├── .gitattributes
├── .github
    └── workflows
    │   ├── build_test.yml
    │   ├── pypi_publish.yml
    │   └── pypi_test.yml
├── .readthedocs.yaml
├── LICENSE
├── README.md
├── docs
    ├── Makefile
    ├── _build
    │   ├── doctrees
    │   │   ├── environment.pickle
    │   │   ├── index.doctree
    │   │   ├── modules.doctree
    │   │   └── pychi.doctree
    │   └── html
    │   │   ├── _modules
    │   │       ├── index.html
    │   │       └── pychi
    │   │       │   ├── light.html
    │   │       │   ├── materials.html
    │   │       │   ├── models.html
    │   │       │   └── solvers.html
    │   │   ├── _sources
    │   │       ├── index.rst.txt
    │   │       ├── modules.rst.txt
    │   │       └── pychi.rst.txt
    │   │   ├── _static
    │   │       ├── basic.css
    │   │       ├── css
    │   │       │   ├── badge_only.css
    │   │       │   ├── fonts
    │   │       │   │   ├── Roboto-Slab-Bold.woff
    │   │       │   │   ├── Roboto-Slab-Bold.woff2
    │   │       │   │   ├── Roboto-Slab-Regular.woff
    │   │       │   │   ├── Roboto-Slab-Regular.woff2
    │   │       │   │   ├── fontawesome-webfont.eot
    │   │       │   │   ├── fontawesome-webfont.svg
    │   │       │   │   ├── fontawesome-webfont.ttf
    │   │       │   │   ├── fontawesome-webfont.woff
    │   │       │   │   ├── fontawesome-webfont.woff2
    │   │       │   │   ├── lato-bold-italic.woff
    │   │       │   │   ├── lato-bold-italic.woff2
    │   │       │   │   ├── lato-bold.woff
    │   │       │   │   ├── lato-bold.woff2
    │   │       │   │   ├── lato-normal-italic.woff
    │   │       │   │   ├── lato-normal-italic.woff2
    │   │       │   │   ├── lato-normal.woff
    │   │       │   │   └── lato-normal.woff2
    │   │       │   └── theme.css
    │   │       ├── doctools.js
    │   │       ├── documentation_options.js
    │   │       ├── file.png
    │   │       ├── jquery-3.4.1.js
    │   │       ├── jquery.js
    │   │       ├── js
    │   │       │   ├── badge_only.js
    │   │       │   ├── html5shiv-printshiv.min.js
    │   │       │   ├── html5shiv.min.js
    │   │       │   └── theme.js
    │   │       ├── language_data.js
    │   │       ├── minus.png
    │   │       ├── plus.png
    │   │       ├── pygments.css
    │   │       ├── searchtools.js
    │   │       ├── underscore-1.3.1.js
    │   │       └── underscore.js
    │   │   ├── genindex.html
    │   │   ├── index.html
    │   │   ├── modules.html
    │   │   ├── objects.inv
    │   │   ├── py-modindex.html
    │   │   ├── pychi.html
    │   │   ├── search.html
    │   │   └── searchindex.js
    ├── conf.py
    ├── index.rst
    ├── make.bat
    ├── modules.rst
    ├── pychi.rst
    ├── readme_link.rst
    └── requirements.txt
├── examples
    ├── Cascaded Nonlinearities
    │   ├── cascaded.png
    │   ├── effective_index.npy
    │   └── pychi_cascaded.py
    ├── LiNb
    │   ├── Experimental_vs_simulation_LiNb.png
    │   ├── exp_LiNb.mat
    │   ├── n_eff_data_LiNb.npy
    │   └── pychi_LiNb_exp_vs_sim.py
    ├── QPM
    │   ├── effective_index.npy
    │   └── pychi_QPM.py
    ├── SPM
    │   ├── frequency_propagation.png
    │   ├── pychi_spm_validation.py
    │   └── time_propagation.png
    ├── SiN
    │   ├── Experimental_vs_simulation_SiN.png
    │   ├── exp_SiN.mat
    │   ├── n_eff_data_SiN.npy
    │   └── pychi_SiN_exp_vs_sim.py
    ├── effective_index.npy
    └── pychi_example.py
├── pyproject.toml
├── requirements.txt
└── src
    └── pychi
        ├── __init__.py
        ├── light.py
        ├── materials.py
        ├── models.py
        └── solvers.py


/.gitattributes:
--------------------------------------------------------------------------------
1 | # Auto detect text files and perform LF normalization
2 | * text=auto
3 | 


--------------------------------------------------------------------------------
/.github/workflows/build_test.yml:
--------------------------------------------------------------------------------
 1 | # This workflow is manually triggered and makes a build test of the package.
 2 | 
 3 | name: Build Python Package
 4 | 
 5 | on: workflow_dispatch
 6 | 
 7 | permissions:
 8 |   contents: read
 9 | 
10 | jobs:
11 |   deploy:
12 | 
13 |     runs-on: ubuntu-latest
14 | 
15 |     steps:
16 |     - uses: actions/checkout@v3
17 |     - name: Set up Python
18 |       uses: actions/setup-python@v3
19 |       with:
20 |         python-version: '3.x'
21 |     - name: Install dependencies
22 |       run: |
23 |         python -m pip install --upgrade pip
24 |         python -m pip install --upgrade build
25 |         python -m pip install --upgrade twine
26 |     - name: Edit Toml
27 |       uses: sandstromviktor/toml-editor@2.0.0
28 |       with:
29 |         file: "pyproject.toml"
30 |         key: "project.version"
31 |         value: 0.0.0
32 |     - name: Build package
33 |       run: python -m build
34 | 


--------------------------------------------------------------------------------
/.github/workflows/pypi_publish.yml:
--------------------------------------------------------------------------------
 1 | # This workflow will upload a Python Package using Twine when a release is created
 2 | # For more information see: https://docs.github.com/en/actions/automating-builds-and-tests/building-and-testing-python#publishing-to-package-registries
 3 | 
 4 | name: Upload Python Package
 5 | 
 6 | #on: workflow_dispatch
 7 | on:
 8 |   release:
 9 |     types: [published]
10 | 
11 | permissions:
12 |   contents: read
13 | 
14 | jobs:
15 |   deploy:
16 | 
17 |     runs-on: ubuntu-latest
18 | 
19 |     steps:
20 |     - uses: actions/checkout@v3
21 |     - name: Set up Python
22 |       uses: actions/setup-python@v3
23 |       with:
24 |         python-version: '3.x'
25 |     - name: Install dependencies
26 |       run: |
27 |         python -m pip install --upgrade pip
28 |         python -m pip install --upgrade build
29 |         python -m pip install --upgrade twine
30 |     - name: Get version
31 |       id: get_version      
32 |       run: echo "VERSION=$(echo $GITHUB_REF | cut -d / -f 3)" >> $GITHUB_OUTPUT
33 |     - name: Edit Toml
34 |       uses: sandstromviktor/toml-editor@2.0.0
35 |       with:
36 |         file: "pyproject.toml"
37 |         key: "project.version"
38 |         value: ${{ steps.get_version.outputs.VERSION }}
39 |     - name: Build package
40 |       run: python -m build
41 |     - name: Publish package
42 |       run: python -m twine upload dist/* --u __token__ --p ${{ secrets.PYPI_API_TOKEN }}
43 | 


--------------------------------------------------------------------------------
/.github/workflows/pypi_test.yml:
--------------------------------------------------------------------------------
 1 | # This workflow will upload a Python Package when triggered. Test file for the automatic release action.
 2 | # For more information see: https://docs.github.com/en/actions/automating-builds-and-tests/building-and-testing-python#publishing-to-package-registries
 3 | 
 4 | name: Upload Python Package
 5 | 
 6 | on: workflow_dispatch
 7 | #on:
 8 | #  release:
 9 | #    types: [published]
10 | 
11 | permissions:
12 |   contents: read
13 | 
14 | jobs:
15 |   deploy:
16 | 
17 |     runs-on: ubuntu-latest
18 | 
19 |     steps:
20 |     - uses: actions/checkout@v3
21 |     - name: Set up Python
22 |       uses: actions/setup-python@v3
23 |       with:
24 |         python-version: '3.x'
25 |     - name: Install dependencies
26 |       run: |
27 |         python -m pip install --upgrade pip
28 |         python -m pip install --upgrade build
29 |         python -m pip install --upgrade twine
30 |     - name: Get version
31 |       id: get_version      
32 |       run: echo "VERSION=$(echo $GITHUB_REF | cut -d / -f 3)" >> $GITHUB_OUTPUT
33 |     - name: Edit Toml
34 |       uses: sandstromviktor/toml-editor@2.0.0
35 |       with:
36 |         file: "pyproject.toml"
37 |         key: "project.version"
38 |         #value: ${{ steps.get_version.outputs.VERSION }}
39 |         value: 0.0.13
40 |     - name: Build package
41 |       run: python -m build
42 |     - name: Publish package
43 |       run: python -m twine upload dist/* --u __token__ --p ${{ secrets.PYPI_API_TOKEN }}
44 | 


--------------------------------------------------------------------------------
/.readthedocs.yaml:
--------------------------------------------------------------------------------
 1 | # .readthedocs.yaml
 2 | # Read the Docs configuration file
 3 | # See https://docs.readthedocs.io/en/stable/config-file/v2.html for details
 4 | 
 5 | # Required
 6 | version: 2
 7 | 
 8 | # Set the version of Python and other tools you might need
 9 | build:
10 |   os: ubuntu-22.04
11 |   tools:
12 |     python: "3.11"
13 |     # You can also specify other tool versions:
14 |     # nodejs: "19"
15 |     # rust: "1.64"
16 |     # golang: "1.19"
17 | 
18 | # Build documentation in the docs/ directory with Sphinx
19 | sphinx:
20 |    configuration: docs/conf.py
21 | 
22 | # If using Sphinx, optionally build your docs in additional formats such as PDF
23 | # formats:
24 | #    - pdf
25 | 
26 | # Optionally declare the Python requirements required to build your docs
27 | python:
28 |    install:
29 |    - requirements: docs/requirements.txt
30 | 
31 | 
32 | submodules:
33 |   include: all
34 | 


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
 1 | MIT License
 2 | 
 3 | Copyright (c) 2023 Ultrafast Microphotonics Group, DESY
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
  1 | # pychi
  2 | 
  3 | A Python package for simulating the propagation of optical pulses in nonlinear materials.
  4 | 
  5 | ## Capabilities
  6 | 
  7 | *pychi* is aimed at simulating the propagation of short pulses in nonlinear media and capturing as much physics as possible. It is based on a unidirectional propagation model, which stays valid even for sub-cycle optical pulses. In particular, this propagation model accounts for
  8 | - Full frequency dependence of the effective refractive index
  9 | - Quadratic nonlinear interactions (sum- and difference-frequency generation)
 10 | - Cubic nonlinear interactions (triple sum-frequency generation, self-phase modulation, conjugated Kerr term)
 11 | - Raman scattering
 12 | - Self-steepening
 13 | - Frequency-dependence of the nonlinear coefficients
 14 | - z-dependence of the effective refractive index and nonlinear coefficients (permitting poling to be simulated)
 15 | 
 16 | The package is built to be as user-friendly as possible, providing a relatively high-level interface for the user while still allowing for physically intricate simulation cases. It leverages a custom-made order 5 solver, although more classical solvers (such as the RK4IP) have also been implemented for completeness and versatility.
 17 | 
 18 | ## Installation
 19 | 
 20 | First, make sure pip is up-to-date using
 21 | ```
 22 | pip install --upgrade pip
 23 | ```
 24 | 
 25 | On Windows, install the package using
 26 | ```
 27 | pip install pychi
 28 | ```
 29 | 
 30 | On Mac, one might have to first run
 31 | ```
 32 | conda install -c conda-forge pyfftw
 33 | ```
 34 | due to some OS specificities in pyFFTW installation.
 35 | 
 36 | Then, one should be able to install pychi normally using
 37 | ```
 38 | pip install pychi
 39 | ```
 40 | 
 41 | 
 42 | ## Documentation
 43 | 
 44 | The documentation is available and best viewed under
 45 | https://pychi.readthedocs.io/en/latest/
 46 | This documentation has been automatically generated using SPHINX, and is still a work in progress. Do not hesitate to contact us for any needed clarifications and examples.
 47 | 
 48 | ## Example
 49 | 
 50 | Here is a typical example of the use of pychi to simulate the propagation of a short optical pulse in a nonlinear waveguide exhibiting both cubic and quadratic nonlinearities.
 51 | 
 52 | ```python
 53 | # -*- coding: utf-8 -*-
 54 | """
 55 | Created on Mon Feb 28 15:31:47 2022
 56 | The waveguide/fiber parameters are first provided, and a Waveguide instance
 57 | is created. Then, the pulse parameters are used to create a Light object.
 58 | A physical model is then chosen, taking into account different nonlinear
 59 | interactions based on the user choice. Finally, a solver is instantiated
 60 | and computes the propagation of the pulse in the waveguide with the chosen
 61 | nonlinear interactions.
 62 | @author: voumardt
 63 | """
 64 | import matplotlib.pyplot as plt
 65 | import numpy as np
 66 | from scipy.constants import c
 67 | 
 68 | import pychi
 69 | 
 70 | 
 71 | """
 72 | User parameters
 73 | """
 74 | ### Simulation
 75 | t_pts = 2**15
 76 | 
 77 | ### Light
 78 | pulse_duration = 100e-15
 79 | pulse_wavelength = 1.56e-06
 80 | pulse_energy = 1e-9
 81 | 
 82 | ### Waveguide
 83 | wg_length = 0.001
 84 | wg_chi_2 = 1.1e-12
 85 | wg_chi_3 = 3.4e-21
 86 | wg_a_eff = 1e-12
 87 | wg_freq, wg_n_eff = np.load('effective_index.npy')
 88 | # wg_n_eff is the effective dispersion of the waveguide considered, sampled on the grid wg_freq
 89 | 
 90 | 
 91 | """
 92 | Nonlinear propagation
 93 | """
 94 | ### Prepare waveguide
 95 | waveguide = pychi.materials.Waveguide(wg_freq, wg_n_eff, wg_chi_2, wg_chi_3,
 96 |                                 wg_a_eff, wg_length, t_pts=t_pts)
 97 | # Additional options:
 98 | # wg_n_eff can be a 2 dimensional array, with first dimension the wavelength dependence
 99 | # and second dimension the z dependence.
100 | #
101 | # chi2 and chi3 can be callables, returning a z dependent value. Alternatively, they
102 | # can be defined as one dimensional arrays describing their z dependence, or
103 | # two dimensional arrays describing their z and frequency dependence. They
104 | # can also be callables of (z, freq).
105 | #
106 | # One can use waveguide.set_gamma(gamma) or waveguide.set_n2(n2) to provide a
107 | # nonlinear coefficient or nonlinear refractive index and overwrite chi3.
108 | #
109 | # Check documentation for more options and details.
110 | 
111 | 
112 | ### Prepare input pulse
113 | pulse = pychi.light.Sech(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
114 | # Other available pulse shapes:
115 | # pulse = pychi.light.Gaussian(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
116 | # pulse = pychi.light.Cw(waveguide, pulse_average_power, pulse_wavelength)
117 | # pulse = pychi.light.Arbitrary(waveguide, pulse_frequency_axis, pulse_electric_field, pulse_energy)
118 | 
119 | 
120 | ### Prepare model
121 | model = pychi.models.SpmChi2Chi3(waveguide, pulse)
122 | # Other models available:
123 | # model = pychi.models.Spm(waveguide, pulse)
124 | # model = pychi.models.Chi2(waveguide, pulse)
125 | # model = pychi.models.Chi3(waveguide, pulse)
126 | # model = pychi.models.SpmChi2(waveguide, pulse)
127 | # model = pychi.models.SpmChi3(waveguide, pulse)
128 | # model = pychi.models.Chi2Chi3(waveguide, pulse)
129 | 
130 | 
131 | ### Prepare solver, solve
132 | solver = pychi.solvers.Solver(model)
133 | solver.solve()
134 | 
135 | 
136 | """
137 | Plots
138 | """
139 | pulse.plot_propagation()
140 | # Results can also be accessed via pulse.z_save, pulse.freq, pulse.spectrum, pulse.waveform
141 | # The refractive index and GVD can be seen with waveguide.plot_refractive_index()
142 | 
143 | 
144 | ```
145 | 
146 | Typical propagation results using the above script would look as follows:
147 | ![grafik](https://user-images.githubusercontent.com/97957751/222731448-ff856390-4325-4f39-8817-f508898e2308.png)
148 | 
149 | Check the examples folder for some specific cases and validation against experimental data.
150 | 
151 | ## Contacts
152 | 
153 | pychi has been developped at DESY by the Ultrafast Microphotonics group. If you use it for publications, please cite the associated paper
154 | https://doi.org/10.1063/5.0135252
155 | 
156 | If you have any questions, remarks, contributions, do not hesitate to contact us at:
157 | pychi@desy.de
158 | or here on GitHub.
159 | 


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/docs/Makefile:
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 1 | # Minimal makefile for Sphinx documentation
 2 | #
 3 | 
 4 | # You can set these variables from the command line, and also
 5 | # from the environment for the first two.
 6 | SPHINXOPTS    ?=
 7 | SPHINXBUILD   ?= sphinx-build
 8 | SOURCEDIR     = .
 9 | BUILDDIR      = _build
10 | 
11 | # Put it first so that "make" without argument is like "make help".
12 | help:
13 | 	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
14 | 
15 | .PHONY: help Makefile
16 | 
17 | # Catch-all target: route all unknown targets to Sphinx using the new
18 | # "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
19 | %: Makefile
20 | 	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
21 | 


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/docs/_build/html/_modules/index.html:
--------------------------------------------------------------------------------
 1 | <!DOCTYPE html>
 2 | <html class="writer-html5" lang="en" >
 3 | <head>
 4 |   <meta charset="utf-8" />
 5 |   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
 6 |   <title>Overview: module code &mdash; pychi 0.0.1 documentation</title><link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
 7 |     <link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
 8 |   <!--[if lt IE 9]>
 9 |     <script src="../_static/js/html5shiv.min.js"></script>
10 |   <![endif]-->
11 |   <script id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
12 |         <script src="../_static/jquery.js"></script>
13 |         <script src="../_static/underscore.js"></script>
14 |         <script src="../_static/doctools.js"></script>
15 |         <script src="../_static/language_data.js"></script>
16 |     <script src="../_static/js/theme.js"></script>
17 |     <link rel="index" title="Index" href="../genindex.html" />
18 |     <link rel="search" title="Search" href="../search.html" /> 
19 | </head>
20 | 
21 | <body class="wy-body-for-nav"> 
22 |   <div class="wy-grid-for-nav">
23 |     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
24 |       <div class="wy-side-scroll">
25 |         <div class="wy-side-nav-search" >
26 |             <a href="../index.html" class="icon icon-home"> pychi
27 |           </a>
28 | <div role="search">
29 |   <form id="rtd-search-form" class="wy-form" action="../search.html" method="get">
30 |     <input type="text" name="q" placeholder="Search docs" />
31 |     <input type="hidden" name="check_keywords" value="yes" />
32 |     <input type="hidden" name="area" value="default" />
33 |   </form>
34 | </div>
35 |         </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
36 |               <p class="caption"><span class="caption-text">Contents:</span></p>
37 | <ul>
38 | <li class="toctree-l1"><a class="reference internal" href="../pychi.html">pychi package</a></li>
39 | </ul>
40 | 
41 |         </div>
42 |       </div>
43 |     </nav>
44 | 
45 |     <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
46 |           <i data-toggle="wy-nav-top" class="fa fa-bars"></i>
47 |           <a href="../index.html">pychi</a>
48 |       </nav>
49 | 
50 |       <div class="wy-nav-content">
51 |         <div class="rst-content">
52 |           <div role="navigation" aria-label="Page navigation">
53 |   <ul class="wy-breadcrumbs">
54 |       <li><a href="../index.html" class="icon icon-home"></a> &raquo;</li>
55 |       <li>Overview: module code</li>
56 |       <li class="wy-breadcrumbs-aside">
57 |       </li>
58 |   </ul>
59 |   <hr/>
60 | </div>
61 |           <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
62 |            <div itemprop="articleBody">
63 |              
64 |   <h1>All modules for which code is available</h1>
65 | <ul><li><a href="pychi/light.html">pychi.light</a></li>
66 | <li><a href="pychi/materials.html">pychi.materials</a></li>
67 | <li><a href="pychi/models.html">pychi.models</a></li>
68 | <li><a href="pychi/solvers.html">pychi.solvers</a></li>
69 | </ul>
70 | 
71 |            </div>
72 |           </div>
73 |           <footer>
74 | 
75 |   <hr/>
76 | 
77 |   <div role="contentinfo">
78 |     <p>&#169; Copyright 2023, Thibault Voumard.</p>
79 |   </div>
80 | 
81 |   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
82 |     <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
83 |     provided by <a href="https://readthedocs.org">Read the Docs</a>.
84 |    
85 | 
86 | </footer>
87 |         </div>
88 |       </div>
89 |     </section>
90 |   </div>
91 |   <script>
92 |       jQuery(function () {
93 |           SphinxRtdTheme.Navigation.enable(true);
94 |       });
95 |   </script> 
96 | 
97 | </body>
98 | </html>


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/docs/_build/html/_sources/index.rst.txt:
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 1 | .. pychi documentation master file, created by
 2 |    sphinx-quickstart on Fri Mar  3 10:39:56 2023.
 3 |    You can adapt this file completely to your liking, but it should at least
 4 |    contain the root `toctree` directive.
 5 | 
 6 | Welcome to pychi's documentation!
 7 | =================================
 8 | 
 9 | .. toctree::
10 |    :maxdepth: 2
11 |    :caption: Contents:
12 | 
13 |    modules
14 | 
15 | Indices and tables
16 | ==================
17 | 
18 | * :ref:`genindex`
19 | * :ref:`modindex`
20 | * :ref:`search`
21 | 


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/docs/_build/html/_sources/modules.rst.txt:
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1 | pychi package
2 | ===
3 | 
4 | .. toctree::
5 |    :maxdepth: 4
6 | 
7 |    pychi
8 | 


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/docs/_build/html/_sources/pychi.rst.txt:
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 1 | pychi package
 2 | =============
 3 | 
 4 | pychi.light module
 5 | ------------------
 6 | 
 7 | .. automodule:: pychi.light
 8 |    :members:
 9 |    :undoc-members:
10 |    :show-inheritance:
11 | 
12 | pychi.materials module
13 | ----------------------
14 | 
15 | .. automodule:: pychi.materials
16 |    :members:
17 |    :undoc-members:
18 |    :show-inheritance:
19 | 
20 | pychi.models module
21 | -------------------
22 | 
23 | .. automodule:: pychi.models
24 |    :members:
25 |    :undoc-members:
26 |    :show-inheritance:
27 | 
28 | pychi.solvers module
29 | --------------------
30 | 
31 | .. automodule:: pychi.solvers
32 |    :members:
33 |    :undoc-members:
34 |    :show-inheritance:
35 | 
36 | 
37 | Module contents
38 | ---------------
39 | 
40 | .. automodule:: pychi
41 |    :members:
42 |    :undoc-members:
43 |    :show-inheritance:
44 | 


