From 27adbdd5fe7e52d2f2b7e5c58515305e8fc619bf Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 16 May 2024 11:59:41 +0200
Subject: [PATCH 01/44] first draft of intro

---
 docs/hello.ipynb    |  51 ------
 docs/index.md       |   3 +-
 docs/intro.ipynb    | 263 ++++++++++++++++++++++++++
 docs/report-0.ipynb | 167 +++++++++++++++++
 pixi.lock           | 437 ++++++++++++++++++++++++++++++++++++++++++--
 pixi.toml           |   3 +
 6 files changed, 861 insertions(+), 63 deletions(-)
 delete mode 100644 docs/hello.ipynb
 create mode 100644 docs/intro.ipynb
 create mode 100644 docs/report-0.ipynb

diff --git a/docs/hello.ipynb b/docs/hello.ipynb
deleted file mode 100644
index cb1c2da..0000000
--- a/docs/hello.ipynb
+++ /dev/null
@@ -1,51 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0",
-   "metadata": {},
-   "source": [
-    "# Starting document"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "1",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print(\"Hello World!\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "2",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.3"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/docs/index.md b/docs/index.md
index ce8b6d0..e26c1a3 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,5 +1,6 @@
 # MyST-NB Quickstart
 
 ```{toctree}
-hello
+intro
+report-0
 ```
diff --git a/docs/intro.ipynb b/docs/intro.ipynb
new file mode 100644
index 0000000..f4f39ae
--- /dev/null
+++ b/docs/intro.ipynb
@@ -0,0 +1,263 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "::::{margin}\n",
+    ":::{card} Amplitude models for photoproduction reaction\n",
+    "PWA101(v2.0): Introduction\n",
+    "^^^\n",
+    "This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),\n",
+    "as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.\n",
+    "Now the focus is the use of symbolic expressions (computations) with `sympy` and the use of [ComPWA packages](https://compwa.github.io/) in general to illustrate the general process in PWA. This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).\n",
+    "+++\n",
+    "✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1)\n",
+    ":::\n",
+    "::::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# # Amplitude Analysis 101 (v2.0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "Address to the issue [ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1), this document is PWA101(v2.0), which shows PWA methodologies and full workflow in the context of hadron physics with symbolic expressions via [ComPWA](https://compwa.github.io/)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "<!-- cspell:ignore Mathieu -->\n",
+    "This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu.\n",
+    "\n",
+    "The (photo-production) reaction is $ \\gamma p \\to \\eta \\pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630\n",
+    ":width: 100%\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "$$\n",
+    "\\begin{eqnarray}\n",
+    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
+    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
+    "\\\n",
+    "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \n",
+    "\\end{eqnarray}\n",
+    "$$ (BW_SH_label)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "where s is the Mandelstam variable, m is the mass, $\\Gamma$ is the width, Y is the spherical harmonics, $\\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    ":::{note}\n",
+    "Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.\n",
+    ":::\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "with  intensity $I$ and amplitude $A$:\n",
+    "\n",
+    "$$\n",
+    "\\begin{eqnarray}\n",
+    "I &=& |A|^2 \\nonumber \\\\\n",
+    "A &=& A^{12} + A^{23} + A^{31}  \\\\\n",
+    "\\end{eqnarray}\n",
+    "$$ (123_label)\n",
+    "\n",
+    "where $\\quad 1 \\equiv \\eta ; \\quad  2 \\equiv \\pi^0 ; \\quad 3 \\equiv p$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "10",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    ":::{note}\n",
+    "The choice of the amplitude model (equations (1) and (2)) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with Spherical harmonics ($l = 2, 1, 0$).\n",
+    ":::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "11",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    ":::{important}\n",
+    "The spin of $\\eta$ meson and $\\pi^0$ meson are all 0. But the spin of proton is not 0, it is spin-$\\frac{1}{2}$.\n",
+    "\n",
+    "In this amplitude model **spin** of baryon is simplified (not realistic):\n",
+    "$\\eta$, $\\pi^0$ and $p$ are all treated as spin-0 particles.\n",
+    "\n",
+    "This means that total intrinsic spin $s$ is ignored in this model,\n",
+    "the total angular momentum \n",
+    "$J$ of the system or any subsystems within this model will solely depend on the orbital angular momentum \n",
+    "$L$, characterized by quantum number $l$.\n",
+    "And this simplifies the use of spherical harmonics $Y_l^m(\\theta,\\phi)$,\n",
+    "since only the orbital angular momentum component is involved, and thus the combination of contribution is not considered (e.g. Clebsch-Gordan Coefficients).\n",
+    "\n",
+    "In our case: \n",
+    "- $A^{12}$ amplitude represents a d-wave interaction, as indicated by $l=2$.\n",
+    "    - The possible $m$ values are $−2,−1,0,1,2$. Each of these values corresponds to different orientations of the d-wave. The wave type is solely determined by $l$ and all these $m$ values still describe d-wave characteristics.\n",
+    "- $A^{23}$ amplitude represents a p-wave interaction, as indicated by $l=1$.\n",
+    "    - The possible $m$ values are $−1,0,1$. Each of these values corresponds to different orientations of the p-wave. Similarly, these values are all p-wave orientations.\n",
+    "- $A^{31}$ amplitude represents a s-wave interaction, as indicated by $l=0$.\n",
+    "    - The only possible $m$ value is 0, which is consistent with the spherical symmetry of s-waves.\n",
+    ":::"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/report-0.ipynb b/docs/report-0.ipynb
new file mode 100644
index 0000000..d89d699
--- /dev/null
+++ b/docs/report-0.ipynb
@@ -0,0 +1,167 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "::::{margin}\n",
+    ":::{card} Create a virtual particle that represents the state pγ in `QRules`\n",
+    "Report-0\n",
+    "^^^\n",
+    "+++\n",
+    "✅&nbsp;[ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5)\n",
+    ":::\n",
+    "::::"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# Virtual particle that represents the state pγ "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "Address to issue [ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5), this section is an investigation of creating a virtual particle that represents the state $p \\gamma$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "As an example, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "from qrules.particle import load_pdg"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db = load_pdg()\n",
+    "print(\"Number of loaded particles:\", len(particle_db))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db.find(2212)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db.find(22)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/pixi.lock b/pixi.lock
index ba33ed9..02b31a0 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -38,6 +38,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/debugpy-1.8.1-py312h30efb56_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/decorator-5.1.1-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/defusedxml-0.7.1-pyhd8ed1ab_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/deprecated-1.2.14-pyh1a96a4e_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/distlib-0.3.8-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/docutils-0.21.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/entrypoints-0.4-pyhd8ed1ab_0.tar.bz2
@@ -67,6 +68,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/h11-0.14.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/h2-4.1.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/harfbuzz-8.4.0-h3d44ed6_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/hepunits-2.3.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/hpack-4.0.0-pyh9f0ad1d_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/httpcore-1.0.5-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/httpx-0.27.0-pyhd8ed1ab_0.conda
@@ -80,6 +82,8 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/importlib_resources-6.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipykernel-6.29.3-pyhd33586a_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipython-8.24.0-pyh707e725_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ipython_genutils-0.2.0-py_1.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ipywidgets-8.1.2-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/isoduration-20.11.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/isort-5.13.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jax-0.4.26-pyhd8ed1ab_0.conda
@@ -91,10 +95,12 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jsonschema-4.22.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jsonschema-specifications-2023.12.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jsonschema-with-format-nongpl-4.22.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-1.0.0-pyhd8ed1ab_10.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-cache-1.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-lsp-2.2.5-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-server-mathjax-0.2.6-pyh5bfe37b_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_client-8.6.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_client-7.4.9-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_console-6.6.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/jupyter_core-5.7.2-py312h7900ff3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_events-0.10.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_server-2.14.0-pyhd8ed1ab_0.conda
@@ -105,6 +111,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-myst-2.4.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_server-2.27.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_widgets-3.0.10-pyhd8ed1ab_0.conda
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+  timestamp: 1715499623651
 - kind: conda
   name: pandocfilters
   version: 1.5.0
@@ -3201,6 +3460,26 @@ packages:
   license_family: MIT
   size: 75191
   timestamp: 1712320447201
+- kind: conda
+  name: particle
+  version: 0.24.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/particle-0.24.0-pyhd8ed1ab_0.conda
+  sha256: 2471b4dde2640283c0c1dfba669b8c322e55c45269ff3dbf95c0cfb3b8ec0b50
+  md5: 58bfa493a4844538a140012c1d120360
+  depends:
+  - attrs >=19.2
+  - deprecated
+  - hepunits >=2.0.0
+  - importlib_resources >=2.0
+  - python >=3.7
+  - typing-extensions >=4.5
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 163439
+  timestamp: 1713892152317
 - kind: conda
   name: pathspec
   version: 0.12.1
@@ -3361,6 +3640,21 @@ packages:
   license_family: BSD
   size: 270398
   timestamp: 1702399557137
+- kind: conda
+  name: prompt_toolkit
+  version: 3.0.42
+  build: hd8ed1ab_0
+  subdir: noarch
+  noarch: generic
+  url: https://conda.anaconda.org/conda-forge/noarch/prompt_toolkit-3.0.42-hd8ed1ab_0.conda
+  sha256: fd2185d501bf34cb4c121f2f5ade9157ac75e1644a9da81355c4c8f9c1b82d4d
+  md5: 85a2189ecd2fcdd86e92b2d4ea8fe461
+  depends:
+  - prompt-toolkit >=3.0.42,<3.0.43.0a0
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 6846
+  timestamp: 1702399567048
 - kind: conda
   name: psutil
   version: 5.9.8
@@ -3521,6 +3815,21 @@ packages:
   license: Python-2.0
   size: 31991381
   timestamp: 1713208036041
+- kind: conda
+  name: python-constraint
+  version: 1.4.0
+  build: py_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/python-constraint-1.4.0-py_0.tar.bz2
+  sha256: 582f244b4f8703dd326e58b66b07aa34a6b211351bd141862ff20d25d680e6f0
+  md5: 34267ea9b6de472c4fc3cb73a5a10207
+  depends:
+  - python
+  license: BSD-2-Clause
+  license_family: BSD
+  size: 21336
+  timestamp: 1541423579379
 - kind: conda
   name: python-dateutil
   version: 2.9.0
@@ -3650,6 +3959,66 @@ packages:
   license_family: BSD
   size: 461684
   timestamp: 1715024520808
+- kind: conda
+  name: qrules
+  version: 0.10.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/qrules-0.10.1-pyhd8ed1ab_0.conda
+  sha256: 289fe3fd2ad41d086a39bc7e73336c467aaa24b29300ba104c93a914de80f2b3
+  md5: 00d71dbda539d5a5ef5f11cfa718a82c
+  depends:
+  - attrs >=20.1.0
+  - jsonschema
+  - particle
+  - python >=3.6
+  - python-constraint
+  - pyyaml
+  - tqdm >=4.24.0
+  - typing-extensions
+  license: GPL-3.0-or-later
+  license_family: GPL
+  size: 74164
+  timestamp: 1709326984310
+- kind: conda
+  name: qtconsole-base
+  version: 5.5.2
+  build: pyha770c72_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/qtconsole-base-5.5.2-pyha770c72_0.conda
+  sha256: 0e7e1fad227f3f4fa5c8cac23e8c49298d55158a85104d1b9d58795e68af0b5a
+  md5: 0f63ec743defb9de6728a98150a80839
+  depends:
+  - ipykernel >=4.1
+  - jupyter_client >=4.1
+  - jupyter_core
+  - packaging
+  - pygments
+  - python >=3.8
+  - qtpy >=2.4.0
+  - traitlets
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 100292
+  timestamp: 1714943047487
+- kind: conda
+  name: qtpy
+  version: 2.4.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/qtpy-2.4.1-pyhd8ed1ab_0.conda
+  sha256: 925bf48e747af6ceff1b073c10b12fc94ef79c88a34729059d253e43466a33f1
+  md5: 7f391bd70d2abfb70f304ba5aa4e1261
+  depends:
+  - packaging
+  - python >=3.7
+  license: MIT
+  license_family: MIT
+  size: 61808
+  timestamp: 1698112171285
 - kind: conda
   name: re2
   version: 2023.09.01
@@ -4215,6 +4584,21 @@ packages:
   license_family: Apache
   size: 840527
   timestamp: 1708363299520
+- kind: conda
+  name: tqdm
+  version: 4.66.4
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/tqdm-4.66.4-pyhd8ed1ab_0.conda
+  sha256: 75342f40a69e434a1a23003c3e254a95dca695fb14955bc32f1819cd503964b2
+  md5: e74cd796e70a4261f86699ee0a3a7a24
+  depends:
+  - colorama
+  - python >=3.7
+  license: MPL-2.0 or MIT
+  size: 89452
+  timestamp: 1714855008479
 - kind: conda
   name: traitlets
   version: 5.14.3
@@ -4480,6 +4864,37 @@ packages:
   license_family: BSD
   size: 201426
   timestamp: 1697914826988
+- kind: conda
+  name: widgetsnbextension
+  version: 4.0.10
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/widgetsnbextension-4.0.10-pyhd8ed1ab_0.conda
+  sha256: 981b06c76a1a86bb84be09522768be0458274926b22f4b0225dfcdd30a6593e0
+  md5: 521f489e3babeddeec638c2add7e9e64
+  depends:
+  - python >=3.7
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 886369
+  timestamp: 1707420479741
+- kind: conda
+  name: wrapt
+  version: 1.16.0
+  build: py312h98912ed_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/wrapt-1.16.0-py312h98912ed_0.conda
+  sha256: dc8431b343961347ad93b33d2d8270e8c15d8825382f4f2540835c94aba2de05
+  md5: fa957a1c7bee7e47ad44633caf7be8bc
+  depends:
+  - libgcc-ng >=12
+  - python >=3.12,<3.13.0a0
+  - python_abi 3.12.* *_cp312
+  license: BSD-2-Clause
+  license_family: BSD
+  size: 62482
+  timestamp: 1699532968076
 - kind: conda
   name: xorg-kbproto
   version: 1.0.7
diff --git a/pixi.toml b/pixi.toml
index 8241a48..71c7429 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -21,9 +21,11 @@ sphinx-autobuild \
 
 [dependencies]
 black = ">=24.4.2,<24.5"
+ipywidgets = ">=8.1.2,<8.2"
 isort = ">=5.13.2,<5.14"
 jax = ">=0.4.26,<0.5"
 jaxlib = ">=0.4.23,<0.5"
+jupyter = ">=1.0.0,<1.1"
 jupyterlab = ">=4.2.0,<4.3"
 jupyterlab-git = ">=0.50.0,<0.51"
 jupyterlab-lsp = ">=5.1.0,<5.2"
@@ -34,6 +36,7 @@ pre-commit = ">=3.7.1,<3.8"
 pydata-sphinx-theme = ">=0.15.2,<0.16"
 python = ">=3.12.3,<3.13"
 python-graphviz = ">=0.20.3,<0.21"
+qrules = ">=0.10.1,<0.11"
 scipy = ">=1.13.0,<1.14"
 sphinx-autobuild = ">=2024.4.16,<2024.5"
 sympy = ">=1.12,<2"

From 5580c93275b75715bd13d12af34c8a650af3a76a Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 16 May 2024 15:15:40 +0200
Subject: [PATCH 02/44] Change of contents and dependency

---
 docs/conf.py                                |   9 +-
 docs/index.md                               |  20 +-
 docs/intro.ipynb                            | 263 ---------
 docs/{report-0.ipynb => pgamma-state.ipynb} |  20 +-
 docs/reaction.md                            |  73 +++
 pixi.lock                                   | 574 ++++++++++++++++++--
 pixi.toml                                   |   2 +
 7 files changed, 632 insertions(+), 329 deletions(-)
 delete mode 100644 docs/intro.ipynb
 rename docs/{report-0.ipynb => pgamma-state.ipynb} (89%)
 create mode 100644 docs/reaction.md

diff --git a/docs/conf.py b/docs/conf.py
index 159dd23..70fccf8 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -6,7 +6,14 @@
     "_build",
 ]
 extensions = ["myst_nb"]
-html_theme = "pydata_sphinx_theme"
+html_theme = "sphinx_book_theme"
 master_doc = "index"
+myst_enable_extensions = [
+    "amsmath",
+    "colon_fence",
+    "dollarmath",
+    "html_image",
+    "smartquotes",
+]
 nitpicky = True
 project = "GlueX N-Star"
diff --git a/docs/index.md b/docs/index.md
index e26c1a3..d0329a7 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,6 +1,20 @@
-# MyST-NB Quickstart
+# Amplitude Analysis 101 / PWA101 (v2.0)
+
+## Amplitude models for photoproduction reaction
+
+This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),
+as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.
+
+Now the focus is the use of symbolic expressions (computations) with the use of [ComPWA packages](https://compwa.github.io/), or CAS(Computer Algebra System)-assisted model building in general (the python package `SymPy` in this case) to illustrate the general process in PWA.
+
+This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).
+
+Furthermore,
+address to the issue ✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1), this document is PWA101(v2.0), which shows PWA methodologies and full workflow in the context of hadron physics with symbolic expressions via [ComPWA](https://compwa.github.io/).
+
+# Table of contents:
 
 ```{toctree}
-intro
-report-0
+reaction
+pgamma-state
 ```
diff --git a/docs/intro.ipynb b/docs/intro.ipynb
deleted file mode 100644
index f4f39ae..0000000
--- a/docs/intro.ipynb
+++ /dev/null
@@ -1,263 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "::::{margin}\n",
-    ":::{card} Amplitude models for photoproduction reaction\n",
-    "PWA101(v2.0): Introduction\n",
-    "^^^\n",
-    "This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),\n",
-    "as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.\n",
-    "Now the focus is the use of symbolic expressions (computations) with `sympy` and the use of [ComPWA packages](https://compwa.github.io/) in general to illustrate the general process in PWA. This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).\n",
-    "+++\n",
-    "✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1)\n",
-    ":::\n",
-    "::::"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "# # Amplitude Analysis 101 (v2.0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "Address to the issue [ComPWA/gluex-nstar#1](https://github.com/ComPWA/gluex-nstar/issues/1), this document is PWA101(v2.0), which shows PWA methodologies and full workflow in the context of hadron physics with symbolic expressions via [ComPWA](https://compwa.github.io/)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "<!-- cspell:ignore Mathieu -->\n",
-    "This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu.\n",
-    "\n",
-    "The (photo-production) reaction is $ \\gamma p \\to \\eta \\pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630\n",
-    ":width: 100%\n",
-    "```"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "5",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "$$\n",
-    "\\begin{eqnarray}\n",
-    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
-    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
-    "\\\n",
-    "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \n",
-    "\\end{eqnarray}\n",
-    "$$ (BW_SH_label)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "where s is the Mandelstam variable, m is the mass, $\\Gamma$ is the width, Y is the spherical harmonics, $\\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    ":::{note}\n",
-    "Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.\n",
-    ":::\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "with  intensity $I$ and amplitude $A$:\n",
-    "\n",
-    "$$\n",
-    "\\begin{eqnarray}\n",
-    "I &=& |A|^2 \\nonumber \\\\\n",
-    "A &=& A^{12} + A^{23} + A^{31}  \\\\\n",
-    "\\end{eqnarray}\n",
-    "$$ (123_label)\n",
-    "\n",
-    "where $\\quad 1 \\equiv \\eta ; \\quad  2 \\equiv \\pi^0 ; \\quad 3 \\equiv p$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "10",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    ":::{note}\n",
-    "The choice of the amplitude model (equations (1) and (2)) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with Spherical harmonics ($l = 2, 1, 0$).\n",
-    ":::"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "11",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    ":::{important}\n",
-    "The spin of $\\eta$ meson and $\\pi^0$ meson are all 0. But the spin of proton is not 0, it is spin-$\\frac{1}{2}$.\n",
-    "\n",
-    "In this amplitude model **spin** of baryon is simplified (not realistic):\n",
-    "$\\eta$, $\\pi^0$ and $p$ are all treated as spin-0 particles.\n",
-    "\n",
-    "This means that total intrinsic spin $s$ is ignored in this model,\n",
-    "the total angular momentum \n",
-    "$J$ of the system or any subsystems within this model will solely depend on the orbital angular momentum \n",
-    "$L$, characterized by quantum number $l$.\n",
-    "And this simplifies the use of spherical harmonics $Y_l^m(\\theta,\\phi)$,\n",
-    "since only the orbital angular momentum component is involved, and thus the combination of contribution is not considered (e.g. Clebsch-Gordan Coefficients).\n",
-    "\n",
-    "In our case: \n",
-    "- $A^{12}$ amplitude represents a d-wave interaction, as indicated by $l=2$.\n",
-    "    - The possible $m$ values are $−2,−1,0,1,2$. Each of these values corresponds to different orientations of the d-wave. The wave type is solely determined by $l$ and all these $m$ values still describe d-wave characteristics.\n",
-    "- $A^{23}$ amplitude represents a p-wave interaction, as indicated by $l=1$.\n",
-    "    - The possible $m$ values are $−1,0,1$. Each of these values corresponds to different orientations of the p-wave. Similarly, these values are all p-wave orientations.\n",
-    "- $A^{31}$ amplitude represents a s-wave interaction, as indicated by $l=0$.\n",
-    "    - The only possible $m$ value is 0, which is consistent with the spherical symmetry of s-waves.\n",
-    ":::"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "12",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.3"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/docs/report-0.ipynb b/docs/pgamma-state.ipynb
similarity index 89%
rename from docs/report-0.ipynb
rename to docs/pgamma-state.ipynb
index d89d699..92e5d8e 100644
--- a/docs/report-0.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -60,13 +60,21 @@
     "tags": []
    },
    "source": [
-    "As an example, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+    "As an example of side note, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4",
+   "metadata": {},
+   "source": [
+    "`QRules` is used for this task"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4",
+   "id": "5",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -82,7 +90,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5",
+   "id": "6",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -99,7 +107,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
+   "id": "7",
    "metadata": {
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diff --git a/docs/reaction.md b/docs/reaction.md
new file mode 100644
index 0000000..0f8a6cd
--- /dev/null
+++ b/docs/reaction.md
@@ -0,0 +1,73 @@
+# Reaction and amplitude models
+
+<!-- cspell:ignore Mathieu -->
+<!-- This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu. -->
+
+## Reaction
+
+The (photo-production) reaction is $ \gamma p \to \eta \pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\Delta^+$, and $N^*$.
+
+```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630
+:width: 100%
+```
+
+## Amplitude models
+
+The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`.
+
+$$
+\begin{eqnarray}
+A^{12} &=& \frac{\sum a_m Y_2^m (\Omega_1)}{s-m^2_{a_2}+im_{a_2} \Gamma_{a_2}} \\
+A^{23} &=& \frac{\sum b_m Y_1^m (\Omega_2)}{s-m^2_{\Delta}+im_{\Delta} \Gamma_{\Delta}}  \\
+\
+A^{31} &=& \frac{c_0}{s-m^2_{N^*}+im_{N^*} \Gamma_{N^*}}
+\end{eqnarray}
+$$ (BW_SH_label)
+
+where s is the Mandelstam variable, m is the mass, $\Gamma$ is the width, Y is the spherical harmonics, $\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients
+
+:::{note}
+Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.
+:::
+
+with  intensity $I$ and amplitude $A$:
+
+
+$$
+
+\begin{eqnarray}
+I &=& |A|^2 \nonumber \\
+A &=& A^{12} + A^{23} + A^{31} \\
+\end{eqnarray}
+
+$$
+(123_label)
+
+where $\quad 1 \equiv \eta ; \quad  2 \equiv \pi^0 ; \quad 3 \equiv p$
+
+:::{note}
+The choice of the amplitude model (equations (1) and (2)) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with Spherical harmonics ($l = 2, 1, 0$).
+:::
+
+:::{important}
+The spin of $\eta$ meson and $\pi^0$ meson are all 0. But the spin of proton is not 0, it is spin-$\frac{1}{2}$.
+
+In this amplitude model **spin** of baryon is simplified (not realistic):
+$\eta$, $\pi^0$ and $p$ are all treated as spin-0 particles.
+
+This means that total intrinsic spin $s$ is ignored in this model,
+the total angular momentum
+$J$ of the system or any subsystems within this model will solely depend on the orbital angular momentum
+$L$, characterized by quantum number $l$.
+And this simplifies the use of spherical harmonics $Y_l^m(\theta,\phi)$,
+since only the orbital angular momentum component is involved, and thus the combination of contribution is not considered (e.g. Clebsch-Gordan Coefficients).
+
+In our case:
+- $A^{12}$ amplitude represents a d-wave interaction, as indicated by $l=2$.
+    - The possible $m$ values are $−2,−1,0,1,2$. Each of these values corresponds to different orientations of the d-wave. The wave type is solely determined by $l$ and all these $m$ values still describe d-wave characteristics.
+- $A^{23}$ amplitude represents a p-wave interaction, as indicated by $l=1$.
+    - The possible $m$ values are $−1,0,1$. Each of these values corresponds to different orientations of the p-wave. Similarly, these values are all p-wave orientations.
+- $A^{31}$ amplitude represents a s-wave interaction, as indicated by $l=0$.
+    - The only possible $m$ value is 0, which is consistent with the spherical symmetry of s-waves.
+:::
+$$
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   license_family: MIT
+  purls:
+  - pkg:pypi/ukkonen
   size: 14050
   timestamp: 1695549556745
 - kind: conda
@@ -4717,6 +5152,8 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/uri-template
   size: 23999
   timestamp: 1688655976471
 - kind: conda
@@ -4734,6 +5171,8 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/urllib3
   size: 94669
   timestamp: 1708239595549
 - kind: conda
@@ -4751,6 +5190,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/uvicorn
   size: 126964
   timestamp: 1710932152563
 - kind: conda
@@ -4768,6 +5209,9 @@ packages:
   - platformdirs <5,>=3.9.1
   - python >=3.8
   license: MIT
+  license_family: MIT
+  purls:
+  - pkg:pypi/virtualenv
   size: 3458445
   timestamp: 1715681264937
 - kind: conda
@@ -4785,6 +5229,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/watchfiles
   size: 1094669
   timestamp: 1701078026995
 - kind: conda
@@ -4800,6 +5246,8 @@ packages:
   - python >=3.8
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/wcwidth
   size: 32709
   timestamp: 1704731373922
 - kind: conda
@@ -4815,6 +5263,8 @@ packages:
   - python >=3.5
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/webcolors
   size: 18186
   timestamp: 1679900907305
 - kind: conda
@@ -4831,6 +5281,8 @@ packages:
   - python >=2.6
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/webencodings
   size: 15600
   timestamp: 1694681458271
 - kind: conda
@@ -4846,6 +5298,8 @@ packages:
   - python >=3.8
   license: Apache-2.0
   license_family: APACHE
+  purls:
+  - pkg:pypi/websocket-client
   size: 47066
   timestamp: 1713923494501
 - kind: conda
@@ -4862,6 +5316,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/websockets
   size: 201426
   timestamp: 1697914826988
 - kind: conda
@@ -4877,6 +5333,8 @@ packages:
   - python >=3.7
   license: BSD-3-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/widgetsnbextension
   size: 886369
   timestamp: 1707420479741
 - kind: conda
@@ -4893,6 +5351,8 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-2-Clause
   license_family: BSD
+  purls:
+  - pkg:pypi/wrapt
   size: 62482
   timestamp: 1699532968076
 - kind: conda
@@ -5095,12 +5555,12 @@ packages:
 - kind: conda
   name: zeromq
   version: 4.3.5
-  build: h75354e8_3
-  build_number: 3
+  build: h75354e8_4
+  build_number: 4
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h75354e8_3.conda
-  sha256: c2f2db5d19b603546db025b47fb71765f8dda0a0fe8feb42bd4e6a46194a5590
-  md5: 1b0ea5d6674e4e7dde0537c890813edb
+  url: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h75354e8_4.conda
+  sha256: bc9aaee39e7be107d7daff237435dfd8f791aca460a98583a36a263615205262
+  md5: 03cc8d9838ad9dd0060ab532e81ccb21
   depends:
   - krb5 >=1.21.2,<1.22.0a0
   - libgcc-ng >=12
@@ -5108,8 +5568,8 @@ packages:
   - libstdcxx-ng >=12
   license: MPL-2.0
   license_family: MOZILLA
-  size: 351803
-  timestamp: 1714545110790
+  size: 353229
+  timestamp: 1715607188837
 - kind: conda
   name: zipp
   version: 3.17.0
@@ -5123,6 +5583,8 @@ packages:
   - python >=3.8
   license: MIT
   license_family: MIT
+  purls:
+  - pkg:pypi/zipp
   size: 18954
   timestamp: 1695255262261
 - kind: conda
diff --git a/pixi.toml b/pixi.toml
index 71c7429..a2de7b2 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -21,6 +21,7 @@ sphinx-autobuild \
 
 [dependencies]
 black = ">=24.4.2,<24.5"
+graphviz = ">=9.0.0,<9.1"
 ipywidgets = ">=8.1.2,<8.2"
 isort = ">=5.13.2,<5.14"
 jax = ">=0.4.26,<0.5"
@@ -39,4 +40,5 @@ python-graphviz = ">=0.20.3,<0.21"
 qrules = ">=0.10.1,<0.11"
 scipy = ">=1.13.0,<1.14"
 sphinx-autobuild = ">=2024.4.16,<2024.5"
+sphinx-book-theme = ">=1.1.2,<1.2"
 sympy = ">=1.12,<2"

From e774af9aefbf6d12842d3a1442b5f4875e11f288 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 16 May 2024 17:39:43 +0200
Subject: [PATCH 03/44] pgamma virtual state generation!

---
 docs/pgamma-state.ipynb | 150 +++++++++++++++++++++++++++++++++++++---
 pixi.lock               |  17 +++++
 pixi.toml               |   1 +
 3 files changed, 157 insertions(+), 11 deletions(-)

diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index 92e5d8e..b00a1db 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -84,7 +84,10 @@
    },
    "outputs": [],
    "source": [
-    "from qrules.particle import load_pdg"
+    "from qrules.particle import load_pdg\n",
+    "\n",
+    "particle_db = load_pdg()\n",
+    "print(\"Number of loaded particles:\", len(particle_db))"
    ]
   },
   {
@@ -100,24 +103,17 @@
    },
    "outputs": [],
    "source": [
-    "particle_db = load_pdg()\n",
-    "print(\"Number of loaded particles:\", len(particle_db))"
+    "particle_db.find(2212)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "id": "7",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "particle_db.find(2212)"
+    "particle_db.find(\"p\")"
    ]
   },
   {
@@ -140,6 +136,16 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db.find(\"gamma\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -148,6 +154,128 @@
     "tags": []
    },
    "outputs": [],
+   "source": [
+    "from IPython.display import Math\n",
+    "\n",
+    "sigmas = particle_db.filter(\n",
+    "    lambda p: p.name.startswith(\"p\") and p.mass == 0.93827208816 and p.charge == 1\n",
+    ")\n",
+    "Math(\", \".join(p.latex for p in sigmas))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from IPython.display import Math\n",
+    "\n",
+    "sigmas = particle_db.filter(lambda p: p.name.startswith(\"gamma\"))\n",
+    "Math(\", \".join(p.latex for p in sigmas))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "proton = particle_db[\"p\"]\n",
+    "proton"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "13",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "gamma = particle_db[\"gamma\"]\n",
+    "gamma"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qrules.particle import Particle, Spin\n",
+    "\n",
+    "pgamma = Particle(\n",
+    "    name=\"p\",\n",
+    "    latex=r\"p \\gamma\",\n",
+    "    spin=0.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99999999,\n",
+    ")\n",
+    "pgamma"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "15",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma_s3over2 = Particle(\n",
+    "    name=\"pgamma\",\n",
+    "    latex=R\"p \\gamma (s3/2)\",\n",
+    "    spin=1.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99999999,\n",
+    ")\n",
+    "pgamma_s3over2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "16",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma_s3over2.latex"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "17",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma.latex"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18",
+   "metadata": {},
+   "source": [
+    "The `pgamma` virtual state generated via `QRules` will be used in later stages!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "19",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],
diff --git a/pixi.lock b/pixi.lock
index b8edcff..1f31ac1 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -111,6 +111,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-git-0.50.0-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-lsp-5.1.0-pyhd8ed1ab_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab-myst-2.4.2-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_code_formatter-2.2.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_pygments-0.3.0-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_server-2.27.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_widgets-3.0.10-pyhd8ed1ab_0.conda
@@ -2320,6 +2321,22 @@ packages:
   - pkg:pypi/jupyterlab-myst
   size: 2127008
   timestamp: 1714146125212
+- kind: conda
+  name: jupyterlab_code_formatter
+  version: 2.2.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_code_formatter-2.2.1-pyhd8ed1ab_0.conda
+  sha256: 8873858a9d3b730a1d6a199be6d4fa67367837d6fa55aa8fe464040522cd906d
+  md5: d67b33450635a2ad1b55d48838eb1eca
+  depends:
+  - jupyter_server >=1.21,<3
+  - python >=3.7
+  license: MIT
+  license_family: MIT
+  size: 28923
+  timestamp: 1684681885304
 - kind: conda
   name: jupyterlab_pygments
   version: 0.3.0
diff --git a/pixi.toml b/pixi.toml
index a2de7b2..c8b913e 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -31,6 +31,7 @@ jupyterlab = ">=4.2.0,<4.3"
 jupyterlab-git = ">=0.50.0,<0.51"
 jupyterlab-lsp = ">=5.1.0,<5.2"
 jupyterlab-myst = ">=2.4.2,<2.5"
+jupyterlab_code_formatter = ">=2.2.1,<2.3"
 myst-nb = ">=1.1.0,<1.2"
 numpy = ">=1.26.4,<1.27"
 pre-commit = ">=3.7.1,<3.8"

From 7aa239afbd2a4c56ba32aa639abe3daecf1efd48 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 17 May 2024 17:24:40 +0200
Subject: [PATCH 04/44] ready to go draft of decay and gamma generation

---
 docs/index.md           |   4 +-
 docs/pgamma-state.ipynb | 285 +++++++++++++++++++++++++++++-----------
 docs/reaction.md        |  10 +-
 3 files changed, 216 insertions(+), 83 deletions(-)

diff --git a/docs/index.md b/docs/index.md
index d0329a7..b08e62e 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -1,11 +1,11 @@
 # Amplitude Analysis 101 / PWA101 (v2.0)
 
-## Amplitude models for photoproduction reaction
+## CAS-assisted Amplitude Models building for photoproduction reaction
 
 This document is a follow-up of PWA101 (v1.0) (temporarily see [here](https://compwa--217.org.readthedocs.build/report/999.html)),
 as an introduction to Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.
 
-Now the focus is the use of symbolic expressions (computations) with the use of [ComPWA packages](https://compwa.github.io/), or CAS(Computer Algebra System)-assisted model building in general (the python package `SymPy` in this case) to illustrate the general process in PWA.
+Now the focus is the use of symbolic expressions (computations), with the use of [ComPWA packages](https://compwa.github.io/), or CAS(Computer Algebra System)-assisted model building in general (the python package `SymPy` in this case) to illustrate the general process in PWA.
 
