also and, of
course, you need the f2c-libs.
--
Hans D. Mittelmann http://plato.la.asu.edu/
Arizona State University Phone: (602) 965-6595
Department of Mathematics Fax: (602) 965-0461
Tempe, AZ 85287-1804 email: mittelmann@asu.edu
Subject: Re: Transpose of a Complex Matrix
From: pecora@zoltar.nrl.navy.mil (Louis M. Pecora)
Date: 26 Nov 1996 15:14:14 GMT
In article , hbaker@netcom.com (Henry
Baker) wrote:
> In article , Bala
> wrote:
>
> > Do u have to take the Conjugate of the elements while finding the
> > Transpose of a Complex Matrix.?
> >
> > I find this so confusing as MATLAB gives a conjugated transpose while
> > MAPLE does not!!!
>
> Technically, the transpose does not conjugate, while the 'tranjugate'
> (some authors) does conjugate. The people who developed MATLAB know
> this, and there is no confusion since they (and most others) found that
> when working with complex matrices the 'tranjugate' is more common and
> more useful than the simple transpose. Therefore, they made the prime
> symbol (') mean conjugated transpose.
>
> I actually consider this an advance, since I've often thought that
> linear algebra books made things _more_ confusing by not presenting
> the conjugated transpose immediately, and then motivating this with
> a number of complex examples. I guess this is another example of the
> discrimination against complex numbers still found in many texts.
Actually, I don't think that's true. Most linear algebra books and
physics books treat the transposes, and tranjugates, etc. more properly as
duals to the original matrix. This is, they are the matrices that operate
in the space dual to the original vector space (e.g. contra- and
co-variant spaces) that preserve the inner product, viz.,
+
= ,
where b is a vector in the original space, a is a vector in the dual
space, <,> is an inner product, and the "+" is often written as a "dagger"
to imply that we looking at a dual of a matrix. The dual is often called
the adjoint. The "+" is the adjoint map and should be looked at as a
function with argument M which outputs the "equivalent" linear map M+ in
the dual space. Then whether the adjoint is just a transpose, or a
transpose plus a complex conjugate, or something else, depends on the
underlying vector space and it's associated field (the real numbers,
complex numbers, etc).
This may sound technical, but it is straightforward, worth learning (not
hard, really), and keeps the ideas of conjugate, transpose, etc. from
becoming entangled and confusing. You really want the adjoint most of the
time. That's what MatLab's (') is for.
--
Louis M. Pecora
pecora@zoltar.nrl.navy.mil
== My views and opinions are not those of the U.S. Navy. ==
--------------------------------------------------------------------
* Check out the home page for the 4th Experimental Chaos Conference!
http://natasha.umsl.edu/Exp_Chaos4
---------------------------------------------------------------------
Subject: Re: HELP - iterativ methods for linear problems
From: Franco Costa
Date: Wed, 27 Nov 1996 09:07:25 +1100
snowback wrote:
>
> Cedric Dourthe wrote:
>
> > I'm looking for iterativ methods package in order to solve linear problems
> > I found C and fortran routines but only for sparse matrix
> > 1) where can I find the same packages for dense and complex matrix?
> > 2) Comparisons iterative methods/direct methods for this type of matrix?
>
> Cedric, as I'm sure you know, for direct methods you need
> to keep the whole matrix in storage whereas for iterative methods
> you need only store the non-zero elements.
> For large problems involving sparse matrices, often we just don't have
> enough RAM to store the whole matrix so we HAVE to use an iterative
> method such as conjugate gradient etc.
>
> If you have a non-sparse matrix, chances are you would be better off
> using a direct method.
>
> --snowback
Cedric, I'll just give you two names which you can point your
web browser to. I haven't used either extensively, so apologies
if I misrepresent them.
I think the LAPACK set of routines includes dense direct matrix
solution methods. Try http://www.netlib.org/lapack/
I think the TEMPLATES book and code includes iterative methods
which can be implemented in any matrix storage method. A full (dense)
storage is actually the simplest. Try
http://www.netlib.org/linalg/html_templates/report.html
My apologies if these URL's are out of date. If so, use your
favourite search engine to search on the appropriate names.
