mm-393

Subject: Re: orthogonal polynomial>> Is there a
relationsp known for the dice between the largest root>> of an
orthogonal polynomial and the endpoint of the orthogonality>>
interval? I would like to know how fast ts dice shrinks as a>>
function of the degree of the polynomial... > non-classical
orthogonal polynomials at hand. I have the orthogonality>
interval and the weight function, but not a closed form of the
polynomials.> Is there some general theory? I've just ordered
Szeg.9a's book Orthogonal> Polynomials. I hope to find sometng
in there.... ===It's difficult to obtain good estimations in
general case, i.e. foran arbitrary weight (positive)
function.where you find an interesting paper by Ilia KRASIKOV,
namely,,On extreme zeros of classical orthogonal
polynomials.Likewise, I remember that 30-35 years ago, Geza
FREUD was interested to give ,,good bounds for the extreme
zeros.(I appreciate that NEVAI has many informations regarding
such problems).====== Subject: Re: Data fitting problem with
chebyshev polynomials> I want to fit some pure complex data x
(only imaginary part) to some other> complex data, y, by a
polynomial with linear least squares.y=p0 T0(x) +p1
T1(x)+...+pn Tn(x)> where Ti(x) represents the i'th Chebyshev
polynomial.> (i thought ts would provide me with better
numerical conditioning,> since i get Vandermonde system to
solve).> Does anyone know what i'm doing wrong, or does ts
technique only work> for real data??>Arnold Neumaier[Chebyshev
is good only if the arguments are in theinterval [-1,1]; the
function values may be arbitrary....]=======Denote (z)_0:=1 ,
(z)_k=z(z+1)...(z+k-1) for k=1,2,...,F_{2,1}(a_1,a_2;b_1;z)=
SUM_{k=0 to k=infty}( (a_1)_k
(a_2)_k/(b_1)_k)z^k/k!F_{p,q}(a_1,a_2,...,a_p;b_1,b_2,...,b_q;
z)==SUM_{k=0 to k=infty}( (a_1)_k (a_2)_k...(a_p)_k
/((b_1)_k...(b_q)_k )) z^k/k!Note that when a_1= -n ,
n=0,1,..., the aboveF_{p,q}(-n,...;b_1,...;z) is a finite
sum.Further, for a>-1 , b>-1 J_n(a,b;x)=
F_{2,1}(-n,n+a+b+1;a+1;(1-x)/2)= Jacobi polynomial ofdegree n
.There are ,,many Chebychev polynomials . More exactly[1.]
(CONTINUOUS CASE) T_n(x) = J_n(-1/2,-1/2;x) = cos(n*arccos x)
, (when |x|=< 1), =first kind U_n(x)= J_n(1/2,1/2;x)=
sin((n+1)*arccos x)/((n+1)*sqrt(1-x^2)) , =second kind
J_n(1/2,-1/2;x)= (T_n(x)-T_{n+1}(x))/((2n+1)*(1-x))= trd
kind==========================================================
====================[2.] (DISCRETE CASE) Let N be a positive
integer and for n=0,1,...,, n =< N-1,denote
======================================================= (1)
t_n(x)= (-1)^k (N-k)_k F_{3,2}(-n,n+1,-x; 1,1-N ; 1)
=======================================================
(Chebychev polynomials of discrete variable,
P.L.Chebychev-[1875] ,,Sur l'interpolation des valeure
equidites , Oeuvres , tomII, Chelsea,New York,1961 ,pp.219-241
) Suppose that f,g:[0,N-1]--->R and define scalar product (#)
(f,g)= SUM_{k=0 to k=N-1} f(k)*g(k) , ||f|| = Sqrt((f,f)) .If
you have the table x| 0 1 ... N-1--------------------- y|f(0)
f(1) ... f(N-1) and you try to find the polynomial T(x) , of
degree m , (m < N-1) ,such that(2) || f- T|| =< ||f-h ||for
all polynomials h of degree =< m , then the solution is
===========================================(3) T(x)=SUM_{k=0
to k=m}w_k*(f,t_k)* t_k(x)
============================================where
w_k=1/(t_k,t_k)=(2k+1)*(N-k-1)!/( k!*(k+1)_N ).Observe that
(2) is the same with (f-T,f-T)=< (f-h,f-h) and (t_k,t_j)= 0
for 0=< j=/=k < N .In the complex, case when f,g: [0,N-1]--->
C , try to change thescalarproduct, more exactly instead of
(#) consider instead ---- (#') (f,g)= SUM_{k=0 to k=N-1}
f(k)*g(k) , ||f|| = Sqrt((f,f)) . -----where g(k) means the
conjugate of g(k) . Other informations you find in :[1] A.F.
NIKIFOROV , S.K. SUSLOV , V.B. UVAROV , ,, Classical
Polynomials of a Discrete Variable , Springer Series in
Computational Physics , Springer-Verlag ,1991.Perhaps help,
============================Subject: Can ts be solved?Can ts
equation be solved?y=a+b*exp(- c * x)At x=L, y=0 and x=M,
y=Alpha (where 1> Alpha>0) x=H, y=1where H>M>L>0My objective
is to find a, b, cAny reference would be appreciated? Online
link is fine too?===Subject: Re: Can ts be solved? >Can ts
equation be solved?y=a+b*exp(- c * x)At x=L, y=0 and > x=M,
y=Alpha (where 1> Alpha>0) > x=H, y=1 >where H>M>L>0My
objective is to find a, b, cAny reference would be
appreciated? Online link is fine too?homework? three equations
in three unknowns, well , nonlinear insert x=L, get a dependent
on b and c, insert x=M , expressing now b as a function of c
insert x=H 1/Alpha =
(exp(-c*H)-exp(-c*L))/(exp(-c*M)-exp(-c*L)) solve for c
numerically: http://www.netlib.org/fmm/fzero.f c>0 very small
gives on the right hand side approximately (H-L)/(M-L) > 1 and
c to infinity gives 1 on the right hand side. so at least for
(H-L)/(M-L) > 1/Alpha there is a solution ===Subject: Re: Too
many iterations in tqli.c> I agree with you that there does
not seem to be any perfect solutions> for matrix computations
in C++ in the same way that LAPACK exists for> FORTRAN (and
C). I have developed my own class library whose primary> goal
is to interface to the core functionality of
LAPACK/ATLAS/Intel> MKL wle ding the details of interfacing
with these libraries. If> you're interested in seeing what
I've got, I'm willing to sht are.RyanSure I'm interested. I
can contribute too. Also, I've found it++> blas and lapack,
and the syntax resembles matlab, wch is good, > but it still
implements its own vector class, so you can only > multiply a
matrix by their own vector. With a little hacking, it > can be
what I need.these libraries having their own vector class. It's
been my feelingthat the STL vector in C++ is not really the
kind of vector class onewould use in linear algebra.
