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

#+PROPERTY: header-args :session 01_zero_temp :kernel python :pandoc t :async yes

* Configuration and Setup
This will be tangled into the [[file:config.py][config file]] that can be used with the HOPS cli.
#+begin_src jupyter-python :results none :tangle config.py
  from hops.core.hierarchy_parameters import HIParams, HiP, IntP, SysP, ResultType
  from hops.core.hierarchyLib import HI
  from hops.util.bcf_fits import get_ohm_g_w
  from hops.util.truncation_schemes import TruncationScheme_Power_multi
  import hops.util.bcf
  import numpy as np
  import hops.util.matrixLib as ml
  from stocproc import StocProc_FFT

  wc = 5
  s = 1

  # The BCF fit
  bcf_terms = 6
  g, w = get_ohm_g_w(bcf_terms, s, wc)

  integration = IntP(t_max=30, t_steps=int(30 // 0.01))
  system = SysP(
      H_sys=0.5 * np.array([[-1, 0], [0, 1]]),
      L=0.5 * np.array([[0, 1], [1, 0]]),
      psi0=np.array([0, 1]),
      g=g,
      w=w,
      bcf_scale=0.8,
      T=0,
  )

  params = HIParams(
      SysP=system,
      IntP=integration,
      HiP=HiP(
          nonlinear=True,
          normalized_by_hand=True,
          result_type=ResultType.ZEROTH_AND_FIRST_ORDER,
          truncation_scheme=TruncationScheme_Power_multi.from_g_w(
              g=g, w=w, p=1, q=0.5, kfac=1.4
          ),
      ),
      Eta=StocProc_FFT(
          spectral_density=hops.util.bcf.OhmicSD_zeroTemp(
              s,
              1,
              wc,
          ),
          alpha=hops.util.bcf.OhmicBCF_zeroTemp(
              s,
              1,
              wc,
          ),
          t_max=integration.t_max,
          intgr_tol=1e-3,
          intpl_tol=1e-3,
          negative_frequencies=False,
      ),
      EtaTherm=None,
  )
#+end_src

* Hops Integration
We can use multiple avenues.

** Local Integration
#+begin_src vterm :term-name integration
hi 500 integrate
#+end_src

 #+RESULTS:
 :RESULTS:
 Linux ArLeenUX 5.15.11-zen1 x86_64
 14:45:17  up 2 days 18:10,  1 user,  load average: 1.55, 1.48, 1.44
 impure  ~/D/P/U/m/m/p/e/01_zero_temperature  hi 500 integrate
 Loading the configuration from config.py. This might take a while... /
 JobManager started on ArLeenUX:36931 (bytearray(b'HOPS36931'))
 [TET 6.88ms     [0.0c/s] TTG --                                      0.0%                                       ETA -- ORT --]

 /nix/store/h9pzzn81vrj2vzhavbjgv101yc52qpx0-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
 rning: num_threads could not be set, MKL / openblas not found
 warnings.warn("num_threads could not be set, MKL / openblas not found")
 /nix/store/h9pzzn81vrj2vzhavbjgv101yc52qpx0-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
 rning: num_threads could not be set, MKL / openblas not found
 warnings.warn("num_threads could not be set, MKL / openblas not found")
 /nix/store/h9pzzn81vrj2vzhavbjgv101yc52qpx0-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
 rning: num_threads could not be set, MKL / openblas not found
 warnings.warn("num_threads could not be set, MKL / openblas not found")
 /nix/store/h9pzzn81vrj2vzhavbjgv101yc52qpx0-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
 [TET 1.01s     [0.0c/s] TTG --                                       0.0%                                       ETA -- ORT --]
 res_q #0 0/s 0kB|rem.:492, done:0, failed:0, prog.:0
 w1:00:00:14 [5.3c/min] #1 - 2.72s [82.5c/s] [==============>                                                    ] TTG 00:00:10
 w2:00:00:14 [5.0c/min] #1 - 2.09s [82.4c/s] [===========>                                                       ] TTG 00:00:11
 w3:00:00:14 [5.1c/min] #1 - 2.20s [82.8c/s] [============>                                                      ] TTG 00:00:10
 w4:00:00:14 [5.0c/min] #1 - 1.97s [82.9c/s] [==========>                                                        ] TTG 00:00:11
 local res_q 0 285.1GB/s
 [TET 00:00:14  [18.4c/min] TTG 00:26:29                        0.8%                        ETA 20220117_15:12:02 ORT 00:26:43]
 res_q #0 2.122GB/s 28.72GB|rem.:484, done:4, failed:0, prog.:4
 ^Ccapi_return is NULL
 Call-back cb_f_in_zvode__user__routines failed.
 capi_return is NULL
 Call-back cb_f_in_zvode__user__routines failed.
 capi_return is NULL
 Call-back cb_f_in_zvode__user__routines failed.
 SystemExit, quit processing, reinsert current argument, please wait
 SystemExit, quit processing, reinsert current argument, please wait
 capi_return is NULL
 Call-back cb_f_in_zvode__user__routines failed.
 [TET 00:00:15  [18.4c/min] TTG 00:26:29                        0.8%                        ETA 20220117_15:12:03 ORT 00:26:44]
 res_q #0 1.976GB/s 28.72GB|rem.:484, done:4, failed:0, prog.:4

