def age_equation(j,
f,
include_decay_error=False,
lambda_k=None,
arar_constants=None):
if isinstance(j, tuple):
j = ufloat(*j)
elif isinstance(j, str):
j = ufloat(j)
if isinstance(f, tuple):
f = ufloat(*f)
elif isinstance(f, str):
f = ufloat(f)
if not lambda_k:
if arar_constants is None:
arar_constants = ArArConstants()
lambda_k = arar_constants.lambda_k
if arar_constants is None:
arar_constants = ArArConstants()
if not include_decay_error:
lambda_k = nominal_value(lambda_k)
try:
# lambda is defined in years, so age is in years
age = lambda_k**-1 * umath.log(1 + j * f)
return arar_constants.scale_age(age, current='a')
except (ValueError, TypeError):
return ufloat(0, 0)
def age_equation(j,
f,
include_decay_error=False,
lambda_k=None,
scalar=None,
arar_constants=None):
if isinstance(j, tuple):
j = ufloat(*j)
elif isinstance(j, str):
j = ufloat(j)
if isinstance(f, tuple):
f = ufloat(*f)
elif isinstance(f, str):
f = ufloat(f)
if not lambda_k:
if arar_constants is None:
arar_constants = ArArConstants()
lambda_k = arar_constants.lambda_k
if not scalar:
if arar_constants is None:
arar_constants = ArArConstants()
scalar = float(arar_constants.age_scalar)
if not include_decay_error:
lambda_k = nominal_value(lambda_k)
try:
return (lambda_k**-1 * umath.log(1 + j * f)) / scalar
except (ValueError, TypeError):
return ufloat(0, 0)
def interference_corrections(a39, a37, production_ratios, arar_constants=None, fixed_k3739=False):
if production_ratios is None:
production_ratios = {}
if arar_constants is None:
arar_constants = ArArConstants()
pr = production_ratios
if arar_constants.k3739_mode.lower() == 'normal' and not fixed_k3739:
ca3937 = pr.get('Ca3937', 0)
k3739 = pr.get('K3739', 0)
k39 = (a39 - ca3937 * a37) / (1 - k3739 * ca3937)
k37 = pr.get('K3739', 0) * k39
ca37 = a37 - k37
ca39 = pr.get('Ca3937', 0) * ca37
else:
if not fixed_k3739:
fixed_k3739 = arar_constants.fixed_k3739
ca37, ca39, k37, k39 = apply_fixed_k3739(a39, pr, fixed_k3739)
k38 = pr.get('K3839', 0) * k39
if not arar_constants.allow_negative_ca_correction:
ca37 = max(ufloat(0, 0), ca37)
ca36 = pr.get('Ca3637', 0) * ca37
ca38 = pr.get('Ca3837', 0) * ca37
return k37, k38, k39, ca36, ca37, ca38, ca39
def calculate(self, age, sensitivity, k2o):
c = ArArConstants()
xs = np.linspace(self.start, self.end)
ys = np.array([self._calculate(wi, age, sensitivity, k2o, c) for wi in xs])
# nxs = np.linspace(max(1e-2, 0), self.end)
# n40 = np.linspace(max(1, ys[0]), ys[-1])
n40 = ys[:]
if ys[0] == 0:
n40 = n40[1:]
# r4039 = 7.78
n39 = n40 / self.r4039
# nys = ys[:]
# print nys
# nys = np.hstack(([1], nys[1:]))
# print nys
p = (0.0021435788651550671, -0.48505328994128016)
e40_scalar = 3
e39 = powerlaw(p, n39)
e40 = powerlaw(p, n40) * e40_scalar
es = (e39 ** 2 + e40 ** 2) ** 0.5
# es = age * 1e3 * es
# es = 0.2 * nys ** (-0.5)
return xs, ys, n40, es * 100
def calculate_atmospheric(a38,
a36,
k38,
ca38,
ca36,
decay_time,
production_ratios=None,
arar_constants=None):
"""
McDougall and Harrison
Roddick 1983
Foland 1993
iteratively calculate atm36
"""
if production_ratios is None:
production_ratios = {}
if arar_constants is None:
arar_constants = ArArConstants()
pr = production_ratios
m = pr.get('cl3638',
0) * arar_constants.lambda_Cl36.nominal_value * decay_time
atm36 = ufloat(0, 1e-20)
for _ in range(5):
ar38atm = arar_constants.atm3836.nominal_value * atm36
cl38 = a38 - ar38atm - k38 - ca38
cl36 = cl38 * m
atm36 = a36 - ca36 - cl36
return atm36, cl36
def calculate(self, age, sensitivity, k2o):
c = ArArConstants()
xs = np.linspace(self.start, self.end)
def to_weight(d, depth, rho):
'''
d== mm
depth==mm
rho==kg/m^3
'''
# convert dimension to meters
d = d / 1000.
