# Log parabola

[3]:

# Parameters
func_name = "Log_parabola"
wide_energy_range = True
x_scale = "log"
y_scale = "log"
linear_range = False


## Description

[5]:

func.display()

• description: A log-parabolic function. NOTE that we use the high-energy convention of using the natural log in place of the base-10 logarithm. This means that beta is a factor 1 / log10(e) larger than what returned by those software using the other convention.
• formula: $K \left( \frac{x}{piv} \right)^{\alpha -\beta \log{\left( \frac{x}{piv} \right)}}$
• parameters:
• K:
• value: 1.0
• desc: Normalization
• min_value: 1e-30
• max_value: 100000.0
• unit:
• is_normalization: True
• delta: 0.1
• free: True
• piv:
• value: 1.0
• desc: Pivot (keep this fixed)
• min_value: None
• max_value: None
• unit:
• is_normalization: False
• delta: 0.1
• free: False
• alpha:
• value: -2.0
• desc: index
• min_value: None
• max_value: None
• unit:
• is_normalization: False
• delta: 0.2
• free: True
• beta:
• value: 1.0
• desc: curvature (positive is concave, negative is convex)
• min_value: None
• max_value: None
• unit:
• is_normalization: False
• delta: 0.1
• free: True

## Shape

The shape of the function.

If this is not a photon model but a prior or linear function then ignore the units as these docs are auto-generated

[6]:

fig, ax = plt.subplots()

ax.plot(energy_grid, func(energy_grid), color=blue)

ax.set_xlabel("energy (keV)")
ax.set_ylabel("photon flux")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)


## F$$_{\nu}$$

The F$$_{\nu}$$ shape of the photon model if this is not a photon model, please ignore this auto-generated plot

[7]:

fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid * func(energy_grid), red)

ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"energy flux (F$_{\nu}$)")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)


## $$\nu$$F$$_{\nu}$$

The $$\nu$$F$$_{\nu}$$ shape of the photon model if this is not a photon model, please ignore this auto-generated plot

[8]:

fig, ax = plt.subplots()

ax.plot(energy_grid, energy_grid**2 * func(energy_grid), color=green)

ax.set_xlabel("energy (keV)")
ax.set_ylabel(r"$\nu$F$_{\nu}$")
ax.set_xscale(x_scale)
ax.set_yscale(y_scale)