def __init__(self, crange=(-10.0, 10.0)):
"""Initialize double Gaussian beam shape.
crange: 2-tuple of limits of the coordinates.
"""
DoubleGaussCore.__init__(self, crange)
for name in [
'xWidthN1', 'xWidthN2', 'yWidthN1', 'yWidthN2', 'xWidthM1',
'xWidthM2', 'yWidthM1', 'yWidthM2'
]:
# Width
par = RealVar(name, 1.3, 3.0)
self._physics_parameters[name] = par
for name in ['rhoN1', 'rhoN2', 'rhoM1', 'rhoM2']:
# Correlation parameter
par = RealVar(name, -0.48, 0.48)
self._physics_parameters[name] = par
for nameA, nameB in [('w1N', 'w1M'), ('w2N', 'w2M')]:
# Weight of narrow component
parA = RealVar(nameA, 0.0, 1.0)
self._physics_parameters[nameA] = parA
# Weight of wide component
formulaB = '1.0-{0}'.format(nameA)
arglistB = ArgList([nameA], self.parameter)
errorB = (lambda a: lambda p: p(a).err(p))(nameA)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB
def __init__(self, crange=(-10.0, 10.0)):
"""Initialize triple Gaussian beam shape.
crange: 2-tuple of limits of the coordinates.
"""
TripleGaussCore.__init__(self, crange)
for name in [
'xWidthN1', 'xWidthN2', 'yWidthN1', 'yWidthN2', 'xWidthM1',
'xWidthM2', 'yWidthM1', 'yWidthM2', 'xWidthW1', 'xWidthW2',
'yWidthW1', 'yWidthW2'
]:
# Width
par = RealVar(name, 1.3, 3.0)
self._physics_parameters[name] = par
for name in ['rhoN1', 'rhoN2', 'rhoM1', 'rhoM2', 'rhoW1', 'rhoW2']:
# Correlation parameter
par = RealVar(name, -0.48, 0.48)
self._physics_parameters[name] = par
for nameA, nameB, nameC in [('w1N', 'w1M', 'w1W'),
('w2N', 'w2M', 'w2W')]:
# Weight of narrow component
parA = RealVar(nameA, 0.0, 1.0)
self._physics_parameters[nameA] = parA
# Fraction of weight of medium component w.r.t. wide component
nameD = '{0}Fraction'.format(nameB)
parD = RealVar(nameD, 0.0, 1.0)
self._fit_parameters[nameD] = parD
# Weight of medium component
formulaB = '(1.0-{0})*{1}'.format(nameA, nameD)
arglistB = ArgList([nameA, nameD], self.parameter)
errorB = (lambda a, d: lambda p: ((p(a).err(p) * p(d).val())**2 + (
(1.0 - p(a).val()) * p(d).err(p))**2)**0.5)(nameA, nameD)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB
# Weight of wide component
formulaC = '(1.0-{0})*(1.0-{1})'.format(nameA, nameD)
arglistC = ArgList([nameA, nameD], self.parameter)
errorC = (lambda a, d: lambda p: (
(p(a).err(p) * (1.0 - p(d).val()))**2 + (
(1.0 - p(a).val()) * p(d).err(p))**2)**0.5)(nameA, nameD)
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._physics_parameters[nameC] = parC
def __init__(self, crange=(-10.0, 10.0)):
"""Initialize super double Gaussian beam shape.
crange: 2-tuple of limits of the coordinates.
