This is NUTs

I have a couple of double-conversion UPSs (i.e. the good kind) powering up two racks on my experiment. These are sophisticated instruments, with inbuilt battery checks and reporting of lots of power quality parameters. The trouble is to read them out into a computer and control them with serial commands, since the serial command set appears to be proprietary.

Enter the NUT project ! It includes drivers for a huge number of UPS systems, and there's a Python wrapper around it all called PyNUT. Code coming soon ...

Prime number density

Prime numbers are almost 'physical'. Spooky.

	import pylab as plt
	import numpy as np
	def primes(x):
	p = []
	mask = range(2,x-1)
	while len(mask)>0:
	p.append(mask[0])
	del mask[::p[-1]]
	return p
	def prime_density(x):
	p = primes(x)
	#print p
	Z = [(1 - 1./pi) for pi in p if pi < x/2.]
	z = reduce( lambda x,y: x*y, Z )
	rho = (len(primes(x+2000)) - len(primes(x-2000)) )/4e3
	print z,rho," ",x
	return (z,rho)
	pd = []
	y = np.arange(3.4,8,0.2)
	x = map(int,10**y)
	for xi in x:
	try: pd.append(prime_density(xi))
	except KeyboardInterrupt: break
	z = np.array([pdi[0] for pdi in pd])
	rho = np.array([pdi[1] for pdi in pd])
	x = x[:len(z)]
	f = 1./(0.5772 + np.log(x))
	plt.figure()
	plt.xlabel("N")
	plt.ylabel("Density of primes")
	plt.semilogx(x,rho,'bo',label="Measured")
	plt.semilogx(x,f,'g',label="1/($\gamma$ + log x)")
	plt.semilogx(x,z,'r',label="product formula")
	plt.semilogx(x,(z+f)/2.,'b',label="average formula")
	plt.legend(loc="upper right")
	plt.show()

view raw prime_density.py hosted with ❤ by GitHub

Listing primes

Naive prime testing compared to the Sieve of Eratosthenes.

	def test2(x):
	""" Sieve of Eratosthenes """
	p = []
	mask = range(2,x-1)
	while len(mask)>0:
	p.append(mask[0])
	del mask[::p[-1]]
	return p

view raw eratosthenes.py hosted with ❤ by GitHub

	def test1(x):
	""" Naive testing by divisibility """
	p = [2,3,5,7]
	for i in xrange(7,x-1):
	isprime = True
	for pi in p:
	isprime = ( isprime and (i%pi) )
	if not isprime: break
	if isprime: p.append(i)
	return p

view raw naive_prime.py hosted with ❤ by GitHub

cProfile says (for N = 100 000):
  naive testing =  7.912 CPU seconds
  sieve method = 0.064 CPU seconds

Sieving is fast !