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


 HIServer  start at 2022-01-17 14:45:19.308956 | runtime 1.500e+01s
 HIServer total number of jobs  : 492
 w1:00:00:15 [5.3c/min] #1 - [TET-3.72s----[74.9c/s]-TTG>00:00:10           27.9%           ETA 20220117_14:45:45 ORT 00:00:13]
 w2:00:00:15 [5.0c/min] #1 - [TET-3.10s----[72.0c/s] TTG 00:00:11           22.3%           ETA 20220117_14:45:46 ORT 00:00:14]
 w3:00:00:15 [5.1c/min] #1 - [TET-3.21s----[73.9c/s]>TTG 00:00:11           23.7%           ETA 20220117_14:45:46 ORT 00:00:14]
 w4:00:00:15 [5.0c/min] #1 - [TET-2.97s----[73.6c/s] TTG 00:00:11           21.9%           ETA 20220117_14:45:46 ORT 00:00:13]
 local res_q 0 285.1GB/s
 impure  ~/D/P/U/m/m/p/e/01_zero_temperature  exit                                                                     18.9s
 :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
  hi 1000 start-server
#+end_src

#+RESULTS:
:RESULTS:
Linux ArLeenUX 5.15.11-zen1 x86_64
 16:34:02  up 2 days 19:58,  1 user,  load average: 1.08, 1.67, 2.52
 impure  ~/D/P/U/m/m/p/e/01_zero_temperature  hi 1000 start-server
Loading the configuration from config.py. This might take a while... /
JobManager started on ArLeenUX:42524 (bytearray(b'hierarchy'))
[TET-00:12:05--[43.6c/min]-TTG-0.00ms-------------------------100%-------------------------ETA-20220117_16:46:11-ORT-00:12:05]
res_q #0 14.84GB/s 10.51TB|rem.:0, done:500, failed:0, prog.:0

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


HIServer  start at 2022-01-17 16:34:05.075876 | runtime 7.280e+02s
HIServer total number of jobs  : 500
         |   processed   : 500
         |     succeeded : 500
         |     failed    : 0
         |     timing in sec: min 1.386e+01 | max 4.145e+01 | avr 2.478e+01
         |   not processed     : 0
         |     queried         : 0
         |     not queried yet : 0
:END:

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

** Client
Starting a client is trivial.

#+begin_src vterm :term-name local-client
  client localhost
#+end_src

#+RESULTS:
:RESULTS:
Linux ArLeenUX 5.15.11-zen1 x86_64
 16:34:08  up 2 days 19:58,  1 user,  load average: 1.07, 1.66, 2.51
 impure  ~/D/P/U/m/m/p/e/01_zero_temperature  client localhost
/nix/store/zwwf4gkrcx2ly273ivhn7a0bwwl0r9ki-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
rning: num_threads could not be set, MKL / openblas not found
  warnings.warn("num_threads could not be set, MKL / openblas not found")
/nix/store/zwwf4gkrcx2ly273ivhn7a0bwwl0r9ki-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
rning: num_threads could not be set, MKL / openblas not found
  warnings.warn("num_threads could not be set, MKL / openblas not found")
/nix/store/zwwf4gkrcx2ly273ivhn7a0bwwl0r9ki-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
rning: num_threads could not be set, MKL / openblas not found
  warnings.warn("num_threads could not be set, MKL / openblas not found")
/nix/store/zwwf4gkrcx2ly273ivhn7a0bwwl0r9ki-python3-3.9.9-env/lib/python3.9/site-packages/jobmanager/jobmanager.py:130: UserWa
rning: num_threads could not be set, MKL / openblas not found
  warnings.warn("num_threads could not be set, MKL / openblas not found")
w1:00:11:55 [2.0c/min] #23 - [TET 7.38s     [0.0c/s] TTG --                        0.0%                         ETA -- ORT --]
w2:00:11:55 [2.0c/min] #23 - [TET 4.46s     [0.0c/s] TTG --                        0.0%                         ETA -- ORT --]
w3:00:11:55 [2.1c/min] #23 - [TET 5.82s     [0.0c/s] TTG --                        0.0%                         ETA -- ORT --]
w4:00:11:55 [2.1c/min] #23 - [TET 9.32s     [0.0c/s] TTG --                        0.0%                         ETA -- ORT --]
local res_q 0 416.7GB/s
:END:

