Re: [Phys-l] Significant figures -- again

[Brian Blais <bblais@bryant.edu>]

On Mar 29, 2012, at 15:05 PM, John Denker wrote:

> However, I happen to know (based on where the matrices come from)
> that the actual distribution of eigenvalues is
>      ev1 = 0.002469(3)                        [4]
>      ev2 = 2.0000(24)

actually, I don't get this.  if all Bob knows is that the matrix elements have an uncertainty of 0.0012, then we should be able to simulate this as 

M + normal(0,0.0012), calculate the eigenvalues, and then look at their distribution.  the uncertainties resulting are much higher than what you report, and consistent with the sig-figs rule...not that I am a fan of the sig figs rule.  

I get:
	ev1: 0.002460 +- 0.001209
	ev2: 2.000002 +- 0.001200

unless I made an error somewhere, which is a distinct possibility.  I put the python code below...

			bb

-- 
Brian Blais
bblais@bryant.edu
http://web.bryant.edu/~bblais
http://brianblais.wordpress.com/



from pylab import *
from numpy import *

d_mat=[]
M=mat("[1.0012346  0.9987654 ; 0.9987654  1.0012346]")

for i in range(10000):
    M2=M+randn(2,2)*.0012
    d,v=eig(M2)
    d.sort()
    d_mat.append(d)


ev1=[d[0] for d in d_mat]
ev2=[d[1] for d in d_mat]

print "ev1: %f +- %f" % (mean(ev1),std(ev1))
print "ev2: %f +- %f" % (mean(ev2),std(ev2))

# result
# ev1: 0.002460 +- 0.001209
# ev2: 2.000002 +- 0.001200