class PolynomialFit: def __init__(self,order): """ The calss to fit Function or SplineCH with a polynomial. """ self.order = order self.polynomial = Polynomial() #self.coef_err_arr is a final array with coef_arr and err_arr for polinomial coefficients self.coef_err_arr = [] #self.x_y_err_arr is initial data with (x,y,y_err) points self.x_y_err_arr = [] def getPolynomial(self): """ It returns an unbounded polynomial. """ polynomial = Polynomial() self.polynomial.copyTo(polynomial) return polynomial def getCoefficientsAndErr(self): """ It returns the list of coefficients and their errors """ return self.coef_err_arr def getCoefficients(self): """ Returns the list of coefficients of the polynomial """ coef_arr = [] for i in range(len(self.coef_err_arr)): [coef,err] = self.coef_err_arr[i] coef_arr.append(coef) return coef_arr def fitFunction(self, function): """ Fit the Function instance """ self.x_y_err_arr = [] for i in range(function.getSize()): x = function.x(i) y = function.y(i) err = function.err(i) self.x_y_err_arr.append([x,y,err]) self._makePolynomial() def fitSpline(self, spline): """ Fit the SplineCH instance """ self.x_y_err_arr = [] for i in range(spline.getSize()): x = spline.x(i) y = spline.y(i) err = 0. self.x_y_err_arr.append([x,y,err]) self._makePolynomial() def _makePolynomial(self): nPoints = len(self.x_y_err_arr) if(nPoints < (self.order+1)): self.order = nPoints - 1 #check if just one of errors is zero infoZeroErr = 1.0 for [x,y,err] in self.x_y_err_arr: infoZeroErr *= err for i in range(nPoints): [x,y,err] = self.x_y_err_arr[i] sigma = 1.0 if(infoZeroErr != 0.): sigma = 1.0/(err*err) self.x_y_err_arr[i][2] = sigma #now make A matrix aMatr = Matrix(nPoints,self.order+1) for i in range(nPoints): for j in range(self.order+1): x = self.x_y_err_arr[i][0] aMatr.set(i,j,math.pow(x,j)) aTCa = Matrix(self.order+1,self.order+1) for i in range(self.order+1): for j in range(self.order+1): a = 0. for k in range(nPoints): sigma = self.x_y_err_arr[k][2] a += aMatr.get(k,i)*sigma*aMatr.get(k,j) aTCa.set(i,j,a) #now the resuting coefficients and errors aTCaI = aTCa.invert() e = aTCaI.mult(aTCa) if(aTCa == None): print "python PolynomialFit: Problem with data." for i in range(nPoints): x = self.x_y_err_arr[i][0] y = self.x_y_err_arr[i][1] err = self.x_y_err_arr[i][2] print " x,y,err = %12.5g %12.5g %12.5g "%(x,y,err) print "Stop." sys.exit(1) coef_arr = [0.]*(self.order+1) err_arr = [0.]*(self.order+1) for i in range(self.order+1): err_arr[i] = math.sqrt(math.fabs(aTCaI.get(i,i))) for i in range(self.order+1): coef_arr[i] = 0. for j in range(self.order+1): for k in range(nPoints): sigma = self.x_y_err_arr[k][2] y = self.x_y_err_arr[k][1] coef_arr[i] += aTCaI.get(i,j)*aMatr.get(k,j)*sigma*y # polinimial coefficients are found self.polynomial.order(self.order) for i in range(len(coef_arr)): self.polynomial.coefficient(i,coef_arr[i]) # now let's calculate errors if(infoZeroErr == 0.): total_sigma = 0. for k in range(nPoints): x = self.x_y_err_arr[k][0] y = self.x_y_err_arr[k][1] total_sigma += (self.polynomial.value(x)-y)**2 total_sigma = math.sqrt(total_sigma/(nPoints-2)) for i in range(len(err_arr)): err_arr[i] *= total_sigma # set the resulting coefficients and errors array self.coef_err_arr = [coef_arr,err_arr]
class PolynomialFit:
def __init__(self, order):
""" The calss to fit Function or SplineCH with a polynomial. """
self.order = order
self.polynomial = Polynomial()
#self.coef_err_arr is a final array with coef_arr and err_arr for polinomial coefficients
self.coef_err_arr = []
#self.x_y_err_arr is initial data with (x,y,y_err) points
self.x_y_err_arr = []
def getPolynomial(self):
""" It returns an unbounded polynomial. """
polynomial = Polynomial()
self.polynomial.copyTo(polynomial)
return polynomial
def getCoefficientsAndErr(self):
""" It returns the list of coefficients and their errors """
return self.coef_err_arr
def getCoefficients(self):
""" Returns the list of coefficients of the polynomial """
coef_arr = []
for i in range(len(self.coef_err_arr)):
[coef, err] = self.coef_err_arr[i]
coef_arr.append(coef)
return coef_arr
def fitFunction(self, function):
""" Fit the Function instance """
self.x_y_err_arr = []
for i in range(function.getSize()):
x = function.x(i)
y = function.y(i)
err = function.err(i)
self.x_y_err_arr.append([x, y, err])
self._makePolynomial()
def fitSpline(self, spline):
""" Fit the SplineCH instance """
self.x_y_err_arr = []
for i in range(spline.getSize()):
x = spline.x(i)
y = spline.y(i)
err = 0.