Additionally, with all the functionalityone would want from a
fully functional vector (from the linear
algebrapoint-of-view), it seems reasonable to me to have a
separate class. In my implementation, though, I do use
std::vector as a private memberto store the data.===Subject:
Re: Too many iterations in tqli.c > these libraries having
their own vector class. It's been my feeling> that the STL
vector in C++ is not really the kind of vector class one>
would use in linear algebra. Additionally, with all the
functionality> one would want from a fully functional vector
(from the linear algebra> point-of-view), it seems reasonable
to me to have a separate class. > In my implementation,
though, I do use std::vector as a private member> to store the
data.STL's vector and valarray already have with the +/-, *,
etc implementedalready, and there are also componentwise
operators that can beapplied to a container, that already come
with STL. I don'tsee any point in re-inventing the wheel, if
STL provides all thebasic operations needed for a
vector.===Subject: Wch finite elements would you recommend for
ts problem?I have a flow field, wch has been found using the
Galerkin finiteelement method to solve the Stokes flow
equation for u1, u2 and p.The velocity has been approximated
using 'Crouzeix-Raviart' elements(as continuous linear
elements don't work so well for ts problem.).These elements
are piecewise linear, triangular elements wch aredefined by
the values of the approximated function at the midpoint ofthe
triangle edges. They are therefore discontinuous in general.
Thepressure has been approximated by piecewise cont elements.
Thecode to find the flow is simple and works quite well.Now I
need to solve a dard linear advection-diffusion equation(with
inhomogeneous diffusivity) for a solute concentration c.
Thevelocity field for the solute transport is that given by
the flowcalculation described above.What finite elements would
you suggest using for the concentrationfield? Should these
elements also be of the 'Crouzeix-Raviart' formdescribed above
or sometng else.I'm concerned in particlular about finding a
consistent form of theterm div(c*[u1,u2]) of the
advection-diffusion equation in theGalerkin problem.Any
thoughts would be very welcome. Yours,===Subject: Re: Wch
finite elements would you recommend for ts problem?> What
finite elements would you suggest using for the concentration>
field? Should these elements also be of the 'Crouzeix-Raviart'
form> described above or sometng else.I'm concerned in
particlular about finding a consistent form of the> term
div(c*[u1,u2]) of the advection-diffusion equation in the>
Galerkin problem.For linear advection-diffusion equation, an
Eulerian-Lagrangiantype of Galerkin method should be suitable.
These will rathereasily incorporate your Crouzeix-Raviart
velocity field analytically,and the diffusion can be handled
implicitly, giving you asymmetrical, positive definite matrix
to be solved for at eachtimestep. === Subject: Re: Wch finite
elements would you recommend for ts problem?> What finite
elements would you suggest using for the concentration> field?
Should these elements also be of the 'Crouzeix-Raviart' form>
described above or sometng else.I'm concerned in particlular
about finding a consistent form of the> term div(c*[u1,u2]) of
the advection-diffusion equation in the> Galerkin problem.Ts is
Stokes flow, so I assume the Re is not too gh. However,
theadvection-diffusion equation may require some form of
stabilization,e.g. SUPG, for it to work. If in general you
expect the concentrationto be a continuous function, then I'd
use a continuous basis for it.-===Subject: Programmers Wanted
for Computer Grapcs Startup Near PladelpaMy name is Schwartz,
and I'm a University of Pennsylvania Ph.D. and an independent
inventor. I'm submitting two computer grapcs patents to the
USPTO during the next several weeks. Technologies derived from
these patents have application in several different et
segments, including still image photomanipulation, movie
special effects and post-production,web animation, and video
games. I'm developing and eting one or more of the
applications through a startup company. I've produced demo
output that clearly demonstrates the viability of my
approaches, wch I've been showing to potential licensees and
investors. Ts demo output is currently being generated through
a loosely connected series of scripts. To be productized the
scripts will need to be recoded into dalone industrial
strength applications that are much faster, bullet-proof, and
that have slick GUIs. I'm looking for a lead/senior programmer
to participate in and organize the implementationside of the
startup and probably one or more junior programmers.