 This tutorial aims to equip readers with deeper understanding of PWA methodologies and full workflow in the context of hadron physics through a practical, hands-on example with symbolic expressions via [ComPWA](https://compwa.github.io/).
 
diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
index b00a1db..d2ff38b 100644
--- a/docs/pgamma-state.ipynb
+++ b/docs/pgamma-state.ipynb
@@ -11,14 +11,7 @@
     "tags": []
    },
    "source": [
-    "::::{margin}\n",
-    ":::{card} Create a virtual particle that represents the state pγ in `QRules`\n",
-    "Report-0\n",
-    "^^^\n",
-    "+++\n",
-    "✅&nbsp;[ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5)\n",
-    ":::\n",
-    "::::"
+    "# Virtual particle that represents the state pγ "
    ]
   },
   {
@@ -32,7 +25,7 @@
     "tags": []
    },
    "source": [
-    "# Virtual particle that represents the state pγ "
+    "Address to issue ✅&nbsp;[ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5), this section is an investigation of creating a virtual particle that represents the state $p \\gamma$ in `QRules`"
    ]
   },
   {
@@ -46,21 +39,15 @@
     "tags": []
    },
    "source": [
-    "Address to issue [ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5), this section is an investigation of creating a virtual particle that represents the state $p \\gamma$"
+    "As an example of side note, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
    ]
   },
   {
    "cell_type": "markdown",
    "id": "3",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
-    "As an example of side note, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
+    "## Finding particles"
    ]
   },
   {
@@ -68,7 +55,7 @@
    "id": "4",
    "metadata": {},
    "source": [
-    "`QRules` is used for this task"
+    "Our reaction is $p + \\gamma \\to \\eta + \\pi^0 + p$, so we can look for each of the reaction and decay particles"
    ]
   },
   {
@@ -90,10 +77,34 @@
     "print(\"Number of loaded particles:\", len(particle_db))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "6",
+   "metadata": {},
+   "source": [
+    "The [`ParticleCollection`](https://qrules.readthedocs.io/0.10.x/api/qrules.particle/#qrules.particle.ParticleCollection) class offers some methods to search for particles by name or by PID, name, or other properties."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7",
+   "metadata": {},
+   "source": [
+    "### Proton"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8",
+   "metadata": {},
+   "source": [
+    "Search by Particle ID (PID) for proton:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
+   "id": "9",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -106,36 +117,57 @@
     "particle_db.find(2212)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "10",
+   "metadata": {},
+   "source": [
+    "Search by Particle name for proton:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7",
+   "id": "11",
    "metadata": {},
    "outputs": [],
    "source": [
-    "particle_db.find(\"p\")"
+    "particle_db.find(\"p\")\n",
+    "proton = particle_db[\"p\"]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "id": "12",
+   "metadata": {},
    "outputs": [],
    "source": [
-    "particle_db.find(22)"
+    "from IPython.display import Math\n",
+    "\n",
+    "Math(proton.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "13",
+   "metadata": {},
+   "source": [
+    "### $\\gamma$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "14",
+   "metadata": {},
+   "source": [
+    "similarly for $\\gamma$:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "15",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -145,63 +177,134 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "id": "16",
+   "metadata": {},
    "outputs": [],
    "source": [
-    "from IPython.display import Math\n",
-    "\n",
-    "sigmas = particle_db.filter(\n",
-    "    lambda p: p.name.startswith(\"p\") and p.mass == 0.93827208816 and p.charge == 1\n",
-    ")\n",
-    "Math(\", \".join(p.latex for p in sigmas))"
+    "gamma = particle_db[\"gamma\"]\n",
+    "Math(gamma.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "17",
+   "metadata": {},
+   "source": [
+    "### $\\eta$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
+   "id": "18",
    "metadata": {},
    "outputs": [],
    "source": [
-    "from IPython.display import Math\n",
-    "\n",
-    "sigmas = particle_db.filter(lambda p: p.name.startswith(\"gamma\"))\n",
-    "Math(\", \".join(p.latex for p in sigmas))"
+    "particle_db.find(\"eta\")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "19",
    "metadata": {},
    "outputs": [],
    "source": [
-    "proton = particle_db[\"p\"]\n",
-    "proton"
+    "eta = particle_db[\"eta\"]\n",
+    "Math(gamma.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "20",
+   "metadata": {},
+   "source": [
+    "### $\\pi^0$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "21",
    "metadata": {},
    "outputs": [],
    "source": [
-    "gamma = particle_db[\"gamma\"]\n",
-    "gamma"
+    "particle_db.find(\"pi0\")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14",
+   "id": "22",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pi0 = particle_db[\"pi0\"]\n",
+    "Math(pi0.latex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "23",
+   "metadata": {},
+   "source": [
+    "# Adding custom particle"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24",
+   "metadata": {},
+   "source": [
+    "We add the virtual particle $p\\gamma$ to represent the state of $p-\\gamma$ system in the photoproduction reaction.\n",
+    "See PWA101 (temporary [here](https://compwa--217.org.readthedocs.build/report/999.html)), the value of the mass of the system $m_{p\\gamma}$ in CM frame is about 4.102 GeV in this analysis.\n",
+    "\n",
+    "\n",
+    "We use `Particle` from `QRules` for adding custom particle, so that some quantum numbers we need to determine for the $p\\gamma$ virtual state particle:\n",
+    "\n",
+    "* (Total) Spin\n",
+    "    * $J_{p\\gamma} = \\frac{1}{2}$ or $\\frac{3}{2}$\n",
+    "      \n",
+    "      because $J_{p\\gamma}$ = from $|s_p-s_{\\gamma}|$ to $s_p + s_{\\gamma}$ = from $|\\frac{1}{2}-1|$ to $\\frac{1}{2} + 1$\n",
+    "      \n",
+    "* Mass\n",
+    "    * $m_{p\\gamma} = E_{p\\gamma} \\approx 4.102$\n",
+    "    \n",
+    "* Charge\n",
+    "    * $Q_{p\\gamma} = Q_p + Q_{\\gamma} = 1 $\n",
+    "      \n",
+    "* Isospin and $3^{rd}# component of isospin\n",
+    "    * $I_{p\\gamma} = I_p = \\frac{1}{2}$\n",
+    "    * $I_{3_{p\\gamma}} = I_{3_p} = +\\frac{1}{2}$\n",
+    "  \n",
+    "* Baryon Number\n",
+    "    * $B_{p\\gamma} = B_p  = 1$\n",
+    "\n",
+    "* Parity\n",
+    "    * $P_{p\\gamma} = P_p \\times P_{\\gamma} = +1 \\times (-1) = -1$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25",
+   "metadata": {},
+   "source": [
+    "These quantum numbers provide a complete and accurate description of the virtual particle representing the p−γ system with a mass of 4.102 GeV.\n",
+    "The pγ virtual particle has two possibilities for the total spin, while the other quantum numbers are fixed."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "26",
+   "metadata": {},
+   "source": [
+    "We add the spin-$\\frac{1}{2}$ $p\\gamma$ virtual particle via `QRules` and named it $p\\gamma$ with a make-up pid number 99990"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "27",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -209,74 +312,104 @@
     "\n",
     "pgamma = Particle(\n",
     "    name=\"p\",\n",
-    "    latex=r\"p \\gamma\",\n",
+    "    latex=r\"p\\gamma (s1/2)\",\n",
     "    spin=0.5,\n",
     "    mass=4.101931071854584,\n",
     "    charge=1,\n",
     "    isospin=Spin(1 / 2, +1 / 2),\n",
     "    baryon_number=1,\n",
     "    parity=-1,\n",
-    "    pid=99999999,\n",
+    "    pid=99990,\n",
     ")\n",
     "pgamma"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "28",
+   "metadata": {},
+   "source": [
+    "We add the spin-$\\frac{3}{2}$ $p\\gamma$ virtual particle via `QRules` and named it $p\\gamma (s3/2)$ with a make-up pid number 99991"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15",
+   "id": "29",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pgamma_s3over2 = Particle(\n",
+    "pgamma_j3over2 = Particle(\n",
     "    name=\"pgamma\",\n",
-    "    latex=R\"p \\gamma (s3/2)\",\n",
+    "    latex=R\"p\\gamma (s3/2)\",\n",
     "    spin=1.5,\n",
     "    mass=4.101931071854584,\n",
     "    charge=1,\n",
     "    isospin=Spin(1 / 2, +1 / 2),\n",
     "    baryon_number=1,\n",
     "    parity=-1,\n",
-    "    pid=99999999,\n",
+    "    pid=99991,\n",
     ")\n",
-    "pgamma_s3over2"
+    "pgamma_j3over2"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
+   "id": "30",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pgamma_s3over2.latex"
+    "Math(pgamma.latex)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17",
+   "id": "31",
    "metadata": {},
    "outputs": [],
    "source": [
-    "pgamma.latex"
+    "Math(pgamma_j3over2.latex)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "18",
+   "id": "32",
    "metadata": {},
    "source": [
-    "The `pgamma` virtual state generated via `QRules` will be used in later stages!"
+    "The $`p\\gamma`$ virtual states generated via `QRules` will be used in later stages, both possible spin states $(J= \\frac{1}{2}$ and $\\frac{3}{2})$ should be taken into account if possible, otherwise simplified if necessary."
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "19",
+   "cell_type": "markdown",
+   "id": "33",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    ":::{important}\n",
+    "It is possible to add any kind of custom Particle, as long as its quantum numbers comply with the [gellmann_nishijima()](https://qrules.readthedocs.io/0.10.x/api/qrules.conservation_rules/#qrules.conservation_rules.gellmann_nishijima) rule:\n",
+    ":::\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34",
+   "metadata": {},
+   "source": [
+    ":::{note}\n",
+    "[Gell-Mann-Nishijima formula](https://en.wikipedia.org/wiki/Gell-Mann–Nishijima_formula):\n",
+    "$Q = I_3 + \\frac{1}{2}(B+S+C+B'+T)$\n",
+    "\n",
+    "where \n",
+    "Q is charge, \n",
+    "$I_3$ is Spin projection of isospin, \n",
+    " B is baryon number, \n",
+    " S is strangeness, \n",
+    " C is charmness, \n",
+    " B' is bottomness, and \n",
+    " T is topness.\n",
+    ":::\n"
+   ]
   }
  ],
  "metadata": {
diff --git a/docs/reaction.md b/docs/reaction.md
index 0f8a6cd..17f3519 100644
--- a/docs/reaction.md
+++ b/docs/reaction.md
@@ -1,17 +1,17 @@
-# Reaction and amplitude models
+# Reaction and Models
 
 <!-- cspell:ignore Mathieu -->
 <!-- This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu. -->
 
-## Reaction
+## Reaction with Resonances and Decay
 
-The (photo-production) reaction is $ \gamma p \to \eta \pi^0 p$, it is described by a amplitude model with three possible resonances: $a_2$, $\Delta^+$, and $N^*$.
+The (photo-production) reaction is $ \gamma p \to \eta \pi^0 p$, its decay is described by an amplitude model with three possible resonances: $a_2$, $\Delta^+$, and $N^*$.
 
 ```{image} https://github.com/ComPWA/compwa-org/assets/17490173/ec6bf191-bd5f-43b0-a6cb-da470b071630
 :width: 100%
 ```
 
-## Amplitude models
+## Amplitude Models
 
 The amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/), only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually, as shown in equation {eq}`BW_SH_label`.
 
@@ -24,7 +24,7 @@ A^{31} &=& \frac{c_0}{s-m^2_{N^*}+im_{N^*} \Gamma_{N^*}}
 \end{eqnarray}
 $$ (BW_SH_label)
 
-where s is the Mandelstam variable, m is the mass, $\Gamma$ is the width, Y is the spherical harmonics, $\Omega$ is the decay angles (a pair of Euler angles), and a, b, and c are coefficients
+where s is the Mandelstam variable, m is the mass, $\Gamma$ is the width, $Y^m_l$ is the spherical harmonics, $\Omega_i$ is the decay angles (a pair of Euler angles), and $a_i$, $b_i$, and $c_i$ are coefficients
 
 :::{note}
 Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$.

From 62d51927a94866cf5233fb2f8aae790e905bdfd7 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 22 May 2024 11:43:43 +0200
Subject: [PATCH 05/44] Add ampform as dependency

---
 pixi.lock | 579 +++++++++---------------------------------------------
 pixi.toml |   1 +
 2 files changed, 95 insertions(+), 485 deletions(-)

diff --git a/pixi.lock b/pixi.lock
index 1f31ac1..948f5fd 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -9,6 +9,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/accessible-pygments-0.0.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/alabaster-0.7.16-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/anyio-4.3.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/argon2-cffi-23.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/argon2-cffi-bindings-21.2.0-py312h98912ed_4.conda
@@ -84,7 +85,6 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/importlib_resources-6.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipykernel-6.29.3-pyhd33586a_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipython-8.24.0-pyh707e725_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/ipython_genutils-0.2.0-py_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipywidgets-8.1.2-pyhd8ed1ab_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/isoduration-20.11.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/isort-5.13.2-pyhd8ed1ab_0.conda
@@ -101,7 +101,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-cache-1.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-lsp-2.2.5-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter-server-mathjax-0.2.6-pyh5bfe37b_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_client-7.4.9-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_client-8.6.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_console-6.6.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/jupyter_core-5.7.2-py312h7900ff3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyter_events-0.10.0-pyhd8ed1ab_0.conda
@@ -160,14 +160,13 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/mdit-py-plugins-0.4.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/mdurl-0.1.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/mistune-3.0.2-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/ml_dtypes-0.4.0-py312hfb8ada1_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/ml_dtypes-0.4.0-py312h1d6d2e6_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/mpc-1.3.1-hfe3b2da_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/mpfr-4.2.1-h9458935_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/mpmath-1.3.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/mypy_extensions-1.0.0-pyha770c72_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/myst-nb-1.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/myst-parser-3.0.1-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/nbclassic-1.0.0-pyhb4ecaf3_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nbclient-0.10.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nbconvert-7.16.4-hd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nbconvert-core-7.16.4-pyhd8ed1ab_0.conda
@@ -177,10 +176,10 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ncurses-6.5-h59595ed_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nest-asyncio-1.6.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nodeenv-1.8.0-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-6.5.7-pyha770c72_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.2.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-shim-0.2.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/numpy-1.26.4-py312heda63a1_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/openssl-3.3.0-hd590300_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/openssl-3.3.0-h4ab18f5_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/opt-einsum-3.3.0-hd8ed1ab_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/opt_einsum-3.3.0-pyhc1e730c_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/overrides-7.7.0-pyhd8ed1ab_0.conda
@@ -225,13 +224,14 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/re2-2023.09.01-h7f4b329_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/readline-8.2-h8228510_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/referencing-0.35.1-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/requests-2.31.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/requests-2.32.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/rfc3339-validator-0.1.4-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/rfc3986-validator-0.1.1-pyh9f0ad1d_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/rpds-py-0.18.1-py312h4413252_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/scipy-1.13.0-py312hc2bc53b_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/send2trash-1.8.3-pyh0d859eb_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/setuptools-69.5.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/setuptools-70.0.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/singledispatchmethod-1.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/six-1.16.0-pyh6c4a22f_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/smmap-5.0.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/sniffio-1.3.1-pyhd8ed1ab_0.conda
@@ -337,8 +337,6 @@ packages:
   - python >=3.6
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/accessible-pygments
   size: 15626
   timestamp: 1679583960534
 - kind: conda
@@ -354,10 +352,29 @@ packages:
   - python >=3.9
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/alabaster
   size: 18365
   timestamp: 1704848898483
+- kind: conda
+  name: ampform
+  version: 0.15.3
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.3-pyhd8ed1ab_0.conda
+  sha256: bd2a51349635cb2dee6f197d7bc75af934710ddb9b2c998070127d1b6ddc0385
+  md5: 7f698ec34d66b9bc40c03375a3efaf2c
+  depends:
+  - attrs >=20.1.0
+  - importlib-metadata
+  - python >=3.7
+  - qrules >=0.9.6
+  - singledispatchmethod
+  - sympy >=1.10
+  - typing-extensions
+  license: GPL-3.0-or-later
+  license_family: GPL
+  size: 76396
+  timestamp: 1716358323855
 - kind: conda
   name: anyio
   version: 4.3.0
@@ -378,8 +395,6 @@ packages:
   - uvloop >=0.17
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/anyio
   size: 102331
   timestamp: 1708355504396
 - kind: conda
@@ -399,8 +414,6 @@ packages:
   - argon2_cffi ==999
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/argon2-cffi
   size: 18602
   timestamp: 1692818472638
 - kind: conda
@@ -419,8 +432,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/argon2-cffi-bindings
   size: 35142
   timestamp: 1695386704886
 - kind: conda
@@ -438,8 +449,6 @@ packages:
   - types-python-dateutil >=2.8.10
   license: Apache-2.0
   license_family: Apache
-  purls:
-  - pkg:pypi/arrow
   size: 100096
   timestamp: 1696129131844
 - kind: conda
@@ -456,8 +465,6 @@ packages:
   - six >=1.12.0
   license: Apache-2.0
   license_family: Apache
-  purls:
-  - pkg:pypi/asttokens
   size: 28922
   timestamp: 1698341257884
 - kind: conda
@@ -474,8 +481,6 @@ packages:
   - typing_extensions >=4.0.0
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/async-lru
   size: 15342
   timestamp: 1690563152778
 - kind: conda
@@ -510,8 +515,6 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/attrs
   size: 54582
   timestamp: 1704011393776
 - kind: conda
@@ -529,8 +532,6 @@ packages:
   - setuptools
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/babel
   size: 7609750
   timestamp: 1702422720584
 - kind: conda
@@ -547,8 +548,6 @@ packages:
   - soupsieve >=1.2
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/beautifulsoup4
   size: 118200
   timestamp: 1705564819537
 - kind: conda
@@ -569,8 +568,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/black
   size: 387770
   timestamp: 1714119755759
 - kind: conda
@@ -590,9 +587,6 @@ packages:
   - webencodings
   license: Apache-2.0
   license_family: Apache
-  purls:
-  - pkg:pypi/html5lib
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@@ -4891,8 +4552,6 @@ packages:
   - typing_extensions >=3.10.0
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/starlette
   size: 57620
   timestamp: 1709667193131
 - kind: conda
@@ -4913,8 +4572,6 @@ packages:
   - python >=3.8
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/sympy
   size: 4256289
   timestamp: 1684180689319
 - kind: conda
@@ -4931,8 +4588,6 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/tabulate
   size: 35912
   timestamp: 1665138565317
 - kind: conda
@@ -4951,8 +4606,6 @@ packages:
   - tornado >=6.1.0
   license: BSD-2-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/terminado
   size: 22452
   timestamp: 1710262728753
 - kind: conda
@@ -4969,8 +4622,6 @@ packages:
   - webencodings >=0.4
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/tinycss2
   size: 25405
   timestamp: 1713975078735
 - kind: conda
@@ -5002,8 +4653,6 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/tomli
   size: 15940
   timestamp: 1644342331069
 - kind: conda
@@ -5020,8 +4669,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: Apache-2.0
   license_family: Apache
-  purls:
-  - pkg:pypi/tornado
   size: 840527
   timestamp: 1708363299520
 - kind: conda
@@ -5037,8 +4684,6 @@ packages:
   - colorama
   - python >=3.7
   license: MPL-2.0 or MIT
-  purls:
-  - pkg:pypi/tqdm
   size: 89452
   timestamp: 1714855008479
 - kind: conda
@@ -5054,8 +4699,6 @@ packages:
   - python >=3.8
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/traitlets
   size: 110187
   timestamp: 1713535244513
 - kind: conda
@@ -5070,8 +4713,6 @@ packages:
   depends:
   - python >=3.6
   license: Apache-2.0 AND MIT
-  purls:
-  - pkg:pypi/types-python-dateutil
   size: 21769
   timestamp: 1710590028155
 - kind: conda
@@ -5102,8 +4743,6 @@ packages:
   - python >=3.8
   license: PSF-2.0
   license_family: PSF
-  purls:
-  - pkg:pypi/typing-extensions
   size: 37583
   timestamp: 1712330089194
 - kind: conda
@@ -5119,8 +4758,6 @@ packages:
   - python >=3.6.1
   license: Apache-2.0
   license_family: APACHE
-  purls:
-  - pkg:pypi/typing-utils
   size: 13829
   timestamp: 1622899345711
 - kind: conda
@@ -5152,8 +4789,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/ukkonen
   size: 14050
   timestamp: 1695549556745
 - kind: conda
@@ -5169,8 +4804,6 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/uri-template
   size: 23999
   timestamp: 1688655976471
 - kind: conda
@@ -5188,8 +4821,6 @@ packages:
   - python >=3.7
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/urllib3
   size: 94669
   timestamp: 1708239595549
 - kind: conda
@@ -5207,8 +4838,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/uvicorn
   size: 126964
   timestamp: 1710932152563
 - kind: conda
@@ -5227,8 +4856,6 @@ packages:
   - python >=3.8
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/virtualenv
   size: 3458445
   timestamp: 1715681264937
 - kind: conda
@@ -5246,8 +4873,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/watchfiles
   size: 1094669
   timestamp: 1701078026995
 - kind: conda
@@ -5263,8 +4888,6 @@ packages:
   - python >=3.8
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/wcwidth
   size: 32709
   timestamp: 1704731373922
 - kind: conda
@@ -5280,8 +4903,6 @@ packages:
   - python >=3.5
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/webcolors
   size: 18186
   timestamp: 1679900907305
 - kind: conda
@@ -5298,8 +4919,6 @@ packages:
   - python >=2.6
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/webencodings
   size: 15600
   timestamp: 1694681458271
 - kind: conda
@@ -5315,8 +4934,6 @@ packages:
   - python >=3.8
   license: Apache-2.0
   license_family: APACHE
-  purls:
-  - pkg:pypi/websocket-client
   size: 47066
   timestamp: 1713923494501
 - kind: conda
@@ -5333,8 +4950,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/websockets
   size: 201426
   timestamp: 1697914826988
 - kind: conda
@@ -5350,8 +4965,6 @@ packages:
   - python >=3.7
   license: BSD-3-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/widgetsnbextension
   size: 886369
   timestamp: 1707420479741
 - kind: conda
@@ -5368,8 +4981,6 @@ packages:
   - python_abi 3.12.* *_cp312
   license: BSD-2-Clause
   license_family: BSD
-  purls:
-  - pkg:pypi/wrapt
   size: 62482
   timestamp: 1699532968076
 - kind: conda
@@ -5600,8 +5211,6 @@ packages:
   - python >=3.8
   license: MIT
   license_family: MIT
-  purls:
-  - pkg:pypi/zipp
   size: 18954
   timestamp: 1695255262261
 - kind: conda
diff --git a/pixi.toml b/pixi.toml
index c8b913e..fba14d9 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -20,6 +20,7 @@ sphinx-autobuild \
 """
 
 [dependencies]
+ampform = ">=0.15.2,<0.16"
 black = ">=24.4.2,<24.5"
 graphviz = ">=9.0.0,<9.1"
 ipywidgets = ">=8.1.2,<8.2"

From 3a620ba1a7eb436dc6dbc14f423e75d1d744c905 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 24 May 2024 18:56:02 +0200
Subject: [PATCH 06/44] draft 1 start to try sp

---
 docs/symbolics.ipynb | 154 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 154 insertions(+)
 create mode 100644 docs/symbolics.ipynb

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
new file mode 100644
index 0000000..52d194d
--- /dev/null
+++ b/docs/symbolics.ipynb
@@ -0,0 +1,154 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {},
+   "source": [
+    "# Symbolic expression for the amplitude model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "$$\n",
+    "\\begin{eqnarray}\n",
+    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
+    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
+    "\\\n",
+    "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}}\n",
+    "\\end{eqnarray}\n",
+    "$$ (BW_SH_label)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import graphviz\n",
+    "import sympy as sp\n",
+    "from sympy import re, im, I, E, symbols, Sum"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "a, b, c, s, m, Γ = sp.symbols(\"a_m b_m c_0 s m Gamma\")\n",
+    "\n",
+    "amplitude12 = a / (s - m**2 + I * m * Γ)\n",
+    "amplitude23 = b / (s - m**2 + I * m * Γ)\n",
+    "amplitude31 = c / (s - m**2 + I * m * Γ)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "amplitude12"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "amplitude23"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "amplitude31"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From e44262f2b8654bc4c49ad7153e870bb74ac7d5ac Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 12:28:55 +0200
Subject: [PATCH 07/44] draft

---
 docs/symbolics.ipynb | 44 +++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 43 insertions(+), 1 deletion(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 52d194d..a14c3fb 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -44,7 +44,7 @@
    "source": [
     "import graphviz\n",
     "import sympy as sp\n",
-    "from sympy import re, im, I, E, symbols, Sum"
+    "from sympy import re, im, I, E, symbols, Sum, IndexedBase, Function"
    ]
   },
   {
@@ -127,6 +127,48 @@
     "tags": []
    },
    "outputs": [],
+   "source": [
+    "s, m_a2, Gamma_a2 = symbols(\"s m_a2 Gamma_a2\")\n",
+    "a_m = IndexedBase(\"a_m\")\n",
+    "Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
+    "m = symbols(\"m\", cls=sp.Idx)\n",
+    "\n",
+    "A12 = sp.Sum(a_m * Y2_m, (m, -2, 2)) / (s - m_a2**2 + I * m_a2 * Gamma_a2)\n",
+    "A12"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m_Delta, Gamma_Delta = symbols(\"m_Delta Gamma_Delta\")\n",
+    "b_m = IndexedBase(\"b_m\")\n",
+    "Y1_m = Function(\"Y_1^m\")(\"Omega_2\")\n",
+    "A23 = Sum(b_m * Y1_m, (m, -1, 1)) / (s - m_Delta**2 + I * m_Delta * Gamma_Delta)\n",
+    "A23"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "c0, m_Nstar, Gamma_Nstar = symbols(\"c_0 m_N* Gamma_N*\")\n",
+    "A31 = c0 / (s - m_Nstar**2 + I * m_Nstar * Gamma_Nstar)\n",
+    "A31"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],

From 1f5fe3c052c84772d592d2d878d0d117c494df92 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 13:19:36 +0200
Subject: [PATCH 08/44] delete test

---
 docs/symbolics.ipynb | 77 +++-----------------------------------------
 1 file changed, 5 insertions(+), 72 deletions(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index a14c3fb..4b91555 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -44,7 +44,8 @@
    "source": [
     "import graphviz\n",
     "import sympy as sp\n",
-    "from sympy import re, im, I, E, symbols, Sum, IndexedBase, Function"
+    "from sympy import re, im, I, E, symbols, Sum, IndexedBase, Function\n",
+    "from IPython.display import display, Latex"
    ]
   },
   {
@@ -59,74 +60,6 @@
     "tags": []
    },
    "outputs": [],
-   "source": [
-    "a, b, c, s, m, Γ = sp.symbols(\"a_m b_m c_0 s m Gamma\")\n",
-    "\n",
-    "amplitude12 = a / (s - m**2 + I * m * Γ)\n",
-    "amplitude23 = b / (s - m**2 + I * m * Γ)\n",
-    "amplitude31 = c / (s - m**2 + I * m * Γ)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "4",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "amplitude12"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "amplitude23"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "6",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "amplitude31"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "7",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
    "source": [
     "s, m_a2, Gamma_a2 = symbols(\"s m_a2 Gamma_a2\")\n",
     "a_m = IndexedBase(\"a_m\")\n",
@@ -140,7 +73,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
+   "id": "4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -154,7 +87,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -166,7 +99,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
+   "id": "6",
    "metadata": {},
    "outputs": [],
    "source": []

From a67db0618479fe92aef3d2770dd82c03994a1fc3 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 15:09:58 +0200
Subject: [PATCH 09/44] add sp.Ynm

---
 docs/symbolics.ipynb | 31 ++++++++++++++++++++++++++-----
 1 file changed, 26 insertions(+), 5 deletions(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 4b91555..ffc4d40 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -44,7 +44,19 @@
    "source": [
     "import graphviz\n",
     "import sympy as sp\n",
-    "from sympy import re, im, I, E, symbols, Sum, IndexedBase, Function\n",
+    "from sympy import (\n",
+    "    re,\n",
+    "    im,\n",
+    "    I,\n",
+    "    E,\n",
+    "    symbols,\n",
+    "    Sum,\n",
+    "    IndexedBase,\n",
+    "    Function,\n",
+    "    Ynm,\n",
+    "    Symbol,\n",
+    "    simplify,\n",
+    ")\n",
     "from IPython.display import display, Latex"
    ]
   },
@@ -61,12 +73,17 @@
    },
    "outputs": [],
    "source": [
-    "s, m_a2, Gamma_a2 = symbols(\"s m_a2 Gamma_a2\")\n",
+    "s, m_a2, Gamma_a2 = symbols(r\"s m_{a_2} \\Gamma_{a_2}\")\n",
+    "l, m, theta1, phi1 = symbols(\"l m theta_1 phi_1\")\n",
+    "Ynm(l, m, theta, phi)\n",
     "a_m = IndexedBase(\"a_m\")\n",
     "Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
     "m = symbols(\"m\", cls=sp.Idx)\n",
+    "Omega1 = symbols(\"Omega_1\")\n",
     "\n",
-    "A12 = sp.Sum(a_m * Y2_m, (m, -2, 2)) / (s - m_a2**2 + I * m_a2 * Gamma_a2)\n",
+    "A12 = sp.Sum(a_m * Ynm(2, m, theta1, phi1), (m, -2, 2)) / (\n",
+    "    s - m_a2**2 + I * m_a2 * Gamma_a2\n",
+    ")\n",
     "A12"
    ]
   },
@@ -80,7 +97,10 @@
     "m_Delta, Gamma_Delta = symbols(\"m_Delta Gamma_Delta\")\n",
     "b_m = IndexedBase(\"b_m\")\n",
     "Y1_m = Function(\"Y_1^m\")(\"Omega_2\")\n",
-    "A23 = Sum(b_m * Y1_m, (m, -1, 1)) / (s - m_Delta**2 + I * m_Delta * Gamma_Delta)\n",
+    "theta2, phi2 = symbols(\"theta_2 phi_2\")\n",
+    "A23 = Sum(b_m * Ynm(1, m, theta2, phi2), (m, -1, 1)) / (\n",
+    "    s - m_Delta**2 + I * m_Delta * Gamma_Delta\n",
+    ")\n",
     "A23"
    ]
   },
@@ -91,7 +111,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "c0, m_Nstar, Gamma_Nstar = symbols(\"c_0 m_N* Gamma_N*\")\n",
+    "c0, m_Nstar, Gamma_Nstar = symbols(r\"c_0 m_{N^*} \\Gamma_{N^*}\")\n",
+    "# r'\\Gamma_{N^*}'\n",
     "A31 = c0 / (s - m_Nstar**2 + I * m_Nstar * Gamma_Nstar)\n",
     "A31"
    ]

From 94858f592650b3eecb329560c7040e478633804a Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 15:31:04 +0200
Subject: [PATCH 10/44] add plot draft

---
 docs/symbolics.ipynb |   49 +-
 pixi.lock            | 1273 ++++++++++++++++++++++++++++++++++++++++++
 pixi.toml            |    1 +
 3 files changed, 1322 insertions(+), 1 deletion(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index ffc4d40..05b86d2 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -42,6 +42,7 @@
    },
    "outputs": [],
    "source": [
+    "import numpy as np\n",
     "import graphviz\n",
     "import sympy as sp\n",
     "from sympy import (\n",
@@ -112,7 +113,6 @@
    "outputs": [],
    "source": [
     "c0, m_Nstar, Gamma_Nstar = symbols(r\"c_0 m_{N^*} \\Gamma_{N^*}\")\n",
-    "# r'\\Gamma_{N^*}'\n",
     "A31 = c0 / (s - m_Nstar**2 + I * m_Nstar * Gamma_Nstar)\n",
     "A31"
    ]
@@ -123,6 +123,53 @@
    "id": "6",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "A31.free_symbols"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sp.lambdify([s, c0, m_Nstar, Gamma_Nstar], A31)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A31_func = sp.lambdify([s, c0, m_Nstar, Gamma_Nstar], A31)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "s_values = np.linspace(0, 5, 100)\n",
+    "A31_values = A31_func(s_values, 1, 1.5, 0.6)\n",
+    "plt.plot(s_values, A31_values.imag)\n",
+    "plt.plot(s_values, A31_values.real)\n",
+    "plt.plot(s_values, np.abs(A31_values) ** 2)\n",
+    "plt.plot(s_values, np.angle(A31_values))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],
diff --git a/pixi.lock b/pixi.lock
index 948f5fd..a04abeb 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -9,6 +9,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/accessible-pygments-0.0.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/alabaster-0.7.16-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/alsa-lib-1.2.11-hd590300_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/anyio-4.3.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/argon2-cffi-23.1.0-pyhd8ed1ab_0.conda
@@ -17,11 +18,14 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/asttokens-2.4.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/async-lru-2.0.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/atk-1.0-2.38.0-h04ea711_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/attr-2.5.1-h166bdaf_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/attrs-23.2.0-pyh71513ae_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/babel-2.14.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/beautifulsoup4-4.12.3-pyha770c72_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/black-24.4.2-py312h7900ff3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/bleach-6.1.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-1.1.0-hd590300_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-bin-1.1.0-hd590300_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-python-1.1.0-py312h30efb56_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/bzip2-1.0.8-hd590300_5.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/c-ares-1.28.1-hd590300_0.conda
@@ -36,6 +40,9 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/click-8.1.7-unix_pyh707e725_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/colorama-0.4.6-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/comm-0.2.2-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/contourpy-1.2.1-py312h8572e83_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/cycler-0.12.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/dbus-1.13.6-h5008d03_3.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/debugpy-1.8.1-py312h30efb56_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/decorator-5.1.1-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/defusedxml-0.7.1-pyhd8ed1ab_0.tar.bz2
@@ -54,18 +61,25 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/fontconfig-2.14.2-h14ed4e7_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/fonts-conda-ecosystem-1-0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/fonts-conda-forge-1-0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.53.0-py312h9a8786e_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/fqdn-1.5.1-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/freetype-2.12.1-h267a509_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/fribidi-1.0.10-h36c2ea0_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gdk-pixbuf-2.42.12-hb9ae30d_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/gettext-0.22.5-h59595ed_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/gettext-tools-0.22.5-h59595ed_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/giflib-5.2.2-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/gitdb-4.0.11-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/gitpython-3.1.43-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/glib-2.80.2-hf974151_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/glib-tools-2.80.2-hb6ce0ca_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gmp-6.3.0-h59595ed_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gmpy2-2.1.5-py312h1d5cde6_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/graphite2-1.3.13-h59595ed_1003.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/graphviz-9.0.0-h78e8752_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/greenlet-3.0.3-py312h30efb56_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/gst-plugins-base-1.24.4-h9ad1361_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/gstreamer-1.24.4-haf2f30d_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gtk2-2.24.33-h280cfa0_4.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gts-0.7.6-h977cf35_4.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/h11-0.14.0-pyhd8ed1ab_0.tar.bz2
@@ -116,46 +130,76 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_server-2.27.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/jupyterlab_widgets-3.0.10-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/keyutils-1.6.1-h166bdaf_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/kiwisolver-1.4.5-py312h8572e83_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/krb5-1.21.2-h659d440_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/lame-3.100-h166bdaf_1003.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/lcms2-2.16-hb7c19ff_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ld_impl_linux-64-2.40-h55db66e_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/lerc-4.0.0-h27087fc_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libabseil-20240116.2-cxx17_h59595ed_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libasprintf-0.22.5-h661eb56_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libasprintf-devel-0.22.5-h661eb56_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libblas-3.9.0-22_linux64_openblas.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libbrotlicommon-1.1.0-hd590300_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libbrotlidec-1.1.0-hd590300_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libbrotlienc-1.1.0-hd590300_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libcap-2.69-h0f662aa_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcblas-3.9.0-22_linux64_openblas.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang-cpp15-15.0.7-default_h127d8a8_5.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang13-18.1.6-default_h5d6823c_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libcups-2.3.3-h4637d8d_4.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libdeflate-1.20-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libedit-3.1.20191231-he28a2e2_2.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libevent-2.1.12-hf998b51_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libexpat-2.6.2-h59595ed_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libffi-3.4.2-h7f98852_5.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libflac-1.4.3-h59595ed_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgcc-ng-13.2.0-h77fa898_7.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgcrypt-1.10.3-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgd-2.3.3-h119a65a_9.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgettextpo-0.22.5-h59595ed_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgettextpo-devel-0.22.5-h59595ed_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgfortran-ng-13.2.0-h69a702a_7.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgfortran5-13.2.0-hca663fb_7.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libglib-2.80.2-hf974151_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgomp-13.2.0-h77fa898_7.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgpg-error-1.49-h4f305b6_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgrpc-1.62.2-h15f2491_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libiconv-1.17-hd590300_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libjpeg-turbo-3.0.0-hd590300_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/liblapack-3.9.0-22_linux64_openblas.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm15-15.0.7-hb3ce162_4.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm18-18.1.6-hb77312f_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libnsl-2.0.1-hd590300_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libogg-1.3.4-h7f98852_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libopenblas-0.3.27-pthreads_h413a1c8_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libopus-1.3.1-h7f98852_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libpng-1.6.43-h2797004_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libpq-16.3-ha72fbe1_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libprotobuf-4.25.3-h08a7969_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libre2-11-2023.09.01-h5a48ba9_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/librsvg-2.58.0-hadf69e7_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libsndfile-1.2.2-hc60ed4a_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libsodium-1.0.18-h36c2ea0_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libsqlite-3.45.3-h2797004_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libstdcxx-ng-13.2.0-hc0a3c3a_7.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libsystemd0-255-h3516f8a_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libtiff-4.6.0-h1dd3fc0_3.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libuuid-2.38.1-h0b41bf4_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libvorbis-1.3.7-h9c3ff4c_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libwebp-1.4.0-h2c329e2_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libwebp-base-1.4.0-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libxcb-1.15-h0b41bf4_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libxcrypt-4.4.36-hd590300_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libxkbcommon-1.7.0-h662e7e4_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libxml2-2.12.7-hc051c1a_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libzlib-1.2.13-hd590300_5.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/livereload-2.6.3-pyh9f0ad1d_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/lz4-c-1.9.4-hcb278e6_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/markdown-it-py-3.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/markupsafe-2.1.5-py312h98912ed_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/matplotlib-3.8.4-py312h7900ff3_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/matplotlib-base-3.8.4-py312h20ab3a6_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/matplotlib-inline-0.1.7-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/mdit-py-plugins-0.4.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/mdurl-0.1.2-pyhd8ed1ab_0.conda
@@ -163,8 +207,12 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ml_dtypes-0.4.0-py312h1d6d2e6_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/mpc-1.3.1-hfe3b2da_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/mpfr-4.2.1-h9458935_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/mpg123-1.32.6-h59595ed_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/mpmath-1.3.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/munkres-1.1.4-pyh9f0ad1d_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/mypy_extensions-1.0.0-pyha770c72_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-common-8.3.0-hf1915f5_4.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/mysql-libs-8.3.0-hca2cd23_4.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/myst-nb-1.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/myst-parser-3.0.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/nbclient-0.10.0-pyhd8ed1ab_0.conda
@@ -178,7 +226,10 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/nodeenv-1.8.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-7.2.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/notebook-shim-0.2.4-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/nspr-4.35-h27087fc_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/nss-3.100-hca3bf56_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/numpy-1.26.4-py312heda63a1_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/openjpeg-2.5.2-h488ebb8_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/openssl-3.3.0-h4ab18f5_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/opt-einsum-3.3.0-hd8ed1ab_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/opt_einsum-3.3.0-pyhc1e730c_2.conda
@@ -193,9 +244,11 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/pcre2-10.43-hcad00b1_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pexpect-4.9.0-pyhd8ed1ab_0.conda
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+      - conda: https://conda.anaconda.org/conda-forge/linux-64/pillow-10.3.0-py312hdcec9eb_0.conda
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+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-image-0.4.0-h8ee46fc_1.conda
+  sha256: 92ffd68d2801dbc27afe223e04ae7e78ef605fc8575f107113c93c7bafbd15b0
+  md5: 9d7bcddf49cbf727730af10e71022c73
+  depends:
+  - libgcc-ng >=12
+  - libxcb >=1.15,<1.16.0a0
+  - xcb-util >=0.4.0,<0.5.0a0
+  license: MIT
+  license_family: MIT
+  size: 24474
+  timestamp: 1684679894554
+- kind: conda
+  name: xcb-util-keysyms
+  version: 0.4.0
+  build: h8ee46fc_1
+  build_number: 1
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-keysyms-0.4.0-h8ee46fc_1.conda
+  sha256: 8451d92f25d6054a941b962179180728c48c62aab5bf20ac10fef713d5da6a9a
+  md5: 632413adcd8bc16b515cab87a2932913
+  depends:
+  - libgcc-ng >=12
+  - libxcb >=1.15,<1.16.0a0
+  license: MIT
+  license_family: MIT
+  size: 14186
+  timestamp: 1684680497805
+- kind: conda
+  name: xcb-util-renderutil
+  version: 0.3.9
+  build: hd590300_1
+  build_number: 1
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-renderutil-0.3.9-hd590300_1.conda
+  sha256: 6987588e6fff5892056021c2ea52f7a0deefb2c7348e70d24750e2d60dabf009
+  md5: e995b155d938b6779da6ace6c6b13816
+  depends:
+  - libgcc-ng >=12
+  - libxcb >=1.13
+  - libxcb >=1.15,<1.16.0a0
+  license: MIT
+  license_family: MIT
+  size: 16955
+  timestamp: 1684639112393
+- kind: conda
+  name: xcb-util-wm
+  version: 0.4.1
+  build: h8ee46fc_1
+  build_number: 1
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-wm-0.4.1-h8ee46fc_1.conda
+  sha256: 08ba7147c7579249b6efd33397dc1a8c2404278053165aaecd39280fee705724
+  md5: 90108a432fb5c6150ccfee3f03388656
+  depends:
+  - libgcc-ng >=12
+  - libxcb >=1.15,<1.16.0a0
+  license: MIT
+  license_family: MIT
+  size: 52114
+  timestamp: 1684679248466
+- kind: conda
+  name: xkeyboard-config
+  version: '2.41'
+  build: hd590300_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/xkeyboard-config-2.41-hd590300_0.conda
+  sha256: 56955610c0747ea7cb026bb8aa9ef165ff41d616e89894538173b8b7dd2ee49a
+  md5: 81f740407b45e3f9047b3174fa94eb9e
+  depends:
+  - libgcc-ng >=12
+  - xorg-libx11 >=1.8.7,<2.0a0
+  license: MIT
+  license_family: MIT
+  size: 898045
+  timestamp: 1707104384997
 - kind: conda
   name: xorg-kbproto
   version: 1.0.7
@@ -5137,6 +6395,21 @@ packages:
   license_family: MIT
   size: 30270
   timestamp: 1677036833037
+- kind: conda
+  name: xorg-xf86vidmodeproto
+  version: 2.3.1
+  build: h7f98852_1002
+  build_number: 1002
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/xorg-xf86vidmodeproto-2.3.1-h7f98852_1002.tar.bz2
+  sha256: 43398aeacad5b8753b7a1c12cb6bca36124e0c842330372635879c350c430791
+  md5: 3ceea9668625c18f19530de98b15d5b0
+  depends:
+  - libgcc-ng >=9.3.0
+  license: MIT
+  license_family: MIT
+  size: 23875
+  timestamp: 1620067286978
 - kind: conda
   name: xorg-xproto
   version: 7.0.31
diff --git a/pixi.toml b/pixi.toml
index fba14d9..0603ee3 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -33,6 +33,7 @@ jupyterlab-git = ">=0.50.0,<0.51"
 jupyterlab-lsp = ">=5.1.0,<5.2"
 jupyterlab-myst = ">=2.4.2,<2.5"
 jupyterlab_code_formatter = ">=2.2.1,<2.3"
+matplotlib = ">=3.8.4,<3.9"
 myst-nb = ">=1.1.0,<1.2"
 numpy = ">=1.26.4,<1.27"
 pre-commit = ">=3.7.1,<3.8"