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/docs/_build/html/_static/basic.css:
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  1 | /*
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  3 |  * ~~~~~~~~~
  4 |  *
  5 |  * Sphinx stylesheet -- basic theme.
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139 | table.contentstable {
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153 | span.linkdescr {
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159 | /* -- general index --------------------------------------------------------- */
160 | 
161 | table.indextable {
162 |     width: 100%;
163 | }
164 | 
165 | table.indextable td {
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167 |     vertical-align: top;
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184 | table.indextable tr.cap {
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197 |     border-bottom: 1px solid #ddd;
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202 | div.genindex-jumpbox {
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204 |     border-bottom: 1px solid #ddd;
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206 |     padding: 0.4em;
207 | }
208 | 
209 | /* -- domain module index --------------------------------------------------- */
210 | 
211 | table.modindextable td {
212 |     padding: 2px;
213 |     border-collapse: collapse;
214 | }
215 | 
216 | /* -- general body styles --------------------------------------------------- */
217 | 
218 | div.body {
219 |     min-width: 450px;
220 |     max-width: 800px;
221 | }
222 | 
223 | div.body p, div.body dd, div.body li, div.body blockquote {
224 |     -moz-hyphens: auto;
225 |     -ms-hyphens: auto;
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228 | }
229 | 
230 | a.headerlink {
231 |     visibility: hidden;
232 | }
233 | 
234 | a.brackets:before,
235 | span.brackets > a:before{
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238 | 
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243 | 
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249 | h6:hover > a.headerlink,
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255 | }
256 | 
257 | div.body p.caption {
258 |     text-align: inherit;
259 | }
260 | 
261 | div.body td {
262 |     text-align: left;
263 | }
264 | 
265 | .first {
266 |     margin-top: 0 !important;
267 | }
268 | 
269 | p.rubric {
270 |     margin-top: 30px;
271 |     font-weight: bold;
272 | }
273 | 
274 | img.align-left, .figure.align-left, object.align-left {
275 |     clear: left;
276 |     float: left;
277 |     margin-right: 1em;
278 | }
279 | 
280 | img.align-right, .figure.align-right, object.align-right {
281 |     clear: right;
282 |     float: right;
283 |     margin-left: 1em;
284 | }
285 | 
286 | img.align-center, .figure.align-center, object.align-center {
287 |   display: block;
288 |   margin-left: auto;
289 |   margin-right: auto;
290 | }
291 | 
292 | img.align-default, .figure.align-default {
293 |   display: block;
294 |   margin-left: auto;
295 |   margin-right: auto;
296 | }
297 | 
298 | .align-left {
299 |     text-align: left;
300 | }
301 | 
302 | .align-center {
303 |     text-align: center;
304 | }
305 | 
306 | .align-default {
307 |     text-align: center;
308 | }
309 | 
310 | .align-right {
311 |     text-align: right;
312 | }
313 | 
314 | /* -- sidebars -------------------------------------------------------------- */
315 | 
316 | div.sidebar {
317 |     margin: 0 0 0.5em 1em;
318 |     border: 1px solid #ddb;
319 |     padding: 7px 7px 0 7px;
320 |     background-color: #ffe;
321 |     width: 40%;
322 |     float: right;
323 | }
324 | 
325 | p.sidebar-title {
326 |     font-weight: bold;
327 | }
328 | 
329 | /* -- topics ---------------------------------------------------------------- */
330 | 
331 | div.topic {
332 |     border: 1px solid #ccc;
333 |     padding: 7px 7px 0 7px;
334 |     margin: 10px 0 10px 0;
335 | }
336 | 
337 | p.topic-title {
338 |     font-size: 1.1em;
339 |     font-weight: bold;
340 |     margin-top: 10px;
341 | }
342 | 
343 | /* -- admonitions ----------------------------------------------------------- */
344 | 
345 | div.admonition {
346 |     margin-top: 10px;
347 |     margin-bottom: 10px;
348 |     padding: 7px;
349 | }
350 | 
351 | div.admonition dt {
352 |     font-weight: bold;
353 | }
354 | 
355 | div.admonition dl {
356 |     margin-bottom: 0;
357 | }
358 | 
359 | p.admonition-title {
360 |     margin: 0px 10px 5px 0px;
361 |     font-weight: bold;
362 | }
363 | 
364 | div.body p.centered {
365 |     text-align: center;
366 |     margin-top: 25px;
367 | }
368 | 
369 | /* -- tables ---------------------------------------------------------------- */
370 | 
371 | table.docutils {
372 |     border: 0;
373 |     border-collapse: collapse;
374 | }
375 | 
376 | table.align-center {
377 |     margin-left: auto;
378 |     margin-right: auto;
379 | }
380 | 
381 | table.align-default {
382 |     margin-left: auto;
383 |     margin-right: auto;
384 | }
385 | 
386 | table caption span.caption-number {
387 |     font-style: italic;
388 | }
389 | 
390 | table caption span.caption-text {
391 | }
392 | 
393 | table.docutils td, table.docutils th {
394 |     padding: 1px 8px 1px 5px;
395 |     border-top: 0;
396 |     border-left: 0;
397 |     border-right: 0;
398 |     border-bottom: 1px solid #aaa;
399 | }
400 | 
401 | table.footnote td, table.footnote th {
402 |     border: 0 !important;
403 | }
404 | 
405 | th {
406 |     text-align: left;
407 |     padding-right: 5px;
408 | }
409 | 
410 | table.citation {
411 |     border-left: solid 1px gray;
412 |     margin-left: 1px;
413 | }
414 | 
415 | table.citation td {
416 |     border-bottom: none;
417 | }
418 | 
419 | th > p:first-child,
420 | td > p:first-child {
421 |     margin-top: 0px;
422 | }
423 | 
424 | th > p:last-child,
425 | td > p:last-child {
426 |     margin-bottom: 0px;
427 | }
428 | 
429 | /* -- figures --------------------------------------------------------------- */
430 | 
431 | div.figure {
432 |     margin: 0.5em;
433 |     padding: 0.5em;
434 | }
435 | 
436 | div.figure p.caption {
437 |     padding: 0.3em;
438 | }
439 | 
440 | div.figure p.caption span.caption-number {
441 |     font-style: italic;
442 | }
443 | 
444 | div.figure p.caption span.caption-text {
445 | }
446 | 
447 | /* -- field list styles ----------------------------------------------------- */
448 | 
449 | table.field-list td, table.field-list th {
450 |     border: 0 !important;
451 | }
452 | 
453 | .field-list ul {
454 |     margin: 0;
455 |     padding-left: 1em;
456 | }
457 | 
458 | .field-list p {
459 |     margin: 0;
460 | }
461 | 
462 | .field-name {
463 |     -moz-hyphens: manual;
464 |     -ms-hyphens: manual;
465 |     -webkit-hyphens: manual;
466 |     hyphens: manual;
467 | }
468 | 
469 | /* -- hlist styles ---------------------------------------------------------- */
470 | 
471 | table.hlist td {
472 |     vertical-align: top;
473 | }
474 | 
475 | 
476 | /* -- other body styles ----------------------------------------------------- */
477 | 
478 | ol.arabic {
479 |     list-style: decimal;
480 | }
481 | 
482 | ol.loweralpha {
483 |     list-style: lower-alpha;
484 | }
485 | 
486 | ol.upperalpha {
487 |     list-style: upper-alpha;
488 | }
489 | 
490 | ol.lowerroman {
491 |     list-style: lower-roman;
492 | }
493 | 
494 | ol.upperroman {
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496 | }
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500 | }
501 | 
502 | li > p:last-child {
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504 | }
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507 | dl.citation > dt {
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511 | dl.footnote > dd,
512 | dl.citation > dd {
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514 | }
515 | 
516 | dl.footnote > dd:after,
517 | dl.citation > dd:after {
518 |     content: "";
519 |     clear: both;
520 | }
521 | 
522 | dl.field-list {
523 |     display: grid;
524 |     grid-template-columns: fit-content(30%) auto;
525 | }
526 | 
527 | dl.field-list > dt {
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529 |     word-break: break-word;
530 |     padding-left: 0.5em;
531 |     padding-right: 5px;
532 | }
533 | 
534 | dl.field-list > dt:after {
535 |     content: ":";
536 | }
537 | 
538 | dl.field-list > dd {
539 |     padding-left: 0.5em;
540 |     margin-top: 0em;
541 |     margin-left: 0em;
542 |     margin-bottom: 0em;
543 | }
544 | 
545 | dl {
546 |     margin-bottom: 15px;
547 | }
548 | 
549 | dd > p:first-child {
550 |     margin-top: 0px;
551 | }
552 | 
553 | dd ul, dd table {
554 |     margin-bottom: 10px;
555 | }
556 | 
557 | dd {
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559 |     margin-bottom: 10px;
560 |     margin-left: 30px;
561 | }
562 | 
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565 | }
566 | 
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569 | }
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573 |     font-size: 1.1em;
574 | }
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578 | }
579 | 
580 | .sig-paren {
581 |     font-size: larger;
582 | }
583 | 
584 | .versionmodified {
585 |     font-style: italic;
586 | }
587 | 
588 | .system-message {
589 |     background-color: #fda;
590 |     padding: 5px;
591 |     border: 3px solid red;
592 | }
593 | 
594 | .footnote:target  {
595 |     background-color: #ffa;
596 | }
597 | 
598 | .line-block {
599 |     display: block;
600 |     margin-top: 1em;
601 |     margin-bottom: 1em;
602 | }
603 | 
604 | .line-block .line-block {
605 |     margin-top: 0;
606 |     margin-bottom: 0;
607 |     margin-left: 1.5em;
608 | }
609 | 
610 | .guilabel, .menuselection {
611 |     font-family: sans-serif;
612 | }
613 | 
614 | .accelerator {
615 |     text-decoration: underline;
616 | }
617 | 
618 | .classifier {
619 |     font-style: oblique;
620 | }
621 | 
622 | .classifier:before {
623 |     font-style: normal;
624 |     margin: 0.5em;
625 |     content: ":";
626 | }
627 | 
628 | abbr, acronym {
629 |     border-bottom: dotted 1px;
630 |     cursor: help;
631 | }
632 | 
633 | /* -- code displays --------------------------------------------------------- */
634 | 
635 | pre {
636 |     overflow: auto;
637 |     overflow-y: hidden;  /* fixes display issues on Chrome browsers */
638 | }
639 | 
640 | span.pre {
641 |     -moz-hyphens: none;
642 |     -ms-hyphens: none;
643 |     -webkit-hyphens: none;
644 |     hyphens: none;
645 | }
646 | 
647 | td.linenos pre {
648 |     padding: 5px 0px;
649 |     border: 0;
650 |     background-color: transparent;
651 |     color: #aaa;
652 | }
653 | 
654 | table.highlighttable {
655 |     margin-left: 0.5em;
656 | }
657 | 
658 | table.highlighttable td {
659 |     padding: 0 0.5em 0 0.5em;
660 | }
661 | 
662 | div.code-block-caption {
663 |     padding: 2px 5px;
664 |     font-size: small;
665 | }
666 | 
667 | div.code-block-caption code {
668 |     background-color: transparent;
669 | }
670 | 
671 | div.code-block-caption + div > div.highlight > pre {
672 |     margin-top: 0;
673 | }
674 | 
675 | div.doctest > div.highlight span.gp {  /* gp: Generic.Prompt */
676 |     user-select: none;
677 | }
678 | 
679 | div.code-block-caption span.caption-number {
680 |     padding: 0.1em 0.3em;
681 |     font-style: italic;
682 | }
683 | 
684 | div.code-block-caption span.caption-text {
685 | }
686 | 
687 | div.literal-block-wrapper {
688 |     padding: 1em 1em 0;
689 | }
690 | 
691 | div.literal-block-wrapper div.highlight {
692 |     margin: 0;
693 | }
694 | 
695 | code.descname {
696 |     background-color: transparent;
697 |     font-weight: bold;
698 |     font-size: 1.2em;
699 | }
700 | 
701 | code.descclassname {
702 |     background-color: transparent;
703 | }
704 | 
705 | code.xref, a code {
706 |     background-color: transparent;
707 |     font-weight: bold;
708 | }
709 | 
710 | h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
711 |     background-color: transparent;
712 | }
713 | 
714 | .viewcode-link {
715 |     float: right;
716 | }
717 | 
718 | .viewcode-back {
719 |     float: right;
720 |     font-family: sans-serif;
721 | }
722 | 
723 | div.viewcode-block:target {
724 |     margin: -1px -10px;
725 |     padding: 0 10px;
726 | }
727 | 
728 | /* -- math display ---------------------------------------------------------- */
729 | 
730 | img.math {
731 |     vertical-align: middle;
732 | }
733 | 
734 | div.body div.math p {
735 |     text-align: center;
736 | }
737 | 
738 | span.eqno {
739 |     float: right;
740 | }
741 | 
742 | span.eqno a.headerlink {
743 |     position: relative;
744 |     left: 0px;
745 |     z-index: 1;
746 | }
747 | 
748 | div.math:hover a.headerlink {
749 |     visibility: visible;
750 | }
751 | 
752 | /* -- printout stylesheet --------------------------------------------------- */
753 | 
754 | @media print {
755 |     div.document,
756 |     div.documentwrapper,
757 |     div.bodywrapper {
758 |         margin: 0 !important;
759 |         width: 100%;
760 |     }
761 | 
762 |     div.sphinxsidebar,
763 |     div.related,
764 |     div.footer,
765 |     #top-link {
766 |         display: none;
767 |     }
768 | }


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  1 | /*
  2 |  * doctools.js
  3 |  * ~~~~~~~~~~~
  4 |  *
  5 |  * Sphinx JavaScript utilities for all documentation.
  6 |  *
  7 |  * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
  8 |  * :license: BSD, see LICENSE for details.
  9 |  *
 10 |  */
 11 | 
 12 | /**
 13 |  * select a different prefix for underscore
 14 |  */
 15 | $u = _.noConflict();
 16 | 
 17 | /**
 18 |  * make the code below compatible with browsers without
 19 |  * an installed firebug like debugger
 20 | if (!window.console || !console.firebug) {
 21 |   var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
 22 |     "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
 23 |     "profile", "profileEnd"];
 24 |   window.console = {};
 25 |   for (var i = 0; i < names.length; ++i)
 26 |     window.console[names[i]] = function() {};
 27 | }
 28 |  */
 29 | 
 30 | /**
 31 |  * small helper function to urldecode strings
 32 |  */
 33 | jQuery.urldecode = function(x) {
 34 |   return decodeURIComponent(x).replace(/\+/g, ' ');
 35 | };
 36 | 
 37 | /**
 38 |  * small helper function to urlencode strings
 39 |  */
 40 | jQuery.urlencode = encodeURIComponent;
 41 | 
 42 | /**
 43 |  * This function returns the parsed url parameters of the
 44 |  * current request. Multiple values per key are supported,
 45 |  * it will always return arrays of strings for the value parts.
 46 |  */
 47 | jQuery.getQueryParameters = function(s) {
 48 |   if (typeof s === 'undefined')
 49 |     s = document.location.search;
 50 |   var parts = s.substr(s.indexOf('?') + 1).split('&');
 51 |   var result = {};
 52 |   for (var i = 0; i < parts.length; i++) {
 53 |     var tmp = parts[i].split('=', 2);
 54 |     var key = jQuery.urldecode(tmp[0]);
 55 |     var value = jQuery.urldecode(tmp[1]);
 56 |     if (key in result)
 57 |       result[key].push(value);
 58 |     else
 59 |       result[key] = [value];
 60 |   }
 61 |   return result;
 62 | };
 63 | 
 64 | /**
 65 |  * highlight a given string on a jquery object by wrapping it in
 66 |  * span elements with the given class name.
 67 |  */
 68 | jQuery.fn.highlightText = function(text, className) {
 69 |   function highlight(node, addItems) {
 70 |     if (node.nodeType === 3) {
 71 |       var val = node.nodeValue;
 72 |       var pos = val.toLowerCase().indexOf(text);
 73 |       if (pos >= 0 &&
 74 |           !jQuery(node.parentNode).hasClass(className) &&
 75 |           !jQuery(node.parentNode).hasClass("nohighlight")) {
 76 |         var span;
 77 |         var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
 78 |         if (isInSVG) {
 79 |           span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
 80 |         } else {
 81 |           span = document.createElement("span");
 82 |           span.className = className;
 83 |         }
 84 |         span.appendChild(document.createTextNode(val.substr(pos, text.length)));
 85 |         node.parentNode.insertBefore(span, node.parentNode.insertBefore(
 86 |           document.createTextNode(val.substr(pos + text.length)),
 87 |           node.nextSibling));
 88 |         node.nodeValue = val.substr(0, pos);
 89 |         if (isInSVG) {
 90 |           var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
 91 |           var bbox = node.parentElement.getBBox();
 92 |           rect.x.baseVal.value = bbox.x;
 93 |           rect.y.baseVal.value = bbox.y;
 94 |           rect.width.baseVal.value = bbox.width;
 95 |           rect.height.baseVal.value = bbox.height;
 96 |           rect.setAttribute('class', className);
 97 |           addItems.push({
 98 |               "parent": node.parentNode,
 99 |               "target": rect});
100 |         }
101 |       }
102 |     }
103 |     else if (!jQuery(node).is("button, select, textarea")) {
104 |       jQuery.each(node.childNodes, function() {
105 |         highlight(this, addItems);
106 |       });
107 |     }
108 |   }
109 |   var addItems = [];
110 |   var result = this.each(function() {
111 |     highlight(this, addItems);
112 |   });
113 |   for (var i = 0; i < addItems.length; ++i) {
114 |     jQuery(addItems[i].parent).before(addItems[i].target);
115 |   }
116 |   return result;
117 | };
118 | 
119 | /*
120 |  * backward compatibility for jQuery.browser
121 |  * This will be supported until firefox bug is fixed.
122 |  */
123 | if (!jQuery.browser) {
124 |   jQuery.uaMatch = function(ua) {
125 |     ua = ua.toLowerCase();
126 | 
127 |     var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
128 |       /(webkit)[ \/]([\w.]+)/.exec(ua) ||
129 |       /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
130 |       /(msie) ([\w.]+)/.exec(ua) ||
131 |       ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
132 |       [];
133 | 
134 |     return {
135 |       browser: match[ 1 ] || "",
136 |       version: match[ 2 ] || "0"
137 |     };
138 |   };
139 |   jQuery.browser = {};
140 |   jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
141 | }
142 | 
143 | /**
144 |  * Small JavaScript module for the documentation.
145 |  */
146 | var Documentation = {
147 | 
148 |   init : function() {
149 |     this.fixFirefoxAnchorBug();
150 |     this.highlightSearchWords();
151 |     this.initIndexTable();
152 |     if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) {
153 |       this.initOnKeyListeners();
154 |     }
155 |   },
156 | 
157 |   /**
158 |    * i18n support
159 |    */
160 |   TRANSLATIONS : {},
161 |   PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
162 |   LOCALE : 'unknown',
163 | 
164 |   // gettext and ngettext don't access this so that the functions
165 |   // can safely bound to a different name (_ = Documentation.gettext)
166 |   gettext : function(string) {
167 |     var translated = Documentation.TRANSLATIONS[string];
168 |     if (typeof translated === 'undefined')
169 |       return string;
170 |     return (typeof translated === 'string') ? translated : translated[0];
171 |   },
172 | 
173 |   ngettext : function(singular, plural, n) {
174 |     var translated = Documentation.TRANSLATIONS[singular];
175 |     if (typeof translated === 'undefined')
176 |       return (n == 1) ? singular : plural;
177 |     return translated[Documentation.PLURALEXPR(n)];
178 |   },
179 | 
180 |   addTranslations : function(catalog) {
181 |     for (var key in catalog.messages)
182 |       this.TRANSLATIONS[key] = catalog.messages[key];
183 |     this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
184 |     this.LOCALE = catalog.locale;
185 |   },
186 | 
187 |   /**
188 |    * add context elements like header anchor links
189 |    */
190 |   addContextElements : function() {
191 |     $('div[id] > :header:first').each(function() {
192 |       $('<a class="headerlink">\u00B6</a>').
193 |       attr('href', '#' + this.id).
194 |       attr('title', _('Permalink to this headline')).
195 |       appendTo(this);
196 |     });
197 |     $('dt[id]').each(function() {
198 |       $('<a class="headerlink">\u00B6</a>').
199 |       attr('href', '#' + this.id).
200 |       attr('title', _('Permalink to this definition')).
201 |       appendTo(this);
202 |     });
203 |   },
204 | 
205 |   /**
206 |    * workaround a firefox stupidity
207 |    * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075
208 |    */
209 |   fixFirefoxAnchorBug : function() {
210 |     if (document.location.hash && $.browser.mozilla)
211 |       window.setTimeout(function() {
212 |         document.location.href += '';
213 |       }, 10);
214 |   },
215 | 
216 |   /**
217 |    * highlight the search words provided in the url in the text
218 |    */
219 |   highlightSearchWords : function() {
220 |     var params = $.getQueryParameters();
221 |     var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : [];
222 |     if (terms.length) {
223 |       var body = $('div.body');
224 |       if (!body.length) {
225 |         body = $('body');
226 |       }
227 |       window.setTimeout(function() {
228 |         $.each(terms, function() {
229 |           body.highlightText(this.toLowerCase(), 'highlighted');
230 |         });
231 |       }, 10);
232 |       $('<p class="highlight-link"><a href="javascript:Documentation.' +
233 |         'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
234 |           .appendTo($('#searchbox'));
235 |     }
236 |   },
237 | 
238 |   /**
239 |    * init the domain index toggle buttons
240 |    */
241 |   initIndexTable : function() {
242 |     var togglers = $('img.toggler').click(function() {
243 |       var src = $(this).attr('src');
244 |       var idnum = $(this).attr('id').substr(7);
245 |       $('tr.cg-' + idnum).toggle();
246 |       if (src.substr(-9) === 'minus.png')
247 |         $(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
248 |       else
249 |         $(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
250 |     }).css('display', '');
251 |     if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
252 |         togglers.click();
253 |     }
254 |   },
255 | 
256 |   /**
257 |    * helper function to hide the search marks again
258 |    */
259 |   hideSearchWords : function() {
260 |     $('#searchbox .highlight-link').fadeOut(300);
261 |     $('span.highlighted').removeClass('highlighted');
262 |   },
263 | 
264 |   /**
265 |    * make the url absolute
266 |    */
267 |   makeURL : function(relativeURL) {
268 |     return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
269 |   },
270 | 
271 |   /**
272 |    * get the current relative url
273 |    */
274 |   getCurrentURL : function() {
275 |     var path = document.location.pathname;
276 |     var parts = path.split(/\//);
277 |     $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
278 |       if (this === '..')
279 |         parts.pop();
280 |     });
281 |     var url = parts.join('/');
282 |     return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
283 |   },
284 | 
285 |   initOnKeyListeners: function() {
286 |     $(document).keydown(function(event) {
287 |       var activeElementType = document.activeElement.tagName;
288 |       // don't navigate when in search box or textarea
289 |       if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
290 |           && !event.altKey && !event.ctrlKey && !event.metaKey && !event.shiftKey) {
291 |         switch (event.keyCode) {
292 |           case 37: // left
293 |             var prevHref = $('link[rel="prev"]').prop('href');
294 |             if (prevHref) {
295 |               window.location.href = prevHref;
296 |               return false;
297 |             }
298 |           case 39: // right
299 |             var nextHref = $('link[rel="next"]').prop('href');
300 |             if (nextHref) {
301 |               window.location.href = nextHref;
302 |               return false;
303 |             }
304 |         }
305 |       }
306 |     });
307 |   }
308 | };
309 | 
310 | // quick alias for translations
311 | _ = Documentation.gettext;
312 | 
313 | $(document).ready(function() {
314 |   Documentation.init();
315 | });
316 | 


