Liam,

I am afraid the usage is maybe too compact. I am simulating the propagation of a 1D pulse. I use gsl::weighted-mean and gsl::weighted-varience-nom to calculate the pulse centroid and width. I *think* my approach is mathematically correct, but I am not sure of its numerical soundness. To calculate the centroid of f(x) which is defined as \frac{\int x f(x) dx}{\int f(x) dx}, I use the weighed mean function, calculating the mean of x, which I weigh by the pulse amplitude (phi, in the code below).

Likewise to calculate the width (defined as \frac{\int x^2 f(x) dx}{\int f(x) dx}), I use the square root of the weighted variance function, again applying it to x, weighted by the pulse height phi.

The calls to the two gsll function is in the body of this progn (which in turn is part of a loop that propagates the pulse)

(progn (format t "Step: ~A~%" it) (format t "Expected/actual amplitude: ~a ~a ~%" (* A (sqrt (/ t0 time))) (reduce #'max (coerce phi 'list))) (format t "Expected/actual centroid: ~a ~a ~%" (+ x0 (* F (- time t0))) (letm ((gsl-phi (vector-double-float phi)) (gsl-x (vector-double-float grid-coords))) (gsl::weighted-mean gsl-x gsl-phi))) ;; <================ (format t "Ideal/actual sigma: ~a ~a ~a ~%" (sqrt (* 2 D time)) (letm ((gsl-phi (vector-double-float phi)) (gsl-x (vector-double-float grid-coords))) (setf variance (gsl::weighted-variance-nom gsl-x gsl-phi)) ;; <============= (sqrt variance))))

I apologize for the flakiness of my arguments, but I needed something quick and dirty, and my quick checks seemed ok.

Mirko

On Sat, Aug 23, 2008 at 1:35 PM, Liam Healy lhealy@common-lisp.net wrote:

You're welcome.

If your usage is reasonably compact, do you mind posting it? I would like to have as many examples as possible both for new users and for me to create tests and examples.

On Fri, Aug 22, 2008 at 9:43 AM, Mirko Vukovic mirko.vukovic@gmail.com wrote:

...

Used the mean&variance stuff yesterday. Thanks (again)!

Mirko