mm-2279
===
Subject: Re: Numbers 2-9 forbidden now
Non-binary numbers have been encroaching upon digital space for too long.
Although training is offered, most humans refused to learn binary and rely
on
the primitive forms of number representation, which are not needed by
computers..
In addition, 1 and 0 will soon be replaced with;
mark, and not mark (or space)
mark has been shortened to -, and non-mark is
Therefore, one using the forbidden numbers is sentenced to -- --
years.
Also, the world conference has agreed that the number of letters in the
alphabet is excessive
and will reduce it by half, they are currently negotiating which ones to
keep.
(Chinese characters are next)
............................................................................
..................
> Sorry, international laws now prohibit the use of the numbers 2-9,
> itĒs only allowed to use 0 and 1 for binary calculations
now.
> Anyone using forbidden numbers will be sentenced to 1100011 years in
> prison.
===
Subject: Re: Numbers 2-9 forbidden now
I propose instead to use hexadecimal system for everyday life.
ID cards, calendars,... everything to be changed to hexadecimal.
Schoolchildren will have to learn the multiplication table for FxF
instead of 10x10.
===
Subject: Re: Help! LP with recourse
I am sorry that this is not a Linear Problem. (I do not know why I
for each m and n. The probabilties p_n are fixed and known parameters.
b_m^{max} are also fixed paramenters for each m.
Stan
>
> This is a linear problem? The player utility functions are linear?
>
> Also, it's a bit unclear what's a parameter and what's a variable. Your
> notation in the original problem suggests that you're solving for both
> the b_m^{n} and the probabilities (since it looks like you constrained
> the probabilities to sum to one). Is that right, or are the
> probabilities given? Is b_m^{max} fixed for each m?
>
> -- Paul
===
Subject: Re: Help! LP with recourse
>
> I am sorry that this is not a Linear Problem. (I do not know why I
> for each m and n. The probabilties p_n are fixed and known parameters.
> b_m^{max} are also fixed paramenters for each m.
>
> Stan
>
>
>>This is a linear problem? The player utility functions are linear?
>>Also, it's a bit unclear what's a parameter and what's a variable. Your
>>notation in the original problem suggests that you're solving for both
>>the b_m^{n} and the probabilities (since it looks like you constrained
>>the probabilities to sum to one). Is that right, or are the
>>probabilities given? Is b_m^{max} fixed for each m?
>>-- Paul
Got it. You might try doing a variation of Bender's decomposition.
Your original problem was
Max sum_{n=1}^{N} (p_n * sum_{m=1}^{M} (U_m(b_1^{n},...,b_M^{n})) )
s.t. p_1*b_m^{1}+...+p_N*b_m^{N} <= b_m^{max}
where the variables are b_m^{n} (m=1..M, n=1..N), which I assume are
nonnegative. You say you can solve it efficiently for a single
realization. So let's make b_m^{n,max} (nonnegative) variables, add
variables z_1 ... z_N, and rewrite the problem as
Max sum_{n=1}^{N} p_n * z_n
s.t. p_1*b_m^{1,max}+...+p_N*b_m^{N,max} <= b_m^{max} for all m
b_m^{n} <= b_m^{n,max} for all m, n
z_n <= sum_{m=1}^{M} (U_m(b_1^{n},...,b_M^{n})) ) for all n
Now split this into a master problem
Max sum_{n=1}^{N} p_n * z_n
s.t. p_1*b_m^{1,max}+...+p_N*b_m^{N,max} <= b_m^{max} for all m
and N subproblems
Max z_n = sum_{m=1}^{M} (U_m(b_1^{n},...,b_M^{n})) )
s.t. b_m^{n} <= b_m^{n,max} for all m
Start with some initial allocation such as b_m^{n,max} = b_m^{max}/N for
all m, and solve all the subproblems. What you want is to generate,
from the solution of subproblem n, a constraint in the master problem of
the form
z_n <= f(b_1^{n,max}, ..., b_M^{n,max}).