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 1 | var DOCUMENTATION_OPTIONS = {
 2 |     URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
 3 |     VERSION: '0.0.1',
 4 |     LANGUAGE: 'None',
 5 |     COLLAPSE_INDEX: false,
 6 |     BUILDER: 'html',
 7 |     FILE_SUFFIX: '.html',
 8 |     HAS_SOURCE: true,
 9 |     SOURCELINK_SUFFIX: '.txt',
10 |     NAVIGATION_WITH_KEYS: false
11 | };


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1 | /**
2 | * @preserve HTML5 Shiv 3.7.3-pre | @afarkas @jdalton @jon_neal @rem | MIT/GPL2 Licensed
3 | */
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1 | /**
2 | * @preserve HTML5 Shiv 3.7.3 | @afarkas @jdalton @jon_neal @rem | MIT/GPL2 Licensed
3 | */
4 | !function(a,b){function c(a,b){var c=a.createElement("p"),d=a.getElementsByTagName("head")[0]||a.documentElement;return c.innerHTML="x<style>"+b+"</style>",d.insertBefore(c.lastChild,d.firstChild)}function d(){var a=t.elements;return"string"==typeof a?a.split(" "):a}function e(a,b){var c=t.elements;"string"!=typeof c&&(c=c.join(" ")),"string"!=typeof a&&(a=a.join(" ")),t.elements=c+" "+a,j(b)}function f(a){var b=s[a[q]];return b||(b={},r++,a[q]=r,s[r]=b),b}function g(a,c,d){if(c||(c=b),l)return c.createElement(a);d||(d=f(c));var e;return e=d.cache[a]?d.cache[a].cloneNode():p.test(a)?(d.cache[a]=d.createElem(a)).cloneNode():d.createElem(a),!e.canHaveChildren||o.test(a)||e.tagUrn?e:d.frag.appendChild(e)}function h(a,c){if(a||(a=b),l)return a.createDocumentFragment();c=c||f(a);for(var e=c.frag.cloneNode(),g=0,h=d(),i=h.length;i>g;g++)e.createElement(h[g]);return e}function i(a,b){b.cache||(b.cache={},b.createElem=a.createElement,b.createFrag=a.createDocumentFragment,b.frag=b.createFrag()),a.createElement=function(c){return t.shivMethods?g(c,a,b):b.createElem(c)},a.createDocumentFragment=Function("h,f","return function(){var n=f.cloneNode(),c=n.createElement;h.shivMethods&&("+d().join().replace(/[\w\-:]+/g,function(a){return b.createElem(a),b.frag.createElement(a),'c("'+a+'")'})+");return n}")(t,b.frag)}function j(a){a||(a=b);var d=f(a);return!t.shivCSS||k||d.hasCSS||(d.hasCSS=!!c(a,"article,aside,dialog,figcaption,figure,footer,header,hgroup,main,nav,section{display:block}mark{background:#FF0;color:#000}template{display:none}")),l||i(a,d),a}var k,l,m="3.7.3-pre",n=a.html5||{},o=/^<|^(?:button|map|select|textarea|object|iframe|option|optgroup)$/i,p=/^(?:a|b|code|div|fieldset|h1|h2|h3|h4|h5|h6|i|label|li|ol|p|q|span|strong|style|table|tbody|td|th|tr|ul)$/i,q="_html5shiv",r=0,s={};!function(){try{var a=b.createElement("a");a.innerHTML="<xyz></xyz>",k="hidden"in a,l=1==a.childNodes.length||function(){b.createElement("a");var a=b.createDocumentFragment();return"undefined"==typeof a.cloneNode||"undefined"==typeof a.createDocumentFragment||"undefined"==typeof a.createElement}()}catch(c){k=!0,l=!0}}();var t={elements:n.elements||"abbr article aside audio bdi canvas data datalist details dialog figcaption figure footer header hgroup main mark meter nav output picture progress section summary template time video",version:m,shivCSS:n.shivCSS!==!1,supportsUnknownElements:l,shivMethods:n.shivMethods!==!1,type:"default",shivDocument:j,createElement:g,createDocumentFragment:h,addElements:e};a.html5=t,j(b),"object"==typeof module&&module.exports&&(module.exports=t)}("undefined"!=typeof window?window:this,document);


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/docs/_build/html/_static/language_data.js:
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  1 | /*
  2 |  * language_data.js
  3 |  * ~~~~~~~~~~~~~~~~
  4 |  *
  5 |  * This script contains the language-specific data used by searchtools.js,
  6 |  * namely the list of stopwords, stemmer, scorer and splitter.
  7 |  *
  8 |  * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
  9 |  * :license: BSD, see LICENSE for details.
 10 |  *
 11 |  */
 12 | 
 13 | var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
 14 | 
 15 | 
 16 | /* Non-minified version JS is _stemmer.js if file is provided */ 
 17 | /**
 18 |  * Porter Stemmer
 19 |  */
 20 | var Stemmer = function() {
 21 | 
 22 |   var step2list = {
 23 |     ational: 'ate',
 24 |     tional: 'tion',
 25 |     enci: 'ence',
 26 |     anci: 'ance',
 27 |     izer: 'ize',
 28 |     bli: 'ble',
 29 |     alli: 'al',
 30 |     entli: 'ent',
 31 |     eli: 'e',
 32 |     ousli: 'ous',
 33 |     ization: 'ize',
 34 |     ation: 'ate',
 35 |     ator: 'ate',
 36 |     alism: 'al',
 37 |     iveness: 'ive',
 38 |     fulness: 'ful',
 39 |     ousness: 'ous',
 40 |     aliti: 'al',
 41 |     iviti: 'ive',
 42 |     biliti: 'ble',
 43 |     logi: 'log'
 44 |   };
 45 | 
 46 |   var step3list = {
 47 |     icate: 'ic',
 48 |     ative: '',
 49 |     alize: 'al',
 50 |     iciti: 'ic',
 51 |     ical: 'ic',
 52 |     ful: '',
 53 |     ness: ''
 54 |   };
 55 | 
 56 |   var c = "[^aeiou]";          // consonant
 57 |   var v = "[aeiouy]";          // vowel
 58 |   var C = c + "[^aeiouy]*";    // consonant sequence
 59 |   var V = v + "[aeiou]*";      // vowel sequence
 60 | 
 61 |   var mgr0 = "^(" + C + ")?" + V + C;                      // [C]VC... is m>0
 62 |   var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$";    // [C]VC[V] is m=1
 63 |   var mgr1 = "^(" + C + ")?" + V + C + V + C;              // [C]VCVC... is m>1
 64 |   var s_v   = "^(" + C + ")?" + v;                         // vowel in stem
 65 | 
 66 |   this.stemWord = function (w) {
 67 |     var stem;
 68 |     var suffix;
 69 |     var firstch;
 70 |     var origword = w;
 71 | 
 72 |     if (w.length < 3)
 73 |       return w;
 74 | 
 75 |     var re;
 76 |     var re2;
 77 |     var re3;
 78 |     var re4;
 79 | 
 80 |     firstch = w.substr(0,1);
 81 |     if (firstch == "y")
 82 |       w = firstch.toUpperCase() + w.substr(1);
 83 | 
 84 |     // Step 1a
 85 |     re = /^(.+?)(ss|i)es$/;
 86 |     re2 = /^(.+?)([^s])s$/;
 87 | 
 88 |     if (re.test(w))
 89 |       w = w.replace(re,"$1$2");
 90 |     else if (re2.test(w))
 91 |       w = w.replace(re2,"$1$2");
 92 | 
 93 |     // Step 1b
 94 |     re = /^(.+?)eed$/;
 95 |     re2 = /^(.+?)(ed|ing)$/;
 96 |     if (re.test(w)) {
 97 |       var fp = re.exec(w);
 98 |       re = new RegExp(mgr0);
 99 |       if (re.test(fp[1])) {
100 |         re = /.$/;
101 |         w = w.replace(re,"");
102 |       }
103 |     }
104 |     else if (re2.test(w)) {
105 |       var fp = re2.exec(w);
106 |       stem = fp[1];
107 |       re2 = new RegExp(s_v);
108 |       if (re2.test(stem)) {
109 |         w = stem;
110 |         re2 = /(at|bl|iz)$/;
111 |         re3 = new RegExp("([^aeiouylsz])\\1$");
112 |         re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
113 |         if (re2.test(w))
114 |           w = w + "e";
115 |         else if (re3.test(w)) {
116 |           re = /.$/;
117 |           w = w.replace(re,"");
118 |         }
119 |         else if (re4.test(w))
120 |           w = w + "e";
121 |       }
122 |     }
123 | 
124 |     // Step 1c
125 |     re = /^(.+?)y$/;
126 |     if (re.test(w)) {
127 |       var fp = re.exec(w);
128 |       stem = fp[1];
129 |       re = new RegExp(s_v);
130 |       if (re.test(stem))
131 |         w = stem + "i";
132 |     }
133 | 
134 |     // Step 2
135 |     re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
136 |     if (re.test(w)) {
137 |       var fp = re.exec(w);
138 |       stem = fp[1];
139 |       suffix = fp[2];
140 |       re = new RegExp(mgr0);
141 |       if (re.test(stem))
142 |         w = stem + step2list[suffix];
143 |     }
144 | 
145 |     // Step 3
146 |     re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
147 |     if (re.test(w)) {
148 |       var fp = re.exec(w);
149 |       stem = fp[1];
150 |       suffix = fp[2];
151 |       re = new RegExp(mgr0);
152 |       if (re.test(stem))
153 |         w = stem + step3list[suffix];
154 |     }
155 | 
156 |     // Step 4
157 |     re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
158 |     re2 = /^(.+?)(s|t)(ion)$/;
159 |     if (re.test(w)) {
160 |       var fp = re.exec(w);
161 |       stem = fp[1];
162 |       re = new RegExp(mgr1);
163 |       if (re.test(stem))
164 |         w = stem;
165 |     }
166 |     else if (re2.test(w)) {
167 |       var fp = re2.exec(w);
168 |       stem = fp[1] + fp[2];
169 |       re2 = new RegExp(mgr1);
170 |       if (re2.test(stem))
171 |         w = stem;
172 |     }
173 | 
174 |     // Step 5
175 |     re = /^(.+?)e$/;
176 |     if (re.test(w)) {
177 |       var fp = re.exec(w);
178 |       stem = fp[1];
179 |       re = new RegExp(mgr1);
180 |       re2 = new RegExp(meq1);
181 |       re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
182 |       if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
183 |         w = stem;
184 |     }
185 |     re = /ll$/;
186 |     re2 = new RegExp(mgr1);
187 |     if (re.test(w) && re2.test(w)) {
188 |       re = /.$/;
189 |       w = w.replace(re,"");
190 |     }
191 | 
192 |     // and turn initial Y back to y
193 |     if (firstch == "y")
194 |       w = firstch.toLowerCase() + w.substr(1);
195 |     return w;
196 |   }
197 | }
198 | 
199 | 
200 | 
201 | 
202 | 
203 | var splitChars = (function() {
204 |     var result = {};
205 |     var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
206 |          1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
207 |          2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
208 |          2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
209 |          3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
210 |          3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
211 |          4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
212 |          8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
213 |          11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
214 |          43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
215 |     var i, j, start, end;
216 |     for (i = 0; i < singles.length; i++) {
217 |         result[singles[i]] = true;
218 |     }
219 |     var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
220 |          [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
221 |          [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
222 |          [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
223 |          [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
224 |          [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
225 |          [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
226 |          [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
227 |          [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
228 |          [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
229 |          [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
230 |          [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
231 |          [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
232 |          [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
233 |          [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
234 |          [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
235 |          [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
236 |          [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
237 |          [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
238 |          [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
239 |          [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
240 |          [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
241 |          [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
242 |          [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
243 |          [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
244 |          [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
245 |          [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
246 |          [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
247 |          [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
248 |          [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
249 |          [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
250 |          [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
251 |          [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
252 |          [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
253 |          [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
254 |          [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
255 |          [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
256 |          [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
257 |          [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
258 |          [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
259 |          [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
260 |          [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
261 |          [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
262 |          [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
263 |          [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
264 |          [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
265 |          [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
266 |          [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
267 |          [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
268 |     for (i = 0; i < ranges.length; i++) {
269 |         start = ranges[i][0];
270 |         end = ranges[i][1];
271 |         for (j = start; j <= end; j++) {
272 |             result[j] = true;
273 |         }
274 |     }
275 |     return result;
276 | })();
277 | 
278 | function splitQuery(query) {
279 |     var result = [];
280 |     var start = -1;
281 |     for (var i = 0; i < query.length; i++) {
282 |         if (splitChars[query.charCodeAt(i)]) {
283 |             if (start !== -1) {
284 |                 result.push(query.slice(start, i));
285 |                 start = -1;
286 |             }
287 |         } else if (start === -1) {
288 |             start = i;
289 |         }
290 |     }
291 |     if (start !== -1) {
292 |         result.push(query.slice(start));
293 |     }
294 |     return result;
295 | }
296 | 
297 | 
298 | 


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17 | .highlight .cs { color: #3D7B7B; font-style: italic } /* Comment.Special */
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21 | .highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
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24 | .highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
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26 | .highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
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30 | .highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
31 | .highlight .kp { color: #008000 } /* Keyword.Pseudo */
32 | .highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
33 | .highlight .kt { color: #B00040 } /* Keyword.Type */
34 | .highlight .m { color: #666666 } /* Literal.Number */
35 | .highlight .s { color: #BA2121 } /* Literal.String */
36 | .highlight .na { color: #687822 } /* Name.Attribute */
37 | .highlight .nb { color: #008000 } /* Name.Builtin */
38 | .highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */
39 | .highlight .no { color: #880000 } /* Name.Constant */
40 | .highlight .nd { color: #AA22FF } /* Name.Decorator */
41 | .highlight .ni { color: #717171; font-weight: bold } /* Name.Entity */
42 | .highlight .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */
43 | .highlight .nf { color: #0000FF } /* Name.Function */
44 | .highlight .nl { color: #767600 } /* Name.Label */
45 | .highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */
46 | .highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */
47 | .highlight .nv { color: #19177C } /* Name.Variable */
48 | .highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */
49 | .highlight .w { color: #bbbbbb } /* Text.Whitespace */
50 | .highlight .mb { color: #666666 } /* Literal.Number.Bin */
51 | .highlight .mf { color: #666666 } /* Literal.Number.Float */
52 | .highlight .mh { color: #666666 } /* Literal.Number.Hex */
53 | .highlight .mi { color: #666666 } /* Literal.Number.Integer */
54 | .highlight .mo { color: #666666 } /* Literal.Number.Oct */
55 | .highlight .sa { color: #BA2121 } /* Literal.String.Affix */
56 | .highlight .sb { color: #BA2121 } /* Literal.String.Backtick */
57 | .highlight .sc { color: #BA2121 } /* Literal.String.Char */
58 | .highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */
59 | .highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */
60 | .highlight .s2 { color: #BA2121 } /* Literal.String.Double */
61 | .highlight .se { color: #AA5D1F; font-weight: bold } /* Literal.String.Escape */
62 | .highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */
63 | .highlight .si { color: #A45A77; font-weight: bold } /* Literal.String.Interpol */
64 | .highlight .sx { color: #008000 } /* Literal.String.Other */
65 | .highlight .sr { color: #A45A77 } /* Literal.String.Regex */
66 | .highlight .s1 { color: #BA2121 } /* Literal.String.Single */
67 | .highlight .ss { color: #19177C } /* Literal.String.Symbol */
68 | .highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */
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70 | .highlight .vc { color: #19177C } /* Name.Variable.Class */
71 | .highlight .vg { color: #19177C } /* Name.Variable.Global */
72 | .highlight .vi { color: #19177C } /* Name.Variable.Instance */
73 | .highlight .vm { color: #19177C } /* Name.Variable.Magic */
74 | .highlight .il { color: #666666 } /* Literal.Number.Integer.Long */


