def arcsin(number):
if isinstance(number, fr.Fraction):
number = Mixed(number)
elif isinstance(number, uc.UFloat):
number = Mixed(number)
elif isinstance(number, int):
number = Mixed(number)
elif isinstance(number, float):
number = Mixed(number)
assert isinstance(number, Mixed), \
"Cannot calculate arcsin of object of type %s." % (type(number))
if isinstance(number.value, uc.UFloat):
return Mixed(unumpy.arcsin(number.value).item())
elif isinstance(number.value, fr.Fraction):
return Mixed(np.arcsin(float(number.value)))
elif isinstance(number.value, int):
return Mixed(np.arcsin(number.value))
elif isinstance(number.value, float):
return Mixed(np.arcsin(number.value))
def arcsin(number):
if isinstance(number, fr.Fraction):
number = Mixed(number)
elif isinstance(number, uc.UFloat):
number = Mixed(number)
elif isinstance(number, int):
number = Mixed(number)
elif isinstance(number, float):
number = Mixed(number)
assert isinstance(number, Mixed), \
"Cannot calculate arcsin of object of type %s." % (type(number))
if isinstance(number.value, uc.UFloat):
return Mixed(unumpy.arcsin(number.value).item())
elif isinstance(number.value, fr.Fraction):
return Mixed(np.arcsin(float(number.value)))
elif isinstance(number.value, int):
return Mixed(np.arcsin(number.value))
elif isinstance(number.value, float):
return Mixed(np.arcsin(number.value))
def darcsin(number):
if isinstance(number, fr.Fraction):
number = Mixed(number)
elif isinstance(number, uc.UFloat):
number = Mixed(number)
elif isinstance(number, int):
number = Mixed(number)
elif isinstance(number, float):
number = Mixed(number)
assert isinstance(number, Mixed), \
"Cannot calculate darcsin of object of type %s." % (type(number))
if isinstance(number.value, uc.UFloat):
return rad2deg(Mixed(unumpy.arcsin((number.value)).item()))
elif isinstance(number.value, fr.Fraction):
if number == -1:
return Mixed(-90)
elif number == -fr.Fraction(1, 2):
return Mixed(-30)
elif number == 0:
return Mixed(0)
elif number == fr.Fraction(1, 2):
return Mixed(30)
elif number == 1:
return Mixed(90)
else:
return rad2deg(Mixed(np.arcsin(float(number.value))))
elif isinstance(number.value, int):
if number == -1:
return Mixed(-90)
elif number == 0:
return Mixed(0)
elif number == 1:
return Mixed(90)
else:
return rad2deg(Mixed(np.arcsin(number.value)))
elif isinstance(number.value, float):
return rad2deg(Mixed(np.arcsin(number.value)))
def darcsin(number):
if isinstance(number, fr.Fraction):
number = Mixed(number)
elif isinstance(number, uc.UFloat):
number = Mixed(number)
elif isinstance(number, int):
number = Mixed(number)
elif isinstance(number, float):
number = Mixed(number)
assert isinstance(number, Mixed), \
"Cannot calculate darcsin of object of type %s." % (type(number))
if isinstance(number.value, uc.UFloat):
return rad2deg(Mixed(unumpy.arcsin((number.value)).item()))
elif isinstance(number.value, fr.Fraction):
if number == -1:
return Mixed(-90)
elif number == -fr.Fraction(1, 2):
return Mixed(-30)
elif number == 0:
return Mixed(0)
elif number == fr.Fraction(1, 2):
return Mixed(30)
elif number == 1:
return Mixed(90)
else:
return rad2deg(Mixed(np.arcsin(float(number.value))))
elif isinstance(number.value, int):
if number == -1:
return Mixed(-90)
elif number == 0:
return Mixed(0)
elif number == 1:
return Mixed(90)
else:
return rad2deg(Mixed(np.arcsin(number.value)))
elif isinstance(number.value, float):
return rad2deg(Mixed(np.arcsin(number.value)))
