master-thesis/python/energy_flow_proper/01_zero_temperature/notebook.org

#+PROPERTY: header-args :session zero_temp_new :kernel python :pandoc t

* Configuration and Setup
The main process configuration is to be found [[file:stg.py][here]].

** Stochastic Processes
We then proceed to initialize the stochastic processes.

#+begin_src vterm
  python ../hops/sp.py -s stg.py
#+end_src

#+RESULTS:
:RESULTS:
Linux ArLeenUX 5.14.15-zen1 x86_64
 16:04:51  up 1 day  4:30,  2 users,  load average: 0.68, 0.52, 0.89
 impure  ~/D/P/U/m/m/p/e/01_zero_temperature  python ../hops/sp.py -s stg.py
StocProc found in database 'SPCache' at '.'
:END:

The stochastic process is initialized and cached in ~./SPCache~.

* Hops Integration
We can use multiple avenues.

** Local Integration
#+begin_src vterm :term-name integration
  python ../hops/hi.py -s stg.py
#+end_src

#+RESULTS:
:RESULTS:
Linux ArLeenUX 5.14.14-zen1 x86_64
 16:06:15  up 3 days 23:48,  1 user,  load average: 1.07, 1.23, 1.22
 impure  ~/D/P/U/m/m/p/e/01_zero_temperature  python ../hops/hi.py -s stg.py
run integrate
init Hi class, use 464 equation
is up event is False
wait ...
  [in server process] add args to server ...
  [in server process] befor bring him up
JobManager started on ArLeenUX:46870 (bytearray(b'HOPS46870'))
hi server is up
  [in server process] set is_up
is up event is now True
[TET 12.69ms     [0.0c/s] TTG --                      0.0%

/nix/store/5v3326rzsryzdkk2q5kimqvf0i20wvzv-python3-3.9.4-env/lib/python3.9/site
anager/jobmanager.py:130: UserWarning: num_threads could not be set, MKL / openb
  warnings.warn("num_threads could not be set, MKL / openblas not found")
/nix/store/5v3326rzsryzdkk2q5kimqvf0i20wvzv-python3-3.9.4-env/lib/python3.9/site
anager/jobmanager.py:130: UserWarning: num_threads could not be set, MKL / openb
  warnings.warn("num_threads could not be set, MKL / openblas not found")
/nix/store/5v3326rzsryzdkk2q5kimqvf0i20wvzv-python3-3.9.4-env/lib/python3.9/site
anager/jobmanager.py:130: UserWarning: num_threads could not be set, MKL / openb
  warnings.warn("num_threads could not be set, MKL / openblas not found")
/nix/store/5v3326rzsryzdkk2q5kimqvf0i20wvzv-python3-3.9.4-env/lib/python3.9/site
[TET 1.01s     [0.0c/s] TTG --                       0.0%
res_q #0 0/s 0kB|rem.:500, done:0, failed:0, prog.:0
w1:00:00:46 [14.7c/min] #11 - 2.25s [245.0c/s] [==================>
w2:00:00:46 [15.0c/min] #11 - 1.90s [241.6c/s] [===============>
w1:00:00:47 [14.7c/min] #11 - 3.25s [255.6c/s] [============================>
   ] TTG 1.00s4.8c/min] #11 - 1.33s [221.7c/s] [=========>
w2:00:00:47 [15.0c/min] #11 - 2.91s [243.3c/s] [========================>
   ] TTG 2.00s [57.3c/min] TTG 00:07:58        8.8%        ETA 20211110_16:15:03
w3:00:00:47 [14.7c/min] #11 - 1.67s [264.0c/s] [==============>
   ] TTG 3.00sGB/s 315.9GB|rem.:452, done:44, failed:0, prog.:4
w4:00:00:47 [14.8c/min] #11 - 2.33s [231.9c/s] [==================>
w1:00:00:48 [14.8c/min] #12 - 292.64ms [160.6c/s] [=>
   ] TTG 6.00s326.1GB/s
w2:00:00:48 [15.0c/min] #11 - 3.91s [231.6c/s] [==============================>
   ] TTG 1.00s [57.3c/min] TTG 00:07:58        8.8%        ETA 20211110_16:15:04
w3:00:00:48 [14.7c/min] #11 - 2.67s [238.4c/s] [=====================>
w1:00:08:43 [15.9c/min] #126 - [TET 996.21ms     [0.0c/s] TTG --      0.0%      ETA -- ORT --]
w2:00:08:43 [15.7c/min] #125 - [TET 2.26s     [0.0c/s] TTG --       0.0%        ETA -- ORT --]
w3:00:08:43 [15.5c/min] #124 - [TET 1.69s     [0.0c/s] TTG --       0.0%        ETA -- ORT --]
w4:00:08:43 [16.5c/min] #125 - [TET 667.44ms     [0.0c/s] TTG --      0.0%      ETA -- ORT --]
local res_q 0 344GB/s
,********************************.00ms---------100%---------ETA-20211110_16:15:01-ORT-00:08:43]
,********************************0, done:500, failed:0, prog.:0
,**    the client has finished early!  stop the server
,********************************
,********************************
[TET-00:08:44-----[1.0c/s]-TTG-0.00ms---------100%---------ETA-20211110_16:15:02-ORT-00:08:44]
res_q #0 7.918GB/s 3.506TB|rem.:0, done:500, failed:0, prog.:0
  [in server process] server has joined!