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  1 | /*
  2 |  * searchtools.js
  3 |  * ~~~~~~~~~~~~~~~~
  4 |  *
  5 |  * Sphinx JavaScript utilities for the full-text search.
  6 |  *
  7 |  * :copyright: Copyright 2007-2020 by the Sphinx team, see AUTHORS.
  8 |  * :license: BSD, see LICENSE for details.
  9 |  *
 10 |  */
 11 | 
 12 | if (!Scorer) {
 13 |   /**
 14 |    * Simple result scoring code.
 15 |    */
 16 |   var Scorer = {
 17 |     // Implement the following function to further tweak the score for each result
 18 |     // The function takes a result array [filename, title, anchor, descr, score]
 19 |     // and returns the new score.
 20 |     /*
 21 |     score: function(result) {
 22 |       return result[4];
 23 |     },
 24 |     */
 25 | 
 26 |     // query matches the full name of an object
 27 |     objNameMatch: 11,
 28 |     // or matches in the last dotted part of the object name
 29 |     objPartialMatch: 6,
 30 |     // Additive scores depending on the priority of the object
 31 |     objPrio: {0:  15,   // used to be importantResults
 32 |               1:  5,   // used to be objectResults
 33 |               2: -5},  // used to be unimportantResults
 34 |     //  Used when the priority is not in the mapping.
 35 |     objPrioDefault: 0,
 36 | 
 37 |     // query found in title
 38 |     title: 15,
 39 |     partialTitle: 7,
 40 |     // query found in terms
 41 |     term: 5,
 42 |     partialTerm: 2
 43 |   };
 44 | }
 45 | 
 46 | if (!splitQuery) {
 47 |   function splitQuery(query) {
 48 |     return query.split(/\s+/);
 49 |   }
 50 | }
 51 | 
 52 | /**
 53 |  * Search Module
 54 |  */
 55 | var Search = {
 56 | 
 57 |   _index : null,
 58 |   _queued_query : null,
 59 |   _pulse_status : -1,
 60 | 
 61 |   htmlToText : function(htmlString) {
 62 |       var htmlElement = document.createElement('span');
 63 |       htmlElement.innerHTML = htmlString;
 64 |       $(htmlElement).find('.headerlink').remove();
 65 |       docContent = $(htmlElement).find('[role=main]')[0];
 66 |       return docContent.textContent || docContent.innerText;
 67 |   },
 68 | 
 69 |   init : function() {
 70 |       var params = $.getQueryParameters();
 71 |       if (params.q) {
 72 |           var query = params.q[0];
 73 |           $('input[name="q"]')[0].value = query;
 74 |           this.performSearch(query);
 75 |       }
 76 |   },
 77 | 
 78 |   loadIndex : function(url) {
 79 |     $.ajax({type: "GET", url: url, data: null,
 80 |             dataType: "script", cache: true,
 81 |             complete: function(jqxhr, textstatus) {
 82 |               if (textstatus != "success") {
 83 |                 document.getElementById("searchindexloader").src = url;
 84 |               }
 85 |             }});
 86 |   },
 87 | 
 88 |   setIndex : function(index) {
 89 |     var q;
 90 |     this._index = index;
 91 |     if ((q = this._queued_query) !== null) {
 92 |       this._queued_query = null;
 93 |       Search.query(q);
 94 |     }
 95 |   },
 96 | 
 97 |   hasIndex : function() {
 98 |       return this._index !== null;
 99 |   },
100 | 
101 |   deferQuery : function(query) {
102 |       this._queued_query = query;
103 |   },
104 | 
105 |   stopPulse : function() {
106 |       this._pulse_status = 0;
107 |   },
108 | 
109 |   startPulse : function() {
110 |     if (this._pulse_status >= 0)
111 |         return;
112 |     function pulse() {
113 |       var i;
114 |       Search._pulse_status = (Search._pulse_status + 1) % 4;
115 |       var dotString = '';
116 |       for (i = 0; i < Search._pulse_status; i++)
117 |         dotString += '.';
118 |       Search.dots.text(dotString);
119 |       if (Search._pulse_status > -1)
120 |         window.setTimeout(pulse, 500);
121 |     }
122 |     pulse();
123 |   },
124 | 
125 |   /**
126 |    * perform a search for something (or wait until index is loaded)
127 |    */
128 |   performSearch : function(query) {
129 |     // create the required interface elements
130 |     this.out = $('#search-results');
131 |     this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
132 |     this.dots = $('<span></span>').appendTo(this.title);
133 |     this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
134 |     this.output = $('<ul class="search"/>').appendTo(this.out);
135 | 
136 |     $('#search-progress').text(_('Preparing search...'));
137 |     this.startPulse();
138 | 
139 |     // index already loaded, the browser was quick!
140 |     if (this.hasIndex())
141 |       this.query(query);
142 |     else
143 |       this.deferQuery(query);
144 |   },
145 | 
146 |   /**
147 |    * execute search (requires search index to be loaded)
148 |    */
149 |   query : function(query) {
150 |     var i;
151 | 
152 |     // stem the searchterms and add them to the correct list
153 |     var stemmer = new Stemmer();
154 |     var searchterms = [];
155 |     var excluded = [];
156 |     var hlterms = [];
157 |     var tmp = splitQuery(query);
158 |     var objectterms = [];
159 |     for (i = 0; i < tmp.length; i++) {
160 |       if (tmp[i] !== "") {
161 |           objectterms.push(tmp[i].toLowerCase());
162 |       }
163 | 
164 |       if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i].match(/^\d+$/) ||
165 |           tmp[i] === "") {
166 |         // skip this "word"
167 |         continue;
168 |       }
169 |       // stem the word
170 |       var word = stemmer.stemWord(tmp[i].toLowerCase());
171 |       // prevent stemmer from cutting word smaller than two chars
172 |       if(word.length < 3 && tmp[i].length >= 3) {
173 |         word = tmp[i];
174 |       }
175 |       var toAppend;
176 |       // select the correct list
177 |       if (word[0] == '-') {
178 |         toAppend = excluded;
179 |         word = word.substr(1);
180 |       }
181 |       else {
182 |         toAppend = searchterms;
183 |         hlterms.push(tmp[i].toLowerCase());
184 |       }
185 |       // only add if not already in the list
186 |       if (!$u.contains(toAppend, word))
187 |         toAppend.push(word);
188 |     }
189 |     var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
190 | 
191 |     // console.debug('SEARCH: searching for:');
192 |     // console.info('required: ', searchterms);
193 |     // console.info('excluded: ', excluded);
194 | 
195 |     // prepare search
196 |     var terms = this._index.terms;
197 |     var titleterms = this._index.titleterms;
198 | 
199 |     // array of [filename, title, anchor, descr, score]
200 |     var results = [];
201 |     $('#search-progress').empty();
202 | 
203 |     // lookup as object
204 |     for (i = 0; i < objectterms.length; i++) {
205 |       var others = [].concat(objectterms.slice(0, i),
206 |                              objectterms.slice(i+1, objectterms.length));
207 |       results = results.concat(this.performObjectSearch(objectterms[i], others));
208 |     }
209 | 
210 |     // lookup as search terms in fulltext
211 |     results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
212 | 
213 |     // let the scorer override scores with a custom scoring function
214 |     if (Scorer.score) {
215 |       for (i = 0; i < results.length; i++)
216 |         results[i][4] = Scorer.score(results[i]);
217 |     }
218 | 
219 |     // now sort the results by score (in opposite order of appearance, since the
220 |     // display function below uses pop() to retrieve items) and then
221 |     // alphabetically
222 |     results.sort(function(a, b) {
223 |       var left = a[4];
224 |       var right = b[4];
225 |       if (left > right) {
226 |         return 1;
227 |       } else if (left < right) {
228 |         return -1;
229 |       } else {
230 |         // same score: sort alphabetically
231 |         left = a[1].toLowerCase();
232 |         right = b[1].toLowerCase();
233 |         return (left > right) ? -1 : ((left < right) ? 1 : 0);
234 |       }
235 |     });
236 | 
237 |     // for debugging
238 |     //Search.lastresults = results.slice();  // a copy
239 |     //console.info('search results:', Search.lastresults);
240 | 
241 |     // print the results
242 |     var resultCount = results.length;
243 |     function displayNextItem() {
244 |       // results left, load the summary and display it
245 |       if (results.length) {
246 |         var item = results.pop();
247 |         var listItem = $('<li style="display:none"></li>');
248 |         if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
249 |           // dirhtml builder
250 |           var dirname = item[0] + '/';
251 |           if (dirname.match(/\/index\/$/)) {
252 |             dirname = dirname.substring(0, dirname.length-6);
253 |           } else if (dirname == 'index/') {
254 |             dirname = '';
255 |           }
256 |           listItem.append($('<a/>').attr('href',
257 |             DOCUMENTATION_OPTIONS.URL_ROOT + dirname +
258 |             highlightstring + item[2]).html(item[1]));
259 |         } else {
260 |           // normal html builders
261 |           listItem.append($('<a/>').attr('href',
262 |             item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX +
263 |             highlightstring + item[2]).html(item[1]));
264 |         }
265 |         if (item[3]) {
266 |           listItem.append($('<span> (' + item[3] + ')</span>'));
267 |           Search.output.append(listItem);
268 |           listItem.slideDown(5, function() {
269 |             displayNextItem();
270 |           });
271 |         } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
272 |           $.ajax({url: DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX,
273 |                   dataType: "text",
274 |                   complete: function(jqxhr, textstatus) {
275 |                     var data = jqxhr.responseText;
276 |                     if (data !== '' && data !== undefined) {
277 |                       listItem.append(Search.makeSearchSummary(data, searchterms, hlterms));
278 |                     }
279 |                     Search.output.append(listItem);
280 |                     listItem.slideDown(5, function() {
281 |                       displayNextItem();
282 |                     });
283 |                   }});
284 |         } else {
285 |           // no source available, just display title
286 |           Search.output.append(listItem);
287 |           listItem.slideDown(5, function() {
288 |             displayNextItem();
289 |           });
290 |         }
291 |       }
292 |       // search finished, update title and status message
293 |       else {
294 |         Search.stopPulse();
295 |         Search.title.text(_('Search Results'));
296 |         if (!resultCount)
297 |           Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
298 |         else
299 |             Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
300 |         Search.status.fadeIn(500);
301 |       }
302 |     }
303 |     displayNextItem();
304 |   },
305 | 
306 |   /**
307 |    * search for object names
308 |    */
309 |   performObjectSearch : function(object, otherterms) {
310 |     var filenames = this._index.filenames;
311 |     var docnames = this._index.docnames;
312 |     var objects = this._index.objects;
313 |     var objnames = this._index.objnames;
314 |     var titles = this._index.titles;
315 | 
316 |     var i;
317 |     var results = [];
318 | 
319 |     for (var prefix in objects) {
320 |       for (var name in objects[prefix]) {
321 |         var fullname = (prefix ? prefix + '.' : '') + name;
322 |         var fullnameLower = fullname.toLowerCase()
323 |         if (fullnameLower.indexOf(object) > -1) {
324 |           var score = 0;
325 |           var parts = fullnameLower.split('.');
326 |           // check for different match types: exact matches of full name or
327 |           // "last name" (i.e. last dotted part)
328 |           if (fullnameLower == object || parts[parts.length - 1] == object) {
329 |             score += Scorer.objNameMatch;
330 |           // matches in last name
331 |           } else if (parts[parts.length - 1].indexOf(object) > -1) {
332 |             score += Scorer.objPartialMatch;
333 |           }
334 |           var match = objects[prefix][name];
335 |           var objname = objnames[match[1]][2];
336 |           var title = titles[match[0]];
337 |           // If more than one term searched for, we require other words to be
338 |           // found in the name/title/description
339 |           if (otherterms.length > 0) {
340 |             var haystack = (prefix + ' ' + name + ' ' +
341 |                             objname + ' ' + title).toLowerCase();
342 |             var allfound = true;
343 |             for (i = 0; i < otherterms.length; i++) {
344 |               if (haystack.indexOf(otherterms[i]) == -1) {
345 |                 allfound = false;
346 |                 break;
347 |               }
348 |             }
349 |             if (!allfound) {
350 |               continue;
351 |             }
352 |           }
353 |           var descr = objname + _(', in ') + title;
354 | 
355 |           var anchor = match[3];
356 |           if (anchor === '')
357 |             anchor = fullname;
358 |           else if (anchor == '-')
359 |             anchor = objnames[match[1]][1] + '-' + fullname;
360 |           // add custom score for some objects according to scorer
361 |           if (Scorer.objPrio.hasOwnProperty(match[2])) {
362 |             score += Scorer.objPrio[match[2]];
363 |           } else {
364 |             score += Scorer.objPrioDefault;
365 |           }
366 |           results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
367 |         }
368 |       }
369 |     }
370 | 
371 |     return results;
372 |   },
373 | 
374 |   /**
375 |    * search for full-text terms in the index
376 |    */
377 |   performTermsSearch : function(searchterms, excluded, terms, titleterms) {
378 |     var docnames = this._index.docnames;
379 |     var filenames = this._index.filenames;
380 |     var titles = this._index.titles;
381 | 
382 |     var i, j, file;
383 |     var fileMap = {};
384 |     var scoreMap = {};
385 |     var results = [];
386 | 
387 |     // perform the search on the required terms
388 |     for (i = 0; i < searchterms.length; i++) {
389 |       var word = searchterms[i];
390 |       var files = [];
391 |       var _o = [
392 |         {files: terms[word], score: Scorer.term},
393 |         {files: titleterms[word], score: Scorer.title}
394 |       ];
395 |       // add support for partial matches
396 |       if (word.length > 2) {
397 |         for (var w in terms) {
398 |           if (w.match(word) && !terms[word]) {
399 |             _o.push({files: terms[w], score: Scorer.partialTerm})
400 |           }
401 |         }
402 |         for (var w in titleterms) {
403 |           if (w.match(word) && !titleterms[word]) {
404 |               _o.push({files: titleterms[w], score: Scorer.partialTitle})
405 |           }
406 |         }
407 |       }
408 | 
409 |       // no match but word was a required one
410 |       if ($u.every(_o, function(o){return o.files === undefined;})) {
411 |         break;
412 |       }
413 |       // found search word in contents
414 |       $u.each(_o, function(o) {
415 |         var _files = o.files;
416 |         if (_files === undefined)
417 |           return
418 | 
419 |         if (_files.length === undefined)
420 |           _files = [_files];
421 |         files = files.concat(_files);
422 | 
423 |         // set score for the word in each file to Scorer.term
424 |         for (j = 0; j < _files.length; j++) {
425 |           file = _files[j];
426 |           if (!(file in scoreMap))
427 |             scoreMap[file] = {};
428 |           scoreMap[file][word] = o.score;
429 |         }
430 |       });
431 | 
432 |       // create the mapping
433 |       for (j = 0; j < files.length; j++) {
434 |         file = files[j];
435 |         if (file in fileMap && fileMap[file].indexOf(word) === -1)
436 |           fileMap[file].push(word);
437 |         else
438 |           fileMap[file] = [word];
439 |       }
440 |     }
441 | 
442 |     // now check if the files don't contain excluded terms
443 |     for (file in fileMap) {
444 |       var valid = true;
445 | 
446 |       // check if all requirements are matched
447 |       var filteredTermCount = // as search terms with length < 3 are discarded: ignore
448 |         searchterms.filter(function(term){return term.length > 2}).length
449 |       if (
450 |         fileMap[file].length != searchterms.length &&
451 |         fileMap[file].length != filteredTermCount
452 |       ) continue;
453 | 
454 |       // ensure that none of the excluded terms is in the search result
455 |       for (i = 0; i < excluded.length; i++) {
456 |         if (terms[excluded[i]] == file ||
457 |             titleterms[excluded[i]] == file ||
458 |             $u.contains(terms[excluded[i]] || [], file) ||
459 |             $u.contains(titleterms[excluded[i]] || [], file)) {
460 |           valid = false;
461 |           break;
462 |         }
463 |       }
464 | 
465 |       // if we have still a valid result we can add it to the result list
466 |       if (valid) {
467 |         // select one (max) score for the file.
468 |         // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
469 |         var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
470 |         results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
471 |       }
472 |     }
473 |     return results;
474 |   },
475 | 
476 |   /**
477 |    * helper function to return a node containing the
478 |    * search summary for a given text. keywords is a list
479 |    * of stemmed words, hlwords is the list of normal, unstemmed
480 |    * words. the first one is used to find the occurrence, the
481 |    * latter for highlighting it.
482 |    */
483 |   makeSearchSummary : function(htmlText, keywords, hlwords) {
484 |     var text = Search.htmlToText(htmlText);
485 |     var textLower = text.toLowerCase();
486 |     var start = 0;
487 |     $.each(keywords, function() {
488 |       var i = textLower.indexOf(this.toLowerCase());
489 |       if (i > -1)
490 |         start = i;
491 |     });
492 |     start = Math.max(start - 120, 0);
493 |     var excerpt = ((start > 0) ? '...' : '') +
494 |       $.trim(text.substr(start, 240)) +
495 |       ((start + 240 - text.length) ? '...' : '');
496 |     var rv = $('<div class="context"></div>').text(excerpt);
497 |     $.each(hlwords, function() {
498 |       rv = rv.highlightText(this, 'highlighted');
499 |     });
500 |     return rv;
501 |   }
502 | };
503 | 
504 | $(document).ready(function() {
505 |   Search.init();
506 | });
507 | 


--------------------------------------------------------------------------------
/docs/_build/html/_static/underscore.js:
--------------------------------------------------------------------------------
 1 | // Underscore.js 1.3.1
 2 | // (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc.
 3 | // Underscore is freely distributable under the MIT license.
 4 | // Portions of Underscore are inspired or borrowed from Prototype,
 5 | // Oliver Steele's Functional, and John Resig's Micro-Templating.
 6 | // For all details and documentation:
 7 | // http://documentcloud.github.com/underscore
 8 | (function(){function q(a,c,d){if(a===c)return a!==0||1/a==1/c;if(a==null||c==null)return a===c;if(a._chain)a=a._wrapped;if(c._chain)c=c._wrapped;if(a.isEqual&&b.isFunction(a.isEqual))return a.isEqual(c);if(c.isEqual&&b.isFunction(c.isEqual))return c.isEqual(a);var e=l.call(a);if(e!=l.call(c))return false;switch(e){case "[object String]":return a==String(c);case "[object Number]":return a!=+a?c!=+c:a==0?1/a==1/c:a==+c;case "[object Date]":case "[object Boolean]":return+a==+c;case "[object RegExp]":return a.source==
 9 | c.source&&a.global==c.global&&a.multiline==c.multiline&&a.ignoreCase==c.ignoreCase}if(typeof a!="object"||typeof c!="object")return false;for(var f=d.length;f--;)if(d[f]==a)return true;d.push(a);var f=0,g=true;if(e=="[object Array]"){if(f=a.length,g=f==c.length)for(;f--;)if(!(g=f in a==f in c&&q(a[f],c[f],d)))break}else{if("constructor"in a!="constructor"in c||a.constructor!=c.constructor)return false;for(var h in a)if(b.has(a,h)&&(f++,!(g=b.has(c,h)&&q(a[h],c[h],d))))break;if(g){for(h in c)if(b.has(c,
10 | h)&&!f--)break;g=!f}}d.pop();return g}var r=this,G=r._,n={},k=Array.prototype,o=Object.prototype,i=k.slice,H=k.unshift,l=o.toString,I=o.hasOwnProperty,w=k.forEach,x=k.map,y=k.reduce,z=k.reduceRight,A=k.filter,B=k.every,C=k.some,p=k.indexOf,D=k.lastIndexOf,o=Array.isArray,J=Object.keys,s=Function.prototype.bind,b=function(a){return new m(a)};if(typeof exports!=="undefined"){if(typeof module!=="undefined"&&module.exports)exports=module.exports=b;exports._=b}else r._=b;b.VERSION="1.3.1";var j=b.each=
11 | b.forEach=function(a,c,d){if(a!=null)if(w&&a.forEach===w)a.forEach(c,d);else if(a.length===+a.length)for(var e=0,f=a.length;e<f;e++){if(e in a&&c.call(d,a[e],e,a)===n)break}else for(e in a)if(b.has(a,e)&&c.call(d,a[e],e,a)===n)break};b.map=b.collect=function(a,c,b){var e=[];if(a==null)return e;if(x&&a.map===x)return a.map(c,b);j(a,function(a,g,h){e[e.length]=c.call(b,a,g,h)});if(a.length===+a.length)e.length=a.length;return e};b.reduce=b.foldl=b.inject=function(a,c,d,e){var f=arguments.length>2;a==
12 | null&&(a=[]);if(y&&a.reduce===y)return e&&(c=b.bind(c,e)),f?a.reduce(c,d):a.reduce(c);j(a,function(a,b,i){f?d=c.call(e,d,a,b,i):(d=a,f=true)});if(!f)throw new TypeError("Reduce of empty array with no initial value");return d};b.reduceRight=b.foldr=function(a,c,d,e){var f=arguments.length>2;a==null&&(a=[]);if(z&&a.reduceRight===z)return e&&(c=b.bind(c,e)),f?a.reduceRight(c,d):a.reduceRight(c);var g=b.toArray(a).reverse();e&&!f&&(c=b.bind(c,e));return f?b.reduce(g,c,d,e):b.reduce(g,c)};b.find=b.detect=
13 | function(a,c,b){var e;E(a,function(a,g,h){if(c.call(b,a,g,h))return e=a,true});return e};b.filter=b.select=function(a,c,b){var e=[];if(a==null)return e;if(A&&a.filter===A)return a.filter(c,b);j(a,function(a,g,h){c.call(b,a,g,h)&&(e[e.length]=a)});return e};b.reject=function(a,c,b){var e=[];if(a==null)return e;j(a,function(a,g,h){c.call(b,a,g,h)||(e[e.length]=a)});return e};b.every=b.all=function(a,c,b){var e=true;if(a==null)return e;if(B&&a.every===B)return a.every(c,b);j(a,function(a,g,h){if(!(e=
14 | e&&c.call(b,a,g,h)))return n});return e};var E=b.some=b.any=function(a,c,d){c||(c=b.identity);var e=false;if(a==null)return e;if(C&&a.some===C)return a.some(c,d);j(a,function(a,b,h){if(e||(e=c.call(d,a,b,h)))return n});return!!e};b.include=b.contains=function(a,c){var b=false;if(a==null)return b;return p&&a.indexOf===p?a.indexOf(c)!=-1:b=E(a,function(a){return a===c})};b.invoke=function(a,c){var d=i.call(arguments,2);return b.map(a,function(a){return(b.isFunction(c)?c||a:a[c]).apply(a,d)})};b.pluck=
15 | function(a,c){return b.map(a,function(a){return a[c]})};b.max=function(a,c,d){if(!c&&b.isArray(a))return Math.max.apply(Math,a);if(!c&&b.isEmpty(a))return-Infinity;var e={computed:-Infinity};j(a,function(a,b,h){b=c?c.call(d,a,b,h):a;b>=e.computed&&(e={value:a,computed:b})});return e.value};b.min=function(a,c,d){if(!c&&b.isArray(a))return Math.min.apply(Math,a);if(!c&&b.isEmpty(a))return Infinity;var e={computed:Infinity};j(a,function(a,b,h){b=c?c.call(d,a,b,h):a;b<e.computed&&(e={value:a,computed:b})});
16 | return e.value};b.shuffle=function(a){var b=[],d;j(a,function(a,f){f==0?b[0]=a:(d=Math.floor(Math.random()*(f+1)),b[f]=b[d],b[d]=a)});return b};b.sortBy=function(a,c,d){return b.pluck(b.map(a,function(a,b,g){return{value:a,criteria:c.call(d,a,b,g)}}).sort(function(a,b){var c=a.criteria,d=b.criteria;return c<d?-1:c>d?1:0}),"value")};b.groupBy=function(a,c){var d={},e=b.isFunction(c)?c:function(a){return a[c]};j(a,function(a,b){var c=e(a,b);(d[c]||(d[c]=[])).push(a)});return d};b.sortedIndex=function(a,
17 | c,d){d||(d=b.identity);for(var e=0,f=a.length;e<f;){var g=e+f>>1;d(a[g])<d(c)?e=g+1:f=g}return e};b.toArray=function(a){return!a?[]:a.toArray?a.toArray():b.isArray(a)?i.call(a):b.isArguments(a)?i.call(a):b.values(a)};b.size=function(a){return b.toArray(a).length};b.first=b.head=function(a,b,d){return b!=null&&!d?i.call(a,0,b):a[0]};b.initial=function(a,b,d){return i.call(a,0,a.length-(b==null||d?1:b))};b.last=function(a,b,d){return b!=null&&!d?i.call(a,Math.max(a.length-b,0)):a[a.length-1]};b.rest=
18 | b.tail=function(a,b,d){return i.call(a,b==null||d?1:b)};b.compact=function(a){return b.filter(a,function(a){return!!a})};b.flatten=function(a,c){return b.reduce(a,function(a,e){if(b.isArray(e))return a.concat(c?e:b.flatten(e));a[a.length]=e;return a},[])};b.without=function(a){return b.difference(a,i.call(arguments,1))};b.uniq=b.unique=function(a,c,d){var d=d?b.map(a,d):a,e=[];b.reduce(d,function(d,g,h){if(0==h||(c===true?b.last(d)!=g:!b.include(d,g)))d[d.length]=g,e[e.length]=a[h];return d},[]);
19 | return e};b.union=function(){return b.uniq(b.flatten(arguments,true))};b.intersection=b.intersect=function(a){var c=i.call(arguments,1);return b.filter(b.uniq(a),function(a){return b.every(c,function(c){return b.indexOf(c,a)>=0})})};b.difference=function(a){var c=b.flatten(i.call(arguments,1));return b.filter(a,function(a){return!b.include(c,a)})};b.zip=function(){for(var a=i.call(arguments),c=b.max(b.pluck(a,"length")),d=Array(c),e=0;e<c;e++)d[e]=b.pluck(a,""+e);return d};b.indexOf=function(a,c,
20 | d){if(a==null)return-1;var e;if(d)return d=b.sortedIndex(a,c),a[d]===c?d:-1;if(p&&a.indexOf===p)return a.indexOf(c);for(d=0,e=a.length;d<e;d++)if(d in a&&a[d]===c)return d;return-1};b.lastIndexOf=function(a,b){if(a==null)return-1;if(D&&a.lastIndexOf===D)return a.lastIndexOf(b);for(var d=a.length;d--;)if(d in a&&a[d]===b)return d;return-1};b.range=function(a,b,d){arguments.length<=1&&(b=a||0,a=0);for(var d=arguments[2]||1,e=Math.max(Math.ceil((b-a)/d),0),f=0,g=Array(e);f<e;)g[f++]=a,a+=d;return g};
21 | var F=function(){};b.bind=function(a,c){var d,e;if(a.bind===s&&s)return s.apply(a,i.call(arguments,1));if(!b.isFunction(a))throw new TypeError;e=i.call(arguments,2);return d=function(){if(!(this instanceof d))return a.apply(c,e.concat(i.call(arguments)));F.prototype=a.prototype;var b=new F,g=a.apply(b,e.concat(i.call(arguments)));return Object(g)===g?g:b}};b.bindAll=function(a){var c=i.call(arguments,1);c.length==0&&(c=b.functions(a));j(c,function(c){a[c]=b.bind(a[c],a)});return a};b.memoize=function(a,
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23 | a.apply(d,e);i();g=true}};b.debounce=function(a,b){var d;return function(){var e=this,f=arguments;clearTimeout(d);d=setTimeout(function(){d=null;a.apply(e,f)},b)}};b.once=function(a){var b=false,d;return function(){if(b)return d;b=true;return d=a.apply(this,arguments)}};b.wrap=function(a,b){return function(){var d=[a].concat(i.call(arguments,0));return b.apply(this,d)}};b.compose=function(){var a=arguments;return function(){for(var b=arguments,d=a.length-1;d>=0;d--)b=[a[d].apply(this,b)];return b[0]}};
24 | b.after=function(a,b){return a<=0?b():function(){if(--a<1)return b.apply(this,arguments)}};b.keys=J||function(a){if(a!==Object(a))throw new TypeError("Invalid object");var c=[],d;for(d in a)b.has(a,d)&&(c[c.length]=d);return c};b.values=function(a){return b.map(a,b.identity)};b.functions=b.methods=function(a){var c=[],d;for(d in a)b.isFunction(a[d])&&c.push(d);return c.sort()};b.extend=function(a){j(i.call(arguments,1),function(b){for(var d in b)a[d]=b[d]});return a};b.defaults=function(a){j(i.call(arguments,
25 | 1),function(b){for(var d in b)a[d]==null&&(a[d]=b[d])});return a};b.clone=function(a){return!b.isObject(a)?a:b.isArray(a)?a.slice():b.extend({},a)};b.tap=function(a,b){b(a);return a};b.isEqual=function(a,b){return q(a,b,[])};b.isEmpty=function(a){if(b.isArray(a)||b.isString(a))return a.length===0;for(var c in a)if(b.has(a,c))return false;return true};b.isElement=function(a){return!!(a&&a.nodeType==1)};b.isArray=o||function(a){return l.call(a)=="[object Array]"};b.isObject=function(a){return a===Object(a)};
26 | b.isArguments=function(a){return l.call(a)=="[object Arguments]"};if(!b.isArguments(arguments))b.isArguments=function(a){return!(!a||!b.has(a,"callee"))};b.isFunction=function(a){return l.call(a)=="[object Function]"};b.isString=function(a){return l.call(a)=="[object String]"};b.isNumber=function(a){return l.call(a)=="[object Number]"};b.isNaN=function(a){return a!==a};b.isBoolean=function(a){return a===true||a===false||l.call(a)=="[object Boolean]"};b.isDate=function(a){return l.call(a)=="[object Date]"};
27 | b.isRegExp=function(a){return l.call(a)=="[object RegExp]"};b.isNull=function(a){return a===null};b.isUndefined=function(a){return a===void 0};b.has=function(a,b){return I.call(a,b)};b.noConflict=function(){r._=G;return this};b.identity=function(a){return a};b.times=function(a,b,d){for(var e=0;e<a;e++)b.call(d,e)};b.escape=function(a){return(""+a).replace(/&/g,"&amp;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/"/g,"&quot;").replace(/'/g,"&#x27;").replace(/\//g,"&#x2F;")};b.mixin=function(a){j(b.functions(a),
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31 | true;return this};m.prototype.value=function(){return this._wrapped}}).call(this);
32 | 