depth = depth / 1000.
if self.shape == 'circle':
v = math.pi * (d / 2.) ** 2 * depth
else:
v = d ** 2 * depth
m = rho * v
# convert mass to mg 1e6 mg in 1 kg
return m * 1e6
# convert dim to weight
ws = [to_weight(di, self.depth, self.rho) for di in xs]
ys = [self._calculate(wi, age, sensitivity, k2o, c) for wi in ws]
return xs, ys, xs, ws
def calculate_f(isotopes, decay_time, interferences=None, arar_constants=None, fixed_k3739=False):
"""
isotope values corrected for blank, baseline, (background)
ic_factor, (discrimination), ar37 and ar39 decay
"""
a40, a39, a38, a37, a36 = isotopes
def calc_f(pr):
k37, k38, k39, ca36, ca37, ca38, ca39 = interference_corrections(a39, a37, pr, arar_constants, fixed_k3739)
atm36, cl36, cl38 = calculate_atmospheric(a38, a36, k38, ca38, ca36,
decay_time,
pr,
arar_constants)
# calculate radiogenic
trapped_4036 = copy(arar_constants.atm4036)
trapped_4036.tag = 'trapped_4036'
atm40 = atm36 * trapped_4036
k4039 = pr.get('K4039', 0)
k40 = k39 * k4039
rad40 = a40 - atm40 - k40
try:
ff = rad40 / k39
except ZeroDivisionError:
ff = ufloat(1.0, 0)
nar = {'k40': k40, 'ca39': ca39, 'k38': k38, 'ca38': ca38,
'cl38': cl38, 'k37': k37, 'ca37': ca37, 'ca36': ca36,
'cl36': cl36}
try:
rp = rad40 / a40 * 100
except ZeroDivisionError:
rp = ufloat(0, 0)
comp = {'rad40': rad40, 'a40': a40, 'radiogenic_yield': rp,
'ca37': ca37, 'ca39': ca39, 'ca36': ca36, 'k39': k39,
'atm40': atm40}
ifc = {'Ar40': a40 - k40, 'Ar39': k39, 'Ar38': a38, 'Ar37': a37, 'Ar36': atm36}
return ff, nar, comp, ifc
if interferences is None:
interferences = {}
if arar_constants is None:
arar_constants = ArArConstants()
# make local copy of interferences
pr = {k: ufloat(nominal_value(v), std_dev=0, tag=v.tag) for k, v in interferences.items()}
f_wo_irrad, _, _, _ = calc_f(pr)
f, non_ar_isotopes, computed, interference_corrected = calc_f(interferences)
return f, f_wo_irrad, non_ar_isotopes, computed, interference_corrected
def __init__(self, *args, **kw):
super(ArArAge, self).__init__(*args, **kw)
self.arar_constants = ArArConstants()
self.isotopes = {}
self.non_ar_isotopes = {}
self.computed = {}
self.corrected_intensities = {}
self.interference_corrections = {}
self.production_ratios = {}
self.temporary_ic_factors = {}
self.discrimination = ufloat(1, 0)
def calculate_error_t(F, ssF, j, ssJ):
'''
McDougall and Harrison
p92 eq. 3.43
'''
JJ = j * j
FF = F * F
constants = ArArConstants()
ll = constants().lambdak.nominal_value**2
sst = (JJ * ssF + FF * ssJ) / (ll * (1 + F * j)**2)
return sst**0.5
def calculate_atmospheric(a38,
a36,
k38,
ca38,
ca36,
decay_time,
production_ratios=None,
arar_constants=None):
"""
McDougall and Harrison
Roddick 1983
Foland 1993
calculate atm36, cl36, cl38