Successful candidates for the programming team should have
some to many of the following
skills/characteristics:Extensible knowledge of/comfort with
math, as exemplified by one or more of: Computer vision
training/experience - feature location/ extraction, motion
estimation, object recognition; Image processing
training/experience - you know what a convolution kernel is;
you've implemented a morpng algorithm; Linear algebra
training/experience - matrix manipulation, familiarity with
numeric computation packages, such as Matlab, or equivalent;
Art/math programming play, mathematical visualization;3D
modeling, especially for character animation, especially if
you've hacked/manipulated low-level 3D data representations in
a variety of formats;GUI design/building, grapc design training
a plus;Analysis of algorithms;C/C++, Linux/Unix a plus;Startup
and/or major fielded product development experience required
for the lead/senior programmer, a plus for juniors;Witn
commuting dice of Pladelpa - we may move and/or outsource, but
ts is where/how we'll start;Relevant educational background is
a plus, but I'm more interested in what you can demonstrate to
me that you know, can do, and have done, than what you've
formally studied;Intellectual flexibility, creativity, and
ability to work and brainstorm collaboratively;Open-ended time
commitment - After growing ts, I have additional ideas in the
queue that could be spun off into future products;
andDemonstrable artistic skills and training in figurative
painting, sculpture, and/or life-drawing are a plus.We have
access to seed capital, and we'd prefer if participants accept
some portion of salary as equity in our venture. If you're
interested in participating, send me a cover letter and resume
at cgstartup@earthlink.net. I'm willing to show you the demo
and provide more details about the technology, although first
you'll have to sign a non-disclosure agreement. The demo can
also be posted temporarily to the web for online viewing,
accompanied by an explanatory phone call. For
Investors/Licensees:If you're a potential investor in the
startup or a representative of a company that is potentially
interested in licensing one of the applications and are
interested in seeing the demo and hearing a description of the
technologies, also under conditions of non-disclosure, please
let me know through the means described above.===Subject: c++
program for nxn matrix by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i0TDrPS15856;good day. can you show me a simple c++ program
that can solve(addition,subtraction,multipilication and
division) an nxn matrix.much.===Subject: Re: c++ program for
nxn matrix> can you show me a simple c++ program that can
solve> (addition,subtraction,multipilication and division) an
nxn matrix.> simple program that can be easily understood by a
student.Take a look atThe C++ Scalar, Vector, Matrix and Tensor
class Library http://www.netwood.net/~edwin/svmtl/===Subject:
Re: c++ program for nxn matrix> good day. can you show me a
simple c++ program that can solve>
(addition,subtraction,multipilication and division) an nxn
matrix.> much.if you use a lib (e.g. newmat) you are able to
work with expressions asfollowsA=B*C.i()+O(where C.i() is the
inverse),can be easily understood, I Tnk. If you want to go
into more details ofe.g. how inverting a matrix, you should
start with a math-book and thantake a look at the sources of
newmat or MTL (find these onwww.oonumerics.org). But of course
that isnot easy, not at any time atleast and depending on your
skills.-- === Subject: 2D FFT source code by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id i0TDrQB15895;I want most efficent
way of implementing fft on image.===Subject: Re: 2D FFT source
code> I want most efficent way of implementing fft on image.Try
searcng the newsgroup first! Plenty of suggestions out
there,===Subject: Re: 2D FFT source code> I want most efficent
way of implementing fft on image.Run 1-D FFT on rows. Call ts
output the intermediate matrix. Run 1-D FFT on columns of
intermediate matrix. Voila! You're done.OUP===Subject: Re: 2D
FFT source code>> I want most efficent way of implementing fft
on image.Run 1-D FFT on rows. Call ts output the intermediate
matrix. Run 1-D > FFT on columns of intermediate matrix.
Voila! You're done.In principle, that row-column method may
not be the most efficient way to compute a 2d FFT. There are
known algorithms such as vector-radix (a recent variant of wch
has been called the dimensionless fft), polynomial transforms
ala Nussbaumer, and a recent algorithm by Bernardini, that can
require fewer arithmetic operations. Vector-radix may also have
cache-related advantages.I point ts out merely for
completeness, though...the actual speed is determined mostly
by quality of implementation, and I'm not aware of
heavily-optimized versions of the above algorithms, wle many
efficient 1d FFTs are readily available.In practice, you are
probably best off just using a canned FFT routine that
performs multidimensional transforms, and for an image you
will www.fftw.org that might serve.===Subject: Re: function
interpolation by using normal distributions>>is there an
algorithm wch permits to abtain a function interpolation>>by
using a set of normal distributions?>>M> do you mean > sum
{i=1,...,n} a_i*exp(-(x-m(i))^2/s(i)^2) > ?> with the m(i) and
s(i) given ts amounts to a linear system of equations> and is a
special case of interpolation by radial functions. ts is known
> also for several independent variables and often used in
scattered data > interpolation. be warned that the linear
systems can be quite illconditioned. > if m(i) and s(i) are
unknown, ts becomes a nasty nonlinear problem and > then
problems with n>=4 already pose severe problems. even worse if
you are> in hger dimensions and have are more general model
involving covariance> matrices.Ts sounds like radial basis
function neural network for regression,assuming the covariance
matrices are multiple of identity matrix.You may as well take a
look at support vector regression withradial basis function
kernel, wch does similar tngs asrbf neural network, but with
the problem formulated differently. ===Subject: FElt for
teacng finite elementsI am going to teach an introductory
course of finite elements. I wantto present simple examples of
1D and 2D problems, using non-structuredtriangular meshes, for
scalar and vector equations. The students willhave practical
classes on computers with linux. I have been usingMODULEF for
ts purpose but I noticed it is too heavy for a studentto learn
the MODULEF syntax and tricks. I wonder if using the
FEltsoftware would be more appropriate. Has anybody used FElt
recently ? Is it a good choice for teacng finite elements ? Do
you recommendanother software instead ? (free software only).
