mm-2359
===
Subject: jacobian matrix
I have trouble uderstanding something.
In FEM:
I have a shape function N={N1,N2,N3,N4,N5,N6}
where:
N1=2*(1-u-v)(1/2-u-v)
N2=u(2u-1)
N3=v(2v-1)
N4=4*u*v
N5=4*v*(1-u-v)
N6=4*u*(1-u-v)
The element is a triangle
(u,v) are area coordinates.
How can I find the jacobian of the coordinate transformation?
(x1,y1)(x2,y2)(x3,y3) are the 3 points of the triangle.
I know that 
if A={
dN1/du dN2/du ... 
dN1/dv dN2/dv ...}
and B={
xa ya
xb yb
...
} then
Jacobian = A.B
The thing is that I don't really understood what are the elements of B 
(real
coordinates) in the given area coordinate example.
Any help?
Originator: lindahl@pbm.com (Greg Lindahl)
There are run-time checks both at program startup and within the Intel
libraries.
We actually like the situation: it increases our performance advantage
on Opteron, and wins us additional customers. It's probably pretty
annoying to ISVs currently using Intel compilers who would like to
-- greg
(employed by, but not speaking for, PathScale)
===
Subject: constitutive error minimization ?
I'm studying the solution of electrical networks.
I've encountered this method for the solution of
general resistive circuits. It's based on the
minimizazion of the cost-function f(phi,vc) where
        phi     nodal potentials
        va      tree-voltage
I've trouble with the form of f(.,.).
_Suggestions or link for this method_ ???
PS. very poor search-results with Google on
costitutive error minimization :-(
----
===
Subject: Re: Re : Good compilable langauge for math and graphics?
I ported a very straightforward Mandelbrot program to Java from C.  No
traps, tricks, pitfalls, all just very straightforward.
I compiled with -O3 (is O2 better than O3 ?, I'm assuming not).
The Java version runs faster than the C version.
So, NOT such a lie.
===
Subject: Re: Re : Good compilable langauge for math and graphics?
I assume that you had to manually inline all types and functions to do with
complex numbers in the Java otherwise it would be much slower than C?
Either can be faster, depending upon the code. Did you use any other
options? e.g. -march=athlon-tbird.
Can you quantify this?
Well, it would be nice if you could post the source so that others can make
sure you haven't done anything stupid in either language.
I've removed a couple of the cross posts but it might be interesting to
compare Fortran and maybe some other suitable languages as well. Note that
there is a similar test on the shootout, although it isn't very well
defined IIRC. What languages have efficient native support for complex
numbers?
-- 
Dr Jon D Harrop, Flying Frog Consultancy
http://www.ffconsultancy.com
===
Subject: chebychev polynomial fit /  binning data? / redistributing data
Hi folks,
I've been a data-miner for several years and a big part of the job is
to create a uniform-like distribution of the data for training
purposes.
I have a question regarding converting general data into a
uniform-like distribution.
Here is some background.
I have a general data set:
x| 1  2  3  4  5 ........N
----------------------
y| y1 y2 y3 y4 y5 .......yN
And for this particular training I would transform y:
y_prime = const*(y_i - mean_y)/std_y
which scales y, centered about the mean.
For training one would now perform a further transformation to make the
distribution more uniform-like.  Note:  I am not trying to learn the
distribution, I am trying to learn each strata within the distribution
equally well, hence the transformation to a more uniform-like
distribution.
My question.  I have come across a reference of creating a chebychev
polynomial fit of the y_prime data as a general purpose conversion
funtion to produce a reasonably looking uniform-like distribution.
Something like:
Input:
|          *
|        *   *
|       *     *
|      *       *
|    *           *
|  *               *
|*                   *
-----------------------
Output(after chebychev conversion of y_prime):
|    *************
|   *             *
|  *               *
|  *               *
| *                 *
| *                 *
|*                   *
-----------------------
I'm suspecting that this is really a binning method where y_prime is
taken into a discrete number of bins by this chebychev method and the
Output is actually a binning of the results more like:
My interpretation of the Output(after chebychev conversion of y_prime):
|    *************
|   ***************
|  *****************
|  *****************
| *******************
| *******************
|*********************
-----------------------
where each vertical slice of stars is really a histogram-like bar chart
where the original values of y are rebinned into y_prime.
Are there any ideas out there about constructing this chebychev
polynomial which accomplishes this re-distributing / binning?
Any ideas would be appreciated.
Tony
===
Subject: Re: Interpolation of discrete Chebsyhev polynomials.
You can use the FFT for that.
Please read a paper by Zachary Battles and Lloyd Nick Trefethen.
http://web.comlab.ox.ac.uk/oucl/work/zachary.battles/
best,
Thomas
===
Subject: orthogonal collocation
Hello everybody.I'm using orthogonal collocation for solving a system
of PDE's.Actually I'm trying to disceretize one of my dimensions and
then solve the system by one of the ODE methods.The only reference I
have is the book by Finlayson,Nonlinear analysis in chemical
engineering.I'm using the general formulas in the book for calculating
the required matrices such as A,B and W.
I want to know that is it right to use these formulas for any kind of
orthogonal polynomials like legendre,hermite & etc or in each case the
matrix definitions vary?
Secondly,how can I solve the whole problem by OC rather than just using
it in one dimension?
Padideh