# starting with the following equations
atm36 = a36 - ca36 - cl36
m = cl3638*lambda_cl36*decay_time
cl36 = cl38 * m
cl38 = a38 - k38 - ca38 - ar38atm
ar38atm = atm3836 * atm36
# rearranging to solve for atm36
cl38 = a38 - k38 - c38 - atm3836 * atm36
cl36 = m * (a38 - k38 - ca38 - atm3836 * atm36)
= m (a38 - k38 - ca38) - m * atm3836 * atm36
atm36 = a36 - ca36 - m (a38 - k38 - ca38) + m * atm3836 * atm36
atm36 - m * atm3836 * atm36 = a36 - ca36 - m (a38 - k38 - ca38)
atm36 * (1 - m*atm3836) = a36 - ca36 - m (a38 - k38 - ca38)
atm36 = (a36 - ca36 - m (a38 - k38 - c38))/(1 - m*atm3836)
"""
if production_ratios is None:
production_ratios = {}
if arar_constants is None:
arar_constants = ArArConstants()
pr = production_ratios
m = pr.get('Cl3638', 0) * nominal_value(
arar_constants.lambda_Cl36) * decay_time
atm3836 = nominal_value(arar_constants.atm3836)
atm36 = (a36 - ca36 - m * (a38 - k38 - ca38)) / (1 - m * atm3836)
ar38atm = atm3836 * atm36
cl38 = a38 - ar38atm - k38 - ca38
cl36 = cl38 * m
return atm36, cl36, cl38
def interference_corrections(a40,
a39,
a38,
a37,
a36,
production_ratios,
arar_constants=None):
if production_ratios is None:
production_ratios = {}
if arar_constants is None:
arar_constants = ArArConstants()
pr = production_ratios
k37 = ufloat(0, 1e-20)
if arar_constants.k3739_mode.lower() == 'normal':
# iteratively calculate 37, 39
for _ in range(5):
ca37 = a37 - k37
ca39 = pr.get('ca3937', 0) * ca37
k39 = a39 - ca39
k37 = pr.get('k3739', 0) * k39
else:
'''
x=ca37/k39
y=ca37/ca39
T=s39dec_cor
T=ca39+k39
T=ca37/y+ca37/x
ca37=(T*x*y)/(x+y)
'''
x = arar_constants.fixed_k3739
y = 1 / pr.get('ca3937', 1)
ca37 = (a39 * x * y) / (x + y)
ca39 = pr.get('ca3937', 0) * ca37
k39 = a39 - ca39
k37 = x * k39
k38 = pr.get('k3839', 0) * k39
ca36 = pr.get('ca3637', 0) * ca37
ca38 = pr.get('ca3837', 0) * ca37
return k37, k38, k39, ca36, ca37, ca38, ca39
def age_equation(j, f, include_decay_error=False, arar_constants=None):
if isinstance(j, (tuple, str)):
j = ufloat(j)
if isinstance(f, (tuple, str)):
f = ufloat(f)
if arar_constants is None:
arar_constants = ArArConstants()
scalar = float(arar_constants.age_scalar)
lk = arar_constants.lambda_k
if not include_decay_error:
lk = lk.nominal_value
try:
return (lk**-1 * umath.log(1 + j * f)) / scalar
except (ValueError, TypeError):
return ufloat(0, 0)
def interference_corrections(a40,
a39,
a38,
a37,
a36,
production_ratios,
arar_constants=None,
fixed_k3739=False):
if production_ratios is None:
production_ratios = {}
if arar_constants is None:
arar_constants = ArArConstants()
pr = production_ratios
k37 = ufloat(0, 1e-20)
if arar_constants.k3739_mode.lower() == 'normal' and not fixed_k3739:
# iteratively calculate 37, 39
for _ in range(5):
ca37 = a37 - k37
ca39 = pr.get('Ca3937', 0) * ca37