From 24bc0427afd79d017f29f90d46f1ae030c59ddf6 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 4 Jun 2024 19:36:08 +0200
Subject: [PATCH 11/44] draft of plots for A31

---
 docs/symbolics.ipynb | 285 +++++++++++++++++++++++++++++++++++++++----
 1 file changed, 260 insertions(+), 25 deletions(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 05b86d2..568669c 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -21,10 +21,10 @@
    "source": [
     "$$\n",
     "\\begin{eqnarray}\n",
-    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
-    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
+    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s_{12}-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
+    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s_{23}-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
     "\\\n",
-    "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}}\n",
+    "A^{31} &=& \\frac{c_0}{s_{31}-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}}\n",
     "\\end{eqnarray}\n",
     "$$ (BW_SH_label)"
    ]
@@ -38,7 +38,9 @@
     "slideshow": {
      "slide_type": ""
     },
-    "tags": []
+    "tags": [
+     "hide-cell"
+    ]
    },
    "outputs": [],
    "source": [
@@ -61,10 +63,24 @@
     "from IPython.display import display, Latex"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# $A^{12}$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3",
+   "id": "4",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -74,16 +90,16 @@
    },
    "outputs": [],
    "source": [
-    "s, m_a2, Gamma_a2 = symbols(r\"s m_{a_2} \\Gamma_{a_2}\")\n",
+    "s12, m_a2, Gamma_a2 = symbols(r\"s_{12} m_{a_2} \\Gamma_{a_2}\")\n",
     "l, m, theta1, phi1 = symbols(\"l m theta_1 phi_1\")\n",
-    "Ynm(l, m, theta, phi)\n",
+    "# Ynm(l, m, theta, phi)\n",
     "a_m = IndexedBase(\"a_m\")\n",
     "Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
     "m = symbols(\"m\", cls=sp.Idx)\n",
     "Omega1 = symbols(\"Omega_1\")\n",
     "\n",
     "A12 = sp.Sum(a_m * Ynm(2, m, theta1, phi1), (m, -2, 2)) / (\n",
-    "    s - m_a2**2 + I * m_a2 * Gamma_a2\n",
+    "    s12 - m_a2**2 + I * m_a2 * Gamma_a2\n",
     ")\n",
     "A12"
    ]
@@ -91,16 +107,69 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4",
-   "metadata": {},
+   "id": "5",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "A12.free_symbols"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "A12_func = sp.lambdify([s12, a_m, m_a2, Gamma_a2, theta1, phi1], A12)\n",
+    "sp.lambdify([s12, a_m, m_a2, Gamma_a2, theta1, phi1], A12)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# $A^{23}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
-    "m_Delta, Gamma_Delta = symbols(\"m_Delta Gamma_Delta\")\n",
+    "s23, m_Delta, Gamma_Delta = symbols(\"s_{23} m_Delta Gamma_Delta\")\n",
     "b_m = IndexedBase(\"b_m\")\n",
     "Y1_m = Function(\"Y_1^m\")(\"Omega_2\")\n",
     "theta2, phi2 = symbols(\"theta_2 phi_2\")\n",
     "A23 = Sum(b_m * Ynm(1, m, theta2, phi2), (m, -1, 1)) / (\n",
-    "    s - m_Delta**2 + I * m_Delta * Gamma_Delta\n",
+    "    s23 - m_Delta**2 + I * m_Delta * Gamma_Delta\n",
     ")\n",
     "A23"
    ]
@@ -108,8 +177,60 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5",
-   "metadata": {},
+   "id": "9",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "A23.free_symbols"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "A23_func = sp.lambdify([s23, b_m, m_Delta, Gamma_Delta, theta2, phi2], A23)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "11",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# $A^{31}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "c0, m_Nstar, Gamma_Nstar = symbols(r\"c_0 m_{N^*} \\Gamma_{N^*}\")\n",
@@ -120,8 +241,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
-   "metadata": {},
+   "id": "13",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "A31.free_symbols"
@@ -130,8 +257,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7",
-   "metadata": {},
+   "id": "14",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "sp.lambdify([s, c0, m_Nstar, Gamma_Nstar], A31)"
@@ -140,8 +273,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
-   "metadata": {},
+   "id": "15",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "A31_func = sp.lambdify([s, c0, m_Nstar, Gamma_Nstar], A31)"
@@ -150,8 +289,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
-   "metadata": {},
+   "id": "16",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
@@ -167,10 +312,100 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
-   "metadata": {},
+   "id": "17",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
-   "source": []
+   "source": [
+    "# Example values for m_Nstar and Gamma_Nstar\n",
+    "m_Nstar_val = 1.5\n",
+    "Gamma_Nstar_val = 0.6\n",
+    "c0_val = 1\n",
+    "\n",
+    "# Generate s values\n",
+    "s_values = np.linspace(0, 5, 100)\n",
+    "A31_values = A31_func(s_values, c0_val, m_Nstar_val, Gamma_Nstar_val)\n",
+    "\n",
+    "# Create the plot\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "\n",
+    "plt.plot(s_values, A31_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
+    "plt.plot(s_values, A31_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "plt.plot(s_values, np.abs(A31_values) ** 2, label=\"|A31|^2\", linestyle=\"-.\", color=\"g\")\n",
+    "plt.plot(\n",
+    "    s_values, np.angle(A31_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
+    ")\n",
+    "\n",
+    "plt.xlabel(\"s\")\n",
+    "plt.ylabel(r\"$A^{31}$ components\")\n",
+    "plt.title(r\"Components of $A^{31}$ vs s\")\n",
+    "plt.legend()\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "18",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "plt.plot(A31_values.real, A31_values.imag)\n",
+    "plt.title(r\"Argand diagram of $A^{31}$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "19",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "# Example values for m_Nstar and Gamma_Nstar\n",
+    "m_Nstar_val = 1.5\n",
+    "Gamma_Nstar_val = 0.6\n",
+    "c0_val = 1\n",
+    "\n",
+    "# Generate s values\n",
+    "s_values = np.linspace(0, 5, 100)\n",
+    "A12_values = A12_func(s_values, c0_val, m_Nstar_val, Gamma_Nstar_val)\n",
+    "\n",
+    "# Create the plot\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "\n",
+    "plt.plot(s_values, A31_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
+    "plt.plot(s_values, A31_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "plt.plot(s_values, np.abs(A31_values) ** 2, label=\"|A31|^2\", linestyle=\"-.\", color=\"g\")\n",
+    "plt.plot(\n",
+    "    s_values, np.angle(A31_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
+    ")\n",
+    "\n",
+    "plt.xlabel(\"s\")\n",
+    "plt.ylabel(r\"$A^{31}$ components\")\n",
+    "plt.title(r\"Components of $A^{31}$ vs s\")\n",
+    "plt.legend()\n",
+    "plt.grid(True)\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {

From 8d4a00dd42f857c9a639331046dfed2ee24ebbed Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 5 Jun 2024 14:23:21 +0200
Subject: [PATCH 12/44] draft2 make index correct

---
 docs/symbolics.ipynb | 172 ++++++++++++++++++++++++++++++-------------
 1 file changed, 122 insertions(+), 50 deletions(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 568669c..4d29c8e 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -60,7 +60,8 @@
     "    Symbol,\n",
     "    simplify,\n",
     ")\n",
-    "from IPython.display import display, Latex"
+    "from IPython.display import display, Latex\n",
+    "import matplotlib.pyplot as plt"
    ]
   },
   {
@@ -81,6 +82,17 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "newa = IndexedBase(\"a\")\n",
+    "type(newa[0])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -93,12 +105,12 @@
     "s12, m_a2, Gamma_a2 = symbols(r\"s_{12} m_{a_2} \\Gamma_{a_2}\")\n",
     "l, m, theta1, phi1 = symbols(\"l m theta_1 phi_1\")\n",
     "# Ynm(l, m, theta, phi)\n",
-    "a_m = IndexedBase(\"a_m\")\n",
+    "a = IndexedBase(\"a\")\n",
     "Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
     "m = symbols(\"m\", cls=sp.Idx)\n",
     "Omega1 = symbols(\"Omega_1\")\n",
     "\n",
-    "A12 = sp.Sum(a_m * Ynm(2, m, theta1, phi1), (m, -2, 2)) / (\n",
+    "A12 = sp.Sum(a[m] * Ynm(2, m, theta1, phi1), (m, -2, 2)) / (\n",
     "    s12 - m_a2**2 + I * m_a2 * Gamma_a2\n",
     ")\n",
     "A12"
@@ -107,7 +119,17 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5",
+   "id": "6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Ynm(2, 1, 1, 1).expand(func=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -123,7 +145,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
+   "id": "8",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -133,13 +155,57 @@
    },
    "outputs": [],
    "source": [
-    "A12_func = sp.lambdify([s12, a_m, m_a2, Gamma_a2, theta1, phi1], A12)\n",
-    "sp.lambdify([s12, a_m, m_a2, Gamma_a2, theta1, phi1], A12)"
+    "A12_func = sp.lambdify(\n",
+    "    [s12, a[-2], a[-1], a[-0], a[1], a[2], m_a2, Gamma_a2, theta1, phi1],\n",
+    "    A12.doit().expand(func=True),\n",
+    ")\n",
+    "A12_func"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Example values for m_Nstar and Gamma_Nstar\n",
+    "m_a2_val = 1.5\n",
+    "Gamma_a2_val = 0.6\n",
+    "a_vals = [1, 2, 3, 4, 5]\n",
+    "\n",
+    "# Generate s values\n",
+    "s_values = np.linspace(0, 5, 100)\n",
+    "PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
+    "THETA = np.linspace(0, np.pi, num=100)\n",
+    "\n",
+    "# PHI, THETA = np.meshgrid(\n",
+    "#     np.linspace(-np.pi, +np.pi, num=100),\n",
+    "#     np.linspace(0, np.pi, num=100),\n",
+    "# )\n",
+    "A12_values = A12_func(s_values, *a_vals, m_a2_val, Gamma_a2_val, THETA, PHI)\n",
+    "\n",
+    "# Create the plot\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "\n",
+    "plt.plot(s_values, A12_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
+    "plt.plot(s_values, A12_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "plt.plot(s_values, np.abs(A12_values) ** 2, label=\"|A12|^2\", linestyle=\"-.\", color=\"g\")\n",
+    "plt.plot(\n",
+    "    s_values, np.angle(A12_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
+    ")\n",
+    "\n",
+    "plt.xlabel(\"s\")\n",
+    "plt.ylabel(r\"$A^{12}$ components\")\n",
+    "plt.title(r\"Components of $A^{12}$ vs s\")\n",
+    "plt.legend()\n",
+    "# plt.grid(True)\n",
+    "plt.show()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "7",
+   "id": "10",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -154,7 +220,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
+   "id": "11",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -165,10 +231,10 @@
    "outputs": [],
    "source": [
     "s23, m_Delta, Gamma_Delta = symbols(\"s_{23} m_Delta Gamma_Delta\")\n",
-    "b_m = IndexedBase(\"b_m\")\n",
+    "b = IndexedBase(\"b\")\n",
     "Y1_m = Function(\"Y_1^m\")(\"Omega_2\")\n",
     "theta2, phi2 = symbols(\"theta_2 phi_2\")\n",
-    "A23 = Sum(b_m * Ynm(1, m, theta2, phi2), (m, -1, 1)) / (\n",
+    "A23 = Sum(b[m] * Ynm(1, m, theta2, phi2), (m, -1, 1)) / (\n",
     "    s23 - m_Delta**2 + I * m_Delta * Gamma_Delta\n",
     ")\n",
     "A23"
@@ -177,7 +243,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "12",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -193,7 +259,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
+   "id": "13",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -203,12 +269,12 @@
    },
    "outputs": [],
    "source": [
-    "A23_func = sp.lambdify([s23, b_m, m_Delta, Gamma_Delta, theta2, phi2], A23)"
+    "# A23_func = sp.lambdify([s23, b_m, m_Delta, Gamma_Delta, theta2, phi2], A23)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "11",
+   "id": "14",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -223,7 +289,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "15",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -233,15 +299,15 @@
    },
    "outputs": [],
    "source": [
-    "c0, m_Nstar, Gamma_Nstar = symbols(r\"c_0 m_{N^*} \\Gamma_{N^*}\")\n",
-    "A31 = c0 / (s - m_Nstar**2 + I * m_Nstar * Gamma_Nstar)\n",
+    "s31, c0, m_Nstar, Gamma_Nstar = symbols(r\"s_{31} c_0 m_{N^*} \\Gamma_{N^*}\")\n",
+    "A31 = c0 / (s31 - m_Nstar**2 + I * m_Nstar * Gamma_Nstar)\n",
     "A31"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "16",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -257,7 +323,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14",
+   "id": "17",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -267,13 +333,13 @@
    },
    "outputs": [],
    "source": [
-    "sp.lambdify([s, c0, m_Nstar, Gamma_Nstar], A31)"
+    "sp.lambdify([s31, c0, m_Nstar, Gamma_Nstar], A31)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15",
+   "id": "18",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -283,13 +349,13 @@
    },
    "outputs": [],
    "source": [
-    "A31_func = sp.lambdify([s, c0, m_Nstar, Gamma_Nstar], A31)"
+    "A31_func = sp.lambdify([s31, c0, m_Nstar, Gamma_Nstar], A31)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
+   "id": "19",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -299,8 +365,6 @@
    },
    "outputs": [],
    "source": [
-    "import matplotlib.pyplot as plt\n",
-    "\n",
     "s_values = np.linspace(0, 5, 100)\n",
     "A31_values = A31_func(s_values, 1, 1.5, 0.6)\n",
     "plt.plot(s_values, A31_values.imag)\n",
@@ -312,7 +376,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17",
+   "id": "20",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -352,7 +416,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "18",
+   "id": "21",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -370,7 +434,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19",
+   "id": "22",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -380,32 +444,40 @@
    },
    "outputs": [],
    "source": [
-    "# Example values for m_Nstar and Gamma_Nstar\n",
-    "m_Nstar_val = 1.5\n",
-    "Gamma_Nstar_val = 0.6\n",
-    "c0_val = 1\n",
+    "# # Example values for m_Nstar and Gamma_Nstar\n",
+    "# m_Nstar_val = 1.5\n",
+    "# Gamma_Nstar_val = 0.6\n",
+    "# c0_val = 1\n",
     "\n",
-    "# Generate s values\n",
-    "s_values = np.linspace(0, 5, 100)\n",
-    "A12_values = A12_func(s_values, c0_val, m_Nstar_val, Gamma_Nstar_val)\n",
+    "# # Generate s values\n",
+    "# s_values = np.linspace(0, 5, 100)\n",
+    "# A12_values = A12_func(s_values, c0_val, m_Nstar_val, Gamma_Nstar_val)\n",
     "\n",
-    "# Create the plot\n",
-    "plt.figure(figsize=(10, 6))\n",
+    "# # Create the plot\n",
+    "# plt.figure(figsize=(10, 6))\n",
     "\n",
-    "plt.plot(s_values, A31_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
-    "plt.plot(s_values, A31_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "plt.plot(s_values, np.abs(A31_values) ** 2, label=\"|A31|^2\", linestyle=\"-.\", color=\"g\")\n",
-    "plt.plot(\n",
-    "    s_values, np.angle(A31_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
-    ")\n",
+    "# plt.plot(s_values, A31_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
+    "# plt.plot(s_values, A31_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "# plt.plot(s_values, np.abs(A31_values) ** 2, label=\"|A31|^2\", linestyle=\"-.\", color=\"g\")\n",
+    "# plt.plot(\n",
+    "#     s_values, np.angle(A31_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
+    "# )\n",
     "\n",
-    "plt.xlabel(\"s\")\n",
-    "plt.ylabel(r\"$A^{31}$ components\")\n",
-    "plt.title(r\"Components of $A^{31}$ vs s\")\n",
-    "plt.legend()\n",
-    "plt.grid(True)\n",
-    "plt.show()"
+    "# plt.xlabel(\"s\")\n",
+    "# plt.ylabel(r\"$A^{31}$ components\")\n",
+    "# plt.title(r\"Components of $A^{31}$ vs s\")\n",
+    "# plt.legend()\n",
+    "# plt.grid(True)\n",
+    "# plt.show()"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "23",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

From b6453748255dd71b413ffad478a53715b0caf968 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 5 Jun 2024 16:18:56 +0200
Subject: [PATCH 13/44] plots of A12

---
 docs/LamKpi.ipynb    | 41 +++++++++++++++++++++
 docs/symbolics.ipynb | 84 +++++++++++++++++++++++++++++++++-----------
 2 files changed, 104 insertions(+), 21 deletions(-)
 create mode 100644 docs/LamKpi.ipynb

diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
new file mode 100644
index 0000000..cbe7ef2
--- /dev/null
+++ b/docs/LamKpi.ipynb
@@ -0,0 +1,41 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {},
+   "source": [
+    "$p \\gamma \\to K^+ \\pi^0 \\Lambda$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 4d29c8e..16eae79 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -106,9 +106,9 @@
     "l, m, theta1, phi1 = symbols(\"l m theta_1 phi_1\")\n",
     "# Ynm(l, m, theta, phi)\n",
     "a = IndexedBase(\"a\")\n",
-    "Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
+    "# Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
     "m = symbols(\"m\", cls=sp.Idx)\n",
-    "Omega1 = symbols(\"Omega_1\")\n",
+    "# Omega1 = symbols(\"Omega_1\")\n",
     "\n",
     "A12 = sp.Sum(a[m] * Ynm(2, m, theta1, phi1), (m, -2, 2)) / (\n",
     "    s12 - m_a2**2 + I * m_a2 * Gamma_a2\n",
@@ -169,16 +169,58 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Example values for m_Nstar and Gamma_Nstar\n",
+    "# Example values\n",
     "m_a2_val = 1.5\n",
     "Gamma_a2_val = 0.6\n",
     "a_vals = [1, 2, 3, 4, 5]\n",
     "\n",
     "# Generate s values\n",
     "s_values = np.linspace(0, 5, 100)\n",
-    "PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
-    "THETA = np.linspace(0, np.pi, num=100)\n",
+    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
+    "# THETA = np.linspace(0, np.pi, num=100)\n",
+    "\n",
+    "PHI, THETA = np.meshgrid(\n",
+    "    np.linspace(-np.pi, +np.pi, num=100),\n",
+    "    np.linspace(0, np.pi, num=100),\n",
+    ")\n",
+    "A12_values = A12_func(s_values, *a_vals, m_a2_val, Gamma_a2_val, THETA, PHI)\n",
+    "\n",
+    "# Create the plot\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "\n",
+    "plt.plot(s_values, A12_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
+    "plt.plot(s_values, A12_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "plt.plot(s_values, np.abs(A12_values) ** 2, label=\"|A12|^2\", linestyle=\"-.\", color=\"g\")\n",
+    "plt.plot(\n",
+    "    s_values, np.angle(A12_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
+    ")\n",
+    "\n",
+    "plt.xlabel(\"s\")\n",
+    "plt.ylabel(r\"$A^{12}$ components\")\n",
+    "plt.title(r\"Components of $A^{12}$ vs s\")\n",
+    "# plt.legend()\n",
+    "# plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Example values\n",
+    "m_a2_val = 1.5\n",
+    "Gamma_a2_val = 0.6\n",
+    "a_vals = [1, 2, 3, 4, 5]\n",
     "\n",
+    "# Generate s values\n",
+    "s_values = np.linspace(0, 5, 100)\n",
+    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
+    "# THETA = np.linspace(0, np.pi, num=100)\n",
+    "PHI = np.pi / 4\n",
+    "THETA = np.pi / 4\n",
     "# PHI, THETA = np.meshgrid(\n",
     "#     np.linspace(-np.pi, +np.pi, num=100),\n",
     "#     np.linspace(0, np.pi, num=100),\n",
@@ -197,7 +239,7 @@
     "\n",
     "plt.xlabel(\"s\")\n",
     "plt.ylabel(r\"$A^{12}$ components\")\n",
-    "plt.title(r\"Components of $A^{12}$ vs s\")\n",
+    "plt.title(r\"Components of $A^{12}$ vs s at 45 degree\")\n",
     "plt.legend()\n",
     "# plt.grid(True)\n",
     "plt.show()"
@@ -205,7 +247,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "10",
+   "id": "11",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -220,7 +262,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
+   "id": "12",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -243,7 +285,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "13",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -259,7 +301,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "14",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -274,7 +316,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14",
+   "id": "15",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -289,7 +331,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15",
+   "id": "16",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -307,7 +349,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
+   "id": "17",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -323,7 +365,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17",
+   "id": "18",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -339,7 +381,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "18",
+   "id": "19",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -355,7 +397,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19",
+   "id": "20",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -376,7 +418,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "20",
+   "id": "21",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -409,14 +451,14 @@
     "plt.ylabel(r\"$A^{31}$ components\")\n",
     "plt.title(r\"Components of $A^{31}$ vs s\")\n",
     "plt.legend()\n",
-    "plt.grid(True)\n",
+    "# plt.grid(True)\n",
     "plt.show()"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "21",
+   "id": "22",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -434,7 +476,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "22",
+   "id": "23",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -474,7 +516,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "23",
+   "id": "24",
    "metadata": {},
    "outputs": [],
    "source": []

From 58138d77462b12441d638605eb7b3240ac0522c8 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 7 Jun 2024 15:08:17 +0200
Subject: [PATCH 14/44] Componenets of A12 A23 A31 and Argand diagrams

---
 docs/symbolics.ipynb | 332 ++++++++++++++++++++++++++++---------------
 1 file changed, 217 insertions(+), 115 deletions(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 16eae79..8e09689 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -103,7 +103,7 @@
    "outputs": [],
    "source": [
     "s12, m_a2, Gamma_a2 = symbols(r\"s_{12} m_{a_2} \\Gamma_{a_2}\")\n",
-    "l, m, theta1, phi1 = symbols(\"l m theta_1 phi_1\")\n",
+    "theta1, phi1 = symbols(\"theta_1 phi_1\")\n",
     "# Ynm(l, m, theta, phi)\n",
     "a = IndexedBase(\"a\")\n",
     "# Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
@@ -123,13 +123,23 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "Ynm(2, 1, 1, 1).expand(func=True)"
+    "Ynm(2, 1, 1, 1).expand(func=False)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "id": "7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Ynm(2, 1, 1, 1).expand(func=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -145,7 +155,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
+   "id": "9",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -156,7 +166,7 @@
    "outputs": [],
    "source": [
     "A12_func = sp.lambdify(\n",
-    "    [s12, a[-2], a[-1], a[-0], a[1], a[2], m_a2, Gamma_a2, theta1, phi1],\n",
+    "    [s12, a[-2], a[-1], a[0], a[1], a[2], m_a2, Gamma_a2, theta1, phi1],\n",
     "    A12.doit().expand(func=True),\n",
     ")\n",
     "A12_func"
@@ -165,24 +175,19 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "10",
    "metadata": {},
    "outputs": [],
    "source": [
     "# Example values\n",
-    "m_a2_val = 1.5\n",
-    "Gamma_a2_val = 0.6\n",
-    "a_vals = [1, 2, 3, 4, 5]\n",
+    "m_a2_val = 1.32\n",
+    "Gamma_a2_val = 0.1\n",
+    "a_vals = [0, 0.5, 3.5, 4, 2.5]\n",
     "\n",
     "# Generate s values\n",
     "s_values = np.linspace(0, 5, 100)\n",
-    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
-    "# THETA = np.linspace(0, np.pi, num=100)\n",
-    "\n",
-    "PHI, THETA = np.meshgrid(\n",
-    "    np.linspace(-np.pi, +np.pi, num=100),\n",
-    "    np.linspace(0, np.pi, num=100),\n",
-    ")\n",
+    "PHI = np.pi / 4\n",
+    "THETA = np.pi / 4\n",
     "A12_values = A12_func(s_values, *a_vals, m_a2_val, Gamma_a2_val, THETA, PHI)\n",
     "\n",
     "# Create the plot\n",
@@ -197,8 +202,8 @@
     "\n",
     "plt.xlabel(\"s\")\n",
     "plt.ylabel(r\"$A^{12}$ components\")\n",
-    "plt.title(r\"Components of $A^{12}$ vs s\")\n",
-    "# plt.legend()\n",
+    "plt.title(r\"Components of $A^{12}$ vs s at 45 degree\")\n",
+    "plt.legend()\n",
     "# plt.grid(True)\n",
     "plt.show()"
    ]
@@ -206,7 +211,19 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
+   "id": "11",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.plot(A12_values.real, A12_values.imag)\n",
+    "plt.title(r\"Argand diagram of $A^{12}$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -219,35 +236,54 @@
     "s_values = np.linspace(0, 5, 100)\n",
     "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
     "# THETA = np.linspace(0, np.pi, num=100)\n",
-    "PHI = np.pi / 4\n",
-    "THETA = np.pi / 4\n",
-    "# PHI, THETA = np.meshgrid(\n",
-    "#     np.linspace(-np.pi, +np.pi, num=100),\n",
-    "#     np.linspace(0, np.pi, num=100),\n",
-    "# )\n",
-    "A12_values = A12_func(s_values, *a_vals, m_a2_val, Gamma_a2_val, THETA, PHI)\n",
+    "\n",
+    "PHI, THETA = np.meshgrid(\n",
+    "    np.linspace(-np.pi, +np.pi, num=100),\n",
+    "    np.linspace(0, np.pi, num=100),\n",
+    ")\n",
+    "A12_Angles_values = A12_func(s_values, *a_vals, m_a2_val, Gamma_a2_val, THETA, PHI)\n",
     "\n",
     "# Create the plot\n",
     "plt.figure(figsize=(10, 6))\n",
     "\n",
-    "plt.plot(s_values, A12_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
-    "plt.plot(s_values, A12_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "plt.plot(s_values, np.abs(A12_values) ** 2, label=\"|A12|^2\", linestyle=\"-.\", color=\"g\")\n",
     "plt.plot(\n",
-    "    s_values, np.angle(A12_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
+    "    s_values, A12_Angles_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\"\n",
+    ")\n",
+    "plt.plot(s_values, A12_Angles_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "plt.plot(\n",
+    "    s_values, np.abs(A12_Angles_values) ** 2, label=\"|A12|^2\", linestyle=\"-.\", color=\"g\"\n",
+    ")\n",
+    "plt.plot(\n",
+    "    s_values,\n",
+    "    np.angle(A12_Angles_values),\n",
+    "    label=\"Phase (angle)\",\n",
+    "    linestyle=\":\",\n",
+    "    color=\"m\",\n",
     ")\n",
     "\n",
     "plt.xlabel(\"s\")\n",
     "plt.ylabel(r\"$A^{12}$ components\")\n",
-    "plt.title(r\"Components of $A^{12}$ vs s at 45 degree\")\n",
-    "plt.legend()\n",
+    "plt.title(r\"Components of $A^{12}$ vs s\")\n",
+    "# plt.legend()\n",
     "# plt.grid(True)\n",
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "13",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.plot(A12_Angles_values.real, A12_Angles_values.imag)\n",
+    "plt.title(r\"Argand diagram of $A^{12}$\")\n",
+    "plt.show()"
+   ]
+  },
   {
    "cell_type": "markdown",
-   "id": "11",
+   "id": "14",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -262,7 +298,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "15",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -274,6 +310,8 @@
    "source": [
     "s23, m_Delta, Gamma_Delta = symbols(\"s_{23} m_Delta Gamma_Delta\")\n",
     "b = IndexedBase(\"b\")\n",
+    "m = symbols(\"m\", cls=sp.Idx)\n",
+    "\n",
     "Y1_m = Function(\"Y_1^m\")(\"Omega_2\")\n",
     "theta2, phi2 = symbols(\"theta_2 phi_2\")\n",
     "A23 = Sum(b[m] * Ynm(1, m, theta2, phi2), (m, -1, 1)) / (\n",
@@ -285,7 +323,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "16",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -301,7 +339,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14",
+   "id": "17",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -311,12 +349,145 @@
    },
    "outputs": [],
    "source": [
-    "# A23_func = sp.lambdify([s23, b_m, m_Delta, Gamma_Delta, theta2, phi2], A23)"
+    "A23_func = sp.lambdify(\n",
+    "    [s23, b[-1], b[0], b[1], m_Delta, Gamma_Delta, theta2, phi2],\n",
+    "    A23.doit().expand(func=True),\n",
+    ")\n",
+    "A23_func"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "18",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Example values\n",
+    "m_Delta_val = 1.54\n",
+    "Gamma_Delta_val = 0.1\n",
+    "b_vals = [-1.5, 4, 0.5]\n",
+    "\n",
+    "# Generate s values\n",
+    "s_values = np.linspace(0, 5, 100)\n",
+    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
+    "# THETA = np.linspace(0, np.pi, num=100)\n",
+    "PHI = np.pi / 4\n",
+    "THETA = np.pi / 4\n",
+    "\n",
+    "A23_values = A23_func(s_values, *b_vals, m_Delta_val, Gamma_Delta_val, THETA, PHI)\n",
+    "\n",
+    "# Create the plot\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "\n",
+    "plt.plot(s_values, A23_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
+    "plt.plot(s_values, A23_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "plt.plot(s_values, np.abs(A23_values) ** 2, label=\"|A23|^2\", linestyle=\"-.\", color=\"g\")\n",
+    "plt.plot(\n",
+    "    s_values, np.angle(A23_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
+    ")\n",
+    "\n",
+    "plt.xlabel(\"s\")\n",
+    "plt.ylabel(r\"$A^{23}$ components\")\n",
+    "plt.title(r\"Components of $A^{23}$ vs s at 45 degree\")\n",
+    "plt.legend()\n",
+    "# plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "19",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.plot(A23_values.real, A23_values.imag)\n",
+    "plt.title(r\"Argand diagram of $A^{23}$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "20",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Example values\n",
+    "m_Delta_val = 1.54\n",
+    "Gamma_Delta_val = 0.1\n",
+    "b_vals = [-1.5, 4, 0.5]\n",
+    "\n",
+    "# Generate s values\n",
+    "s_values = np.linspace(0, 5, 100)\n",
+    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
+    "# THETA = np.linspace(0, np.pi, num=100)\n",
+    "\n",
+    "PHI, THETA = np.meshgrid(\n",
+    "    np.linspace(-np.pi, +np.pi, num=100),\n",
+    "    np.linspace(0, np.pi, num=100),\n",
+    ")\n",
+    "A23_Angles_values = A23_func(\n",
+    "    s_values, *b_vals, m_Delta_val, Gamma_Delta_val, THETA, PHI\n",
+    ")\n",
+    "\n",
+    "# Create the plot\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "\n",
+    "plt.plot(\n",
+    "    s_values, A23_Angles_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\"\n",
+    ")\n",
+    "plt.plot(s_values, A23_Angles_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
+    "# plt.plot(s_values, np.abs(A23_values) ** 2, label=\"|A23|^2\", linestyle=\"-.\", color=\"g\")\n",
+    "plt.plot(\n",
+    "    s_values,\n",
+    "    np.angle(A23_Angles_values),\n",
+    "    label=\"Phase (angle)\",\n",
+    "    linestyle=\":\",\n",
+    "    color=\"m\",\n",
+    ")\n",
+    "\n",
+    "plt.xlabel(\"s\")\n",
+    "plt.ylabel(r\"$A^{23}$ components\")\n",
+    "plt.title(r\"Components of $A^{23}$ vs s\")\n",
+    "# plt.legend()\n",
+    "# plt.grid(True)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "21",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.figure(figsize=(10, 6))\n",
+    "plt.plot(\n",
+    "    s_values, np.abs(A23_Angles_values) ** 2, label=\"|A23|^2\", linestyle=\"-.\", color=\"g\"\n",
+    ")\n",
+    "plt.xlabel(\"s\")\n",
+    "plt.ylabel(r\"$A^{23}$ components\")\n",
+    "plt.title(r\"Components of $A^{23}$ vs s\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "22",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.plot(A23_Angles_values.real, A23_Angles_values.imag)\n",
+    "plt.title(r\"Argand diagram of $A^{23}$\")\n",
+    "plt.show()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "15",
+   "id": "23",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -331,7 +502,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
+   "id": "24",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -349,7 +520,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17",
+   "id": "25",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -365,7 +536,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "18",
+   "id": "26",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -381,7 +552,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19",
+   "id": "27",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -397,28 +568,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "20",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "s_values = np.linspace(0, 5, 100)\n",
-    "A31_values = A31_func(s_values, 1, 1.5, 0.6)\n",
-    "plt.plot(s_values, A31_values.imag)\n",
-    "plt.plot(s_values, A31_values.real)\n",
-    "plt.plot(s_values, np.abs(A31_values) ** 2)\n",
-    "plt.plot(s_values, np.angle(A31_values))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "21",
+   "id": "28",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -429,9 +579,9 @@
    "outputs": [],
    "source": [
     "# Example values for m_Nstar and Gamma_Nstar\n",
-    "m_Nstar_val = 1.5\n",
-    "Gamma_Nstar_val = 0.6\n",
-    "c0_val = 1\n",
+    "m_Nstar_val = 1.87\n",
+    "Gamma_Nstar_val = 0.1\n",
+    "c0_val = 2.5\n",
     "\n",
     "# Generate s values\n",
     "s_values = np.linspace(0, 5, 100)\n",
@@ -458,7 +608,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "22",
+   "id": "29",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -472,54 +622,6 @@
     "plt.title(r\"Argand diagram of $A^{31}$\")\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "23",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "# # Example values for m_Nstar and Gamma_Nstar\n",
-    "# m_Nstar_val = 1.5\n",
-    "# Gamma_Nstar_val = 0.6\n",
-    "# c0_val = 1\n",
-    "\n",
-    "# # Generate s values\n",
-    "# s_values = np.linspace(0, 5, 100)\n",
-    "# A12_values = A12_func(s_values, c0_val, m_Nstar_val, Gamma_Nstar_val)\n",
-    "\n",
-    "# # Create the plot\n",
-    "# plt.figure(figsize=(10, 6))\n",
-    "\n",
-    "# plt.plot(s_values, A31_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
-    "# plt.plot(s_values, A31_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "# plt.plot(s_values, np.abs(A31_values) ** 2, label=\"|A31|^2\", linestyle=\"-.\", color=\"g\")\n",
-    "# plt.plot(\n",
-    "#     s_values, np.angle(A31_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
-    "# )\n",
-    "\n",
-    "# plt.xlabel(\"s\")\n",
-    "# plt.ylabel(r\"$A^{31}$ components\")\n",
-    "# plt.title(r\"Components of $A^{31}$ vs s\")\n",
-    "# plt.legend()\n",
-    "# plt.grid(True)\n",
-    "# plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "24",
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {

From 5bf3922370cec7ecddd74014c49b2e9e14a82de5 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 7 Jun 2024 15:12:06 +0200
Subject: [PATCH 15/44] delete duplicate equation label

---
 docs/symbolics.ipynb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 8e09689..def95b8 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -26,7 +26,7 @@
     "\\\n",
     "A^{31} &=& \\frac{c_0}{s_{31}-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}}\n",
     "\\end{eqnarray}\n",
-    "$$ (BW_SH_label)"
+    "$$"
    ]
   },
   {

From b7310d4423f3569bc17f4f072b0483a39a68eb68 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 12 Jun 2024 12:08:41 +0200
Subject: [PATCH 16/44] matplotlib

---
 pixi.lock | 69 +++++++++++++++++++++++++++----------------------------
 1 file changed, 34 insertions(+), 35 deletions(-)

diff --git a/pixi.lock b/pixi.lock
index a04abeb..7bb7a25 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -9,7 +9,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/accessible-pygments-0.0.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/alabaster-0.7.16-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/alsa-lib-1.2.11-hd590300_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/alsa-lib-1.2.12-h4ab18f5_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/anyio-4.3.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/argon2-cffi-23.1.0-pyhd8ed1ab_0.conda
@@ -146,7 +146,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcap-2.69-h0f662aa_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcblas-3.9.0-22_linux64_openblas.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang-cpp15-15.0.7-default_h127d8a8_5.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang13-18.1.6-default_h5d6823c_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang13-18.1.7-default_h087397f_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcups-2.3.3-h4637d8d_4.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libdeflate-1.20-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libedit-3.1.20191231-he28a2e2_2.tar.bz2
@@ -169,7 +169,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libjpeg-turbo-3.0.0-hd590300_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/liblapack-3.9.0-22_linux64_openblas.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm15-15.0.7-hb3ce162_4.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm18-18.1.6-hb77312f_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm18-18.1.7-hb77312f_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libnsl-2.0.1-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libogg-1.3.4-h7f98852_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libopenblas-0.3.27-pthreads_h413a1c8_0.conda
@@ -341,7 +341,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-keysyms-0.4.0-h8ee46fc_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-renderutil-0.3.9-hd590300_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-wm-0.4.1-h8ee46fc_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/xkeyboard-config-2.41-hd590300_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/xkeyboard-config-2.42-h4ab18f5_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xorg-kbproto-1.0.7-h7f98852_1002.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xorg-libice-1.1.1-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xorg-libsm-1.2.4-h7391055_0.conda
@@ -423,19 +423,18 @@ packages:
   timestamp: 1704848898483
 - kind: conda
   name: alsa-lib
-  version: 1.2.11
-  build: hd590300_1
-  build_number: 1
+  version: 1.2.12
+  build: h4ab18f5_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/alsa-lib-1.2.11-hd590300_1.conda
-  sha256: 0e2b75b9834a6e520b13db516f7cf5c9cea8f0bbc9157c978444173dacb98fec
-  md5: 0bb492cca54017ea314b809b1ee3a176
+  url: https://conda.anaconda.org/conda-forge/linux-64/alsa-lib-1.2.12-h4ab18f5_0.conda
+  sha256: 64b95dd06d7ca6b54cea03b02da8f1657b9899ca376d0ca7b47823064f55fb16
+  md5: 7ed427f0871fd41cb1d9c17727c17589
   depends:
   - libgcc-ng >=12
   license: LGPL-2.1-or-later
   license_family: GPL
-  size: 554699
-  timestamp: 1709396557528
+  size: 555868
+  timestamp: 1718118368236
 - kind: conda
   name: ampform
   version: 0.15.3
@@ -2841,20 +2840,20 @@ packages:
   timestamp: 1711063711931
 - kind: conda
   name: libclang13
-  version: 18.1.6
-  build: default_h5d6823c_0
+  version: 18.1.7
+  build: default_h087397f_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/libclang13-18.1.6-default_h5d6823c_0.conda
-  sha256: aa8246dca2e738a6e4dda87b448b1c01be00035489bd4f1cf409830ab7ce7d7d
-  md5: fbe666f653068958eb27f549cb12f202
+  url: https://conda.anaconda.org/conda-forge/linux-64/libclang13-18.1.7-default_h087397f_0.conda
+  sha256: d981a2734c3af6217dd42c1bccc13b99fc3ca5a64c379739612d6cf67f992a1d
+  md5: 536526073c2e7f9056fdce8584da779e
   depends:
   - libgcc-ng >=12
-  - libllvm18 >=18.1.6,<18.2.0a0
+  - libllvm18 >=18.1.7,<18.2.0a0
   - libstdcxx-ng >=12
   license: Apache-2.0 WITH LLVM-exception
   license_family: Apache
-  size: 11057117
-  timestamp: 1716714834549
+  size: 11057579
+  timestamp: 1717819075043
 - kind: conda
   name: libcups
   version: 2.3.3
@@ -3239,22 +3238,22 @@ packages:
   timestamp: 1701375836233
 - kind: conda
   name: libllvm18
-  version: 18.1.6
+  version: 18.1.7
   build: hb77312f_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/libllvm18-18.1.6-hb77312f_0.conda
-  sha256: 0f529a258d0e586f4d443b5c4df9c36b1fcf5391d867e7e0a2b2cb6084337477
-  md5: 1246fc4b9f4db452e69cc297967d4b3e
+  url: https://conda.anaconda.org/conda-forge/linux-64/libllvm18-18.1.7-hb77312f_0.conda
+  sha256: 9a9167b3e8e05abc517671fe45e5d40ae866d3e8195865ddad3c68131d059e25
+  md5: bc0ea7e1f75a9b1c8467597fbbd9f86b
   depends:
   - libgcc-ng >=12
   - libstdcxx-ng >=12
   - libxml2 >=2.12.7,<3.0a0
-  - libzlib >=1.2.13,<2.0.0a0
+  - libzlib >=1.2.13,<2.0a0
   - zstd >=1.5.6,<1.6.0a0
   license: Apache-2.0 WITH LLVM-exception
   license_family: Apache
-  size: 38428999
-  timestamp: 1716642164972
+  size: 38423980
+  timestamp: 1717781615068
 - kind: conda
   name: libnsl
   version: 2.0.1
@@ -6228,19 +6227,19 @@ packages:
   timestamp: 1684679248466
 - kind: conda
   name: xkeyboard-config
-  version: '2.41'
-  build: hd590300_0
+  version: '2.42'
+  build: h4ab18f5_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/xkeyboard-config-2.41-hd590300_0.conda
-  sha256: 56955610c0747ea7cb026bb8aa9ef165ff41d616e89894538173b8b7dd2ee49a
-  md5: 81f740407b45e3f9047b3174fa94eb9e
+  url: https://conda.anaconda.org/conda-forge/linux-64/xkeyboard-config-2.42-h4ab18f5_0.conda
+  sha256: 240caab7d9d85154ef373ecbac3ff9fb424add2029dbb124e949c6cbab2996dd
+  md5: b193af204da1bfb8c13882d131a14bd2
   depends:
   - libgcc-ng >=12
-  - xorg-libx11 >=1.8.7,<2.0a0
+  - xorg-libx11 >=1.8.9,<2.0a0
   license: MIT
   license_family: MIT
-  size: 898045
-  timestamp: 1707104384997
+  size: 388998
+  timestamp: 1717817668629
 - kind: conda
   name: xorg-kbproto
   version: 1.0.7