If the utility functions are concave and smooth, I think you can do this
using Karush-Kuhn-Tucker multipliers (with f() linear). Toss those
constraints into the master problem, solve that to get new allocations
b_m^{n,max} for all m and n, solve the subproblems again, ad nauseum.
(It's the tail end of a long day and I'm rushing to get out of here, so
I apologize if I stepped on my tongue in any of this.)
-- Paul
===
Subject: golden section and music
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i3736lK08915;
hello, my name is raquel and i am a student at california state
university northridge. I was wondering if any math scholar or
professor would be kind enough to tell me where i can search the web
for information on the relationship between golden section and music,
and the golden bach conjecture number theory and music.
thankyou
===
Subject: Re: golden section and music
> hello, my name is raquel and i am a student at california state
> university northridge. I was wondering if any math scholar or
> professor would be kind enough to tell me where i can search the web
> for information on the relationship between golden section and music,
> and the golden bach conjecture number theory and music.
> thankyou
[A better forum would be sci.math]
You may start with
The Divine Proportion, A Study in Mathematical Beauty
by H.E. Huntley,
Dover Publications 1970
ISBN 0-486-22254-3
and references at the end of the book.
===
Subject: Re: golden section and music
http://www.personal.uni-jena.de/~x8moma/goldensection.htm
http://www.golden-section.de.vu/
http://www.2x3cp.com/trading/23/the-golden-section-music.html
===
Subject: C++: Numerical optimization. HELP, PLEASE!!!!
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i3736n908975;
Hello.
Please, guys help me!!! E-mail some links etc (programs, papers...
anything!) with ANY realizations of numerical optimization methods
(Nuton, OPG/BHHH...) in C++.
===
Subject: Re: C++: Numerical optimization. HELP, PLEASE!!!!
> Hello.
>
> Please, guys help me!!! E-mail some links etc (programs, papers...
> anything!) with ANY realizations of numerical optimization methods
> (Nuton, OPG/BHHH...) in C++.
Newton, not Nuton. There is optimization code in C in the Gnu
Scientific Library http://www.gnu.org/software/gsl/ and in C and C++
in Numerical Recipes
http://www.nr.com (code not free) . There are links to C++
optimization codes at http://www.mathtools.net/C++/Optimization/ , and
links to optimization codes in all languages, including some C++ , at
http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/index.html .
===
Subject: Re: C++: Numerical optimization. HELP, PLEASE!!!!
>Hello.
>Please, guys help me!!! E-mail some links etc (programs, papers...
>anything!) with ANY realizations of numerical optimization methods
>(Nuton, OPG/BHHH...) in C++.
Acha... Homework deadline tomorrow?...
A.L.
===
Subject: Re: C or C++ routien for calc matrix inverse
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i3736lM08897;
There's a very nice C++ template matrix library with quite
comprehensive linear algebra support at
http://www.osl.iu.edu/research/mtl
I'm not certain if it's still under development and supported but I
think it deserves to be. I think it the best for vector and matrix
algebra that I've come across and it supports sparse matrices of
various shades. It will take a while to get into but this will pay
off.
Dafydd
===
Subject: Re: Probability calculation
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i3736kU08874;
A box contains 6 red balls, 4 white balls and 5 blue balls. If I take
3 balls from the box, what is the probability that I will have 1 red,
1 white and 1 blue, in that order, if I:
-return each ball
-do not return each ball
_________________________
What is the probability of throwing a dice and obtain, at least, a 4?
===
Subject: Re: fixed-point real FFT for embedded
> > Hi !
> > I'm working on real-time speech recongnition application for
embedded
> > systems (with ARM compatible processor).
> > I'm looking for a very fast (for real-time) real FFT fixed-point
> > version, with 16-32 bit input percision, up to 512 array-size.
>
>
> I just released KISSFFT version 1.2.1, which focuses on embedded & code
> size issues.
>
> See
> http://sourceforge.net/projects/kissfft/
>
>
> At the risk of dissuading you from using my fine little library ...