"""
TripleGaussCore.__init__(self, crange)
for nameA, nameB, nameC in [('xWidthN1', 'xWidthM1', 'xWidthW1'),
('xWidthN2', 'xWidthM2', 'xWidthW2'),
('yWidthN1', 'yWidthM1', 'yWidthW1'),
('yWidthN2', 'yWidthM2', 'yWidthW2')]:
# Narrow width
parA = RealVar(nameA, 1.3, 3.0)
self._physics_parameters[nameA] = parA
# Medium width
parB = RealVar(nameB, 1.3, 3.0)
self._physics_parameters[nameB] = parB
# Wide width
parC = RealVar(nameC, 1.3, 3.0)
self._physics_parameters[nameC] = parC
# Ratio of narrow width to medium width
nameD = '{0}Ratio'.format(nameA)
formulaD = '{0}/{1}'.format(nameA, nameB)
arglistD = ArgList([nameA, nameB], self.parameter)
errorD = (lambda: lambda p: 0.0)()
parD = FormulaVar(nameD, formulaD, arglistD, errorD)
self._auxiliary_parameters[nameD] = parD
# Ratio of wide width to medium width
nameE = '{0}Ratio'.format(nameC)
formulaE = '{0}/{1}'.format(nameC, nameB)
arglistE = ArgList([nameC, nameB], self.parameter)
errorE = (lambda: lambda p: 0.0)()
parE = FormulaVar(nameE, formulaE, arglistE, errorE)
self._auxiliary_parameters[nameE] = parE
for nameA, nameB, nameC in [('rhoN1', 'rhoM1', 'rhoW1'),
('rhoN2', 'rhoM2', 'rhoW2')]:
nameD = 'xWidthN{0}Ratio'.format(nameA[-1])
nameE = 'yWidthN{0}Ratio'.format(nameA[-1])
nameF = 'xWidthW{0}Ratio'.format(nameA[-1])
nameG = 'yWidthW{0}Ratio'.format(nameA[-1])
# Correlation parameter of medium component
parB = RealVar(nameB, -0.48, 0.48)
self._physics_parameters[nameB] = parB
# Minimum value of correlation parameter (wide component)
nameH = '{0}Min'.format(nameC)
formulaH = ('max(-0.99,({0}-sqrt(1.0-{1})*sqrt(1.0-{2}))/{3}/{4}'
'-sqrt(1.0-({1}/{3})^2)*sqrt(1.0-({2}/{4})^2))') \
.format(nameB, nameD, nameE, nameF, nameG)
arglistH = ArgList([nameB, nameD, nameE, nameF, nameG],
self.parameter)
errorH = (lambda: lambda p: 0.0)()
parH = FormulaVar(nameH, formulaH, arglistH, errorH)
self._auxiliary_parameters[nameH] = parH
# Maximum value of correlation parameter (wide component)
nameI = '{0}Max'.format(nameC)
formulaI = ('min(0.99,({0}+sqrt(1.0-{1})*sqrt(1.0-{2}))/{3}/{4}'
'+sqrt(1.0-({1}/{3})^2)*sqrt(1.0-({2}/{4})^2))') \
.format(nameB, nameD, nameE, nameF, nameG)
arglistI = ArgList([nameB, nameD, nameE, nameF, nameG],
self.parameter)
errorI = (lambda: lambda p: 0.0)()
parI = FormulaVar(nameI, formulaI, arglistI, errorI)
self._auxiliary_parameters[nameI] = parI
# Position between minimum and maximum value of correlation
# parameter (wide component)
nameJ = '{0}Factor'.format(nameC)
parJ = RealVar(nameJ, 0.0, 1.0)
self._fit_parameters[nameJ] = parJ
# Correlation parameter of wide component
formulaC = '{0}+({1}-{0})*{2}'.format(nameH, nameI, nameJ)
arglistC = ArgList([nameH, nameI, nameJ], self.parameter)
errorC = (lambda h, i, j: lambda p:
(p(i).val() - p(h).val()) * p(j).err(p))
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._physics_parameters[nameC] = parC
# Minimum value of correlation parameter (narrow component)
nameK = '{0}Min'.format(nameA)
formulaK = ('max(-0.99,max({0}/{1}/{2}-sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0),{5}*{3}*{4}/{1}/{2}'
'-sqrt(({3}/{1})^2-1.0)*sqrt(({4}/{2})^2-1.0)))') \
.format(nameB, nameD, nameE, nameF, nameG, nameC)
arglistK = ArgList([nameB, nameD, nameE, nameF, nameG, nameC],
self.parameter)
errorK = (lambda: lambda p: 0.0)()
parK = FormulaVar(nameK, formulaK, arglistK, errorK)
self._auxiliary_parameters[nameK] = parK
# Maximum value of correlation parameter (narrow component)
nameL = '{0}Max'.format(nameA)
