def visualize_Lines():
Lorentzian = LorentzianLine("Lorentzian1", (-energy_from_lambda(6.0), 15),
x0=-0.3,
width=0.5,
c=0.0)
F_c = F_cLine("F_c1", (-energy_from_lambda(6.0), 15),
x0=-0.3,
width=0.5,
A=350.0,
q=0.02,
c=0.0,
weight=1)
F_I = F_ILine("F_I1", (-energy_from_lambda(6.0), 15),
x0=-0.3,
width=0.008,
A=350.0,
q=0.02,
kappa=0.01,
c=0.0,
weight=1)
print(F_I.integrate())
F_I2 = F_ILine("F_I2", (-energy_from_lambda(6.0), 15),
x0=-0.3,
width=0.1,
A=367.0,
q=0.124,
kappa=0.065,
c=0.0,
weight=1)
print(F_I2.integrate())
e = np.linspace(-0.5, 0.0, 1201)
plt.plot(e, Lorentzian(e))
plt.plot(e, F_c(e) * F_c.normalize(), ls="--", lw=2.0)
plt.plot(e, F_I(e), ls="dotted", lw=4.0)
plt.plot(e, F_I2(e), ls="-.", lw=1.0)
plt.show()
def test_normalization():
Lorentzian = LorentzianLine("Lorentzian1", (-5., 5),
x0=0.0,
width=0.5,
c=0.0)
n = Lorentzian.normalize()
from scipy.integrate import quad
to_integrate = lambda x: Lorentzian(x)
val, err = quad(to_integrate, min(Lorentzian.domain),
max(Lorentzian.domain))
print(
f"Integration value: {val:.5f} +- {err:.5f} | normalization factor: {n:.5f}"
)
print(f"Normalized Line area: {val*n}")
# - - - - - - - - - - - - - - - - - - - -
F_c = F_cLine("FcLine1", (-15, 15),
x0=0.0,
width=0.02,
A=350.0,
q=0.023,
c=0.0,
weight=1.0)
nfc = F_c.normalize()
ifc = F_c.integrate()
x = np.linspace(-1000, 1000, 5000000)
y = F_c.calc(x, **F_c.line_params)
ifctrapz = np.trapz(y, x)
ifcquadv, ifcquade = quad(lambda x: nfc * F_c(x), min(F_c.domain),
max(F_c.domain))
print(f"{F_c.line_params}")
print(f"Standard Integration value for 10000 steps: {ifc}")
print(
f"QUADPACK Integration value (after normal.): {ifcquadv} +- {ifcquade}"
)
print(f"TRAPEZOID Integration value -1e3 from 1e3 : {ifctrapz}")
# - - - - - - - - - - - - - - - - - - - -
F_I = F_ILine("FILine1", (-15, 15),
x0=0.0,
width=0.02,
A=350.0,
q=0.023,
kappa=0.01,
c=0.0,
weight=1.0)
nfI = F_I.normalize()
ifI = F_I.integrate()
x = np.linspace(-1000, 1000, 5000000)
y = F_I.calc(x, **F_I.line_params)
ifItrapz = np.trapz(y, x)
ifIquadv, ifIquade = quad(lambda x: F_I(x), min(F_I.domain),
max(F_I.domain))
print(f"{F_I.line_params}")
print(f"Standard Integration value for 10000 steps: {ifI}")
print(
f"QUADPACK Integration value : {ifIquadv} +- {ifIquade}"
)
print(f"TRAPEZOID Integration value -1e3 from 1e3 : {ifItrapz}")