Regards
--
Franco Costa email:franco@moldflow.com.au
Research Engineer
Moldflow Pty. Ltd. phone:+61-3-97202088
Melbourne, Australia fax :+61-3-97290433
Subject: Re: Complex Numbers in C
From: wayne@cs.toronto.edu (Wayne Hayes)
Date: 26 Nov 96 20:52:28 GMT
In article ,
John E. Davis wrote:
>You might try using gcc. For example, the following code
>
>#include
>#include
>
>int main ()
>{
> __complex__ double z;
> double z2;
>
> z = 3.0 + 4.0i;
>
> z2 = z * ~z;
>
> fprintf (stdout, "z = %f + i%f; |z|^2 = %f\n",
> __real__ z, __imag__ z, z2);
>
> return 0;
>}
>
>produces:
>
>z = 3.000000 + i4.000000; |z|^2 = 25.000000
Yes, but none of the standard math functions work correctly, and even
worse, no errors or warnings are printed if you try:
$ cat foo.c
#include
#include
int main()
{
__complex__ z = 1.0i;
printf ("exp(%gi) = %g + %gi\n", __imag__ z,
__real__ exp(z), __imag__ exp(z));
return 0;
}
$ gcc -Wall foo.c -lm
$ ./a.out
exp(1i) = 1 + 0i
It appears that exp() (and sin()) just take the real part of it's argument,
ignoring the imaginary part.
--
"Unix is simple and coherent, but it takes || Wayne Hayes, wayne@cs.utoronto.ca
a genius (or at any rate, a programmer) to || Astrophysics & Computer Science
appreciate its simplicity." -Dennis Ritchie|| http://www.cs.utoronto.ca/~wayne
Subject: Re: Computing derivative of det(A), A singular
From: shepard@tcg.anl.gov (Ron Shepard)
Date: Tue, 26 Nov 1996 17:39:04 -0600
In article <3299C149.3A9659B2@asu.edu>, Hans D Mittelmann
wrote:
[...]
>here is my theorem. Unless it can be found in the literature, I'd like
>to be quoted as the source.
>
> D det(a) = sum(i=1,n) product(j.ne.i) lambda_j(A)
>
>This requires one call of, say, the QR algorithm and is thus a O(n^3)
>method.
I think there is a factor missing. I get:
D det(A) = sum(i=1,n) (D(lambda_i) Product(j.ne.i) lambda_j )
and therefore you need the derivatives of the eigenvalues, which can be
computed from the perturbation-theory expression (I'm assuming all the
derivatives are evaluated at the same reference point, 0; oh yeah, and the
matrix A is normal). I'm not sure this is the best way of solving this
problem, but the above expression points out that the value is zero if
there is more than one zero eigenvalue (the product terms will always be
zero in this case, having at least 1 and sometimes more zero factors), and
the expression is zero if the zero eigenvalue is quadratic (i.e. O(2) or
higher, the D(lambda) term is zero for the surviving product term in this
case; BTW, I think this must be true if A is semidefinite or if its
inertia triplet is locally constant). So in case both of these conditions
are satisfied, there is only one term that contributes to the summation,
D det(A) = D(lambda_i) Product(j.ne.i) lambda_j ;where lambda_i=0
which is why I suspect that this may not be the best computational
approach (too much effort, too simple a result ;-).
$.02 -Ron Shepard
Subject: Research position in Mathematics (Final Posting)
From: pmd@maths.uq.oz.au (phil diamond)
Date: 27 Nov 1996 02:33:02 GMT
Particulars relating to the position of
RESEARCH OFFICER, Level A,
in the Department of Mathematics within THE UNIVERSITY OF QUEENSLAND
Duties: The successful applicant will be required to work with Drs Phil
Diamond and Darryn Bryant, of The University of Queensland, and Professor
Nikolai Kuznetsov of the Russian Academy of Sciences, on the Australian
Research Council funded project "Statistical Laws for Computational
Collapse of Chaotic Systems". The applicant must be prepared to make
a commitment to work FULL-TIME on the project.
Salary: $37,170 -- $38,587 -- $40,004 (Annual increments, in Australian
Dollars). It is expected that there will be a 5%--8% increase in
these figures, granted by mid 1997.
Qualifications: Applicants should have research interests in Dynamical
Systems Theory or a closely related field of Mathematics,
with strengths in measure theory, probability, asymptotics
and functional analysis. They should either hold a Ph.D.
or be nearing completion of their Ph.D. They should be able
to work independently, albeit under supervision.
Date of
commencement: This will be as soon as possible after January 1st 1997.
Applicants who would wish to commence late in 1996 SHOULD NOT
BE DETERRED FROM APPLYING. If the successful applicant does not
hold a Ph.D., he/she must have submitted their thesis for exam-
ination prior to taking up the post.