############## in JM SERVER EXIT


HI_Server  start at 2021-11-10 16:06:18.129421 | runtime 5.260e+02s
HI_Server total number of jobs  : 500
          |   processed   : 500
          |     succeeded : 500
          |     failed    : 0
          |     timing in sec: min 2.973e+00 | max 7.906e+00 | avr 4.164e+00
          |   not processed     : 0
          |     queried         : 0
          |     not queried yet : 0
    ,* has joined
server process is not running anymore (exit with 0)
:END:

And there we go. It is better to run the above command in a
vterm-session.

** Remote/Distributed Integration
We start the server locally.
#+begin_src vterm :term-name local-server
  python ../hops/hi.py -s stg.py server
#+end_src

#+RESULTS:
:RESULTS:
Linux ArLeenUX 5.14.15-zen1 x86_64
 16:05:44  up 1 day  4:31,  2 users,  load average: 0.80, 0.57, 0.89
 impure  ~/D/P/U/m/m/p/e/01_zero_temperature  python ../hops/hi.py -s stg.py server
run server
init Hi class, use 464 equation
JobManager started on ArLeenUX:35254 (bytearray(b'SBM2'))
hi server is running
[TET-00:03:56-----[2.4c/s]-TTG-0.00ms---------100%---------ETA-20211112_16:09:44-ORT-00:03:56]
res_q #0 16.58GB/s 3.506TB|rem.:0, done:500, failed:0, prog.:0

############## in JM SERVER EXIT


HI_Server  start at 2021-11-12 16:05:47.695696 | runtime 2.380e+02s
HI_Server total number of jobs  : 500
          |   processed   : 500
          |     succeeded : 500
          |     failed    : 0
          |     timing in sec: min 3.320e+00 | max 6.207e+00 | avr 4.835e+00
          |   not processed     : 0
          |     queried         : 0
          |     not queried yet : 0
:END:

And jack in with a remote client. In this case my box at home.

* Using the Data
** Jupyter Setup
#+begin_src jupyter-python
  import matplotlib.pyplot as plt
  import numpy as np
#+end_src

#+RESULTS:

** Check the Freshness of the Data
This doesn't check for modifications in this file though!
#+begin_src jupyter-python
  from deps import deps

  deps.report()
#+end_src

#+RESULTS:
: Is fresh: True
: Overall Hash: bfe5a79a9c7e767f4b470f1096cbbf22d05e3977

~True~ means that no important code has changed. In this case it even
checks if we have all the samples.

** Load the Data
Stghelper seems to be what we want.
#+begin_src jupyter-python
  import stg_helper
  import stg
  import hopsflow
  from hopsflow import util
#+end_src

#+RESULTS:

Now let's load the system parameters.
#+begin_src jupyter-python
  system_params = stg_helper.get_system_param(stg)
  system_params
#+end_src

#+RESULTS:
#+begin_example
  H_dynamic : []
      H_sys : Operator with format 'coo' and shape(2, 2)
    (0, 0)      -0.5
    (1, 1)      0.5
          L : Operator with format 'coo' and shape(2, 2)
    (0, 1)      0.5
    (1, 0)      0.5
  bcf_scale : 0.8
          g : [-0.06469402-0.02291455j -0.51837826-0.63817493j -0.9180341 -0.03207301j
    0.79032868-3.79162312j  0.92537272+5.45668527j  7.74372319-0.97260702j]
       psi0 : [0 1]
          w : [ 0.33112135 +0.0369207j   1.4655583  +0.35463741j
   20.83418848+27.9612112j   3.94583654 +1.66419407j
   13.81649632+13.01348981j  8.09528316 +5.28092745j]
  --- extra info ---
          T : 0.0
   T_method : stoc_pot
    gw_info : None
     len_gw : None
#+end_example

Now we read the trajectory data.
#+begin_src jupyter-python
  class result:
      with stg_helper.get_hierarchy_data(stg, read_only=True) as hd:
          N = hd.get_samples()
          τ = hd.get_time()
          ρ = hd.get_rho_t()
          ψ_1 = np.array(hd.aux_states)[0:N]
          ψ = np.array(hd.stoc_traj)[0:N]
#+end_src

#+RESULTS:

** Calculate System Energy
Simple sanity check.
#+begin_src jupyter-python
  e_sys = util.operator_expectation(result.ρ, system_params.H_sys.todense())
  plt.plot(result.τ, e_sys)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3bcd61c0> |
[[file:./.ob-jupyter/a7742fc7d6826fdc3a3005e8f06e017744c80631.svg]]
:END:

The energy bleeds out of the system. We don't reach the steady state
yet. Also we don't loose all the energy.

