def test_Lorentzian_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}")
L3 = LineFactory.create('lorentzian',
name="Lorentzian3",
domain=(-5.0, 5.0),
x0=-1.0,
width=0.4,
c=0.02,
weight=1)
### Evaluate a Line directly
### compare it with its normalized version and plot it
f1 = plt.figure(figsize=(6.0, 4.0))
ax1 = f1.add_subplot(111)
ax1_label = f"A simple Lorentzian line\n$\int L_1(E)\,dE= ${quad(L1, *L1.domain)[0]:.4f}"
ax1.plot(e, L1(e), color="C0", lw=2.0, label=ax1_label)
ax1.plot(e,
L1(e) * L1.normalize(),
color="C1",
ls="--",
lw=1.0,
label="(re)normalized")
ax1.set_title("A simple Line")
ax1.legend()
#plt.show()
#------------------------------------------------------------------------------
### Create a SqE model from the three lines
### Add the three weighted lines individually
icalcstrat = InelasticCalcStrategy(T=20.)
qcalcstrat = QuasielasticCalcStrategy()
# This creates the sqe model
sqe1 = SqE(lines=(L1, L2, L3), lam=6.0, dlam=0.12, l_SD=3.43, T=20)
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}")