from scipy.optimize import curve_fit
from scipy.stats import sem
import scipy.constants as const
import uncertainties.unumpy as unp
A, B = np.genfromtxt("../data/A4grün.dat", unpack=True)
a = np.deg2rad(A) #ist alpha_1
b = np.deg2rad(B) #ist alhpa_2
c = const.physical_constants["speed of light in vacuum"]
n = ufloat(1.45108, 0.01991)
aERR = np.array([])
bERR = np.array([])
for i in range(len(a)):
aERR = np.append(aERR, ufloat(a[i], 0.00872665))
for i in range(len(b)):
bERR = np.append(bERR, ufloat(b[i], 0.00872665))
#bestimme beta 1
beta = unp.arcsin(unp.sin(aERR) / n)
beta2 = np.deg2rad(60) - beta
print(beta * 180 / np.pi)
print(beta2 * 180 / np.pi)
delta = (aERR + bERR) - (beta + beta2)
deltamean = np.mean(delta)
print("###### delta grün:")
print(delta * 180 / np.pi)
print(f"Abweichung delta= {(deltamean*180/np.pi):.4f}")
# Extrapolation
def fit_lin(b, a, n_0):
return a*b + n_0
sl_grenz=slice(13, 18)
popt_grenz, pstats_grenz = papstats.curve_fit(fit_lin, b[sl_grenz], n[sl_grenz])
b_G = (n_U-popt_grenz[1])/popt_grenz[0]
y_G = y_bragg(b_G)
# Berechnung
print "Grenzwellenlänge:", papstats.pformat(y_G/const.pico, label='y_G', unit='pm', format='.2u')
print "Plancksches Wirkungsquantum:"
papstats.print_rdiff(h_planck(y=y_G, U_B=30*const.kilo), h_erw)
# 2. Ordnung
print "2. Ordung ab:", papstats.pformat(unp.arcsin(y_G/d)/2/const.pi*360, label='b', unit='°', format='.2u')
# Plot
plt.clf()
plt.title(u'Diagramm 3.1: Bremsspektrum von LiF mit Untergrund und Extrapolation am kurzwelligen Ende')
axmain = plt.subplot(111)
plt.xlabel(ur'Bestrahlungswinkel $\beta \, [^\circ]$')
plt.ylabel(ur'Zählrate $n \, [\frac{Ereignisse}{s}]$')
xlim = [b[0], b[-1]]
xspace = np.linspace(*xlim, num=1000)
axmain.set_xlim(*xlim)
papstats.plot_data(b, n, label='Messpunkte')
plt.fill_between(unp.nominal_values(b), 0, unp.nominal_values(n), color='g', alpha=0.2)
from mpl_toolkits.axes_grid1.inset_locator import zoomed_inset_axes
from mpl_toolkits.axes_grid1.inset_locator import mark_inset
xerror = 1e-3 * np.ones(len(xsigma)) * 0.05 a = 1 b = 1 usigma_x = usigma_x**2 * a usigma_y = usigma_y**2 * a uheight = unp.uarray(heigh_m, xerror) * b alpha = unp.arctan((usigma_x - omega_0) / (uheight - z_0)) x = 150e-6 d_1 = x * unp.tan(unp.arcsin(1 / 3.551)) print(d_1) usigma_x -= 2 * unp.sqrt(d_1**2) print(usigma_x) #print(alpha,uheight) ################## Plot and Fit with ROOT ############################ root.gStyle.SetLabelSize(.055, "XY") root.gStyle.SetLabelFont(42, "XY") root.gStyle.SetTitleSize(.055, "YY") root.gStyle.SetTitleSize(.053, "X")
sl_grenz = slice(13, 18)
popt_grenz, pstats_grenz = papstats.curve_fit(fit_lin, b[sl_grenz],
n[sl_grenz])
b_G = (n_U - popt_grenz[1]) / popt_grenz[0]
y_G = y_bragg(b_G)
# Berechnung
print "Grenzwellenlänge:", papstats.pformat(y_G / const.pico,
label='y_G',
unit='pm',
format='.2u')
print "Plancksches Wirkungsquantum:"
papstats.print_rdiff(h_planck(y=y_G, U_B=30 * const.kilo), h_erw)
# 2. Ordnung
print "2. Ordung ab:", papstats.pformat(unp.arcsin(y_G / d) / 2 / const.pi *
360,
label='b',
unit='°',
format='.2u')
# Plot
plt.clf()
plt.title(
u'Diagramm 3.1: Bremsspektrum von LiF mit Untergrund und Extrapolation am kurzwelligen Ende'
)
axmain = plt.subplot(111)
plt.xlabel(ur'Bestrahlungswinkel $\beta \, [^\circ]$')
plt.ylabel(ur'Zählrate $n \, [\frac{Ereignisse}{s}]$')
xlim = [b[0], b[-1]]
xspace = np.linspace(*xlim, num=1000)
def theta(x):
return unp.arcsin(n * c * h / (2 * x * d))