I´m trying to transform the integral:
I need to transform it to an integral that goes from 0 to 1 in order to apply the algorithm of Montecarlo I implemented. I´m comfortable applying the identities on single integrals, but I don´t really know how to apply the following identities to a double integral.
I investigated on books and found this hint, but I still don´t understand how to use it on a double integral. Can anyone help me?
After several hours, I was able to get the transformation. Hope it helps :)
Related
My problem is similar to this one Numerical Integration, and I have already calculated the numerical solution of my ODEs using bvp4c, with the boundary conditions imposed at rmin=1e-5 (near r=0) and rmax=50. I do not have to keep the infinite interval, since even for $\frac{\lambda}{e^2}<<1$ the solution reaches the asymptotic behavior really fast.
So, I calculated my integral using trapz, but I would like to know if Matlab has a preciser way of doing this. I searched the methods user #drjrm3 mentioned in the question above, but I didn't understand what method I can implement when the integrand involves a combination of components of a vector which keeps the solution.
What I have so far is something like this:
f=trapz(xint,Sxint(3,:).^2. + 0.5*(1-Sxint(1,:).^2.).^2./xint.^2. + 0.5*xint.^2.*Sxint(4,:).^2. + ...
Sxint(1,:).^2.*Sxint(2,:).^2. + 0.1*0.25*xint.^2.*(Sxint(2,:).^2. - 1).^2.)
Thanks in advance for any hint!
integral() and quadqk().
The exact method of integral() in Matlab changes over time. I haven't followed it for a while. A few years ago, I remember reading how it uses adaptive quadrature and were a slightly more advanced version of Guass-Kronrod. Now it seems Matlab doesn't talk about its integration method in the official documentation. Maybe they developed something good and proprietary. You can read the paper they linked the the documentation page and see if what they do is to your liking.
I have a program using PSO algorithm using penalty function for Constraint Satisfaction. But when I run the program for different iterations, the output of the algorithm would be :
"Iteration 1: Best Cost = Inf"
.
Does anyone know why I always get inf answer?
There could be many reasons for that, none of which will be accurate if you don't provide a MWE with the code you have already tried or a context of the function you are analysing.
For instance, while studying the PSO algorithm you might use it on functions which have analytical solutions first. By doing this you can study the behaviour of the algorithm before applying to a similar problem, and fine tune its parameters.
My guess is that you might not be providing either the right function (I have done that already, getting a signal wrong is easy!), the right constraints (same logic applies), your weights for the penalty function and velocity update are way off.
In MATLAB R2014b there is a new function, pca(), that performs PCA that can handle missing data. In the documentation it says that it performs pca with the "alternating least squares" algorithm in order to estimate the missing values.
I would like to know if there are any practical references in how to apply PCA with this algorithm without the use of the function, or if there is a good reference on als. The reason is, there is no such function in Octave that can handle missing data and so I would like to code it myself.
Thanks for all your help. I went through the references and was able to find their matlab code on the als algorithm from two of the references. For anybody wondering, the source code can be found in these two links:
1) http://research.ics.aalto.fi/bayes/software/index.shtml
2) https://www.cs.nyu.edu/~roweis/code.html
I have a big matrix with dimensions 2.000X98.000 and i want to perform unsupervised clustering on it. My problem is that when i try the clustering with Scipy.cluster.vq.kmeans2, i get an error that says "Matrix is not positive definite", when I try it with scipy.cluster.vq.kmeans it takes hours and hours to calculate and when i try it with sklearn.cluster.KMeans, the computation is fast and presents no errors. I have read the documentation for all the algorithms and i have researched through the internet for answers , but still i cannot understand this kind of difference between the three of them. Could someone explain to me this fundamental difference between them and why the need of a positive definite matrix is necessary only for scipy.kmeans2? Thank you in advance for your time and consideration.
This is a question that possibly borders on the intersection of the general usage of MATLAB and/or signal processing. Thought I would first ask the question in a MATLAB forum before trying signal processing.
So our lecturer read out his notes/paper and said the equation
could be implemented as a filter.
At first, it seemed difficult to follow the idea but when realizing that integration is same as finding areas under the curve which seems similar to applying a low pass filter so that only the portion of the signal under the threshold is allowed to pass through, it made a bit of sense. But how - meaning to say which function - can I use to implement the above equation? Do I need three filters or can I use just one? How do I use the terms preceding the integrals in the filter?
Thanks in advance