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/docs/_build/html/genindex.html:
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  1 | 
  2 | <!DOCTYPE html>
  3 | <html class="writer-html5" lang="en" >
  4 | <head>
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 37 |               <p class="caption"><span class="caption-text">Contents:</span></p>
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 64 |              
 65 | 
 66 | <h1 id="index">Index</h1>
 67 | 
 68 | <div class="genindex-jumpbox">
 69 |  <a href="#A"><strong>A</strong></a>
 70 |  | <a href="#C"><strong>C</strong></a>
 71 |  | <a href="#D"><strong>D</strong></a>
 72 |  | <a href="#G"><strong>G</strong></a>
 73 |  | <a href="#K"><strong>K</strong></a>
 74 |  | <a href="#L"><strong>L</strong></a>
 75 |  | <a href="#M"><strong>M</strong></a>
 76 |  | <a href="#N"><strong>N</strong></a>
 77 |  | <a href="#P"><strong>P</strong></a>
 78 |  | <a href="#R"><strong>R</strong></a>
 79 |  | <a href="#S"><strong>S</strong></a>
 80 |  | <a href="#W"><strong>W</strong></a>
 81 |  
 82 | </div>
 83 | <h2 id="A">A</h2>
 84 | <table style="width: 100%" class="indextable genindextable"><tr>
 85 |   <td style="width: 33%; vertical-align: top;"><ul>
 86 |       <li><a href="pychi.html#pychi.light.Light.add_shot_noise">add_shot_noise() (pychi.light.Light method)</a>
 87 | </li>
 88 |   </ul></td>
 89 |   <td style="width: 33%; vertical-align: top;"><ul>
 90 |       <li><a href="pychi.html#pychi.light.Arbitrary">Arbitrary (class in pychi.light)</a>
 91 | </li>
 92 |   </ul></td>
 93 | </tr></table>
 94 | 
 95 | <h2 id="C">C</h2>
 96 | <table style="width: 100%" class="indextable genindextable"><tr>
 97 |   <td style="width: 33%; vertical-align: top;"><ul>
 98 |       <li><a href="pychi.html#pychi.models.Chi2">Chi2 (class in pychi.models)</a>
 99 | </li>
100 |       <li><a href="pychi.html#pychi.models.Chi2Chi3">Chi2Chi3 (class in pychi.models)</a>
101 | </li>
102 |       <li><a href="pychi.html#pychi.models.Chi3">Chi3 (class in pychi.models)</a>
103 | </li>
104 |   </ul></td>
105 |   <td style="width: 33%; vertical-align: top;"><ul>
106 |       <li><a href="pychi.html#pychi.materials.Waveguide.chi_2">chi_2() (pychi.materials.Waveguide property)</a>
107 | </li>
108 |       <li><a href="pychi.html#pychi.materials.Waveguide.chi_3">chi_3() (pychi.materials.Waveguide property)</a>
109 | </li>
110 |       <li><a href="pychi.html#pychi.materials.Waveguide.compute_betas">compute_betas() (pychi.materials.Waveguide method)</a>
111 | </li>
112 |       <li><a href="pychi.html#pychi.light.Cw">Cw (class in pychi.light)</a>
113 | </li>
114 |   </ul></td>
115 | </tr></table>
116 | 
117 | <h2 id="D">D</h2>
118 | <table style="width: 100%" class="indextable genindextable"><tr>
119 |   <td style="width: 33%; vertical-align: top;"><ul>
120 |       <li><a href="pychi.html#pychi.models.Model.dispersion_step">dispersion_step() (pychi.models.Model method)</a>
121 | </li>
122 |   </ul></td>
123 | </tr></table>
124 | 
125 | <h2 id="G">G</h2>
126 | <table style="width: 100%" class="indextable genindextable"><tr>
127 |   <td style="width: 33%; vertical-align: top;"><ul>
128 |       <li><a href="pychi.html#pychi.light.Gaussian">Gaussian (class in pychi.light)</a>
129 | </li>
130 |   </ul></td>
131 | </tr></table>
132 | 
133 | <h2 id="K">K</h2>
134 | <table style="width: 100%" class="indextable genindextable"><tr>
135 |   <td style="width: 33%; vertical-align: top;"><ul>
136 |       <li><a href="pychi.html#pychi.materials.Waveguide.k">k() (pychi.materials.Waveguide property)</a>
137 | </li>
138 |   </ul></td>
139 | </tr></table>
140 | 
141 | <h2 id="L">L</h2>
142 | <table style="width: 100%" class="indextable genindextable"><tr>
143 |   <td style="width: 33%; vertical-align: top;"><ul>
144 |       <li><a href="pychi.html#pychi.light.Light">Light (class in pychi.light)</a>
145 | </li>
146 |   </ul></td>
147 | </tr></table>
148 | 
149 | <h2 id="M">M</h2>
150 | <table style="width: 100%" class="indextable genindextable"><tr>
151 |   <td style="width: 33%; vertical-align: top;"><ul>
152 |       <li><a href="pychi.html#pychi.models.Model">Model (class in pychi.models)</a>
153 | </li>
154 |   </ul></td>
155 | </tr></table>
156 | 
157 | <h2 id="N">N</h2>
158 | <table style="width: 100%" class="indextable genindextable"><tr>
159 |   <td style="width: 33%; vertical-align: top;"><ul>
160 |       <li><a href="pychi.html#pychi.materials.Waveguide.n_eff">n_eff() (pychi.materials.Waveguide property)</a>
161 | </li>
162 |       <li><a href="pychi.html#pychi.models.Chi2.nonlinear_term">nonlinear_term() (pychi.models.Chi2 method)</a>
163 | 
164 |       <ul>
165 |         <li><a href="pychi.html#pychi.models.Chi2Chi3.nonlinear_term">(pychi.models.Chi2Chi3 method)</a>
166 | </li>
167 |         <li><a href="pychi.html#pychi.models.Chi3.nonlinear_term">(pychi.models.Chi3 method)</a>
168 | </li>
169 |         <li><a href="pychi.html#pychi.models.Model.nonlinear_term">(pychi.models.Model method)</a>
170 | </li>
171 |         <li><a href="pychi.html#pychi.models.Spm.nonlinear_term">(pychi.models.Spm method)</a>
172 | </li>
173 |         <li><a href="pychi.html#pychi.models.SpmChi2.nonlinear_term">(pychi.models.SpmChi2 method)</a>
174 | </li>
175 |         <li><a href="pychi.html#pychi.models.SpmChi2Chi3.nonlinear_term">(pychi.models.SpmChi2Chi3 method)</a>
176 | </li>
177 |         <li><a href="pychi.html#pychi.models.SpmChi3.nonlinear_term">(pychi.models.SpmChi3 method)</a>
178 | </li>
179 |       </ul></li>
180 |   </ul></td>
181 |   <td style="width: 33%; vertical-align: top;"><ul>
182 |       <li><a href="pychi.html#pychi.models.numbaconj">numbaconj (in module pychi.models)</a>
183 | </li>
184 |       <li><a href="pychi.html#pychi.models.numbacopy">numbacopy (in module pychi.models)</a>
185 | </li>
186 |       <li><a href="pychi.html#pychi.models.numbaexp">numbaexp (in module pychi.models)</a>
187 | 
188 |       <ul>
189 |         <li><a href="pychi.html#pychi.solvers.numbaexp">(in module pychi.solvers)</a>
190 | </li>
191 |       </ul></li>
192 |       <li><a href="pychi.html#pychi.solvers.numbanorm">numbanorm (in module pychi.solvers)</a>
193 | </li>
194 |   </ul></td>
195 | </tr></table>
196 | 
197 | <h2 id="P">P</h2>
198 | <table style="width: 100%" class="indextable genindextable"><tr>
199 |   <td style="width: 33%; vertical-align: top;"><ul>
200 |       <li><a href="pychi.html#pychi.light.Light.plot_propagation">plot_propagation() (pychi.light.Light method)</a>
201 | </li>
202 |       <li><a href="pychi.html#pychi.materials.Waveguide.plot_refractive_index">plot_refractive_index() (pychi.materials.Waveguide method)</a>
203 | </li>
204 |       <li><a href="pychi.html#module-pychi">pychi (module)</a>
205 | </li>
206 |   </ul></td>
207 |   <td style="width: 33%; vertical-align: top;"><ul>
208 |       <li><a href="pychi.html#module-pychi.light">pychi.light (module)</a>
209 | </li>
210 |       <li><a href="pychi.html#module-pychi.materials">pychi.materials (module)</a>
211 | </li>
212 |       <li><a href="pychi.html#module-pychi.models">pychi.models (module)</a>
213 | </li>
214 |       <li><a href="pychi.html#module-pychi.solvers">pychi.solvers (module)</a>
215 | </li>
216 |   </ul></td>
217 | </tr></table>
218 | 
219 | <h2 id="R">R</h2>
220 | <table style="width: 100%" class="indextable genindextable"><tr>
221 |   <td style="width: 33%; vertical-align: top;"><ul>
222 |       <li><a href="pychi.html#pychi.materials.Waveguide.rhs_prefactor">rhs_prefactor() (pychi.materials.Waveguide property)</a>
223 | </li>
224 |   </ul></td>
225 | </tr></table>
226 | 
227 | <h2 id="S">S</h2>
228 | <table style="width: 100%" class="indextable genindextable"><tr>
229 |   <td style="width: 33%; vertical-align: top;"><ul>
230 |       <li><a href="pychi.html#pychi.light.Sech">Sech (class in pychi.light)</a>
231 | </li>
232 |       <li><a href="pychi.html#pychi.materials.Waveguide.set_betas">set_betas() (pychi.materials.Waveguide method)</a>
233 | </li>
234 |       <li><a href="pychi.html#pychi.materials.Waveguide.set_gamma">set_gamma() (pychi.materials.Waveguide method)</a>
235 | </li>
236 |       <li><a href="pychi.html#pychi.materials.Waveguide.set_n2">set_n2() (pychi.materials.Waveguide method)</a>
237 | </li>
238 |       <li><a href="pychi.html#pychi.light.Light.set_result_as_start">set_result_as_start() (pychi.light.Light method)</a>
239 | </li>
240 |   </ul></td>
241 |   <td style="width: 33%; vertical-align: top;"><ul>
242 |       <li><a href="pychi.html#pychi.solvers.Solver.solve">solve() (pychi.solvers.Solver method)</a>
243 | </li>
244 |       <li><a href="pychi.html#pychi.solvers.Solver">Solver (class in pychi.solvers)</a>
245 | </li>
246 |       <li><a href="pychi.html#pychi.models.Spm">Spm (class in pychi.models)</a>
247 | </li>
248 |       <li><a href="pychi.html#pychi.models.SpmChi2">SpmChi2 (class in pychi.models)</a>
249 | </li>
250 |       <li><a href="pychi.html#pychi.models.SpmChi2Chi3">SpmChi2Chi3 (class in pychi.models)</a>
251 | </li>
252 |       <li><a href="pychi.html#pychi.models.SpmChi3">SpmChi3 (class in pychi.models)</a>
253 | </li>
254 |   </ul></td>
255 | </tr></table>
256 | 
257 | <h2 id="W">W</h2>
258 | <table style="width: 100%" class="indextable genindextable"><tr>
259 |   <td style="width: 33%; vertical-align: top;"><ul>
260 |       <li><a href="pychi.html#pychi.materials.Waveguide">Waveguide (class in pychi.materials)</a>
261 | </li>
262 |   </ul></td>
263 | </tr></table>
264 | 
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  1 | <!DOCTYPE html>
  2 | <html class="writer-html5" lang="en" >
  3 | <head>
  4 |   <meta charset="utf-8" />
  5 |   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
  6 |   <title>Python Module Index &mdash; pychi 0.0.1 documentation</title><link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
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 66 |              
 67 | 
 68 |    <h1>Python Module Index</h1>
 69 | 
 70 |    <div class="modindex-jumpbox">
 71 |    <a href="#cap-p"><strong>p</strong></a>
 72 |    </div>
 73 | 
 74 |    <table class="indextable modindextable">
 75 |      <tr class="pcap"><td></td><td>&#160;</td><td></td></tr>
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 87 |        <a href="pychi.html#module-pychi.light"><code class="xref">pychi.light</code></a></td><td>
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 91 |        <td>&#160;&#160;&#160;
 92 |        <a href="pychi.html#module-pychi.materials"><code class="xref">pychi.materials</code></a></td><td>
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 99 |      <tr class="cg-1">
100 |        <td></td>
101 |        <td>&#160;&#160;&#160;
102 |        <a href="pychi.html#module-pychi.solvers"><code class="xref">pychi.solvers</code></a></td><td>
103 |        <em></em></td></tr>
104 |    </table>
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 10 |     <script src="_static/js/html5shiv.min.js"></script>
 11 |   <![endif]-->
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 20 |     <link rel="index" title="Index" href="genindex.html" />
 21 |     <link rel="search" title="Search" href="#" /> 
 22 | </head>
 23 | 
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/docs/conf.py:
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 1 | # Configuration file for the Sphinx documentation builder.
 2 | #
 3 | # This file only contains a selection of the most common options. For a full
 4 | # list see the documentation:
 5 | # https://www.sphinx-doc.org/en/master/usage/configuration.html
 6 | 
 7 | # -- Path setup --------------------------------------------------------------
 8 | 
 9 | # If extensions (or modules to document with autodoc) are in another directory,
10 | # add these directories to sys.path here. If the directory is relative to the
11 | # documentation root, use os.path.abspath to make it absolute, like shown here.
12 | #
13 | import os
14 | import sys
15 | 
16 | sys.path.insert(0, os.path.abspath('../src'))
17 | 
18 | 
19 | # -- Project information -----------------------------------------------------
20 | 
21 | project = 'pychi'
22 | copyright = '2023, Thibault Voumard'
23 | author = 'Thibault Voumard'
24 | 
25 | # The full version, including alpha/beta/rc tags
26 | release = '0.0.12'
27 | 
28 | 
29 | # -- General configuration ---------------------------------------------------
30 | 
31 | # Add any Sphinx extension module names here, as strings. They can be
32 | # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
33 | # ones.
34 | extensions = [
35 | 'sphinx.ext.autodoc',
36 | 'sphinx.ext.viewcode',
37 | 'sphinx.ext.napoleon',
38 | 'sphinx_rtd_theme',
39 | 'myst_parser'
40 | ]
41 | 
42 | # Add any paths that contain templates here, relative to this directory.
43 | templates_path = ['_templates']
44 | 
45 | # List of patterns, relative to source directory, that match files and
46 | # directories to ignore when looking for source files.
47 | # This pattern also affects html_static_path and html_extra_path.
48 | exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']
49 | 
50 | 
51 | # -- Options for HTML output -------------------------------------------------
52 | 
53 | # Tell Sphinx to document private methods
54 | #autodoc_default_options = {
55 | #    "members": True,
56 | #    "undoc-members": True,
57 | #    "private-members": True
58 | #}
59 | 
60 | autodoc_mock_imports = ["matplotlib", "scipy", "numpy", "pyfftw", "numba"]
61 | 
62 | # The theme to use for HTML and HTML Help pages.  See the documentation for
63 | # a list of builtin themes.
64 | #
65 | html_theme = 'sphinx_rtd_theme'
66 | 
67 | # Add any paths that contain custom static files (such as style sheets) here,
68 | # relative to this directory. They are copied after the builtin static files,
69 | # so a file named "default.css" will overwrite the builtin "default.css".
70 | html_static_path = []
71 | 


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/docs/index.rst:
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 1 | .. pychi documentation master file, created by
 2 |    sphinx-quickstart on Fri Mar  3 10:39:56 2023.
 3 |    You can adapt this file completely to your liking, but it should at least
 4 |    contain the root `toctree` directive.
 5 | 
 6 | Welcome to pychi's documentation!
 7 | =================================
 8 | 
 9 | .. toctree::
10 |    :maxdepth: 2
11 |    :caption: Contents:
12 | 
13 |    readme_link
14 |    pychi
15 | 


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/docs/make.bat:
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 1 | @ECHO OFF
 2 | 
 3 | pushd %~dp0
 4 | 
 5 | REM Command file for Sphinx documentation
 6 | 
 7 | if "%SPHINXBUILD%" == "" (
 8 | 	set SPHINXBUILD=sphinx-build
 9 | )
10 | set SOURCEDIR=.
11 | set BUILDDIR=_build
12 | 
13 | if "%1" == "" goto help
14 | 
15 | %SPHINXBUILD% >NUL 2>NUL
16 | if errorlevel 9009 (
17 | 	echo.
18 | 	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
19 | 	echo.installed, then set the SPHINXBUILD environment variable to point
20 | 	echo.to the full path of the 'sphinx-build' executable. Alternatively you
21 | 	echo.may add the Sphinx directory to PATH.
22 | 	echo.
23 | 	echo.If you don't have Sphinx installed, grab it from
24 | 	echo.http://sphinx-doc.org/
25 | 	exit /b 1
26 | )
27 | 
28 | %SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
29 | goto end
30 | 
31 | :help
32 | %SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
33 | 
34 | :end
35 | popd
36 | 


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/docs/modules.rst:
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1 | pychi package
2 | ===
3 | 
4 | .. toctree::
5 |    :maxdepth: 4
6 | 
7 |    pychi
8 | 


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/docs/pychi.rst:
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 1 | pychi package
 2 | =============
 3 | 
 4 | pychi.light module
 5 | ------------------
 6 | 
 7 | .. automodule:: pychi.light
 8 |    :members:
 9 |    :undoc-members:
10 |    :show-inheritance:
11 | 
12 | pychi.materials module
13 | ----------------------
14 | 
15 | .. automodule:: pychi.materials
16 |    :members:
17 |    :undoc-members:
18 |    :show-inheritance:
19 | 
20 | pychi.models module
21 | -------------------
22 | 
23 | .. automodule:: pychi.models
24 |    :members:
25 |    :undoc-members:
26 |    :show-inheritance:
27 | 
28 | pychi.solvers module
29 | --------------------
30 | 
31 | .. automodule:: pychi.solvers
32 |    :members:
33 |    :undoc-members:
34 |    :show-inheritance:
35 | 
36 | 


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/docs/readme_link.rst:
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1 | .. include:: ../README.md
2 |    :parser: myst_parser.sphinx_


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/docs/requirements.txt:
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1 | myst-parser
2 | sphinx_rtd_theme
3 | 


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/examples/Cascaded Nonlinearities/pychi_cascaded.py:
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 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Mon Feb 28 15:31:47 2022
 4 | 
 5 | The waveguide/fiber parameters are first provided, and a Waveguide instance
 6 | is created. Then, the pulse parameters are used to create a Light object.
 7 | A physical model is then chosen, taking into account different nonlinear
 8 | interactions based on the user choice. Finally, a solver is instantiated
 9 | and computes the propagation of the pulse in the waveguide with the chosen
10 | nonlinear interactions.
11 | 
12 | @author: voumardt
13 | """
14 | import matplotlib.pyplot as plt
15 | import numpy as np
16 | import os
17 | from scipy.constants import c
18 | 
19 | import sys
20 | sys.path.append(os.getcwd() + '../../../')
21 | 
22 | from src import  *
23 | 
24 | 
25 | """
26 | User parameters
27 | """
28 | ### Simulation
29 | t_pts = 2**17
30 | 
31 | ### Light
32 | pulse_duration = 100e-15
33 | pulse_wavelength = 1.56e-06
34 | pulse_energy = 1.6e-9
35 | 
36 | ### Waveguide
37 | wg_length = 0.001
38 | wg_chi_2 = 1.1e-12
39 | wg_chi_3 = 3.4e-21
40 | wg_a_eff = 1e-12
41 | wg_freq, wg_n_eff = np.load('effective_index.npy')
42 | 
43 | 
44 | """
45 | Nonlinear propagation
46 | """
47 | ### Prepare waveguide
48 | waveguide = materials.Waveguide(wg_freq, wg_n_eff, wg_chi_2, wg_chi_3,
49 |                                 wg_a_eff, wg_length, t_pts=t_pts)
50 | 
51 | ### Prepare input pulse
52 | pulse = light.Sech(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
53 | 
54 | ### Prepare model
55 | model = models.SpmChi2Chi3(waveguide, pulse)
56 | 
57 | ### Prepare solver, solve
58 | solver = solvers.Solver(model)
59 | solver.solve()
60 | 
61 | 
62 | """
63 | Plots
64 | """
65 | pulse.plot_propagation('cascaded.png')
66 | 
67 | 