Period of
appointment: The post will be offered for a maximum of three years, on a
one-year renewable basis. The post will terminate on 31st
December 1999. For applicants without a Ph.D., appointment to a
second year will be dependent on their successfully completing
the requirements of the degree.
Method of
application: Applications should be forwarded as soon as possible to Dr
Phil Diamond at the address below, preferably by e-mail (a
speedy acknowledgement will follow) or FAX, and by no later
than 9th December 1996. Applications should include a full
curriculum vitae (resume), together with the names, addresses
and telephone numbers of THREE referees. It would be helpful if
e-mail addresses and/or FAX numbers could be provided for each
referee.
Relocation
expenses: A single one-way economy airfare to Brisbane will be provided.
Interested parties are urged to make contact as soon as possible.
+------------------------------+--------------------------------------------+
| Phil Diamond | Telephone (+61 7) 3365 3253 |
| Department of Mathematics | |
| The University of Queensland | e- mail pmd@axiom.maths.uq.oz.au |
| Queensland 4072 | |
| AUSTRALIA | Fax (+61 7) 3365 1477 |
+------------------------------+--------------------------------------------+
Subject: Re: HELP - iterativ methods for linear problems
From: Bruce Rosen
Date: Tue, 26 Nov 1996 21:50:57 -0500
I have lots of matrices to solve in my free-surface wave work. Both
real and imaginary, and dense. I have "GMRES" type in-core iterative
solvers for both, but they took a long time to develop and I'd want
a software license fee for their use. They work great.
If you want a cheaper route, try a search on GMRES.
--
************************************************************************
Bruce Rosen, President E-mail: brosen@panix.com
South Bay Simulations, Inc. http://www.panix.com/~brosen
44 Sumpwams Avenue
Babylon, NY 11702 USA Tel/Fax: (516) 587-3770
************************************************************************
Subject: Kalman filter design and analysis software
From: harmonic@world.std.com
Date: Wed, 27 Nov 1996 04:15:19 GMT
KBF - The Kalman Filter Visual Interface Pack for O-Matrix
Harmonic Software Inc. has released KBF, The Kalman Filter Visual Interface
Pack for O-Matrix. The KBF interface simplifies the design of a filter
or smoother by dividing the design process into simple steps with each
step corresponding to an input window or dialog. Extensive plotting of
results, including residuals and correlations is also automated. In
addition, a simulation feature is included to aid in testing the validity
of the design. KBF is used in a wide range of applications such as tracking,
weather and earth process modeling, economic forecasting and bioengineering.
Please visit our web site at
http://world.std.com/~harmonic
for more details on KBF, or contact us directly at
Harmonic Software Inc.
12223 Dayton Avenue North
Seattle, WA 98133
(800) 895-4546, (206) 367-8742
FAX: (206) 367-1067
harmonic@world.std.com
Subject: Re: clapack question ...
From: Hans D Mittelmann
Date: Tue, 26 Nov 1996 20:19:59 -0700
Jenny Sanchez wrote:
>
> i just downloaded dgels.c from netlib. I got the version that supposedly
> includes all dependencies. I also got the f2clibs.
>
> however the routines are still calling subroutines i didn't get.
> These are
>
> ld: Undefined symbol
> _dgemv_
> _dtrmv_
> _dcopy_
> _dtrsm_
> _dger_
> _dgemm_
> _dscal_
> _dtrmm_
> _dnrm2_
>
> I've searched around the clapack offerings, and can't find these. anyone
> know where these routines are?
>
> thanks, Jenny
Hi,
these are BLAS routines. Get the BLAS lib, it's in CLAPACK also.
Hans
--
Hans D. Mittelmann http://plato.la.asu.edu/
Arizona State University Phone: (602) 965-6595
Department of Mathematics Fax: (602) 965-0461
Tempe, AZ 85287-1804 email: mittelmann@asu.edu
Subject: ANN: Some New Results in the Field of Discrete Math/Designs/Codes (repost)
From: bm373592@muenchen.org (Uenal Mutlu)
Date: Wed, 27 Nov 1996 07:07:54 GMT
SOME NEW RESULTS IN THE FIELD OF DISCRETE MATH/DESIGNS/CODES
Date : 96/11/27 We
Author: Uenal Mutlu (bm373592@muenchen.org)
The following bounds of enumerated 'm=t COVERING DESIGNS' are to
the best of my knowledge *NEW* upper bound results compared to
known published or online available results (cf. [1],[2],[4]).
