I’m a French student that is taking a look at the matrix entropy ! Could you please explain me how do you manually calculate the entropy of a matrix ? My goal is to calculate it with a python programm.
Thanks for answer :)
Trying to calculate the entropy of a matrix
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I'm trying to implement the 1-D Pseudo Wigner Distribution. The distribution has this expression:
where n and k represent time and frequency, m is the shifting parameter. z[n] is a vector and z* is the complex conjugate. The author of this article say that
it can be interpreted as the Discrete Fourier Transform of the product z[n+m]z*[n-m].
I would like to know which is the smartest and fastest way to implement this (in particular the product z[m+n]z*[n-m], if I get this then I can apply the fft) because I need to use this expression a lot of times. Any help is greatly appreciated!
What does this mean:
Find discrete multivariate distributions which have explicit formula for their joint probability generating function?
Please if anyone understand this question , just give an example or expression for me!
I am assuming that you know what an MGF is. So, looking at this question, you will have to find the MGFS of multiple variate distributions.
For example,
Lets take the Poisson distribution.
1. It is univariate
2. It is discrete
and has an MGF
https://en.wikipedia.org/wiki/Poisson_distribution
MGF can be calculated by E(e^tx) for any distribution.
I am using the lsqcurvefit function in Matlab to model some experimental data. The data takes a specific shape and so the algorithm is just adjusting the coefficients of this shape to change its amplitude etc.
The model works fine and gives a good fit (I have calculated chi-sq). Other implementations of the Levenberg-Marquardt algorithm give covariance as an output but in Matlab it is not an option for output (only 1st order optimality, no of iterations, Lambda and Jaccobian along with the bounds) .
Does anybody know how to calculate the covariance matrix either from the outputs given (I'm not 100% on what use lambda and jaccobian could be or 1st order optimallity) by lsqcurvefit or independantly?
Any help would be greatly appreciated, thanks!
I think I have solved this myself but will post how here if anyone else is having the same trouble.
The covariance matrix can be calculated from the Jacobian by:
C = inv(J'*J)*MSE
Where MSE is mean-square error:
MSE = (R'*R)/(N-p)
Where R = residuals, N = number of observations, p = number of coefficients estimated.
Or MSE can be calculated via iteration.
Hopefully this will help someone else in the future.
If anyone spots error please let me know. Thanks
I would like to generate some pseudorandom numbers on (-infinity, infinity) with a Gaussian distribution of standard deviation s and mean m. Any suggestions about how to do this? I'd appreciate any help in the right direction, as there seems to be a huge literature out there as how best to generate pseudorandom numbers.
You can generate a Gaussian distribution (also known as a normal distribution) buy using a uniform random number generator and an appropriate algorithm. Check out [stackoverflow link to Gaussian algorithms][1]
Do you really want to go from +/- infinity? Does that make sense?
A simple algorithm to use is the Box-Muller method.
Normal Dist. Random # = SQRT(-2*LN(RAND()))*SIN(2*PI()*RAND())
The Box-Muller method is mathematically exact if implemented with a perfect uniform random number generator and infinite precision. (oops.. in that formula, mu/mean =0 and sigma = 1 and random #'s are between 0 and 1) see http://mathworld.wolfram.com/Box-MullerTransformation.html
any one can help me, i want to generate a matrix with elements being zero mean and unit variance independent and identically distributed (i.i.d.) circularly symmetric Gaussian variables using Matlab any one know the code for this and how to do it
It is easy to generate a matrix with elements being zero mean and unit variance by using this command in matlab:
normrnd(mu, sigma)
mu is the mean
sigma is the standard deviation.
More detail please help normrnd in MATLAB.