def dOmega(theta_lab, n):
"""
function to find dΩlab/dΩcm
Arguments
---------
theta_lab : scattering angle in the lab system [rad]
n : A_t / A_i; A_t, A_i means mass number of target particle or incident particle
Return
------
dΩlab/dΩcm : factor to convert differential cross-section in the lab system to differential cross-section in the center-of-mass system
Notice
------
This function do not consider relativity
"""
if isinstance(theta_lab, uncertainties.core.AffineScalarFunc):
return umath.pow(
2.0 * umath.cos(theta_lab) / n +
(1.0 + umath.cos(2.0 * theta_lab) / (n**2.0)) /
umath.sqrt(1.0 - umath.pow(umath.sin(theta_lab) / n, 2.0)), -1.0)
elif isinstance(theta_lab, np.ndarray) and isinstance(
theta_lab[0], uncertainties.core.AffineScalarFunc):
return unp.pow(
2.0 * unp.cos(theta_lab) / n +
(1.0 + unp.cos(2.0 * theta_lab) /
(n**2.0)) / unp.sqrt(1.0 - unp.pow(unp.sin(theta_lab) / n, 2.0)),
-1.0)
else:
return np.power(
2.0 * np.cos(theta_lab) / n +
(1.0 + np.cos(2.0 * theta_lab) /
(n**2.0)) / np.sqrt(1.0 - np.power(np.sin(theta_lab) / n, 2.0)),
-1.0)
def dOmega(theta_cm, n):
"""
function to find dΩcm/dΩlab
Arguments
---------
theta_cm : scattering angle in the center-of-mass system [rad]
n : A_t / A_i; A_t, A_i means mass number of target particle or incident particle
Return
------
dΩcm/dΩlab : factor to convert differential cross-section in the center-of-mass system to one in the lab system
Notice
------
This function does not consider relativity
"""
if isinstance(theta_cm, uncertainties.core.AffineScalarFunc):
return umath.pow(1.0 + 2.0 * umath.cos(theta_cm) / n + 1.0 / n**2.0, 3 / 2) \
/ (1.0 + umath.cos(theta_cm) / n)
elif isinstance(theta_cm, np.ndarray) and isinstance(
theta_cm[0], uncertainties.core.AffineScalarFunc):
return unp.pow(1.0 + 2.0 * unp.cos(theta_cm) / n + 1.0 / n**2.0, 3 / 2) \
/ (1.0 + unp.cos(theta_cm) / n)
else:
return np.power(1.0 + 2.0 * np.cos(theta_cm) / n + 1.0 / n**2.0, 3 / 2) \
/ (1.0 + np.cos(theta_cm) / n)
def cornerFidDist(self, cornerData):
angle = np.mean(self.angles())
diff = []
# rotMat=np.array([[unp.cos(angle),unp.sin(angle)],[-unp.sin(angle),unp.cos(angle)]])
#v1=np.matmul(rotMat,self.points[0].means.T)
#v2=np.matmul(rotMat,cornerData[0].T)
#diff=abs(v2-v1)
for i in range(4):
#v1=unp.matmul(rotMat,self.points[i].means.T)
#v2=unp.matmul(rotMat,cornerData[i].T)
v1 = np.array([
self.points[i].means[0] * unp.cos(angle) +
self.points[i].means[1] * unp.sin(angle),
-self.points[i].means[0] * unp.sin(angle) +
self.points[i].means[1] * unp.cos(angle)
])
v2 = np.array([
cornerData[i][0] * unp.cos(angle) +
cornerData[i][1] * unp.sin(angle),
-cornerData[i][0] * unp.sin(angle) +
cornerData[i][1] * unp.cos(angle)
])
diff.append(abs(v2 - v1))
return diff
def f_unc(coordinates, amplitude, xo, yo, sigma_x, sigma_y, theta, offset):
"""
similar to the raw function call, but uses unp instead of np for uncertainties calculations.
:return:
"""
x = coordinates[0]
y = coordinates[1]
xo = float(xo)
yo = float(yo)
a = (unp.cos(theta)**2)/(2*sigma_x**2) + (unp.sin(theta)**2)/(2*sigma_y**2)
b = -(unp.sin(2*theta))/(4*sigma_x**2) + (unp.sin(2*theta))/(4*sigma_y**2)
c = (unp.sin(theta)**2)/(2*sigma_x**2) + (unp.cos(theta)**2)/(2*sigma_y**2)
g = offset + amplitude*unp.exp(- (a*((x-xo)**2) + 2*b*(x-xo)*(y-yo) + c*((y-yo)**2)))
return g.ravel()
def rutherford(theta, T, Zi, Zt, which="inc"):
"""
Rutherford Scattering in the center-of-mass system
Arguments
---------
theta : scattering angle in the center-of-mass system
T : kinetic energy of incident particle in the center-of-mass system
Zi : atomic number of incident particle; charge in units of e
Zt : atomic number of target particle; charge in units of e
which : if which="inc", calc dσ/dΩ(θ) of incident particle.
if which="tar", calc dσ/dΩ(θ) of target particle.
if which="sum", calc dσ/dΩ(θ) of incident particle + dσ/dΩ(θ) of target particle.
