leastSquaresApprox.py

import numpy, math
from scipy import linalg

# Let |terms| be a list of lambdas... one for each term
# the result is a linear combination of them applied to x
terms = [
      lambda x: 1,
      lambda x: math.log( x ),
      lambda x: math.log( x ) ** 3
      ]
resTerm = lambda y: 1.0 / y

data = [
      ( 106.0, 283.15 ),
      ( 72.3, 290 ),
      ( 64, 293 ),
      ( 57, 295.15 ),
      ( 47.3, 299 ),
      ( 42.5, 302 ),
      ( 20, 320.15 ),
      ( 15, 328 ),
      ( 10, 341 )
      ]

A = numpy.array(
      [ [ f( x ) for f in terms ]
         for x, y in data ] )
b = numpy.array(
      [ [ resTerm( y ) ]
         for x, y in data ] )

A_T = numpy.transpose( A )

A_TxA = numpy.dot( A_T, A )
A_Txb = numpy.dot( A_T, b )

print A_TxA
print A_Txb

res = linalg.inv( A_TxA ).dot( A_Txb )
print res

print "A=" + str( res[ 0 ][ 0 ] )
print "B=" + str( res[ 1 ][ 0 ] )
print "C=" + str( res[ 2 ][ 0 ] )