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#!/usr/bin/env python
"""
1d model representation for polynomials
References::
[1] Storn, R. and Price, K. Differential Evolution - A Simple and Efficient
Heuristic for Global Optimization over Continuous Spaces. Journal of Global
Optimization 11: 341-359, 1997.
[2] Storn, R. and Price, K.
(Same title as above, but as a technical report.)
http://www.icsi.berkeley.edu/~storn/deshort1.ps
"""
from numpy import sum as numpysum
from numpy import polyval
def poly(x, c):
return polyval(c,x)
# coefficients for specific Chebyshev polynomials
chebyshev8coeffs = [128., 0., -256., 0., 160., 0., -32., 0., 1.]
chebyshev16coeffs = [32768., 0., -131072., 0., 212992., 0., -180224., 0., 84480., 0., -21504., 0., 2688., 0., -128., 0., 1]
class Chebyshev(Polynomial):
"""Chebyshev polynomial models and functions,
including specific methods for T8(z) & T16(z), Equation (27-33) of [2]
NOTE: default is T8(z)"""
def __init__(self,order=8,name='poly',metric=lambda x: numpysum(x*x),sigma=1.0):
Polynomial.__init__(self,name,metric,sigma)
if order == 8: self.coeffs = chebyshev8coeffs
elif order == 16: self.coeffs = chebyshev16coeffs
else: raise NotImplementedError("provide self.coeffs 'by hand'")
return
def cost(self,trial,M=61):
"""The costfunction for order-n Chebyshev fitting.
M evaluation points between [-1, 1], and two end points"""# % (len(self.coeffs)-1)
#XXX: throw error when len(trial) != len(self.coeffs) ?
myCost = chebyshevcostfactory(self.coeffs)
return myCost(trial,M)
pass
# faster implementation
def chebyshevcostfactory(target):
def chebyshevcost(trial,M=61):
"""The costfunction for order-n Chebyshev fitting.
M evaluation points between [-1, 1], and two end points"""
result=0.0
x=-1.0
dx = 2.0 / (M-1)
for i in range(M):
px = polyeval(trial, x)
if px<-1 or px>1:
result += (1 - px) * (1 - px)
x += dx
px = polyeval(trial, 1.2) - polyeval(target, 1.2)
if px<0: result += px*px
px = polyeval(trial, -1.2) - polyeval(target, -1.2)
if px<0: result += px*px
return result
return chebyshevcost
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