Return
------
dσ/dΩ(θ) in the center-of-mass system [mb/str]
"""
# dσ/dΩ[mb/str]
# 10.0 : fm^2 --> mb
if which == "inc":
# incident particle
if isinstance(theta, uncertainties.core.AffineScalarFunc):
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 * umath.pow(umath.sin(theta / 2.0), -4.0)
elif isinstance(theta, np.ndarray) and isinstance(theta[0], uncertainties.core.AffineScalarFunc):
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 * unp.pow(unp.sin(theta / 2.0), -4.0)
else:
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 * np.power(np.sin(theta / 2.0), -4.0)
elif which == "tar":
# target particle
if isinstance(theta, uncertainties.core.AffineScalarFunc):
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 * umath.pow(umath.cos(theta / 2.0), -4.0)
elif isinstance(theta, np.ndarray) and isinstance(theta[0], uncertainties.core.AffineScalarFunc):
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 * unp.pow(unp.cos(theta / 2.0), -4.0)
else:
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 * np.power(np.cos(theta / 2.0), -4.0)
elif which == "sum":
# incident particle + target particle
if isinstance(theta, uncertainties.core.AffineScalarFunc):
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 \
* (umath.pow(umath.sin(theta / 2.0), -4.0) + umath.pow(umath.cos(theta / 2.0), -4.0))
elif isinstance(theta, np.ndarray) and isinstance(theta[0], uncertainties.core.AffineScalarFunc):
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 \
* (unp.pow(unp.sin(theta / 2.0), -4.0) + unp.power(unp.cos(theta / 2.0), -4.0))
else:
return 10.0 * (Zi * Zt * E2 / (4.0 * T))**2.0 \
* (np.power(np.sin(theta / 2.0), -4.0) + np.power(np.cos(theta / 2.0), -4.0))
else:
raise ValueError(
f"Unrecognized which option:{which}. which must be inc/tar/sum.")
def unfunc(x, a, b, c):
lock_effect = lock * np.heaviside(
x - lock_start, 0.5) * (x - lock_start) + amp * (unp.cos(
(x - ph) * (1 / 365) * math.pi * 2) - 1)
lock_effect += np.exp(-vacc_const * (x**2))
return a * unp.exp((b) * x + lock_effect) + c * unp.exp(
(b + mut_effect) * x + lock_effect)
def theta(theta_cm, n):
"""
function to convert θ in the center-of-mass system to θ in the lab system
Arguments
---------
theta_cm : scattering angle in the center-of-mass system [rad]
n : A_t / A_i; A_t, A_i means mass number of target particle or incident particle
Return
------
theta_lab : scattering angle in the lab system [rad]
Notice
------
This function does not consider relativity
"""
if isinstance(theta_cm, uncertainties.core.AffineScalarFunc):
return umath.arctan(
umath.sin(theta_cm) / (1.0 / n + umath.cos(theta_cm)))
elif isinstance(theta_cm, np.ndarray) and isinstance(
theta_cm[0], uncertainties.core.AffineScalarFunc):
return unp.arctan(unp.sin(theta_cm) / (1.0 / n + unp.cos(theta_cm)))
else:
return np.arctan(np.sin(theta_cm) / (1.0 / n + np.cos(theta_cm)))
def inertia_components(jay, beta):
'''Returns the 2D orthogonal inertia tensor.
When at least three moments of inertia and their axes orientations are
known relative to a common inertial frame of a planar object, the orthoganl
moments of inertia relative the frame are computed.
Parameters
----------
jay : ndarray, shape(n,)
An array of at least three moments of inertia. (n >= 3)
beta : ndarray, shape(n,)
An array of orientation angles corresponding to the moments of inertia
in jay.
Returns
-------
eye : ndarray, shape(3,)
Ixx, Ixz, Izz
'''
sb = unumpy.sin(beta)
cb = unumpy.cos(beta)
betaMat = unumpy.matrix(np.vstack((cb**2, -2 * sb * cb, sb**2)).T)
eye = np.squeeze(np.asarray(np.dot(betaMat.I, jay)))
return eye
def dS(self, a):
"""
Arguments
---------
a : angle of rotation [rad]
Return
------
ΔS : detection area [mm^2]
"""
Rd = self.R + self.d
r = self.r
AT = self.AT
D0 = self.D(0.0)
A0 = umath.acos((Rd**2.0 + D0**2.0 - r**2.0) / (2.0 * Rd * D0))
d = self.d
w = self.w
h = self.h
if isinstance(a, (int, float, np.number, uncertainties.core.AffineScalarFunc)):
phi = umath.fabs(a - A0 - self.theta(a))
# ΔS
return w * h * umath.cos(phi) - d * h * umath.sin(phi)
elif isinstance(a, np.ndarray):
phi = unp.fabs(a - A0 - self.theta(a))
return w * h * unp.cos(phi) - d * h * unp.sin(phi)
else:
raise ValueError(
f"This function not supported for the input types. argument 'a' must be number or array")
def theta(self, a):
"""
Arguments
---------
a : angle of rotation [rad]
Return
------
θ : scattering angle in the lab system [rad]
"""
D0 = self.D(0.0)
D = self.D(a)
Rd = self.R + self.d
if isinstance(a, (int, float, np.number, uncertainties.core.AffineScalarFunc)):
return np.sign(a) * umath.acos(
(D0**2.0 + D**2.0 - 2.0 * Rd**2.0 *
(1.0 - umath.cos(a))) / (2.0 * D0 * D)
)
elif isinstance(a, np.ndarray):
return np.sign(a) * unp.arccos(
(D0**2.0 + D**2.0 - 2.0 * Rd**2.0 *
(1.0 - unp.cos(a))) / (2.0 * D0 * D)
)
else:
raise ValueError(
f"This function not supported for the input types. argument 'a' must be number or array")
def cos(
x: np.ndarray,
amp: float = 1.0,
freq: float = 1 / (2 * np.pi),
phase: float = 0.0,
baseline: float = 0.0,
) -> np.ndarray:
r"""Cosine function.
.. math::
y = {\rm amp} \cdot \cos\left(2 \pi {\rm freq} \cdot x
+ {\rm phase}\right) + {\rm baseline}
"""
return amp * unp.cos(2 * np.pi * freq * x + phase) + baseline
def bloch_oscillation_z(x: np.ndarray,
px: float = 0.0,
py: float = 0.0,
pz: float = 0.0,
baseline: float = 0.0):
r"""Bloch oscillation in z basis.
