Log uniform prior

[3]:

# Parameters
func_name = "Log_uniform_prior"
wide_energy_range = True
x_scale = "linear"
y_scale = "linear"
linear_range = True

Description

[5]:

func.display()
  • description: A function which is K/x on the interval lower_bound - upper_bound and 0 outside the interval. The extremes of the interval are NOT counted as part of the interval. Lower_bound must be >= 0.
  • formula: $ f(x)=K~\begin{cases}0 & x \le \text{lower_bound} \\\frac{1}{x} & \text{lower_bound} < x < \text{upper_bound} \\ 0 & x \ge \text{upper_bound} \end{cases}$
  • parameters:
    • lower_bound:
      • value: 1e-20
      • desc: Lower bound for the interval
      • min_value: 1e-30
      • max_value: inf
      • unit:
      • is_normalization: False
      • delta: 1e-21
      • free: True
    • upper_bound:
      • value: 100.0
      • desc: Upper bound for the interval
      • min_value: 1e-30
      • max_value: inf
      • unit:
      • is_normalization: False
      • delta: 10.0
      • free: True
    • K:
      • value: 1.0
      • desc: Normalization
      • min_value: None
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 0.1
      • free: False

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)
../_images/notebooks_Log_uniform_prior_8_0.png

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)

../_images/notebooks_Log_uniform_prior_10_0.png

\(\nu\)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)
../_images/notebooks_Log_uniform_prior_12_0.png