#+PROPERTY: header-args :session eta_deriv :kernel python :pandoc t :async yes :tangle no

* Setup
** Jupyter
#+begin_src jupyter-python
  %load_ext autoreload
  %autoreload 2
  %load_ext jupyter_spaces
#+end_src

#+RESULTS:

** Matplotlib
#+begin_src jupyter-python
  import matplotlib
  import matplotlib.pyplot as plt

  #matplotlib.use("TkCairo", force=True)
  %gui tk
  %matplotlib inline
  plt.style.use('ggplot')
#+end_src

#+RESULTS:

** Richard (old) HOPS
#+begin_src jupyter-python
  import hierarchyLib
  import hierarchyData
  import numpy as np

  from stocproc.stocproc import StocProc_FFT, StocProc_KLE
  import bcf
  from dataclasses import dataclass
  import scipy
  import scipy.misc
  import scipy.signal
#+end_src

#+RESULTS:

* Model Setup
Basic parameters.
#+begin_src jupyter-python
  ω_c = 0  # center of spect. dens
  σ = 1  # breadth BCF
  t_max = 1
  seed = 100
#+end_src

#+RESULTS:

** BCF
#+begin_src jupyter-python
   @dataclass
   class GaussBCF:
       σ: float
       ω_c: float

       def I(self, ω):
           return (
               np.exp(-(((ω - self.ω_c) / self.σ) ** 2) / 2)
               ,* 1
               / (np.sqrt(2 * np.pi) * self.σ)
           )

       def __call__(self, τ):
           return (
               np.exp(-(((τ - self.ω_c) / self.σ) ** 2) / 2)
               ,* 1
               / (np.sqrt(2 * np.pi) * self.σ)
           )

       def __bfkey__(self):
           return self.σ, self.ω_c


   @dataclass
   class GaussBCFD:
       α: GaussBCF

       def __call__(self, τ):
           # minus is important
           return self.α(τ)/self.α.σ**4 * (self.α.σ**2 - τ**2 + 2*τ*self.α.ω_c-self.α.ω_c**2)

       def __bfkey__(self):
           return self.α.__bfkey__()


  α = GaussBCF(σ, ω_c)
  α_td = GaussBCFD(α)
#+end_src

#+RESULTS:

*** Plot
#+begin_src jupyter-python
  %%space plot
  t = np.linspace(-t_max, t_max, 1000)
  ω = np.linspace(ω_c - 10, ω_c + 10, 1000)
  fig, axs = plt.subplots(2)
  axs[0].plot(t, np.real(α(t)))
  axs[0].plot(t, np.real(α_td(t)))
  #axs[1].plot(ω, α_td.I(ω))
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6440edd8e0> |
| <matplotlib.lines.Line2D | at | 0x7f6440eddca0> |
[[file:./.ob-jupyter/9aa5b8d02f8eefddb2d3408172d2dd9d039cd715.png]]
:END:

** Make stoch-procs
Normal.
#+begin_src jupyter-python
  η = StocProc_KLE(
      α,
      t_max,
      seed=seed,
      tol=1e-3
  )

  η_d = StocProc_KLE(
      α_td,
      t_max,
      seed=seed,
      tol=1e-3
  )
#+end_src

#+RESULTS:
: stocproc.method_kle - INFO - check 33 grid points
: stocproc.method_kle - INFO - calc_ac 3.504%, fredholm 6.936%, integr_intp 1.506%, spline 6.846%, calc_diff 51.646%, rest 29.561%
: stocproc.method_kle - INFO - auto ng SUCCESSFUL max diff 1.439e-04 < tol 1.000e-03 ng 33 num evec 3
: stocproc.method_kle - INFO - check 33 grid points
: stocproc.method_kle - INFO - calc_ac 9.515%, fredholm 4.745%, integr_intp 1.916%, spline 6.469%, calc_diff 49.757%, rest 27.598%
: stocproc.method_kle - INFO - auto ng SUCCESSFUL max diff 7.083e-04 < tol 1.000e-03 ng 33 num evec 3
: alpha_k is real
: alpha_k is real
#+RESULTS:

#+begin_src jupyter-python
  η.new_process(seed=seed)
  η_d.new_process(seed=seed)
  #plt.plot(η.t, np.real(η()), label="orig")
  plt.plot(η.t, np.real(η_d()))
  plt.plot(η.t, scipy.misc.derivative(η, η.t, dx=1e-6).real, label="deriv")
  plt.legend()
#+end_src

#+RESULTS:
:RESULTS:
: stocproc.stocproc - INFO - use fixed seed (100) for new process
: stocproc.stocproc - INFO - use fixed seed (100) for new process
: <matplotlib.legend.Legend at 0x7f6440e64640>
[[file:./.ob-jupyter/5d3b2c2f7a314432526a414fe86aa167976b1e7c.png]]
:END:


# Time Derivative.
# #+begin_src jupyter-python
#   Eta = StocProc_FFT(
#       α_td.I,
#       t_max,
#       α_td,
#       negative_frequencies=True,
#       seed=seed,
#       intgr_tol=1e-1,
#       intpl_tol=1e-1,
#       scale=1,
#   )
# #+end_src

# #+RESULTS:
# : 1b9c7948-872d-4205-9cac-6aa91fa67982