.. math::
y = \frac{\left( p_z^2 + (p_x^2 + p_y^2) \cos (\omega x) \right)}{\omega^2}
+ {\rm baseline},
where :math:`\omega = \sqrt{p_x^2 + p_y^2 + p_z^2}`. The `p_i` stands for the
measured probability in :math:`i \in \left\{ X, Y, Z \right\}` basis.
"""
w = unp.sqrt(px**2 + py**2 + pz**2)
return (pz**2 + (px**2 + py**2) * unp.cos(w * x)) / (w**2) + baseline
def e_geo(x, d=0):
d /= 2
a = unumpy.sqrt(x**2 + (2 - d) ** 2)
# Look at geometric_efficiency.png to see what these mean
h1 = ufloat(2,0.1)
h2 = ufloat(3,0.1)
w1 = ufloat(22, 0.1)
w2 = ufloat(30, 0.1)
if x < 8:
c = unumpy.sqrt(((w1 + w2) / 2)**2 + (h2 - h1)**2)
b = unumpy.sqrt((h2 - d)**2 + ((w1 + w2) / 2 - x)**2)
else:
c = w1
b = unumpy.sqrt((w1 - x)**2 + (h1 - d)**2)
theta = unumpy.arccos((a**2 + b**2 - c**2) / (2 * a * b))
return (1 - unumpy.cos(theta / 2)) / 2
def cos(number):
if isinstance(number, fr.Fraction):
number = Mixed(number)
elif isinstance(number, uc.UFloat):
number = Mixed(number)
elif isinstance(number, float):
number = Mixed(number)
elif isinstance(number, int):
number = Mixed(number)
assert isinstance(number, Mixed), \
"Connot calculate cos of an object of type %s." % (type(number))
if isinstance(number.value, fr.Fraction):
return Mixed(np.cos(float(number.value)))
elif isinstance(number.value, uc.UFloat):
return Mixed(unumpy.cos(number.value).item())
elif isinstance(number.value, float):
return Mixed(np.cos(number.value))
elif isinstance(number.value, int):
return Mixed(np.cos(number.value))
def cos(number):
if isinstance(number, fr.Fraction):
number = Mixed(number)
elif isinstance(number, uc.UFloat):
number = Mixed(number)
elif isinstance(number, float):
number = Mixed(number)
elif isinstance(number, int):
number = Mixed(number)
assert isinstance(number, Mixed), \
"Connot calculate cos of an object of type %s." % (type(number))
if isinstance(number.value, fr.Fraction):
return Mixed(np.cos(float(number.value)))
elif isinstance(number.value, uc.UFloat):
return Mixed(unumpy.cos(number.value).item())
elif isinstance(number.value, float):
return Mixed(np.cos(number.value))
elif isinstance(number.value, int):
return Mixed(np.cos(number.value))
def plotphase(frequenz, spannung):
verschiebung = 250e-9 # s
frequenz = unp.uarray(frequenz, 0.005)
spannung = unp.uarray(spannung, 0.001)
frequenz *= 10**(6)
umlaufdauer = 1 / frequenz
phase = 2 * np.pi * verschiebung / umlaufdauer
# print('Umlaufdauer=', umlaufdauer)
# print('Phase= ', phase)
y = unp.cos(phase)
x = spannung
plt.errorbar(unp.nominal_values(x),
unp.nominal_values(y),
xerr=unp.std_devs(x),
yerr=unp.std_devs(y),
fmt='kx',
label='Messwerte')
# fitten:
params, covariance = curve_fit(fitfunktion,
unp.nominal_values(x),
unp.nominal_values(y),
p0=[-0.1, 1])
errors = np.sqrt(np.diag(covariance))
print('m= ', params[0], '±', errors[0], ' yabschnitt= ', params[1], '±',
errors[1])
x_fit = np.linspace(-0.2, 0.2)
plt.plot(x_fit, fitfunktion(x_fit, *params), label='Fit')
# aussehen:
plt.xlim(-0.19, 0.19)
plt.ylabel(r'$\cos(\Delta\phi)$')
plt.xlabel(r'$U \:/\: \si{\volt}$')
plt.legend(loc='best')
# in matplotlibrc leider (noch) nicht möglich
plt.tight_layout(pad=0, h_pad=1.08, w_pad=1.08)
plt.savefig('build/plotphase.pdf')
plt.close()
return phase
def test_broadcast_funcs():
"""
Test of mathematical functions that work with NumPy arrays of
numbers with uncertainties.
"""
x = uncertainties.ufloat((0.2, 0.1))
arr = numpy.array([x, 2*x])
assert unumpy.cos(arr)[1] == uncertainties.umath.cos(arr[1])
# Some functions do not bear the same name in the math module and
# in NumPy (acos instead of arccos, etc.):
assert unumpy.arccos(arr)[1] == uncertainties.umath.acos(arr[1])
# The acos() function should not exist in unumpy because it does
# not exist in numpy:
assert not hasattr(numpy, 'acos')
assert not hasattr(unumpy, 'acos')
# Test of the __all__ variable:
assert 'acos' not in unumpy.__all__
def test_broadcast_funcs():
"""
Test of mathematical functions that work with NumPy arrays of
numbers with uncertainties.
