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from numpy import matrix
from numpy import linalg
import numpy as np
from numpy import *
from pylab import *
import scipy
#matrix with input values from Q-package simulations
A = matrix( [[-782,28,-445],[-743,38,-416],[-697,29,-376],[-707,36,-389],[-813,14,-466 ],[-796,20,-455],[-771,25,-439],
[-722,33,-406],[-698, 22,-373], [-699,29,-382], [-821,17,-471],[-808,23,-462],[-782,27,-445],[-743,36,-418],[-704,28,-382],
[-709,36,-393],[-768,25,-438],[-715,31,-403],[-699,20,-372],[-699,26,-381]])


#making a list with numbers smaller than 1
a2list = linspace(0.5, 0.6, 101)
b2list = linspace (0.2, 0.6, 101)

amin=0.0
bmin=0.0
chi2min=1e10

output = open('square_deviation.txt', 'w')
flist = []
for a in range (0,len(a2list)):
    flist.append([])
    for b in range (0,len(b2list)):
        x = matrix([[a2list[a]], [b2list[b]], [-1]])
        z=A*x                                         # Matrix multiplication of A and x.  
        converttoArray_Square=asarray(z)**2
        sum_sqrt_Elements = sqrt(converttoArray_Square.sum())
        f= sum_sqrt_Elements
#append mode to add new data to a text file
        output.write('{0:5f} {1:5f} {2:10f}\n'.format(a2list[a], b2list[b], f))
#append sum of squared elements with one combination of a and b to a list        
        flist[a].append(f)
        if f < chi2min:
          amin = a2list[a]
          bmin = b2list[b]
          chi2min = f
output.close()
array = scipy.array(flist)
matrix= asmatrix(array)

print 'Minimum at :', amin, bmin, chi2min
A, B = meshgrid(a2list,b2list)
figure()
levels = range(10, 200, 20)

cset1 = contourf(A, B,matrix, levels,
                        cmap=cm.get_cmap('jet', len(levels)-1),
                        )
cset2 = contour(A, B,matrix, cset1.levels,
                        colors = 'k',
                        hold='on')
for c in cset2.collections:
    c.set_linestyle('solid')

cset3 = contour(A, B,matrix, (0,),
                colors = 'g',
                linewidths = 2,
                hold='on')
title('Filled contours')
colorbar(cset1)
show()