Conspiracy Theory

# -*- coding: utf-8 -*-
"""
Created on Mon May 21 12:04:35 2012

Feel free to change and republish this file and its generated figures.
Just give a link to the original post at:
    http://pnoq.blogspot.com/2012/05/conspiracy-theory.html
For start, you can change the srings at lines:
    20, 21 and 22
Have fun!
The original file was taken from:
    http://www.scipy.org/Cookbook/LinearRegression
"""

# -*- coding: utf-8 -*-

from scipy import linspace, polyval, polyfit, sqrt, randn
from pylab import plot, title, show , legend, gca, savefig

data='Observations'
lfit='Theory'
pfit='Conspiracy Theory'
# These strings are used to produce legends and output filename.
# The output file name will be like:
#   lfit-pfit.png

#Linear regression example
# This is a very simple example of using two scipy tools
# for linear regression, polyfit and stats.linregress

#Sample data creation
#number of points
n=10    #number of data points to be created.
nplot=1000  #number of points to be plotted.
t=linspace(-5,5,n)
tplot=linspace(-5.1,5.1,nplot)  #plotting range.


#parameters
a=0.8; b=-4
x=polyval([a,b],t) #This is artificial data points, taken from a line.
#add some noise
xn=x+randn(n)

#Linear regressison -polyfit - polyfit can be used other orders polys

pr=polyfit(t,xn,10) #fit a 10 degree polinomial.
xpr=polyval(pr,t)       #calculate the data point according to above fit.
xpr_plot=polyval(pr,tplot)

lr=polyfit(t,xn,1)  #fit a line
xlr=polyval(lr,t)       #calculate the data point according to above fit.
xlr_plot=polyval(lr,tplot)

#compute the mean square error
err_line=sqrt(sum((xlr-xn)**2)/n)
err_poly=sqrt(sum((xpr-xn)**2)/n)
print('Linear regression using polyfit')
print('Linear fit error= %.3f, Polynomial fit error= %.3f' % (err_line,err_poly))

#matplotlib ploting
title('%s vs %s' % (lfit,pfit))
plot(t,xn,'ko')
plot(tplot,xlr_plot,'g-')
plot(tplot,xpr_plot,'r-')

l1=legend([data, lfit, pfit],loc=2)

# You can remove following two lines if you don't want the error legend.
l2=legend([ 'Error of %s is %.3f' % (lfit,err_line) , 'Error of %s is %.3f' % (pfit,err_poly)],loc=4) # this removes l1 from the axes.
gca().add_artist(l1) # add l1 as a separate artist to the axes.

savefig('%s-%s.png' % (lfit, pfit))
show()