From 9e030baaeb77adc12b347a675be339390f1f058b Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 12 Jun 2024 15:46:35 +0200
Subject: [PATCH 17/44] remove pgamma state file which is in report0 branch

---
 docs/pgamma-state.ipynb | 436 ----------------------------------------
 1 file changed, 436 deletions(-)
 delete mode 100644 docs/pgamma-state.ipynb

diff --git a/docs/pgamma-state.ipynb b/docs/pgamma-state.ipynb
deleted file mode 100644
index d2ff38b..0000000
--- a/docs/pgamma-state.ipynb
+++ /dev/null
@@ -1,436 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "# Virtual particle that represents the state pγ "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "Address to issue ✅&nbsp;[ComPWA/gluex-nstar#5](https://github.com/ComPWA/gluex-nstar/issues/5), this section is an investigation of creating a virtual particle that represents the state $p \\gamma$ in `QRules`"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "2",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "As an example of side note, create a virtual particle that represents state $e^+ e^-$ can be seen [here](https://qrules.readthedocs.io/0.10.x/usage/particle/#adding-custom-particle-definitions-through-python)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3",
-   "metadata": {},
-   "source": [
-    "## Finding particles"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4",
-   "metadata": {},
-   "source": [
-    "Our reaction is $p + \\gamma \\to \\eta + \\pi^0 + p$, so we can look for each of the reaction and decay particles"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "from qrules.particle import load_pdg\n",
-    "\n",
-    "particle_db = load_pdg()\n",
-    "print(\"Number of loaded particles:\", len(particle_db))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6",
-   "metadata": {},
-   "source": [
-    "The [`ParticleCollection`](https://qrules.readthedocs.io/0.10.x/api/qrules.particle/#qrules.particle.ParticleCollection) class offers some methods to search for particles by name or by PID, name, or other properties."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7",
-   "metadata": {},
-   "source": [
-    "### Proton"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8",
-   "metadata": {},
-   "source": [
-    "Search by Particle ID (PID) for proton:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "9",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "particle_db.find(2212)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "10",
-   "metadata": {},
-   "source": [
-    "Search by Particle name for proton:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "11",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db.find(\"p\")\n",
-    "proton = particle_db[\"p\"]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "12",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from IPython.display import Math\n",
-    "\n",
-    "Math(proton.latex)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "13",
-   "metadata": {},
-   "source": [
-    "### $\\gamma$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "14",
-   "metadata": {},
-   "source": [
-    "similarly for $\\gamma$:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "15",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db.find(\"gamma\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "16",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "gamma = particle_db[\"gamma\"]\n",
-    "Math(gamma.latex)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "17",
-   "metadata": {},
-   "source": [
-    "### $\\eta$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "18",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db.find(\"eta\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "19",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "eta = particle_db[\"eta\"]\n",
-    "Math(gamma.latex)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "20",
-   "metadata": {},
-   "source": [
-    "### $\\pi^0$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "21",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db.find(\"pi0\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "22",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "pi0 = particle_db[\"pi0\"]\n",
-    "Math(pi0.latex)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "23",
-   "metadata": {},
-   "source": [
-    "# Adding custom particle"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "24",
-   "metadata": {},
-   "source": [
-    "We add the virtual particle $p\\gamma$ to represent the state of $p-\\gamma$ system in the photoproduction reaction.\n",
-    "See PWA101 (temporary [here](https://compwa--217.org.readthedocs.build/report/999.html)), the value of the mass of the system $m_{p\\gamma}$ in CM frame is about 4.102 GeV in this analysis.\n",
-    "\n",
-    "\n",
-    "We use `Particle` from `QRules` for adding custom particle, so that some quantum numbers we need to determine for the $p\\gamma$ virtual state particle:\n",
-    "\n",
-    "* (Total) Spin\n",
-    "    * $J_{p\\gamma} = \\frac{1}{2}$ or $\\frac{3}{2}$\n",
-    "      \n",
-    "      because $J_{p\\gamma}$ = from $|s_p-s_{\\gamma}|$ to $s_p + s_{\\gamma}$ = from $|\\frac{1}{2}-1|$ to $\\frac{1}{2} + 1$\n",
-    "      \n",
-    "* Mass\n",
-    "    * $m_{p\\gamma} = E_{p\\gamma} \\approx 4.102$\n",
-    "    \n",
-    "* Charge\n",
-    "    * $Q_{p\\gamma} = Q_p + Q_{\\gamma} = 1 $\n",
-    "      \n",
-    "* Isospin and $3^{rd}# component of isospin\n",
-    "    * $I_{p\\gamma} = I_p = \\frac{1}{2}$\n",
-    "    * $I_{3_{p\\gamma}} = I_{3_p} = +\\frac{1}{2}$\n",
-    "  \n",
-    "* Baryon Number\n",
-    "    * $B_{p\\gamma} = B_p  = 1$\n",
-    "\n",
-    "* Parity\n",
-    "    * $P_{p\\gamma} = P_p \\times P_{\\gamma} = +1 \\times (-1) = -1$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "25",
-   "metadata": {},
-   "source": [
-    "These quantum numbers provide a complete and accurate description of the virtual particle representing the p−γ system with a mass of 4.102 GeV.\n",
-    "The pγ virtual particle has two possibilities for the total spin, while the other quantum numbers are fixed."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "26",
-   "metadata": {},
-   "source": [
-    "We add the spin-$\\frac{1}{2}$ $p\\gamma$ virtual particle via `QRules` and named it $p\\gamma$ with a make-up pid number 99990"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "27",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from qrules.particle import Particle, Spin\n",
-    "\n",
-    "pgamma = Particle(\n",
-    "    name=\"p\",\n",
-    "    latex=r\"p\\gamma (s1/2)\",\n",
-    "    spin=0.5,\n",
-    "    mass=4.101931071854584,\n",
-    "    charge=1,\n",
-    "    isospin=Spin(1 / 2, +1 / 2),\n",
-    "    baryon_number=1,\n",
-    "    parity=-1,\n",
-    "    pid=99990,\n",
-    ")\n",
-    "pgamma"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "28",
-   "metadata": {},
-   "source": [
-    "We add the spin-$\\frac{3}{2}$ $p\\gamma$ virtual particle via `QRules` and named it $p\\gamma (s3/2)$ with a make-up pid number 99991"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "29",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "pgamma_j3over2 = Particle(\n",
-    "    name=\"pgamma\",\n",
-    "    latex=R\"p\\gamma (s3/2)\",\n",
-    "    spin=1.5,\n",
-    "    mass=4.101931071854584,\n",
-    "    charge=1,\n",
-    "    isospin=Spin(1 / 2, +1 / 2),\n",
-    "    baryon_number=1,\n",
-    "    parity=-1,\n",
-    "    pid=99991,\n",
-    ")\n",
-    "pgamma_j3over2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "30",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Math(pgamma.latex)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "31",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Math(pgamma_j3over2.latex)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "32",
-   "metadata": {},
-   "source": [
-    "The $`p\\gamma`$ virtual states generated via `QRules` will be used in later stages, both possible spin states $(J= \\frac{1}{2}$ and $\\frac{3}{2})$ should be taken into account if possible, otherwise simplified if necessary."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "33",
-   "metadata": {},
-   "source": [
-    ":::{important}\n",
-    "It is possible to add any kind of custom Particle, as long as its quantum numbers comply with the [gellmann_nishijima()](https://qrules.readthedocs.io/0.10.x/api/qrules.conservation_rules/#qrules.conservation_rules.gellmann_nishijima) rule:\n",
-    ":::\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "34",
-   "metadata": {},
-   "source": [
-    ":::{note}\n",
-    "[Gell-Mann-Nishijima formula](https://en.wikipedia.org/wiki/Gell-Mann–Nishijima_formula):\n",
-    "$Q = I_3 + \\frac{1}{2}(B+S+C+B'+T)$\n",
-    "\n",
-    "where \n",
-    "Q is charge, \n",
-    "$I_3$ is Spin projection of isospin, \n",
-    " B is baryon number, \n",
-    " S is strangeness, \n",
-    " C is charmness, \n",
-    " B' is bottomness, and \n",
-    " T is topness.\n",
-    ":::\n"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.3"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}

From 1ea37feb15af71b691d2803fc28e08fecba02e5b Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 12 Jun 2024 16:05:39 +0200
Subject: [PATCH 18/44] Add all-in-one for sections of transitions and
 amplitude model

---
 docs/all-in-one.ipynb | 185 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 185 insertions(+)
 create mode 100644 docs/all-in-one.ipynb

diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
new file mode 100644
index 0000000..1dda022
--- /dev/null
+++ b/docs/all-in-one.ipynb
@@ -0,0 +1,185 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "0",
+   "metadata": {},
+   "source": [
+    "# Formulate Model"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {},
+   "source": [
+    "## Generate Transitions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from __future__ import annotations\n",
+    "from IPython.display import Math\n",
+    "from qrules.particle import load_pdg\n",
+    "from ampform.io import aslatex, improve_latex_rendering\n",
+    "\n",
+    "improve_latex_rendering()\n",
+    "particle_db = load_pdg()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qrules.particle import Particle, Spin\n",
+    "\n",
+    "pgamma = Particle(\n",
+    "    name=\"pgamma\",\n",
+    "    latex=r\"p\\gamma (s1/2)\",\n",
+    "    spin=0.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99990,\n",
+    ")\n",
+    "pgamma"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma2 = Particle(\n",
+    "    name=\"pgamma2\",\n",
+    "    latex=R\"p\\gamma (s3/2)\",\n",
+    "    spin=1.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99991,\n",
+    ")\n",
+    "pgamma2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db.add(pgamma)\n",
+    "particle_db.add(pgamma2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import qrules\n",
+    "import graphviz\n",
+    "\n",
+    "reaction1_strong_EM = qrules.generate_transitions(\n",
+    "    initial_state=(\"pgamma\"),\n",
+    "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
+    "    allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
+    "    allowed_interaction_types=[\"strong\", \"EM\"],\n",
+    "    formalism=\"canonical-helicity\",\n",
+    "    particle_db=particle_db,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dot_se = qrules.io.asdot(reaction1_strong_EM, collapse_graphs=True)\n",
+    "graphviz.Source(dot_se)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8",
+   "metadata": {},
+   "source": [
+    "## Build Amplitude Models"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import ampform\n",
+    "\n",
+    "model_builder = ampform.get_builder(reaction1_strong_EM)\n",
+    "model_no_dynamics = model_builder.formulate()\n",
+    "model_no_dynamics.intensity"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ampform.io import aslatex\n",
+    "\n",
+    "Math(aslatex(model_no_dynamics.amplitudes))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From f613efbcd400cd7e1869954a3b3706d664ef2550 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 13 Jun 2024 09:29:24 +0200
Subject: [PATCH 19/44] Add full example until generate data section

---
 docs/all-in-one.ipynb | 428 ++++++++++++++++++-
 pixi.lock             | 952 +++++++++++++++++++++++++++++++++++++++++-
 pixi.toml             |   7 +-
 3 files changed, 1364 insertions(+), 23 deletions(-)

diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
index 1dda022..835fd37 100644
--- a/docs/all-in-one.ipynb
+++ b/docs/all-in-one.ipynb
@@ -126,10 +126,18 @@
     "## Build Amplitude Models"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "9",
+   "metadata": {},
+   "source": [
+    "we use ampform to formulate the transitions as an amplitude model (here: HelicityModel). "
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "10",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -143,7 +151,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
+   "id": "11",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -155,10 +163,422 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
+   "id": "12",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Math(aslatex(model_no_dynamics.parameter_defaults))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "13",
+   "metadata": {},
+   "source": [
+    "We choose to use relativistic_breit_wigner_with_ff() as the lineshape for all resonances and use a Blatt-Weisskopf form factor (create_non_dynamic_with_ff()) for the production decay. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ampform.dynamics.builder import (\n",
+    "    create_non_dynamic_with_ff,\n",
+    "    create_relativistic_breit_wigner_with_ff,\n",
+    ")\n",
+    "\n",
+    "model_builder.dynamics.assign(\"pgamma\", create_non_dynamic_with_ff)\n",
+    "for name in reaction1_strong_EM.get_intermediate_particles().names:\n",
+    "    model_builder.dynamics.assign(name, create_relativistic_breit_wigner_with_ff)\n",
+    "model = model_builder.formulate()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "15",
+   "metadata": {},
+   "source": [
+    "take another look at the parameters of the model to see which new parameters are there:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "16",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sorted_parameter_defaults = {\n",
+    "    symbol: model.parameter_defaults[symbol]\n",
+    "    for symbol in sorted(model.parameter_defaults, key=str)\n",
+    "}\n",
+    "src = aslatex(sorted_parameter_defaults)\n",
+    "Math(src)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "17",
+   "metadata": {},
+   "source": [
+    "Optionally, we can backup the HelicityModel to disk via pickle."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "18",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pickle\n",
+    "\n",
+    "qrules.io.write(reaction1_strong_EM, \"transitions.json\")\n",
+    "with open(\"helicity_model.pickle\", \"wb\") as stream:\n",
+    "    pickle.dump(model, stream)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "19",
+   "metadata": {},
+   "source": [
+    "# Generate data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "20",
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "import pickle\n",
+    "\n",
+    "from ampform.helicity import HelicityModel\n",
+    "\n",
+    "with open(\"helicity_model.pickle\", \"rb\") as model_file:\n",
+    "    imported_model: HelicityModel = pickle.load(model_file)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "21",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "initial_state, *_ = imported_model.reaction_info.initial_state.values()\n",
+    "print(\"Initial state:\")\n",
+    "print(\" \", initial_state.name)\n",
+    "print(\"Final state:\")\n",
+    "for i, p in imported_model.reaction_info.final_state.items():\n",
+    "    print(f\"  {i}: {p.name}\")\n",
+    "del initial_state"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22",
+   "metadata": {},
+   "source": [
+    "## Generate phase space sample"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "23",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from tensorwaves.data import TFPhaseSpaceGenerator, TFUniformRealNumberGenerator\n",
+    "\n",
+    "rng = TFUniformRealNumberGenerator(seed=0)\n",
+    "phsp_generator = TFPhaseSpaceGenerator(\n",
+    "    initial_state_mass=reaction1_strong_EM.initial_state[-1].mass,\n",
+    "    final_state_masses={i: p.mass for i, p in reaction1_strong_EM.final_state.items()},\n",
+    ")\n",
+    "phsp_momenta = phsp_generator.generate(100_000, rng)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "24",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "\n",
+    "pd.DataFrame(\n",
+    "    {\n",
+    "        (k, label): np.transpose(v)[i]\n",
+    "        for k, v in phsp_momenta.items()\n",
+    "        for i, label in enumerate([\"E\", \"px\", \"py\", \"pz\"])\n",
+    "    }\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "25",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "p = np.array(list(phsp_momenta.values()))\n",
+    "p.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "26",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "p.sum(axis=0).round(decimals=14)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "27",
+   "metadata": {},
+   "source": [
+    "## Generate intensity-based sample"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "28",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from tensorwaves.function.sympy import create_parametrized_function\n",
+    "\n",
+    "unfolded_expression = model.expression.doit()\n",
+    "intensity_func = create_parametrized_function(\n",
+    "    expression=unfolded_expression,\n",
+    "    parameters=model.parameter_defaults,\n",
+    "    backend=\"numpy\",\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "29",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Math(aslatex(model.kinematic_variables))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "30",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from tensorwaves.data import SympyDataTransformer\n",
+    "\n",
+    "helicity_transformer = SympyDataTransformer.from_sympy(\n",
+    "    model.kinematic_variables, backend=\"jax\"\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "31",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from tensorwaves.data import (\n",
+    "    IntensityDistributionGenerator,\n",
+    "    TFWeightedPhaseSpaceGenerator,\n",
+    ")\n",
+    "\n",
+    "weighted_phsp_generator = TFWeightedPhaseSpaceGenerator(\n",
+    "    initial_state_mass=reaction1_strong_EM.initial_state[-1].mass,\n",
+    "    final_state_masses={i: p.mass for i, p in reaction1_strong_EM.final_state.items()},\n",
+    ")\n",
+    "data_generator = IntensityDistributionGenerator(\n",
+    "    domain_generator=weighted_phsp_generator,\n",
+    "    function=intensity_func,\n",
+    "    domain_transformer=helicity_transformer,\n",
+    ")\n",
+    "data_momenta = data_generator.generate(10_000, rng)\n",
+    "pd.DataFrame(\n",
+    "    {\n",
+    "        (k, label): np.transpose(v)[i]\n",
+    "        for k, v in data_momenta.items()\n",
+    "        for i, label in enumerate([\"E\", \"px\", \"py\", \"pz\"])\n",
+    "    }\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "32",
+   "metadata": {},
+   "source": [
+    "## Visualize kinematic variables"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "33",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "phsp = helicity_transformer(phsp_momenta)\n",
+    "data = helicity_transformer(data_momenta)\n",
+    "list(data)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "34",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for state_id, particle in reaction1_strong_EM.final_state.items():\n",
+    "    print(f\"ID {state_id}:\", particle.name)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "35",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "\n",
+    "data_frame = pd.DataFrame(data)\n",
+    "phsp_frame = pd.DataFrame(phsp)\n",
+    "data_frame"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "36",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_formats = ['svg']\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "resonances = sorted(\n",
+    "    reaction1_strong_EM.get_intermediate_particles(),\n",
+    "    key=lambda p: p.mass,\n",
+    ")\n",
+    "evenly_spaced_interval = np.linspace(0, 1, len(resonances))\n",
+    "colors = [plt.cm.rainbow(x) for x in evenly_spaced_interval]\n",
+    "fig, ax = plt.subplots(figsize=(9, 4))\n",
+    "ax.hist(\n",
+    "    np.real(data_frame[\"m_12\"]),\n",
+    "    bins=100,\n",
+    "    alpha=0.5,\n",
+    "    density=True,\n",
+    ")\n",
+    "ax.set_xlabel(\"$m$ [GeV]\")\n",
+    "for p, color in zip(resonances, colors):\n",
+    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
+    "ax.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "37",
+   "metadata": {},
+   "source": [
+    "## Export data sets"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "38",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pickle\n",
+    "\n",
+    "with open(\"data.pickle\", \"wb\") as stream:\n",
+    "    pickle.dump(data, stream)\n",
+    "with open(\"phsp.pickle\", \"wb\") as stream:\n",
+    "    pickle.dump(phsp, stream)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "39",
+   "metadata": {},
+   "source": [
+    "# Perform fit"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "40",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "reaction = qrules.io.load(\"transitions.json\")\n",
+    "with open(\"helicity_model.pickle\", \"rb\") as stream:\n",
+    "    model: HelicityModel = pickle.load(stream)\n",
+    "with open(\"data.pickle\", \"rb\") as stream:\n",
+    "    data = pickle.load(stream)\n",
+    "with open(\"phsp.pickle\", \"rb\") as stream:\n",
+    "    phsp = pickle.load(stream)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "41",
+   "metadata": {},
+   "source": [
+    "## Prepare parametrized function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "42",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "initial_parameters = {\n",
+    "    R\"C_{p\\gamma \\to {f_{0}(1500)}_{0} \\gamma_{+1}; f_{0}(1500) \\to  \\eta \\pi^{0} p}\": (\n",
+    "        1.0 + 0.0j\n",
+    "    ),\n",
+    "    \"m_{f_{0}(500)}\": 0.4,\n",
+    "    \"m_{f_{0}(980)}\": 0.88,\n",
+    "    \"m_{f_{0}(1370)}\": 1.22,\n",
+    "    \"m_{f_{0}(1500)}\": 1.45,\n",
+    "    \"m_{f_{0}(1710)}\": 1.83,\n",
+    "    R\"\\Gamma_{f_{0}(500)}\": 0.3,\n",
+    "    R\"\\Gamma_{f_{0}(980)}\": 0.1,\n",
+    "    R\"\\Gamma_{f_{0}(1710)}\": 0.3,\n",
+    "}"
+   ]
   }
  ],
  "metadata": {
diff --git a/pixi.lock b/pixi.lock
index 7bb7a25..8e85dd2 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -7,20 +7,23 @@ environments:
       linux-64:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_libgcc_mutex-0.1-conda_forge.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/absl-py-2.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/accessible-pygments-0.0.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/alabaster-0.7.16-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/alsa-lib-1.2.12-h4ab18f5_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.3-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ampform-0.15.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/anyio-4.3.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/argon2-cffi-23.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/argon2-cffi-bindings-21.2.0-py312h98912ed_4.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/arrow-1.3.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/asttokens-2.4.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/astunparse-1.6.3-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/async-lru-2.0.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/atk-1.0-2.38.0-h04ea711_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/attr-2.5.1-h166bdaf_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/attrs-23.2.0-pyh71513ae_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/babel-2.14.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/bcrypt-4.1.3-py312h4413252_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/beautifulsoup4-4.12.3-pyha770c72_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/black-24.4.2-py312h7900ff3_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/bleach-6.1.0-pyhd8ed1ab_0.conda
@@ -38,22 +41,27 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/cfgv-3.3.1-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/charset-normalizer-3.3.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/click-8.1.7-unix_pyh707e725_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/cloudpickle-3.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/colorama-0.4.6-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/comm-0.2.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/contourpy-1.2.1-py312h8572e83_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/cryptography-42.0.7-py312hbcc2302_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/cycler-0.12.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/dbus-1.13.6-h5008d03_3.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/debugpy-1.8.1-py312h30efb56_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/decaylanguage-0.18.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/decorator-5.1.1-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/defusedxml-0.7.1-pyhd8ed1ab_0.tar.bz2
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       - conda: https://conda.anaconda.org/conda-forge/noarch/smmap-5.0.0-pyhd8ed1ab_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/snappy-1.2.0-hdb0a2a9_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/sniffio-1.3.1-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/soupsieve-2.5-pyhd8ed1ab_1.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/tabulate-0.9.0-pyhd8ed1ab_1.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/tensorboard-2.16.2-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/tensorboard-data-server-0.7.0-py312h241aef2_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/tensorflow-2.16.1-cpu_py312hfe0d8c0_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/tensorflow-base-2.16.1-cpu_py312hc526dda_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/tensorflow-estimator-2.16.1-cpu_py312hbf2973a_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/tensorflow-probability-0.24.0-pyh4af843d_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/tensorwaves-0.4.12-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/termcolor-2.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/terminado-0.18.1-pyh0d859eb_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/tf-keras-2.16.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/tinycss2-1.3.0-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/uvicorn-0.29.0-py312h7900ff3_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/vector-1.4.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/virtualenv-20.26.2-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/websockets-12.0-py312h98912ed_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/werkzeug-3.0.3-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/widgetsnbextension-4.0.10-pyhd8ed1ab_0.conda
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@@ -390,6 +436,21 @@ packages:
   license_family: BSD
   size: 23621
   timestamp: 1650670423406
+- kind: conda
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+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/absl-py-2.1.0-pyhd8ed1ab_0.conda
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+  md5: 035d1d58677c13ec93122d9eb6b8803b
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+  license_family: Apache
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   name: ampform
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+  version: 0.15.4
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   noarch: python
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+  md5: b84e06a4afa0667bb831782d42aff262
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   license_family: GPL
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   size: 28922
   timestamp: 1698341257884
+- kind: conda
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+  url: https://conda.anaconda.org/conda-forge/noarch/astunparse-1.6.3-pyhd8ed1ab_0.tar.bz2
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 - kind: conda
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@@ -630,6 +706,22 @@ packages:
   license_family: BSD
   size: 7609750
   timestamp: 1702422720584
+- kind: conda
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+  url: https://conda.anaconda.org/conda-forge/linux-64/bcrypt-4.1.3-py312h4413252_0.conda
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+  - python_abi 3.12.* *_cp312
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 - kind: conda
   name: beautifulsoup4
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@@ -919,6 +1011,21 @@ packages:
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   size: 84437
   timestamp: 1692311973840
+- kind: conda
+  name: cloudpickle
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+  build: pyhd8ed1ab_0
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+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/cloudpickle-3.0.0-pyhd8ed1ab_0.conda
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 - kind: conda
   name: colorama
   version: 0.4.6
@@ -968,6 +1075,24 @@ packages:
   license_family: BSD
   size: 256764
   timestamp: 1712430146809
+- kind: conda
+  name: cryptography
+  version: 42.0.7
+  build: py312hbcc2302_0
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+  url: https://conda.anaconda.org/conda-forge/linux-64/cryptography-42.0.7-py312hbcc2302_0.conda
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+  - python_abi 3.12.* *_cp312
+  license: Apache-2.0 AND BSD-3-Clause AND PSF-2.0 AND MIT
+  license_family: BSD
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 - kind: conda
   name: cycler
   version: 0.12.1
@@ -1017,6 +1142,30 @@ packages:
   license_family: MIT
   size: 2079306
   timestamp: 1707444570818
+- kind: conda
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+  - particle >=0.22.0
+  - plumbum >=1.7.0
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+  - python-graphviz
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+  license_family: BSD
+  size: 164952
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   name: decorator
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   license_family: APACHE
   size: 274915
   timestamp: 1702383349284
+- kind: conda
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+  build: py312h72fbbdf_4
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+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/dm-tree-0.1.8-py312h72fbbdf_4.conda
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+  - libstdcxx-ng >=12
+  - python >=3.12,<3.13.0a0
+  - python_abi 3.12.* *_cp312
+  license: Apache-2.0
+  license_family: Apache
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   name: docutils
   version: 0.21.2
@@ -1166,6 +1335,21 @@ packages:
   license: Unlicense
   size: 15902
   timestamp: 1714422911808
+- kind: conda
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+  version: 24.3.25
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 - kind: conda
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   version: '2.37'
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   license: LGPL-2.1
   size: 114383
   timestamp: 1604416621168
+- kind: conda
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+  build: pyhd8ed1ab_0
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+  url: https://conda.anaconda.org/conda-forge/noarch/gast-0.5.4-pyhd8ed1ab_0.conda
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   version: 2.42.12
@@ -1499,6 +1700,22 @@ packages:
   license_family: LGPL
   size: 212406
   timestamp: 1715527440339
+- kind: conda
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+  version: 0.2.0
+  build: pyh8c360ce_0
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+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/google-pasta-0.2.0-pyh8c360ce_0.tar.bz2
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   timestamp: 1703201779255
+- kind: conda
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+  build: py312hb06c811_0
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+  url: https://conda.anaconda.org/conda-forge/linux-64/grpcio-1.62.2-py312hb06c811_0.conda
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   timestamp: 1634280590080
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+  build: nompi_py312hb7ab980_102
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   license_family: MIT
   size: 1598244
   timestamp: 1715701061364
+- kind: conda
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@@ -1851,6 +2129,24 @@ packages:
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   timestamp: 1656939625410
+- kind: conda
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+  build: py312h30efb56_0
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+  url: https://conda.anaconda.org/conda-forge/linux-64/iminuit-2.25.2-py312h30efb56_0.conda
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   size: 187135
   timestamp: 1707422097508
+- kind: conda
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+  build: pyhd8ed1ab_0
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+  - jax 0.4.*
+  - tensorflow >=2.15.0,<2.17.0a
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@@ -2626,6 +2949,21 @@ packages:
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   size: 508258
   timestamp: 1664996250081
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+  build: pyhd8ed1ab_0
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+  url: https://conda.anaconda.org/conda-forge/noarch/lark-1.1.9-pyhd8ed1ab_0.conda
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+  version: 2.16.1
+  build: cpu_py312hc526dda_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/tensorflow-base-2.16.1-cpu_py312hc526dda_0.conda
+  sha256: 4800b30312d396e53cfe8d0f7c1588d1f53ddbdeb7742f2bfbdd2006ff683a30
+  md5: 6789495ea21302dbd6bba70edefa4702
+  depends:
+  - absl-py >=1.0.0
+  - astunparse >=1.6.0
+  - flatbuffers >=24.3.25,<24.3.26.0a0
+  - gast >=0.2.1,!=0.5.0,!=0.5.1,!=0.5.2
+  - giflib >=5.2.2,<5.3.0a0
+  - google-pasta >=0.1.1
+  - grpcio 1.62.*
+  - h5py >=3.10
+  - icu >=73.2,<74.0a0
+  - keras >=3.0
+  - libabseil * cxx17*
+  - libabseil >=20240116.2,<20240117.0a0
+  - libcurl >=8.8.0,<9.0a0
+  - libgcc-ng >=12
+  - libgrpc >=1.62.2,<1.63.0a0
+  - libjpeg-turbo >=3.0.0,<4.0a0
+  - libpng >=1.6.43,<1.7.0a0
+  - libprotobuf >=4.25.3,<4.25.4.0a0
+  - libsqlite >=3.45.3,<4.0a0
+  - libstdcxx-ng >=12
+  - libzlib >=1.2.13,<2.0.0a0
+  - ml_dtypes >=0.3.1,<0.4
+  - numpy >=1.22,<2.0a0
+  - numpy >=1.26.4,<2.0a0
+  - openssl >=3.3.0,<4.0a0
+  - opt_einsum >=2.3.2
+  - packaging
+  - protobuf >=3.20.3,<5,!=4.21.0,!=4.21.1,!=4.21.2,!=4.21.3,!=4.21.4,!=4.21.5
+  - python >=3.12,<3.13.0a0
+  - python-flatbuffers >=23.5.26
+  - python_abi 3.12.* *_cp312
+  - requests >=2.21.0,<3
+  - six >=1.12
+  - snappy >=1.2.0,<1.3.0a0
+  - tensorboard >=2.16,<2.17
+  - termcolor >=1.1.0
+  - typing_extensions >=3.6.6
+  - wrapt >=1.11.0
+  track_features:
+  - tensorflow-cpu
+  license: Apache-2.0
+  license_family: Apache
+  size: 157134694
+  timestamp: 1716522780480
+- kind: conda
+  name: tensorflow-estimator
+  version: 2.16.1
+  build: cpu_py312hbf2973a_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/tensorflow-estimator-2.16.1-cpu_py312hbf2973a_0.conda
+  sha256: 6e8f471539c542158b8f3acfa7a963f7fa161af81fd862d322643989da1cffc3
+  md5: 492b9e434c37820acc6512f1a53ddd12
+  depends:
+  - libgcc-ng >=12
+  - libstdcxx-ng >=12
+  - openssl >=3.3.0,<4.0a0
+  - python >=3.12,<3.13.0a0
+  - python_abi 3.12.* *_cp312
+  - tensorflow-base 2.16.1 cpu_py312hc526dda_0
+  license: Apache-2.0
+  license_family: Apache
+  size: 697840
+  timestamp: 1716523349151
+- kind: conda
+  name: tensorflow-probability
+  version: 0.24.0
+  build: pyh4af843d_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/tensorflow-probability-0.24.0-pyh4af843d_0.conda
+  sha256: 5e5361240be6a53ece2d749837b24d95f6037a2dc95e3201d0659a9dc3c07362
+  md5: a39fabe06f10f544e7adde5f10743bd3
+  depends:
+  - absl-py
+  - cloudpickle >=1.3
+  - decorator
+  - dm-tree
+  - gast >=0.3.2
+  - jax >=0.4.25,<0.5.0
+  - numpy >=1.13.3
+  - python >=3.9
+  - six >=1.10.0
+  - tensorflow-base >=2.16.0,<2.17.0
+  - tf-keras >=2.16
+  license: Apache-2.0
+  license_family: Apache
+  size: 2186303
+  timestamp: 1716814596258
+- kind: conda
+  name: tensorwaves
+  version: 0.4.12
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/tensorwaves-0.4.12-pyhd8ed1ab_0.conda
+  sha256: 6fdcc45cf9172fb8f5e3998393caf44fb948b3a901742db4a512d7239504c729
+  md5: bc8a2954ac8f11698f91a209281c898f
+  depends:
+  - attrs >=20.1.0
+  - iminuit >=2.0
+  - numpy
+  - python >=3.8
+  - pyyaml >=5.1
+  - sympy >=1.9
+  - tqdm >=4.24.0
+  license: GPL-3.0-or-later
+  license_family: GPL
+  size: 43302
+  timestamp: 1709885857040
+- kind: conda
+  name: termcolor
+  version: 2.4.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/termcolor-2.4.0-pyhd8ed1ab_0.conda
+  sha256: 59588d41f2c02d599fd6528583013d85bd47d17b1acec11edbb29deadd81fbca
+  md5: a5033708ad9283907c3b1bc1f90d0d0d
+  depends:
+  - python >=3.8
+  license: MIT
+  license_family: MIT
+  size: 12721
+  timestamp: 1704358124294
 - kind: conda
   name: terminado
   version: 0.18.1
@@ -5752,6 +6618,23 @@ packages:
   license_family: BSD
   size: 22452
   timestamp: 1710262728753
+- kind: conda
+  name: tf-keras
+  version: 2.16.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/tf-keras-2.16.0-pyhd8ed1ab_0.conda
+  sha256: f075ea95d9fbb18d2c3a15aa63d484e3ca7e79af5f148ceea007565cd334adee
+  md5: 84d6a4b73d13bf11fc35df60fcb27b29
+  depends:
+  - numpy >=1.23
+  - python >=3.8
+  - tensorflow >=2.16,<2.17
+  license: Apache-2.0
+  license_family: APACHE
+  size: 906195
+  timestamp: 1716750135979
 - kind: conda
   name: tinycss2
   version: 1.3.0
@@ -5999,6 +6882,25 @@ packages:
   license_family: BSD
   size: 126964
   timestamp: 1710932152563
+- kind: conda
+  name: vector
+  version: 1.4.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/vector-1.4.1-pyhd8ed1ab_0.conda
+  sha256: e8806a7dc862bf169de681672e261af18bf7889f2292febd6c5ec217e415c3d6
+  md5: bb95ca87b1a3cd4af3f3f49bc4718777
+  depends:
+  - importlib_metadata >=0.22
+  - numpy >=1.14.5
+  - packaging
+  - python >=3.8
+  - typing-extensions
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 95437
+  timestamp: 1718033105021
 - kind: conda
   name: virtualenv
   version: 20.26.2
@@ -6111,6 +7013,22 @@ packages:
   license_family: BSD
   size: 201426
   timestamp: 1697914826988
+- kind: conda
+  name: werkzeug
+  version: 3.0.3
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/werkzeug-3.0.3-pyhd8ed1ab_0.conda
+  sha256: a77d0c67096999c35854e0480e3b978ef72ee008e295e92b0dc67116b2398661
+  md5: 2e60f5f388845027ee87fca6bee4ac23
+  depends:
+  - markupsafe >=2.1.1
+  - python >=3.8
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 242920
+  timestamp: 1715000337645
 - kind: conda
   name: widgetsnbextension
   version: 4.0.10
diff --git a/pixi.toml b/pixi.toml
index 0603ee3..bf4ae1c 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -20,12 +20,12 @@ sphinx-autobuild \
 """
 
 [dependencies]
-ampform = ">=0.15.2,<0.16"
+ampform = ">=0.15.4,<0.16"
 black = ">=24.4.2,<24.5"
 graphviz = ">=9.0.0,<9.1"
 ipywidgets = ">=8.1.2,<8.2"
 isort = ">=5.13.2,<5.14"
-jax = ">=0.4.26,<0.5"
+jax = ">=0.4.27,<0.5"
 jaxlib = ">=0.4.23,<0.5"
 jupyter = ">=1.0.0,<1.1"
 jupyterlab = ">=4.2.0,<4.3"
@@ -36,6 +36,7 @@ jupyterlab_code_formatter = ">=2.2.1,<2.3"
 matplotlib = ">=3.8.4,<3.9"
 myst-nb = ">=1.1.0,<1.2"
 numpy = ">=1.26.4,<1.27"
+phasespace = ">=1.10.3,<1.11"
 pre-commit = ">=3.7.1,<3.8"
 pydata-sphinx-theme = ">=0.15.2,<0.16"
 python = ">=3.12.3,<3.13"
@@ -45,3 +46,5 @@ scipy = ">=1.13.0,<1.14"
 sphinx-autobuild = ">=2024.4.16,<2024.5"
 sphinx-book-theme = ">=1.1.2,<1.2"
 sympy = ">=1.12,<2"
+tensorflow = ">=2.16.1,<2.17"
+tensorwaves = ">=0.4.12,<0.5"

From b35f4456e99e6bf1f5757f046e7218788abff373 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 13 Jun 2024 14:31:55 +0200
Subject: [PATCH 20/44] draft in start of perform fit

---
 docs/all-in-one.ipynb | 26 +++++++++++++-------------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
index 835fd37..b9d8816 100644
--- a/docs/all-in-one.ipynb
+++ b/docs/all-in-one.ipynb
@@ -565,19 +565,19 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "initial_parameters = {\n",
-    "    R\"C_{p\\gamma \\to {f_{0}(1500)}_{0} \\gamma_{+1}; f_{0}(1500) \\to  \\eta \\pi^{0} p}\": (\n",
-    "        1.0 + 0.0j\n",
-    "    ),\n",
-    "    \"m_{f_{0}(500)}\": 0.4,\n",
-    "    \"m_{f_{0}(980)}\": 0.88,\n",
-    "    \"m_{f_{0}(1370)}\": 1.22,\n",
-    "    \"m_{f_{0}(1500)}\": 1.45,\n",
-    "    \"m_{f_{0}(1710)}\": 1.83,\n",
-    "    R\"\\Gamma_{f_{0}(500)}\": 0.3,\n",
-    "    R\"\\Gamma_{f_{0}(980)}\": 0.1,\n",
-    "    R\"\\Gamma_{f_{0}(1710)}\": 0.3,\n",
-    "}"
+    "# initial_parameters = {\n",
+    "#     R\"C_{p\\gamma \\to {f_{0}(1500)}_{0} \\gamma_{+1}; f_{0}(1500) \\to  \\eta \\pi^{0} p}\": (\n",
+    "#         1.0 + 0.0j\n",
+    "#     ),\n",
+    "#     \"m_{f_{0}(500)}\": 0.4,\n",
+    "#     \"m_{f_{0}(980)}\": 0.88,\n",
+    "#     \"m_{f_{0}(1370)}\": 1.22,\n",
+    "#     \"m_{f_{0}(1500)}\": 1.45,\n",
+    "#     \"m_{f_{0}(1710)}\": 1.83,\n",
+    "#     R\"\\Gamma_{f_{0}(500)}\": 0.3,\n",
+    "#     R\"\\Gamma_{f_{0}(980)}\": 0.1,\n",
+    "#     R\"\\Gamma_{f_{0}(1710)}\": 0.3,\n",
+    "# }"
    ]
   }
  ],