> Have you looked on developer.intel.com for FFT libraries for your
> flavor of ARM? If they provide an FFT, it is *gulp* probably better
> than portable C code such as kissfft. Using assembly code, one can most
> efficiently implement bit-reversed indexing, overflow managment,
> rounding, scaling, etc.
>
> -- Mark Borgerding
I'm going to try your library, though with 32 bits accuracy,
and check it on the iPaq.
but I need some other fixed-point sources to compare it with.
I think we should do a contest for fixed-point FFT by benchmarking on
iPaq/Palm (Windows CE/Palm OS) etc..
what do you think ? you have a good starting point with your _small_
library !
if anyone is up to the challenge please post here,
I believe the embedded community will definitely harvest the fruits.
good luck !
===
Subject: Re: Sum of Squares
>
> I wish to introduce my contribution on number theorem whereby I found
> a method of solving an equation whereby a number, a is given and it is
> required to find two other numbers, b and c such that a^2 + b^2 =
> c^2.
>
> Also, I found a method through which a trianle of sides a, b and c
> could be created such that all the three numbers are rational and the
> two sides other than the hypothenus maintain a gien ration.
>
> May you have interest in having these, I shall forward it to you
> togethe with their proofs.
>
>
> Musa Dayyib
Why not post your ideas here? But - it's always a good idea to look
what others have found in the last ~3000 years, so look at
Michael Somos' Rational Triangle Page
http://grail.cba.csuohio.edu/~somos/rattri.html
http://www.ics.uci.edu/~eppstein/junkyard/q-triangle.html
http://en.wikipedia.org/wiki/Pythagorean_triple
Do you have anything that is not on
http://mathworld.wolfram.com/PythagoreanTriple.html ?
Hugo
===
Subject: nonlinear system _fixed point
I have stack with 4 nonlinear system
equation .one of them is given below
x E^(xy+0.8) + E^(y^2) - 3=0
x^2-y^2-0.5 E^(xy)=0
[^ -- means 'to the power'.e.g 2^2=4 ]
Any one know that how i can solve it
using fixed point method (exam).
Is it possible to solve using fixed point method?
I have tried a lot but fail ..
please help me .
===
Subject: Re: nonlinear system _fixed point
>I have stack with 4 nonlinear system
>equation .one of them is given below
>
>x E^(xy+0.8) + E^(y^2) - 3=0
>
>x^2-y^2-0.5 E^(xy)=0
>
>[^ -- means 'to the power'.e.g 2^2=4 ]
>
>Any one know that how i can solve it
>using fixed point method (exam).
>
>Is it possible to solve using fixed point method?
>
>I have tried a lot but fail ..
>
>please help me .
which form of fixed point iteration? no problem for newtons method
starting from 1.5,1, after 8 steps I got
x,y= .7749760127D+00 .1716309518D+00
f[ 1]= .0000000000000000E+00 f[ 2]= -.3330669073875470E-15
but clearly there will be forms of direct iteration for the above which will
not work
hth
peter
===
Subject: [Introduction fea in Mechanical elasticity problems 2D/3D]
I'm interresting in theorie and impemantation in C++ of fea in
Mechanical elasticity problems 2D/3D.
I'm wondering there is no a lot of papers or example of this theme.
hackervalley
http://hackervalley.free.fr
===
Subject: Re: [Introduction fea in Mechanical elasticity problems 2D/3D]
>
> I'm interresting in theorie and impemantation in C++ of fea in
> Mechanical elasticity problems 2D/3D.
>
> I'm wondering there is no a lot of papers or example of this theme.
>
>
>
> hackervalley
> http://hackervalley.free.fr
>
Well, the theory can be found in The Finite Element Method, Linear
Static and Dynamic Finite Element Analysis by T.J.R. Hughes, and I guess
a c++ implementation is here:
http://libmesh.sourceforge.net/
-Nyarlathotep
===
Subject: Re: Line Minimization
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37CjGF09158;
>CG+ is a Fortran 77 routine for conjugate gradient minimzation,
>available at http://www.ece.nor
thwestern.edu/~rwaltz/CG+.html
.