k39 = a39 - ca39
k37 = pr.get('K3739', 0) * k39
else:
if not fixed_k3739:
fixed_k3739 = arar_constants.fixed_k3739
ca37, ca39, k37, k39 = apply_fixed_k3739(a39, pr, fixed_k3739)
k38 = pr.get('K3839', 0) * k39
if not arar_constants.allow_negative_ca_correction:
ca37 = max(ufloat(0, 0), ca37)
ca36 = pr.get('Ca3637', 0) * ca37
ca38 = pr.get('Ca3837', 0) * ca37
return k37, k38, k39, ca36, ca37, ca38, ca39
def calculate_flux(f, age, arar_constants=None):
"""
#rad40: radiogenic 40Ar
#k39: 39Ar from potassium
f: F value rad40Ar/39Ar
age: age of monitor in years
solve age equation for J
"""
if isinstance(f, (list, tuple)):
f = ufloat(*f)
if isinstance(age, (list, tuple)):
age = ufloat(*age)
try:
if arar_constants is None:
arar_constants = ArArConstants()
j = (umath.exp(age * arar_constants.lambda_k.nominal_value) - 1) / f
return j.nominal_value, j.std_dev
except ZeroDivisionError:
return 1, 0
def calculate_flux(rad40, k39, age, arar_constants=None):
'''
rad40: radiogenic 40Ar
k39: 39Ar from potassium
age: age of monitor in years
solve age equation for J
'''
if isinstance(rad40, (list, tuple)):
rad40 = ufloat(*rad40)
if isinstance(k39, (list, tuple)):
k39 = ufloat(*k39)
if isinstance(age, (list, tuple)):
age = ufloat(*age)
# age = (1 / constants.lambdak) * umath.log(1 + JR)
try:
r = rad40 / k39
if arar_constants is None:
arar_constants = ArArConstants()
j = (umath.exp(age * arar_constants.lambda_k) - 1) / r
return j.nominal_value, j.std_dev
except ZeroDivisionError:
return 1, 0
def calculate_F(isotopes, decay_time, interferences=None, arar_constants=None):
"""
isotope values corrected for blank, baseline, (background)
ic_factor, (discrimination), ar37 and ar39 decay
"""
a40, a39, a38, a37, a36 = isotopes
#a37*=113
if interferences is None:
interferences = {}
if arar_constants is None:
arar_constants = ArArConstants()
#make local copy of interferences
pr = dict(((k, v.__copy__()) for k, v in interferences.iteritems()))
#for k,v in pr.iteritems():
# print k, v
k37, k38, k39, ca36, ca37, ca38, ca39 = interference_corrections(
a40, a39, a38, a37, a36, pr, arar_constants)
atm36, cl36 = calculate_atmospheric(a38, a36, k38, ca38, ca36, decay_time,
pr, arar_constants)
# calculate rodiogenic
# dont include error in 40/36
atm40 = atm36 * arar_constants.atm4036.nominal_value
k40 = k39 * pr.get('k4039', 1)
rad40 = a40 - atm40 - k40
try:
f = rad40 / k39
except ZeroDivisionError:
f = ufloat(1.0, 0)
rf = deepcopy(f)
# f = ufloat(f.nominal_value, f.std_dev, tag='F')
non_ar_isotopes = dict(k38=k38,
k37=k37,
ca36=ca36,
ca37=ca37,
ca38=ca38,
ca39=ca39,
cl36=cl36)
try:
rp = rad40 / a40 * 100
except ZeroDivisionError:
rp = ufloat(0, 0)
computed = dict(rad40=rad40, rad40_percent=rp, k39=k39)
#print 'Ar40', a40-k40, a40, k40