formulaL = ('min(0.99,min({0}/{1}/{2}+sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0),{5}*{3}*{4}/{1}/{2}'
'+sqrt(({3}/{1})^2-1.0)*sqrt(({4}/{2})^2-1.0)))') \
.format(nameB, nameD, nameE, nameF, nameG, nameC)
arglistL = ArgList([nameB, nameD, nameE, nameF, nameG, nameC],
self.parameter)
errorL = (lambda: lambda p: 0.0)()
parL = FormulaVar(nameL, formulaL, arglistL, errorL)
self._auxiliary_parameters[nameL] = parL
# Position between minimum and maximum value of correlation
# parameter (narrow component)
nameM = '{0}Factor'.format(nameA)
parM = RealVar(nameM, 0.0, 1.0)
self._fit_parameters[nameM] = parM
# Correlation parameter of narrow component
formulaA = '{0}+({1}-{0})*{2}'.format(nameK, nameL, nameM)
arglistA = ArgList([nameK, nameL, nameM], self.parameter)
errorA = (lambda k, l, m: lambda p:
(p(l).val() - p(k).val()) * p(m).err(p))
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
for nameA, nameB, nameC, nameD in [('w1N', 'w1M', 'w1W', 'omega1'),
('w2N', 'w2M', 'w2W', 'omega2')]:
nameE = 'xWidthN{0}Ratio'.format(nameD[-1])
nameF = 'yWidthN{0}Ratio'.format(nameD[-1])
nameG = 'xWidthW{0}Ratio'.format(nameD[-1])
nameH = 'yWidthW{0}Ratio'.format(nameD[-1])
nameI = 'rhoN{0}'.format(nameD[-1])
nameJ = 'rhoM{0}'.format(nameD[-1])
nameK = 'rhoW{0}'.format(nameD[-1])
# Fraction of weight of medium component w.r.t. wide component
nameL = '{0}Fraction'.format(nameB)
parL = RealVar(nameL, 0.0, 1.0)
self._fit_parameters[nameL] = parL
# Maximum value of weight parameter (narrow component)
nameM = '{0}Max'.format(nameD)
formulaM = (
'{0}*{1}*sqrt(1.0-{2}^2)*({3}/sqrt(1.0-{4}^2)+(1.0-{3})'
'/sqrt(1.0-{5}^2)/{6}/{7})').format(nameE, nameF, nameI, nameL,
nameJ, nameK, nameG, nameH)
arglistM = ArgList(
[nameE, nameF, nameI, nameL, nameJ, nameK, nameG, nameH],
self.parameter)
errorM = (lambda: lambda p: 0.0)()
parM = FormulaVar(nameM, formulaM, arglistM, errorM)
self._auxiliary_parameters[nameM] = parM
# Position between minimum and maximum value of weight parameter
# (narrow component)
nameN = '{0}Prime'.format(nameD)
parN = RealVar(nameN, 0.0, 1.0)
self._fit_parameters[nameN] = parN
# Weight parameter of narrow component
formulaD = '{0}*{1}'.format(nameM, nameN)
arglistD = ArgList([nameM, nameN], self.parameter)
errorD = (lambda m, n: lambda p: p(m).val() * p(n).err(p))(nameM,
nameN)
parD = FormulaVar(nameD, formulaD, arglistD, errorD)
self._auxiliary_parameters[nameD] = parD
# Weight of narrow component
formulaA = '-{0}/(1.0-{0})'.format(nameD)
arglistA = ArgList([nameD], self.parameter)
errorA = (lambda d: lambda p: p(d).err(p) /
(1.0 - p(d).val())**2)(nameD)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
# Weight of medium component
formulaB = '{0}/(1.0-{1})'.format(nameL, nameD)
arglistB = ArgList([nameL, nameD], self.parameter)
errorB = (lambda l, d: lambda p: 1.0 / (1.0 - p(d).val()) *
(p(l).err(p)**2 + (p(d).err(p) * p(l).val() /
(1.0 - p(d).val()))**2)**0.5)(nameL,
nameD)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB
# Weight of wide component
formulaC = '(1.0-{0})/(1.0-{1})'.format(nameL, nameD)
arglistC = ArgList([nameL, nameD], self.parameter)
errorC = (lambda l, d: lambda p: 1.0 / (1.0 - p(d).val()) *
(p(l).err(p)**2 + (p(d).err(p) * (1.0 - p(l).val()) /
(1.0 - p(d).val()))**2)**0.5)(nameL,
nameD)
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._physics_parameters[nameC] = parC
def __init__(self, crange=(-10.0, 10.0)):
"""Initialize super double Gaussian beam shape.
crange: 2-tuple of limits of the coordinates.
