Log normal
[3]:
# Parameters
func_name = "Log_normal"
wide_energy_range = True
x_scale = "linear"
y_scale = "linear"
linear_range = True
Description
[5]:
func.display()
- description: A log normal function
- formula: $ K \frac{1}{ x \sigma \sqrt{2 \pi}}\exp{\frac{(\log x/piv - \mu/piv)^2}{2~(\sigma)^2}} $
- parameters:
- F:
- value: 1.0
- desc: Integral between 0and +inf. Fix this to 1 to obtain a log Normal distribution
- min_value: None
- max_value: None
- unit:
- is_normalization: False
- delta: 0.1
- free: True
- mu:
- value: 0.0
- desc: Central value
- min_value: None
- max_value: None
- unit:
- is_normalization: False
- delta: 0.1
- free: True
- sigma:
- value: 1.0
- desc: standard deviation
- min_value: 1e-12
- max_value: None
- unit:
- is_normalization: False
- delta: 0.1
- free: True
- piv:
- value: 1.0
- desc: pivot. Leave this to 1 for a proper log normal distribution
- min_value: None
- max_value: None
- unit:
- is_normalization: False
- delta: 0.1
- free: False
- F:
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)