"""
x = uncertainties.ufloat((0.2, 0.1))
arr = numpy.array([x, 2*x])
assert unumpy.cos(arr)[1] == uncertainties.umath.cos(arr[1])
# Some functions do not bear the same name in the math module and
# in NumPy (acos instead of arccos, etc.):
assert unumpy.arccos(arr)[1] == uncertainties.umath.acos(arr[1])
# The acos() function should not exist in unumpy because it does
# not exist in numpy:
assert not hasattr(numpy, 'acos')
assert not hasattr(unumpy, 'acos')
# Test of the __all__ variable:
assert 'acos' not in unumpy.__all__
def D(self, a):
"""
Arguments
---------
a : angle of rotation [rad]
Return
------
D : distance between target and detector [mm]
"""
Rd = self.R + self.d
r = self.r
AT = self.AT
if isinstance(a, (int, float, np.number, uncertainties.core.AffineScalarFunc)):
return umath.sqrt(Rd**2.0 + r**2.0 - 2.0 * Rd * r * umath.cos(a + AT))
elif isinstance(a, np.ndarray):
return unp.sqrt(Rd**2.0 + r**2.0 - 2.0 * Rd * r * unp.cos(a + AT))
else:
raise ValueError(
f"This function not supported for the input types. argument 'a' must be number or array")
def theta(theta_lab, n):
"""
function to convert θ in the lab system to θ in the center-of-mass system
Arguments
---------
theta_lab : scattering angle in the lab system [rad]
n : A_t / A_i; A_t, A_i means mass number of target particle or incident particle
Return
------
theta_cm : scattering angle in the center-of-mass system [rad]
Notice
------
This function do not consider relativity
"""
if isinstance(theta_lab, uncertainties.core.AffineScalarFunc):
coslab2 = umath.pow(umath.cos(theta_lab), 2.0)
coscm = (coslab2 - 1.0) / n \
+ umath.sqrt((1.0 - 1.0 / n**2.0) * coslab2 +
umath.pow(coslab2 / n, 2.0))
return np.sign(theta_lab) * umath.acos(coscm)
elif isinstance(theta_lab, np.ndarray) and isinstance(
theta_lab[0], uncertainties.core.AffineScalarFunc):
coslab2 = unp.pow(unp.cos(theta_lab), 2.0)
coscm = (coslab2 - 1.0) / n \
+ unp.sqrt((1.0 - 1.0 / n**2.0) * coslab2 +
unp.pow(coslab2 / n, 2.0))
return np.sign(theta_lab) * unp.arccos(coscm)
else:
coslab2 = np.power(np.cos(theta_lab), 2.0)
coscm = (coslab2 - 1.0) / n \
+ np.sqrt((1.0 - 1.0 / n**2.0) * coslab2 +
np.power(coslab2 / n, 2.0))
return np.sign(theta_lab) * np.arccos(coscm)
def output(n_refl,
gitter,
theta,
lam,
pathrefl,
pathfig,
pathparams,
rem=0):
theta = theta[:n_refl]
for x in new_m:
print(unumpy.nominal_values(gittertest(x[:n_refl], theta)))
abstand = gitterabstand(lam, new_m[gitter][:n_refl], theta)
x = unumpy.cos(theta)**2
popt, pcov = curve_fit(linear_func, unumpy.nominal_values(x[rem:]),
unumpy.nominal_values(abstand[rem:]))
print('parameter:', popt, np.sqrt(np.diag(pcov)))
with open(pathparams, "w") as text_file:
text_file.write(
'\\num{' + '{}'.format(round(popt[1] * 10**10, 2)) + '+-' +
'{}'.format(np.round(np.sqrt(pcov[1, 1]) * 10**10, 2)) +
'} & ' + '\\num{' + '{}'.format(round(popt[0] * 10**10, 2)) +
'+-' + '{}'.format(np.round(np.sqrt(pcov[0, 0]) * 10**10, 2)) +
'} \\\\')
plt.errorbar(unumpy.nominal_values(x),
unumpy.nominal_values(abstand),
xerr=unumpy.std_devs(x),
yerr=unumpy.std_devs(abstand),
fmt='o')
plt.plot(np.linspace(0, 1, 10),
linear_func(np.linspace(0, 1, 10), *popt), '--')
plt.xlabel(r'$\cos^2(\theta)$')
plt.ylabel(r'$a$ / m')
plt.tight_layout(pad=0)
plt.savefig(pathfig)
plt.close()
with open(pathrefl, "w") as text_file:
i = 1
for theta, m in zip(theta, new_m[gitter][:n_refl]):
theta_deg = round(np.degrees(unumpy.nominal_values(theta)), 1)
theta_deg_err = round(np.degrees(unumpy.std_devs(theta)), 0)
m_sin = round(
np.asscalar(unumpy.nominal_values(gittertest(m, theta))))
cosinus = round(
np.asscalar(np.cos(unumpy.nominal_values(theta))**2), 3)
abstand = round(
np.asscalar(
unumpy.nominal_values(
10**10 * gitterabstand(lam, m, theta))), 2)
abstand_err = round(
np.asscalar(
unumpy.std_devs(10**10 *
gitterabstand(lam, m, theta))), 2)
text_file.write('{} &'.format(i) + ' \\num{'+'{}'.format(theta_deg) +
' +- ' '{}'.format(theta_deg_err) + '} ' + \
'& {} & {} & {} & '.format(m, m_sin, cosinus) + '\\num{'
+ '{}'.format(abstand) + ' +- '+ '{}'.format(abstand_err) +
' } \\\\ \n')
i += 1
#!/usr/bin/env python #example taken from https://pypi.python.org/pypi/uncertainties/3.0.1 from __future__ import print_function from uncertainties import ufloat x = ufloat(2, 0.25) print(x) square = x**2 # Transparent calculations print(square) print(square.nominal_value) print(square.std_dev) # Standard deviation print(square - x * x) from uncertainties.umath import * # sin(), etc. print(sin(1 + x**2)) print((2 * x + 1000).derivatives[x]) # Automatic calculation of derivatives from uncertainties import unumpy # Array manipulation random_vars = unumpy.uarray([1, 2], [0.1, 0.2]) print(random_vars) print(random_vars.mean()) print(unumpy.cos(random_vars))