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/examples/LiNb/pychi_LiNb_exp_vs_sim.py:
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 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Mon Feb 28 15:31:47 2022
 4 | 
 5 | @author: voumardt
 6 | """
 7 | import matplotlib.pyplot as plt
 8 | import numpy as np
 9 | import os
10 | import pandas
11 | from scipy.constants import c
12 | from scipy.io import loadmat
13 | 
14 | import sys
15 | sys.path.append(os.getcwd() + '../../../')
16 | 
17 | from src import  *
18 | 
19 | 
20 | """
21 | User parameters
22 | """
23 | ### Simulation
24 | t_pts = 2**16
25 | 
26 | ### Light
27 | pulse_duration = 80e-15
28 | pulse_wavelength = 1.58e-06
29 | pulse_energy = 1.056e-11
30 | 
31 | ### Waveguide
32 | wg_length = 0.006
33 | wg_chi_2 = 20e-12
34 | wg_chi_3 = 2.5e-21 # Raman lasing and soliton mode-locking in lithium niobate microresonators
35 | wg_a_eff = 1e-12
36 | wg_freq, wg_n_eff = np.load('n_eff_data_LiNb.npy')
37 | 
38 | 
39 | """
40 | Nonlinear propagation
41 | """
42 | waveguide = materials.Waveguide(wg_freq, wg_n_eff, wg_chi_2, wg_chi_3,
43 |                                 wg_a_eff, wg_length, t_pts=t_pts)
44 | pulse = light.Sech(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
45 | model = models.SpmChi2(waveguide, pulse)
46 | solver = solvers.Solver(model)
47 | solver.solve()
48 | 
49 | 
50 | """
51 | Plots
52 | """
53 | pulse.plot_propagation()
54 | 
55 | # Load experimental results
56 | exp_data = loadmat('exp_LiNb.mat')
57 | exp_wl = exp_data['wavelength'][0]
58 | exp_int = exp_data['intensity'][0]
59 | 
60 | # Compare experimental results and simulation
61 | plt.figure()
62 | plt.plot(pulse.wl, 10*np.log10(pulse.spectrum_wl[-1]/np.amax(pulse.spectrum_wl[-1]))-3)
63 | plt.plot(exp_wl, exp_int - np.amax(exp_int))
64 | plt.xlim(3.5e-7, 1.75e-6)
65 | plt.ylim(-75, 5)
66 | plt.title('Experimental vs simulation - LiNb')
67 | plt.xlabel('Wavelength [m]')
68 | plt.ylabel('Intensity [dB]')
69 | plt.legend(('Simulation', 'Experiment'))
70 | plt.savefig('Experimental_vs_simulation_LiNb.png')
71 | 


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/examples/QPM/pychi_QPM.py:
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 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Mon Feb 28 15:31:47 2022
 4 | 
 5 | The waveguide/fiber parameters are first provided, and a Waveguide instance
 6 | is created. Then, the pulse parameters are used to create a Light object.
 7 | A physical model is then chosen, taking into account different nonlinear
 8 | interactions based on the user choice. Finally, a solver is instantiated
 9 | and computes the propagation of the pulse in the waveguide with the chosen
10 | nonlinear interactions. This particular examples shows how to define a poling
11 | and breakpoints forcing computation at some desired distances.
12 | 
13 | @author: voumardt
14 | """
15 | import matplotlib.pyplot as plt
16 | import numpy as np
17 | import os
18 | 
19 | import sys
20 | sys.path.append(os.getcwd() + '../../../')
21 | 
22 | from src import  *
23 | 
24 | 
25 | """
26 | User parameters
27 | """
28 | ### Simulation
29 | t_pts = 2**15
30 | 
31 | ### Light
32 | pulse_duration = 100e-15
33 | pulse_wavelength = 1.56e-06
34 | pulse_energy = 1e-9
35 | 
36 | ### Waveguide
37 | wg_length = 0.001
38 | const_wg_chi_2 = 1.1e-12
39 | 
40 | # poling period
41 | qpm_length = 3.3e-5/2
42 | 
43 | wg_chi_3 = 3.4e-21
44 | wg_a_eff = 1e-12
45 | wg_freq, wg_n_eff = np.load('effective_index.npy')
46 | 
47 | # Define the nonlinearity as a function of z
48 | def wg_chi_2(z):
49 |     return (-1)**(np.floor(z/qpm_length)%2)*const_wg_chi_2
50 | 
51 | # Define breakpoints to force computation whenever the poling changes sign
52 | breakpoints = np.arange(wg_length//qpm_length)*qpm_length + 1e-10
53 | 
54 | """
55 | Nonlinear propagation
56 | """
57 | waveguide = materials.Waveguide(wg_freq, wg_n_eff, wg_chi_2, wg_chi_3,
58 |                                 wg_a_eff, wg_length, t_pts=t_pts)
59 | pulse = light.Sech(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
60 | model = models.Chi2(waveguide, pulse)
61 | solver = solvers.Solver(model, method='ERK4IP', breakpoints=breakpoints)
62 | solver.solve()
63 | 
64 | 
65 | """
66 | Plots
67 | """
68 | pulse.plot_propagation()
69 | 


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/examples/SPM/pychi_spm_validation.py:
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  1 | # -*- coding: utf-8 -*-
  2 | """
  3 | Created on Mon Feb 28 15:31:47 2022
  4 | 
  5 | @author: voumardt
  6 | """
  7 | import matplotlib.pyplot as plt
  8 | import numpy as np
  9 | from scipy.constants import c
 10 | eps_0 = 8.8541878128e-12
 11 | import math
 12 | import os
 13 | 
 14 | import sys
 15 | sys.path.append(os.getcwd() + '../../../')
 16 | 
 17 | from src import  *
 18 | 
 19 | 
 20 | """
 21 | User parameters
 22 | 
 23 | Parameters taken from 'Supercontinuum generation in photonic crystal fiber',
 24 | John M. Dudley, Goëry Genty, and Stéphane Coen, DOI: https://doi.org/10.1103/RevModPhys.78.1135
 25 | to reproduce figure 3 therein.
 26 | """
 27 | ### Simulation
 28 | t_pts = 2**14
 29 | 
 30 | ### Light
 31 | pulse_duration = 50e-15
 32 | pulse_wavelength = 0.835e-06
 33 | pulse_peak_power = 1e4
 34 | pulse_energy = pulse_peak_power*pulse_duration/np.log(1+2**0.5)
 35 | 
 36 | ### Waveguide
 37 | wg_length = 0.15
 38 | wg_chi_2 = 0
 39 | wg_a_eff = 1e-12
 40 | wg_n = 1.45
 41 | gamma = 0.11
 42 | wg_chi_3 = 4*wg_n**2*c*eps_0*gamma*pulse_wavelength*wg_a_eff/6/np.pi
 43 | wg_omega = np.linspace(c/1670e-9*2*np.pi, c/417.5e-9*2*np.pi, t_pts)
 44 | betas = [wg_n*2*np.pi/pulse_wavelength, wg_n/c, -1.183e-26, 8.1038e-41,
 45 |          -9.5205e-56, 2.0737e-70, -5.3943e-85, 1.3486e-99, -2.5495e-114,
 46 |          3.0524e-129, -1.7140e-144]
 47 | 
 48 | ### Compute refractive index
 49 | wg_freq = wg_omega/2/np.pi
 50 | def compute_n_eff(wg_omega, pulse_wavelength, betas):
 51 |     k = np.zeros(t_pts, dtype='float64')
 52 |     for i, beta in enumerate(betas):
 53 |         k += beta*(wg_omega - 2*np.pi*c/pulse_wavelength)**i/math.factorial(i)
 54 |     n_eff = k*c/wg_omega
 55 |     return n_eff
 56 | wg_n_eff = compute_n_eff(wg_omega, pulse_wavelength, betas)
 57 | 
 58 | 
 59 | """
 60 | Nonlinear propagation
 61 | """
 62 | ### Prepare waveguide
 63 | waveguide = materials.Waveguide(wg_freq, wg_n_eff, wg_chi_2, wg_chi_3,
 64 |                                 wg_a_eff, wg_length, t_pts=t_pts)
 65 | 
 66 | ### Prepare input pulse
 67 | pulse = light.Sech(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
 68 | 
 69 | ### Prepare model
 70 | model = models.Spm(waveguide, pulse)
 71 | 
 72 | ### Prepare solver
 73 | solver = solvers.Solver(model)
 74 | 
 75 | ### Solve
 76 | solver.solve()
 77 | 
 78 | 
 79 | """
 80 | Plots
 81 | """
 82 | z_pos = pulse.z_save
 83 | wl = pulse.wl
 84 | spec_wl = pulse.spectrum_wl[:, (wl>450e-9)&(wl<1300e-9)]
 85 | wl = wl[(wl>450e-9)&(wl<1300e-9)]
 86 | spec_wl_db = 20*np.log10(np.abs(spec_wl) + 1e-20)
 87 | 
 88 | 
 89 | plt.figure()
 90 | plt.subplot(121)
 91 | plt.imshow(spec_wl_db[::-1], cmap='jet', aspect='auto', vmin=np.amax(spec_wl_db) - 40,
 92 |            extent=(np.amin(wl)*1e9, np.amax(wl)*1e9, 0, np.amax(z_pos)))
 93 | plt.xlabel('Wavelength [nm]')
 94 | plt.ylabel('Distance [m]')
 95 | 
 96 | waveform = 10*np.log10(np.abs(pulse.waveform)**2 + 1e-20) - np.amax(10*np.log10(np.abs(pulse.waveform)**2 + 1e-20))
 97 | time = waveguide.time
 98 | waveform = waveform[:, (time<5e-12)&(time>-2e-12)]
 99 | time = time[(time<5e-12)&(time>-2e-12)]
100 | 
101 | plt.subplot(122)
102 | plt.imshow(waveform[::-1], cmap='jet', aspect='auto', vmin = np.amax(waveform) - 40,
103 |            extent=(np.amin(time)*1e12, np.amax(time)*1e12, 0, np.amax(z_pos)))
104 | plt.xlabel('Time [ps]')
105 | plt.ylabel('Distance [m]')
106 | plt.colorbar(label='Intensity [dB]')
107 | plt.tight_layout()
108 | plt.savefig('propagation.png')
109 | 


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/examples/SiN/pychi_SiN_exp_vs_sim.py:
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 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Mon Feb 28 15:31:47 2022
 4 | 
 5 | @author: voumardt
 6 | """
 7 | import matplotlib.pyplot as plt
 8 | import numpy as np
 9 | import os
10 | import pandas
11 | from scipy.constants import c
12 | from scipy.io import loadmat
13 | 
14 | import sys
15 | sys.path.append(os.getcwd() + '../../../')
16 | 
17 | from src import  *
18 | 
19 | 
20 | """
21 | User parameters
22 | """
23 | ### Simulation
24 | t_pts = 2**17
25 | 
26 | ### Light
27 | pulse_duration = 80e-15
28 | pulse_wavelength = 1.56e-6
29 | pulse_energy = 1e-10
30 | 
31 | ### Waveguide
32 | wg_length = 0.0058
33 | wg_chi_2 = 0
34 | wg_chi_3 = 2.8e-21
35 | wg_a_eff = 3e-13
36 | wg_freq, wg_n_eff = np.load('n_eff_data_SiN.npy')
37 | 
38 | 
39 | """
40 | Nonlinear propagation
41 | """
42 | waveguide = materials.Waveguide(wg_freq, wg_n_eff, wg_chi_2, wg_chi_3,
43 |                                 wg_a_eff, wg_length, t_pts=t_pts)
44 | pulse = light.Sech(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
45 | model = models.SpmChi3(waveguide, pulse)
46 | solver = solvers.Solver(model)
47 | solver.solve()
48 | 
49 | 
50 | """
51 | Plots
52 | """
53 | pulse.plot_propagation()
54 | 
55 | # Load experimental results
56 | exp_data = loadmat('exp_SiN.mat')
57 | exp_wl = exp_data['wavelength'][0]
58 | exp_int = exp_data['intensity'][0]
59 | 
60 | # Compare experimental results and simulation
61 | plt.figure()
62 | plt.plot(pulse.wl, 10*np.log10(pulse.spectrum_wl[-1]/np.amax(pulse.spectrum_wl[-1]))-15)
63 | plt.plot(exp_wl, exp_int - np.amax(exp_int))
64 | plt.xlim(3.5e-7, 1.75e-6)
65 | plt.ylim(-75, 5)
66 | plt.title('Experimental vs simulation - SiN')
67 | plt.xlabel('Wavelength [m]')
68 | plt.ylabel('Intensity [dB]')
69 | plt.legend(('Simulation', 'Experiment'))
70 | plt.savefig('Experimental_vs_simulation_SiN.png')
71 | 


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/examples/pychi_example.py:
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 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Mon Feb 28 15:31:47 2022
 4 | 
 5 | The waveguide/fiber parameters are first provided, and a Waveguide instance
 6 | is created. Then, the pulse parameters are used to create a Light object.
 7 | A physical model is then chosen, taking into account different nonlinear
 8 | interactions based on the user choice. Finally, a solver is instantiated
 9 | and computes the propagation of the pulse in the waveguide with the chosen
10 | nonlinear interactions.
11 | 
12 | @author: voumardt
13 | """
14 | import matplotlib.pyplot as plt
15 | import numpy as np
16 | from scipy.constants import c
17 | 
18 | from src import  *
19 | 
20 | 
21 | """
22 | User parameters
23 | """
24 | ### Simulation
25 | t_pts = 2**15
26 | 
27 | ### Light
28 | pulse_duration = 100e-15
29 | pulse_wavelength = 1.56e-06
30 | pulse_energy = 1e-9
31 | 
32 | ### Waveguide
33 | wg_length = 0.001
34 | wg_chi_2 = 1.1e-12
35 | wg_chi_3 = 3.4e-21
36 | wg_a_eff = 1e-12
37 | wg_freq, wg_n_eff = np.load('effective_index.npy')
38 | 
39 | 
40 | """
41 | Nonlinear propagation
42 | """
43 | ### Prepare waveguide
44 | waveguide = materials.Waveguide(wg_freq, wg_n_eff, wg_chi_2, wg_chi_3,
45 |                                 wg_a_eff, wg_length, t_pts=t_pts)
46 | # Additional options:
47 | # One can provide beta coefficients (strongly discouraged) overwriting the refractive
48 | # index using waveguide.set_betas(betas, wavelength)
49 | #
50 | # wg_n_eff can be a 2 dimensional array, with first dimension the wavelength dependence
51 | # and second dimension the z dependence.
52 | #
53 | # chi2 and chi3 can be callables, returning a z dependent value. Alternatively, they
54 | # can be defined as one dimensional arrays describing their z dependence, or
55 | # two dimensional arrays describing their z and frequency dependence.
56 | #
57 | # One can use waveguide.set_gamma(gamma) or waveguide.set_n2(n2) to provide
58 | # nonlinear coefficient or nonlinear refractive index and overwrite chi3.
59 | #
60 | # Check documentation for more options and details.
61 | 
62 | 
63 | ### Prepare input pulse
64 | pulse = light.Sech(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
65 | # Other available pulse shapes:
66 | # pulse = light.Gaussian(waveguide, pulse_duration, pulse_energy, pulse_wavelength)
67 | # pulse = light.Cw(waveguide, pulse_average_power, pulse_wavelength)
68 | # pulse = light.Arbitrary(waveguide, pulse_frequency_axis, pulse_electric_field, pulse_energy)
69 | 
70 | 
71 | ### Prepare model
72 | model = models.SpmChi2Chi3(waveguide, pulse)
73 | # Other models available:
74 | # model = models.Spm(waveguide, pulse)
75 | # model = models.Chi2(waveguide, pulse)
76 | # model = models.Chi3(waveguide, pulse)
77 | # model = models.SpmChi2(waveguide, pulse)
78 | # model = models.SpmChi3(waveguide, pulse)
79 | # model = models.Chi2Chi3(waveguide, pulse)
80 | 
81 | 
82 | ### Prepare solver, solve
83 | solver = solvers.Solver(model)
84 | solver.solve()
85 | 
86 | 
87 | """
88 | Plots
89 | """
90 | pulse.plot_propagation()
91 | # Results can also be accessed via pulse.z_save, pulse.freq, pulse.spectrum, pulse.waveform
92 | # The refractive index and GVD can be seen with waveguide.plot_refractive_index()
93 | 


--------------------------------------------------------------------------------
/pyproject.toml:
--------------------------------------------------------------------------------
 1 | [build-system]
 2 | requires = ["setuptools"]
 3 | build-backend = "setuptools.build_meta"
 4 | 
 5 | [tool.setuptools]
 6 | package-dir = {"" = "src"}
 7 | 
 8 | [project]
 9 | name = "pychi"
10 | version = ""
11 | authors = [
12 |   { name="Ultrafast Microphotonics Group - DESY", email="pychi@desy.de" },
13 | ]
14 | description = "Simulation package for the propagation of optical pulses in nonlinear media"
15 | readme = "README.md"
16 | requires-python = ">=3.7"
17 | classifiers = [
18 |     "Programming Language :: Python :: 3",
19 |     "License :: OSI Approved :: MIT License",
20 |     "Operating System :: OS Independent",
21 | ]
22 | 
23 | dependencies = [
24 |     "matplotlib>=3.1.3",
25 |     "numpy>=1.21.6",
26 |     "scipy>=1.4.1",
27 |     "numba>=0.56.0",
28 |     "pyFFTW>=0.12.0",
29 | ]
30 | 
31 | 
32 | [project.urls]
33 | "Homepage" = "https://github.com/pychi-code/pychi"
34 | "Documentation" = "https://pychi.readthedocs.io/en/latest/index.html"
35 | "PyPI" = "https://pypi.org/project/pychi/"
36 | 


--------------------------------------------------------------------------------
/requirements.txt:
--------------------------------------------------------------------------------
1 | matplotlib>=3.1.3
2 | numpy>=1.21.6
3 | scipy>=1.4.1
4 | numba>=0.56.0
5 | pyFFTW>=0.12.0
6 | 


--------------------------------------------------------------------------------
/src/pychi/__init__.py:
--------------------------------------------------------------------------------
 1 | # -*- coding: utf-8 -*-
 2 | """
 3 | Created on Thu Feb 17 12:32:49 2022
 4 | 
 5 | @author: voumardt
 6 | """
 7 | __version__ = '0.0.5'
 8 | 
 9 | from . import light
10 | from . import materials
11 | from . import models
12 | from . import solvers
13 | 


