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The calculation of coefficient errors in the Polynomial fitting class was modified to assume equal accuracy in the fitted y(x) data.
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‎examples/OrbitUtils_Tests/Polynomials/polynomial_fitting_test.py‎

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#----------------------------------------------
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# This is an example of a polymonial fitting
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#----------------------------------------------
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import sys
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import math
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import random
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from orbit.core.orbit_utils import Matrix
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from orbit.core.orbit_utils import Function
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from orbit.core.orbit_utils import SplineCH
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from orbit.utils.fitting import PolynomialFit
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random_err_range = 0.001
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f = Function()
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for i in range(15):
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x = 0.1*i
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y = -1+1.0*x**2+2.0*x**3 + 0.01*x**4
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y += random.uniform(-random_err_range,+random_err_range)
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f.add(x,y)
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print ("polynomial for fitting = y = -1+1.0*x**2+2.0*x**3 + 0.01*x**4")
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print ("================Function====================================")
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poly = PolynomialFit(4)
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poly.fitFunction(f)
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[coef_arr,err_arr] = poly.getCoefficientsAndErr()
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for i in range(len(coef_arr)):
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print ("i=",i," coef = %8.5f +- %8.5f"%(coef_arr[i],err_arr[i]))
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print ("================SplineCH====================================")
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spline = SplineCH()
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spline.compile(f)
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poly.fitSpline(f)
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[coef_arr,err_arr] = poly.getCoefficientsAndErr()
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for i in range(len(coef_arr)):
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print ("i=",i," coef = %8.5f +- %8.5f"%(coef_arr[i],err_arr[i]))
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print ("Stop.")
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sys.exit(0)

‎examples/OrbitUtils_Tests/Polynomials/polynomial_test.py‎

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#-------------------------------------------------------------
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# This is an example of Polynomial class
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# The methods "derivativeTo","derivative", "copyTo" and "value" are included.
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#-------------------------------------------------------------
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import sys
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import math
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from orbit.core.orbit_utils import Polynomial
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poly = Polynomial(4)
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print ("initial order = ",poly.order())
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poly.coefficient(2,2.0)
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print ("========Polynomial=======")
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order = poly.order()
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for i in range(order+1):
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print ("i=",i," coef=",poly.coefficient(i))
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x = 10.
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y = poly.value(x)
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print ("x=",x," y=",y)
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poly1 = Polynomial()
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poly.derivativeTo(poly1)
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print ("========Derivative polynomial=======")
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order = poly1.order()
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for i in range(order+1):
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print ("i=",i," coef=",poly1.coefficient(i))
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x = 10.
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y = poly1.value(x)
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yp = poly.derivative(x)
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print ("x=",x," y_prime=",y," yp =",yp)
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print ("========Copy of initial polynomial=======")
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poly2 = Polynomial()
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poly.copyTo(poly2)
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order = poly2.order()
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for i in range(order+1):
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print ("i=",i," coef=",poly2.coefficient(i))
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x = 10.
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y = poly2.value(x)
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yp = poly2.derivative(x)
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print ("x=",x," y=",y," y_prime=",yp)
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"""
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# Memory leak test
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count = 1
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while(1 < 2):
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poly1 = Polynomial()
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poly2 = Polynomial()
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poly.derivativeTo(poly1)
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poly.copyTo(poly2)
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count += 1
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if(count % 100000 == 0):
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print ("count=",count)
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"""
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print ("Stop.")
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sys.exit(0)
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‎py/orbit/utils/fitting/PolynomialFit.py‎