def cos_abs(x, a, f, phi):
'''a*|cos(2*π*f*(x-phi))|'''
return a * np.abs(unp.cos(2 * np.pi * f * (x - phi)))
########## Aufgabenteil b) ##########
# Kalibrierung des Okularmikrometers
lambda_kalibrierung = np.array(
[438.8, 447.1, 501.6, 504.8]) * 1e-9 # in m
Eichgroesse = unp.uarray(np.zeros(np.size(lambda_kalibrierung)/2), np.zeros(np.size(lambda_kalibrierung)/2)) # in m Skt Skt = Sektor
phi_mean = unp.uarray(np.zeros(np.size(phi_kalib)/2), np.zeros(np.size(phi_kalib)/2)) # in rad
eichgroesse_mit_fehler = ufloat(0,0) # in m Skt Skt = Sektor
i = 0
for eichgroesse in Eichgroesse:
j = 2*i # index für die 2*size(Eichgroesse) arrays, in unserem Fall arrays mit 4 Einträgen
phi_mean[i] = ufloat(np.mean(phi_kalib[j:j+2]), np.std(phi_kalib[j:j+2])) # Indizierung für i= 0: von 0 bis < 2 also 0 bis 1, dh. wir bilden Mittelwert aus zwei Werten
Eichgroesse[i] = np.abs(lambda_kalibrierung[j] - lambda_kalibrierung[j+1]) / ( np.abs(t_kalib[j] - t_kalib[j+1]) * unp.cos(phi_mean[i]) ) # Formel aus "zu b:"
eichgroesse_mit_fehler += Eichgroesse[i]
i += 1
eichgroesse_mit_fehler *= 1/(np.size(lambda_kalibrierung)/2) # in m
write('build/Eichgroesse.tex', make_SI(eichgroesse_mit_fehler*1e9, r'\nano\meter', figures=1) ) # hier fehlt noch Skt^-1 das geht allerdings schlecht mit make_si..
# Tabelle für LaTeX:
phi1 = np.array([phi_kalib[0], phi_kalib[2]]) # crappy weil hart codiert aber was will man machen
phi2 = np.array([phi_kalib[1], phi_kalib[3]]) # in rad
lambda1 = [lambda_kalibrierung[0]*1e9, lambda_kalibrierung[2]*1e9] # in nm
lambda2 = [lambda_kalibrierung[1]*1e9, lambda_kalibrierung[3]*1e9] # in nm
t1 = [t_kalib[0], t_kalib[2]]
t2 = [t_kalib[1], t_kalib[3]]
write('build/Tabelle_b.tex', make_table([-phi1,lambda1,t1,-phi2,lambda2,t2,-phi_mean],[3, 1, 1, 3, 1, 1, 1])) # Jeder fehlerbehaftete Wert bekommt zwei Spalten
write('build/Tabelle_b_texformat.tex', make_full_table(
'Messdaten zur Bestimmung der Eichgröße.',
def f_unc(x, A, tau, freq, phi, offset):
return offset + A * unp.exp(-x / tau) * unp.cos(2 * np.pi * freq * x + phi)
#!/usr/bin/env python #example taken from https://pypi.python.org/pypi/uncertainties/3.0.1 from __future__ import print_function from uncertainties import ufloat x = ufloat(2, 0.25) print(x) square = x**2 # Transparent calculations print(square) print(square.nominal_value) print(square.std_dev) # Standard deviation print(square - x*x) from uncertainties.umath import * # sin(), etc. print(sin(1+x**2)) print((2*x+1000).derivatives[x]) # Automatic calculation of derivatives from uncertainties import unumpy # Array manipulation random_vars = unumpy.uarray([1, 2], [0.1, 0.2]) print(random_vars) print(random_vars.mean()) print(unumpy.cos(random_vars))
def cos(x, a, f, phi):
return a * unp.cos(2*np.pi*f*(x-phi))
def cos_abs(x, a, f, phi):
return a * np.abs(unp.cos(2*np.pi*f*(x-phi)))
plt.legend()
plt.xlabel('$\\alpha$ / $^\circ$')
plt.ylabel('relative Intensität')
plt.savefig('../../pics/rot.png')
d = unp.uarray([403.609], [9.666])*1e-9
w_B = unp.uarray([135],[1])
w_G = unp.uarray([83],[1])
alpha_1 = unp.uarray([popt[0]],[popt_error[0]])
alpha_2 = unp.uarray([popt[3]],[popt_error[3]])
delta_beta = -alpha_2+alpha_1
print('\n delta beta')
print(delta_beta)
delta_beta_value = unp.nominal_values(delta_beta)
delta_beta_error = unp.std_devs(delta_beta)
delta_lamda = d*unp.cos(unp.radians(w_B)+unp.radians(w_G)-np.radians(180))*unp.radians(delta_beta)
print('\n delta lambda')
print(delta_lamda)
####
# Rechne Linienbreite in nm um
####
delta_alpha_a = unp.uarray(-a_x_0+a_x_1, (a_x_0-a_x_1)*0.01)
delta_alpha_b = unp.uarray(-b_x_0+b_x_1, (b_x_0-b_x_1)*0.01)
delta_doppler_a = d*unp.cos(unp.radians(w_B)+unp.radians(w_G)-np.radians(180))*unp.radians(delta_alpha_a)
delta_doppler_b = d*unp.cos(unp.radians(w_B)+unp.radians(w_G)-np.radians(180))*unp.radians(delta_alpha_b)
print('\nDoppler')
print(delta_doppler_a)
print(delta_doppler_b)
def main():
print('\n#################### Analyse für Salz ####################\n')
Xi2_best = [
'SC', 20, 'CuF'
] # SC ist in dem Fall ein Platzhalter. Die 20 garantiert, dass ein jedes Xi zunächst kleiner ist.