#print 'Ar39', a39-k39, a39, k39
interference_corrected = dict(Ar40=a40 - k40,
Ar39=k39,
Ar38=a38 - k38 - ca38,
Ar37=a37 - ca37 - k37,
Ar36=a36)
##clear errors in irrad
for pp in pr.itervalues():
pp.std_dev = 0
f_wo_irrad = f
return rf, f_wo_irrad, non_ar_isotopes, computed, interference_corrected
def calculate_F(isotopes,
decay_time,
interferences=None,
arar_constants=None,
fixed_k3739=False):
"""
isotope values corrected for blank, baseline, (background)
ic_factor, (discrimination), ar37 and ar39 decay
"""
a40, a39, a38, a37, a36 = isotopes
if interferences is None:
interferences = {}
if arar_constants is None:
arar_constants = ArArConstants()
# make local copy of interferences
pr = {k: v.__copy__() for k, v in interferences.iteritems()}
k37, k38, k39, ca36, ca37, ca38, ca39 = interference_corrections(
a40, a39, a38, a37, a36, pr, arar_constants, fixed_k3739)
atm36, cl36, cl38 = calculate_atmospheric(a38, a36, k38, ca38, ca36,
decay_time, pr, arar_constants)
# calculate radiogenic
# dont include error in 40/36
atm40 = atm36 * nominal_value(arar_constants.atm4036)
k4039 = pr.get('K4039', 0)
k40 = k39 * k4039
rad40 = a40 - atm40 - k40
try:
f = rad40 / k39
except ZeroDivisionError:
f = ufloat(1.0, 0)
rf = deepcopy(f)
non_ar_isotopes = dict(k40=k40,
ca39=ca39,
k38=k38,
ca38=ca38,
cl38=cl38,
k37=k37,
ca37=ca37,
ca36=ca36,
cl36=cl36)
try:
rp = rad40 / a40 * 100
except ZeroDivisionError:
rp = ufloat(0, 0)
computed = dict(rad40=rad40, rad40_percent=rp, k39=k39, atm40=atm40)
interference_corrected = dict(Ar40=a40 - k40,
Ar39=k39,
Ar38=a38,
Ar37=a37,
Ar36=atm36)
# clear errors in irrad
for pp in pr.itervalues():
pp.std_dev = 0
f_wo_irrad = f
return rf, f_wo_irrad, non_ar_isotopes, computed, interference_corrected
# fractional error from ar39
err39 = fe39 * Re * feJR
errJ = Je * feJR
errLambdaK = feLambdaK
# print 'exception', err40, err36, err39, errJ
# print 'exception', err36 + err40 + err39 + errJ
# print 'exception', err36 + err37 + err38 + err40 + err39 + errJ + errLambdaK - 1
assert abs(err36 + err37 + err38 + err40 + err39 + errJ + errLambdaK -
1) < 1e-10
return err40, err39, err38, err37, err36, errJ, errLambdaK
if __name__ == '__main__':
constants = ArArConstants()
s40 = ufloat(5.50986, 5.50986 * 0.0004)
s39 = ufloat(3.65491e-1, 3.65491e-1 * 0.0011)
s38 = ufloat(4.4904e-3, 4.4904e-3 * 0.0117)
s37 = ufloat(2.47163e-3, 2.47163e-3 * 0.038)
# s38 = ufloat((4.4904e-3, 0))
# s37 = ufloat((2.47163e-3, 0))
s36 = ufloat(2.623e-5, 2.623e-5 * 0.5955)
J = ufloat(1, 0)
k4039 = 0
ca3637 = 2.8e-4
cl3638 = 0
cl38 = s38
ar39 = s39
def __init__(self, make_arar_constants=True, *args, **kw):
super(IdeogramPlotable, self).__init__(*args, **kw)
if make_arar_constants:
self.arar_constants = ArArConstants()