Cristian Barbarosie
http://cmaf.ptmat.fc.ul.pt/~barbaros===Subject: calculating a
formula from numbersI'm looking for a tool what can help me
with calculating a formulafrom numbers.I want to feed ts tool
5000 numbers (15 digits) as 'questions' and5000 numbers (8
digits) as 'answers'. Ts tool should be able toderive one
formula.Im not sure if 5000 numbers is enough. Can someone
give me some adviceon ts matter.Andy===Subject: Re:
calculating a formula from numbers> I'm looking for a tool
what can help me with calculating a formula> from numbers.> I
want to feed ts tool 5000 numbers (15 digits) as 'questions'
and> 5000 numbers (8 digits) as 'answers'. Ts tool should be
able to> derive one formula.> Im not sure if 5000 numbers is
enough. Can someone give me some advice> on ts matter.>
AndyYou did not specify what you want from the formula (choose
one or moreoptions):* to retrieve answers only to already asked
questions, in some time-savingmanner?* to estimate (predict)
answers to nearby questions wch may not havebeen asked yet?*
to predict answers to questions away from the range of already
askedquestions?* to respect the values of questions and answers
as precise numbers, toall digits?* to respect bounds resulting
from rounding? Explanation: The statement x=2.447 to 4 digits
represents an inequality 2.4465 <= x <= 2.4475.* should the
formula be polynomial (a popular, albeit not always
suitable,form)? Or from another class of formulas (rational,
exponential, ...)Ts may be a key to success: for example,
approximating periodic data bypolynomials is silly, but
approximating them with trigonometric functionsis wiser.*
should the formula represent a trade-off between brevity
anddeliberately allowed extra errors? (Least squares come to
mind).Consult the web (Google or another search program) under
key expressionscurve fitting, data compression, approximation
of data, andthe like.A true but possibly useless answer to the
original inquiry: Yes, apolynomial formula exists (if the data
are functional -- every questionhas exactly one answer), and
it can have degree up to 4999, depending onyour data. The
process is called polynomial interpolation.===Subject: dealing
with noisy data by support1.mathforum.org (8.11.6/8.11.6/The
Math Forum, $Revision: 1.9 primary) id i0UE5OX08639;,iam doing
my project in the area of Reverse Engineering.wle thelaser is
scanning the part its giving some noisy data because of
theinternal reflection between surfaces.iam applying gaussian
distribution to the data.i don't know how toproceed.is it
possible tp apply gaussian distribution to discrete values.the
suggestios in ts regard is ghly helpful.,=== Subject:
RungeKuttta by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i0UF7te14072;I'm using a
runge-kutta 4th order to simulate a vecle moving in acircle. I
create an acceleration vector that is ALWAYS perpendicularto
the velocity vector. However, I noticted that the velocity
vectorof my vecle is slowly getting bigger. Why is the
velocity vectorgetting bigger if the acceleration that I'm
giving to rk4 is alwaysorthogonal with the velocity? Anybody
know if there is a betterintegrator to use for ts
problem?Eric===Subject: Re: RungeKuttta> I'm using a
runge-kutta 4th order to simulate a vecle moving in a> circle.
I create an acceleration vector that is ALWAYS perpendicular>
to the velocity vector. However, I noticted that the velocity
vector> of my vecle is slowly getting bigger. Why is the
velocity vector> getting bigger if the acceleration that I'm
giving to rk4 is always> orthogonal with the velocity? Anybody
know if there is a better> integrator to use for ts
problem?Eric> You're probably using an explicit RK4.Explicit
RK schemes do not conserve energy.That is probably the reason
for your troubles.You should try a symplectic implicit RK.You
can also improve an explicit RK byperforming, if possible, an
analyticintegration of the linear part of the equations.BTW,
are you using a cont step RK$or an automatic selection of time
step ?The second case is MORE efficient for longtime
simulations.You'll find all the informations you need in:Ernst
Hairer, Syvert Nrsett, Gerhard WannerSolving Ordinary
Differential Equations I. Nonstiff Problems.Springer Series in
Comput. Mathematics, Vol. 8, Springer-Verlag 1987, Second
revised edition 1993.Ernst Hairer, Gerhard Wanner.Solving
Ordinary Differential Equations II. Stiff and
Differential-Algebraic Problems.Springer Series in Comput.
Mathematics, Vol. 14, Springer-Verlag 1991, Second revised
edition 1996.Ernst Hairer, Christian Lubich, Gerhard
WannerGeometric Numerical Integration. Structure-Preserving
Algorithms for Ordinary Differential Equations.Springer Series
in Comput. Mathematics, Vol. 31, Springer-Verlag 2002.Have a
nice time reading,D.===Subject: Re: RungeKuttta> I'm using a
runge-kutta 4th order to simulate a vecle moving in a> circle.
I create an acceleration vector that is ALWAYS perpendicular>
to the velocity vector. However, I noticted that the velocity
vector> of my vecle is slowly getting bigger. Why is the
velocity vector> getting bigger if the acceleration that I'm
giving to rk4 is always> orthogonal with the velocity? Anybody
know if there is a better> integrator to use for ts
problem?Eric> You're probably using an explicit RK4.> Explicit
RK schemes do not conserve energy.> That is probably the reason
for your troubles.You should try a symplectic implicit
RK.Simplectic methods do not necessarilyconserve energy.
Neither condition impliesthe other.===Subject: Re: Numerical
quadratures for irregular gridsI am looking for the algorithms
of numerically evaluating> integrals of functions of one (x)
and two (x,y) variables, at the> assumption that the function
values are available exclusively as a> collection of discrete
values, and that the grids of x or (x,y) points> at wch the
function values are given are generally irregular> (please
note that dard textbooks discuss almost exclusively the case>
of regular grids, with cont grid spacings).> I am interested
not only in the theory of various approximations> to the
integrals in such cases, but also in practical algorithms> of
navigating through the sets of discrete function
data.<SNIP>The Fortran 90 code INTEGRAL_TEST by Burkardt,
available
athttp://www.csit.fsu.edu/~burkardt/f_src/integral_test/
integral_test.html, may be applicable (I have not used it).
Quoting the site, Eachintegral is to be approximated simply by
averaging the integrandvalues at each point in the dataset, and
multiplying by the volume ofthe integration region. (In a few
cases, where the integral is notover the unit hypercube, the
dataset points are suitably adjusted).===Subject: real
analysis by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i0UMJF720606;A polynomial P
of degree n (n> k)has the property that P(c)=...=P(k)(c)=0,
where P(j)(c) is the jth derivative of P at c.Show that
P(c)=(x-c)(k+1)Q(x){(x-c)(k+1)represents (x-c)to the power
(k+1)}whereQ(x) is a polynomial of degree n-k-1.===Subject:
Looking for an area in Mathematics by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i0UMuvD23728;I want to know if there is a particular area of
mathematics thatstudies the nature of equations of state in
mathematical models as themagnitude of variables
change.Specifically, ways of producing and characterizing as
families (orsometng) the symbolic form of approximating
functions.E.G.