# daten1, daten2 = np.genfromtxt('SalzRadius.txt', unpack=True)
# daten = np.array([23, 34.50, 41, 43, 51, 57, 58.5, 65, 70, 78, 83, 84.5, 90,95.5, 103, 108,110,116, 123, 133, 116 +43])
daten = np.array([
23, 34.50, 43, 51, 57, 65, 78, 83, 90, 95.5, 103, 108, 123, 133,
116 + 43
])
# daten = np.array([23, 34.50, 43, 51, 57, 65, 78, 83,95.5, 103, 108, 123, 133, 116 +43]) #9. raus
# maske = [True,True,False,True,True,True,True,True,True,True,True,True,True,True,True,True,True,True,True,True,True]
# daten = daten[maske]
daten = daten + 4.5
# daten = daten[daten != 0]
daten = (daten * np.pi) / (360)
print('Daten: ', daten)
# theta = theta_radiant(radius())
theta = daten
print('Theta mit Fehler: ', theta)
netzebenenabstand = bragg(lambda_1, noms(theta))
reflexe_Zinkblende = []
reflexe_Steinsalz = []
reflexe_Caesiumchlorid = []
reflexe_Fluorit = []
verhaeltnisse_temp = []
for gitter in gitter_moegl:
if gitter == 'Zinkblende':
############## CuF ##################
argg = 'CuF'
print('Berechnung ' + gitter + ' für ' + argg + ':')
infos = Strukturamplitude_Salz(28, 10, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
############## CuCl ##################
argg = 'CuCl'
print('Berechnung ' + gitter + ' für ' + argg + ':')
infos = Strukturamplitude_Salz(28, 18, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
elif gitter == 'Steinsalz':
############## KF ##################
argg = 'KF'
print('Berechnung ' + gitter + ' für ' + argg + ':')
infos = Strukturamplitude_Salz(18, 10, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
############## KCl ##################
argg = 'KCl'
print('Berechnung ' + gitter + ' für ' + argg + ':')
infos = Strukturamplitude_Salz(18, 18, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
elif gitter == 'Caesiumchlorid':
############## CsJ ##################
argg = 'CsJ'
print('Berechnung ' + gitter + ' für ' + argg + ':')
infos = Strukturamplitude_Salz(54, 54, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
############## CsCl ################## -> könnte komisch sein
argg = 'CsCl'
print('Berechnung ' + gitter + ' für ' + argg +
'(könnte komisch sein):')
infos = Strukturamplitude_Salz(54, 18, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
elif gitter == 'Fluorit':
############## CaF ##################
argg = 'CaF'
print('Berechnung ' + gitter + ' für ' + argg + ':')
infos = Strukturamplitude_Salz(18, 10, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
############## CaCl ################## -> könnte komisch sein
argg = 'CaCl'
print('Berechnung ' + gitter + ' für ' + argg +
'(könnte komisch sein):')
infos = Strukturamplitude_Salz(18, 18, gitter=gitter)
reflexe = np.array(infos[0])
# print(gitter +': ',reflexe[np.argsort(infos[1])])
m = infos[1]
m = np.sort(m)
verhaeltnisse = findStructure(m, netzebenenabstand)
verhaeltnisse_temp = verhaeltnisse[0]
# verhaeltnis_m = np.sort(verhaeltnisse[0])
verhaeltnis_m = verhaeltnisse[0]
if gitter == 'Zinkblende':
reflexe_Zinkblende = verhaeltnis_m
elif gitter == 'Steinsalz':
reflexe_Steinsalz = verhaeltnis_m
elif gitter == 'Caesiumchlorid':
reflexe_Caesiumchlorid = verhaeltnis_m
elif gitter == 'Fluorit':
reflexe_Fluorit = verhaeltnis_m
verhaeltnis_d = np.sort(verhaeltnisse[1])
print('sqrt(m_i/m_1): ', verhaeltnis_m)
print('d_1/d_i: ', verhaeltnis_d)
print('Verhältnisse für die m Werte: ', verhaeltnis_m)
print('Verhältnisse für die d Werte: ', verhaeltnis_d)
print(
'Abweichung Xi^2 für die ' + gitter + ' Struktur für ' + argg +
': ', abweichung(verhaeltnis_m, verhaeltnis_d))
if abweichung(verhaeltnis_m, verhaeltnis_d) < Xi2_best[1]:
Xi2_best = [
gitter,
abweichung(verhaeltnis_m, verhaeltnis_d), argg
]
print('Struktur mit der kleinsten Abweichung: ', Xi2_best[0], ' für ',
Xi2_best[2])
print('Abweichung Xi^2: ', Xi2_best[1])
m = Strukturamplitude_Salz(18, 18, gitter=Xi2_best[0])[1]
a = np.array(gitterkonstanteBragg(m, netzebenenabstand))
print('Gitterkonstanten für ' + Xi2_best[0] + ' Struktur: ', ' für ',
Xi2_best[2], a)
####################################################################################################
# Systematischer Fehler
####################################################################################################
# systematischer Fehler Absorption der Röntgenstrahlung
DeltaA = (radius_rohr /
