def _calculate_r(self, age):
oma = self._original_monitor_age
torig = self._original_total_decay_constant
ex_orig = umath.exp(torig * oma * 1e6) - 1
ex = umath.exp(torig * age * 1e6) - 1
r = ex / ex_orig
return r, ex, ex_orig
def _calculate_r(self, age):
oma = self._original_monitor_age
torig = self._original_total_decay_constant
ex_orig = umath.exp(torig * oma * 1e6) - 1
ex = umath.exp(torig * age * 1e6) - 1
r = ex / ex_orig
return r, ex, ex_orig
def get_dl_and_kpc_per_asec(z, H0=70, WM=0.26, WV=0.74):
"""Get luminosity distance. See
"""
WR = 0. # Omega(radiation)
WK = 0. # Omega curvaturve = 1-Omega(total)
c = 299792.458 # velocity of light in km/sec
DTT = 0.5 # time from z to now in units of 1/H0
age = 0.5 # age of Universe in units of 1/H0
zage = 0.1 # age of Universe at redshift z in units of 1/H0
DCMR = 0.0 # comoving radial distance in units of c/H0
DA = 0.0 # angular size distance
DA_Mpc = 0.0
kpc_DA = 0.0
DL = 0.0 # luminosity distance
DL_Mpc = 0.0
a = 1.0 # 1/(1+z), the scale factor of the Universe
az = 0.5 # 1/(1+z(object))
h = H0 / 100.
WR = 4.165E-5 / (h * h) # includes 3 massless neutrino species,
WK = 1 - WM - WR - WV
az = 1.0 / (1 + 1.0 * z)
age = 0.
n = 1000 # number of points in integrals
for i in range(n):
a = az * (i + 0.5) / n
adot = sqrt(WK + (WM / a) + (WR / (a * a)) + (WV * a * a))
age = age + 1. / adot
zage = az * age / n
DTT = 0.0
DCMR = 0.0
for i in range(n):
a = az + (1 - az) * (i + 0.5) / n
adot = sqrt(WK + (WM / a) + (WR / (a * a)) + (WV * a * a))
DTT = DTT + 1. / adot
DCMR = DCMR + 1. / (a * adot)
DTT = (1. - az) * DTT / n
DCMR = (1. - az) * DCMR / n
age = DTT + zage
ratio = 1.00
x = sqrt(abs(WK)) * DCMR
if x > 0.1:
if WK > 0:
ratio = 0.5 * (exp(x) - exp(-x)) / x
else:
ratio = sin(x) / x
else:
y = x * x
if WK < 0:
y = -y
ratio = 1. + y / 6. + y * y / 120.
return (c / H0) * ((az * ratio * DCMR) / (az * az)) * 3.086e22, ((c / H0) * az * ratio * DCMR) / 206.264806
def _linear_error_propagation(self, age, r, sr):
"""
age in years
:param age:
:param r:
:return: linear error propagation age error in years
"""
lambda_total = self._lambda_t
b = self._lambda_b
el = self._lambda_ec
f = self._f
# partial derivatives
pd_el = -(1. / lambda_total) * (age + (b * f * r / (
(el**2) * umath.exp(lambda_total * age))))
pd_b = (1 / lambda_total) * (
(f * r / (el * umath.exp(lambda_total * age))) - age)
pd_f = r / (el * umath.exp(lambda_total * age))
pd_r = f / (el * umath.exp(lambda_total * age))
sel = std_dev(el)
sb = std_dev(b)
sf = std_dev(self._f)
# sr = std_dev(r)
# (partial derivatives x sigma) ** 2
pd_el2 = (pd_el * sel)**2
pd_b2 = (pd_b * sb)**2
pd_f2 = (pd_f * sf)**2
pd_r2 = (pd_r * sr)**2
sum_pd = pd_el2 + pd_b2 + pd_f2 + pd_r2
# covariances
cov_f_el = 7.1903e-19
cov_f_b = -6.5839e-19