"""
TripleGaussCore.__init__(self, crange)
for nameA, nameB, nameC in [('xWidthN1', 'xWidthM1', 'xWidthW1'),
('xWidthN2', 'xWidthM2', 'xWidthW2'),
('yWidthN1', 'yWidthM1', 'yWidthW1'),
('yWidthN2', 'yWidthM2', 'yWidthW2')]:
# Medium width
parB = RealVar(nameB, 1.3, 3.0)
self._physics_parameters[nameB] = parB
# Ratio of narrow width to medium width
nameD = '{0}Ratio'.format(nameA)
parD = RealVar(nameD, 0.1, 0.99)
self._fit_parameters[nameD] = parD
# Narrow width
formulaA = '{0}*{1}'.format(nameB, nameD)
arglistA = ArgList([nameB, nameD], self.parameter)
errorA = (lambda b, d: lambda p:
((p(b).val() * p(d).err(p))**2 +
(p(d).val() * p(b).err(p))**2)**0.5)(nameB, nameD)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
# Difference of wide width to medium width
nameE = '{0}Diff'.format(nameC)
parE = RealVar(nameE, 0.01, 1.7)
self._fit_parameters[nameE] = parE
# Wide width
formulaC = '{0}+{1}'.format(nameB, nameE)
arglistC = ArgList([nameB, nameE], self.parameter)
errorC = (lambda b, e: lambda p:
(p(b).err(p)**2 + p(e).err(p)**2)**0.5)(nameB, nameE)
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._physics_parameters[nameC] = parC
# Ratio of wide width to medium width
nameF = '{0}Ratio'.format(nameC)
formulaF = '{0}/{1}'.format(nameC, nameB)
arglistF = ArgList([nameC, nameB], self.parameter)
errorF = (lambda: lambda p: 0.0)()
parF = FormulaVar(nameF, formulaF, arglistF, errorF)
self._auxiliary_parameters[nameF] = parF
for nameA, nameB, nameC in [('rhoN1', 'rhoM1', 'rhoW1'),
('rhoN2', 'rhoM2', 'rhoW2')]:
nameD = 'xWidthN{0}Ratio'.format(nameA[-1])
nameE = 'yWidthN{0}Ratio'.format(nameA[-1])
nameF = 'xWidthW{0}Ratio'.format(nameA[-1])
nameG = 'yWidthW{0}Ratio'.format(nameA[-1])
# Correlation parameter of medium component
parB = RealVar(nameB, -0.48, 0.48)
self._physics_parameters[nameB] = parB
# Minimum value of correlation parameter (wide component)
nameH = '{0}Min'.format(nameC)
formulaH = ('max(-0.99,({0}-sqrt(1.0-{1})*sqrt(1.0-{2}))/{3}/{4}'
'-sqrt(1.0-({1}/{3})^2)*sqrt(1.0-({2}/{4})^2))') \
.format(nameB, nameD, nameE, nameF, nameG)
arglistH = ArgList([nameB, nameD, nameE, nameF, nameG],
self.parameter)
errorH = (lambda: lambda p: 0.0)()
parH = FormulaVar(nameH, formulaH, arglistH, errorH)
self._auxiliary_parameters[nameH] = parH
# Maximum value of correlation parameter (wide component)
nameI = '{0}Max'.format(nameC)
formulaI = ('min(0.99,({0}+sqrt(1.0-{1})*sqrt(1.0-{2}))/{3}/{4}'
'+sqrt(1.0-({1}/{3})^2)*sqrt(1.0-({2}/{4})^2))') \
.format(nameB, nameD, nameE, nameF, nameG)
arglistI = ArgList([nameB, nameD, nameE, nameF, nameG],
self.parameter)
errorI = (lambda: lambda p: 0.0)()
parI = FormulaVar(nameI, formulaI, arglistI, errorI)
self._auxiliary_parameters[nameI] = parI
# Correlation parameter of wide component
parC = RealVar(nameC, -0.48, 0.48)
parC.set_fixed_minimum(parH)
parC.set_fixed_maximum(parI)
self._physics_parameters[nameC] = parC
# Minimum value of correlation parameter (narrow component)
nameJ = '{0}Min'.format(nameA)
formulaJ = ('max(-0.99,max({0}/{1}/{2}-sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0),{5}*{3}*{4}/{1}/{2}'
'-sqrt(({3}/{1})^2-1.0)*sqrt(({4}/{2})^2-1.0)))') \