consider:Z=(1-w^2*(C1+C2)*L)/((1-w^2*C2*L)*(i*w*C1+G))As L or
w gets small, Z kinda = 1/(i*w*C1+G), though in one
conditionit is a beeter approximation than the other.As C2
gets small, Z kinda = (1-w^2*C1*L)/(i*w*C1+G)If there were
less brute force yet more powerful/general ways ofcomming up
with simple symbolic approximations to formulae, I wouldlike
to know about it. I am hoping to find powerful theorems and
toleverage insights from great Mathematical minds.Is there a
field or sub-feild I should investigate to find
informationalong these lines. ===Subject: pairing/partitioning
algorithmi'm working on a problem where you have a class of N
students who haveM projects. on each project the students will
work in pairs.. and ifthere is an odd number of students then
there will be one threesome. Students should never work with
the same person twice (even if one ofthose times was a
threesome).I am stuck coming up with an algorith to determine
all of the possiblegroupings for any number N. If N is even
then the problem is trivialbut if N is odd.. it seems quite
difficult to me. When N=5, M canonly be one, when N=7, max M =
3. when N=11, max M = 6.Any help???===Subject: Intel Fortran
for Windows: student edition $29>Wle browsing Programmer's
Paradise, I saw that a student edition of>Intel Visual Fortran
for Windows 8.0 is available for $29. The link
is>http://www.programmersparadise.com/Product.pasp?txtCatalog=
Paradise&txtCategory=&txtProductID=I23+0D03> Ts product should
give Matlab a run for its money, and> run your problems in
seconds instead of days!===Subject: Re: Intel Fortran for
Windows: student edition $29Has anyone tried Visual Fortran?
What is it like - anytng like Delp,uilder, etc?>Wle browsing
Programmer's Paradise, I saw that a student edition of>Intel
Visual Fortran for Windows 8.0 is available for $29. The link
is>http://www.programmersparadise.com/Product.pasp?txtCatalog=
Paradise&txtCate > Ts product should give Matlab a run for its
money, and> run your problems in seconds instead of
days!===Subject: Re: Intel Fortran for Windows: student
edition $29>Wle browsing Programmer's Paradise, I saw that a
student edition of>Intel Visual Fortran for Windows 8.0 is
available for $29. The link is>
>http://www.programmersparadise.com/Product.pasp?txtCatalog=
Paradise&txtCategory=&txtProductID=I23+0D03> Ts product should
give Matlab a run for its money, and> run your problems in
seconds instead of days!You mean people actually *pay* for
FORTRAN compilers???===Subject: Re: Intel Fortran for Windows:
student edition $29Wle browsing Programmer's Paradise, I saw
that a student edition ofIntel Visual Fortran for Windows 8.0
is available for $29. The link is>
>http://www.programmersparadise.com/Product.pasp?txtCatalog=
Paradise&txtCategory=&txtProductID=I23+0D03 Ts product should
give Matlab a run for its money, and run your problems in
seconds instead of days!You mean people actually *pay* for
FORTRAN compilers???Yes, they do, for at least two reasons.
(1) Most commercial Fortran compilers run Fortran 77 codes
faster thang77 -- see the Fortran 77 Execution Time Benchs
atwww.polyhedron.co.uk. For certains codes, the difference can
bedramatic -- a factor of more than 3.(2) G77 is a Fortran 77
compiler. Fortran has advanced past Fortran77, the latest dard
being Fortran 95, wch offers many newfeatures, such as
structures, array operations and modules (wchallow for
automatic procedure interface checking). F77 is retained asa
subset in F95. One site discussing the differences between
Fortran77 and 90 is
http://www.nsc.liu.se/~boein/f77to90/f77to90.html .===Subject:
Re: Nonlinear curve fit for saturation data> I need an
automated method to fit a curve of the form y =>
c*x*(1+a*e^(b*x)) to test data.> Voc(PU) Igf(A)> 0.196 5.00>
0.304 7.85> 0.399 10.43> 0.616 16.20> 0.797 21.54> 0.906
25.89> 0.942 29.01> 1.014 32.75> 1.051 37.25> 1.105 44.80>
1.196 61.18> 1.304 105.61Ts is approximately fit with:a =
0.000232> b = 7.005> c = 25.74Fitting to lowest sum of squared
relative error, I get:a = 2.45216969e-004b = 6.96242410e+000c =
2.56948865e+001wch seemed to me the best result of the
fittingtargets I tried. Fitting to lowest sum of
squaredabsolute error, I get:a = 0.02081207b = 4.03580003c =
15.44149065wch is rather a bit different. I'm adding ts
equationto my curve fitting site now. James Pllips
http://zunzun.com===Subject: 2-D convolution using FFTW3, I
want to do a 2-D real discrete convolution using FFTW3, but
theresult is wrong compared with the directly convolution. Can
anybody tell me the reason and the proper solution using
FFTW3?===Subject: 2-D convolution using FFTW3 everyone, I want
to do a 2D real discrete convolution using FFTW3, can anybody
hel me?=== Subject: C routines for Special FunctionsSome
heroes out there generously provide a tarball(usually called
specfun.tar.gz) containingroutines that compute special
functions like Gamma,Confluent Hypergeometric, Struve, and
other dardand exotic beasts. I've found ts collection
inFortran77 and Matlab (see links below), but I've beenunable
to locate the analogous routines written in C.Does anyone know
a link where I can get these routinesin C?Here's some links for
the interested:Fortran77
http://iris-lee3.ece.uiuc.edu/~jjin/routines/
routines.htmlMatlab http://ceta.mit.edu/comp_spec_func/===
Subject: Re: C routines for Special Functions so much for the
Fortran Source> Some heroes out there generously provide a
tarball> (usually called specfun.tar.gz) containing> routines
that compute special functions like Gamma,> Confluent
Hypergeometric, Struve, and other dard> and exotic beasts.