From 387351c3d532432b76b148647421be094668968d Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 18 Jun 2024 16:55:52 +0200
Subject: [PATCH 21/44] limit resonances and add max angular momentum and spin
 magnitude

---
 docs/all-in-one.ipynb | 110 ++++++++-----
 pixi.lock             | 363 ++++++++++++++++++++++++++++++++++++++++++
 pixi.toml             |   2 +
 3 files changed, 438 insertions(+), 37 deletions(-)

diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
index b9d8816..37aca79 100644
--- a/docs/all-in-one.ipynb
+++ b/docs/all-in-one.ipynb
@@ -93,6 +93,40 @@
    "id": "6",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "particle_db[\"N(1680)+\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db[\"N(1650)+\"]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8",
+   "metadata": {},
+   "source": [
+    "For simplicity, we limit the intermediate resonances to be:\n",
+    "\n",
+    "\"$a(2)$\" for $\\eta \\pi^0$, \n",
+    "\n",
+    "\"$\\Delta^*$\" for $\\pi^0 p$, \n",
+    "\n",
+    "\"$N^*$\" for $\\eta p$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {},
+   "outputs": [],
    "source": [
     "import qrules\n",
     "import graphviz\n",
@@ -100,17 +134,19 @@
     "reaction1_strong_EM = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    allowed_intermediate_particles=[\"a(2)\", \"Delta\", \"N\"],\n",
+    "    allowed_intermediate_particles=[\"a(2)(1320)\", \"Delta(1232)\", \"N(1535)\"],\n",
     "    allowed_interaction_types=[\"strong\", \"EM\"],\n",
     "    formalism=\"canonical-helicity\",\n",
     "    particle_db=particle_db,\n",
+    "    max_angular_momentum=3,\n",
+    "    max_spin_magnitude=3,\n",
     ")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7",
+   "id": "10",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -120,7 +156,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8",
+   "id": "11",
    "metadata": {},
    "source": [
     "## Build Amplitude Models"
@@ -128,7 +164,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9",
+   "id": "12",
    "metadata": {},
    "source": [
     "we use ampform to formulate the transitions as an amplitude model (here: HelicityModel). "
@@ -137,7 +173,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
+   "id": "13",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -151,7 +187,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
+   "id": "14",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -163,7 +199,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "15",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -172,7 +208,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13",
+   "id": "16",
    "metadata": {},
    "source": [
     "We choose to use relativistic_breit_wigner_with_ff() as the lineshape for all resonances and use a Blatt-Weisskopf form factor (create_non_dynamic_with_ff()) for the production decay. "
@@ -181,7 +217,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14",
+   "id": "17",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -198,7 +234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15",
+   "id": "18",
    "metadata": {},
    "source": [
     "take another look at the parameters of the model to see which new parameters are there:"
@@ -207,7 +243,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
+   "id": "19",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -221,7 +257,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17",
+   "id": "20",
    "metadata": {},
    "source": [
     "Optionally, we can backup the HelicityModel to disk via pickle."
@@ -230,7 +266,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "18",
+   "id": "21",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -243,7 +279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19",
+   "id": "22",
    "metadata": {},
    "source": [
     "# Generate data"
@@ -252,7 +288,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "20",
+   "id": "23",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -267,7 +303,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "21",
+   "id": "24",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -282,7 +318,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22",
+   "id": "25",
    "metadata": {},
    "source": [
     "## Generate phase space sample"
@@ -291,7 +327,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "23",
+   "id": "26",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -308,7 +344,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "24",
+   "id": "27",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -327,7 +363,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "25",
+   "id": "28",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -340,7 +376,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "26",
+   "id": "29",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -349,7 +385,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27",
+   "id": "30",
    "metadata": {},
    "source": [
     "## Generate intensity-based sample"
@@ -358,7 +394,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "28",
+   "id": "31",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -375,7 +411,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29",
+   "id": "32",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -385,7 +421,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "30",
+   "id": "33",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -399,7 +435,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31",
+   "id": "34",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -429,7 +465,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32",
+   "id": "35",
    "metadata": {},
    "source": [
     "## Visualize kinematic variables"
@@ -438,7 +474,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33",
+   "id": "36",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -450,7 +486,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34",
+   "id": "37",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -461,7 +497,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "35",
+   "id": "38",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -475,7 +511,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36",
+   "id": "39",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -505,7 +541,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37",
+   "id": "40",
    "metadata": {},
    "source": [
     "## Export data sets"
@@ -514,7 +550,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "38",
+   "id": "41",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -528,7 +564,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39",
+   "id": "42",
    "metadata": {},
    "source": [
     "# Perform fit"
@@ -537,7 +573,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "40",
+   "id": "43",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -552,7 +588,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41",
+   "id": "44",
    "metadata": {},
    "source": [
     "## Prepare parametrized function"
@@ -561,7 +597,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42",
+   "id": "45",
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/pixi.lock b/pixi.lock
index 8e85dd2..cbc9783 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -16,12 +16,14 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/noarch/asttokens-2.4.1-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/attrs-23.2.0-pyh71513ae_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/docutils-0.21.2-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/filelock-3.14.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/flake8-7.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/flatbuffers-24.3.25-h59595ed_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/matplotlib-inline-0.1.7-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/mccabe-0.7.0-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/mdit-py-plugins-0.4.1-pyhd8ed1ab_0.conda
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@@ -275,6 +281,7 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/noarch/pure_eval-0.2.2-pyhd8ed1ab_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/pycodestyle-2.11.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pycparser-2.22-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/pydata-sphinx-theme-0.15.2-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/pydocstyle-6.3.0-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/pygments-2.18.0-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/pynacl-1.5.0-py312h98912ed_3.conda
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@@ -302,8 +313,12 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/noarch/python-json-logger-2.0.7-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/python-lsp-jsonrpc-1.1.2-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/python-lsp-server-1.11.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/python-lsp-server-base-1.11.0-pyhd8ed1ab_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/python_abi-3.12-4_cp312.conda
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       - conda: https://conda.anaconda.org/conda-forge/noarch/tomli-2.0.1-pyhd8ed1ab_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/tomlkit-0.12.5-pyha770c72_0.conda
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+      - conda: https://conda.anaconda.org/conda-forge/noarch/yapf-0.40.1-pyhd8ed1ab_0.conda
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@@ -593,6 +613,21 @@ packages:
   license_family: Apache
   size: 100096
   timestamp: 1696129131844
+- kind: conda
+  name: astroid
+  version: 3.2.2
+  build: py312h7900ff3_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/astroid-3.2.2-py312h7900ff3_0.conda
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+  md5: 2acaebd0ea2aeaf38e996bda79545c0b
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+  - python_abi 3.12.* *_cp312
+  license: LGPL-2.1-or-later
+  license_family: LGPL
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+  timestamp: 1716193798370
 - kind: conda
   name: asttokens
   version: 2.4.1
@@ -689,6 +724,24 @@ packages:
   license_family: MIT
   size: 54582
   timestamp: 1704011393776
+- kind: conda
+  name: autopep8
+  version: 2.0.4
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/autopep8-2.0.4-pyhd8ed1ab_0.conda
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+  - pycodestyle >=2.10.0
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+  license: MIT
+  license_family: MIT
+  size: 45709
+  timestamp: 1693061409657
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   name: babel
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@@ -1212,6 +1265,21 @@ packages:
   license_family: MIT
   size: 14033
   timestamp: 1685233463632
+- kind: conda
+  name: dill
+  version: 0.3.8
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/dill-0.3.8-pyhd8ed1ab_0.conda
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+  license: BSD-3-Clause
+  license_family: BSD
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   name: distlib
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@@ -1247,6 +1315,20 @@ packages:
   license_family: Apache
   size: 118694
   timestamp: 1709887014156
+- kind: conda
+  name: docstring-to-markdown
+  version: '0.15'
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/docstring-to-markdown-0.15-pyhd8ed1ab_0.conda
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+  md5: a3a1e6af2926a3affcd6f2072871f551
+  depends:
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+  license: LGPL-2.1-or-later
+  size: 34061
+  timestamp: 1708563226581
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   name: docutils
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@@ -1335,6 +1417,24 @@ packages:
   license: Unlicense
   size: 15902
   timestamp: 1714422911808
+- kind: conda
+  name: flake8
+  version: 7.0.0
+  build: pyhd8ed1ab_0
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+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/flake8-7.0.0-pyhd8ed1ab_0.conda
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+  license: MIT
+  license_family: MIT
+  size: 110938
+  timestamp: 1704483964269
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+- kind: conda
+  name: mccabe
+  version: 0.7.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/mccabe-0.7.0-pyhd8ed1ab_0.tar.bz2
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+- kind: conda
+  name: pluggy
+  version: 1.5.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/pluggy-1.5.0-pyhd8ed1ab_0.conda
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+  license: MIT
+  license_family: MIT
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@@ -5346,6 +5476,21 @@ packages:
   license_family: MIT
   size: 14551
   timestamp: 1642876055775
+- kind: conda
+  name: pycodestyle
+  version: 2.11.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/pycodestyle-2.11.1-pyhd8ed1ab_0.conda
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+  license: MIT
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+  timestamp: 1697203012487
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   license_family: BSD
   size: 1375728
   timestamp: 1705630287042
+- kind: conda
+  name: pydocstyle
+  version: 6.3.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/pydocstyle-6.3.0-pyhd8ed1ab_0.conda
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+  md5: 7e23a61a7fbaedfef6eb0e1ac775c8e5
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+  - snowballstemmer >=2.2.0
+  - tomli >=1.2.3
+  license: MIT
+  license_family: MIT
+  size: 39851
+  timestamp: 1673997613432
+- kind: conda
+  name: pyflakes
+  version: 3.2.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/pyflakes-3.2.0-pyhd8ed1ab_0.conda
+  sha256: b1582410fcfa30b3597629e39b688ead87833c4a64f7c4637068f80aa1411d49
+  md5: 0cf7fef6aa123df28adb21a590065e3d
+  depends:
+  - python ==2.7.*|>=3.5
+  license: MIT
+  license_family: MIT
+  size: 58654
+  timestamp: 1704424729210
 - kind: conda
   name: pygments
   version: 2.18.0
@@ -5399,6 +5576,30 @@ packages:
   license_family: BSD
   size: 879295
   timestamp: 1714846885370
+- kind: conda
+  name: pylint
+  version: 3.2.3
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/pylint-3.2.3-pyhd8ed1ab_0.conda
+  sha256: 4d67967d4fbcb57859cb2162d1e621fa9cd649e9660448023d68cff440234da6
+  md5: 206e71eea41f956fd1bb606d6b0c87fd
+  depends:
+  - astroid >=3.2.2,<3.3.0-dev0
+  - colorama >=0.4.5
+  - dill >=0.3.7
+  - isort >=4.2.5,<6,!=5.13.0
+  - mccabe >=0.6,<0.8
+  - platformdirs >=2.2.0
+  - python >=3.8.0
+  - tomli >=1.1.0
+  - tomlkit >=0.10.1
+  - typing_extensions >=3.10.0
+  license: GPL-2.0-or-later
+  license_family: GPL
+  size: 351223
+  timestamp: 1717705700460
 - kind: conda
   name: pynacl
   version: 1.5.0
@@ -5615,6 +5816,69 @@ packages:
   license_family: BSD
   size: 13383
   timestamp: 1677079727691
+- kind: conda
+  name: python-lsp-jsonrpc
+  version: 1.1.2
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/python-lsp-jsonrpc-1.1.2-pyhd8ed1ab_0.conda
+  sha256: 9d60c2ebce844420946beed1aca571f2bb8001269352c70ff0168a07bdc656e1
+  md5: ff30dbdb341a54947c4fa183900380b7
+  depends:
+  - python >=3.8
+  - ujson >=3.0.0
+  license: MIT
+  license_family: MIT
+  size: 13984
+  timestamp: 1695528516444
+- kind: conda
+  name: python-lsp-server
+  version: 1.11.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/python-lsp-server-1.11.0-pyhd8ed1ab_0.conda
+  sha256: 99b31fe02bf4dafc6f151d8dffd412014f273acd97dadf59476a446269c9646b
+  md5: c1db1a6057f7f2d7299ed2b59c51bd34
+  depends:
+  - autopep8 >=2.0.4,<2.1.0
+  - flake8 >=7.0.0,<8.0.0
+  - mccabe >=0.7.0,<0.8.0
+  - pycodestyle >=2.11.0,<2.12.0
+  - pydocstyle >=6.3.0,<6.4.0
+  - pyflakes >=3.2.0,<3.3.0
+  - pylint >=3.1.0,<4.0.0
+  - python
+  - python-lsp-server-base 1.11.0 pyhd8ed1ab_0
+  - rope >=1.11.0
+  - whatthepatch >=1.0.2,<2.0.0
+  - yapf >=0.33.0
+  license: MIT
+  license_family: MIT
+  size: 7170
+  timestamp: 1711734928412
+- kind: conda
+  name: python-lsp-server-base
+  version: 1.11.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/python-lsp-server-base-1.11.0-pyhd8ed1ab_0.conda
+  sha256: 34fc82a789d94e97e40f57f1e24c3ae276a37cdc548c8ab13bf6001411f58377
+  md5: 6ae8c26c3ebf7d148d7000f7fbad9512
+  depends:
+  - docstring-to-markdown
+  - importlib_metadata >=4.8.3
+  - jedi >=0.17.2,<0.20
+  - pluggy >=1.0.0
+  - python >=3.8
+  - python-lsp-jsonrpc >=1.1.0,<2.0.0
+  - ujson >=3.0.0
+  license: MIT
+  license_family: MIT
+  size: 60864
+  timestamp: 1711734907043
 - kind: conda
   name: python-tzdata
   version: '2024.1'
@@ -5645,6 +5909,24 @@ packages:
   license_family: BSD
   size: 6385
   timestamp: 1695147396604
+- kind: conda
+  name: pytoolconfig
+  version: 1.2.5
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/pytoolconfig-1.2.5-pyhd8ed1ab_0.conda
+  sha256: a76ca96ab4abd3d444917322ff4627961d4114cb1d4e14c4c25f934b38244107
+  md5: 2d6bdf5a69cfcd1fcc7f2b900cb4082f
+  depends:
+  - packaging >=22.0
+  - python >=3.7
+  - tomli >=2.0.1
+  - typing-extensions >=4.4.0
+  license: LGPL-3.0-or-later
+  license_family: LGPL
+  size: 21331
+  timestamp: 1675124885156
 - kind: conda
   name: pytz
   version: '2024.1'
@@ -5951,6 +6233,22 @@ packages:
   license_family: MIT
   size: 184347
   timestamp: 1709150578093
+- kind: conda
+  name: rope
+  version: 1.13.0
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/rope-1.13.0-pyhd8ed1ab_0.conda
+  sha256: 6807bf6955e193d0c725f5d1db2c9348343263fb70153537e16f34190cf9abf9
+  md5: dffa002fbd3d86924b7992c718efa7bc
+  depends:
+  - python >=3.8
+  - pytoolconfig >=1.2.2
+  license: LGPL-3.0-or-later
+  license_family: LGPL
+  size: 150446
+  timestamp: 1711296424635
 - kind: conda
   name: rpds-py
   version: 0.18.1
@@ -6697,6 +6995,21 @@ packages:
   license_family: MIT
   size: 15940
   timestamp: 1644342331069
+- kind: conda
+  name: tomlkit
+  version: 0.12.5
+  build: pyha770c72_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/tomlkit-0.12.5-pyha770c72_0.conda
+  sha256: 5117eff35992d896ca177dfffc08be8a9b3bf3d306ddc3d8bf4b699cdf1e1b79
+  md5: e5dde5caf905e9d95895e05f94967e14
+  depends:
+  - python >=3.7
+  license: MIT
+  license_family: MIT
+  size: 37297
+  timestamp: 1715185504185
 - kind: conda
   name: tornado
   version: '6.4'
@@ -6814,6 +7127,23 @@ packages:
   license: LicenseRef-Public-Domain
   size: 119815
   timestamp: 1706886945727
+- kind: conda
+  name: ujson
+  version: 5.10.0
+  build: py312h7070661_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/ujson-5.10.0-py312h7070661_0.conda
+  sha256: 36c39df244b96e501300ff9f11fb9648e9d82ea8a33ebb9afa17795e08875c0d
+  md5: dd19f5820a3fd57aea70aaf88e6dd191
+  depends:
+  - libgcc-ng >=12
+  - libstdcxx-ng >=12
+  - python >=3.12,<3.13.0a0
+  - python_abi 3.12.* *_cp312
+  license: BSD-3-Clause
+  license_family: BSD
+  size: 52337
+  timestamp: 1715783243655
 - kind: conda
   name: ukkonen
   version: 1.0.1
@@ -7029,6 +7359,21 @@ packages:
   license_family: BSD
   size: 242920
   timestamp: 1715000337645
+- kind: conda
+  name: whatthepatch
+  version: 1.0.5
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/whatthepatch-1.0.5-pyhd8ed1ab_0.conda
+  sha256: e88752339157f78c7ea3e506627a8f9fede7869a3f2d34020b3a899e9dfc3c30
+  md5: e62ea65e1979c18c4c9034567e7105c5
+  depends:
+  - python >=3.7
+  license: MIT
+  license_family: MIT
+  size: 16986
+  timestamp: 1683396918646
 - kind: conda
   name: widgetsnbextension
   version: 4.0.10
@@ -7370,6 +7715,24 @@ packages:
   license_family: MIT
   size: 89141
   timestamp: 1641346969816
+- kind: conda
+  name: yapf
+  version: 0.40.1
+  build: pyhd8ed1ab_0
+  subdir: noarch
+  noarch: python
+  url: https://conda.anaconda.org/conda-forge/noarch/yapf-0.40.1-pyhd8ed1ab_0.conda
+  sha256: b227bb911a88e08d985aa09a636d0b23f273eb85fe47b6be8a47c86e6bd52c31
+  md5: f269942e802d5e148632143d4c37acc9
+  depends:
+  - importlib-metadata >=6.6.0
+  - platformdirs >=3.5.1
+  - python >=3.7
+  - tomli >=2.0.1
+  license: Apache-2.0
+  license_family: APACHE
+  size: 176345
+  timestamp: 1690388073748
 - kind: conda
   name: zeromq
   version: 4.3.5
diff --git a/pixi.toml b/pixi.toml
index bf4ae1c..78e99ed 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -28,6 +28,7 @@ isort = ">=5.13.2,<5.14"
 jax = ">=0.4.27,<0.5"
 jaxlib = ">=0.4.23,<0.5"
 jupyter = ">=1.0.0,<1.1"
+jupyter-lsp = ">=2.2.5,<2.3"
 jupyterlab = ">=4.2.0,<4.3"
 jupyterlab-git = ">=0.50.0,<0.51"
 jupyterlab-lsp = ">=5.1.0,<5.2"
@@ -41,6 +42,7 @@ pre-commit = ">=3.7.1,<3.8"
 pydata-sphinx-theme = ">=0.15.2,<0.16"
 python = ">=3.12.3,<3.13"
 python-graphviz = ">=0.20.3,<0.21"
+python-lsp-server = ">=1.11.0,<1.12"
 qrules = ">=0.10.1,<0.11"
 scipy = ">=1.13.0,<1.14"
 sphinx-autobuild = ">=2024.4.16,<2024.5"

From 28ba866e8c9df871053c9752a0123acbb48a065d Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 19 Jun 2024 11:06:43 +0200
Subject: [PATCH 22/44] add section to index

---
 docs/index.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/docs/index.md b/docs/index.md
index b08e62e..d126a3f 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -17,4 +17,6 @@ address to the issue ✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/g
 ```{toctree}
 reaction
 pgamma-state
+symbolics
+all-in-one
 ```

From f4f74f9709a189dacabd05a21b92a806ddb5128c Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 19 Jun 2024 16:11:19 +0200
Subject: [PATCH 23/44] draft before splitting the branch

---
 .gitignore            |   3 +
 docs/LamKpi.ipynb     | 171 ++++++++++++++++++++++++++++++++-
 docs/all-in-one.ipynb | 216 +++++++++++++++++++++++++++++++++---------
 docs/index.md         |   1 +
 docs/symbolics.ipynb  |   2 +-
 5 files changed, 346 insertions(+), 47 deletions(-)

