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ENH: add sliders in sympy etapipi notebook #95

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merged 15 commits into from
Aug 27, 2024
Merged

ENH: add sliders in sympy etapipi notebook #95

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3b650d5
add slider UI
shenvitor Aug 23, 2024
7df3173
Add add phi function and slider for Dalitz plot
shenvitor Aug 23, 2024
124704b
remove static Dalitz plot
shenvitor Aug 23, 2024
de63c76
step=0.01 in sliders
shenvitor Aug 25, 2024
dc11ad9
Merge branch 'main' into etapip-sympy-sliders
redeboer Aug 26, 2024
55a64ad
Add 1d projection with slider
shenvitor Aug 26, 2024
a53b663
static filename
shenvitor Aug 26, 2024
bcc2196
draft
shenvitor Aug 26, 2024
634f06f
update 1d interactive plot for theta nad phi too
shenvitor Aug 26, 2024
9db46cb
note
shenvitor Aug 27, 2024
ab8ee26
more minor formatting
shenvitor Aug 27, 2024
52b0ad9
import section hide-cell
shenvitor Aug 27, 2024
e6b77c8
delete the original static projection
shenvitor Aug 27, 2024
e323d6e
MAINT: reduce diff
redeboer Aug 27, 2024
6ff2ece
MAINT: ignore Ruff rules inline
redeboer Aug 27, 2024
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276 changes: 245 additions & 31 deletions docs/eta-pi-p/manual.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -11,7 +11,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"This section is a follow-up to formulate the amplitude model for the $\\gamma p \\to \\eta\\pi^0 p$ channel example symbolically. See **[TR‑033](https://compwa.github.io/report/033)** for a purely numerical tutorial.\n",
"This section is a follow-up of previous chapter:[Reaction and Models](reaction-model.md), to formulate the amplitude model for the $\\gamma p \\to \\eta\\pi^0 p$ channel example symbolically. See **[TR‑033](https://compwa.github.io/report/033)** for a purely numerical tutorial.\n",
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"\n",
"The model we want to implement is"
]
Expand All @@ -24,7 +24,7 @@
"\\begin{array}{rcl}\n",
"I &=& \\left|A^{12} + A^{23} + A^{31}\\right|^2 \\\\\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",
"A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s_{23}-m^2_{\\Delta^+}+im_{\\Delta^+} \\Gamma_{\\Delta^+}} \\\\\n",
"A^{31} &=& \\frac{c_0}{s_{31}-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \\,,\n",
"\\end{array}\n",
"$$"
Expand All @@ -41,17 +41,24 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
"jupyter": {
"source_hidden": true
},
"mystnb": {
"code_prompt_show": "Import Python libraries"
},
"tags": [
"hide-cell"
]
}
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},
"outputs": [],
"source": [
"from __future__ import annotations\n",
"\n",
"import logging\n",
"import os\n",
"import warnings\n",
"from collections import defaultdict\n",
"\n",
"import ipywidgets as w\n",
"import jax.numpy as jnp\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import sympy as sp\n",
Expand All @@ -71,13 +78,19 @@
")\n",
"from ampform.sympy import unevaluated\n",
"from ampform.sympy._array_expressions import ArraySum\n",
"from IPython.display import Latex\n",
"from IPython.display import Image, Latex, display\n",
"from tensorwaves.data import (\n",
" SympyDataTransformer,\n",
" TFPhaseSpaceGenerator,\n",
" TFUniformRealNumberGenerator,\n",
")\n",
"from tensorwaves.function.sympy import create_parametrized_function"
"from tensorwaves.function.sympy import create_parametrized_function\n",
"\n",
"STATIC_PAGE = \"EXECUTE_NB\" in os.environ\n",
"\n",
"os.environ[\"TF_CPP_MIN_LOG_LEVEL\"] = \"3\"\n",
"logging.disable(logging.WARNING)\n",
"warnings.filterwarnings(\"ignore\")"
]
},
{
Expand Down Expand Up @@ -171,7 +184,7 @@
"metadata": {},
"outputs": [],
"source": [
"s23, m_delta, gamma_delta = sp.symbols(\"s_{23} m_Delta Gamma_Delta\")\n",
"s23, m_delta, gamma_delta = sp.symbols(r\"s_{23} m_{\\Delta^+} \\Gamma_{\\Delta^+}\")\n",
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"b = sp.IndexedBase(\"b\")\n",
"m = sp.symbols(\"m\", cls=sp.Idx)\n",
"theta2, phi2 = sp.symbols(\"theta_2 phi_2\")\n",
Expand Down Expand Up @@ -431,9 +444,6 @@
"cell_type": "code",
"execution_count": null,
"metadata": {
"jupyter": {
"source_hidden": true
},
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"tags": [
"hide-input"
]
Expand Down Expand Up @@ -471,6 +481,67 @@
"Latex(aslatex(parameters_default))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
":::{note}\n",