--------------------------------------------------------------------------------
/src/pychi/light.py:
--------------------------------------------------------------------------------
  1 | # -*- coding: utf-8 -*-
  2 | """
  3 | Created on Fri Aug 13 12:01:48 2021
  4 | 
  5 | @author: Thibault
  6 | 
  7 | This module contains the classes used to instantiate light. Different
  8 | standard pulse shapes are built-in, and a class is dedicated to accomodating
  9 | user-provided light with arbitrary spectral shape. Note that the electric
 10 | field is stored as an analytical envelope, thus is a complex quantity.
 11 | """
 12 | import matplotlib.pyplot as plt
 13 | import numpy as np
 14 | from scipy.constants import c, h
 15 | from scipy.interpolate import interp1d
 16 | eps_0 = 8.8541878128e-12
 17 | 
 18 | 
 19 | class Light():
 20 |     """
 21 |     Parent light class. Implement support for adding pulses,
 22 |     saving the results of a propagation and plotting these
 23 |     results. Not suitable for light instantiation.
 24 |     """
 25 |     def __init__(self, waveguide, field_t_in):
 26 |         """
 27 |         Light is here defined by a time axis coming from a
 28 |         waveguide object, and a temporal waveform.
 29 | 
 30 |         Parameters
 31 |         ----------
 32 |         waveguide : Waveguide
 33 |             Waveguide object containing the material properties.
 34 |         field_t_in : array
 35 |             Array containing the complex temporal waveform of the
 36 |             initial analytical electric field.
 37 |         """
 38 |         self.waveguide = waveguide
 39 |         self.field_t_in = field_t_in
 40 |     
 41 |     def __add__(self, light):
 42 |         """
 43 |         Addition operator overload. Allow one to add pulses easily.
 44 | 
 45 |         Parameters
 46 |         ----------
 47 |         light : Light object
 48 |             Light with field to be added.
 49 | 
 50 |         Returns
 51 |         -------
 52 |         Light
 53 |             New Light object with field added.
 54 |         """
 55 |         tot_field = self.field_t_in + light.field_t_in
 56 |         return Light(self.waveguide, tot_field)
 57 |         
 58 |     def _set_propagation(self, z_save, freq, spectrum, waveform):
 59 |         """
 60 |         Store propagation results. Called from the solver module
 61 |         after finishing propagation.
 62 |         """
 63 |         self.z_save = z_save
 64 |         self.freq = freq
 65 |         self.spectrum = spectrum
 66 |         self.waveform = waveform
 67 |         self.wl, self.spectrum_wl = self._compute_equidistant_wl_spectrum()
 68 |         
 69 |     def _compute_equidistant_wl_spectrum(self):
 70 |         """
 71 |         Compute a properly normalized field representation in the wavelength
 72 |         domain with equidistantly spaced sampling points.
 73 | 
 74 |         Returns
 75 |         -------
 76 |         array
 77 |             Field in the wavelength domain.
 78 |         """
 79 |         wl = c/self.freq
 80 |         wl_ener = np.abs(self.freq*self.spectrum/np.sqrt(c))**2*wl
 81 |         wl_ener_interp = interp1d(wl, wl_ener, kind='linear')
 82 |         wl_eq = np.linspace(np.amin(wl), np.amax(wl), len(self.field_t_in))
 83 |         ener_wl_eq = wl_ener_interp(wl_eq)
 84 |         return wl_eq, np.sqrt(ener_wl_eq/wl_eq)
 85 |         
 86 |     def _set_dB(self):
 87 |         """
 88 |         Return a function to compute the dB representation of a field
 89 |         normalized to the input light spectrum.
 90 |         """
 91 |         if self.spectrum is not None:
 92 |             return lambda field: 20*np.log10(np.abs(field) + 1e-20) - np.amax(20*np.log10(np.abs(self.spectrum[0]) + 1e-20))
 93 |         else:
 94 |             pass
 95 | 
 96 |     def add_group_delay_dispersion(self, d2):
 97 |         """
 98 |         Add group delay dispersion (chirp) to the light field.
 99 | 
100 |         Parameters
101 |         ----------
102 |         d2 : float
103 |             Group delay dispersion
104 |         """
105 |         field_angle = np.angle(self.field_t_in)
106 |         field_angle *= d2/2*self.waveguide.rel_omega**2
107 |         self.field_t_in = np.abs(self.field_t_in)*np.exp(1j*field_angle)
108 |         
109 |     def add_shot_noise(self, seed=None):
110 |         """
111 |         Add shot noise to the pulse, useful for coherence study.
112 | 
113 |         Parameters
114 |         ----------
115 |         seed : int
116 |             Seed for the random number generator for reproducibility.
117 |         """
118 |         if seed is not None:
119 |             np.random.seed(seed)
120 |             
121 |         field_angle = np.angle(self.field_t_in)
122 |         
123 |         e_to_n_fac = eps_0*self.waveguide.n_eff_inter(c/self.pulse_wavelength)
124 |         e_to_n_fac *= self.pulse_wavelength*self.waveguide.eff_area
125 |         e_to_n_fac *= self.waveguide.delta_t/2/h
126 |         
127 |         photons_per_bin = e_to_n_fac*np.abs(self.field_t_in)**2
128 |         photons_per_bin = np.random.poisson(photons_per_bin)
129 | 
130 |         noisy_field = np.sqrt(photons_per_bin/e_to_n_fac).astype(np.complex128)
131 |         noisy_field *= np.exp(1j*field_angle)
132 |         self.field_t_in = noisy_field
133 |         
134 |     def plot_propagation(self, savename=None):
135 |         """
136 |         Plot propagation results.
137 |         """
138 |         if self.spectrum is not None:
139 |             self.dB = self._set_dB()
140 |             ### Overall figure
141 |             fig = plt.figure(figsize=(10,10))
142 |             ax0 = plt.subplot2grid((3,2), (0, 0), rowspan=1)
143 |             ax1 = plt.subplot2grid((3,2), (0, 1), rowspan=1)
144 |             ax2 = plt.subplot2grid((3,2), (1, 0), rowspan=2, sharex=ax0)
145 |             ax3 = plt.subplot2grid((3,2), (1, 1), rowspan=2, sharex=ax1)
146 |             
147 |             # Input and output spectrum
148 |             ax0.plot(self.freq, self.dB(self.spectrum)[0], color='b')
149 |             ax0.plot(self.freq, self.dB(self.spectrum)[-1], color='r')
150 |             ax0.set_ylabel('Intensity [dB]')
151 |             ax0.set_ylim(-100, 5)
152 |             
153 |             # Input and output pulse
154 |             ax1.plot(self.waveguide.time, np.abs(self.waveform)[-1], color='r')
155 |             ax1.plot(self.waveguide.time, np.abs(self.waveform)[0], color='b')
156 |             
157 |             # Spectrum color map
158 |             extent = (np.amin(self.freq[self.freq>0]), np.max(self.freq), 0, self.waveguide.length)
159 |             ax2.imshow(self.dB(self.spectrum[:, self.freq>0]), extent=extent, vmin=np.amax(self.dB(self.spectrum)) - 100.0,
160 |                               vmax=np.amax(self.dB(self.spectrum)), aspect='auto', origin='lower')
161 |             ax2.set_xlabel('Frequency [Hz]')
162 |             ax2.set_ylabel('Propagation distance [m]')
163 |             
164 |             # Pulse color map
165 |             extent = (np.min(self.waveguide.time), np.max(self.waveguide.time), 0, self.waveguide.length)
166 |             plt_waveform = np.abs(self.waveform)
167 |             ax3.imshow(plt_waveform, extent=extent, vmin=np.amin(plt_waveform[-1]),
168 |                         vmax=np.amax(plt_waveform), aspect='auto', origin='lower')
169 |             ax3.set_xlabel('Time [s]')
170 |             
171 |             plt.suptitle('Propagation results')
172 |             fig.tight_layout()
173 |             plt.show()
174 |             if savename is not None:
175 |                 plt.savefig(savename)
176 | 
177 |             ### Spectrogram
178 |             plt.figure(22222)
179 |             specgram, _, _, _ = plt.specgram(self.waveform[-1],
180 |                          Fs=np.amax(self.freq)-np.amin(self.freq),
181 |                          Fc=(np.amax(self.freq)+np.amin(self.freq))/2,
182 |                          xextent=(np.amin(self.waveguide.time), np.amax(self.waveguide.time)),
183 |                          mode='magnitude',
184 |                          scale='dB',
185 |                          sides='twosided')
186 |             plt.close(22222)
187 |             plt.figure()
188 |             ax0 = plt.subplot(221)
189 |             plt.specgram(self.waveform[-1],
190 |                          Fs=np.amax(self.freq)-np.amin(self.freq),
191 |                          Fc=(np.amax(self.freq)+np.amin(self.freq))/2,
192 |                          xextent=(np.amin(self.waveguide.time), np.amax(self.waveguide.time)),
193 |                          mode='magnitude',
194 |                          scale='dB',
195 |                          vmax=20*np.log10(np.amax(specgram)),
196 |                          vmin=20*np.log10(np.amax(specgram))-100,
197 |                          sides='twosided')
198 |             plt.ylabel('Frequency [Hz]')
199 |             
200 |             plt.subplot(222, sharey=ax0)
201 |             plt.plot(20*np.log10(np.abs(self.spectrum[-1])) - np.amax(20*np.log10(np.abs(self.spectrum[-1]))), self.freq)
202 |             plt.xlabel('Intensity [dB]')
203 |             plt.xlim(5, -100)
204 |             plt.ylim((np.amin(self.freq), np.amax(self.freq)))
205 |             
206 |             plt.subplot(223, sharex=ax0)
207 |             plt.plot(self.waveguide.time, np.abs(self.waveform[-1])**2)
208 |             plt.xlabel('Time [s]')
209 |             plt.ylabel('Intensity [a.u.]')
210 |             plt.xlim((np.amin(self.waveguide.time), np.amax(self.waveguide.time)))
211 |             plt.tight_layout()
212 |             if savename is not None:
213 |                 plt.savefig('spec_' + savename)
214 |             
215 |         else:
216 |             pass
217 |         
218 |     def set_result_as_start(self, waveguide=None):
219 |         """
220 |         Set output field from propagation as initial field for a new
221 |         propagation.
222 | 
223 |         Returns
224 |         -------
225 |         Light
226 |             New Light object with final propagation result as input field.
227 |         """
228 |         if waveguide is None:
229 |             waveguide = self.waveguide
230 |         if self.spectrum is not None:
231 |             field_t_in = self.waveform[-1]
232 |             return Light(waveguide, field_t_in)
233 |         else:
234 |             pass
235 | 
236 | 
237 | class Sech(Light):
238 |     """
239 |     Class for a sech pulse.
240 |     """
241 |     def __init__(self, waveguide, pulse_duration, pulse_energy,
242 |                  pulse_wavelength, delay=0):
243 |         """
244 |         Construct a sech pulse.
245 | 
246 |         Parameters
247 |         ----------
248 |         waveguide : Waveguide
249 |             Waveguide object containing the material properties.
250 |         pulse_duration : float
251 |             Pulse FWHM duration.
252 |         pulse_energy : float
253 |             Energy per pulse.
254 |         pulse_wavelength : float
255 |             Central wavelength of the pulse.
256 |         delay: float, defaults to 0.
257 |             Time offset of the pulse.
258 |         """
259 |         self.pulse_duration = pulse_duration
260 |         self.pulse_energy = pulse_energy
261 |         self.pulse_wavelength = pulse_wavelength
262 |         self.waveguide = waveguide
263 |         self.delay = delay
264 |         self.field_t_in = self._compute_field()
265 |     
266 |     def _compute_field(self):
267 |         """
268 |         Instantiate electric field as a sech pulse.
269 | 
270 |         Returns
271 |         -------
272 |         array
273 |             Analytical envelope of the electric field.
274 |         """
275 |         pulse_peak_power = 0.8813736*self.pulse_energy/self.pulse_duration
276 |         field_t_in = np.sqrt(pulse_peak_power)/np.cosh(1.7627472*(self.waveguide.time - self.delay)/self.pulse_duration)\
277 |             *np.exp(1j*(2*np.pi*c/self.pulse_wavelength - self.waveguide.center_omega)*(self.waveguide.time - self.delay))
278 |         field_t_in /= np.sqrt(self.waveguide.n_eff_inter(c/self.pulse_wavelength)*eps_0*c*self.waveguide.eff_area/2)
279 |         return field_t_in
280 | 
281 | 
282 | class Gaussian(Light):
283 |     """
284 |     Class for a Gaussian pulse.
285 |     """
286 |     def __init__(self, waveguide, pulse_duration, pulse_energy,
287 |                  pulse_wavelength, delay=0):
288 |         """
289 |         Construct a Gaussian pulse.
290 | 
291 |         Parameters
292 |         ----------
293 |         waveguide : Waveguide
294 |             Waveguide object containing the material properties.
295 |         pulse_duration : float
296 |             Pulse FWHM duration.
297 |         pulse_energy : float
298 |             Energy per pulse.
299 |         pulse_wavelength : float
300 |             Central wavelength of the pulse.
301 |         delay: float, defaults to 0.
302 |             Time offset of the pulse.
303 |         """
304 |         self.pulse_duration = pulse_duration
305 |         self.pulse_energy = pulse_energy
306 |         self.pulse_wavelength = pulse_wavelength
307 |         self.waveguide = waveguide
308 |         self.delay = delay
309 |         self.field_t_in = self._compute_field()
310 |     
311 |     def _compute_field(self):
312 |         """
313 |         Instantiate electric field as a gaussian pulse.
314 | 
315 |         Returns
316 |         -------
317 |         array
318 |             Analytical envelope of the electric field.
319 |         """
320 |         amplitude = 2*self.pulse_energy*np.sqrt(8*np.log(2)/np.pi)
321 |         amplitude /= self.waveguide.n_eff_inter(c/self.pulse_wavelength)
322 |         amplitude /= eps_0*c*self.pulse_duration*self.waveguide.eff_area
323 |         field_t_in = np.sqrt(amplitude)*np.exp(-4*np.log(2)*(self.waveguide.time - self.delay)**2/self.pulse_duration**2)\
324 |             *np.exp(1j*(2*np.pi*c/self.pulse_wavelength - self.waveguide.center_omega)*(self.waveguide.time - self.delay))
325 |         return field_t_in
326 | 
327 | 
328 | class Cw(Light):
329 |     """
330 |     Class for CW light.
331 |     """
332 |     def __init__(self, waveguide, average_power, wavelength):
333 |         """
334 |         Construct CW light.
335 |         
336 |         Parameters
337 |         ----------
338 |         waveguide : Waveguide
339 |             Waveguide object containing the material properties.
340 |         pulse_average_power : float
341 |             Average power of the CW light.
342 |         pulse_wavelength : float
343 |             Central wavelength of the light.
344 |         """
345 |         self.pulse_average_power = average_power
346 |         self.pulse_wavelength = wavelength
347 |         self.waveguide = waveguide
348 |         self.field_t_in = self._compute_field()
349 |         
350 |     def _compute_field(self):
351 |         """
352 |         Instantiate electric field as a continuous wave.
353 | 
354 |         Returns
355 |         -------
356 |         array
357 |             Analytical envelope of the electric field.
358 |         """
359 |         field_t_in = np.exp(1j*(2*np.pi*c/self.pulse_wavelength - self.waveguide.center_omega)*self.waveguide.time)
360 |         field_t_in *= np.sqrt(2*self.pulse_average_power/self.waveguide.n_eff_inter(c/self.pulse_wavelength)/eps_0/c/self.waveguide.eff_area)
361 |         return field_t_in
362 |     
363 | 
364 | class Arbitrary(Light):
365 |     """
366 |     Class for arbitrary light waveform, specified in frequency domain.
367 |     """
368 |     def __init__(self, waveguide, pulse_frequency_axis, pulse_electric_field,
369 |                  pulse_energy):
370 |         """
371 |         Construct an arbitrary waveform from its frequency domain field.
372 | 
373 |         Parameters
374 |         ----------
375 |         waveguide : Waveguide
376 |             Waveguide object containing the material properties.
377 |         pulse_frequency_axis : array
378 |             Frequency axis associated to the field.
379 |         pulse_electric_field : array
380 |             Analytical envelope representation of electric field in the frequency domain.
381 |         pulse_energy : float
382 |             Energy per pulse, used to normalize the field amplitude.
383 |         """
384 |         self.pulse_energy = pulse_energy
385 |         self.data_freq = pulse_frequency_axis
386 |         self.data_field = pulse_electric_field
387 |         self.pulse_wavelength = self._compute_center_wavelength()
388 |         self.waveguide = waveguide
389 |         self.field_t_in = self._compute_field()
390 |     
391 |     def _compute_center_wavelength(self):
392 |         """
393 |         Compute the carrier wavelength of the pulse.
394 |         """
395 |         pw = np.sum(np.abs(self.data_field)*self.data_freq)
396 |         pw /= np.sum(np.abs(self.data_field))
397 |         return c/pw
398 |         
399 |     def _compute_field(self):
400 |         """
401 |         Instantiate input light as a user-specified waveform.
402 | 
403 |         Returns
404 |         -------
405 |         array
406 |             Analytical envelope of the electric field.
407 |         """
408 |         field_interp = interp1d(self.data_freq, self.data_field, kind='cubic',
409 |                                 bounds_error=False, fill_value=0.0)
410 |         field_f_in = field_interp(self.waveguide.freq)
411 |         field_t_in = np.fft.fftshift(np.fft.ifft(np.fft.ifftshift(field_f_in)))
412 |         temp = np.sum(np.abs(field_t_in)**2)*self.waveguide.delta_t
413 |         field_t_in *= np.sqrt(2*self.pulse_energy/(temp*self.waveguide.n_eff_inter(c/self.pulse_wavelength)*eps_0*c*self.waveguide.eff_area))
414 |         return field_t_in
415 |         
416 | 


--------------------------------------------------------------------------------
/src/pychi/materials.py:
--------------------------------------------------------------------------------
  1 | # -*- coding: utf-8 -*-
  2 | from inspect import signature
  3 | from math import factorial
  4 | import matplotlib.pyplot as plt
  5 | import numpy as np
  6 | from scipy.interpolate import interp1d
  7 | from scipy.constants import c
  8 | eps_0 = 8.8541878128e-12
  9 | 
 10 | class Waveguide():
 11 |     """
 12 |     Waveguide class. Contains all material related information, i.e. the
 13 |     refractive index curve versus frequency, the Raman parameters, the
 14 |     nonlinear coefficients, the effective area and length. This object
 15 |     should be the first object instantiated, as the time/frequency axes of
 16 |     the simulation are derived here from the available refractive
 17 |     index data.
 18 | 
 19 |     Parameters
 20 |     ----------
 21 |     frequency : array
 22 |         Frequency axis on which the effective refractive index is given.
 23 |     n_eff : float, vector, array or callable
 24 |         Effective refractive index of the material.
 25 |     chi_2 : float, vector, array or callable
 26 |         Order 2 material nonlinearity. 
 27 |     chi_3 : float, vector, array or callable
 28 |         Order 3 material nonlinearity.
 29 |     effective_area : float
 30 |         Effective area at the pump wavelength.
 31 |     length : float
 32 |         Length of the material.
 33 |     raman_fraction : float
 34 |         Fractional contribution of the Raman effect to the Kerr effect.
 35 |         The default is 0.18.
 36 |     raman_tau_1 : float
 37 |         Raman effect primary time scale. The default is 0.0122e-12.
 38 |     raman_tau_2 : float
 39 |         Raman effect secondary time scale. The default is 0.032e-12.
 40 |     t_pts : float, optional
 41 |         Number of points in the time and frequency axes, will be rounded
 42 |         to nearest higher power of 2. The default is 2**14.
 43 |     """
 44 |     def __init__(self, frequency, n_eff, chi_2, chi_3,
 45 |                  effective_area, length, raman_fraction=0.18,
 46 |                  raman_tau_1=0.0122e-12, raman_tau_2=0.032e-12,
 47 |                  t_pts=2**14):
 48 |         self.z = 0
 49 |         self.t_pts = int(2**np.ceil(np.log2(t_pts)))
 50 |         self.length = length
 51 |         self.data_freq = frequency
 52 |         self.center_freq, self.freq = self._compute_frequency_axis()
 53 |         self.center_omega, self.omega, self.rel_omega = self._compute_omega_axis()
 54 |         self.time, self.delta_t = self._compute_time_axis()
 55 |         
 56 |         self.n_eff = n_eff
 57 |         
 58 |         self.chi_2 = chi_2
 59 |         self.chi_3 = chi_3
 60 |         self.eff_area = effective_area
 61 |         
 62 |         # Standard Raman response for fibers
 63 |         self.raman_fraction = raman_fraction
 64 |         self.raman_tau_1 = raman_tau_1
 65 |         self.raman_tau_2 = raman_tau_2
 66 |         self.raman_effect = self._compute_raman_effect()
 67 |     
 68 |     @property
 69 |     def n_eff(self):
 70 |         """Get the effective refractive index at position z."""
 71 |         return self._n_eff(self.z)
 72 |     
 73 |     @n_eff.setter
 74 |     def n_eff(self, n_eff):
 75 |         """
 76 |         Set the effective refractive index. Change any float, vector or
 77 |         array provided by the user into a z-callable function. A version
 78 |         interpolated in frequency is also kept for other operations.
 79 |         Beta coefficients are computed at this stage - they are
 80 |         solely used for plotting purpose.
 81 |         """
 82 |         self._n_eff = self._make_callable(n_eff)
 83 |         self.n_eff_inter = self._interpolate_n_eff()
 84 |         self.betas = self.compute_betas()
 85 |     
 86 |     @property
 87 |     def chi_2(self):
 88 |         """Get the quadratic nonlinear coefficient at position z."""
 89 |         return self._chi_2(self.z)
 90 |     
 91 |     @chi_2.setter
 92 |     def chi_2(self, chi_2):
 93 |         """
 94 |         Set the quadractic nonlinear coefficient. Change any float,
 95 |         vector or array provided by the user into a z-callable
 96 |         function.
 97 |         """
 98 |         self._chi_2 = self._make_callable(chi_2)
 99 |         
100 |     @property
101 |     def chi_3(self):
102 |         """Get the cubic nonlinear coefficient at position z."""
103 |         return self._chi_3(self.z)
104 |     
105 |     @chi_3.setter
106 |     def chi_3(self, chi_3):
107 |         """
108 |         Set the quadractic nonlinear coefficient. Change any float,
109 |         vector or array provided by the user into a z-callable
110 |         function.
111 |         """
112 |         self._chi_3 = self._make_callable(chi_3)
113 |     
114 |     @property
115 |     def k(self):
116 |         """Get the wavevectors at position z."""
117 |         return np.fft.fftshift(self.n_eff*self.omega/c)
118 |         
119 |     @property
120 |     def rhs_prefactor(self):
121 |         """Get the GNLSE right-hand-side prefactor at position z."""
122 |         return -1j*np.fft.fftshift(self.omega/(2*self.n_eff*c))
123 |     
124 |     def _make_callable(self, var):
125 |         """
126 |         Transform an input vector, array, float or callable into a z-callable,
127 |         allowing the user to provide z-dependant quantities.
128 |         
129 |         Note that a provided callable should have as arguments exactly at most
130 |         'z' and 'freq', e.g. var(z, freq), var(freq, z), var(z) or var(freq).
131 |         A bit wonky, but couldn't figure out a better way to do that. Another
132 |         alternative would be to implement derived classes with overwritten
133 |         properties, which is not very elegant either. Actually found out that
134 |         singledispatch from functools is probably the way to go here.
135 |         
136 |         Note that a provided array should have first dimension coinciding with
137 |         the frequency axis given along the refractive index data. The second
138 |         dimension is assumed to be evenly distributed along the whole length
139 |         of the waveguide.
140 |         
141 |         Note that if a vector is provided it will be assumed that it describes
142 |         a z dependent quantity, unless it has the same dimension as the
143 |         frequency axis. Wavelength dependent only quantities can also be
144 |         provided through callables.
145 | 
146 |         Parameters
147 |         ----------
148 |         var : float, vector, array or callable
149 |             Some simulation parameter.
150 | 
151 |         Returns
152 |         -------
153 |         function
154 |             A z-callable version of the provided variable.
155 |         """
156 |         # Case when the argument is callable
157 |         if callable(var):
158 |             return self._parse_callable(var)
159 |         # Case when the argument is an array or a vector
160 |         elif hasattr(var, '__len__'):
161 |             return self._parse_array(var)
162 |         # Otherwise (float)
163 |         else:
164 |             return lambda _: var
165 |             
166 |     def _parse_array(self, var):
167 |         """
168 |         Parse the correct arguments for a callable parameter.
169 | 
170 |         Parameters
171 |         ----------
172 |         var : array
173 |             A one or two dimensional array representing z and/or frequency
174 |             dependence of a parameter.
175 | 
176 |         Returns
177 |         -------
178 |         function
179 |             A z-callable function.
180 |         """
181 |         # Case of an array
182 |         if len(np.shape(var)) == 2:
183 |             arr_inter = interp1d(self.data_freq, var.T, kind='cubic',
184 |                                  bounds_error=False, fill_value='extrapolate')
185 |             arr = arr_inter(self.freq).T
186 |             z = np.linspace(0, self.length, np.shape(arr)[-1])
187 |             arr_inter = interp1d(z, arr, kind='cubic', bounds_error=False,
188 |                                  fill_value='extrapolate')
189 |             return arr_inter
190 |         # Case of a vector
191 |         elif len(np.shape(var)) == 1:
192 |             if len(var) == len(self.data_freq):
193 |                 arr_inter = interp1d(self.data_freq, var, kind='cubic',
194 |                                      bounds_error=False, fill_value='extrapolate')
195 |                 arr = arr_inter(self.freq)
196 |                 return lambda _: arr
197 |             else:
198 |                 z = np.linspace(0, self.length, len(var))
199 |                 var_inter = interp1d(z, var, kind='cubic', bounds_error=False,
200 |                                      fill_value='extrapolate')
201 |                 return var_inter
202 |         else:
203 |             raise ValueError
204 |                 
205 |     def _parse_callable(self, var):
206 |         """
207 |         Parse the correct arguments for a callable parameter.
208 | 
209 |         Parameters
210 |         ----------
211 |         var : callable
212 |             A z or frequency (or both) dependent callable.
213 | 
214 |         Returns
215 |         -------
216 |         function
217 |             A z-callable function.
218 |         """
219 |         # Get funtion signature
220 |         z_flag = False
221 |         freq_flag = False
222 |         order_flag = False
223 |         args = signature(var).parameters
224 |         for arg in args:
225 |             if arg == 'z':
226 |                 z_flag = True
227 |             if arg == 'freq':
228 |                 freq_flag = True
229 |                 if z_flag:
230 |                     order_flag = True
231 |         
232 |         # Reorder arguments and evaluate the frequency axis
233 |         if z_flag:
234 |             if freq_flag:
235 |                 if order_flag:
236 |                     return lambda _: var(_, self.freq)
237 |                 else:
238 |                     return lambda _: var(self.freq, _)
239 |             else:
240 |                 return var
241 |         else:
242 |             if freq_flag:
243 |                 return lambda _: var(self.freq)
244 |             else:
245 |                 return lambda _: var
246 |     
247 |     def _compute_frequency_axis(self):
248 |         """
249 |         Define a frequency axis covering exactly the data range available.
250 |         """
251 |         min_freq = np.amin(self.data_freq)
252 |         max_freq = np.amax(self.data_freq)
253 |         center_freq = min_freq/2 + max_freq/2
254 |         freq = np.linspace(min_freq, max_freq, self.t_pts)
255 |         return center_freq, freq
256 |         
257 |     def _compute_omega_axis(self):
258 |         """
259 |         Compute the angular frequency axis associated to the frequency axis
260 |         """
261 |         center_omega = 2*np.pi*self.center_freq
262 |         omega = 2*np.pi*self.freq
263 |         rel_omega = omega - center_omega
264 |         return center_omega, omega, rel_omega
265 |     
266 |     def _compute_time_axis(self):
267 |         """
268 |         Compute the time axis associated to the frequency axis
269 |         """
270 |         time = np.fft.fftshift(np.fft.fftfreq(self.t_pts, np.mean(np.diff(self.freq))))
271 |         delta_t = np.mean(np.diff(time))
272 |         return time, delta_t
273 |     
274 |     def _interpolate_n_eff(self):
275 |         """
276 |         Interpolate the refractive index data on the simulation frequency axis
277 |         """
278 |         n_eff_inter = interp1d(self.freq, self.n_eff, kind='cubic',
279 |                                bounds_error=False, fill_value='extrapolate')
280 |         return n_eff_inter
281 |     
282 |     def _compute_raman_effect(self):
283 |         """
284 |         Compute the Raman term for the simulation frequency axis
285 |         """
286 |         raman_time = (self.raman_tau_1**2 + self.raman_tau_2**2)
287 |         raman_time = raman_time/self.raman_tau_1/self.raman_tau_2**2
288 |         raman_time *= np.exp(-np.abs(self.time)/self.raman_tau_2)*np.sin(self.time/self.raman_tau_1)
289 |         raman_time[self.time < 0] = 0
290 |         raman_effect = np.conjugate(self.t_pts*np.fft.ifft(np.fft.fftshift(raman_time)))
291 |         raman_effect *= self.delta_t*self.raman_fraction
292 |         return raman_effect
293 |     
294 |     def compute_betas(self, wavelength=None, order=6):
295 |         """
296 |         Compute beta coefficients at a given wavelength and order.
297 | 
298 |         Parameters
299 |         ----------
300 |         wavelength : float, optional
301 |             Wavelength at which the beta coefficients are computed. The default is
302 |             the center of the simulation axis.
303 |         order : int, optional
304 |             Highest order of the beta coefficients to be computed. The default is 6.
305 | 
306 |         Returns
307 |         -------
308 |         beta : array
309 |             Beta coefficients of the material at the given wavelength.
310 |         """
311 |         if wavelength is None:
312 |             center_omega = self.center_omega
313 |         else:
314 |             center_omega = 2*np.pi*c/wavelength
315 |         
316 |         om = 2*np.pi*self.freq
317 |         dk = np.real(self.n_eff)*om/c
318 |         b_inter = interp1d(om, dk, kind='cubic')
319 |         beta = np.zeros(order+1)
320 |         beta[0] = b_inter(center_omega)
321 |         for i in np.arange(order):
322 |             dk = np.diff(dk)
323 |             dom = np.diff(om)
324 |             om = om[:-1] + dom/2
325 |             der = dk/dom
326 |             der_inter = interp1d(om, der, kind='cubic')
327 |             beta[i+1] = der_inter(center_omega)
328 |             dk = der
329 |         return beta
330 |     
331 |     def set_betas(self, betas, wavelength):
332 |         """
333 |         Convenience only. Allow the use to provide the beta coefficients
334 |         instead of n_eff. Should be avoided.
335 |         """
336 |         rel_om = self.omega - 2*np.pi*c/wavelength
337 |         n = np.ones(self.t_pts)*betas[0]
338 |         factorial = 1
339 |         for i, b in enumerate(betas[1:]):
340 |             factorial *= (i+1)
341 |             n += b*rel_om**(i+1)/factorial
342 |         n *= c/self.omega
343 |         self.n_eff = n
344 | 
345 |     def set_n2(self, n2, wavelength=None):
346 |         """
347 |         Convenience only. Allow the user to give the nonlinear index instead
348 |         of chi3. Overwrite the initialized chi3 value accordingly.
349 | 
350 |         Parameters
351 |         ----------
352 |         n2 : float
353 |             Nonlinear index.
354 |         """
355 |         if wavelength is None:
356 |             freq = self.center_freq
357 |         else:
358 |             freq = c/wavelength
359 |         self.chi_3 = 4*n2*eps_0*c*self.n_eff_inter(freq)**2/3
360 |         
361 |     def set_gamma(self, gamma, wavelength=None):
362 |         """
363 |         Convenience only. Allow the user to give the nonlinear coefficient instead
364 |         of chi3. Overwrite the initialized chi3 value accordingly.
365 | 
366 |         Parameters
367 |         ----------
368 |         gamma : float
369 |             Nonlinear coefficient.
370 |         """
371 |         if wavelength is None:
372 |             freq = self.center_freq
373 |         else:
374 |             freq = c/wavelength
375 |         self.chi_3 = 2*self.n_eff_inter(freq)**2*c**2*eps_0*gamma*self.eff_area/3/np.pi/freq
376 | 
377 |     def plot_refractive_index(self, savename=None):
378 |         """
379 |         Plot refractive index
380 |         """        
381 |         k = self.n_eff*2*np.pi*self.freq/c
382 |         inverse_group_velocity = np.gradient(k, 2*np.pi*self.freq)
383 |         group_velocity_dispersion = np.gradient(inverse_group_velocity, 2*np.pi*self.freq)
384 |         
385 |         fig, axs = plt.subplots(3)
386 |         axs[0].plot(self.freq, self.n_eff)
387 |         axs[0].set_ylabel('Refractive index')
388 |         axs[1].plot(self.freq, inverse_group_velocity)
389 |         axs[1].set_ylabel('IGV [s/m]')
390 |         axs[2].plot(self.freq, group_velocity_dispersion)
391 |         axs[2].set_ylabel('GVD [s^2/m]')
392 |         axs[2].set_xlabel('Frequency [Hz]')
393 |         fig.tight_layout()
394 | 