self.x_y_err_arr.append([x, y, err])
self._makePolynomial()
def _makePolynomial(self):
nPoints = len(self.x_y_err_arr)
if (nPoints < (self.order + 1)):
self.order = nPoints - 1
#check if just one of errors is zero
infoZeroErr = 1.0
for [x, y, err] in self.x_y_err_arr:
infoZeroErr *= err
for i in range(nPoints):
[x, y, err] = self.x_y_err_arr[i]
sigma = 1.0
if (infoZeroErr != 0.):
sigma = 1.0 / (err * err)
self.x_y_err_arr[i][2] = sigma
#now make A matrix
aMatr = Matrix(nPoints, self.order + 1)
for i in range(nPoints):
for j in range(self.order + 1):
x = self.x_y_err_arr[i][0]
aMatr.set(i, j, math.pow(x, j))
aTCa = Matrix(self.order + 1, self.order + 1)
for i in range(self.order + 1):
for j in range(self.order + 1):
a = 0.
for k in range(nPoints):
sigma = self.x_y_err_arr[k][2]
a += aMatr.get(k, i) * sigma * aMatr.get(k, j)
aTCa.set(i, j, a)
#now the resuting coefficients and errors
aTCaI = aTCa.invert()
e = aTCaI.mult(aTCa)
if (aTCa == None):
print "python PolynomialFit: Problem with data."
for i in range(nPoints):
x = self.x_y_err_arr[i][0]
y = self.x_y_err_arr[i][1]
err = self.x_y_err_arr[i][2]
print " x,y,err = %12.5g %12.5g %12.5g " % (x, y, err)
print "Stop."
sys.exit(1)
coef_arr = [0.] * (self.order + 1)
err_arr = [0.] * (self.order + 1)
for i in range(self.order + 1):
err_arr[i] = math.sqrt(math.fabs(aTCaI.get(i, i)))
for i in range(self.order + 1):
coef_arr[i] = 0.
for j in range(self.order + 1):
for k in range(nPoints):
sigma = self.x_y_err_arr[k][2]
y = self.x_y_err_arr[k][1]
coef_arr[i] += aTCaI.get(i, j) * aMatr.get(k,
j) * sigma * y
# polinimial coefficients are found
self.polynomial.order(self.order)
for i in range(len(coef_arr)):
self.polynomial.coefficient(i, coef_arr[i])
# now let's calculate errors
if (infoZeroErr == 0.):
total_sigma = 0.
for k in range(nPoints):
x = self.x_y_err_arr[k][0]
y = self.x_y_err_arr[k][1]
total_sigma += (self.polynomial.value(x) - y)**2
total_sigma = math.sqrt(total_sigma / (nPoints - 2))
for i in range(len(err_arr)):
err_arr[i] *= total_sigma
# set the resulting coefficients and errors array
self.coef_err_arr = [coef_arr, err_arr]
#-------------------------------------------------------------
# This is an example of Polynomial class
# The methods "derivativeTo","derivative", "copyTo" and "value" are included.
#-------------------------------------------------------------
import sys
import math
from orbit_utils import Polynomial
poly = Polynomial(4)
print "initial order = ", poly.order()
poly.coefficient(2, 2.0)
print "========Polynomial======="
order = poly.order()
for i in range(order + 1):
print "i=", i, " coef=", poly.coefficient(i)
x = 10.
y = poly.value(x)
print "x=", x, " y=", y
poly1 = Polynomial()
poly.derivativeTo(poly1)
print "========Derivative polynomial======="
order = poly1.order()
for i in range(order + 1):
print "i=", i, " coef=", poly1.coefficient(i)