graph.py

#!/usr/bin/env python
'''
	semilog.py
	Eric Ayars
	10/4/16

	Graphing demonstration showing how to create semi-log 
	plots and curve fits relevant to Advanced Lab.
'''

from pylab import *
from scipy.optimize import curve_fit

# Data (Made-up, with realistic error)
t = array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])
N = array([ 90.,  64.,  54.,  57.,  52.,  51.,  32.,  35.,  32.,  26.,  23., 22.,  18.,   9.,   9.,   9.,  11.,   5.,   5.,   4.,   2.,   2., 4.,   3.,   3.])
time = linspace(0,25,100)

# Linear plot, with curve fits
errorbar(t, N, yerr=sqrt(N), fmt='bo')
title('Radioactive Decay')
xlabel('Time (minutes)')
ylabel('Counts')

# Equation for curve fit
def decay(t, A, B):
    return A*exp(-t/B)

guess = [100,5]   # Doesn't have to be a particulary good guess, usually.
params, cov = curve_fit(decay, t, N, guess)
print('A = %0.3f, B = %0.3f' % (params[0], params[1]))
print('dA = %0.3f, dB = %0.3f' % (sqrt(cov[0,0]), sqrt(cov[1,1])))
plot(time, decay(time, params[0], params[1]), 'g-')

# Add a legend
legend(['Data', 'Curve Fit'], loc='upper right')

# add annotations
text(19,65, r'$N = N_o e^{-t/\tau}$')
text(19,60, r'$N_o = %0.2f \pm %0.2f$' %(params[0], sqrt(cov[0,0])))
text(19,55, r'$\tau = %0.2f \pm %0.2f$' %(params[1], sqrt(cov[1,1])))

# limit y range on display
#ylim(0,100)

# If you want to save the graph...
#savefig('semilog_plot.pdf')

show()