--------------------------------------------------------------------------------
/src/pychi/solvers.py:
--------------------------------------------------------------------------------
  1 | # -*- coding: utf-8 -*-
  2 | """
  3 | Created on Fri Feb 18 17:54:20 2022
  4 | 
  5 | @author: voumardt
  6 | """
  7 | import matplotlib.pyplot as plt
  8 | import numba
  9 | import numpy as np
 10 | from scipy.constants import c
 11 | import time as timing
 12 | 
 13 | 
 14 | class Solver():
 15 |     def __init__(self, model, z_pts=500, local_error=0.00001, adaptive_factor=1.1,
 16 |                  max_dz=None, method=None, breakpoints=[]):
 17 |         """
 18 |         Solver class. Provides a stepper which performs integration of the PDE
 19 |         as well as error control and results saving.
 20 | 
 21 |         Parameters
 22 |         ----------
 23 |         model : Model object
 24 |             Physical model of the problem to be integrated.
 25 |         z_pts : int, optional
 26 |             Number of results to keep along the propagation axis. The default is 500.
 27 |         local_error : float, optional
 28 |             Tolerated local error. The default is 0.00001.
 29 |         adaptive_factor : float, optional
 30 |             Adaptive factor for the step size control. Bigger values lead to
 31 |             more aggressive step size control. The default is 1.1.
 32 |         max_dz : float, optional
 33 |             Maximum step size allowed. Particularly useful when simulating
 34 |             quasi-phase matched structures. The default is None.
 35 |         method: string
 36 |             Method used for integration. Can be RK4IP, ERK4IP or DP5IP.
 37 |             Default is DP5IP.
 38 |         breakpoints: array
 39 |             This array contains z coordinates where the solver will be forced
 40 |             to compute a result. Useful for poled structures, to avoid having
 41 |             a step larger than the poling. The default is an empty array.
 42 |         """
 43 |         self.model = model
 44 |         self.z_pts = z_pts
 45 |         self.local_error = local_error
 46 |         self.adaptive_factor = adaptive_factor
 47 |         self.max_dz = max_dz
 48 |         self.z_save = np.linspace(0, self.model.waveguide.length, self.z_pts)
 49 |         self.method_name = self._set_method_name(method)
 50 |         self.breakpoints = breakpoints
 51 |         self.stepsize_save = []
 52 |     
 53 |     def _set_method_name(self, method):
 54 |         """
 55 |         Helper function to choose an appropriate solver. If a method is not
 56 |         provided by the user, it  will look into the model used to see if
 57 |         there is a recommended solver. Otherwise, defaults to the model that
 58 |         should be mostly used, i.e. DP5IP.
 59 | 
 60 |         Parameters
 61 |         ----------
 62 |         method : string
 63 |             Name of the solver.
 64 | 
 65 |         Returns
 66 |         -------
 67 |         string
 68 |             Name of the solver.
 69 |         """
 70 |         if method is None:
 71 |             if hasattr(self.model, '_recommended_solver'):
 72 |                 return self.model._recommended_solver
 73 |             else:
 74 |                 return 'DP5IP'
 75 |         else:
 76 |             return method
 77 |         
 78 |     def _compute_error(self, field_1, field_2):
 79 |         """
 80 |         Error estimation for adaptive step size
 81 | 
 82 |         Parameters
 83 |         ----------
 84 |         field_1 : array
 85 |             Reference field.
 86 |         field_2 : array
 87 |             Test field.
 88 | 
 89 |         Returns
 90 |         -------
 91 |         float
 92 |             Error estimate between the two fields.
 93 |         """
 94 |         return numbanorm(field_1 - field_2)/numbanorm(field_1)
 95 |     
 96 |     def _dormand_prince_step(self, field, dz):
 97 |         """
 98 |         Dormand Prince order 5(4) adaptive scheme in the interaction picture. This
 99 |         new stepper uses the interaction picture in an embedded scheme of order 5.
100 |         Tests have shown it to be up to four times faster than RK4IP.
101 | 
102 |         Parameters
103 |         ----------
104 |         field : array
105 |             Current field.
106 |         dz : float
107 |             Current step size.
108 | 
109 |         Returns
110 |         -------
111 |         array
112 |             New field estimate.
113 |         
114 |         float
115 |             Error estimate.
116 |         """
117 |         if self._k_7 is None:
118 |             k_1 = dz*self.model.dispersion_step(self.model.nonlinear_term(field), dz)
119 |         else:
120 |             k_1 = self.model.dispersion_step(self._k_7, dz)
121 |         a_int = self.model.dispersion_step(field, dz)
122 |         k_2 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(a_int + k_1/5, -4*dz/5)), 4*dz/5)
123 |         k_3 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(a_int + 3*k_1/40 + 9*k_2/40, -7*dz/10)), 7*dz/10)
124 |         k_4 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(a_int + 44*k_1/45 - 56*k_2/15 + 32*k_3/9, -dz/5)), dz/5)
125 |         k_5 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(a_int + 19372*k_1/6561 - 25360*k_2/2187 + 64448*k_3/6561 - 212*k_4/729, -dz/9)), dz/9)
126 |         k_6 = dz*self.model.nonlinear_term(a_int + 9017*k_1/3168 - 355*k_2/33 + 46732*k_3/5247 + 49*k_4/176 - 5103*k_5/18656)
127 |         sol_5 = a_int + 35*k_1/384 + 500*k_3/1113 + 125*k_4/192 - 2187*k_5/6784 + 11*k_6/84
128 |         self._k_7 = dz*self.model.nonlinear_term(sol_5)
129 |         sol_4 = a_int + 5179*k_1/57600 + 7571*k_3/16695 + 393*k_4/640 - 92097*k_5/339200 + 187*k_6/2100 + self._k_7/40
130 |         error = self._compute_error(sol_5, sol_4)
131 |         return sol_5, error
132 |     
133 |     def _rk546m(self, field, dz):
134 |         """
135 |         Some other Dormand-Prince method that has one less step but does not
136 |         leverage the interaction picture and does not have the FSAL property.
137 |         Usually worse than the other dormand-prince method.
138 |         References:
139 |             DOI: 10.1016/0771-050X(80)90013-3
140 | 
141 |         Parameters
142 |         ----------
143 |         field : array
144 |             Current field.
145 |         dz : float
146 |             Current step size.
147 | 
148 |         Returns
149 |         -------
150 |         array
151 |             New field estimate.
152 |         
153 |         float
154 |             Error estimate.
155 |         """
156 |         k_1 = dz*self.model.nonlinear_term(field)
157 |         k_2 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(field + k_1/5, dz/5)), -dz/5)
158 |         k_3 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(field + 3*k_1/40 + 9*k_2/40, 3*dz/10)), -3*dz/10)
159 |         k_4 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(field + 3*k_1/10 - 9*k_2/10 + 6*k_3/5, 3*dz/5)), -3*dz/5)
160 |         k_5 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(field + 226*k_1/729 - 25*k_2/27 + 880*k_3/729 + 55*k_4/729, 2*dz/3)), -2*dz/3)
161 |         k_6 = dz*self.model.dispersion_step(self.model.nonlinear_term(self.model.dispersion_step(field  - 181*k_1/270 + 5*k_2/2 - 266*k_3/297 - 91*k_4/27 + 189*k_5/55, dz)), -dz)
162 |         sol_5 = self.model.dispersion_step(field + 19*k_1/216 + 1000*k_3/2079 - 125*k_4/216 + 81*k_5/88 + 5*k_6/56, dz)
163 |         sol_4 = self.model.dispersion_step(field + 31*k_1/540 + 190*k_3/297 - 145*k_4/108 + 351*k_5/220 + k_6/20, dz)
164 |         error = self._compute_error(sol_5, sol_4)
165 |         return sol_5, error
166 |     
167 |     def _adams_bashforth54_step(self, field, dz):
168 |         """To be implemented"""
169 |         pass
170 | 
171 |     def _rk4ip_single_step(self, field, dz):
172 |         """
173 |         Runge-Kutta order 4 step in the interaction picture (RK4IP)
174 | 
175 |         Parameters
176 |         ----------
177 |         field : array
178 |             Current field.
179 |         dz : float
180 |             Current step size.
181 | 
182 |         Returns
183 |         -------
184 |         array
185 |             New field estimate.
186 |         """
187 |         dispersion_op = numbaexp(-1j*self.model.waveguide.k*dz/2)
188 |         a_int = dispersion_op*field
189 |         k_1 = dz*dispersion_op*self.model.nonlinear_term(field)
190 |         k_2 = dz*self.model.nonlinear_term(a_int + k_1/2)
191 |         k_3 = dz*self.model.nonlinear_term(a_int + k_2/2)
192 |         k_4 = dz*self.model.nonlinear_term(dispersion_op*(a_int + k_3))
193 |         return dispersion_op*(a_int + k_1/6 + k_2/3 + k_3/3) + k_4/6
194 |     
195 |     def _rk4ip_step(self, field, dz):
196 |         """
197 |         Runge-Kutta order 4 adaptive scheme in the interaction picture (RK4IP)
198 |         with step doubling and combining. Provided for comparison but slower
199 |         than the dormand-prince method.
200 |         References:
201 |             DOI: 10.1109/JLT.2007.909373
202 |             DOI: 10.1109/JLT.2009.2021538
203 | 
204 |         Parameters
205 |         ----------
206 |         field : array
207 |             Current field.
208 |         dz : float
209 |             Current step size.
210 | 
211 |         Returns
212 |         -------
213 |         array
214 |             New field estimate.
215 |         
216 |         float
217 |             Error estimate.
218 |         """
219 |         sol_single = self._rk4ip_single_step(field, dz)
220 |         sol_double = self._rk4ip_single_step(field, dz/2)
221 |         sol_double = self._rk4ip_single_step(sol_double, dz/2)
222 |         error = self._compute_error(sol_double, sol_single)
223 |         sol_5 = (sol_double*16 - sol_single)/15
224 |         return sol_5, error
225 |     
226 |     def _erk4ip_step(self, field, dz):
227 |         """
228 |         Embedded Runge-Kutta order 4(3) adaptive scheme in the interaction
229 |         picture (ERK4IP). Can be faster than DP5IP if accuracy is irrelevant,
230 |         for example in SPM only cases. Otherwise, DP5IP performs better.
231 |         References:
232 |             DOI: 10.1016/j.cpc.2012.12.020
233 | 
234 |         Parameters
235 |         ----------
236 |         field : array
237 |             Current field.
238 |         dz : float
239 |             Current step size.
240 | 
241 |         Returns
242 |         -------
243 |         array
244 |             New field estimate.
245 |         
246 |         float
247 |             Error estimate.
248 |         """
249 |         dispersion_op = numbaexp(-1j*self.model.waveguide.k*dz/2)
250 |         a_int = dispersion_op*field
251 |         if self._k_5 is None:
252 |             k_1 = dz*dispersion_op*self.model.nonlinear_term(field)
253 |         else:
254 |             k_1 = dispersion_op*self._k_5
255 |         k_2 = dz*self.model.nonlinear_term(a_int + k_1/2)
256 |         k_3 = dz*self.model.nonlinear_term(a_int + k_2/2)
257 |         k_4 = dz*self.model.nonlinear_term(dispersion_op*(a_int + k_3))
258 |         beta = dispersion_op*(a_int + k_1/6 + k_2/3 + k_3/3)
259 |         sol_4 = beta + k_4/6
260 |         self._k_5 = dz*self.model.nonlinear_term(sol_4)
261 |         sol_3 = beta + k_4/15 + self._k_5/10
262 |         error = self._compute_error(sol_4, sol_3)
263 |         return sol_4, error
264 |     
265 |     def _integrate_to_z(self, z):
266 |         """
267 |         Integrate to z with adaptive step size.
268 | 
269 |         Parameters
270 |         -------
271 |         z : float
272 |             Target propagation length.
273 |         """
274 |         while self.stock_z < z:
275 |             # Actuate position inside the waveguide
276 |             self.model.waveguide.z = self.stock_z
277 |             
278 |             # Check for forcing breakpoints
279 |             if (len(self.breakpoints) != 0 and (self.stock_z + self.dz > self.breakpoints[0])):
280 |                 
281 |                 # Step to breakpoint
282 |                 dz = self.breakpoints[0] - self.stock_z + 1e-20
283 |                 vec_eval, _ = self.step(self.stock_vec, dz)
284 |                 
285 |                 # Remove breakpoint
286 |                 self.breakpoints = self.breakpoints[1:]
287 |                 
288 |                 # Update z pos and field
289 |                 self.stock_z += dz
290 |                 self.stock_vec = vec_eval
291 |                 self.stepsize_save = np.append(self.stepsize_save, dz)
292 |             
293 |             else:
294 |             
295 |                 # Step of dz
296 |                 vec_eval, error = self.step(self.stock_vec, self.dz)
297 |                 
298 |                 # Error control
299 |                 if error >= 2*self.local_error:
300 |                     self.dz /= 2
301 |                     print('Discarded')
302 |                     if self.method_name == 'DP5IP':
303 |                         self._k_7 = None
304 |                     if self.method_name == 'ERK4IP':
305 |                         self._k_5 = None
306 |                     continue
307 |                 elif self.local_error <= error < 2*self.local_error:
308 |                     self.stock_z += self.dz
309 |                     self.stepsize_save = np.append(self.stepsize_save, self.dz)
310 |                     self.dz /= self.adaptive_factor
311 |                 elif 0.5*self.local_error <= error < self.local_error:
312 |                     self.stock_z += self.dz
313 |                     self.stepsize_save = np.append(self.stepsize_save, self.dz)
314 |                 else:
315 |                     self.stock_z += self.dz
316 |                     self.stepsize_save = np.append(self.stepsize_save, self.dz)
317 |                     if self.max_dz is None or self.dz*self.adaptive_factor < self.max_dz:
318 |                         self.dz *= self.adaptive_factor
319 |                 self.stock_vec = vec_eval
320 |     
321 |     def solve(self):
322 |         """
323 |         Integrate over waveguide length with adaptive step size
324 |         """
325 |         # Initialization
326 |         self.spectrum = np.zeros((self.z_pts, self.model.waveguide.t_pts), dtype='complex128')
327 |         self.dz = np.mean(np.diff(self.z_save))*np.sqrt(np.sqrt(self.local_error))
328 |         self.stock_z = 0
329 |         self.stock_vec = np.fft.fft(self.model.light.field_t_in)
330 |         if self.method_name == 'DP5IP':
331 |             self._k_7 = None
332 |             self.step = self._dormand_prince_step
333 |         elif self.method_name == 'ERK4IP':
334 |             self._k_5 = None
335 |             self.step = self._erk4ip_step
336 |         elif self.method_name == 'RK4IP':
337 |             self.step = self._rk4ip_step
338 |         elif self.method_name == 'RK546M':
339 |             self.step = self._rk546m
340 |         timer = timing.perf_counter()
341 |             
342 |         # Total integration
343 |         for i, z in enumerate(self.z_save):
344 |             print('z: {}/{}'.format(i+1, self.z_pts))
345 |             
346 |             # Integrate over dz
347 |             self._integrate_to_z(z)
348 |             
349 |             # Save spectrum
350 |             self.spectrum[i, :] = np.fft.fftshift(self.stock_vec)\
351 |                 *numbaexp(1j*(self.model.waveguide.betas[0] + self.model.waveguide.betas[1]*self.model.waveguide.rel_omega)*self.stock_z)
352 |         
353 |         # Save waveform
354 |         print(f"{timing.perf_counter() - timer} seconds for integration.")                
355 |         self.waveform = np.fft.ifft(np.fft.ifftshift(self.spectrum, axes=1), axis=1)
356 |         self.model.light._set_propagation(self.z_save, self.model.waveguide.freq, self.spectrum, self.waveform)
357 | 
358 |     def plot_stepsize(self):
359 |         """
360 |         Plot the evolution of the stepsize against the position in the waveguide
361 |         """
362 |         plt.figure()
363 |         plt.plot(np.cumsum(self.stepsize_save), self.stepsize_save)
364 |         plt.xlabel('Distance [m]')
365 |         plt.ylabel('Step size [m]')
366 |         
367 | 
368 | """
369 | Optimized functions
370 | """
371 | ### Numba exponential
372 | @numba.njit([numba.complex128[:](numba.complex128[:]),numba.complex64[:](numba.complex64[:])])
373 | def numbaexp(x):
374 |     return np.exp(x)
375 | 
376 | ### Numba norm
377 | @numba.njit([numba.float64(numba.complex128[:])])
378 | def numbanorm(field):
379 |     return np.linalg.norm(field)
380 | 


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