Definition:
A Covering Design C(v,k,t,m,l,b) is a pair (V,B), where V is a set
of v elements (called points) and B is a collection of b k-subsets
of V (called blocks), such that every m-subset of V intersects at
least l members of B in at least t points (v >= k >= t and m >= t).
New upper bounds for C(v,k,t,m,l=1,b). Listed are m=t designs only:
k t m v b (bOld) Remarks/Author/Method
------------------------------------------------------------------
6 4 4 15 118 (120) Rade Belic, [3]
6 5 5 14 377 (378) Rade Belic, [3]
6 5 5 15 609 (610) Combine-Construction [1]
7 5 5 17 408 (463) Rade Belic, [3]
7 5 5 18 618 (663) Combine-Construction [1]
7 5 5 19 772 (824) Turan Theory/Sidorenko Construction [1]
7 5 5 20 1115 (1153) Combine-Construction [1]
7 5 5 21 1424 (1476) [3]
7 5 5 22 1938 (1990) [3]
7 5 5 23 2405 (2458) [3]
7 5 5 24 3096 (3208) [3]
7 5 5 25 3772 (3830) [3]
(bOld refers to the upper bounds of [2] on 96/11/26)
The new upper bounds were obtained by some published (see [1]) and
some not yet published algorithms and programs of Rade Belic [3]
and Uenal Mutlu (including implementations of some recursive
constructions from [1]).
These results will also improve some other designs with higher
k,t,m if at least some of the well known recursive construction
methods are applied.
Not shown are the latest improvements and new upper bounds for
designs with m > t. A list containing all upper bounds of enumerated
designs in the range k <= 7, v <= 54, t <= 7, m <= 7 and b <= 9999
can be requested from the author [5]).
Pointers to further improvements and new results are welcome.
Uenal Mutlu
References:
[1] D.M.Gordon, O.Patashnik, G.Kuperberg "New Constructions for
Covering Designs", J.Combin.Designs 3.4 (1995) 269-284
(for updates and errata see [2])
[2] Dan Gordon's "La Jolla Covering Repository" at
http://sdcc12.ucsd.edu/~xm3dg/cover.html
(as of 96/11/26)
[3] SOPT v1.0 07/96 (96/11/19) - Design Optimization Program
written by Rade Belic
[4] D.R.Stinson "Coverings" in C.J.Colbourn, J.H.Dinitz (eds.)
"The CRC Handbook of Combinatorics" CRC Press (1996) 260-265
[5] Uenal Mutlu "List of Covering Designs" (enumerated upper bounds)
Includes also m > t designs. Current list is LST1127A.ZIP
-- Uenal Mutlu (bm373592@muenchen.org)
Math Research, Designs/Codes, Data Compression Algorithms, C/C++
Loc : Istanbul/Turkey + Munich/Germany
Subject: Optimization problem
From: mcau@ee.cuhk.hk (Au_Yeung_Man_Ching)
Date: 27 Nov 1996 05:33:52 GMT
Hi,
I would like to ask some questions:
(1) Given the following problem,
min J(q,S)
q,S
in doing the above problem, we do the
above problem like this:
min min J(q,S)
q S
i.e. doing the problem sequentially as two
parallel independent minimization problem.
With a fixed q first, minimize J(q,S) w.r.t.
S to obtain S*. Then, minimize J(q,S*) w.r.t.
q. Finally, get the optimal point(local/global??)
(q*,S*).
CAN WE DO THE PROBLEM AS DESCRIBED ABOVE??
IF CANNOT, how can we do?
Thanks in advance!!
Regards,
--
+------------------------+--------------------+
| Au Yeung Man Ching | Rm 304 |
| Electronic Engineering | Ho Sin Hang Bldg. |
| CUHK | CUHK |
+------------------------+--------------------+
| Email : mcau@ee.cuhk.edu.hk |
| Homepage : http://www.ee.cuhk.edu.hk/~mcau/ |
+---------------------------------------------+
--
+------------------------+--------------------+
| Au Yeung Man Ching | Rm 304 |
| Electronic Engineering | Ho Sin Hang Bldg. |
| CUHK | CUHK |
+------------------------+--------------------+
| Email : mcau@ee.cuhk.edu.hk |
| Homepage : http://www.ee.cuhk.edu.hk/~mcau/ |
+---------------------------------------------+