cov_el_b = -3.4711e-26
cov_f_el2 = 2. * cov_f_el * pd_f * pd_el
cov_f_b2 = 2. * cov_f_b * pd_f * pd_b
cov_el_b = 2. * cov_el_b * pd_el * pd_b
sum_cov = cov_f_el2 + cov_f_b2 + cov_el_b
ss = sum_pd + sum_cov
# uncertainty in age
st = ss**0.5
return nominal_value(st)
def _linear_error_propagation(self, age, r, sr):
"""
age in years
:param age:
:param r:
:return: linear error propagation age error in years
"""
lambda_total = self._lambda_t
b = self._lambda_b
el = self._lambda_ec
f = self._f
# partial derivatives
pd_el = -(1. / lambda_total) * (age + (b * f * r / ((el ** 2) * umath.exp(lambda_total * age))))
pd_b = (1 / lambda_total) * ((f * r / (el * umath.exp(lambda_total * age))) - age)
pd_f = r / (el * umath.exp(lambda_total * age))
pd_r = f / (el * umath.exp(lambda_total * age))
sel = std_dev(el)
sb = std_dev(b)
sf = std_dev(self._f)
# sr = std_dev(r)
# (partial derivatives x sigma) ** 2
pd_el2 = (pd_el * sel) ** 2
pd_b2 = (pd_b * sb) ** 2
pd_f2 = (pd_f * sf) ** 2
pd_r2 = (pd_r * sr) ** 2
sum_pd = pd_el2 + pd_b2 + pd_f2 + pd_r2
# covariances
cov_f_el = 7.1903e-19
cov_f_b = -6.5839e-19
cov_el_b = -3.4711e-26
cov_f_el2 = 2. * cov_f_el * pd_f * pd_el
cov_f_b2 = 2. * cov_f_b * pd_f * pd_b
cov_el_b = 2. * cov_el_b * pd_el * pd_b
sum_cov = cov_f_el2 + cov_f_b2 + cov_el_b
ss = sum_pd + sum_cov
# uncertainty in age
st = ss ** 0.5
return nominal_value(st)
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(rad40, (list, tuple)):
# rad40 = ufloat(*rad40)
# if isinstance(k39, (list, tuple)):
# k39 = ufloat(*k39)
if isinstance(f, (list, tuple)):
f = ufloat(*f)
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.nominal_value) - 1) / f
return j.nominal_value, j.std_dev
except ZeroDivisionError:
return 1, 0
def value(self, E):
try:
value = E.value
except AttributeError:
value = E
return self.norm * exp(self.TF1.Eval(log(value), 0.0, 0.0, 0.0))
def error(self, E):
# TODO: this need checking
try:
value = E.value
except AttributeError:
value = E
ln_err = _Efficiency.error(self, log(value))
ln_eff = self.TF1.Eval(log(value), 0.0, 0.0, 0.0)
tmp1 = self.norm * exp(ln_eff + ln_err)
tmp2 = self.norm * exp(ln_eff - ln_err)
error = abs(tmp1 - tmp2) / 2.0
return self.norm * error
def eval_saturation(self, pO2, A, T):
"""Calculate saturation by curve.
(Saturation can be measured by multiwavelength hemoximetry.)
S = ODC(P,A,T)
References
----------
.. [1] Radiometer ABL800 Flex Reference Manual English US.
chapter 6-44, p. 280, equation 46-47.
:param float pO2: measured partial O2 pressure, kPa (46.1)
:param float A: an curve displacement along axis x (46.5).
:param float T: Body temperature, °C (46.7).
:return:
s, hemoglobin saturation at given pO2 and T conditions for current
ODC, fraction. No hemoglobin corrections performed.