.format(nameB, nameD, nameE, nameF, nameG, nameC)
arglistJ = ArgList([nameB, nameD, nameE, nameF, nameG, nameC],
self.parameter)
errorJ = (lambda: lambda p: 0.0)()
parJ = FormulaVar(nameJ, formulaJ, arglistJ, errorJ)
self._auxiliary_parameters[nameJ] = parJ
# Maximum value of correlation parameter (narrow component)
nameK = '{0}Max'.format(nameA)
formulaK = ('min(0.99,min({0}/{1}/{2}+sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0),{5}*{3}*{4}/{1}/{2}'
'+sqrt(({3}/{1})^2-1.0)*sqrt(({4}/{2})^2-1.0)))') \
.format(nameB, nameD, nameE, nameF, nameG, nameC)
arglistK = ArgList([nameB, nameD, nameE, nameF, nameG, nameC],
self.parameter)
errorK = (lambda: lambda p: 0.0)()
parK = FormulaVar(nameK, formulaK, arglistK, errorK)
self._auxiliary_parameters[nameK] = parK
# Correlation parameter of narrow component
parA = RealVar(nameA, -0.48, 0.48)
parA.set_fixed_minimum(parJ)
parA.set_fixed_maximum(parK)
self._physics_parameters[nameA] = parA
for nameA, nameB, nameC, nameD in [('w1N', 'w1M', 'w1W', 'omega1'),
('w2N', 'w2M', 'w2W', 'omega2')]:
nameE = 'xWidthN{0}Ratio'.format(nameD[-1])
nameF = 'yWidthN{0}Ratio'.format(nameD[-1])
nameG = 'xWidthW{0}Ratio'.format(nameD[-1])
nameH = 'yWidthW{0}Ratio'.format(nameD[-1])
nameI = 'rhoN{0}'.format(nameD[-1])
nameJ = 'rhoM{0}'.format(nameD[-1])
nameK = 'rhoW{0}'.format(nameD[-1])
# Fraction of weight of medium component w.r.t. wide component
nameL = '{0}Fraction'.format(nameB)
parL = RealVar(nameL, 0.0, 1.0)
self._fit_parameters[nameL] = parL
# Maximum value of weight parameter (narrow component)
nameM = '{0}Max'.format(nameD)
formulaM = (
'{0}*{1}*sqrt(1.0-{2}^2)*({3}/sqrt(1.0-{4}^2)+(1.0-{3})'
'/sqrt(1.0-{5}^2)/{6}/{7})').format(nameE, nameF, nameI, nameL,
nameJ, nameK, nameG, nameH)
arglistM = ArgList(
[nameE, nameF, nameI, nameL, nameJ, nameK, nameG, nameH],
self.parameter)
errorM = (lambda: lambda p: 0.0)()
parM = FormulaVar(nameM, formulaM, arglistM, errorM)
self._auxiliary_parameters[nameM] = parM
# Weight parameter of narrow component
parD = RealVar(nameD, 0.0, 0.99)
parD.set_fixed_maximum(parM)
self._fit_parameters[nameD] = parD
# Weight of narrow component
formulaA = '-{0}/(1.0-{0})'.format(nameD)
arglistA = ArgList([nameD], self.parameter)
errorA = (lambda d: lambda p: p(d).err(p) /
(1.0 - p(d).val())**2)(nameD)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
# Weight of medium component
formulaB = '{0}/(1.0-{1})'.format(nameL, nameD)
arglistB = ArgList([nameL, nameD], self.parameter)
errorB = (lambda l, d: lambda p: 1.0 / (1.0 - p(d).val()) *
(p(l).err(p)**2 + (p(d).err(p) * p(l).val() /
(1.0 - p(d).val()))**2)**0.5)(nameL,
nameD)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB
# Weight of wide component
formulaC = '(1.0-{0})/(1.0-{1})'.format(nameL, nameD)
arglistC = ArgList([nameL, nameD], self.parameter)
errorC = (lambda l, d: lambda p: 1.0 / (1.0 - p(d).val()) *
(p(l).err(p)**2 + (p(d).err(p) * (1.0 - p(l).val()) /
(1.0 - p(d).val()))**2)**0.5)(nameL,
nameD)
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._physics_parameters[nameC] = parC
def __init__(self, crange=(-10.0, 10.0)):
"""Initialize triple Gaussian beam shape.
crange: 2-tuple of limits of the coordinates.
