numerical

I have some expressions such as x^2+y^2 that I'd like to use for some math calculations. One of the things I'd like to do is to take partial derivatives of the expressions. So if f(x,y) = x^2 + y^2 then the partial of f with respect to x would be 2x , the partial with respect to y would be 2y . I wrote a dinky function using a finite differences method but I'm running into lots of problems with floating point precision. For example, I end up with 1.99234 instead of 2 . Are there any libraries that support symbolic differentiation? Any other suggestions? I've implemented such libraries in

Possible Duplicate: identifying or coding unique factors using R I'm having some trouble with R. I have a data set similar to the following, but much longer. A B Pulse 1 2 23 2 2 24 2 2 12 2 3 25 1 1 65 1 3 45 Basically, the first 2 columns are coded. A has 1, 2 which represent 2 different weights. B has 1, 2, 3 which represent 3 different times. As they are coded numerical values, R will treat them as numerical variables. I need to use the factor function to convert these variables into factors. Help? Here's an example: #Create a data frame > d<- data.frame(a=1:3, b=2:4) > d a b 1 1 2 2 2 3 3

Is there an open-source alternative to MATLAB's fmincon function for constrained linear optimization? I'm rewriting a MATLAB program to use Python / NumPy / SciPy and this is the only function I haven't found an equivalent to. A NumPy-based solution would be ideal, but any language will do. Is your problem convex? Linear? Non-linear? I agree that SciPy.optimize will probably do the job, but fmincon is a sort of bazooka for solving optimization problems, and you'll be better off if you can confine it to one of the categories below (in increasing level of difficulty to solve efficiently) Linear

I would like to learn more about low level code optimization, and how to take advantage of the underlying machine architecture. I am looking for good pointers on where to read about this topic. More details: I am interested in optimization in the context of scientific computing (which is a lot of number crunching but not only ) in low level languages such as C/C++. I am in particular interested in optimization methods that are not obvious unless one has a good understanding of how the machine works (which I don't---yet). For example, it's clear that a better algorithm is faster, without

I'm trying to implement the Jacobi iteration in MATLAB but am unable to get it to converge. I have looked online and elsewhere for working code for comparison but am unable to find any that is something similar to my code and still works. Here is what I have: function x = Jacobi(A,b,tol,maxiter) n = size(A,1); xp = zeros(n,1); x = zeros(n,1); k=0; % number of steps while(k<=maxiter) k=k+1; for i=1:n xp(i) = 1/A(i,i)*(b(i) - A(i,1:i-1)*x(1:i-1) - A(i,i+1:n)*x(i+1:n)); end err = norm(A*xp-b); if(err<tol) x=xp; break; end x=xp; end This just blows up no matter what A and b I use. It's probably a

I'm working on a scientific computation & visualization project in C#/.NET, and we use double s to represent all the physical quantities. Since floating-point numbers always include a bit of rounding, we have simple methods to do equality comparisons, such as: static double EPSILON = 1e-6; bool ApproxEquals(double d1, double d2) { return Math.Abs(d1 - d2) < EPSILON; } Pretty standard. However, we constantly find ourselves having to adjust the magnitude of EPSILON as we encounter situations in which the error of "equal" quantities is greater than we had anticipated. For example, if you multiply