I've found ts collection in> Fortran77 and Matlab (see links
below), but I've been> unable to locate the analogous routines
written in C.> Does anyone know a link where I can get these
routines> in C?Here's some links for the interested:Fortran77
>
http://iris-lee3.ece.uiuc.edu/~jjin/routines/
routines.htmlMatlab >
http://ceta.mit.edu/comp_spec_func/===Subject: Re: C routines
for Special Functions> Some heroes out there generously
provide a tarball> (usually called specfun.tar.gz) containing>
routines that compute special functions like Gamma,> Confluent
Hypergeometric, Struve, and other dard> and exotic beasts.
I've found ts collection in> Fortran77 and Matlab (see links
below), but I've been> unable to locate the analogous routines
written in C.> Does anyone know a link where I can get these
routines> in C?<SNIP>Some sources of C code for special
functions, the first two being themost important, areC
Mathematical Function Handbook (1992)by Louis Baker Atlas for
Computing Mathematical Functions: An Illustrated Guide
forPractitioners: With Programs in C and Mathematica (1997)by
William J. ThompsonA Numerical Library in C for Scientists and
Engineers (1994)by H. T. Lauwww.nr.comNumerical Recipes in C,
2nd Edition (1992)by Press, Flannery, Teukolsky, and
Vetterling===Subject: Re: C routines for Special
FunctionsDistribution: inet> Some heroes out there generously
provide a tarball> (usually called specfun.tar.gz) containing>
routines that compute special functions like Gamma,> Confluent
Hypergeometric, Struve, and other dard> and exotic beasts.
I've found ts collection in> Fortran77 and Matlab (see links
below), but I've been> unable to locate the analogous routines
written in C.> Does anyone know a link where I can get these
routines> in C?I did a Google search for Computation of
Special Functions C sourceand found:
http://www.esg.dees.unict.it/esg/gborzi/mathlib.html
http://www.crbond.com/math.htmBut comp.lang.c is not
comp.sources.wanted, so please take tsdiscussion elsewhere.,
-===Subject: Re: C routines for Special Functions>Some heroes
out there generously provide a tarball>(usually called
specfun.tar.gz) containing>routines that compute special
functions like Gamma,>Confluent Hypergeometric, Struve, and
other dard>and exotic beasts. I've found ts collection
in>Fortran77 and Matlab (see links below), but I've
been>unable to locate the analogous routines written in
C.>Does anyone know a link where I can get these routines>in
C?Have a look at http://www.netlib.org/cephes/. GSL ties you
into a numberof bad design decisions that make it clumsy to
use.===Subject: Re: C routines for Special Functions> Have a
look at http://www.netlib.org/cephes/. GSL ties you into a
number> of bad design decisions that make it clumsy to
use.response to another poster, I am aware of the GSLsoftware.
I avoid it when I can for a variety of reasons,none of them
particularly deep. I'll mention a couple oftngs though. I
don't like the cumbersome routine nameswith gsl_blah_blah
tacked onto everytng in sight. Itmakes for ugly code, in my
opinion. Second, they'll havetngs like the F-distribution, but
no function for theinverse of the F-distribution. Tngs like
that are annoying...GSL is incomplete for my purposes. Fortran
and Matlab havemany free routines available for the special
functions and Ijust figured the same tng was out there for C,
that's all.By the way, from my brief perusal of ts newsgroup,
I must sayI'm stunned that so much time is spent by people
bitcng aboutnetiquette (for what seem usually to be rather
innocent or trivialbreaches). Must be that programmer
mentality at work...===Subject: Re: C routines for Special
Functions> GSL ties you into a number of bad design decisions>
that make it clumsy to use.Would you care to
elaborate?===Subject: Re: C routines for Special Functions>>
GSL ties you into a number of bad design decisions>> that make
it clumsy to use.>Would you care to elaborate?Of course ts is
just my opinion. I tnk the GSL group is doinga great service
and since the code is GPL I should really be rollingup my
sleeves and coding instead of complaining. :-)When the first
example program in their documentation defines 'intmain(void)
{ ... }' you have to wonder a bit. Why the 'void'? Itis
perfectly legal, just odd looking and unnecessary. When I
wasevaluating ts for use in a production library at a large
EquityDerivatives firm a couple of years ago, I kept finding
'odd' tngs.Ultimately I chose a Fortran library because GSL
was not sufficientlymature at that time. It has definitely
come a long way since then.If you belive a modern library
should be written in C instead of C++,you can stop reading
now. Many of my qualms are due to issues relatingto the
gyrations GSL goes to because it does not use C++. I've
takenflak over the years for insisting on writing certain
libraries in C (andeven more flak for using Fortran) but I
have come to the conclusion thatthe small audience that
insists on C is, well, small. I'm open to dataindicating
otherwise.Error HandlingI'm not a fan of the 'int status =
gsl_function(...); if (status){...' method of error handling
for functions that return doubles.I am especially not a fan of
having default error handlers callabort(), like the assert
macro in C. Of course I've had the headof IT tear me a new
asshole when a programmer of mine left an assertin production
code that got called 15 minutes before et open,so I can't
claim to be unbiased.GSL does have 'natural form' calling
conventions available (morecode on their side to maintain) but
they do not permit errorchecking. I prefer returning NaN's that
have embedded errorinformation. If you don't check the return
codes, at least yourprogram is more likely to return gibberish
than to crash.Vector and Matrix RoutinesThey do a fine job, but
I would love to see sometng more alongthe lines of
http://okmij.org/ftp/LinAlg.README.txt. I've tried outevery
vector/matix library on the planet, I tnk, from BLAS and
LAPACKto the compiler busting Blitz++. Simple C++ wrappers for
the former seemto be the best solution for my needs.General
CommentsExcessive use of C macros in source code. Makes the
code hard tounderd/fix/maintain.Not modular. Dependencies
between modules should be explicit.At any rate, that's my 2
cents. Feel free to disagree, it's an internetnewsgroup after
all. Comments are welcome.===Subject: Re: C routines for
Special Functions> When the first example program in their
documentation defines 'int> main(void) { ... }' you have to
wonder a bit. Why the 'void'? It> is perfectly legal, just odd
looking and unnecessary.... and I replied that in C, as opposed
to C++, it is necessary.That was an error; I apologize. It is
unnecessary in C as wellas in C++. However, I don't tnk it's
odd looking in C. Afterall, when you're declaring but not
defining a no-argument functionin C you have to[1] include the
void, so C programmers areused to seeing no-argument functions
with (void) for argument list. [1] If you want the compiler to
be able to check that the function is being used properly,
anyway.-- === Subject: Re: C routines for Special Functions>
GSL ties you into a number of bad design decisions> that make
it clumsy to use....> When the first example program in their
documentation defines 'int> main(void) { ... }' you have to
wonder a bit. Why the 'void'? It> is perfectly legal, just odd
looking and unnecessary.It would be unnecessary in C++, but not
in C.> I'm not a fan of the 'int status = gsl_function(...); if
(status)> {...' method of error handling for functions that
return doubles.> I am especially not a fan of having default
error handlers call> abort(), like the assert macro in C. Of
course I've had the head> of IT tear me a new asshole when a
programmer of mine left an assert> in production code that got
called 15 minutes before et open,> so I can't claim to be
unbiased.GSL does have 'natural form' calling conventions
available (more> code on their side to maintain) but they do
not permit error> checking. I prefer returning NaN's that have
embedded error> information. If you don't check the return
codes, at least your> program is more likely to return
gibberish than to crash.It could be argued that it's better
for your programto crash than to return gibberish, especially
if it'sbecause you haven't bothered to check for errors...--
===Subject: Re: C routines for Special FunctionsSee the GNU
GSL library.===Subject: Re: C routines for Special Functions>
See the GNU GSL library.