Lines changed: 34 additions & 58 deletions
Original file line numberDiff line numberDiff line change
@@ -7,7 +7,9 @@
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import sys
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import math
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10-
from orbit.core.orbit_utils import Function, SplineCH, Matrix, Polynomial
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from orbit.core.orbit_utils import Function, SplineCH
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from orbit.core.orbit_utils import PhaseVector, Matrix
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from orbit.core.orbit_utils import Polynomial
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class PolynomialFit:
@@ -60,68 +62,42 @@ def fitSpline(self, spline):
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def _makePolynomial(self):
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nPoints = len(self.x_y_err_arr)
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if nPoints < (self.order + 1):
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if(nPoints < (self.order + 1)):
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self.order = nPoints - 1
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# check if just one of errors is zero
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infoZeroErr = 1.0
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for [x, y, err] in self.x_y_err_arr:
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infoZeroErr *= err
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for i in range(nPoints):
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[x, y, err] = self.x_y_err_arr[i]
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sigma = 1.0
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if infoZeroErr != 0.0:
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sigma = 1.0 / (err * err)
74-
self.x_y_err_arr[i][2] = sigma
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# now make A matrix
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aMatr = Matrix(nPoints, self.order + 1)
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#---- now make A and A^T matrices and y-vector
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aMtr = Matrix(nPoints, self.order + 1)
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yVct = PhaseVector(nPoints)
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for i in range(nPoints):
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y = self.x_y_err_arr[i][1]
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yVct.set(i,y)
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for j in range(self.order + 1):
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x = self.x_y_err_arr[i][0]
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aMatr.set(i, j, math.pow(x, j))
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aTCa = Matrix(self.order + 1, self.order + 1)
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for i in range(self.order + 1):
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for j in range(self.order + 1):
84-
a = 0.0
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for k in range(nPoints):
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sigma = self.x_y_err_arr[k][2]
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a += aMatr.get(k, i) * sigma * aMatr.get(k, j)
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aTCa.set(i, j, a)
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aMtr.set(i, j, math.pow(x, j))
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aMtrT = aMtr.transpose()
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# now the resuting coefficients and errors
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aTCaI = aTCa.invert()
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if aTCaI == None:
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print("python PolynomialFit: Problem with data.")
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for i in range(nPoints):
94-
x = self.x_y_err_arr[i][0]
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y = self.x_y_err_arr[i][1]
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err = self.x_y_err_arr[i][2]
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print(" x,y,err = %12.5g %12.5g %12.5g " % (x, y, err))
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print("Stop.")
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sys.exit(1)
100-
e = aTCaI.mult(aTCa)
101-
coef_arr = [0.0] * (self.order + 1)
102-
err_arr = [0.0] * (self.order + 1)
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ATA_inv = (aMtrT.mult(aMtr)).invert()
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coeffVct = (ATA_inv.mult(aMtrT)).mult(yVct)
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# polinimial coefficients have been found -> coeffVct
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coef_arr = [0.0] * (self.order + 1)
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self.polynomial.order(self.order)
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for i in range(self.order + 1):
104-
err_arr[i] = math.sqrt(math.fabs(aTCaI.get(i, i)))
84+
coef_arr[i] = coeffVct.get(i)
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self.polynomial.coefficient(i,coef_arr[i])
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#---- here we estimate errors by deviation y_fit from y_init only
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#---- It means that we do not pay attention to different weights
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#---- of the initial Y data errors
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coeff_err_arr = [0.0] * (self.order + 1)
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for i in range(self.order + 1):
106-
coef_arr[i] = 0.0
107-
for j in range(self.order + 1):
108-
for k in range(nPoints):
109-
sigma = self.x_y_err_arr[k][2]
110-
y = self.x_y_err_arr[k][1]
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coef_arr[i] += aTCaI.get(i, j) * aMatr.get(k, j) * sigma * y
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# polinimial coefficients have been found
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self.polynomial.order(self.order)
114-
for i in range(len(coef_arr)):
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self.polynomial.coefficient(i, coef_arr[i])
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# now let's calculate errors
117-
if infoZeroErr == 0.0:
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total_sigma = 0.0
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for k in range(nPoints):
120-
x = self.x_y_err_arr[k][0]
121-
y = self.x_y_err_arr[k][1]
122-
total_sigma += (self.polynomial.value(x) - y) ** 2
123-
total_sigma = math.sqrt(total_sigma / (nPoints - 2))
124-
for i in range(len(err_arr)):
125-
err_arr[i] *= total_sigma
91+
coeff_err_arr[i] = math.sqrt(ATA_inv.get(i,i))
92+
total_sigma = 0.0
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for k in range(nPoints):
94+
x = self.x_y_err_arr[k][0]
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y = self.x_y_err_arr[k][1]
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total_sigma += (self.polynomial.value(x) - y) ** 2
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degrees_of_freedom = int(abs(nPoints - (self.order + 1)))
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if(degrees_of_freedom == 0): degrees_of_freedom = 1
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total_sigma = math.sqrt(total_sigma / degrees_of_freedom)
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for i in range(self.order + 1):
101+
coeff_err_arr[i] *= total_sigma
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# set the resulting coefficients and errors array
127-
self.coef_err_arr = [coef_arr, err_arr]
103+
self.coef_err_arr = [coef_arr, coeff_err_arr]

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