:rtype: float
"""
x_0 = eval_x_0(a=A, T=T)
# 46.1
x = math.log(pO2)
y = haldane_odc(x=x, x_0=x_0, y_0=self.y_0, a=A)
s = 1 / (math.exp(-y) + 1) # Reverse 46.2
return s
def calc_tiT_diff(pO2, sO2, T, A):
# Derivative from paper
alphaO2 = 9.83 * 10 ** -3 * math.exp(
-1.15 * 10 ** -2 * (T - 37) + 2.1 * 10 ** -4 * (T - 37) ** 2)
x = math.log(pO2)
x_0 = eval_x_0(a=A, T=T)
n = haldane_odc_diff(x=x, x_0=x_0, y_0=self.y_0, a=A)
return alphaO2 + ctHb * n * (1 - sO2) / pO2
def normalize(self):
# Normalize the efficiency function
try:
self.norm = 1.0 / exp(
self.TF1.GetMaximum(min([p[0] for p in self._fitInput]),
max([p[0] for p in self._fitInput])))
except ZeroDivisionError:
self.norm = 1.0
self.TF1.SetParameter(0, self.norm)
normfunc = TF2("norm_" + hex(id(self)), "[0]*y")
normfunc.SetParameter(0, self.norm)
self.TGraph.Apply(normfunc)
def fo2_cal_single(P,T,PV,r,method='earth',flag=False,fit='fit3'):
"""
calculate fo2 for a single P,T point
P : pressure, GPa, P is actually not used, it is included in PV integration info
T : temperature, K
PV : term int\{P0 to P0, deltaV}, it requires to get the dV at every single pressure
and temperature, and then integrate. This could be very time demanding.
r : Fe3/Fe2 ratio
method : earth, mars, moon, specify the composition, default is earth
flag : boolean, uncertainty flag, default is False
fit3 : W model, default is fit3
Note
----
Term int\{P0 to P0, deltaV}, deltaV is at reference temperature, not along geotherm.
That means, to calcualte this term, for every point in geotherm, P,T, one needs to
calculate the dV from P0 to P along T, and then integrate.
Note this is different from just calculate dV along the goetherm, then integrate.
Typically, the 2nd method will underestimate the PV term since goetherm is T0 to T,
whereas here we need keep T as T.
Nevertheless, `cal_PV_geo` function in the package solve this problem. The obtained
PV term along the geotherm is then used as input and kept in the excel eos.xlsx
"""
Fe2 = (1-r)*planets.loc[method]['FeO']
Fe3 = r*planets.loc[method]['FeO']
Si = planets.loc[method]['SiO2'];
Mg = planets.loc[method]['MgO'];
Al = planets.loc[method]['Al2O3'];
Ca = planets.loc[method]['CaO'];
K = planets.loc[method]['K2O'];
Na = planets.loc[method]['Na2O'];
Ph = planets.loc[method]['P2O5'];
Ti = planets.loc[method]['TiO2'];
a,b,W_Fe,W_Mg,W_Si,W_Al,W_Ca,W_Na,W_K,W_Ph,W_Ti = unpack_par(W.loc[fit],flag)
Gterm = np.array(tl.Gr_janaf(T,flag))/R/T
Wterm = (W_Fe*(Fe2 - Fe3) + W_Mg*Mg + W_Al*Al + W_Si*Si +
W_Ca*Ca +W_Na*Na + W_K*K + W_Ph*Ph + W_Ti*Ti)/R/T
tmp = (PV + Gterm + Wterm)*4
lnXfe3_Xfe2 = np.log(Fe3/Fe2)*4
fg = umath.exp(tmp+lnXfe3_Xfe2)
log10fg = (umath.log10(fg))
return log10fg
def test_against_uncertainties_package():
try:
from uncertainties import ufloat
from uncertainties import umath
from math import sqrt as math_sqrt
