Polynomial Fitting

A quick demonstration of polynomial fitting.

c:\users\jmfranck\git_repos\pyspecdata\pyspecdata\core.py:1959: UserWarning: marker is redundantly defined by the 'marker' keyword argument and the fmt string "o" (-> marker='o'). The keyword argument will take precedence.
  retval = myplotfunc(*plotargs,**kwargs)
I found the minimum here at 1.688282491103677

from pylab import *
from pyspecdata import *
# {{{ generate fake data
x = nddata(r_[0:10:7j], 'x')
y = (x-2.0)**2
y.add_noise(2)
# }}}
plot(y,'o')
c = y.polyfit('x', order=2)
assert len(c)==3
# math for min:
# a(x-b)²= ax² - 2abx + ab²
# c₂ = a
# c₁ = -2ab
# c₀ = ab²
# b = -c₁/(c₂2)
print("I found the minimum here at",-c[1]/c[2]/2)
# generate a polynomial that's more finely spaced
x = nddata(r_[0:10:100j], 'x')
plot(x.eval_poly(c,'x'))
# {{{ not a good idea, but force the y intercept to 0
#     to show the code works
c = y.polyfit('x', order=3, force_y_intercept=0)
x = nddata(r_[0:10:100j], 'x')
plot(x.eval_poly(c,'x'))
# }}}
show()