diff --git a/.gitignore b/.gitignore
index edef47a..9bdcb24 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,7 @@
 *.egg-info
 .ipynb_checkpoints/
 .pixi
+.virtual_documents/
 node_modules/
+**/*.pickle
+**/*.json
diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
index cbe7ef2..66e56a3 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/LamKpi.ipynb
@@ -14,6 +14,175 @@
    "id": "1",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "from __future__ import annotations\n",
+    "from IPython.display import Math\n",
+    "from qrules.particle import load_pdg\n",
+    "from ampform.io import aslatex, improve_latex_rendering\n",
+    "\n",
+    "improve_latex_rendering()\n",
+    "particle_db = load_pdg()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qrules.particle import Particle, Spin\n",
+    "\n",
+    "pgamma = Particle(\n",
+    "    name=\"pgamma\",\n",
+    "    latex=r\"p\\gamma (s1/2)\",\n",
+    "    spin=0.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99990,\n",
+    ")\n",
+    "pgamma"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "pgamma2 = Particle(\n",
+    "    name=\"pgamma2\",\n",
+    "    latex=R\"p\\gamma (s3/2)\",\n",
+    "    spin=1.5,\n",
+    "    mass=4.101931071854584,\n",
+    "    charge=1,\n",
+    "    isospin=Spin(1 / 2, +1 / 2),\n",
+    "    baryon_number=1,\n",
+    "    parity=-1,\n",
+    "    pid=99991,\n",
+    ")\n",
+    "pgamma2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db.add(pgamma)\n",
+    "particle_db.add(pgamma2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import qrules\n",
+    "import graphviz\n",
+    "\n",
+    "reaction1 = qrules.generate_transitions(\n",
+    "    initial_state=(\"pgamma\"),\n",
+    "    final_state=[\"Lambda\", \"K+\", \"pi0\"],\n",
+    "    # allowed_intermediate_particles=[\"a(2)(1320)\",\"N\",\"Delta\"],\n",
+    "    allowed_interaction_types=[\"strong\"],\n",
+    "    formalism=\"canonical-helicity\",\n",
+    "    particle_db=particle_db,\n",
+    "    max_angular_momentum=3,\n",
+    "    max_spin_magnitude=3,\n",
+    "    mass_conservation_factor=0,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db[\"Lambda\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dot_se = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
+    "graphviz.Source(dot_se)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import ampform\n",
+    "\n",
+    "model_builder = ampform.get_builder(reaction1)\n",
+    "model_no_dynamics = model_builder.formulate()\n",
+    "model_no_dynamics.intensity"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ampform.io import aslatex\n",
+    "\n",
+    "Math(aslatex(model_no_dynamics.amplitudes))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "10",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Math(aslatex(model_no_dynamics.parameter_defaults))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ampform.dynamics.builder import (\n",
+    "    create_non_dynamic_with_ff,\n",
+    "    create_relativistic_breit_wigner_with_ff,\n",
+    ")\n",
+    "\n",
+    "model_builder.dynamics.assign(\"pgamma\", create_non_dynamic_with_ff)\n",
+    "for name in reaction1_strong_EM.get_intermediate_particles().names:\n",
+    "    model_builder.dynamics.assign(name, create_relativistic_breit_wigner_with_ff)\n",
+    "model = model_builder.formulate()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],
@@ -33,7 +202,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.3"
+   "version": "3.12.4"
   }
  },
  "nbformat": 4,
diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
index 37aca79..185997f 100644
--- a/docs/all-in-one.ipynb
+++ b/docs/all-in-one.ipynb
@@ -108,23 +108,32 @@
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "8",
    "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_db[\"Delta(1232)+\"]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9",
+   "metadata": {},
    "source": [
     "For simplicity, we limit the intermediate resonances to be:\n",
     "\n",
     "\"$a(2)$\" for $\\eta \\pi^0$, \n",
     "\n",
-    "\"$\\Delta^*$\" for $\\pi^0 p$, \n",
-    "\n",
-    "\"$N^*$\" for $\\eta p$"
+    "Both \"$N*$\" for $\\pi^0 p$\n",
+    "and $\\eta p$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "10",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -134,19 +143,20 @@
     "reaction1_strong_EM = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    allowed_intermediate_particles=[\"a(2)(1320)\", \"Delta(1232)\", \"N(1535)\"],\n",
+    "    allowed_intermediate_particles=[\"a(2)(1320)\", \"N\", \"Delta\"],\n",
     "    allowed_interaction_types=[\"strong\", \"EM\"],\n",
     "    formalism=\"canonical-helicity\",\n",
     "    particle_db=particle_db,\n",
     "    max_angular_momentum=3,\n",
     "    max_spin_magnitude=3,\n",
+    "    mass_conservation_factor=0,\n",
     ")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
+   "id": "11",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -156,7 +166,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11",
+   "id": "12",
    "metadata": {},
    "source": [
     "## Build Amplitude Models"
@@ -164,7 +174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12",
+   "id": "13",
    "metadata": {},
    "source": [
     "we use ampform to formulate the transitions as an amplitude model (here: HelicityModel). "
@@ -173,7 +183,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "14",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -187,7 +197,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14",
+   "id": "15",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -199,7 +209,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15",
+   "id": "16",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -208,7 +218,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16",
+   "id": "17",
    "metadata": {},
    "source": [
     "We choose to use relativistic_breit_wigner_with_ff() as the lineshape for all resonances and use a Blatt-Weisskopf form factor (create_non_dynamic_with_ff()) for the production decay. "
@@ -217,7 +227,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17",
+   "id": "18",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -234,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18",
+   "id": "19",
    "metadata": {},
    "source": [
     "take another look at the parameters of the model to see which new parameters are there:"
@@ -243,7 +253,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19",
+   "id": "20",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -257,7 +267,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20",
+   "id": "21",
    "metadata": {},
    "source": [
     "Optionally, we can backup the HelicityModel to disk via pickle."
@@ -266,7 +276,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "21",
+   "id": "22",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -279,7 +289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22",
+   "id": "23",
    "metadata": {},
    "source": [
     "# Generate data"
@@ -288,7 +298,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "23",
+   "id": "24",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -303,7 +313,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "24",
+   "id": "25",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -318,7 +328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25",
+   "id": "26",
    "metadata": {},
    "source": [
     "## Generate phase space sample"
@@ -327,7 +337,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "26",
+   "id": "27",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -338,13 +348,13 @@
     "    initial_state_mass=reaction1_strong_EM.initial_state[-1].mass,\n",
     "    final_state_masses={i: p.mass for i, p in reaction1_strong_EM.final_state.items()},\n",
     ")\n",
-    "phsp_momenta = phsp_generator.generate(100_000, rng)"
+    "phsp_momenta = phsp_generator.generate(1_000_000, rng)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27",
+   "id": "28",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -363,7 +373,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "28",
+   "id": "29",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -376,16 +386,62 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29",
+   "id": "30",
    "metadata": {},
    "outputs": [],
    "source": [
     "p.sum(axis=0).round(decimals=14)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "31",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "E0 = p[0].T[0]\n",
+    "px0 = p[0].T[1]\n",
+    "py0 = p[0].T[2]\n",
+    "pz0 = p[0].T[3]\n",
+    "p0 = np.sqrt(px0**2 + py0**2 + pz0**2)\n",
+    "\n",
+    "E1 = p[1].T[0]\n",
+    "px1 = p[1].T[1]\n",
+    "py1 = p[1].T[2]\n",
+    "pz1 = p[1].T[3]\n",
+    "p1 = np.sqrt(px1**2 + py1**2 + pz1**2)\n",
+    "\n",
+    "E2 = p[2].T[0]\n",
+    "px2 = p[2].T[1]\n",
+    "py2 = p[2].T[2]\n",
+    "pz2 = p[2].T[3]\n",
+    "p2 = np.sqrt(px2**2 + py2**2 + pz2**2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "32",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "np.sqrt(px0**2 + py0**2 + pz0**2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "33",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "phsp_momenta"
+   ]
+  },
   {
    "cell_type": "markdown",
-   "id": "30",
+   "id": "34",
    "metadata": {},
    "source": [
     "## Generate intensity-based sample"
@@ -394,7 +450,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31",
+   "id": "35",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -411,7 +467,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "32",
+   "id": "36",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -421,7 +477,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33",
+   "id": "37",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -435,7 +491,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34",
+   "id": "38",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -453,7 +509,7 @@
     "    function=intensity_func,\n",
     "    domain_transformer=helicity_transformer,\n",
     ")\n",
-    "data_momenta = data_generator.generate(10_000, rng)\n",
+    "data_momenta = data_generator.generate(100_000, rng)\n",
     "pd.DataFrame(\n",
     "    {\n",
     "        (k, label): np.transpose(v)[i]\n",
@@ -465,7 +521,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35",
+   "id": "39",
    "metadata": {},
    "source": [
     "## Visualize kinematic variables"
@@ -474,7 +530,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36",
+   "id": "40",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -486,7 +542,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37",
+   "id": "41",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -497,7 +553,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "38",
+   "id": "42",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -511,7 +567,77 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39",
+   "id": "43",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "44",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "45",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "46",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.hist2d(phsp[\"m_01\"] ** 2, phsp[\"m_12\"] ** 2, bins=100, cmin=1)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "47",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "48",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "49",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "50",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.hist2d(data[\"m_01\"] ** 2, data[\"m_12\"] ** 2, bins=100, cmin=1)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "51",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -541,7 +667,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40",
+   "id": "52",
    "metadata": {},
    "source": [
     "## Export data sets"
@@ -550,7 +676,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "41",
+   "id": "53",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -564,7 +690,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "42",
+   "id": "54",
    "metadata": {},
    "source": [
     "# Perform fit"
@@ -573,7 +699,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "43",
+   "id": "55",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -588,7 +714,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44",
+   "id": "56",
    "metadata": {},
    "source": [
     "## Prepare parametrized function"
@@ -597,7 +723,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "45",
+   "id": "57",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -633,7 +759,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.3"
+   "version": "3.12.4"
   }
  },
  "nbformat": 4,
diff --git a/docs/index.md b/docs/index.md
index d126a3f..ff2bd0f 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -19,4 +19,5 @@ reaction
 pgamma-state
 symbolics
 all-in-one
+LamKpi
 ```
diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index def95b8..2719da2 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -640,7 +640,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.3"
+   "version": "3.12.4"
   }
  },
  "nbformat": 4,

From e9ac6a52912870ec95a1e07506fae9a1fd9da5ef Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 20 Jun 2024 15:41:09 +0200
Subject: [PATCH 24/44] fix naming error

---
 docs/LamKpi.ipynb     |  2 +-
 docs/all-in-one.ipynb | 73 ++++++++-----------------------------------
 docs/symbolics.ipynb  | 22 ++++++-------
 3 files changed, 25 insertions(+), 72 deletions(-)

diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
index 66e56a3..62aa5db 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/LamKpi.ipynb
@@ -172,7 +172,7 @@
     ")\n",
     "\n",
     "model_builder.dynamics.assign(\"pgamma\", create_non_dynamic_with_ff)\n",
-    "for name in reaction1_strong_EM.get_intermediate_particles().names:\n",
+    "for name in reaction1.get_intermediate_particles().names:\n",
     "    model_builder.dynamics.assign(name, create_relativistic_breit_wigner_with_ff)\n",
     "model = model_builder.formulate()"
    ]
diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
index 185997f..bc7b6bd 100644
--- a/docs/all-in-one.ipynb
+++ b/docs/all-in-one.ipynb
@@ -27,6 +27,7 @@
     "from IPython.display import Math\n",
     "from qrules.particle import load_pdg\n",
     "from ampform.io import aslatex, improve_latex_rendering\n",
+    "import matplotlib.pyplot as plt\n",
     "\n",
     "improve_latex_rendering()\n",
     "particle_db = load_pdg()"
@@ -143,13 +144,13 @@
     "reaction1_strong_EM = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    allowed_intermediate_particles=[\"a(2)(1320)\", \"N\", \"Delta\"],\n",
+    "    allowed_intermediate_particles=[\"a(2)(1320)\", \"N(1440)\", \"Delta(1232)\"],\n",
     "    allowed_interaction_types=[\"strong\", \"EM\"],\n",
     "    formalism=\"canonical-helicity\",\n",
     "    particle_db=particle_db,\n",
     "    max_angular_momentum=3,\n",
     "    max_spin_magnitude=3,\n",
-    "    mass_conservation_factor=0,\n",
+    "    # mass_conservation_factor=0,\n",
     ")"
    ]
   },
@@ -348,7 +349,7 @@
     "    initial_state_mass=reaction1_strong_EM.initial_state[-1].mass,\n",
     "    final_state_masses={i: p.mass for i, p in reaction1_strong_EM.final_state.items()},\n",
     ")\n",
-    "phsp_momenta = phsp_generator.generate(1_000_000, rng)"
+    "phsp_momenta = phsp_generator.generate(100_000, rng)"
    ]
   },
   {
@@ -509,7 +510,7 @@
     "    function=intensity_func,\n",
     "    domain_transformer=helicity_transformer,\n",
     ")\n",
-    "data_momenta = data_generator.generate(100_000, rng)\n",
+    "data_momenta = data_generator.generate(10_000, rng)\n",
     "pd.DataFrame(\n",
     "    {\n",
     "        (k, label): np.transpose(v)[i]\n",
@@ -570,30 +571,6 @@
    "id": "43",
    "metadata": {},
    "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "44",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "45",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "46",
-   "metadata": {},
-   "outputs": [],
    "source": [
     "plt.hist2d(phsp[\"m_01\"] ** 2, phsp[\"m_12\"] ** 2, bins=100, cmin=1)\n",
     "plt.show()"
@@ -602,31 +579,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "48",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "49",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "50",
+   "id": "44",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -637,7 +590,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "51",
+   "id": "45",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -667,7 +620,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52",
+   "id": "46",
    "metadata": {},
    "source": [
     "## Export data sets"
@@ -676,7 +629,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "53",
+   "id": "47",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -690,7 +643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54",
+   "id": "48",
    "metadata": {},
    "source": [
     "# Perform fit"
@@ -699,7 +652,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "55",
+   "id": "49",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -714,7 +667,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56",
+   "id": "50",
    "metadata": {},
    "source": [
     "## Prepare parametrized function"
@@ -723,7 +676,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57",
+   "id": "51",
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
index 2719da2..d1369d1 100644
--- a/docs/symbolics.ipynb
+++ b/docs/symbolics.ipynb
@@ -44,24 +44,24 @@
    },
    "outputs": [],
    "source": [
-    "import numpy as np\n",
     "import graphviz\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
     "import sympy as sp\n",
+    "from IPython.display import Latex, display\n",
     "from sympy import (\n",
-    "    re,\n",
-    "    im,\n",
-    "    I,\n",
     "    E,\n",
-    "    symbols,\n",
-    "    Sum,\n",
-    "    IndexedBase,\n",
     "    Function,\n",
-    "    Ynm,\n",
+    "    I,\n",
+    "    IndexedBase,\n",
+    "    Sum,\n",
     "    Symbol,\n",
+    "    Ynm,\n",
+    "    im,\n",
+    "    re,\n",
     "    simplify,\n",
-    ")\n",
-    "from IPython.display import display, Latex\n",
-    "import matplotlib.pyplot as plt"
+    "    symbols,\n",
+    ")"
    ]
   },
   {

From a390b9a86a41b3f8f2e1e5cd48b78abe6a076b00 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 20 Jun 2024 16:04:03 +0200
Subject: [PATCH 25/44] number of events

---
 docs/all-in-one.ipynb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
index bc7b6bd..17cd366 100644
--- a/docs/all-in-one.ipynb
+++ b/docs/all-in-one.ipynb
@@ -349,7 +349,7 @@
     "    initial_state_mass=reaction1_strong_EM.initial_state[-1].mass,\n",
     "    final_state_masses={i: p.mass for i, p in reaction1_strong_EM.final_state.items()},\n",
     ")\n",
-    "phsp_momenta = phsp_generator.generate(100_000, rng)"
+    "phsp_momenta = phsp_generator.generate(1_000_000, rng)"
    ]
   },
   {
@@ -510,7 +510,7 @@
     "    function=intensity_func,\n",
     "    domain_transformer=helicity_transformer,\n",
     ")\n",
-    "data_momenta = data_generator.generate(10_000, rng)\n",
+    "data_momenta = data_generator.generate(100_000, rng)\n",
     "pd.DataFrame(\n",
     "    {\n",
     "        (k, label): np.transpose(v)[i]\n",

From 187b837aa2fad96e55199a4fc0376ef190c1516d Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 20 Jun 2024 16:36:42 +0200
Subject: [PATCH 26/44] new branch for Lambda K Pi via ComPWA

---
 docs/all-in-one.ipynb | 720 ------------------------------------------
 docs/index.md         |   2 -
 docs/symbolics.ipynb  | 648 -------------------------------------
 3 files changed, 1370 deletions(-)
 delete mode 100644 docs/all-in-one.ipynb
 delete mode 100644 docs/symbolics.ipynb

diff --git a/docs/all-in-one.ipynb b/docs/all-in-one.ipynb
deleted file mode 100644
index 17cd366..0000000
--- a/docs/all-in-one.ipynb
+++ /dev/null
@@ -1,720 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0",
-   "metadata": {},
-   "source": [
-    "# Formulate Model"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1",
-   "metadata": {},
-   "source": [
-    "## Generate Transitions"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "2",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from __future__ import annotations\n",
-    "from IPython.display import Math\n",
-    "from qrules.particle import load_pdg\n",
-    "from ampform.io import aslatex, improve_latex_rendering\n",
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "improve_latex_rendering()\n",
-    "particle_db = load_pdg()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "3",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from qrules.particle import Particle, Spin\n",
-    "\n",
-    "pgamma = Particle(\n",
-    "    name=\"pgamma\",\n",
-    "    latex=r\"p\\gamma (s1/2)\",\n",
-    "    spin=0.5,\n",
-    "    mass=4.101931071854584,\n",
-    "    charge=1,\n",
-    "    isospin=Spin(1 / 2, +1 / 2),\n",
-    "    baryon_number=1,\n",
-    "    parity=-1,\n",
-    "    pid=99990,\n",
-    ")\n",
-    "pgamma"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "4",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "pgamma2 = Particle(\n",
-    "    name=\"pgamma2\",\n",
-    "    latex=R\"p\\gamma (s3/2)\",\n",
-    "    spin=1.5,\n",
-    "    mass=4.101931071854584,\n",
-    "    charge=1,\n",
-    "    isospin=Spin(1 / 2, +1 / 2),\n",
-    "    baryon_number=1,\n",
-    "    parity=-1,\n",
-    "    pid=99991,\n",
-    ")\n",
-    "pgamma2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db.add(pgamma)\n",
-    "particle_db.add(pgamma2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "6",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db[\"N(1680)+\"]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "7",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db[\"N(1650)+\"]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "8",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "particle_db[\"Delta(1232)+\"]"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "9",
-   "metadata": {},
-   "source": [
-    "For simplicity, we limit the intermediate resonances to be:\n",
-    "\n",
-    "\"$a(2)$\" for $\\eta \\pi^0$, \n",
-    "\n",
-    "Both \"$N*$\" for $\\pi^0 p$\n",
-    "and $\\eta p$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "10",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import qrules\n",
-    "import graphviz\n",
-    "\n",
-    "reaction1_strong_EM = qrules.generate_transitions(\n",
-    "    initial_state=(\"pgamma\"),\n",
-    "    final_state=[\"eta\", \"pi0\", \"p\"],\n",
-    "    allowed_intermediate_particles=[\"a(2)(1320)\", \"N(1440)\", \"Delta(1232)\"],\n",
-    "    allowed_interaction_types=[\"strong\", \"EM\"],\n",
-    "    formalism=\"canonical-helicity\",\n",
-    "    particle_db=particle_db,\n",
-    "    max_angular_momentum=3,\n",
-    "    max_spin_magnitude=3,\n",
-    "    # mass_conservation_factor=0,\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "11",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "dot_se = qrules.io.asdot(reaction1_strong_EM, collapse_graphs=True)\n",
-    "graphviz.Source(dot_se)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "12",
-   "metadata": {},
-   "source": [
-    "## Build Amplitude Models"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "13",
-   "metadata": {},
-   "source": [
-    "we use ampform to formulate the transitions as an amplitude model (here: HelicityModel). "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "14",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import ampform\n",
-    "\n",
-    "model_builder = ampform.get_builder(reaction1_strong_EM)\n",
-    "model_no_dynamics = model_builder.formulate()\n",
-    "model_no_dynamics.intensity"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "15",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from ampform.io import aslatex\n",
-    "\n",
-    "Math(aslatex(model_no_dynamics.amplitudes))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "16",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Math(aslatex(model_no_dynamics.parameter_defaults))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "17",
-   "metadata": {},
-   "source": [
-    "We choose to use relativistic_breit_wigner_with_ff() as the lineshape for all resonances and use a Blatt-Weisskopf form factor (create_non_dynamic_with_ff()) for the production decay. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "18",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from ampform.dynamics.builder import (\n",
-    "    create_non_dynamic_with_ff,\n",
-    "    create_relativistic_breit_wigner_with_ff,\n",
-    ")\n",
-    "\n",
-    "model_builder.dynamics.assign(\"pgamma\", create_non_dynamic_with_ff)\n",
-    "for name in reaction1_strong_EM.get_intermediate_particles().names:\n",
-    "    model_builder.dynamics.assign(name, create_relativistic_breit_wigner_with_ff)\n",
-    "model = model_builder.formulate()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "19",
-   "metadata": {},
-   "source": [
-    "take another look at the parameters of the model to see which new parameters are there:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "20",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "sorted_parameter_defaults = {\n",
-    "    symbol: model.parameter_defaults[symbol]\n",
-    "    for symbol in sorted(model.parameter_defaults, key=str)\n",
-    "}\n",
-    "src = aslatex(sorted_parameter_defaults)\n",
-    "Math(src)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "21",
-   "metadata": {},
-   "source": [
-    "Optionally, we can backup the HelicityModel to disk via pickle."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "22",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import pickle\n",
-    "\n",
-    "qrules.io.write(reaction1_strong_EM, \"transitions.json\")\n",
-    "with open(\"helicity_model.pickle\", \"wb\") as stream:\n",
-    "    pickle.dump(model, stream)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "23",
-   "metadata": {},
-   "source": [
-    "# Generate data"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "24",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import pickle\n",
-    "\n",
-    "from ampform.helicity import HelicityModel\n",
-    "\n",
-    "with open(\"helicity_model.pickle\", \"rb\") as model_file:\n",
-    "    imported_model: HelicityModel = pickle.load(model_file)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "25",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "initial_state, *_ = imported_model.reaction_info.initial_state.values()\n",
-    "print(\"Initial state:\")\n",
-    "print(\" \", initial_state.name)\n",
-    "print(\"Final state:\")\n",
-    "for i, p in imported_model.reaction_info.final_state.items():\n",
-    "    print(f\"  {i}: {p.name}\")\n",
-    "del initial_state"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "26",
-   "metadata": {},
-   "source": [
-    "## Generate phase space sample"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "27",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from tensorwaves.data import TFPhaseSpaceGenerator, TFUniformRealNumberGenerator\n",
-    "\n",
-    "rng = TFUniformRealNumberGenerator(seed=0)\n",
-    "phsp_generator = TFPhaseSpaceGenerator(\n",
-    "    initial_state_mass=reaction1_strong_EM.initial_state[-1].mass,\n",
-    "    final_state_masses={i: p.mass for i, p in reaction1_strong_EM.final_state.items()},\n",
-    ")\n",
-    "phsp_momenta = phsp_generator.generate(1_000_000, rng)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "28",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "import pandas as pd\n",
-    "\n",
-    "pd.DataFrame(\n",
-    "    {\n",
-    "        (k, label): np.transpose(v)[i]\n",
-    "        for k, v in phsp_momenta.items()\n",
-    "        for i, label in enumerate([\"E\", \"px\", \"py\", \"pz\"])\n",
-    "    }\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "29",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "p = np.array(list(phsp_momenta.values()))\n",
-    "p.shape"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "30",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "p.sum(axis=0).round(decimals=14)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "31",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "E0 = p[0].T[0]\n",
-    "px0 = p[0].T[1]\n",
-    "py0 = p[0].T[2]\n",
-    "pz0 = p[0].T[3]\n",
-    "p0 = np.sqrt(px0**2 + py0**2 + pz0**2)\n",
-    "\n",
-    "E1 = p[1].T[0]\n",
-    "px1 = p[1].T[1]\n",
-    "py1 = p[1].T[2]\n",
-    "pz1 = p[1].T[3]\n",
-    "p1 = np.sqrt(px1**2 + py1**2 + pz1**2)\n",
-    "\n",
-    "E2 = p[2].T[0]\n",
-    "px2 = p[2].T[1]\n",
-    "py2 = p[2].T[2]\n",
-    "pz2 = p[2].T[3]\n",
-    "p2 = np.sqrt(px2**2 + py2**2 + pz2**2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "32",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "np.sqrt(px0**2 + py0**2 + pz0**2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "33",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "phsp_momenta"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "34",
-   "metadata": {},
-   "source": [
-    "## Generate intensity-based sample"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "35",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from tensorwaves.function.sympy import create_parametrized_function\n",
-    "\n",
-    "unfolded_expression = model.expression.doit()\n",
-    "intensity_func = create_parametrized_function(\n",
-    "    expression=unfolded_expression,\n",
-    "    parameters=model.parameter_defaults,\n",
-    "    backend=\"numpy\",\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "36",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Math(aslatex(model.kinematic_variables))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "37",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from tensorwaves.data import SympyDataTransformer\n",
-    "\n",
-    "helicity_transformer = SympyDataTransformer.from_sympy(\n",
-    "    model.kinematic_variables, backend=\"jax\"\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "38",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from tensorwaves.data import (\n",
-    "    IntensityDistributionGenerator,\n",
-    "    TFWeightedPhaseSpaceGenerator,\n",
-    ")\n",
-    "\n",
-    "weighted_phsp_generator = TFWeightedPhaseSpaceGenerator(\n",
-    "    initial_state_mass=reaction1_strong_EM.initial_state[-1].mass,\n",
-    "    final_state_masses={i: p.mass for i, p in reaction1_strong_EM.final_state.items()},\n",
-    ")\n",
-    "data_generator = IntensityDistributionGenerator(\n",
-    "    domain_generator=weighted_phsp_generator,\n",
-    "    function=intensity_func,\n",
-    "    domain_transformer=helicity_transformer,\n",
-    ")\n",
-    "data_momenta = data_generator.generate(100_000, rng)\n",
-    "pd.DataFrame(\n",
-    "    {\n",
-    "        (k, label): np.transpose(v)[i]\n",
-    "        for k, v in data_momenta.items()\n",
-    "        for i, label in enumerate([\"E\", \"px\", \"py\", \"pz\"])\n",
-    "    }\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "39",
-   "metadata": {},
-   "source": [
-    "## Visualize kinematic variables"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "40",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "phsp = helicity_transformer(phsp_momenta)\n",
-    "data = helicity_transformer(data_momenta)\n",
-    "list(data)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "41",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "for state_id, particle in reaction1_strong_EM.final_state.items():\n",
-    "    print(f\"ID {state_id}:\", particle.name)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "42",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import pandas as pd\n",
-    "\n",
-    "data_frame = pd.DataFrame(data)\n",
-    "phsp_frame = pd.DataFrame(phsp)\n",
-    "data_frame"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "43",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.hist2d(phsp[\"m_01\"] ** 2, phsp[\"m_12\"] ** 2, bins=100, cmin=1)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "44",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.hist2d(data[\"m_01\"] ** 2, data[\"m_12\"] ** 2, bins=100, cmin=1)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "45",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "%config InlineBackend.figure_formats = ['svg']\n",
-    "\n",
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "resonances = sorted(\n",
-    "    reaction1_strong_EM.get_intermediate_particles(),\n",
-    "    key=lambda p: p.mass,\n",
-    ")\n",
-    "evenly_spaced_interval = np.linspace(0, 1, len(resonances))\n",
-    "colors = [plt.cm.rainbow(x) for x in evenly_spaced_interval]\n",
-    "fig, ax = plt.subplots(figsize=(9, 4))\n",
-    "ax.hist(\n",
-    "    np.real(data_frame[\"m_12\"]),\n",
-    "    bins=100,\n",
-    "    alpha=0.5,\n",
-    "    density=True,\n",
-    ")\n",
-    "ax.set_xlabel(\"$m$ [GeV]\")\n",
-    "for p, color in zip(resonances, colors):\n",
-    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
-    "ax.legend()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "46",
-   "metadata": {},
-   "source": [
-    "## Export data sets"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "47",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import pickle\n",
-    "\n",
-    "with open(\"data.pickle\", \"wb\") as stream:\n",
-    "    pickle.dump(data, stream)\n",
-    "with open(\"phsp.pickle\", \"wb\") as stream:\n",
-    "    pickle.dump(phsp, stream)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "48",
-   "metadata": {},
-   "source": [
-    "# Perform fit"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "49",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "reaction = qrules.io.load(\"transitions.json\")\n",
-    "with open(\"helicity_model.pickle\", \"rb\") as stream:\n",
-    "    model: HelicityModel = pickle.load(stream)\n",
-    "with open(\"data.pickle\", \"rb\") as stream:\n",
-    "    data = pickle.load(stream)\n",
-    "with open(\"phsp.pickle\", \"rb\") as stream:\n",
-    "    phsp = pickle.load(stream)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "50",
-   "metadata": {},
-   "source": [
-    "## Prepare parametrized function"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "51",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# initial_parameters = {\n",
-    "#     R\"C_{p\\gamma \\to {f_{0}(1500)}_{0} \\gamma_{+1}; f_{0}(1500) \\to  \\eta \\pi^{0} p}\": (\n",
-    "#         1.0 + 0.0j\n",
-    "#     ),\n",
-    "#     \"m_{f_{0}(500)}\": 0.4,\n",
-    "#     \"m_{f_{0}(980)}\": 0.88,\n",
-    "#     \"m_{f_{0}(1370)}\": 1.22,\n",
-    "#     \"m_{f_{0}(1500)}\": 1.45,\n",
-    "#     \"m_{f_{0}(1710)}\": 1.83,\n",
-    "#     R\"\\Gamma_{f_{0}(500)}\": 0.3,\n",
-    "#     R\"\\Gamma_{f_{0}(980)}\": 0.1,\n",
-    "#     R\"\\Gamma_{f_{0}(1710)}\": 0.3,\n",
-    "# }"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.4"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/docs/index.md b/docs/index.md
index ff2bd0f..0eaf3c8 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -17,7 +17,5 @@ address to the issue ✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/g
 ```{toctree}
 reaction
 pgamma-state
-symbolics
-all-in-one
 LamKpi
 ```
diff --git a/docs/symbolics.ipynb b/docs/symbolics.ipynb
deleted file mode 100644
index d1369d1..0000000
--- a/docs/symbolics.ipynb
+++ /dev/null
@@ -1,648 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "0",
-   "metadata": {},
-   "source": [
-    "# Symbolic expression for the amplitude model"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "1",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "$$\n",
-    "\\begin{eqnarray}\n",
-    "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s_{12}-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n",
-    "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s_{23}-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}}  \\\\\n",
-    "\\\n",
-    "A^{31} &=& \\frac{c_0}{s_{31}-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}}\n",
-    "\\end{eqnarray}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "2",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": [
-     "hide-cell"
-    ]
-   },
-   "outputs": [],
-   "source": [
-    "import graphviz\n",
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "import sympy as sp\n",
-    "from IPython.display import Latex, display\n",
-    "from sympy import (\n",
-    "    E,\n",
-    "    Function,\n",
-    "    I,\n",
-    "    IndexedBase,\n",
-    "    Sum,\n",
-    "    Symbol,\n",
-    "    Ynm,\n",
-    "    im,\n",
-    "    re,\n",
-    "    simplify,\n",
-    "    symbols,\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "3",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "# $A^{12}$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "4",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "newa = IndexedBase(\"a\")\n",
-    "type(newa[0])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "s12, m_a2, Gamma_a2 = symbols(r\"s_{12} m_{a_2} \\Gamma_{a_2}\")\n",
-    "theta1, phi1 = symbols(\"theta_1 phi_1\")\n",
-    "# Ynm(l, m, theta, phi)\n",
-    "a = IndexedBase(\"a\")\n",
-    "# Y2_m = Function(\"Y_2^m\")(\"Omega_1\")\n",
-    "m = symbols(\"m\", cls=sp.Idx)\n",
-    "# Omega1 = symbols(\"Omega_1\")\n",
-    "\n",
-    "A12 = sp.Sum(a[m] * Ynm(2, m, theta1, phi1), (m, -2, 2)) / (\n",
-    "    s12 - m_a2**2 + I * m_a2 * Gamma_a2\n",
-    ")\n",
-    "A12"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "6",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Ynm(2, 1, 1, 1).expand(func=False)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "7",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Ynm(2, 1, 1, 1).expand(func=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "8",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "A12.free_symbols"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "9",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "A12_func = sp.lambdify(\n",
-    "    [s12, a[-2], a[-1], a[0], a[1], a[2], m_a2, Gamma_a2, theta1, phi1],\n",
-    "    A12.doit().expand(func=True),\n",
-    ")\n",
-    "A12_func"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "10",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Example values\n",
-    "m_a2_val = 1.32\n",
-    "Gamma_a2_val = 0.1\n",
-    "a_vals = [0, 0.5, 3.5, 4, 2.5]\n",
-    "\n",
-    "# Generate s values\n",
-    "s_values = np.linspace(0, 5, 100)\n",
-    "PHI = np.pi / 4\n",
-    "THETA = np.pi / 4\n",
-    "A12_values = A12_func(s_values, *a_vals, m_a2_val, Gamma_a2_val, THETA, PHI)\n",
-    "\n",
-    "# Create the plot\n",
-    "plt.figure(figsize=(10, 6))\n",
-    "\n",
-    "plt.plot(s_values, A12_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
-    "plt.plot(s_values, A12_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "plt.plot(s_values, np.abs(A12_values) ** 2, label=\"|A12|^2\", linestyle=\"-.\", color=\"g\")\n",
-    "plt.plot(\n",
-    "    s_values, np.angle(A12_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
-    ")\n",
-    "\n",
-    "plt.xlabel(\"s\")\n",
-    "plt.ylabel(r\"$A^{12}$ components\")\n",
-    "plt.title(r\"Components of $A^{12}$ vs s at 45 degree\")\n",
-    "plt.legend()\n",
-    "# plt.grid(True)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "11",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.plot(A12_values.real, A12_values.imag)\n",
-    "plt.title(r\"Argand diagram of $A^{12}$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "12",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Example values\n",
-    "m_a2_val = 1.5\n",
-    "Gamma_a2_val = 0.6\n",
-    "a_vals = [1, 2, 3, 4, 5]\n",
-    "\n",
-    "# Generate s values\n",
-    "s_values = np.linspace(0, 5, 100)\n",
-    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
-    "# THETA = np.linspace(0, np.pi, num=100)\n",
-    "\n",
-    "PHI, THETA = np.meshgrid(\n",
-    "    np.linspace(-np.pi, +np.pi, num=100),\n",
-    "    np.linspace(0, np.pi, num=100),\n",
-    ")\n",
-    "A12_Angles_values = A12_func(s_values, *a_vals, m_a2_val, Gamma_a2_val, THETA, PHI)\n",
-    "\n",
-    "# Create the plot\n",
-    "plt.figure(figsize=(10, 6))\n",
-    "\n",
-    "plt.plot(\n",
-    "    s_values, A12_Angles_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\"\n",
-    ")\n",
-    "plt.plot(s_values, A12_Angles_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "plt.plot(\n",
-    "    s_values, np.abs(A12_Angles_values) ** 2, label=\"|A12|^2\", linestyle=\"-.\", color=\"g\"\n",
-    ")\n",
-    "plt.plot(\n",
-    "    s_values,\n",
-    "    np.angle(A12_Angles_values),\n",
-    "    label=\"Phase (angle)\",\n",
-    "    linestyle=\":\",\n",
-    "    color=\"m\",\n",
-    ")\n",
-    "\n",
-    "plt.xlabel(\"s\")\n",
-    "plt.ylabel(r\"$A^{12}$ components\")\n",
-    "plt.title(r\"Components of $A^{12}$ vs s\")\n",
-    "# plt.legend()\n",
-    "# plt.grid(True)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "13",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.plot(A12_Angles_values.real, A12_Angles_values.imag)\n",
-    "plt.title(r\"Argand diagram of $A^{12}$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "14",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "# $A^{23}$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "15",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "s23, m_Delta, Gamma_Delta = symbols(\"s_{23} m_Delta Gamma_Delta\")\n",
-    "b = IndexedBase(\"b\")\n",
-    "m = symbols(\"m\", cls=sp.Idx)\n",
-    "\n",
-    "Y1_m = Function(\"Y_1^m\")(\"Omega_2\")\n",
-    "theta2, phi2 = symbols(\"theta_2 phi_2\")\n",
-    "A23 = Sum(b[m] * Ynm(1, m, theta2, phi2), (m, -1, 1)) / (\n",
-    "    s23 - m_Delta**2 + I * m_Delta * Gamma_Delta\n",
-    ")\n",
-    "A23"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "16",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "A23.free_symbols"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "17",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "A23_func = sp.lambdify(\n",
-    "    [s23, b[-1], b[0], b[1], m_Delta, Gamma_Delta, theta2, phi2],\n",
-    "    A23.doit().expand(func=True),\n",
-    ")\n",
-    "A23_func"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "18",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Example values\n",
-    "m_Delta_val = 1.54\n",
-    "Gamma_Delta_val = 0.1\n",
-    "b_vals = [-1.5, 4, 0.5]\n",
-    "\n",
-    "# Generate s values\n",
-    "s_values = np.linspace(0, 5, 100)\n",
-    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
-    "# THETA = np.linspace(0, np.pi, num=100)\n",
-    "PHI = np.pi / 4\n",
-    "THETA = np.pi / 4\n",
-    "\n",
-    "A23_values = A23_func(s_values, *b_vals, m_Delta_val, Gamma_Delta_val, THETA, PHI)\n",
-    "\n",
-    "# Create the plot\n",
-    "plt.figure(figsize=(10, 6))\n",
-    "\n",
-    "plt.plot(s_values, A23_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
-    "plt.plot(s_values, A23_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "plt.plot(s_values, np.abs(A23_values) ** 2, label=\"|A23|^2\", linestyle=\"-.\", color=\"g\")\n",
-    "plt.plot(\n",
-    "    s_values, np.angle(A23_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
-    ")\n",
-    "\n",
-    "plt.xlabel(\"s\")\n",
-    "plt.ylabel(r\"$A^{23}$ components\")\n",
-    "plt.title(r\"Components of $A^{23}$ vs s at 45 degree\")\n",
-    "plt.legend()\n",
-    "# plt.grid(True)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "19",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.plot(A23_values.real, A23_values.imag)\n",
-    "plt.title(r\"Argand diagram of $A^{23}$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "20",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Example values\n",
-    "m_Delta_val = 1.54\n",
-    "Gamma_Delta_val = 0.1\n",
-    "b_vals = [-1.5, 4, 0.5]\n",
-    "\n",
-    "# Generate s values\n",
-    "s_values = np.linspace(0, 5, 100)\n",
-    "# PHI = np.linspace(-np.pi, +np.pi, num=100)\n",
-    "# THETA = np.linspace(0, np.pi, num=100)\n",
-    "\n",
-    "PHI, THETA = np.meshgrid(\n",
-    "    np.linspace(-np.pi, +np.pi, num=100),\n",
-    "    np.linspace(0, np.pi, num=100),\n",
-    ")\n",
-    "A23_Angles_values = A23_func(\n",
-    "    s_values, *b_vals, m_Delta_val, Gamma_Delta_val, THETA, PHI\n",
-    ")\n",
-    "\n",
-    "# Create the plot\n",
-    "plt.figure(figsize=(10, 6))\n",
-    "\n",
-    "plt.plot(\n",
-    "    s_values, A23_Angles_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\"\n",
-    ")\n",
-    "plt.plot(s_values, A23_Angles_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "# plt.plot(s_values, np.abs(A23_values) ** 2, label=\"|A23|^2\", linestyle=\"-.\", color=\"g\")\n",
-    "plt.plot(\n",
-    "    s_values,\n",
-    "    np.angle(A23_Angles_values),\n",
-    "    label=\"Phase (angle)\",\n",
-    "    linestyle=\":\",\n",
-    "    color=\"m\",\n",
-    ")\n",
-    "\n",
-    "plt.xlabel(\"s\")\n",
-    "plt.ylabel(r\"$A^{23}$ components\")\n",
-    "plt.title(r\"Components of $A^{23}$ vs s\")\n",
-    "# plt.legend()\n",
-    "# plt.grid(True)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "21",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.figure(figsize=(10, 6))\n",
-    "plt.plot(\n",
-    "    s_values, np.abs(A23_Angles_values) ** 2, label=\"|A23|^2\", linestyle=\"-.\", color=\"g\"\n",
-    ")\n",
-    "plt.xlabel(\"s\")\n",
-    "plt.ylabel(r\"$A^{23}$ components\")\n",
-    "plt.title(r\"Components of $A^{23}$ vs s\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "22",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.plot(A23_Angles_values.real, A23_Angles_values.imag)\n",
-    "plt.title(r\"Argand diagram of $A^{23}$\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "23",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "# $A^{31}$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "24",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "s31, c0, m_Nstar, Gamma_Nstar = symbols(r\"s_{31} c_0 m_{N^*} \\Gamma_{N^*}\")\n",
-    "A31 = c0 / (s31 - m_Nstar**2 + I * m_Nstar * Gamma_Nstar)\n",
-    "A31"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "25",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "A31.free_symbols"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "26",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "sp.lambdify([s31, c0, m_Nstar, Gamma_Nstar], A31)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "27",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "A31_func = sp.lambdify([s31, c0, m_Nstar, Gamma_Nstar], A31)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "28",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "# Example values for m_Nstar and Gamma_Nstar\n",
-    "m_Nstar_val = 1.87\n",
-    "Gamma_Nstar_val = 0.1\n",
-    "c0_val = 2.5\n",
-    "\n",
-    "# Generate s values\n",
-    "s_values = np.linspace(0, 5, 100)\n",
-    "A31_values = A31_func(s_values, c0_val, m_Nstar_val, Gamma_Nstar_val)\n",
-    "\n",
-    "# Create the plot\n",
-    "plt.figure(figsize=(10, 6))\n",
-    "\n",
-    "plt.plot(s_values, A31_values.imag, label=\"Imaginary Part\", linestyle=\"-\", color=\"b\")\n",
-    "plt.plot(s_values, A31_values.real, label=\"Real Part\", linestyle=\"--\", color=\"r\")\n",
-    "plt.plot(s_values, np.abs(A31_values) ** 2, label=\"|A31|^2\", linestyle=\"-.\", color=\"g\")\n",
-    "plt.plot(\n",
-    "    s_values, np.angle(A31_values), label=\"Phase (angle)\", linestyle=\":\", color=\"m\"\n",
-    ")\n",
-    "\n",
-    "plt.xlabel(\"s\")\n",
-    "plt.ylabel(r\"$A^{31}$ components\")\n",
-    "plt.title(r\"Components of $A^{31}$ vs s\")\n",
-    "plt.legend()\n",
-    "# plt.grid(True)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "29",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "plt.plot(A31_values.real, A31_values.imag)\n",
-    "plt.title(r\"Argand diagram of $A^{31}$\")\n",
-    "plt.show()"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.12.4"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}

From 5794adfff5906f6d2d7b3c1665b58aec998516a9 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 20 Jun 2024 17:05:05 +0200
Subject: [PATCH 27/44] Add document title

---
 docs/LamKpi.ipynb | 34 +++++++++++++++++++++-------------
 1 file changed, 21 insertions(+), 13 deletions(-)

diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
index 62aa5db..452a2a0 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/LamKpi.ipynb
@@ -5,13 +5,21 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "$p \\gamma \\to K^+ \\pi^0 \\Lambda$"
+    "# PWA for pγ → ΛK⁺π⁰ via `ComPWA`"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1",
+   "metadata": {},
+   "source": [
+    "PWA study on $p \\gamma \\to K^+ \\pi^0 \\Lambda$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1",
+   "id": "2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -27,7 +35,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2",
+   "id": "3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -50,7 +58,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3",
+   "id": "4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -71,7 +79,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4",
+   "id": "5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -82,7 +90,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5",
+   "id": "6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -105,7 +113,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
+   "id": "7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -115,7 +123,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7",
+   "id": "8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -126,7 +134,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
+   "id": "9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -140,7 +148,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
+   "id": "10",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -152,7 +160,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
+   "id": "11",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -162,7 +170,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
+   "id": "12",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -180,7 +188,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "13",
    "metadata": {},
    "outputs": [],
    "source": []

From 88b58022a6be48857a71ad5b0162eeecf4311d1d Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Mon, 24 Jun 2024 12:29:30 +0200
Subject: [PATCH 28/44] resolve pixi.lock conflict

---
 pixi.lock | 527 +++++++++++++++++++++++++++---------------------------
 1 file changed, 259 insertions(+), 268 deletions(-)

diff --git a/pixi.lock b/pixi.lock
index 9c524b7..19af638 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -37,7 +37,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/ca-certificates-2024.6.2-hbcca054_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/cached-property-1.5.2-hd8ed1ab_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/cached_property-1.5.2-pyha770c72_1.tar.bz2
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/cairo-1.18.0-h3faef2a_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/cairo-1.18.0-hbb29018_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/certifi-2024.6.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/cffi-1.16.0-py312hf06ca03_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/cfgv-3.3.1-pyhd8ed1ab_0.tar.bz2
@@ -64,7 +64,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/exceptiongroup-1.2.0-pyhd8ed1ab_2.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/executing-2.0.1-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/expat-2.6.2-h59595ed_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/filelock-3.15.1-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/filelock-3.15.4-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/flake8-7.0.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/flatbuffers-24.3.25-h59595ed_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/font-ttf-dejavu-sans-mono-2.37-hab24e00_0.tar.bz2
@@ -87,15 +87,15 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/glib-2.80.2-h8a4344b_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/glib-tools-2.80.2-h73ef956_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/gmp-6.3.0-h59595ed_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/gmp-6.3.0-hac33072_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gmpy2-2.1.5-py312h1d5cde6_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/google-pasta-0.2.0-pyh8c360ce_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/graphite2-1.3.13-h59595ed_1003.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/graphviz-9.0.0-h78e8752_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/greenlet-3.0.3-py312h30efb56_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/grpcio-1.62.2-py312hb06c811_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/gst-plugins-base-1.24.4-h9ad1361_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/gstreamer-1.24.4-haf2f30d_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/gst-plugins-base-1.24.5-hbaaba92_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/gstreamer-1.24.5-haf2f30d_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gtk2-2.24.33-h280cfa0_4.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gts-0.7.6-h977cf35_4.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/h11-0.14.0-pyhd8ed1ab_0.tar.bz2
@@ -113,8 +113,8 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/idna-3.7-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/imagesize-1.4.1-pyhd8ed1ab_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/iminuit-2.25.2-py312h30efb56_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/importlib-metadata-7.1.0-pyha770c72_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/importlib_metadata-7.1.0-hd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/importlib-metadata-7.2.1-pyha770c72_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/importlib_metadata-7.2.1-hd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/importlib_resources-6.4.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipykernel-6.29.4-pyh3099207_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/ipython-8.25.0-pyh707e725_0.conda
@@ -168,7 +168,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcap-2.69-h0f662aa_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcblas-3.9.0-22_linux64_openblas.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang-cpp15-15.0.7-default_h127d8a8_5.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang13-18.1.7-default_h087397f_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libclang13-18.1.8-default_h6ae225f_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcups-2.3.3-h4637d8d_4.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libcurl-8.8.0-hca28451_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libdeflate-1.20-hd590300_0.conda
@@ -178,22 +178,22 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/libffi-3.4.2-h7f98852_5.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libflac-1.4.3-h59595ed_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgcc-ng-13.2.0-h77fa898_10.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgcc-ng-13.2.0-h77fa898_13.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgcrypt-1.10.3-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgd-2.3.3-h119a65a_9.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgettextpo-0.22.5-h59595ed_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgettextpo-devel-0.22.5-h59595ed_2.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgfortran-ng-13.2.0-h69a702a_10.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgfortran5-13.2.0-h3d2ce59_10.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgfortran-ng-13.2.0-h69a702a_13.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgfortran5-13.2.0-h3d2ce59_13.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libglib-2.80.2-h8a4344b_1.conda
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+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libgomp-13.2.0-h77fa898_13.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgpg-error-1.49-h4f305b6_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libgrpc-1.62.2-h15f2491_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libiconv-1.17-hd590300_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libjpeg-turbo-3.0.0-hd590300_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/liblapack-3.9.0-22_linux64_openblas.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm15-15.0.7-hb3ce162_4.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm18-18.1.7-hc9dba70_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libllvm18-18.1.8-hc9dba70_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libnghttp2-1.58.0-h47da74e_1.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/libogg-1.3.4-h7f98852_1.tar.bz2
@@ -208,19 +208,19 @@ environments:
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/libsqlite-3.46.0-hde9e2c9_0.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libstdcxx-ng-13.2.0-hc0a3c3a_10.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libstdcxx-ng-13.2.0-hc0a3c3a_13.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libsystemd0-255-h3516f8a_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libtiff-4.6.0-h1dd3fc0_3.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/libvorbis-1.3.7-h9c3ff4c_0.tar.bz2
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libxkbcommon-1.7.0-h662e7e4_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libxkbcommon-1.7.0-h2c5496b_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libxml2-2.12.7-hc051c1a_1.conda
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-      - conda: https://conda.anaconda.org/conda-forge/noarch/livereload-2.6.3-pyh9f0ad1d_0.tar.bz2
+      - conda: https://conda.anaconda.org/conda-forge/noarch/livereload-2.7.0-pyhd8ed1ab_0.conda
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@@ -277,7 +277,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/pillow-10.3.0-py312hdcec9eb_0.conda
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@@ -324,7 +324,7 @@ environments:
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@@ -338,7 +338,7 @@ environments:
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@@ -390,7 +390,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/xorg-libx11-1.8.9-h8ee46fc_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/xorg-libxau-1.0.11-hd590300_0.conda
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       - conda: https://conda.anaconda.org/conda-forge/linux-64/xorg-libxext-1.3.4-h0b41bf4_2.conda
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   name: cairo
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-  build: h3faef2a_0
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-  md5: f907bb958910dc404647326ca80c263e
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-  - libzlib >=1.2.13,<2.0.0a0
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   - xorg-libsm >=1.2.4,<2.0a0
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   timestamp: 1713390905173
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   name: gst-plugins-base
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-  build: h9ad1361_0
+  version: 1.24.5
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-  md5: 147cce520ec59367549fd0d96d404213
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+  version: 18.1.8
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   license: Apache-2.0 WITH LLVM-exception
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   license_family: MIT
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-  timestamp: 1682082368177
+  size: 394932
+  timestamp: 1693088990429
 - kind: conda
   name: libxcrypt
   version: 4.4.36
@@ -4138,22 +4134,23 @@ packages:
 - kind: conda
   name: libxkbcommon
   version: 1.7.0
-  build: h662e7e4_0
+  build: h2c5496b_1
+  build_number: 1
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/libxkbcommon-1.7.0-h662e7e4_0.conda
-  sha256: 3d97d7f964237f42452295d461afdbc51e93f72e2c80be516f56de80e3bb6621
-  md5: b32c0da42b1f24a98577bb3d7fc0b995
+  url: https://conda.anaconda.org/conda-forge/linux-64/libxkbcommon-1.7.0-h2c5496b_1.conda
+  sha256: 6804c2a7062d10de6f159f7106dc45ebccc8d42bfb925f7919e26e567fa6da6b
+  md5: e2eaefa4de2b7237af7c907b8bbc760a
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   - libstdcxx-ng >=12
-  - libxcb >=1.15,<1.16.0a0
-  - libxml2 >=2.12.6,<3.0a0
+  - libxcb >=1.16,<1.17.0a0
+  - libxml2 >=2.12.7,<3.0a0
   - xkeyboard-config
   - xorg-libxau >=1.0.11,<2.0a0
   license: MIT/X11 Derivative
   license_family: MIT
-  size: 593534
-  timestamp: 1711303445595
+  size: 593336
+  timestamp: 1718819935698
 - kind: conda
   name: libxml2
   version: 2.12.7
@@ -4192,22 +4189,19 @@ packages:
   timestamp: 1716874187109
 - kind: conda
   name: livereload
-  version: 2.6.3
-  build: pyh9f0ad1d_0
+  version: 2.7.0
+  build: pyhd8ed1ab_0
   subdir: noarch
   noarch: python
-  url: https://conda.anaconda.org/conda-forge/noarch/livereload-2.6.3-pyh9f0ad1d_0.tar.bz2
-  sha256: 0e88f8f8abc0a641c2f3b1b306258fab87c39a95f3495e53e6b3873107da1765
-  md5: b7190e3ec3eff52839434bf4698e2d62
+  url: https://conda.anaconda.org/conda-forge/noarch/livereload-2.7.0-pyhd8ed1ab_0.conda
+  sha256: 9c2cd37b052996cc3f787f9caae74d9a2b616c48c6e1f27796680cb882c45bfc
+  md5: c6aa475c46f6bdd203841dd8525f3b91
   depends:
-  - python
-  - setuptools
-  - six
+  - python >=3.7
   - tornado
   license: BSD-3-Clause
-  license_family: BSD
-  size: 24973
-  timestamp: 1598114846810
+  size: 25951
+  timestamp: 1719215280117
 - kind: conda
   name: lz4-c
   version: 1.9.4
@@ -5199,27 +5193,28 @@ packages:
 - kind: conda
   name: pillow
   version: 10.3.0
-  build: py312hdcec9eb_0
+  build: py312h287a98d_1
+  build_number: 1
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/pillow-10.3.0-py312hdcec9eb_0.conda
-  sha256: a7fdcc1e56b66d95622bad073cc8d347cc180988040419754abb2a4ed7b29471
-  md5: 425bb325f970e57a047ac57c4586489d
+  url: https://conda.anaconda.org/conda-forge/linux-64/pillow-10.3.0-py312h287a98d_1.conda
+  sha256: e1a2426f23535fc15e577d799685229a93117b645734e5cca60597bb23cef09e
+  md5: b1325cda3f250f9f842180607054e6ed
   depends:
   - freetype >=2.12.1,<3.0a0
   - lcms2 >=2.16,<3.0a0
   - libgcc-ng >=12
   - libjpeg-turbo >=3.0.0,<4.0a0
   - libtiff >=4.6.0,<4.7.0a0
-  - libwebp-base >=1.3.2,<2.0a0
-  - libxcb >=1.15,<1.16.0a0
-  - libzlib >=1.2.13,<2.0.0a0
+  - libwebp-base >=1.4.0,<2.0a0
+  - libxcb >=1.16,<1.17.0a0
+  - libzlib >=1.3.1,<2.0a0
   - openjpeg >=2.5.2,<3.0a0
   - python >=3.12,<3.13.0a0
   - python_abi 3.12.* *_cp312
   - tk >=8.6.13,<8.7.0a0
   license: HPND
-  size: 41991755
-  timestamp: 1712154634705
+  size: 41702764
+  timestamp: 1718833930009
 - kind: conda
   name: pixman
   version: 0.43.2
@@ -6027,22 +6022,22 @@ packages:
 - kind: conda
   name: qt-main
   version: 5.15.8
-  build: hc9dc06e_21
-  build_number: 21
+  build: ha2b5568_22
+  build_number: 22
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/qt-main-5.15.8-hc9dc06e_21.conda
-  sha256: 6b4594f6f2fad65a7ed52993f602e3ab183193755fe4a492aaa48e463b23105b
-  md5: b325046180590c868ce0dbf267b82eb8
+  url: https://conda.anaconda.org/conda-forge/linux-64/qt-main-5.15.8-ha2b5568_22.conda
+  sha256: e621b4445b08c353cd754e8b1e529ed6d27b53d23629064e504727225e291017
+  md5: 15de976572f24032540236006d6d0e9f
   depends:
   - __glibc >=2.17,<3.0.a0
-  - alsa-lib >=1.2.11,<1.3.0a0
+  - alsa-lib >=1.2.12,<1.3.0a0
   - dbus >=1.13.6,<2.0a0
   - fontconfig >=2.14.2,<3.0a0
   - fonts-conda-ecosystem
   - freetype >=2.12.1,<3.0a0
-  - gst-plugins-base >=1.24.1,<1.25.0a0
-  - gstreamer >=1.24.1,<1.25.0a0
-  - harfbuzz >=8.3.0,<9.0a0
+  - gst-plugins-base >=1.24.5,<1.25.0a0
+  - gstreamer >=1.24.5,<1.25.0a0
+  - harfbuzz >=8.5.0,<9.0a0
   - icu >=73.2,<74.0a0
   - krb5 >=1.21.2,<1.22.0a0
   - libclang-cpp15 >=15.0.7,<15.1.0a0
@@ -6051,39 +6046,39 @@ packages:
   - libevent >=2.1.12,<2.1.13.0a0
   - libexpat >=2.6.2,<3.0a0
   - libgcc-ng >=12
-  - libglib >=2.80.0,<3.0a0
+  - libglib >=2.80.2,<3.0a0
   - libjpeg-turbo >=3.0.0,<4.0a0
   - libllvm15 >=15.0.7,<15.1.0a0
   - libpng >=1.6.43,<1.7.0a0
-  - libpq >=16.2,<17.0a0
-  - libsqlite >=3.45.2,<4.0a0
+  - libpq >=16.3,<17.0a0
+  - libsqlite >=3.46.0,<4.0a0
   - libstdcxx-ng >=12
-  - libxcb >=1.15,<1.16.0a0
+  - libxcb >=1.16,<1.17.0a0
   - libxkbcommon >=1.7.0,<2.0a0
-  - libxml2 >=2.12.6,<3.0a0
-  - libzlib >=1.2.13,<2.0.0a0
+  - libxml2 >=2.12.7,<3.0a0
+  - libzlib >=1.3.1,<2.0a0
   - mysql-libs >=8.3.0,<8.4.0a0
   - nspr >=4.35,<5.0a0
-  - nss >=3.98,<4.0a0
-  - openssl >=3.2.1,<4.0a0
+  - nss >=3.101,<4.0a0
+  - openssl >=3.3.1,<4.0a0
   - pulseaudio-client >=17.0,<17.1.0a0
-  - xcb-util >=0.4.0,<0.5.0a0
+  - xcb-util >=0.4.1,<0.5.0a0
   - xcb-util-image >=0.4.0,<0.5.0a0
-  - xcb-util-keysyms >=0.4.0,<0.5.0a0
-  - xcb-util-renderutil >=0.3.9,<0.4.0a0
-  - xcb-util-wm >=0.4.1,<0.5.0a0
+  - xcb-util-keysyms >=0.4.1,<0.5.0a0
+  - xcb-util-renderutil >=0.3.10,<0.4.0a0
+  - xcb-util-wm >=0.4.2,<0.5.0a0
   - xorg-libice >=1.1.1,<2.0a0
   - xorg-libsm >=1.2.4,<2.0a0
   - xorg-libx11 >=1.8.9,<2.0a0
   - xorg-libxext >=1.3.4,<2.0a0
   - xorg-xf86vidmodeproto
-  - zstd >=1.5.5,<1.6.0a0
+  - zstd >=1.5.6,<1.6.0a0
   constrains:
   - qt 5.15.8
   license: LGPL-3.0-only
   license_family: LGPL
-  size: 61305384
-  timestamp: 1712549380352
+  size: 61406677
+  timestamp: 1719032641557
 - kind: conda
   name: qtconsole-base
   version: 5.5.2
@@ -6314,19 +6309,19 @@ packages:
   timestamp: 1712585140895
 - kind: conda
   name: setuptools
-  version: 70.0.0
+  version: 70.1.0
   build: pyhd8ed1ab_0
   subdir: noarch
   noarch: python
-  url: https://conda.anaconda.org/conda-forge/noarch/setuptools-70.0.0-pyhd8ed1ab_0.conda
-  sha256: daa4638d288cfdf3b0ecea395d8efa25cafc4ebf4026464a36c797c84541d2be
-  md5: c8ddb4f34a208df4dd42509a0f6a1c89
+  url: https://conda.anaconda.org/conda-forge/noarch/setuptools-70.1.0-pyhd8ed1ab_0.conda
+  sha256: a43d33436f4ac57ebd6ee15f700b33b26a2d37b7e43981b1fa036908579dafd6
+  md5: 258e66f95f814d51ada2a1fe9274039b
   depends:
   - python >=3.8
   license: MIT
   license_family: MIT
-  size: 483015
-  timestamp: 1716368141661
+  size: 495951
+  timestamp: 1718881009207
 - kind: conda
   name: singledispatchmethod
   version: '1.0'
@@ -6636,6 +6631,7 @@ packages:
   - python_abi 3.12.* *_cp312
   - typing-extensions >=4.6.0
   license: MIT
+  license_family: MIT
   size: 3494447
   timestamp: 1718781304578
 - kind: conda
@@ -7238,22 +7234,21 @@ packages:
   timestamp: 1718033105021
 - kind: conda
   name: virtualenv
-  version: 20.26.2
+  version: 20.26.3
   build: pyhd8ed1ab_0
   subdir: noarch
   noarch: python
-  url: https://conda.anaconda.org/conda-forge/noarch/virtualenv-20.26.2-pyhd8ed1ab_0.conda
-  sha256: 1eefd180723fb2fd295352323b53777eeae5765b24d62ae75fc9f1e71b455f11
-  md5: 7d36e7a485ea2f5829408813bdbbfb38
+  url: https://conda.anaconda.org/conda-forge/noarch/virtualenv-20.26.3-pyhd8ed1ab_0.conda
+  sha256: f78961b194e33eed5fdccb668774651ec9423a043069fa7a4e3e2f853b08aa0c
+  md5: 284008712816c64c85bf2b7fa9f3b264
   depends:
   - distlib <1,>=0.3.7
   - filelock <4,>=3.12.2
   - platformdirs <5,>=3.9.1
   - python >=3.8
   license: MIT
-  license_family: MIT
-  size: 3458445
-  timestamp: 1715681264937
+  size: 4363507
+  timestamp: 1719150878323
 - kind: conda
   name: watchfiles
   version: 0.22.0
@@ -7412,87 +7407,82 @@ packages:
   timestamp: 1699532968076
 - kind: conda
   name: xcb-util
-  version: 0.4.0
-  build: hd590300_1
-  build_number: 1
+  version: 0.4.1
+  build: hb711507_2
+  build_number: 2
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-0.4.0-hd590300_1.conda
-  sha256: 0c91d87f0efdaadd4e56a5f024f8aab20ec30f90aa2ce9e4ebea05fbc20f71ad
-  md5: 9bfac7ccd94d54fd21a0501296d60424
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-0.4.1-hb711507_2.conda
+  sha256: 416aa55d946ce4ab173ab338796564893a2f820e80e04e098ff00c25fb981263
+  md5: 8637c3e5821654d0edf97e2b0404b443
   depends:
   - libgcc-ng >=12
-  - libxcb >=1.13
-  - libxcb >=1.15,<1.16.0a0
+  - libxcb >=1.16,<1.17.0a0
   license: MIT
   license_family: MIT
-  size: 19728
-  timestamp: 1684639166048
+  size: 19965
+  timestamp: 1718843348208
 - kind: conda
   name: xcb-util-image
   version: 0.4.0
-  build: h8ee46fc_1
-  build_number: 1
+  build: hb711507_2
+  build_number: 2
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-image-0.4.0-h8ee46fc_1.conda
-  sha256: 92ffd68d2801dbc27afe223e04ae7e78ef605fc8575f107113c93c7bafbd15b0
-  md5: 9d7bcddf49cbf727730af10e71022c73
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-image-0.4.0-hb711507_2.conda
+  sha256: 94b12ff8b30260d9de4fd7a28cca12e028e572cbc504fd42aa2646ec4a5bded7
+  md5: a0901183f08b6c7107aab109733a3c91
   depends:
   - libgcc-ng >=12
-  - libxcb >=1.15,<1.16.0a0
-  - xcb-util >=0.4.0,<0.5.0a0
+  - libxcb >=1.16,<1.17.0a0
+  - xcb-util >=0.4.1,<0.5.0a0
   license: MIT
   license_family: MIT
-  size: 24474
-  timestamp: 1684679894554
+  size: 24551
+  timestamp: 1718880534789
 - kind: conda
   name: xcb-util-keysyms
-  version: 0.4.0
-  build: h8ee46fc_1
-  build_number: 1
+  version: 0.4.1
+  build: hb711507_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-keysyms-0.4.0-h8ee46fc_1.conda