(2 * Radius_kamera)) * (1 - Radius_kamera / Abstand_FP) * (
np.cos(noms(theta))**2 / noms(theta)) * a
a_mitFehler = unp.uarray(a, DeltaA)
print('Gitterkonstanten mit Fehler durch die Absorption: ', a_mitFehler)
####################################################################################################
# curve_fit zeugs
####################################################################################################
# linearer fit für a gegen cos^2
# params, cov = curve_fit(lin,np.cos(noms(theta))**2,noms(a_mitFehler), sigma = stds(a_mitFehler))
params, cov = curve_fit(lin, np.cos(noms(theta))**2, noms(a_mitFehler))
err = np.sqrt(np.diag(cov))
a_extrp = ufloat(params[1], err[1])
print('Extrapolierte Gitterkonstante: ', a_extrp)
####################################################################################################
# Plots
####################################################################################################
cos2Theta = unp.cos(theta)**2
cos2Theta_fit = np.linspace(0, 1)
####### ab hier der a gegen cos^2 Plot ########
plt.errorbar(np.cos(noms(theta))**2,
a,
xerr=stds(cos2Theta),
yerr=DeltaA,
fmt='x',
label='Daten')
plt.plot(cos2Theta_fit, lin(cos2Theta_fit, *params), label='Fit')
plt.legend(loc='best')
plt.xlabel('cos$^2(\Theta)$')
plt.ylabel('$a$ in Angtröm')
# plt.xlim(0.6,1)
# plt.ylim(4.8e-10,5.8e-10)
plt.tight_layout()
plt.grid()
plt.savefig('Plots/Salz_Fit_Egor.pdf')
plt.close()
i = np.linspace(1, len(daten), len(daten))
verhaeltnisse_daten = []
for j in range(0, len(daten)):
verhaeltnisse_daten.append(unp.sin(daten[j]) / unp.sin(daten[0]))
plt.plot(i, reflexe_Zinkblende, 'x', label='Zinkblende')
plt.plot(i, reflexe_Steinsalz, 'x', label='Steinsalz')
plt.plot(i, reflexe_Caesiumchlorid, 'x', label='Caesiumchlorid')
plt.plot(i, reflexe_Fluorit, 'o', label='Fluorit')
plt.plot(i, noms(verhaeltnisse_daten), 'x', label='data')
plt.xlabel('i')
# plt.xlim(0,7)
# plt.ylim(0,4.5)
plt.ylabel('verhältnisse')
plt.legend(loc='best')
plt.tight_layout()
plt.grid()
plt.savefig('Plots/verhaeltnisse_Salz.pdf')
plt.close()
def structurfactor(self, h, k, l):
structurfactor = 0
for g_1, g_2, g_3 in self.base_vec:
structurfactor += self.formfaktor * unumpy.cos(
2 * np.pi * (g_1 * h + g_2 * k + g_3 * l))
return structurfactor
print(a1, b1)
print(a2, b2)
# print(a3, b3)
with open('build/fitresults.tex', 'w') as f:
lines = [
r'\begin{align}',
r'm_1 &= \num{{{:0.3f} +- {:0.3f}}} & b_1 &= \SI{{{:0.3f} +- {:0.3f}}}{{\nano\meter}} \\'.format(a1.n, a1.s, b1.n, b1.s),
r'm_2 &= \num{{{:0.3f} +- {:0.3f}}} & b_2 &= \SI{{{:0.3f} +- {:0.3f}}}{{\nano\meter}}'.format(a2.n, a2.s, b2.n, b2.s),
r'\end{align}',
]
f.write('\n'.join(lines) + '\n')
a = (a1 + a2) / 2
delta_h = unp.cos(unp.arctan(a)) * (b1 - b2)
print(delta_h)
with open('build/height.tex', 'w') as f:
f.write(r'\SI{{{:.1f} +- {:.1f}}}{{\pico\meter}}'.format(
delta_h.n * 1000, delta_h.s * 1000)
)
f.write('\n')
grid_constant_gold = 407.82
step_factor = np.sqrt(3)*delta_h*1000/grid_constant_gold
print(step_factor)
with open('build/step_factor.tex', 'w') as f:
f.write(r'\num{{{:.1f} +- {:.1f}}}'.format(
step_factor.n, step_factor.s)
)
#!/usr/bin/env python #example taken from https://pypi.python.org/pypi/uncertainties/3.0.1 from uncertainties import ufloat x = ufloat(2, 0.25) print x square = x**2 # Transparent calculations print square print square.nominal_value print square.std_dev # Standard deviation print square - x*x from uncertainties.umath import * # sin(), etc. print sin(1+x**2) print (2*x+1000).derivatives[x] # Automatic calculation of derivatives from uncertainties import unumpy # Array manipulation random_vars = unumpy.uarray([1, 2], [0.1, 0.2]) print random_vars print random_vars.mean() print unumpy.cos(random_vars)
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
from uncertainties import ufloat
from scipy.stats import linregress
import uncertainties.unumpy as unp
phi, lamda, t = np.genfromtxt('Daten/eichung.txt', unpack=True)
phi *= (1 / 360) * 2 * np.pi #in rad umrechnen
phi_01 = np.array([phi[0], phi[1]]) #phi in array
#print(phi_12, np.mean(phi_12), np.std(phi_12))
phi_gem1 = ufloat(np.mean(phi_01), np.std(phi_01)) #phi mitteln
lamda_0_1 = lamda[0] - lamda[1]