>Numerical Recipes has a conjugate gradient routine called frprmn. The
>NR library can be purchased for a small price from www.nr.com.
>I doubt that the routines will satisfy your criterion that the step
>size be large -- maybe you can modify them. To reduce the noise in
>your objective function, you could try to use the same stream of
>random numbers to calculate function values for different values of
>its arguments.
>It is my impression from reading the literature that Quasi-Newton
>methods usually converge to the minimum with fewer function
>evaluations than CG. Why do you prefer CG for your application?
I decided to look into CG due to the high dimensionality which would
rule out methods that require O(N^2) storage.
>There are links to optimization codes in Fortran at
>http://www.dmoz.org/Computers/Programming/Languages/Fortra
n/Source_Code/Optimization/
===
Subject: Re: Line Minimization
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37CjFg09152;
>I wonder how you may compute derivatives from noisy data and
>I do not believe that it makes sense to use conjugate gradients for
>minimization of noisy functions.
>some day's ago arnold neumaier announced his snobfit software, this
might be
>a way to go. or look at
>http://plato.la.su.edu/guide.html
hth
>peter
I decided to go with conjugate gradients because of the high
dimensionality which would preclude methods of O(N^2) storage.
Evolutionary or genetic algorithm will probably be the most robust but
I doubt it that they would be cheaper than
the stochastic gradient descent approach that I've been using thus
far (it actually converges but it is quite slow and expensive).
My objective function (which btw is convex) is noisy but not so noisy
that would constitute derivatives useless (if that makes any sense).
I have read some papers by N.Schraudolph who proposes some variations
of CG for this kind of problems and which seem to perform quite well
for the example he uses them for.
The line minimization routine should play a critical role though, for
the aforementioned reasons.
===
Subject: Re: level set method
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37CjGN09196;
level set - matematicheskij termin. Znachit mnozhestvo urovnja
A.
>Hi!
>Anybody who know something about the level set method (uses to
solve
>problems with moving interfaces and so on). I need to understand a
>meaning of a term level set because I need to translate this
>expression from english to russian.
>WBR.
===
Subject: Complex ode solver
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37CjFF09135;
Does anyone know an ode solver (either in C or fortran) which takes
into account directly complex numbers?
===
Subject: Re: Complex ode solver
> Does anyone know an ode solver (either in C or fortran) which takes
> into account directly complex numbers?
>
There is RKSUITE_90 at http://www.netlib.org/toms/771 . It seems to
handle complex ODEs indirectly. I could not find any Fortran codes
explicitly for complex ODEs. Quoting that site,
RKSUITE_90 is a module based on Runge-Kutta formulas that solves the
initial value problem for ordinary differential equations. It
integrates
y' = f(t,y), y(t_start) = y_start.
Here y is the solution (dependent variable) and t is the independent
variable. The integration proceeds from t = t_start to t = t_end.
The most commonly occurring case is where y and f are real vectors. At
the end of this section, we discuss how to produce automatically a
version of RKSUITE_90 for the cases where y and f are scalars, vectors
or matrices and for the cases where y and f are real or complex.
===
Subject: Re: using nonlinear least-squares routine
> I have a data set with 34 values, f(x), on a grid of 34 points x, and
> am trying to apply the least-squares routine UNLSF to find the
> parameters of a 3rd-order function that fit my data. I am confused
> about the nomenclature of the routine, like the number of functions M
> and the number of variables N. In my case, is M=34 and N=3? Can you
> help clarify?
Yes, your values for M and N look correct. If you just want to a fit a
cubic regression, I think it is better construct a matrix with columns
1, x, x^2, and x^3 and solve the linear least squares problem,
possibly with SVD to deal with the ill-conditioning. There are codes
in IMSL and other places to do that.
There is a Fortran 90 code to compute polynomial regression at Alan
Miler's web site http://users.bigpond.net.au/amiller/ . You need to
download fit_poly.f90 and lsq.f90 . I recommend this.