"""
TripleGaussCore.__init__(self, crange)
for nameA, nameB, nameC in [('xWidthN1', 'xWidthM1', 'xWidthW1'),
('xWidthN2', 'xWidthM2', 'xWidthW2'),
('yWidthN1', 'yWidthM1', 'yWidthW1'),
('yWidthN2', 'yWidthM2', 'yWidthW2')]:
# Narrow width
parA = RealVar(nameA, 1.3, 3.0)
self._physics_parameters[nameA] = parA
# Difference of narrow width to medium width
nameD = '{0}Diff'.format(nameB)
parD = RealVar(nameD, 0.01, 1.7)
self._fit_parameters[nameD] = parD
# Medium width
formulaB = '{0}+{1}'.format(nameA, nameD)
arglistB = ArgList([nameA, nameD], self.parameter)
errorB = (lambda a, d: lambda p:
(p(a).err(p)**2 + p(d).err(p)**2)**0.5)(nameA, nameD)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB
# Difference of medium width to wide width
nameE = '{0}Diff'.format(nameC)
parE = RealVar(nameE, 0.01, 1.7)
self._fit_parameters[nameE] = parE
# Wide width
formulaC = '{0}+{1}'.format(nameB, nameE)
arglistC = ArgList([nameB, nameE], self.parameter)
errorC = (lambda b, e: lambda p:
(p(b).err(p)**2 + p(e).err(p)**2)**0.5)(nameB, nameE)
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._physics_parameters[nameC] = parC
for name in ['rhoN1', 'rhoN2', 'rhoM1', 'rhoM2', 'rhoW1', 'rhoW2']:
# Correlation parameter
par = RealVar(name, -0.48, 0.48)
self._physics_parameters[name] = par
for nameA, nameB, nameC, nameD, nameE in [
('w1N', 'w1M', 'w1W', 'theta1', 'phi1'),
('w2N', 'w2M', 'w2W', 'theta2', 'phi2')
]:
# First weight parameter
parD = RealVar(nameD, 0.0, 0.5 * pi)
self._fit_parameters[nameD] = parD
# Second weight parameter
parE = RealVar(nameE, 0.0, 0.5 * pi)
self._fit_parameters[nameE] = parE
# Weight of narrow component
formulaA = 'cos({0})^2'.format(nameD)
arglistA = ArgList([nameD], self.parameter)
errorA = (lambda d: lambda p: 2.0 * sin(p(d).val()) * cos(
p(d).val()) * p(d).err(p))(nameD)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
# Weight of medium component
formulaB = 'sin({0})^2*cos({1})^2'.format(nameD, nameE)
arglistB = ArgList([nameD, nameE], self.parameter)
errorB = (lambda d, e: lambda p: 2.0 * sin(p(d).val(
)) * cos(p(e).val()) * (
(p(d).err(p) * cos(p(d).val()) * cos(p(e).val()))**2 +
(p(e).err(p) * sin(p(d).val()) * sin(p(e).val()))**2)**0.5)(
nameD, nameE)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB
# Weight of wide component
formulaC = 'sin({0})^2*sin({1})^2'.format(nameD, nameE)
arglistC = ArgList([nameD, nameE], self.parameter)
errorC = (lambda d, e: lambda p: 2.0 * sin(p(d).val(
)) * sin(p(e).val()) * (
(p(d).err(p) * cos(p(d).val()) * sin(p(e).val()))**2 +
(p(e).err(p) * sin(p(d).val()) * cos(p(e).val()))**2)**0.5)(
nameD, nameE)
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._physics_parameters[nameC] = parC
def __init__(self, crange=(-10.0, 10.0)):
"""Initialize super Gaussian beam shape.
crange: 2-tuple of limits of the coordinates.