http://sources.redhat.com/gsl/===Subject: Finding all possible
bit patternsI am looking for a formula to calculate the number
of all possibledifferent patterns of bit with the following
parameters:- The vector has 13 free spaces.- There are 7 bits
to place.For example, here are all the possibilities for a
vector with 4 freespaces and 2 bits to
place.110010101001011001010011Total = 6 possibilities. very
much.===Subject: Re: Finding all possible bit patternsI am
looking for a formula to calculate the number of all possible>
different patterns of bit with the following parameters:- The
vector has 13 free spaces.> - There are 7 bits to place.For
example, here are all the possibilities for a vector with 4
free> spaces and 2 bits to place.1100> 1010> 1001> 0110> 0101>
0011Total = 6 possibilities. very much.The answer is the
binomial coeffient pronounced 13 choose 7. Youusually see it
written as a large set of parentheses with one letteror number
above the other, but without a fraction bar, such as/ 13 | |. 7
/ The formula for n choose k is n!/((n-k)! * k!), where
theexclamation point indicates factorial. Thus, in your
example, 4choose 2 = 4!/((4-2)! * 2!) = 4!/(2! * 2!) =
1*2*3*4/(1*2 * 1*2) =24/4 = 6. I'll let you work out 13 choose
7.Dave===Subject: Re: Finding all possible bit patternsI am
looking for a formula to calculate the number of all possible>
different patterns of bit with the following parameters:- The
vector has 13 free spaces.> - There are 7 bits to place.For
example, here are all the possibilities for a vector with 4
free> spaces and 2 bits to place.1100> 1010> 1001> 0110> 0101>
0011Total = 6 possibilities. very much.let n be free spaces, m
be places to putpossibilities = n choose m :=
n!/(m!*(n-m)!)===Subject: 2D discrete hartley transformI'm
trying (unsuccessfully) to find some C code that can perform a
2D-DHT onreal-valued data obtained from a 2D image. Does anyone
have workable codethey are willing to share? I've been plugging
away with the implementationof fftw_dhtin fftw, but I'm finding
it more than challenging to sort through theircode.-- ===
Subject: Re: 2D discrete hartley transform> I'm trying
(unsuccessfully) to find some C code that can perform a 2D-DHT
on> real-valued data obtained from a 2D image. Does anyone have
workable code> they are willing to share? I've been plugging
away with the implementation> of fftw_dht> in fftw, but I'm
finding it more than challenging to sort through their>
code.Note, first of all, that the true 2D DHT is not the
separable product of 1D DHTs along the rows and columns
(unlike the 2D DFT). FFTW's DHT would compute the latter if
you ask it for a 2d transform, as described in the
manual...you need an additional post-processing pass for the
non-separable 2D DHT (see the FFTW manual for references). I
haven't seen any other free code that computes a true 2d DHT
lying around, either; it's all 1d DHTs.Second, why do you need
a 2D DHT? I'm very curious to know what it is good for that a
2D real-input DFT is not as good or better at.Trd, if by sort
through their code you mean compile it, I'm guessing you are a
Windows user, in wch case see fftw.org/install/windows.html for
precompiled packages; otherwise, compilation is easy. If you
want to read source code for learning the algorithms, though,
then FFTW is not ideal for beginners.=== Subject: Sorgenfrey
line / closed-open topology by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i113m1x28883;R with the closed-open topology IS separable,
first countable (it hasa countable open base), but NOT secound
countable.Since any separable metric space is second countable,
we see thatR with ts topology is not a metric space (not
metrizable).In fact, every second countable, normal T1-space
is metrizable;R with the closed-open topology is normal and
T-1 but not secondcountable. ===Subject: Problems with
equationsI need to solve these
equations:|x+a|=Sqrt[(y-b)^2+(z-c)^2]|x+d|=Sqrt[(y-e)^2+(z-f)^
2]|x+g|=Sqrt[(y-h)^2+(z-i)^2]where x,y,z - variablesCould
someone, who has Mathematica program or sth else, solve
theseequations and send me solution (txt, jpg, ... etc).