eich1 = (abs(lamda[0] - lamda[1]) / (abs(t[0] - t[1])) * unp.cos(phi_gem1)
) #erste eichgroesse
print(eich1)
phi_23 = np.array([phi[2], phi[3]])
#print(phi_12, np.mean(phi_12), np.std(phi_12))
phi_gem2 = ufloat(np.mean(phi_23), np.std(phi_23))
lamda_2_3 = lamda[2] - lamda[3]
eich2 = (abs(lamda[2] - lamda[3]) / (abs(t[2] - t[3])) * unp.cos(phi_gem2))
print(eich2)
eichgroesse = (1 / 2) * (eich1 + eich2)
print(eichgroesse)
np.savetxt(
'build/eichgroesse.txt',
#!/usr/bin/env python #example taken from https://pypi.python.org/pypi/uncertainties/3.0.1 from uncertainties import ufloat x = ufloat(2, 0.25) print x square = x**2 # Transparent calculations print square print square.nominal_value print square.std_dev # Standard deviation print square - x * x from uncertainties.umath import * # sin(), etc. print sin(1 + x**2) print(2 * x + 1000).derivatives[x] # Automatic calculation of derivatives from uncertainties import unumpy # Array manipulation random_vars = unumpy.uarray([1, 2], [0.1, 0.2]) print random_vars print random_vars.mean() print unumpy.cos(random_vars)
def delta_lambda(phi1,phi2,s):
return unp.cos(phimittelwert(phi1,phi2))*eichzahl*s
########## Aufgabenteil b) ##########
# Kalibrierung des Okularmikrometers
lambda_kalibrierung = np.array([438.8, 447.1, 501.6, 504.8]) * 1e-9 # in m
Eichgroesse = unp.uarray(
np.zeros(np.size(lambda_kalibrierung) / 2), np.zeros(np.size(lambda_kalibrierung) / 2)
) # in m Skt^(-1) Skt = Sektor
phi_mean = unp.uarray(np.zeros(np.size(phi_kalib) / 2), np.zeros(np.size(phi_kalib) / 2)) # in rad
eichgroesse_mit_fehler = ufloat(0, 0) # in m Skt^(-1) Skt = Sektor
i = 0
for eichgroesse in Eichgroesse:
j = 2 * i # index für die 2*size(Eichgroesse) arrays, in unserem Fall arrays mit 4 Einträgen
phi_mean[i] = ufloat(
np.mean(phi_kalib[j : j + 2]), np.std(phi_kalib[j : j + 2])
) # Indizierung für i= 0: von 0 bis < 2 also 0 bis 1, dh. wir bilden Mittelwert aus zwei Werten
Eichgroesse[i] = np.abs(lambda_kalibrierung[j] - lambda_kalibrierung[j + 1]) / (
np.abs(t_kalib[j] - t_kalib[j + 1]) * unp.cos(phi_mean[i])
) # Formel aus "zu b:"
eichgroesse_mit_fehler += Eichgroesse[i]
i += 1
eichgroesse_mit_fehler *= 1 / (np.size(lambda_kalibrierung) / 2) # in m
write("build/Eichgroesse.tex", make_SI(eichgroesse_mit_fehler * 1e9, r"\nano\meter", figures=1))
# Tabelle für LaTeX:
phi1 = np.array([phi_kalib[0], phi_kalib[2]]) # crappy weil hart codiert aber was will man machen
phi2 = np.array([phi_kalib[1], phi_kalib[3]]) # in rad
lambda1 = [lambda_kalibrierung[0] * 1e9, lambda_kalibrierung[2] * 1e9] # in nm
lambda2 = [lambda_kalibrierung[1] * 1e9, lambda_kalibrierung[3] * 1e9] # in nm
t1 = [t_kalib[0], t_kalib[2]]
t2 = [t_kalib[1], t_kalib[3]]
write(
"build/Tabelle_b.tex", make_table([-phi1, lambda1, t1, -phi2, lambda2, t2, -phi_mean], [3, 1, 1, 3, 1, 1, 1])
w_G_error = unp.std_devs(w_G)
d = unp.uarray([403.609], [9.666]) * 1e-9
a = unp.uarray(data[1:, 3], [0.05])
a_value = unp.nominal_values(a)
a_error = unp.std_devs(a)
f = unp.uarray(300, 10)
lamda = d * (unp.sin(unp.radians(w_G)) -
unp.sin(unp.radians(w_G) + unp.radians(w_B)))
lamda_value = unp.nominal_values(lamda)
lamda_error = unp.std_devs(lamda)
delta_beta = a / f
delta_beta_value = unp.nominal_values(delta_beta)
delta_beta_error = unp.std_devs(delta_beta)
delta_lamda = d * unp.cos(unp.radians(w_G) + unp.radians(w_B)) * delta_beta
delta_lamda_value = unp.nominal_values(delta_lamda)
delta_lamda_error = unp.std_devs(delta_lamda)
print(
'\nFarbe & $\lambda$ / nm & Abstand a / mm &$\Delta \beta$ / 10^{-3}^{\circ}$ & $\Delta \lambda$ / nm\\\\'
)
for i in range(0, len(w_B)):
print('%s & %.3f\pm%.3f & %.1f\pm %.1f & %.3f\pm%.3f & %.3f\pm%.3f\\\\' %
(Farbe[i], lamda_value[i] * 1e9, lamda_error[i] * 1e9, a_value[i],
a_error[i], delta_beta_value[i] * 1e3, delta_beta_error[i] * 1e3,
-delta_lamda_value[i] * 1e9, delta_lamda_error[i] * 1e9))
print('\nFarbe & $w_B$ / $^\circ$ & $w_G$ / $^\circ$ & Abstand a / mm\\\\')
for i in range(0, len(w_B)):
print('%s & %.1f\pm %.1f & %.1f\pm %.1f & %.1f\pm%.1f\\\\' %
(Farbe[i], w_B_value[i], w_B_error[i], w_G_value[i], w_G_error[i],
def eichgr(lam1,lam2,delta_t,phi1,phi2):
phimitt = unp.uarray([np.average([phi1,phi2])],[np.std([phi1,phi2])])
print('phi12',phimitt)
print('delta t',delta_t)
return((lam1-lam2)/(delta_t*unp.cos(phimitt)))