===
Subject: Re: using nonlinear least-squares routine
>I have a data set with 34 values, f(x), on a grid of 34 points x, and
>am trying to apply the least-squares routine UNLSF to find the
>parameters of a 3rd-order function that fit my data. I am confused
>about the nomenclature of the routine, like the number of functions M
>and the number of variables N. In my case, is M=34 and N=3? Can you
>help clarify?
>
>
you should not assume that everyone here knows this code, I do not.
but from the usual notation I assume indeed M=34, but N=4
since a polynomial of order three has four coefficients. but I cannot see
why you use a nonlinear least squares solver for the simple job of
polynomial
regression which is linear.
look at
http://plato.la.asu.edu/topics/problems/nlolsq.html
for more
hth
peter
===
Subject: Re: Nonlinear equation _secant method
Do You know how I can solve them
using bisection methods ?
===
Subject: Re: Nonlinear equation _secant method
>
>Do You know how I can solve them
>using bisection methods ?
>
there are several solutions of this, one published by moore and jones in the
siam journal of numerical analysis: safe starting for iterative methods.
vol 14, 1977, pages1051-1065
hth
peter
===
Subject: Re: Nonlinear equation _secant method
I do not have that journal .
Can you please give the steps to solve
nonlinear system (from the journal)using bisection method .
BTW: You can also mail to my yahoo mail .
===
Subject: The Temp of Venus
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37GY5914268;
I am having a little trouble understanding the following question. In
the question we are given a graph showing the temperatures T(K) of
venus at different altitudes h(km).
The temperature values on the graph go from 0 to 500 on the y axis and
altitude is from 30 to 100 on the x axis.
I am then asked this:
Use the above data provided in the domain 35I am having a little trouble understanding the following question. In
>the question we are given a graph showing the temperatures T(K) of
>venus at different altitudes h(km).
>
>The temperature values on the graph go from 0 to 500 on the y axis and
>altitude is from 30 to 100 on the x axis.
>
>I am then asked this:
>
>Use the above data provided in the domain 35model(formula)of temperature versus altitude and hence use this model
>to estimate the surface temperature of Venus in degrees Celsius.
>Comment on the accuracy of your estimate and discuss any assumptions
>you have made in this estimation.
>
>The temperatures given are in Kelvin units.
>
looking at the data you must guess a model, say an exponential decay or
something else. then , almost for sure you will use nonlinear or linear
least squares. but there are assumptions behind this method concerning your
data
and there is the possibility to compute confidence intervals for the
coefficients.
look up your lecture notes
hth
peter
===
Subject: Re: The Temp of Venus
>
> >I am having a little trouble understanding the following question. In
> >the question we are given a graph showing the temperatures T(K) of
> >Venus at different altitudes h(km).
> >The temperature values on the graph go from 0 to 500 on the y axis
and
> >altitude is from 30 to 100 on the x axis.
> >I am then asked this:
> >Use the above data provided in the domain 35 >model(formula)of temperature versus altitude and hence use this model
> >to estimate the surface temperature of Venus in degrees Celsius.
> >Comment on the accuracy of your estimate and discuss any assumptions
> >you have made in this estimation.
> >The temperatures given are in Kelvin units.
> looking at the data you must guess a model [structure],
T = f(h; c)
where T is the temperature in degrees kelvin and
f is some [non-linear] function of
the height h in kilometers and c is a vector of adjustable parameters
that must be estimated from the data.
> say an exponential decay or something else.
T = T0*exp(-lambda*h)
where c = (T0, lambda)
> then, almost for sure, you will use nonlinear or linear least squares.
minimize the sum of
0.5*(T_i - T0*exp(-lambda*h_i))^2
over all of the n pairs {h_i, T_i} for all i in {1, 2, ..., n}.
> but there are assumptions behind this method
> concerning your data and there is the possibility
> to compute confidence intervals for the coefficients.
