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.
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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!
I need to compute the determinant of complex matrix which is symmetric. Size of matrix ranges from 500*500 to 2000*2000. Is there any subroutine for me to call? By the way, I use ifort to compile.
The easiest way would be to do an LU-decomposition as described here. I would suggest using LAPACK for this task...
This article has some code in C doing that for a real-valued symmetric matrix, so you need to exchange dspsv by zspsv to handle double-precision complex matrices.
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
What is the algorithm that Excel uses to calculate a 2nd-order polynomial regression (curve fitting)? Is there sample code or pseudo-code available?
I found a solution that returns the same formula that Excel gives:
Put together an augmented matrix of values used in a Least-Squares Parabola. See the sum equations in http://www.efunda.com/math/leastsquares/lstsqr2dcurve.cfm
Use Gaussian elimination to solve the matrix. Here is C# code that will do that http://www.codeproject.com/Tips/388179/Linear-Equation-Solver-Gaussian-Elimination-Csharp
After running that, the left-over values in the matrix (M) will equal the coefficients given in Excel.
Maybe I can find the R^2 somehow, but I don't need it for my purposes.
The polynomial trendlines in charts use least squares based on a QR decomposition method like the LINEST worksheet function ( http://support.microsoft.com/kb/828533 ). A second order or quadratic trend for given (x,y) data could be calculated using =LINEST(y,x^{1,2}).
You can call worksheet formulas from C# using the Worksheet.Evaluate method.
It depends, because there are a lot of ways to do such a thing depending on the data you supply and how important it is to have the curve pass through those points.
I'm guessing that you have many more points than you do coefficients in the polynomial (e.g. more than three points for a 2nd order curve).
If that's true, then the best you can do is least square fitting, which calculates the coefficients that minimize the mean square error between all the points and the resulting curve.
Since this is second order, my recommendation would be just create the damn second order terms and do a linear regression.
Ex. If you are doing z~second_order(x,y), it is equivalent to doing z~first_order(x,y,x^2,y^2, xy).
I'm writing a program that simulates various random walks (with differing distributions). At each timestep, I need randomly generated, two dimensional step distances and angles from the distribution of the random walk. I'm hoping someone can check my understanding of how to generate these random numbers.
As I understand it I can use Inverse Transform Sampling as follows:
If f(x) is the pdf of our random walk that has a non-uniform distribution, and y is a random number from a uniform distribution.
Then if we let f(x) = y and solve to find x then we have a random number from the non-uniform distribution.
Is this a feasible solution?
Not quite. The function that needs to be inverted is not f(x), the pdf, but F(x)=P(X<=x)=int_{-inf}^{x}f(t)dt, the cdf. The good thing is that F is monotone, so actually has a unique inverse (unlike f).
There are multiple other ways of generating random numbers according to a given distribution. For example, if the cdf F is difficult to compute or to invert, rejection sampling can be a good option if f is easy to compute.
You are close, but not quite. Every probability density function (pdf) has a corresponding cumulative density function (cdf). An important property about CDF(x) is that they are always between 0 and 1. Because it is relatively easy to draw a random number between 0 and 1, we can use that to work our way backwards to the distribution. So changing the word pdf to CDF in your question makes the statement correct.
As an aside for this to make sense computationally you need to find an easy to calculate inverse of the CDF. One way to do this is to fit a polynomial approximation to the CDF and find the inverse of that function. There are more advanced techniques for simulating probability distributions with messy distributions. See this book chapter for the details.