"""
DoubleGaussCore.__init__(self, crange)
for nameA, nameB in [
('xWidthN1', 'xWidthM1'), ('xWidthN2', 'xWidthM2'),
('yWidthN1', 'yWidthM1'), ('yWidthN2', 'yWidthM2')
]:
# Narrow width
parA = RealVar(nameA, 1.3, 3.0)
self._physics_parameters[nameA] = parA
# Wide width
parB = RealVar(nameB, 1.3, 3.0)
self._physics_parameters[nameB] = parB
# Ratio of narrow width to wide width
nameC = '{0}Ratio'.format(nameA)
formulaC = '{0}/{1}'.format(nameA, nameB)
arglistC = ArgList([nameA, nameB], self.parameter)
errorC = (lambda: lambda p: 0.0)()
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._auxiliary_parameters[nameC] = parC
for nameA, nameB in [('rhoN1', 'rhoM1'), ('rhoN2', 'rhoM2')]:
nameC = 'xWidthN{0}Ratio'.format(nameA[-1])
nameD = 'yWidthN{0}Ratio'.format(nameA[-1])
# Correlation parameter of wide component
parB = RealVar(nameB, -0.48, 0.48)
self._physics_parameters[nameB] = parB
# Minimum value of correlation parameter (narrow component)
nameE = '{0}Min'.format(nameA)
formulaE = ('max(-0.99,{0}/{1}/{2}-sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0))').format(nameB, nameC, nameD)
arglistE = ArgList([nameB, nameC, nameD], self.parameter)
errorE = (lambda: lambda p: 0.0)()
parE = FormulaVar(nameE, formulaE, arglistE, errorE)
self._auxiliary_parameters[nameE] = parE
# Maximum value of correlation parameter (narrow component)
nameF = '{0}Max'.format(nameA)
formulaF = ('min(0.99,{0}/{1}/{2}+sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0))').format(nameB, nameC, nameD)
arglistF = ArgList([nameB, nameC, nameD], self.parameter)
errorF = (lambda: lambda p: 0.0)()
parF = FormulaVar(nameF, formulaF, arglistF, errorF)
self._auxiliary_parameters[nameF] = parF
# Position between minimum and maximum value of correlation
# parameter (narrow component)
nameG = '{0}Factor'.format(nameA)
parG = RealVar(nameG, 0.0, 1.0)
self._fit_parameters[nameG] = parG
# Correlation parameter of narrow component
formulaA = '{0}+({1}-{0})*{2}'.format(nameE, nameF, nameG)
arglistA = ArgList([nameE, nameF, nameG], self.parameter)
errorA = (lambda e, f, g: lambda p:
(p(f).val() - p(e).val()) * p(g).err(p))(nameE, nameF,
nameG)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
for nameA, nameB, nameC in [('w1N', 'w1M', 'omega1'),
('w2N', 'w2M', 'omega2')]:
nameD = 'xWidthN{0}Ratio'.format(nameC[-1])
nameE = 'yWidthN{0}Ratio'.format(nameC[-1])
nameF = 'rhoN{0}'.format(nameC[-1])
nameG = 'rhoM{0}'.format(nameC[-1])
# Maximum value of weight parameter
nameH = '{0}Max'.format(nameC)
formulaH = '{0}*{1}*sqrt((1.0-{2}^2)/(1.0-{3}^2))' \
.format(nameD, nameE, nameF, nameG)
arglistH = ArgList([nameD, nameE, nameF, nameG], self.parameter)
errorH = (lambda: lambda p: 0.0)()
parH = FormulaVar(nameH, formulaH, arglistH, errorH)
self._auxiliary_parameters[nameH] = parH
# Position between minimum and maximum value of weight parameter
nameI = '{0}Prime'.format(nameC)
parI = RealVar(nameI, 0.0, 1.0)
self._fit_parameters[nameI] = parI
# Weight parameter
formulaC = '{0}*{1}'.format(nameH, nameI)
arglistC = ArgList([nameH, nameI], self.parameter)
errorC = (lambda h, i: lambda p: p(h).val() * p(i).err(p))(nameH,
nameI)
parC = FormulaVar(nameC, formulaC, arglistC, errorC)
self._auxiliary_parameters[nameC] = parC
# Weight of narrow component
formulaA = '-{0}/(1.0-{0})'.format(nameC)
arglistA = ArgList([nameC], self.parameter)
errorA = (lambda c: lambda p: p(c).err(p) /
(1.0 - p(c).val()**2))(nameC)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
# Weight of wide component
formulaB = '1.0/(1.0-{0})'.format(nameC)
arglistB = ArgList([nameC], self.parameter)
errorB = (lambda c: lambda p: p(c).err(p) /
(1.0 - p(c).val()**2))(nameC)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB
def __init__(self, crange=(-10.0, 10.0)):
"""Initialize super Gaussian beam shape.
crange: 2-tuple of limits of the coordinates.