-  sha256: 8451d92f25d6054a941b962179180728c48c62aab5bf20ac10fef713d5da6a9a
-  md5: 632413adcd8bc16b515cab87a2932913
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-keysyms-0.4.1-hb711507_0.conda
+  sha256: 546e3ee01e95a4c884b6401284bb22da449a2f4daf508d038fdfa0712fe4cc69
+  md5: ad748ccca349aec3e91743e08b5e2b50
   depends:
   - libgcc-ng >=12
-  - libxcb >=1.15,<1.16.0a0
+  - libxcb >=1.16,<1.17.0a0
   license: MIT
   license_family: MIT
-  size: 14186
-  timestamp: 1684680497805
+  size: 14314
+  timestamp: 1718846569232
 - kind: conda
   name: xcb-util-renderutil
-  version: 0.3.9
-  build: hd590300_1
-  build_number: 1
+  version: 0.3.10
+  build: hb711507_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-renderutil-0.3.9-hd590300_1.conda
-  sha256: 6987588e6fff5892056021c2ea52f7a0deefb2c7348e70d24750e2d60dabf009
-  md5: e995b155d938b6779da6ace6c6b13816
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-renderutil-0.3.10-hb711507_0.conda
+  sha256: 2d401dadc43855971ce008344a4b5bd804aca9487d8ebd83328592217daca3df
+  md5: 0e0cbe0564d03a99afd5fd7b362feecd
   depends:
   - libgcc-ng >=12
-  - libxcb >=1.13
-  - libxcb >=1.15,<1.16.0a0
+  - libxcb >=1.16,<1.17.0a0
   license: MIT
   license_family: MIT
-  size: 16955
-  timestamp: 1684639112393
+  size: 16978
+  timestamp: 1718848865819
 - kind: conda
   name: xcb-util-wm
-  version: 0.4.1
-  build: h8ee46fc_1
-  build_number: 1
+  version: 0.4.2
+  build: hb711507_0
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-wm-0.4.1-h8ee46fc_1.conda
-  sha256: 08ba7147c7579249b6efd33397dc1a8c2404278053165aaecd39280fee705724
-  md5: 90108a432fb5c6150ccfee3f03388656
+  url: https://conda.anaconda.org/conda-forge/linux-64/xcb-util-wm-0.4.2-hb711507_0.conda
+  sha256: 31d44f297ad87a1e6510895740325a635dd204556aa7e079194a0034cdd7e66a
+  md5: 608e0ef8256b81d04456e8d211eee3e8
   depends:
   - libgcc-ng >=12
-  - libxcb >=1.15,<1.16.0a0
+  - libxcb >=1.16,<1.17.0a0
   license: MIT
   license_family: MIT
-  size: 52114
-  timestamp: 1684679248466
+  size: 51689
+  timestamp: 1718844051451
 - kind: conda
   name: xkeyboard-config
   version: '2.42'
@@ -7556,21 +7546,22 @@ packages:
 - kind: conda
   name: xorg-libx11
   version: 1.8.9
-  build: h8ee46fc_0
+  build: hb711507_1
+  build_number: 1
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/xorg-libx11-1.8.9-h8ee46fc_0.conda
-  sha256: 3e53ba247f1ad68353f18aceba5bf8ce87e3dea930de85d36946844a7658c9fb
-  md5: 077b6e8ad6a3ddb741fce2496dd01bec
+  url: https://conda.anaconda.org/conda-forge/linux-64/xorg-libx11-1.8.9-hb711507_1.conda
+  sha256: 66eabe62b66c1597c4a755dcd3f4ce2c78adaf7b32e25dfee45504d67d7735c1
+  md5: 4a6d410296d7e39f00bacdee7df046e9
   depends:
   - libgcc-ng >=12
-  - libxcb >=1.15,<1.16.0a0
+  - libxcb >=1.16,<1.17.0a0
   - xorg-kbproto
   - xorg-xextproto >=7.3.0,<8.0a0
   - xorg-xproto
   license: MIT
   license_family: MIT
-  size: 828060
-  timestamp: 1712415742569
+  size: 832198
+  timestamp: 1718846846409
 - kind: conda
   name: xorg-libxau
   version: 1.0.11

From 228d59b8228e7fabcd6990c7159e941ed60101b5 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Tue, 25 Jun 2024 19:24:51 +0200
Subject: [PATCH 29/44] Add Dalitz plot

---
 docs/LamKpi.ipynb | 622 +++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 589 insertions(+), 33 deletions(-)

diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
index 452a2a0..b2e9080 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/LamKpi.ipynb
@@ -3,7 +3,13 @@
   {
    "cell_type": "markdown",
    "id": "0",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "# PWA for pγ → ΛK⁺π⁰ via `ComPWA`"
    ]
@@ -11,7 +17,13 @@
   {
    "cell_type": "markdown",
    "id": "1",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "PWA study on $p \\gamma \\to K^+ \\pi^0 \\Lambda$"
    ]
@@ -20,23 +32,158 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "2",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "from __future__ import annotations\n",
     "from IPython.display import Math\n",
     "from qrules.particle import load_pdg\n",
     "from ampform.io import aslatex, improve_latex_rendering\n",
+    "import matplotlib.pyplot as plt\n",
     "\n",
     "improve_latex_rendering()\n",
     "particle_db = load_pdg()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "3",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "## Inital and final state"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "### Check existing particles in `PDG`"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3",
-   "metadata": {},
+   "id": "5",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db[\"Lambda\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db[\"K+\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db[\"pi0\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db[\"gamma\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "particle_db[\"p\"]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "10",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "### Add custom particle for initial state"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "11",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "from qrules.particle import Particle, Spin\n",
@@ -58,8 +205,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4",
-   "metadata": {},
+   "id": "12",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "pgamma2 = Particle(\n",
@@ -79,19 +232,45 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5",
-   "metadata": {},
+   "id": "13",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "particle_db.add(pgamma)\n",
     "particle_db.add(pgamma2)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "14",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "### Generate Transitions"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
-   "metadata": {},
+   "id": "15",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "import qrules\n",
@@ -113,55 +292,131 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7",
-   "metadata": {},
+   "id": "16",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
-    "particle_db[\"Lambda\"]"
+    "dot_se = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
+    "graphviz.Source(dot_se)"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "8",
-   "metadata": {},
-   "outputs": [],
+   "cell_type": "markdown",
+   "id": "17",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "dot_se = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
-    "graphviz.Source(dot_se)"
+    "## Build Helicity Amplitude Models"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "### Intensity"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
-   "metadata": {},
+   "id": "19",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "import ampform\n",
     "\n",
     "model_builder = ampform.get_builder(reaction1)\n",
+    "model_builder.config.scalar_initial_state_mass = True\n",
+    "model_builder.config.stable_final_state_ids = 0, 1, 2\n",
     "model_no_dynamics = model_builder.formulate()\n",
     "model_no_dynamics.intensity"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "20",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "### Amplitudes"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10",
-   "metadata": {},
+   "id": "21",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
-    "from ampform.io import aslatex\n",
-    "\n",
     "Math(aslatex(model_no_dynamics.amplitudes))"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "22",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "### Parameters"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
-   "metadata": {},
+   "id": "23",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "Math(aslatex(model_no_dynamics.parameter_defaults))"
@@ -170,7 +425,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "24",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -185,13 +440,314 @@
     "model = model_builder.formulate()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "25",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "## Reaction Info"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
-   "metadata": {},
+   "id": "26",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
-   "source": []
+   "source": [
+    "initial_state, *_ = model.reaction_info.initial_state.values()\n",
+    "print(\"Initial state:\")\n",
+    "print(\"-1: \", initial_state.name)\n",
+    "print(\"Final state:\")\n",
+    "for i, p in model.reaction_info.final_state.items():\n",
+    "    print(f\"  {i}: {p.name}\")\n",
+    "del initial_state"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "27",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "## Generate phase space sample"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "28",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "phsp_event = 1_000_000\n",
+    "from tensorwaves.data import TFPhaseSpaceGenerator, TFUniformRealNumberGenerator\n",
+    "\n",
+    "rng = TFUniformRealNumberGenerator(seed=0)\n",
+    "phsp_generator = TFPhaseSpaceGenerator(\n",
+    "    initial_state_mass=reaction1.initial_state[-1].mass,\n",
+    "    final_state_masses={i: p.mass for i, p in reaction1.final_state.items()},\n",
+    ")\n",
+    "phsp_momenta = phsp_generator.generate(phsp_event, rng)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "29",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "\n",
+    "pd.DataFrame(\n",
+    "    {\n",
+    "        (k, label): np.transpose(v)[i]\n",
+    "        for k, v in phsp_momenta.items()\n",
+    "        for i, label in enumerate([\"E\", \"px\", \"py\", \"pz\"])\n",
+    "    }\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "30",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "## Visualize kinematic variables"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "31",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "from tensorwaves.function.sympy import create_parametrized_function\n",
+    "\n",
+    "unfolded_expression = model.expression.doit()\n",
+    "intensity_func = create_parametrized_function(\n",
+    "    expression=unfolded_expression,\n",
+    "    parameters=model.parameter_defaults,\n",
+    "    backend=\"numpy\",\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "32",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "Math(aslatex(model.kinematic_variables))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "33",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "from tensorwaves.data import SympyDataTransformer\n",
+    "\n",
+    "helicity_transformer = SympyDataTransformer.from_sympy(\n",
+    "    model.kinematic_variables, backend=\"jax\"\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "34",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "phsp = helicity_transformer(phsp_momenta)\n",
+    "list(phsp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "35",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "for state_id, particle in reaction1.final_state.items():\n",
+    "    print(f\"ID {state_id}:\", particle.name)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "36",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "\n",
+    "phsp_frame = pd.DataFrame(phsp)\n",
+    "phsp_frame"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "37",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "## Visualize model and intensity-based sample"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "38",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_formats = ['png']\n",
+    "fig, ax = plt.subplots()\n",
+    "hist = ax.hist2d(\n",
+    "    phsp[\"m_01\"].real ** 2,\n",
+    "    phsp[\"m_12\"].real ** 2,\n",
+    "    bins=200,\n",
+    "    cmin=1e-6,\n",
+    "    density=True,\n",
+    "    cmap=\"jet\",\n",
+    "    # vmax=0.15,\n",
+    ")\n",
+    "ax.set_title(\"Phase Space Dalitz Plot\")\n",
+    "ax.set_xlabel(R\"$m^2(\\Lambda K^+)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax.set_ylabel(R\"$m^2(K^+ \\pi^0)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "cbar = fig.colorbar(hist[3], ax=ax)\n",
+    "fig.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "39",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "# %config InlineBackend.figure_formats = ['png']\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "hist = ax.hist2d(\n",
+    "    phsp[\"m_01\"].real ** 2,\n",
+    "    phsp[\"m_12\"].real ** 2,\n",
+    "    bins=200,\n",
+    "    cmin=1e-6,\n",
+    "    density=True,\n",
+    "    cmap=\"jet\",\n",
+    "    vmax=0.15,\n",
+    "    weights=intensity_func(phsp),\n",
+    ")\n",
+    "ax.set_title(\"Model-weighted Phase space Dalitz Plot\")\n",
+    "ax.set_xlabel(R\"$m^2(\\Lambda K^+)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax.set_ylabel(R\"$m^2(K^+ \\pi^0)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "cbar = fig.colorbar(hist[3], ax=ax)\n",
+    "fig.tight_layout()\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {

From f62148c11b886cfcdd23915556881cffb830c492 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Wed, 26 Jun 2024 12:47:34 +0200
Subject: [PATCH 30/44] full-width

---
 docs/LamKpi.ipynb | 56 ++++++++++++++++++++++++++++++++++++-----------
 1 file changed, 43 insertions(+), 13 deletions(-)

diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
index b2e9080..e5b6d5f 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/LamKpi.ipynb
@@ -25,7 +25,7 @@
     "tags": []
    },
    "source": [
-    "PWA study on $p \\gamma \\to K^+ \\pi^0 \\Lambda$"
+    "PWA study on $p \\gamma \\to \\Lambda K^+ \\pi^0 $"
    ]
   },
   {
@@ -376,13 +376,12 @@
    "id": "21",
    "metadata": {
     "editable": true,
-    "jupyter": {
-     "outputs_hidden": true
-    },
     "slideshow": {
      "slide_type": ""
     },
-    "tags": []
+    "tags": [
+     "full-width"
+    ]
    },
    "outputs": [],
    "source": [
@@ -409,9 +408,6 @@
    "id": "23",
    "metadata": {
     "editable": true,
-    "jupyter": {
-     "outputs_hidden": true
-    },
     "slideshow": {
      "slide_type": ""
     },
@@ -523,7 +519,9 @@
     "slideshow": {
      "slide_type": ""
     },
-    "tags": []
+    "tags": [
+     "full-width"
+    ]
    },
    "outputs": [],
    "source": [
@@ -655,7 +653,9 @@
     "slideshow": {
      "slide_type": ""
     },
-    "tags": []
+    "tags": [
+     "full-width"
+    ]
    },
    "outputs": [],
    "source": [
@@ -683,13 +683,28 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "38",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "39",
    "metadata": {
     "editable": true,
     "slideshow": {
      "slide_type": ""
     },
     "tags": [
-     "hide-input"
+     "hide-input",
+     "full-width"
     ]
    },
    "outputs": [],
@@ -716,14 +731,15 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39",
+   "id": "40",
    "metadata": {
     "editable": true,
     "slideshow": {
      "slide_type": ""
     },
     "tags": [
-     "hide-input"
+     "hide-input",
+     "full-width"
     ]
    },
    "outputs": [],
@@ -748,6 +764,20 @@
     "fig.tight_layout()\n",
     "plt.show()"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "41",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

From 47167ad01b2d7fc4051462b21741294ac26e3aab Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 27 Jun 2024 16:16:05 +0200
Subject: [PATCH 31/44] Add the l and pz to 4

---
 docs/LamKpi.ipynb | 225 +++++++++++++++++++++++++++++++++++++---------
 1 file changed, 181 insertions(+), 44 deletions(-)

diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
index e5b6d5f..050f633 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/LamKpi.ipynb
@@ -46,6 +46,7 @@
     "from qrules.particle import load_pdg\n",
     "from ampform.io import aslatex, improve_latex_rendering\n",
     "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
     "\n",
     "improve_latex_rendering()\n",
     "particle_db = load_pdg()"
@@ -70,6 +71,7 @@
    "id": "4",
    "metadata": {
     "editable": true,
+    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -164,6 +166,7 @@
    "id": "10",
    "metadata": {
     "editable": true,
+    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -177,6 +180,22 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "11",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "E_lab_gamma = 8.5\n",
+    "# E_lab_gamma = 5\n",
+    "m_proton = 0.938\n",
+    "m_0 = np.sqrt(2 * E_lab_gamma * m_proton + m_proton**2)\n",
+    "m_eta = 0.548\n",
+    "m_pi = 0.135\n",
+    "m_0"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "12",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -192,7 +211,7 @@
     "    name=\"pgamma\",\n",
     "    latex=r\"p\\gamma (s1/2)\",\n",
     "    spin=0.5,\n",
-    "    mass=4.101931071854584,\n",
+    "    mass=m_0,\n",
     "    charge=1,\n",
     "    isospin=Spin(1 / 2, +1 / 2),\n",
     "    baryon_number=1,\n",
@@ -205,7 +224,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
+   "id": "13",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -219,7 +238,7 @@
     "    name=\"pgamma2\",\n",
     "    latex=R\"p\\gamma (s3/2)\",\n",
     "    spin=1.5,\n",
-    "    mass=4.101931071854584,\n",
+    "    mass=m_0,\n",
     "    charge=1,\n",
     "    isospin=Spin(1 / 2, +1 / 2),\n",
     "    baryon_number=1,\n",
@@ -232,7 +251,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
+   "id": "14",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -248,7 +267,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14",
+   "id": "15",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -263,7 +282,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15",
+   "id": "16",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -282,9 +301,10 @@
     "    # allowed_intermediate_particles=[\"a(2)(1320)\",\"N\",\"Delta\"],\n",
     "    allowed_interaction_types=[\"strong\"],\n",
     "    formalism=\"canonical-helicity\",\n",
+    "    # formalism=\"helicity\",\n",
     "    particle_db=particle_db,\n",
-    "    max_angular_momentum=3,\n",
-    "    max_spin_magnitude=3,\n",
+    "    max_angular_momentum=4,\n",
+    "    max_spin_magnitude=4,\n",
     "    mass_conservation_factor=0,\n",
     ")"
    ]
@@ -292,7 +312,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
+   "id": "17",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -308,9 +328,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17",
+   "id": "18",
    "metadata": {
     "editable": true,
+    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -322,7 +343,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18",
+   "id": "19",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -337,7 +358,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19",
+   "id": "20",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -358,7 +379,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20",
+   "id": "21",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -373,7 +394,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "21",
+   "id": "22",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -390,7 +411,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22",
+   "id": "23",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -405,7 +426,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "23",
+   "id": "24",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -421,7 +442,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "24",
+   "id": "25",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -438,9 +459,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25",
+   "id": "26",
    "metadata": {
     "editable": true,
+    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -453,7 +475,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "26",
+   "id": "27",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -474,9 +496,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27",
+   "id": "28",
    "metadata": {
     "editable": true,
+    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -489,7 +512,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "28",
+   "id": "29",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -499,7 +522,7 @@
    },
    "outputs": [],
    "source": [
-    "phsp_event = 1_000_000\n",
+    "phsp_event = 500_000\n",
     "from tensorwaves.data import TFPhaseSpaceGenerator, TFUniformRealNumberGenerator\n",
     "\n",
     "rng = TFUniformRealNumberGenerator(seed=0)\n",
@@ -513,7 +536,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29",
+   "id": "30",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -539,9 +562,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30",
+   "id": "31",
    "metadata": {
     "editable": true,
+    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -554,7 +578,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31",
+   "id": "32",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -577,7 +601,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "32",
+   "id": "33",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -593,7 +617,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33",
+   "id": "34",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -613,7 +637,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34",
+   "id": "35",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -630,7 +654,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "35",
+   "id": "36",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -647,7 +671,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36",
+   "id": "37",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -667,7 +691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37",
+   "id": "38",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -682,23 +706,139 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "38",
+   "id": "39",
    "metadata": {
     "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
     "slideshow": {
      "slide_type": ""
     },
-    "tags": []
+    "tags": [
+     "full-width",
+     "hide-input"
+    ]
    },
    "outputs": [],
-   "source": []
+   "source": [
+    "%config InlineBackend.figure_formats = ['svg']\n",
+    "\n",
+    "resonances = sorted(\n",
+    "    reaction1.get_intermediate_particles(),\n",
+    "    key=lambda p: p.mass,\n",
+    ")\n",
+    "evenly_spaced_interval = np.linspace(0, 1, len(resonances))\n",
+    "colors = [plt.cm.rainbow(x) for x in evenly_spaced_interval]\n",
+    "fig, ax = plt.subplots(figsize=(10, 6))\n",
+    "ax.hist(\n",
+    "    np.real(phsp_frame[\"m_01\"]),\n",
+    "    bins=100,\n",
+    "    alpha=0.5,\n",
+    "    density=True,\n",
+    "    color=\"orange\",\n",
+    "    # color = colors[1],\n",
+    "    label=\"Weighted PHSP\",\n",
+    "    weights=intensity_func(phsp),\n",
+    ")\n",
+    "ax.set_xlabel(R\"$m(\\Lambda K^+)\\;\\left[\\mathrm{GeV}^2\\right]$ [GeV]\")\n",
+    "N_stars = [p for p in resonances if \"N\" in p.name]\n",
+    "for p, color in zip(N_stars, colors):\n",
+    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
+    "ax.legend()\n",
+    "plt.show()"
+   ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39",
+   "id": "40",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "full-width",
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_formats = ['svg']\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(10, 6))\n",
+    "\n",
+    "ax.hist(\n",
+    "    np.real(phsp_frame[\"m_12\"]),\n",
+    "    bins=100,\n",
+    "    alpha=0.5,\n",
+    "    density=True,\n",
+    "    color=\"yellow\",\n",
+    "    label=\"Weighted PHSP\",\n",
+    "    weights=intensity_func(phsp),\n",
+    ")\n",
+    "\n",
+    "ax.set_xlabel(R\"$m(K^+ \\pi^0)$ [GeV]\")\n",
+    "\n",
+    "K_stars = [p for p in resonances if \"K\" in p.name]\n",
+    "for p, color in zip(K_stars, colors):\n",
+    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
+    "ax.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "41",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "full-width",
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "%config InlineBackend.figure_formats = ['svg']\n",
+    "\n",
+    "fig, ax = plt.subplots(figsize=(10, 6))\n",
+    "ax.hist(\n",
+    "    np.real(phsp_frame[\"m_02\"]),\n",
+    "    bins=100,\n",
+    "    alpha=0.5,\n",
+    "    density=True,\n",
+    "    color=\"red\",\n",
+    "    label=\"Weighted PHSP\",\n",
+    "    weights=intensity_func(phsp),\n",
+    ")\n",
+    "ax.set_xlabel(R\"$m(\\Lambda \\pi^0)$ [GeV]\")\n",
+    "Sigma_stars = [p for p in resonances if \"Sigma\" in p.name]\n",
+    "for p, color in zip(Sigma_stars, colors):\n",
+    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
+    "ax.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "42",
    "metadata": {
     "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
     "slideshow": {
      "slide_type": ""
     },
@@ -731,9 +871,12 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "40",
+   "id": "43",
    "metadata": {
     "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
     "slideshow": {
      "slide_type": ""
     },
@@ -768,14 +911,8 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "41",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "id": "44",
+   "metadata": {},
    "outputs": [],
    "source": []
   }

From 46e862452c531a7b53e3a56d3521c71a49b5b771 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 4 Jul 2024 17:07:20 +0200
Subject: [PATCH 32/44] hide full amplitude model expression

---
 docs/LamKpi.ipynb | 77 ++++++++++++++++++++++++++++++-----------------
 1 file changed, 50 insertions(+), 27 deletions(-)

diff --git a/docs/LamKpi.ipynb b/docs/LamKpi.ipynb
index 050f633..19df9b8 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/LamKpi.ipynb
@@ -71,7 +71,6 @@
    "id": "4",
    "metadata": {
     "editable": true,
-    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -166,7 +165,6 @@
    "id": "10",
    "metadata": {
     "editable": true,
-    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -331,7 +329,6 @@
    "id": "18",
    "metadata": {
     "editable": true,
-    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -391,17 +388,43 @@
     "### Amplitudes"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "22",
+   "metadata": {},
+   "source": [
+    "The first term in the amplitude model:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "22",
+   "id": "23",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ampform.io import aslatex\n",
+    "\n",
+    "(symbol, expr), *_ = model.amplitudes.items()\n",
+    "Math(aslatex({symbol: expr}, terms_per_line=1))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "24",
    "metadata": {
     "editable": true,
+    "mystnb": {
+     "code_prompt_show": "Full expression of the amplitude model (It takes long time to render)"
+    },
     "slideshow": {
      "slide_type": ""
     },
     "tags": [
-     "full-width"
+     "full-width",
+     "hide-input",
+     "hide-output"
     ]
    },
    "outputs": [],
@@ -411,7 +434,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23",
+   "id": "25",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -426,7 +449,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "24",
+   "id": "26",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -442,7 +465,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "25",
+   "id": "27",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -459,7 +482,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26",
+   "id": "28",
    "metadata": {
     "editable": true,
     "jp-MarkdownHeadingCollapsed": true,
@@ -475,7 +498,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27",
+   "id": "29",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -496,7 +519,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28",
+   "id": "30",
    "metadata": {
     "editable": true,
     "jp-MarkdownHeadingCollapsed": true,
@@ -512,7 +535,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29",
+   "id": "31",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -536,7 +559,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "30",
+   "id": "32",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -562,7 +585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31",
+   "id": "33",
    "metadata": {
     "editable": true,
     "jp-MarkdownHeadingCollapsed": true,
@@ -578,7 +601,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "32",
+   "id": "34",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -601,7 +624,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33",
+   "id": "35",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -617,7 +640,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34",
+   "id": "36",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -637,7 +660,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "35",
+   "id": "37",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -654,7 +677,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36",
+   "id": "38",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -671,7 +694,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37",
+   "id": "39",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -691,7 +714,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38",
+   "id": "40",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -706,7 +729,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39",
+   "id": "41",
    "metadata": {
     "editable": true,
     "jupyter": {
@@ -752,7 +775,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "40",
+   "id": "42",
    "metadata": {
     "editable": true,
     "jupyter": {
@@ -794,7 +817,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "41",
+   "id": "43",
    "metadata": {
     "editable": true,
     "jupyter": {
@@ -833,7 +856,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42",
+   "id": "44",
    "metadata": {
     "editable": true,
     "jupyter": {
@@ -871,7 +894,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "43",
+   "id": "45",
    "metadata": {
     "editable": true,
     "jupyter": {
@@ -911,7 +934,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "44",
+   "id": "46",
    "metadata": {},
    "outputs": [],
    "source": []

From 3cce4caeff47107d8dd7de6d1006281ce68425e3 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Thu, 11 Jul 2024 16:11:12 +0200
Subject: [PATCH 33/44] showing only first term of model

---
 docs/{ => ampform}/LamKpi.ipynb | 134 +++++++++++++++++++-------------
 docs/index.md                   |   2 +-
 2 files changed, 80 insertions(+), 56 deletions(-)
 rename docs/{ => ampform}/LamKpi.ipynb (91%)

diff --git a/docs/LamKpi.ipynb b/docs/ampform/LamKpi.ipynb
similarity index 91%
rename from docs/LamKpi.ipynb
rename to docs/ampform/LamKpi.ipynb
index 19df9b8..ac8e9bc 100644
--- a/docs/LamKpi.ipynb
+++ b/docs/ampform/LamKpi.ipynb
@@ -42,11 +42,23 @@
    "outputs": [],
    "source": [
     "from __future__ import annotations\n",
-    "from IPython.display import Math\n",
-    "from qrules.particle import load_pdg\n",
-    "from ampform.io import aslatex, improve_latex_rendering\n",
+    "\n",
+    "import ampform\n",
+    "import graphviz\n",
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
+    "import pandas as pd\n",
+    "import qrules\n",
+    "from ampform.dynamics.builder import RelativisticBreitWignerBuilder\n",
+    "from ampform.io import aslatex, improve_latex_rendering\n",
+    "from IPython.display import Math\n",
+    "from qrules.particle import Particle, Spin, load_pdg\n",
+    "from tensorwaves.data import (\n",
+    "    SympyDataTransformer,\n",
+    "    TFPhaseSpaceGenerator,\n",
+    "    TFUniformRealNumberGenerator,\n",
+    ")\n",
+    "from tensorwaves.function.sympy import create_parametrized_function\n",
     "\n",
     "improve_latex_rendering()\n",
     "particle_db = load_pdg()"
@@ -178,7 +190,13 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "11",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "E_lab_gamma = 8.5\n",
@@ -203,8 +221,6 @@
    },
    "outputs": [],
    "source": [
-    "from qrules.particle import Particle, Spin\n",
-    "\n",
     "pgamma = Particle(\n",
     "    name=\"pgamma\",\n",
     "    latex=r\"p\\gamma (s1/2)\",\n",
@@ -290,10 +306,7 @@
    },
    "outputs": [],
    "source": [
-    "import qrules\n",
-    "import graphviz\n",
-    "\n",
-    "reaction1 = qrules.generate_transitions(\n",
+    "reaction = qrules.generate_transitions(\n",
     "    initial_state=(\"pgamma\"),\n",
     "    final_state=[\"Lambda\", \"K+\", \"pi0\"],\n",
     "    # allowed_intermediate_particles=[\"a(2)(1320)\",\"N\",\"Delta\"],\n",
@@ -320,7 +333,7 @@
    },
    "outputs": [],
    "source": [
-    "dot_se = qrules.io.asdot(reaction1, collapse_graphs=True)\n",
+    "dot_se = qrules.io.asdot(reaction, collapse_graphs=True)\n",
     "graphviz.Source(dot_se)"
    ]
   },
@@ -339,7 +352,8 @@
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "19",
    "metadata": {
     "editable": true,
@@ -348,13 +362,24 @@
     },
     "tags": []
    },
+   "outputs": [],
    "source": [
-    "### Intensity"
+    "model_builder = ampform.get_builder(reaction)\n",
+    "model_builder.config.scalar_initial_state_mass = True\n",
+    "model_builder.config.stable_final_state_ids = 0, 1, 2\n",
+    "\n",
+    "bw_builder = RelativisticBreitWignerBuilder(\n",
+    "    energy_dependent_width=False,\n",
+    "    form_factor=False,\n",
+    ")\n",
+    "\n",
+    "for name in reaction.get_intermediate_particles().names:\n",
+    "    model_builder.dynamics.assign(name, bw_builder)\n",
+    "model = model_builder.formulate()"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "id": "20",
    "metadata": {
     "editable": true,
@@ -363,19 +388,13 @@
     },
     "tags": []
    },
-   "outputs": [],
    "source": [
-    "import ampform\n",
-    "\n",
-    "model_builder = ampform.get_builder(reaction1)\n",
-    "model_builder.config.scalar_initial_state_mass = True\n",
-    "model_builder.config.stable_final_state_ids = 0, 1, 2\n",
-    "model_no_dynamics = model_builder.formulate()\n",
-    "model_no_dynamics.intensity"
+    "### Intensity"
    ]
   },
   {
-   "cell_type": "markdown",
+   "cell_type": "code",
+   "execution_count": null,
    "id": "21",
    "metadata": {
     "editable": true,
@@ -384,29 +403,37 @@
     },
     "tags": []
    },
+   "outputs": [],
    "source": [
-    "### Amplitudes"
+    "model_no_dynamics.intensity"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "22",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "The first term in the amplitude model:"
+    "### Amplitudes"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "id": "23",
-   "metadata": {},
-   "outputs": [],
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "from ampform.io import aslatex\n",
-    "\n",
-    "(symbol, expr), *_ = model.amplitudes.items()\n",
-    "Math(aslatex({symbol: expr}, terms_per_line=1))"
+    "The first term in the amplitude model:"
    ]
   },
   {
@@ -415,21 +442,17 @@
    "id": "24",
    "metadata": {
     "editable": true,
-    "mystnb": {
-     "code_prompt_show": "Full expression of the amplitude model (It takes long time to render)"
-    },
     "slideshow": {
      "slide_type": ""
     },
-    "tags": [
-     "full-width",
-     "hide-input",
-     "hide-output"
-    ]
+    "tags": []
    },
    "outputs": [],
    "source": [
-    "Math(aslatex(model_no_dynamics.amplitudes))"
+    "from ampform.io import aslatex\n",
+    "\n",
+    "(symbol, expr), *_ = model.amplitudes.items()\n",
+    "Math(aslatex({symbol: expr}, terms_per_line=1))"
    ]
   },
   {
@@ -466,7 +489,13 @@
    "cell_type": "code",
    "execution_count": null,
    "id": "27",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "outputs": [],
    "source": [
     "from ampform.dynamics.builder import (\n",
@@ -475,7 +504,7 @@
     ")\n",
     "\n",
     "model_builder.dynamics.assign(\"pgamma\", create_non_dynamic_with_ff)\n",
-    "for name in reaction1.get_intermediate_particles().names:\n",
+    "for name in reaction.get_intermediate_particles().names:\n",
     "    model_builder.dynamics.assign(name, create_relativistic_breit_wigner_with_ff)\n",
     "model = model_builder.formulate()"
    ]
@@ -522,7 +551,6 @@
    "id": "30",
    "metadata": {
     "editable": true,
-    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -550,8 +578,8 @@
     "\n",
     "rng = TFUniformRealNumberGenerator(seed=0)\n",
     "phsp_generator = TFPhaseSpaceGenerator(\n",
-    "    initial_state_mass=reaction1.initial_state[-1].mass,\n",
-    "    final_state_masses={i: p.mass for i, p in reaction1.final_state.items()},\n",
+    "    initial_state_mass=reaction.initial_state[-1].mass,\n",
+    "    final_state_masses={i: p.mass for i, p in reaction.final_state.items()},\n",
     ")\n",
     "phsp_momenta = phsp_generator.generate(phsp_event, rng)"
    ]
@@ -588,7 +616,6 @@
    "id": "33",
    "metadata": {
     "editable": true,
-    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -687,7 +714,7 @@
    },
    "outputs": [],
    "source": [
-    "for state_id, particle in reaction1.final_state.items():\n",
+    "for state_id, particle in reaction.final_state.items():\n",
     "    print(f\"ID {state_id}:\", particle.name)"
    ]
   },
@@ -732,9 +759,6 @@
    "id": "41",
    "metadata": {
     "editable": true,
-    "jupyter": {
-     "source_hidden": true
-    },
     "slideshow": {
      "slide_type": ""
     },
@@ -748,7 +772,7 @@
     "%config InlineBackend.figure_formats = ['svg']\n",
     "\n",
     "resonances = sorted(\n",
-    "    reaction1.get_intermediate_particles(),\n",
+    "    reaction.get_intermediate_particles(),\n",
     "    key=lambda p: p.mass,\n",
     ")\n",
     "evenly_spaced_interval = np.linspace(0, 1, len(resonances))\n",
diff --git a/docs/index.md b/docs/index.md
index 0eaf3c8..a9732aa 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -17,5 +17,5 @@ address to the issue ✅&nbsp;[ComPWA/gluex-nstar#1](https://github.com/ComPWA/g
 ```{toctree}
 reaction
 pgamma-state
-LamKpi
+ampform/LamKpi
 ```

From 76cb63b29883b98275048baa1d849492b4b3ba1c Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 11 Jul 2024 14:13:46 +0000
Subject: [PATCH 34/44] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 docs/ampform/LamKpi.ipynb | 401 ++++----------------------------------
 pixi.toml                 |   2 +-
 2 files changed, 44 insertions(+), 359 deletions(-)

diff --git a/docs/ampform/LamKpi.ipynb b/docs/ampform/LamKpi.ipynb
index ac8e9bc..afdc0ae 100644
--- a/docs/ampform/LamKpi.ipynb
+++ b/docs/ampform/LamKpi.ipynb
@@ -2,28 +2,14 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "# PWA for pγ → ΛK⁺π⁰ via `ComPWA`"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "1",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "PWA study on $p \\gamma \\to \\Lambda K^+ \\pi^0 $"
    ]
@@ -31,14 +17,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from __future__ import annotations\n",
@@ -66,28 +45,14 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "## Inital and final state"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "### Check existing particles in `PDG`"
    ]
@@ -95,14 +60,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "particle_db[\"Lambda\"]"
@@ -111,14 +69,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "particle_db[\"K+\"]"
@@ -127,14 +78,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "particle_db[\"pi0\"]"
@@ -143,14 +87,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "particle_db[\"gamma\"]"
@@ -159,14 +96,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "particle_db[\"p\"]"
@@ -174,14 +104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "10",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "### Add custom particle for initial state"
    ]
@@ -189,14 +112,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "E_lab_gamma = 8.5\n",
@@ -211,14 +127,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "pgamma = Particle(\n",
@@ -238,14 +147,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "pgamma2 = Particle(\n",
@@ -265,14 +167,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "particle_db.add(pgamma)\n",
@@ -281,14 +176,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "### Generate Transitions"
    ]
@@ -296,14 +184,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "reaction = qrules.generate_transitions(\n",
@@ -323,14 +204,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "dot_se = qrules.io.asdot(reaction, collapse_graphs=True)\n",
@@ -339,14 +213,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "## Build Helicity Amplitude Models"
    ]
@@ -354,14 +221,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "model_builder = ampform.get_builder(reaction)\n",
@@ -380,14 +240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "### Intensity"
    ]
@@ -395,14 +248,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "21",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "model_no_dynamics.intensity"
@@ -410,28 +256,14 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "### Amplitudes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "23",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "The first term in the amplitude model:"
    ]
@@ -439,32 +271,16 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "24",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "from ampform.io import aslatex\n",
-    "\n",
     "(symbol, expr), *_ = model.amplitudes.items()\n",
     "Math(aslatex({symbol: expr}, terms_per_line=1))"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "25",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "### Parameters"
    ]
@@ -472,14 +288,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "26",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "Math(aslatex(model_no_dynamics.parameter_defaults))"
@@ -488,14 +297,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "from ampform.dynamics.builder import (\n",
@@ -511,14 +313,8 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28",
    "metadata": {
-    "editable": true,
-    "jp-MarkdownHeadingCollapsed": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
+    "jp-MarkdownHeadingCollapsed": true
    },
    "source": [
     "## Reaction Info"
@@ -527,14 +323,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "29",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "initial_state, *_ = model.reaction_info.initial_state.values()\n",
@@ -548,14 +337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "## Generate phase space sample"
    ]
@@ -563,18 +345,10 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "phsp_event = 500_000\n",
-    "from tensorwaves.data import TFPhaseSpaceGenerator, TFUniformRealNumberGenerator\n",
     "\n",
     "rng = TFUniformRealNumberGenerator(seed=0)\n",
     "phsp_generator = TFPhaseSpaceGenerator(\n",
@@ -587,12 +361,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "32",
    "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
     "tags": [
      "full-width"
     ]
@@ -600,27 +369,19 @@
    "outputs": [],
    "source": [
     "import numpy as np\n",
-    "import pandas as pd\n",
     "\n",
     "pd.DataFrame(\n",
     "    {\n",
     "        (k, label): np.transpose(v)[i]\n",
     "        for k, v in phsp_momenta.items()\n",
     "        for i, label in enumerate([\"E\", \"px\", \"py\", \"pz\"])\n",
-    "    }\n",
+    "    },\n",
     ")"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "33",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "## Visualize kinematic variables"
    ]
@@ -628,18 +389,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "from tensorwaves.function.sympy import create_parametrized_function\n",
-    "\n",
     "unfolded_expression = model.expression.doit()\n",
     "intensity_func = create_parametrized_function(\n",
     "    expression=unfolded_expression,\n",
@@ -651,14 +403,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "35",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "Math(aslatex(model.kinematic_variables))"
@@ -667,34 +412,19 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "from tensorwaves.data import SympyDataTransformer\n",
-    "\n",
     "helicity_transformer = SympyDataTransformer.from_sympy(\n",
-    "    model.kinematic_variables, backend=\"jax\"\n",
+    "    model.kinematic_variables,\n",
+    "    backend=\"jax\",\n",
     ")"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "phsp = helicity_transformer(phsp_momenta)\n",
@@ -704,14 +434,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "38",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
     "for state_id, particle in reaction.final_state.items():\n",
@@ -721,12 +444,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39",
    "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
     "tags": [
      "full-width"
     ]
@@ -741,14 +459,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
+   "metadata": {},
    "source": [
     "## Visualize model and intensity-based sample"
    ]
@@ -756,12 +467,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "41",
    "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
     "tags": [
      "full-width",
      "hide-input"
@@ -799,15 +505,10 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42",
    "metadata": {
-    "editable": true,
     "jupyter": {
      "source_hidden": true
     },
-    "slideshow": {
-     "slide_type": ""
-    },
     "tags": [
      "full-width",
      "hide-input"
@@ -841,15 +542,10 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "43",
    "metadata": {
-    "editable": true,
     "jupyter": {
      "source_hidden": true
     },
-    "slideshow": {
-     "slide_type": ""
-    },
     "tags": [
      "full-width",
      "hide-input"
@@ -880,15 +576,10 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "44",
    "metadata": {
-    "editable": true,
     "jupyter": {
      "source_hidden": true
     },
-    "slideshow": {
-     "slide_type": ""
-    },
     "tags": [
      "hide-input",
      "full-width"
@@ -918,15 +609,10 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "45",
    "metadata": {
-    "editable": true,
     "jupyter": {
      "source_hidden": true
     },
-    "slideshow": {
-     "slide_type": ""
-    },
     "tags": [
      "hide-input",
      "full-width"
@@ -958,7 +644,6 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "46",
    "metadata": {},
    "outputs": [],
    "source": []
@@ -984,5 +669,5 @@
   }
  },
  "nbformat": 4,
- "nbformat_minor": 5
+ "nbformat_minor": 4
 }
diff --git a/pixi.toml b/pixi.toml
index 5eace1b..25f0012 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -74,4 +74,4 @@ sphinx-autobuild \
     -b html \
     docs/ docs/_build/html
 """
-env = {EXECUTE_NB = "yes"}
\ No newline at end of file
+env = {EXECUTE_NB = "yes"}

From 10250b316bce6d011cea1dc63b3f9a4748ff4bf4 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 12 Jul 2024 13:50:43 +0200
Subject: [PATCH 35/44] Overall structure improvement

---
 docs/ampform/LamKpi.ipynb  | 494 +++++++++++++++++--------------------
 docs/ampform/etapi0p.ipynb |   2 +-
 2 files changed, 226 insertions(+), 270 deletions(-)

diff --git a/docs/ampform/LamKpi.ipynb b/docs/ampform/LamKpi.ipynb
index afdc0ae..1ee9604 100644
--- a/docs/ampform/LamKpi.ipynb
+++ b/docs/ampform/LamKpi.ipynb
@@ -4,34 +4,66 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# PWA for pγ → ΛK⁺π⁰ via `ComPWA`"
+    "# pγ → ΛK⁺π⁰ `Ampform` amplitude model"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "PWA study on $p \\gamma \\to \\Lambda K^+ \\pi^0 $"
+    "PWA study on $p \\gamma \\to \\Lambda K^+ \\pi^0$.\n",
+    "We formulate the helicity amplitude model symbolically using `AmpForm` here."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "Hide warnings"
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
    "outputs": [],
    "source": [
     "from __future__ import annotations\n",
     "\n",
+    "import logging\n",
+    "import os\n",
+    "import warnings\n",
+    "\n",
+    "os.environ[\"TF_CPP_MIN_LOG_LEVEL\"] = \"3\"\n",
+    "logging.disable(logging.WARNING)\n",
+    "warnings.filterwarnings(\"ignore\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "Import Python Libraries"
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "from collections import defaultdict\n",
+    "\n",
     "import ampform\n",
     "import graphviz\n",
+    "import jax\n",
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
-    "import pandas as pd\n",
     "import qrules\n",
     "from ampform.dynamics.builder import RelativisticBreitWignerBuilder\n",
     "from ampform.io import aslatex, improve_latex_rendering\n",
     "from IPython.display import Math\n",
-    "from qrules.particle import Particle, Spin, load_pdg\n",
+    "from qrules.particle import Particle, Spin, create_particle, load_pdg\n",
     "from tensorwaves.data import (\n",
     "    SympyDataTransformer,\n",
     "    TFPhaseSpaceGenerator,\n",
@@ -60,7 +92,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "Lambda"
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
    "outputs": [],
    "source": [
     "particle_db[\"Lambda\"]"
@@ -69,7 +108,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "K+"
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
    "outputs": [],
    "source": [
     "particle_db[\"K+\"]"
@@ -78,7 +124,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "pi0"
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
    "outputs": [],
    "source": [
     "particle_db[\"pi0\"]"
@@ -87,7 +140,14 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "gamma"
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
    "outputs": [],
    "source": [
     "particle_db[\"gamma\"]"
@@ -96,12 +156,40 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "p"
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
    "outputs": [],
    "source": [
     "particle_db[\"p\"]"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "| Particle         | Lambda            | K+               | pi0              | gamma            | p                |\n",
+    "|------------------|-------------------|------------------|------------------|------------------|------------------|\n",
+    "| **Name**         | Lambda            | K+               | pi0              | gamma            | p                |\n",
+    "| **PID**          | 3122              | 321              | 111              | 22               | 2212             |\n",
+    "| **Latex**        | \\(\\Lambda\\)       | \\(K^{+}\\)        | \\(\\pi^{0}\\)      | \\(\\gamma\\)       | \\(p\\)            |\n",
+    "| **Spin**         | 0.5               | 0.0              | 0.0              | 1.0              | 0.5              |\n",
+    "| **Mass**         | 1.115683          | 0.49367700000000003 | 0.1349768       | 0.0              | 0.93827208816    |\n",
+    "| **Width**        | 2.501e-15         | 5.317e-17        | 7.81e-09         |                  |                  |\n",
+    "| **Charge**       |                   | 1                |                  |                  | 1                |\n",
+    "| **Isospin**      | Spin(0, 0)        | Spin(1/2, +1/2)  | Spin(1, 0)       |                  | Spin(1/2, +1/2)  |\n",
+    "| **Strangeness**  | -1                | 1                |                  |                  |                  |\n",
+    "| **Baryon Number**| 1                 |                  |                  |                  | 1                |\n",
+    "| **Parity**       | +1                | -1               | -1               | -1               | +1               |\n",
+    "| **C Parity**     |                   |                  | +1               | -1               |                  |\n",
+    "| **G Parity**     |                   |                  | -1               |                  |                  |\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -109,6 +197,13 @@
     "### Add custom particle for initial state"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Mass for $p \\gamma$ system"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -116,7 +211,6 @@
    "outputs": [],
    "source": [
     "E_lab_gamma = 8.5\n",
-    "# E_lab_gamma = 5\n",
     "m_proton = 0.938\n",
     "m_0 = np.sqrt(2 * E_lab_gamma * m_proton + m_proton**2)\n",
     "m_eta = 0.548\n",
@@ -124,14 +218,21 @@
     "m_0"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Add custom particle $p \\gamma$"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
-    "pgamma = Particle(\n",
-    "    name=\"pgamma\",\n",
+    "pgamma1 = Particle(\n",
+    "    name=\"pgamma1\",\n",
     "    latex=r\"p\\gamma (s1/2)\",\n",
     "    spin=0.5,\n",
     "    mass=m_0,\n",
@@ -141,44 +242,39 @@
     "    parity=-1,\n",
     "    pid=99990,\n",
     ")\n",
-    "pgamma"
+    "pgamma2 = create_particle(\n",
+    "    template_particle=pgamma1,\n",
+    "    name=\"pgamma2\",\n",
+    "    latex=R\"p\\gamma (s3/2)\",\n",
+    "    spin=1.5,\n",
+    "    pid=pgamma1.pid + 1,\n",
+    ")\n",
+    "particle_db.update([pgamma1, pgamma2])"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "pgamma2 = Particle(\n",
-    "    name=\"pgamma2\",\n",
-    "    latex=R\"p\\gamma (s3/2)\",\n",
-    "    spin=1.5,\n",
-    "    mass=m_0,\n",
-    "    charge=1,\n",
-    "    isospin=Spin(1 / 2, +1 / 2),\n",
-    "    baryon_number=1,\n",
-    "    parity=-1,\n",
-    "    pid=99991,\n",
-    ")\n",
-    "pgamma2"
+    "### Generate Transitions"
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
    "source": [
-    "particle_db.add(pgamma)\n",
-    "particle_db.add(pgamma2)"
+    "For simplicity, we use the initial state $p \\gamma$ (with spin-$\\frac{1}{2}$), \n",
+    "and set the allowed interaction type to be strong only,\n",
+    "the formalism is selected to be helicity formalism instead of canonical."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Generate Transitions"
+    ":::{seealso}\n",
+    "[Helicity versus canonical](https://ampform.readthedocs.io/stable/usage/helicity/formalism.html)\n",
+    ":::"
    ]
   },
   {
@@ -188,12 +284,10 @@
    "outputs": [],
    "source": [
     "reaction = qrules.generate_transitions(\n",
-    "    initial_state=(\"pgamma\"),\n",
+    "    initial_state=(\"pgamma1\"),\n",
     "    final_state=[\"Lambda\", \"K+\", \"pi0\"],\n",
-    "    # allowed_intermediate_particles=[\"a(2)(1320)\",\"N\",\"Delta\"],\n",
     "    allowed_interaction_types=[\"strong\"],\n",
-    "    formalism=\"canonical-helicity\",\n",
-    "    # formalism=\"helicity\",\n",
+    "    formalism=\"helicity\",\n",
     "    particle_db=particle_db,\n",
     "    max_angular_momentum=4,\n",
     "    max_spin_magnitude=4,\n",
@@ -251,7 +345,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "model_no_dynamics.intensity"
+    "model.intensity"
    ]
   },
   {
@@ -288,36 +382,24 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Math(aslatex(model_no_dynamics.parameter_defaults))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "mystnb": {
+     "code_prompt_show": "m, Gamma, C"
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
    "outputs": [],
    "source": [
-    "from ampform.dynamics.builder import (\n",
-    "    create_non_dynamic_with_ff,\n",
-    "    create_relativistic_breit_wigner_with_ff,\n",
-    ")\n",
-    "\n",
-    "model_builder.dynamics.assign(\"pgamma\", create_non_dynamic_with_ff)\n",
-    "for name in reaction.get_intermediate_particles().names:\n",
-    "    model_builder.dynamics.assign(name, create_relativistic_breit_wigner_with_ff)\n",
-    "model = model_builder.formulate()"
+    "Math(aslatex(model.parameter_defaults))"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {
-    "jp-MarkdownHeadingCollapsed": true
-   },
+   "metadata": {},
    "source": [
-    "## Reaction Info"
+    "### Kinematic variables"
    ]
   },
   {
@@ -326,13 +408,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "initial_state, *_ = model.reaction_info.initial_state.values()\n",
-    "print(\"Initial state:\")\n",
-    "print(\"-1: \", initial_state.name)\n",
-    "print(\"Final state:\")\n",
-    "for i, p in model.reaction_info.final_state.items():\n",
-    "    print(f\"  {i}: {p.name}\")\n",
-    "del initial_state"
+    "Math(aslatex(model.kinematic_variables))"
    ]
   },
   {
@@ -345,7 +421,11 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": [
+     "hide-output"
+    ]
+   },
    "outputs": [],
    "source": [
     "phsp_event = 500_000\n",
@@ -358,32 +438,11 @@
     "phsp_momenta = phsp_generator.generate(phsp_event, rng)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "tags": [
-     "full-width"
-    ]
-   },
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "pd.DataFrame(\n",
-    "    {\n",
-    "        (k, label): np.transpose(v)[i]\n",
-    "        for k, v in phsp_momenta.items()\n",
-    "        for i, label in enumerate([\"E\", \"px\", \"py\", \"pz\"])\n",
-    "    },\n",
-    ")"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Visualize kinematic variables"
+    "## Visualization"
    ]
   },
   {
@@ -396,19 +455,10 @@
     "intensity_func = create_parametrized_function(\n",
     "    expression=unfolded_expression,\n",
     "    parameters=model.parameter_defaults,\n",
-    "    backend=\"numpy\",\n",
+    "    backend=\"jax\",\n",
     ")"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Math(aslatex(model.kinematic_variables))"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -421,165 +471,24 @@
     ")"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "phsp = helicity_transformer(phsp_momenta)\n",
-    "list(phsp)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "for state_id, particle in reaction.final_state.items():\n",
-    "    print(f\"ID {state_id}:\", particle.name)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "tags": [
-     "full-width"
-    ]
-   },
-   "outputs": [],
-   "source": [
-    "import pandas as pd\n",
-    "\n",
-    "phsp_frame = pd.DataFrame(phsp)\n",
-    "phsp_frame"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Visualize model and intensity-based sample"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "tags": [
-     "full-width",
-     "hide-input"
-    ]
-   },
-   "outputs": [],
-   "source": [
-    "%config InlineBackend.figure_formats = ['svg']\n",
-    "\n",
-    "resonances = sorted(\n",
-    "    reaction.get_intermediate_particles(),\n",
-    "    key=lambda p: p.mass,\n",
-    ")\n",
-    "evenly_spaced_interval = np.linspace(0, 1, len(resonances))\n",
-    "colors = [plt.cm.rainbow(x) for x in evenly_spaced_interval]\n",
-    "fig, ax = plt.subplots(figsize=(10, 6))\n",
-    "ax.hist(\n",
-    "    np.real(phsp_frame[\"m_01\"]),\n",
-    "    bins=100,\n",
-    "    alpha=0.5,\n",
-    "    density=True,\n",
-    "    color=\"orange\",\n",
-    "    # color = colors[1],\n",
-    "    label=\"Weighted PHSP\",\n",
-    "    weights=intensity_func(phsp),\n",
-    ")\n",
-    "ax.set_xlabel(R\"$m(\\Lambda K^+)\\;\\left[\\mathrm{GeV}^2\\right]$ [GeV]\")\n",
-    "N_stars = [p for p in resonances if \"N\" in p.name]\n",
-    "for p, color in zip(N_stars, colors):\n",
-    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
-    "ax.legend()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "jupyter": {
-     "source_hidden": true
-    },
-    "tags": [
-     "full-width",
-     "hide-input"
-    ]
-   },
-   "outputs": [],
-   "source": [
-    "%config InlineBackend.figure_formats = ['svg']\n",
-    "\n",
-    "fig, ax = plt.subplots(figsize=(10, 6))\n",
-    "\n",
-    "ax.hist(\n",
-    "    np.real(phsp_frame[\"m_12\"]),\n",
-    "    bins=100,\n",
-    "    alpha=0.5,\n",
-    "    density=True,\n",
-    "    color=\"yellow\",\n",
-    "    label=\"Weighted PHSP\",\n",
-    "    weights=intensity_func(phsp),\n",
-    ")\n",
-    "\n",
-    "ax.set_xlabel(R\"$m(K^+ \\pi^0)$ [GeV]\")\n",
-    "\n",
-    "K_stars = [p for p in resonances if \"K\" in p.name]\n",
-    "for p, color in zip(K_stars, colors):\n",
-    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
-    "ax.legend()\n",
-    "plt.show()"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "jupyter": {
-     "source_hidden": true
-    },
     "tags": [
-     "full-width",
-     "hide-input"
+     "hide-output"
     ]
    },
    "outputs": [],
    "source": [
-    "%config InlineBackend.figure_formats = ['svg']\n",
-    "\n",
-    "fig, ax = plt.subplots(figsize=(10, 6))\n",
-    "ax.hist(\n",
-    "    np.real(phsp_frame[\"m_02\"]),\n",
-    "    bins=100,\n",
-    "    alpha=0.5,\n",
-    "    density=True,\n",
-    "    color=\"red\",\n",
-    "    label=\"Weighted PHSP\",\n",
-    "    weights=intensity_func(phsp),\n",
-    ")\n",
-    "ax.set_xlabel(R\"$m(\\Lambda \\pi^0)$ [GeV]\")\n",
-    "Sigma_stars = [p for p in resonances if \"Sigma\" in p.name]\n",
-    "for p, color in zip(Sigma_stars, colors):\n",
-    "    ax.axvline(x=p.mass, linestyle=\"dotted\", label=p.name, color=color)\n",
-    "ax.legend()\n",
-    "plt.show()"
+    "phsp = helicity_transformer(phsp_momenta)\n",
+    "list(phsp)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "jupyter": {
-     "source_hidden": true
-    },
     "tags": [
      "hide-input",
      "full-width"
@@ -588,7 +497,7 @@
    "outputs": [],
    "source": [
     "%config InlineBackend.figure_formats = ['png']\n",
-    "fig, ax = plt.subplots()\n",
+    "fig, ax = plt.subplots(dpi=200)\n",
     "hist = ax.hist2d(\n",
     "    phsp[\"m_01\"].real ** 2,\n",
     "    phsp[\"m_12\"].real ** 2,\n",
@@ -596,9 +505,10 @@
     "    cmin=1e-6,\n",
     "    density=True,\n",
     "    cmap=\"jet\",\n",
-    "    # vmax=0.15,\n",
+    "    vmax=0.15,\n",
+    "    weights=intensity_func(phsp),\n",
     ")\n",
-    "ax.set_title(\"Phase Space Dalitz Plot\")\n",
+    "ax.set_title(\"Model-weighted Phase space Dalitz Plot\")\n",
     "ax.set_xlabel(R\"$m^2(\\Lambda K^+)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
     "ax.set_ylabel(R\"$m^2(K^+ \\pi^0)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
     "cbar = fig.colorbar(hist[3], ax=ax)\n",
@@ -606,6 +516,23 @@
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "resonances = defaultdict(set)\n",
+    "for transition in reaction.transitions:\n",
+    "    topology = transition.topology\n",
+    "    top_decay_products = topology.get_edge_ids_outgoing_from_node(0)\n",
+    "    (resonance_id, resonance), *_ = transition.intermediate_states.items()\n",
+    "    recoil_id, *_ = top_decay_products - {resonance_id}\n",
+    "    resonances[recoil_id].add(resonance.particle)\n",
+    "resonances = {k: sorted(v, key=lambda p: p.mass) for k, v in resonances.items()}\n",
+    "{k: [p.name for p in v] for k, v in resonances.items()}"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -614,31 +541,60 @@
      "source_hidden": true
     },
     "tags": [
-     "hide-input",
-     "full-width"
+     "hide-input"
     ]
    },
    "outputs": [],
    "source": [
-    "# %config InlineBackend.figure_formats = ['png']\n",
+    "%config InlineBackend.figure_formats = ['svg']\n",
+    "fig, axes = plt.subplots(figsize=(14, 4), ncols=3, sharey=True)\n",
+    "ax1, ax2, ax3 = axes\n",
+    "\n",
+    "max_value = 0\n",
+    "color_id = 0\n",
+    "intensities = intensity_func(phsp)\n",
+    "for recoil_id, ax in enumerate(axes):\n",
+    "    decay_products = sorted({0, 1, 2} - {recoil_id})\n",
+    "    key = f\"m_{''.join(str(i) for i in decay_products)}\"\n",
+    "    bin_values, bin_edges = jax.numpy.histogram(\n",
+    "        phsp[key].real,\n",
+    "        bins=100,\n",
+    "        density=True,\n",
+    "        weights=intensities,\n",
+    "    )\n",
+    "    max_value = max(max_value, bin_values.max())\n",
+    "    ax.fill_between(\n",
+    "        bin_edges[:-1],\n",
+    "        bin_values,\n",
+    "        alpha=0.5,\n",
+    "        step=\"pre\",\n",
+    "    )\n",
+    "    ax.set_ylim(0, None)\n",
+    "    for resonance in resonances[recoil_id]:\n",
+    "        ax.axvline(\n",
+    "            resonance.mass,\n",
+    "            c=f\"C{color_id}\",\n",
+    "            ls=\"dotted\",\n",
+    "            label=resonance.name,\n",
+    "        )\n",
+    "        color_id += 1\n",
+    "\n",
+    "        product_latex = \" \".join(\n",
+    "            [reaction.final_state[i].latex for i in decay_products],\n",
+    "        )\n",
+    "        ax.set_xlabel(f\"$m({product_latex})$ [GeV]\")\n",
+    "\n",
+    "        if recoil_id == 0:\n",
+    "            ax.legend(fontsize=\"small\", loc=\"upper right\")\n",
+    "        elif recoil_id == 1:\n",
+    "            ax.legend(fontsize=\"small\", loc=\"upper center\", bbox_to_anchor=(0.6, 1.0))\n",
+    "        else:\n",
+    "            ax.legend(fontsize=\"small\", loc=\"upper center\")\n",
+    "for ax in axes:\n",
+    "    ax.set_ylim(0, max_value * 1.1)\n",
     "\n",
-    "fig, ax = plt.subplots()\n",
-    "hist = ax.hist2d(\n",
-    "    phsp[\"m_01\"].real ** 2,\n",
-    "    phsp[\"m_12\"].real ** 2,\n",
-    "    bins=200,\n",
-    "    cmin=1e-6,\n",
-    "    density=True,\n",
-    "    cmap=\"jet\",\n",
-    "    vmax=0.15,\n",
-    "    weights=intensity_func(phsp),\n",
-    ")\n",
-    "ax.set_title(\"Model-weighted Phase space Dalitz Plot\")\n",
-    "ax.set_xlabel(R\"$m^2(\\Lambda K^+)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
-    "ax.set_ylabel(R\"$m^2(K^+ \\pi^0)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
-    "cbar = fig.colorbar(hist[3], ax=ax)\n",
     "fig.tight_layout()\n",
-    "plt.show()"
+    "plt.show(fig)"
    ]
   },
   {
diff --git a/docs/ampform/etapi0p.ipynb b/docs/ampform/etapi0p.ipynb
index 69434b5..0a2f875 100644
--- a/docs/ampform/etapi0p.ipynb
+++ b/docs/ampform/etapi0p.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# pγ→ηπ⁰p amplitude model"
+    "# pγ→ηπ⁰p `AmpForm` amplitude model"
    ]
   },
   {

From b879ace7821c0c7337e82ec032ff2e7b9b4238b6 Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 12 Jul 2024 14:27:57 +0200
Subject: [PATCH 36/44] full width for plot

---
 docs/ampform/LamKpi.ipynb | 19 ++++++++++---------
 1 file changed, 10 insertions(+), 9 deletions(-)

diff --git a/docs/ampform/LamKpi.ipynb b/docs/ampform/LamKpi.ipynb
index 1ee9604..c892d09 100644
--- a/docs/ampform/LamKpi.ipynb
+++ b/docs/ampform/LamKpi.ipynb
@@ -365,7 +365,11 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": [
+     "full-width"
+    ]
+   },
    "outputs": [],
    "source": [
     "(symbol, expr), *_ = model.amplitudes.items()\n",
@@ -489,6 +493,9 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
     "tags": [
      "hide-input",
      "full-width"
@@ -541,7 +548,8 @@
      "source_hidden": true
     },
     "tags": [
-     "hide-input"
+     "hide-input",
+     "full-width"
     ]
    },
    "outputs": [],
@@ -596,13 +604,6 @@
     "fig.tight_layout()\n",
     "plt.show(fig)"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {

From cd22417e75bdabc9f5a440ce2335813317d09c7a Mon Sep 17 00:00:00 2001
From: Vitor Shen <17490173+shenvitor@users.noreply.github.com>
Date: Fri, 12 Jul 2024 14:54:43 +0200
Subject: [PATCH 37/44] rename file

---
 docs/ampform/{LamKpi.ipynb => Lambda0Kpi0.ipynb} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename docs/ampform/{LamKpi.ipynb => Lambda0Kpi0.ipynb} (100%)

diff --git a/docs/ampform/LamKpi.ipynb b/docs/ampform/Lambda0Kpi0.ipynb
similarity index 100%
rename from docs/ampform/LamKpi.ipynb
rename to docs/ampform/Lambda0Kpi0.ipynb

From 03fc047d1e59a6dccd425ebf8f9dd5fadda2cbdc Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 12 Jul 2024 14:55:40 +0200
Subject: [PATCH 38/44] DX: define `lab` task for pixi

---
 pixi.toml | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/pixi.toml b/pixi.toml
index 25f0012..feb35a6 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -75,3 +75,6 @@ sphinx-autobuild \
     docs/ docs/_build/html
 """
 env = {EXECUTE_NB = "yes"}
+
+[tasks.lab]
+cmd = "jupyter lab docs"

From bc7b6257744d13c474b961df6102e81f87554ac9 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 12 Jul 2024 14:59:32 +0200
Subject: [PATCH 39/44] MAINT: remove 0 from filename

---
 docs/ampform/{Lambda0Kpi0.ipynb => LambdaKpi0.ipynb} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename docs/ampform/{Lambda0Kpi0.ipynb => LambdaKpi0.ipynb} (100%)

diff --git a/docs/ampform/Lambda0Kpi0.ipynb b/docs/ampform/LambdaKpi0.ipynb
similarity index 100%
rename from docs/ampform/Lambda0Kpi0.ipynb
rename to docs/ampform/LambdaKpi0.ipynb

From b27403bea882c7d596beb963051742540520484b Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 12 Jul 2024 15:07:59 +0200
Subject: [PATCH 40/44] DX: remove `.virtual_documents` from toctree

---
 docs/conf.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/docs/conf.py b/docs/conf.py
index 71a2ab7..f884a50 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -4,11 +4,12 @@
     "hypothesis": True,
 }
 exclude_patterns = [
-    "**.ipynb_checkpoints",
+    "_build",
     ".DS_Store",
     ".pixi",
+    ".virtual_documents",
+    "**.ipynb_checkpoints",
     "Thumbs.db",
-    "_build",
 ]
 extensions = [
     "myst_nb",

From 8de34525ade0c70b1cc91f9bb350c5b9136a7749 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 12 Jul 2024 15:08:18 +0200
Subject: [PATCH 41/44] FIX: update filename in `toctree`

---
 docs/index.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/index.md b/docs/index.md
index 3508384..ed23ae0 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -20,5 +20,5 @@ symbolics
 pgamma-state
 branching-fraction
 ampform/etapi0p
-ampform/LamKpi
+ampform/LambdaKpi0
 ```