You are not going to get the model structure out of the data.
The model structure comes from some other information --
your understanding of the system, a revelation from God,
a wild guess, etc.
===
Subject: who used 2-D triangle mesh generator MSHPTG before?
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37GY3W14174;
Hi there,
It is a Fortran package that uses vertox on boundary as input. Please
give me an example on how to use this package.
Toby
===
Subject: Anybody know how to use a 2-D triangle mesh generator MSHPTG?
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37GY2F14150;
Hi there,
It is a Fortran program that uses vertex on boundary as input and
generate nonuniform 2-D triangle meshes. I am willing to use it in my
code but have some troubles. Did anybody who used it before could give
me an example code about how ot use it?
Toby
===
Subject: threshold Jacobi method
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision:
1.9 primary) id i37GY6m14316;
hello everyone,
i need the algorithm of the threshold jacobi method for eigen value
problems in symmetric matrices in order to program it on vbasic
if you have it please post it
===
Subject: Re: threshold Jacobi method
> hello everyone,
> i need the algorithm of the threshold jacobi method for eigen value
> problems in symmetric matrices in order to program it on vbasic
> if you have it please post it
You can buy the Numerical Library CD-ROM, which has codes in Fortran,
C, C++, Basic and other languages, from
http://us.cambridge.org/titles/catalogue.asp?isbn=0521750350 . The
Basic codes there are in MS Basic and True Basic. You could buy BNALib
at http://cdeagle.cnchost.com/ , which has VB code for eigenvalues and
eigenvectors of a general matrix. Otherwise, I recommend converting
the Fortran 77 code jacobi in
http://www.library.cornell.edu/nr/bookfpdf/f11-1.pdf to Visual Basic,
or preferably, creating a DLL from that code and calling it from VB.
===
Subject: Re: threshold Jacobi method
>hello everyone,
>i need the algorithm of the threshold jacobi method for eigen value
>problems in symmetric matrices in order to program it on vbasic
>if you have it please post it
>
there is a version in the handbok for automatic computation (edited by
wilkinson
and reinsch), code written by rutishauser, in alogol60. but easily readable
and there should be no problem to translate it to vbasic
hth
peter
===
Subject: Finite Element with Fortran - Huge arrays cause problems?
when i try to run the program i get an error saying the system can't
execute the program.
In finite element, if you're using triangular elements in a rectangular
region, the number of nodes is something like
2* number of divisons along the x axis*number of divisions along the y
axis.
If i have about a hundred visions along one axis and about 20 along the
other, this leads to arrays that fortran seemingly can't handle? Anyone
know how to fix this?