The energy eigenvalues of the system are.
#+begin_src jupyter-python
  np.linalg.eig(system_params.H_sys.todense())[0]
#+end_src

#+RESULTS:
: array([-0.5,  0.5])

The begin and and values of the system energy expectation are.
#+begin_src jupyter-python
  e_sys[0], e_sys[-1]
#+end_src

#+RESULTS:
| 0.5 | -0.44815376641059734 |

And the total energy lost is:
#+begin_src jupyter-python
  e_sys[0] - e_sys[-1]
#+end_src

#+RESULTS:
: 0.9481537664105973

We do start in the state.
#+begin_src jupyter-python
  system_params.psi0
#+end_src

#+RESULTS:
: array([0, 1])

** Calculate the Heat Flow
Now let's calculate the heatflow. In this simple case it is engouh to
know the first hierarchy states.

First we set up some parameter objects for the alogrithm.
#+begin_src jupyter-python
  hf_system = hopsflow.SystemParams(
      system_params.L.todense(), stg.__g, stg.__w, stg.__bcf_scale, stg.__HI_nonlinear
  )
#+end_src

#+RESULTS:

Now we can apply our tooling to one trajectory for testing.
#+begin_src jupyter-python
  hf_sample_run = hopsflow.HOPSRun(result.ψ[0], result.ψ_1[0], hf_system)
  first_flow = hopsflow.flow_trajectory_coupling(hf_sample_run, hf_system)
  plt.plot(result.τ, first_flow)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3bcb9fa0> |
[[file:./.ob-jupyter/efdf662d48ebc0cfa16c163932cc45b205466fba.svg]]
:END:

And now for all trajectories.
#+begin_src jupyter-python
  full_flow = hopsflow.heat_flow_ensemble(result.ψ, result.ψ_1, hf_system, result.N)
  plt.plot(result.τ, full_flow)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3bfee0d0> |
[[file:./.ob-jupyter/3850d1b72e60f2311045d24399e69ba792255439.svg]]
:END:

We can integrate the energy change in the bath:
#+begin_src jupyter-python
  e_bath = util.integrate_array(-full_flow, result.τ)
  plt.plot(result.τ, e_bath)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3c3119a0> |
[[file:./.ob-jupyter/db755c0365ed1377a36986466fa4e617fef9ebdd.svg]]
:END:

** Calculate the Interaction Energy
First we calculate it from energy conservation.
#+begin_src jupyter-python
  e_int = 1/2 - e_sys - e_bath
  plt.plot(result.τ, e_int)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3c376ee0> |
[[file:./.ob-jupyter/97d391819a65d8e5bf37e1c5b5eaba576667f120.svg]]
:END:

And then from first principles:
#+begin_src jupyter-python
  e_int_ex = hopsflow.interaction_energy_ensemble(result.ψ, result.ψ_1, hf_system, result.N)
  plt.plot(result.τ, e_int_ex)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3c1cb880> |
[[file:./.ob-jupyter/86e89b1f1f342f53929294909d1b6834f81e9758.svg]]
:END:

And both together:
#+begin_src jupyter-python
  plt.plot(result.τ, e_int)
  plt.plot(result.τ, e_int_ex)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3bf153a0> |
[[file:./.ob-jupyter/2f62c356fed1d7133aa3ef68bb29b3efca86b58e.svg]]
:END:


** Scratch
So the ~G~ and ~W~ do function as expected
#+begin_src jupyter-python
  t = np.linspace(0, stg.t_max, 100)
  #plt.plot(t, stg.__bcf(t).real)
  plt.plot(t, stg.__bcf(t).imag)
  plt.plot(t, hopsflow.util.α_apprx(t, stg.__g, stg.__w).imag)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f6a3c04a5e0> |
[[file:./.ob-jupyter/99df85a9e29da5768f796ed82ac9827df688e8d9.svg]]
:END:

#+begin_src jupyter-python
  import os

  path = os.path.dirname(hopsflow.__file__)
  path
#+end_src

#+RESULTS:
: /home/hiro/Documents/Projects/UNI/master/masterarb/python/energy_flow_proper/hopsflow

* Update Dependency Hash
When we're done we update the dependency hash. This helps us to check
if we have to recompute anything later on.
#+begin_src jupyter-python
  deps.write_hash()
  deps.get_hash()[0]
#+end_src

#+RESULTS:
: bfe5a79a9c7e767f4b470f1096cbbf22d05e3977