From 2f69399a9aee15c6c6aa27447ad11ffc96549fc2 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 12 Jul 2024 15:09:15 +0200
Subject: [PATCH 42/44] DOC: shorten document titles

---
 docs/ampform/LambdaKpi0.ipynb | 4 ++--
 docs/ampform/etapi0p.ipynb    | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/docs/ampform/LambdaKpi0.ipynb b/docs/ampform/LambdaKpi0.ipynb
index c892d09..a213f15 100644
--- a/docs/ampform/LambdaKpi0.ipynb
+++ b/docs/ampform/LambdaKpi0.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# pγ → ΛK⁺π⁰ `Ampform` amplitude model"
+    "# pγ → ΛK⁺π⁰ amplitude model"
    ]
   },
   {
@@ -12,7 +12,7 @@
    "metadata": {},
    "source": [
     "PWA study on $p \\gamma \\to \\Lambda K^+ \\pi^0$.\n",
-    "We formulate the helicity amplitude model symbolically using `AmpForm` here."
+    "We formulate the helicity amplitude model symbolically using AmpForm here."
    ]
   },
   {
diff --git a/docs/ampform/etapi0p.ipynb b/docs/ampform/etapi0p.ipynb
index 0a2f875..69434b5 100644
--- a/docs/ampform/etapi0p.ipynb
+++ b/docs/ampform/etapi0p.ipynb
@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# pγ→ηπ⁰p `AmpForm` amplitude model"
+    "# pγ→ηπ⁰p amplitude model"
    ]
   },
   {

From 937184a6ce736bba4cdc00f5096afa41a9b69084 Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 12 Jul 2024 15:22:50 +0200
Subject: [PATCH 43/44] DOC: improve cell rendering on webpage

---
 docs/ampform/LambdaKpi0.ipynb | 146 +++++++++++++++-------------------
 1 file changed, 64 insertions(+), 82 deletions(-)

diff --git a/docs/ampform/LambdaKpi0.ipynb b/docs/ampform/LambdaKpi0.ipynb
index a213f15..68a05c2 100644
--- a/docs/ampform/LambdaKpi0.ipynb
+++ b/docs/ampform/LambdaKpi0.ipynb
@@ -12,13 +12,16 @@
    "metadata": {},
    "source": [
     "PWA study on $p \\gamma \\to \\Lambda K^+ \\pi^0$.\n",
-    "We formulate the helicity amplitude model symbolically using AmpForm here."
+    "We formulate the helicity amplitude model symbolically using `AmpForm` here."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
     "mystnb": {
      "code_prompt_show": "Hide warnings"
     },
@@ -43,6 +46,9 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
     "mystnb": {
      "code_prompt_show": "Import Python Libraries"
     },
@@ -79,14 +85,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Inital and final state"
+    "## Decay definition"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Check existing particles in `PDG`"
+    "### Particle definitions"
    ]
   },
   {
@@ -194,7 +200,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Add custom particle for initial state"
+    "### Initial state definition"
    ]
   },
   {
@@ -256,7 +262,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Generate Transitions"
+    "### Generate transitions"
    ]
   },
   {
@@ -298,18 +304,25 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
    "outputs": [],
    "source": [
-    "dot_se = qrules.io.asdot(reaction, collapse_graphs=True)\n",
-    "graphviz.Source(dot_se)"
+    "dot = qrules.io.asdot(reaction, collapse_graphs=True)\n",
+    "graphviz.Source(dot)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Build Helicity Amplitude Models"
+    "## Formulate amplitude model"
    ]
   },
   {
@@ -321,24 +334,15 @@
     "model_builder = ampform.get_builder(reaction)\n",
     "model_builder.config.scalar_initial_state_mass = True\n",
     "model_builder.config.stable_final_state_ids = 0, 1, 2\n",
-    "\n",
     "bw_builder = RelativisticBreitWignerBuilder(\n",
     "    energy_dependent_width=False,\n",
     "    form_factor=False,\n",
     ")\n",
-    "\n",
     "for name in reaction.get_intermediate_particles().names:\n",
     "    model_builder.dynamics.assign(name, bw_builder)\n",
     "model = model_builder.formulate()"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Intensity"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -348,13 +352,6 @@
     "model.intensity"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Amplitudes"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -366,8 +363,12 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
     "tags": [
-     "full-width"
+     "hide-input",
+     "scroll-output"
     ]
    },
    "outputs": [],
@@ -376,22 +377,16 @@
     "Math(aslatex({symbol: expr}, terms_per_line=1))"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Parameters"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
     "mystnb": {
-     "code_prompt_show": "m, Gamma, C"
+     "code_prompt_show": "Model parameters"
     },
     "tags": [
-     "hide-cell"
+     "scroll-output",
+     "hide-input"
     ]
    },
    "outputs": [],
@@ -399,47 +394,21 @@
     "Math(aslatex(model.parameter_defaults))"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Kinematic variables"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "Math(aslatex(model.kinematic_variables))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Generate phase space sample"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
+    "mystnb": {
+     "code_prompt_show": "Kinematic variable definitions"
+    },
     "tags": [
-     "hide-output"
+     "hide-input",
+     "scroll-output"
     ]
    },
    "outputs": [],
    "source": [
-    "phsp_event = 500_000\n",
-    "\n",
-    "rng = TFUniformRealNumberGenerator(seed=0)\n",
-    "phsp_generator = TFPhaseSpaceGenerator(\n",
-    "    initial_state_mass=reaction.initial_state[-1].mass,\n",
-    "    final_state_masses={i: p.mass for i, p in reaction.final_state.items()},\n",
-    ")\n",
-    "phsp_momenta = phsp_generator.generate(phsp_event, rng)"
+    "Math(aslatex(model.kinematic_variables))"
    ]
   },
   {
@@ -466,27 +435,33 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "tags": [
+     "remove-output"
+    ]
+   },
    "outputs": [],
    "source": [
-    "helicity_transformer = SympyDataTransformer.from_sympy(\n",
-    "    model.kinematic_variables,\n",
-    "    backend=\"jax\",\n",
-    ")"
+    "phsp_event = 500_000\n",
+    "rng = TFUniformRealNumberGenerator(seed=0)\n",
+    "phsp_generator = TFPhaseSpaceGenerator(\n",
+    "    initial_state_mass=reaction.initial_state[-1].mass,\n",
+    "    final_state_masses={i: p.mass for i, p in reaction.final_state.items()},\n",
+    ")\n",
+    "phsp_momenta = phsp_generator.generate(phsp_event, rng)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "tags": [
-     "hide-output"
-    ]
-   },
+   "metadata": {},
    "outputs": [],
    "source": [
-    "phsp = helicity_transformer(phsp_momenta)\n",
-    "list(phsp)"
+    "helicity_transformer = SympyDataTransformer.from_sympy(\n",
+    "    model.kinematic_variables,\n",
+    "    backend=\"jax\",\n",
+    ")\n",
+    "phsp = helicity_transformer(phsp_momenta)"
    ]
   },
   {
@@ -497,8 +472,7 @@
      "source_hidden": true
     },
     "tags": [
-     "hide-input",
-     "full-width"
+     "hide-input"
     ]
    },
    "outputs": [],
@@ -526,7 +500,15 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "jupyter": {
+     "source_hidden": true
+    },
+    "tags": [
+     "hide-output",
+     "hide-input"
+    ]
+   },
    "outputs": [],
    "source": [
     "resonances = defaultdict(set)\n",

From 43f96fb6ce617394a02ea267b042af48d3aa2f2e Mon Sep 17 00:00:00 2001
From: Remco de Boer <29308176+redeboer@users.noreply.github.com>
Date: Fri, 12 Jul 2024 15:26:05 +0200
Subject: [PATCH 44/44] MAINT: revert `jax` lower boundary upgrade

---
 pixi.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pixi.toml b/pixi.toml
index feb35a6..bfcd8f5 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -13,7 +13,7 @@ black = ">=24.4.2,<24.5"
 graphviz = ">=9.0.0,<9.1"
 ipywidgets = ">=8.1.2,<8.2"
 isort = ">=5.13.2,<5.14"
-jax = ">=0.4.27,<0.5"
+jax = ">=0.4.26,<0.5"
 jaxlib = ">=0.4.23,<0.5"
 jupyter = ">=1.0.0,<1.1"
 jupyterlab = ">=4.2.0,<4.3"