except ImportError:
return
X, varX = 0.5, 0.04
Y, varY = 3, 0.09
N = 3
ux = ufloat(X, math_sqrt(varX))
uy = ufloat(Y, math_sqrt(varY))
def _compare(result, u):
Z, varZ = result
assert abs(Z-u.n)/u.n < 1e-13 and (varZ-u.s**2)/u.s**2 < 1e-13, \
"expected (%g,%g) got (%g,%g)"%(u.n,u.s**2,Z,varZ)
def _check_pow(u):
_compare(pow(X, varX, N), u)
def _check_unary(op, u):
_compare(op(X, varX), u)
def _check_binary(op, u):
_compare(op(X, varX, Y, varY), u)
_check_pow(ux**N)
_check_binary(add, ux+uy)
_check_binary(sub, ux-uy)
_check_binary(mul, ux*uy)
_check_binary(div, ux/uy)
_check_binary(pow2, ux**uy)
_check_unary(exp, umath.exp(ux))
_check_unary(log, umath.log(ux))
_check_unary(sin, umath.sin(ux))
_check_unary(cos, umath.cos(ux))
_check_unary(tan, umath.tan(ux))
_check_unary(arcsin, umath.asin(ux))
_check_unary(arccos, umath.acos(ux))
_check_unary(arctan, umath.atan(ux))
_check_binary(arctan2, umath.atan2(ux, uy))
def test_against_uncertainties_package():
try:
from uncertainties import ufloat
from uncertainties import umath
from math import sqrt as math_sqrt
except ImportError:
return
X, varX = 0.5, 0.04
Y, varY = 3, 0.09
N = 3
ux = ufloat(X, math_sqrt(varX))
uy = ufloat(Y, math_sqrt(varY))
def _compare(result, u):
Z, varZ = result
assert abs(Z-u.n)/u.n < 1e-13 and (varZ-u.s**2)/u.s**2 < 1e-13, \
"expected (%g,%g) got (%g,%g)"%(u.n, u.s**2, Z, varZ)
def _check_pow(u):
_compare(pow(X, varX, N), u)
def _check_unary(op, u):
_compare(op(X, varX), u)
def _check_binary(op, u):
_compare(op(X, varX, Y, varY), u)
_check_pow(ux**N)
_check_binary(add, ux + uy)
_check_binary(sub, ux - uy)
_check_binary(mul, ux * uy)
_check_binary(div, ux / uy)
_check_binary(pow2, ux**uy)
_check_unary(exp, umath.exp(ux))
_check_unary(log, umath.log(ux))
_check_unary(sin, umath.sin(ux))
_check_unary(cos, umath.cos(ux))
_check_unary(tan, umath.tan(ux))
_check_unary(arcsin, umath.asin(ux))
_check_unary(arccos, umath.acos(ux))
_check_unary(arctan, umath.atan(ux))
_check_binary(arctan2, umath.atan2(ux, uy))
def eval_pressure(self, sO2, A, T):
"""Calculate O2 pressure by saturation.
P = ODC(S,A,T)
[16] Siggaard-Andersen O, Wimberley PD, Göthgen IH,
Siggaard-Andersen M.
A mathematical model of the hemoglobin-oxygen dissociation curve
of human blood and of the oxygen partial pressure as a function
of temperature. Clin Chem 1984; 30: 1646-51.
[18] Siggaard-Andersen O, Siggaard-Andersen M.
The oxygen status algorithm: a computer program for calculating and
displaying pH and blood gas data.
Scand J Clin Lab Invest 1990; 50, Suppl 203: 29-45.
:param float sO2: measured hemoglobin saturation, fraction (46.2)
:param float A: an curve displacement along axis x (46.5).
:param float T: Body temperature, °C (46.7).
:return:
p, partial O2 pressure at given sO2 and T conditions for current
ODC, kPa. No hemoglobin corrections performed.