* Using the Data
** Jupyter Setup
#+begin_src jupyter-python :results none
  import matplotlib.pyplot as plt
  import numpy as np
  import utilities as ut
#+end_src


** Load the Data
#+begin_src jupyter-python :results none
  from hopsflow import hopsflow, util
  from hops.core.hierarchyLib import HI
#+end_src

Now we read the trajectory data.
#+begin_src jupyter-python
  class result:
      with HI(params, 500).get_data(read_only=True) as hd:
          N = hd.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]
  result.N
#+end_src

#+RESULTS:
: 1000

** Calculate System Energy
Simple sanity check.
#+begin_src jupyter-python
  _, e_sys, σ_e_sys = util.operator_expectation_ensemble(
        iter(result.ψ),
        system.H_sys,
        result.N,
        params.HiP.nonlinear,
        save="./results/energy.npy"
    )

  plt.errorbar(result.τ, e_sys.real, yerr=σ_e_sys.real, ecolor="yellow")
#+end_src

#+RESULTS:
:RESULTS:
: 100% 999/999 [00:00<00:00, 1645.43it/s]
: <ErrorbarContainer object of 3 artists>
[[file:./.ob-jupyter/bd7fe1b1f16f9711d71689389818fa54480dba99.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.H_sys)[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].real, e_sys[-1].real
#+end_src

#+RESULTS:
| 0.5 | -0.44770384926040235 |

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

#+RESULTS:
: 0.9477038492604024

We do start in the state.
#+begin_src jupyter-python
  system.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 :results none
  hf_system = hopsflow.SystemParams(
      system.L, system.g, system.w, system.bcf_scale, params.HiP.nonlinear
  )
#+end_src


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)
  with ut.hiro_style():
      plt.plot(result.τ, first_flow)
#+end_src

#+RESULTS:
[[file:./.ob-jupyter/c7984b39bab2dfd43f7a9f95bdf0badd202394a0.svg]]

And now for all trajectories.
#+begin_src jupyter-python
  full_flow = hopsflow.heat_flow_ensemble(
      result.ψ, result.ψ_1, hf_system, result.N, every=result.N // 10, save="results/flow.npy"
  )

  with ut.hiro_style():
      _, ax = ut.plot_convergence(result.τ, full_flow, transform=lambda y: -y)
      ax.legend()
#+end_src

#+RESULTS:
:RESULTS:
: 100% 999/999 [00:01<00:00, 503.21it/s]
[[file:./.ob-jupyter/c998467651c2660a92b64ec40f17672cbd6f16aa.svg]]
:END:

We can integrate the energy change in the bath:
#+begin_src jupyter-python
  e_bath = util.integrate_array(-full_flow[-1][1], result.τ)
  plt.plot(result.τ, e_bath)
#+end_src

#+RESULTS:
:RESULTS:
| <matplotlib.lines.Line2D | at | 0x7f700280b220> |
[[file:./.ob-jupyter/1ef90eca2ed89295be26af97745a08d32a9aa037.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).real
  with ut.hiro_style():
      plt.plot(result.τ, e_int)
#+end_src

#+RESULTS:
[[file:./.ob-jupyter/10f25f6b2f73d65ae8fb7775fef8dce0379fd08e.svg]]

And then from first principles:
#+begin_src jupyter-python
  _, e_int_ex, σ_e_int_ex = hopsflow.interaction_energy_ensemble(result.ψ, result.ψ_1, hf_system, result.N)
  with ut.hiro_style():
      plt.errorbar(result.τ, e_int_ex, yerr=σ_e_int_ex, ecolor="yellow")
#+end_src

#+RESULTS:
:RESULTS:
: 100% 999/999 [00:02<00:00, 406.62it/s]
[[file:./.ob-jupyter/d14fe1b04f0527eec44c69990195936cdcbbd965.svg]]
:END:

And both together:
#+begin_src jupyter-python
  with ut.hiro_style():
       plt.errorbar(result.τ, e_int_ex, yerr=σ_e_int_ex, ecolor="yellow")
       plt.plot(result.τ, e_int)
#+end_src

#+RESULTS:
[[file:./.ob-jupyter/7cebf22e2e864368752a1919b342b685fcdd1303.svg]]