Please.Solution can be very large.===Subject: Re: Problems
with equations> I need to solve these
equations:|x+a|=Sqrt[(y-b)^2+(z-c)^2]>
|x+d|=Sqrt[(y-e)^2+(z-f)^2]> |x+g|=Sqrt[(y-h)^2+(z-i)^2]where
x,y,z - variablesCould someone, who has Mathematica program or
sth else, solve these> equations and send me solution (txt,
jpg, ... etc). Please.Solution can be very large.It doesn't
look that hard. Let's give it a try...Start by squaring both
sides of each equation.(x+a)^2 = (y-b)^2+(z-c)^2(x+d)^2 =
(y-e)^2+(z-f)^2(x+g)^2 = (y-h)^2+(z-i)^2Now expand the
binomials.x^2 + 2ax + a^2 = y^2 -2by + b^2 + z^2 - 2cz +
c^2x^2 + 2dx + d^2 = y^2 -2ey + e^2 + z^2 - 2fz + f^2x^2 + 2gx
+ g^2 = y^2 -2hy + h^2 + z^2 - 2iz + i^2Subtract the second
from the first, subtract the trd from the first,and then
subtract the trd from the second.2ax - 2dx + a^2 - d^2 = -2by
+ 2ey - 2cz + 2fz + b^2 - e^2 + c^2 - f^22ax - 2gx + a^2 - g^2
= -2by + 2hy - 2cz + 2iz + b^2 - h^2 + c^2 - i^22dx - 2gx + d^2
- g^2 = -2ey + 2hy - 2fz + 2iz + e^2 - h^2 + f^2 - i^2Put the
x, y, and z terms on the left and the conts on the right,and
factor.(2a-2d)x + (2b-2e)y + (2c-2f)z = -a^2 + b^2 + c^2 + d^2
- e^2 - f^2(2a-2g)x + (2b-2h)y + (2c-2i)z = -a^2 + b^2 + c^2 +
g^2 - h^2 - i^2(2d-2g)x + (2e-2h)y + (2f-2i)z = -d^2 + e^2 +
f^2 + g^2 - h^2 - i^2Now, you notice that the three equations
are linearly dependent: thetrd equation equals the second
minus the first. Thus, you reallyhave two equations in three
unknowns. Therefore, you can't expect aunique solution.Tnk
about the two-dimensional version of your equations:
twoequations involving only x and y. They would represent
theintersection of two circles. There are four cases: the
circles areidentical so that they intersect at an infinite
number of points, (2)the circles overlap so they intersect at
two points, (3) the circlesare tangent so they intersect at
only one point, or (4) the circlesmiss each other completely
so they do not intersect at all.In your case, you have the
intersection of three spheres, so you havecorrespondingly more
possibilities. I am going to leave you to findthe general
solution of the any set of two of the above three
linearequations. If the conts a through i are such that the
equationsare consistent, then there will be one or more
solutions. Otherwise,there will be no
solutions.Dave===Subject: Re: Problems with equations> I need
to solve these equations:|x+a|=Sqrt[(y-b)^2+(z-c)^2]>
|x+d|=Sqrt[(y-e)^2+(z-f)^2]> |x+g|=Sqrt[(y-h)^2+(z-i)^2]...>
x^2 + 2ax + a^2 = y^2 -2by + b^2 + z^2 - 2cz + c^2> x^2 + 2dx
+ d^2 = y^2 -2ey + e^2 + z^2 - 2fz + f^2> x^2 + 2gx + g^2 =
y^2 -2hy + h^2 + z^2 - 2iz + i^2...> (2a-2d)x + (2b-2e)y +
(2c-2f)z = -a^2 + b^2 + c^2 + d^2 - e^2 - f^2> (2a-2g)x +
(2b-2h)y + (2c-2i)z = -a^2 + b^2 + c^2 + g^2 - h^2 - i^2>
(2d-2g)x + (2e-2h)y + (2f-2i)z = -d^2 + e^2 + f^2 + g^2 - h^2
- i^2Now, you notice that the three equations are linearly
dependent: the> trd equation equals the second minus the
first. Thus, you really> have two equations in three unknowns.
Therefore, you can't expect a> unique solution.But you've
thrown away some information with all thesubtraction you've
done. What you have there is P-Q, P-R, Q-R,and those *aren't*
equivalent to P,Q,R.> In your case, you have the intersection
of three spheres, so you have> correspondingly more
possibilities.They are cones, not spheres. But it's much
better to tnkof it as the intersection between *one* cone and
the solutionto two of those linear equations.-- ===Subject:
Re: Problems with equations> I need to solve these
equations:|x+a|=Sqrt[(y-b)^2+(z-c)^2]>
|x+d|=Sqrt[(y-e)^2+(z-f)^2]> |x+g|=Sqrt[(y-h)^2+(z-i)^2]where
x,y,z - variablesTs looks like a homework problem to me. Here
aresome nts. - You can get rid of the square roots. - What
happens when you subtract one of the resulting equations
(after eliminating the square roots) from another?--
===Subject: intriguing numbers. by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i11Cisg08313;i just read sometng in a magazine (forgot what
title.) a smalltrue or not. because it seems very interesting.
two numbers intriguedme. one is the number  (psi) and they said
that its the so-calledlast finite number. the number right
before infinity. and a veryshort mention on sometng called the
end number. the end number isthe ghest in the kingdom of
numbers and makes absolute infinity adust on its shoulder.
notng is gher than the end number because bytheory it is the
last number. now i was very intrigued and suddenly itbecame my
favorite number. so please verify ts for me.===Subject: Re:
intriguing numbers.I tnk you are nuts! If you would like to
learn more about the(real) math of infinity, check out ts page
from mathworld and thepages linked to
it.http://mathworld.wolfram.com/Aleph-0.html ===Subject: small
eigenvalues Suppose 0<=l1 <= l2 <= ... <=ln are the eigenvalues
of a real symmetric matrix. Let lr be the first non-zero
eigenvalue, i.e. 0=l1=...=l(r-1)<lr<=...<=ln.Obviously,
numerically, the 0 eigenvalues are not exactly 0.There must be
a mathematical argument or a heuristic for decidingwhat r is.
Forgive my ignorance, I'm not a numerical analysis person, but
trying to learn these tricks as I run into them.