"""
DoubleGaussCore.__init__(self, crange)
for nameA, nameB in [
('xWidthN1', 'xWidthM1'), ('xWidthN2', 'xWidthM2'),
('yWidthN1', 'yWidthM1'), ('yWidthN2', 'yWidthM2')
]:
# Wide width
parB = RealVar(nameB, 1.3, 3.0)
self._physics_parameters[nameB] = parB
# Ratio of narrow width to wide width
nameC = '{0}Ratio'.format(nameA)
parC = RealVar(nameC, 0.1, 0.99)
self._fit_parameters[nameC] = parC
# Narrow width
formulaA = '{0}*{1}'.format(nameB, nameC)
arglistA = ArgList([nameB, nameC], self.parameter)
errorA = (lambda b, c: lambda p:
((p(b).val() * p(c).err(p))**2 +
(p(c).val() * p(b).err(p))**2)**0.5)(nameB, nameC)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
for nameA, nameB in [('rhoN1', 'rhoM1'), ('rhoN2', 'rhoM2')]:
nameC = 'xWidthN{0}Ratio'.format(nameA[-1])
nameD = 'yWidthN{0}Ratio'.format(nameA[-1])
# Correlation parameter of wide component
parB = RealVar(nameB, -0.48, 0.48)
self._physics_parameters[nameB] = parB
# Minimum value of correlation parameter (narrow component)
nameE = '{0}Min'.format(nameA)
formulaE = ('max(-0.99,{0}/{1}/{2}-sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0))').format(nameB, nameC, nameD)
arglistE = ArgList([nameB, nameC, nameD], self.parameter)
errorE = (lambda: lambda p: 0.0)()
parE = FormulaVar(nameE, formulaE, arglistE, errorE)
self._auxiliary_parameters[nameE] = parE
# Maximum value of correlation parameter (narrow component)
nameF = '{0}Max'.format(nameA)
formulaF = ('min(0.99,{0}/{1}/{2}+sqrt(1.0/{1}^2-1.0)'
'*sqrt(1.0/{2}^2-1.0))').format(nameB, nameC, nameD)
arglistF = ArgList([nameB, nameC, nameD], self.parameter)
errorF = (lambda: lambda p: 0.0)()
parF = FormulaVar(nameF, formulaF, arglistF, errorF)
self._auxiliary_parameters[nameF] = parF
# Correlation parameter of narrow component
parA = RealVar(nameA, -0.48, 0.48)
parA.set_fixed_minimum(parE)
parA.set_fixed_maximum(parF)
self._physics_parameters[nameA] = parA
for nameA, nameB, nameC in [('w1N', 'w1M', 'omega1'),
('w2N', 'w2M', 'omega2')]:
nameD = 'xWidthN{0}Ratio'.format(nameC[-1])
nameE = 'yWidthN{0}Ratio'.format(nameC[-1])
nameF = 'rhoN{0}'.format(nameC[-1])
nameG = 'rhoM{0}'.format(nameC[-1])
# Maximum value of weight parameter
nameH = '{}Max'.format(nameC)
formulaH = '{0}*{1}*sqrt((1.0-{2}^2)/(1.0-{3}^2))' \
.format(nameD, nameE, nameF, nameG)
arglistH = ArgList([nameD, nameE, nameF, nameG], self.parameter)
errorH = (lambda: lambda p: 0.0)()
parH = FormulaVar(nameH, formulaH, arglistH, errorH)
self._auxiliary_parameters[nameH] = parH
# Weight parameter
parC = RealVar(nameC, 0.0, 0.99)
parC.set_fixed_maximum(parH)
self._fit_parameters[nameC] = parC
# Weight of narrow component
formulaA = '-{0}/(1.0-{0})'.format(nameC)
arglistA = ArgList([nameC], self.parameter)
errorA = (lambda c: lambda p: p(c).err(p) /
(1.0 - p(c).val()**2))(nameC)
parA = FormulaVar(nameA, formulaA, arglistA, errorA)
self._physics_parameters[nameA] = parA
# Weight of wide component
formulaB = '1.0/(1.0-{0})'.format(nameC)
arglistB = ArgList([nameC], self.parameter)
errorB = (lambda c: lambda p: p(c).err(p) /
(1.0 - p(c).val())**2)(nameC)
parB = FormulaVar(nameB, formulaB, arglistB, errorB)
self._physics_parameters[nameB] = parB