:rtype: float
"""
# 46.2
y = math.log(sO2 / (1 - sO2))
# Newtom-Rapson iterative method
x_0 = eval_x_0(a=A, T=T)
x = x_0 # Start value, as described in paper
while True:
y_i = haldane_odc(x=x, x_0=x_0, y_0=self.y_0, a=A)
if abs(y - y_i) < epsilon:
# print("FOUND x", x)
break
# n ~ 2.7 according to paper
n = haldane_odc_diff(x, x_0, self.y_0, A)
x = x + (y - y_i) / n
# print(y, y_i)
# print('y', y, 'x', x)
# print('\n%s y ~ \n%s y_hal\n' % (
# y, haldane_odc(x, x_0, self.y_0, A)))
p = math.exp(x) # Reverse 46.1
return p
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, str)):
rad40 = ufloat(rad40)
if isinstance(k39, (list, tuple, str)):
k39 = ufloat(k39)
if isinstance(age, (list, tuple, str)):
age = ufloat(age)
# age = (1 / constants.lambdak) * umath.log(1 + JR)
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
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_flux(f, age, arar_constants=None, lambda_k=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 not lambda_k:
if arar_constants is None:
arar_constants = ArArConstants()
lambda_k = nominal_value(arar_constants.lambda_k)
j = (umath.exp(age * lambda_k) - 1) / f
return j
except ZeroDivisionError:
return ufloat(1, 0)
xlim(0,0.02)
ylim(10,32)
errorbar(d_1,A_1-A_0,A_1_err,0, "x", label="Messwerte")
legend()
savefig("gamma1_lin.png")
#Lineare Regression
from Tools import lin_reg, make_LaTeX_table
m_1, b_1 = lin_reg(d_1,log(A_1-A_0))
print "mu %s und A(0) = %s" % (m_1,b_1)
print "A_0:%s " % umath.exp(b_1)
#Plot LinFit
yscale("log")
ylim(10,100)
d = linspace(0,0.02)
plot(d,exp(m_1.n * d+b_1.n), label = "Lineare Regression")
legend()
savefig("gamma1_log.png")
#Latex Tabelle erzeugen
data = array([[int(d_1[i]*1e3),int(N_1[i]), ufloat(A_1[i]-A_0, A_1_err[i]) ]for i in range(7)])
#print make_LaTeX_table(data, [r'{$\frac{d}{\si{\milli\meter}}$} ',r'$N$' ,r'{ $\frac{A-A_0}{\si{\second^{-1}}}$ }'])
Tlist = np.arange(minT, maxT + 10, 10)
Authorlist = np.array(data['Author'])
klist = np.zeros((len(Tlist), len(Authorlist)))
kulist = np.zeros((len(Tlist), len(Authorlist)))
#print(klist)
for i in range(len(data.index)):
# print(i)
A = ufloat(data.iloc[i]['A'], data.iloc[i]['Au'])
n = ufloat(data.iloc[i]['n'], data.iloc[i]['nu'])
E = ufloat(data.iloc[i]['E'], data.iloc[i]['Eu'])
for j in range(len(Tlist)):
T = j * 10 + minT
# print(T)
if data.iloc[i]['min T'] <= T <= data.iloc[i]['max T']:
k = (A * (T / 298)**n) * umath.exp(-E * 1000 / 8.314 / T)
klist[j][i] = k.n
kulist[j][i] = k.s
else:
klist[j][i] = np.nan
kulist[j][i] = np.nan
rate = pd.DataFrame(klist, columns=Authorlist, index=Tlist)
rateu = pd.DataFrame(kulist, columns=Authorlist, index=Tlist)
rate.dropna(axis=0, how='all', inplace=True)
print(len(rate.index))
klist = rate.values.tolist()
rateu.dropna(axis=0, how='all', inplace=True)
Tlist = rateu.index.tolist()
def fit_value3(th, a, b, c, d, e, g, f):
return a * umath.exp(-(th**2) / b) + c * umath.exp(
-(th**2) / d) + e * umath.exp(-(th**2) / g)
def fit_value1(x, a, b, c, d, e, g, f):
return a * umath.exp(b * x) + c * umath.exp(
-(x**2) / d) + e * umath.exp(-(x * g))
def fit_value4(th, a, b, c, d, f):
return a * umath.exp(-th * b) + c * umath.exp(-(th**2) / d)
def calc_tiT(pO2, sO2, T):
"""O2 content. Based on eq. 19 from paper.
"""
alphaO2 = 9.83 * 10 ** -3 * math.exp(
-1.15 * 10 ** -2 * (T - 37) + 2.1 * 10 ** -4 * (T - 37) ** 2)
return ctHb * (1 - self.FCOHb - self.FMetHb) * sO2 + alphaO2 * pO2