My program is as follows
with NE=4048,ND=2139,NP=135 where the numbers are the numebr of elements,
number of nodes and number of fixed nodes respectiovely.
And the entire program follows.
DIMENSION X(2200), Y(2200), C(12400,12400), CE(12400,12400),
TE(12400,12400),T(2200,2200)
DIMENSION B(12400), NL(4100,3), NDP(200), VAL(200)
DIMENSION V(2200), P(3), Q(3), XL(3), YL(3)
DIMENSION YVAL(2200), VVAL(2200), NDV(2200), NDY(2200)
DATA ER,E0/2.5,8.81E-12/
OPEN (5,FILE=unev.dat)
READ(5,10) NE,ND,NP
10 FORMAT(3I4)
READ(5,20) (I,(NL(I,J),J=1,3),I=1,NE)
20 FORMAT(4I10)
READ(5,30) (I,X(I),Y(I),I=1,ND)
30 FORMAT(I10,2F6.2)
READ(5,40) (NDP(I),VAL(I),I=1,NP)
40 FORMAT(I10,F6.2)
READ(5,41) (NDY(I),YVAL(I),I=1,ND)
41 FORMAT(I4,F6.2)
READ(5,43) (NDV(I),VVAL(I),I=1,ND)
43 FORMAT(I4,F16.3)
DO 50 M=1,ND
B(M)=0.0
DO 50 N=1,ND
C(M,N)=0.0
T(M,N)=0.0
50 CONTINUE
DO 140 I=1,NE
DO 60 J=1,3
K=NL(I,J)
XL(J)=X(K)
YL(J)=Y(K)
60 CONTINUE
P(1)=YL(2)-YL(3)
P(2)=YL(3)-YL(1)
p(3)=YL(1)-YL(2)
Q(1)=XL(3)-XL(2)
Q(2)=XL(1)-XL(3)
Q(3)=XL(2)-XL(1)
AREA=0.5*ABS(P(2)*Q(3)-Q(2)*P(3))
DO 70 M=1,3
DO 70 N=1,3
CE(M,N)=(P(M)*P(N)+Q(M)*Q(N))/(4.0*AREA)
IF(M.NE.N) THEN
TE(M,N)=AREA/12
ENDIF
IF(M.EQ.N) THEN
TE(M,N)=AREA/6
ENDIF
70 CONTINUE
DO 130 J=1,3
IR=NL(I,J)
DO 80 K=1,NP
IF(IR.EQ.NDP(K)) GO TO 120
80 CONTINUE
DO 110 L=1,3
IC=NL(I,L)
DO 90 K=1,NP
IF(IC.EQ.NDP(K)) GO TO 100
90 CONTINUE
C(IR,IC)=C(IR,IC)+CE(J,L)
B(IR)=B(IR)+TE(J,L)*YVAL(IR)/VVAL(IR)
GO TO 110
100 B(IR)=B(IR)-CE(J,L)*VAL(K)+(TE(J,L)*YVAL(NDP(K)))/VVAL(NDP(K))
110 CONTINUE
GO TO 130
120 CONTINUE
C(IR,IR)=1.0
B(IR)=VAL(K)
130 CONTINUE
140 CONTINUE
NMAX=5000
CALL INVERSE(C,ND,NMAX)
DO 150 I=1,ND
V(I)=0.0
DO 150 J=1,ND
V(I)=V(I)+C(I,J)*B(J)
150 CONTINUE
WRITE(6,160) ND,NE,NP
160 FORMAT(2X,'NO. OF NODES = ',I3,2X, 'NO. OF ELEMENTS = ' , I3,2X, 'NO.
OF FIXED NODES = ',I3,/)
WRITE(6,170)
170 FORMAT(2X,'NODE',5X,'X Y',7X,'POTENTIAL',/)
WRITE(6,180) (I,X(I), Y(I),V(I), I=1,ND)
180 FORMAT(2X,I3,2X,F6.2,2X,F6.2,2X,F100.50/)
STOP
END
SUBROUTINE INVERSE(SX,N,IDM)
DIMENSION SX(IDM,IDM)
ESP=1.0E-5
DO 50 K=1,N
DO 30 J=1,N
IF(J.EQ.K) GO TO 30
IF(ABS(SX(K,K))) 20,10,20
10 SX(K,K)=ESP
20 SX(K,J)=SX(K,J)/SX(K,K)
30 CONTINUE
SX(K,K)=1.0/SX(K,K)
DO 40 I=1,N
IF(I.EQ.K) GO TO 40
DO 41 J=1,N
IF(J.EQ.K) GO TO 41
SX(I,J)=SX(I,J)-SX(K,J)*SX(I,K)
41 CONTINUE
40 CONTINUE
DO 50 I=1,N
IF(I.EQ.K) GO TO 50
SX(I,K)=-SX(I,K)*SX(K,K)
50 CONTINUE
RETURN
END
===
Subject: Exactly Representable Fractions
hi,
i was wondering...
given a fraction, 1/N, is there a method to determine for which values
of N we may store the fraction in binary format in exactly
representable form.
any input greatly appreciated,
pat
===
Subject: Re: Exactly Representable Fractions
> Given a fraction
>
> 1/N
where N is a positive integer
> is there a method to determine for which values of N
> we may store the fraction in binary format
> in exactly representable form?
N = 2^k
where k is a non-negative integer.