Truncated gaussian

[3]:

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

Description

[5]:

func.display()
  • description: A truncated Gaussian function defined on the interval between the lower_bound (a) and upper_bound (b)
  • formula: $\begin{split}f(x;\mu,\sigma,a,b)=\frac{\frac{1}{\sigma} \phi\left( \frac{x-\mu}{\sigma} \right)}{\Phi\left( \frac{b-\mu}{\sigma} \right) - \Phi\left( \frac{a-\mu}{\sigma} \right)}\\\phi\left(z\right)=\frac{1}{\sqrt{2 \pi}}\exp\left(-\frac{1}{2}z^2\right)\\\Phi\left(z\right)=\frac{1}{2}\left(1+erf\left(\frac{z}{\sqrt(2)}\right)\right)\end{split}$
  • parameters:
    • F:
      • value: 1.0
      • desc: Integral between -inf and +inf. Fix this to 1 to obtain a 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
    • lower_bound:
      • value: -1.0
      • desc: lower bound of gaussian, setting to -np.inf results in half normal distribution
      • min_value: None
      • max_value: None
      • unit:
      • is_normalization: False
      • delta: 0.1
      • free: True
    • upper_bound:
      • value: 1.0
      • desc: upper bound of gaussian setting to np.inf results in half normal distribution
      • 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)
../_images/notebooks_Truncated_gaussian_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_Truncated_gaussian_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_Truncated_gaussian_12_0.png