"The mass and width of resonances are customsed to make the resonance bands in a better visible form.\n",
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":::"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"tags": [
"remove-cell"
]
},
"outputs": [],
"source": [
"isinstance(a[-2], sp.Indexed)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"tags": [
"remove-cell"
]
},
"outputs": [],
"source": [
"isinstance(m_a2, sp.Indexed)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"tags": [
"remove-cell"
]
},
"outputs": [],
"source": [
"type(m_a2).__mro__"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"tags": [
"remove-cell"
]
},
"outputs": [],
"source": [
"type(a[-2]).__mro__"
]
},
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{
"cell_type": "markdown",
"metadata": {},
Expand Down Expand Up @@ -601,6 +672,98 @@
"### Dalitz Plot"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"jupyter": {
"source_hidden": true
}
},
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"outputs": [],
"source": [
"sliders = {}\n",
"categorized_sliders_m = defaultdict(list)\n",
"categorized_sliders_gamma = defaultdict(list)\n",
"categorized_cphi_pair = defaultdict(list)\n",
"\n",
"for symbol, value in parameters_default.items():\n",
" if symbol.name.startswith(R\"\\Gamma_{\"):\n",
" slider = w.FloatSlider(\n",
" description=Rf\"\\({sp.latex(symbol)}\\)\",\n",
" min=0.0,\n",
" max=1.0,\n",
" step=0.01,\n",
" value=value,\n",
" continuous_update=False,\n",
" )\n",
" sliders[symbol.name] = slider\n",
" if symbol.name.startswith(R\"\\Gamma_{N\"):\n",
" categorized_sliders_gamma[0].append(slider)\n",
" elif symbol.name.startswith(R\"\\Gamma_{\\D\"):\n",
" categorized_sliders_gamma[1].append(slider)\n",
" elif symbol.name.startswith(R\"\\Gamma_{a\"):\n",
" categorized_sliders_gamma[2].append(slider)\n",
"\n",
" elif symbol.name.startswith(\"m_{\"):\n",
" slider = w.FloatSlider(\n",
" description=Rf\"\\({sp.latex(symbol)}\\)\",\n",
" min=0.63,\n",
" max=4,\n",
" step=0.01,\n",
" value=value,\n",
" continuous_update=False,\n",
" )\n",
" sliders[symbol.name] = slider\n",
" if symbol.name.startswith(\"m_{N\"):\n",
" categorized_sliders_m[0].append(slider)\n",
" elif symbol.name.startswith(R\"m_{\\D\"):\n",
" categorized_sliders_m[1].append(slider)\n",
" elif symbol.name.startswith(\"m_{a\"):\n",
" categorized_sliders_m[2].append(slider)\n",
"\n",
" else:\n",
" c_latex = sp.latex(symbol)\n",
" phi_latex = Rf\"\\phi_{{{c_latex}}}\"\n",
" slider_c = w.FloatSlider(\n",
" description=Rf\"\\({c_latex}\\)\",\n",
" min=0,\n",
" max=10,\n",
" value=abs(value),\n",
" continuous_update=False,\n",
" )\n",
" slider_phi = w.FloatSlider(\n",
" description=Rf\"\\({phi_latex}\\)\",\n",
" min=-np.pi,\n",
" max=+np.pi,\n",
" value=np.angle(value),\n",
" continuous_update=False,\n",
" )\n",
"\n",
" sliders[symbol.name] = slider_c\n",
" sliders[f\"phi_{symbol.name}\"] = slider_phi\n",
" cphi_hbox = w.HBox([slider_c, slider_phi])\n",
" if symbol.base is a:\n",
" categorized_cphi_pair[2].append(cphi_hbox)\n",
" elif symbol.base is b:\n",
" categorized_cphi_pair[1].append(cphi_hbox)\n",
" elif symbol.base is c:\n",
" categorized_cphi_pair[0].append(cphi_hbox)\n",
" else:\n",
" raise NotImplementedError(symbol.name)\n",
"\n",
"tab_contents = []\n",
"resonances_name = [\"N*\", \"Δ*\", \"a₂*\"]\n",
"for i in range(len(resonances_name)):\n",
" tab_content = w.VBox([\n",
" w.HBox(categorized_sliders_m[i] + categorized_sliders_gamma[i]),\n",
" w.VBox(categorized_cphi_pair[i]),\n",
" ])\n",
" tab_contents.append(tab_content)\n",
"UI = w.Tab(tab_contents, titles=resonances_name)\n",
"UI"
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]
},
{
"cell_type": "code",
"execution_count": null,
Expand All @@ -624,6 +787,34 @@
"intensities = intensity_func(phsp)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"jupyter": {
"source_hidden": true
},
"tags": [
"hide-input"
]
},
"outputs": [],
"source": [
"def insert_phi(parameters: dict) -> dict:\n",
" updated_parameters = {}\n",
" for key, value in parameters.items():\n",
" if key.startswith(\"phi_\"):\n",
" continue\n",
" if key.startswith((\"a\", \"b\", \"c\")):\n",
" phi_key = f\"phi_{key}\"\n",
" if phi_key in parameters:\n",
" phi = parameters[phi_key]\n",
" value *= np.exp(1j * phi) # noqa:PLW2901\n",
" updated_parameters[key] = value\n",
"\n",
" return updated_parameters"
]
},
{
"cell_type": "code",
"execution_count": null,
Expand All @@ -638,25 +829,48 @@
},
"outputs": [],
"source": [
"%matplotlib widget\n",
"%config InlineBackend.figure_formats = ['png']\n",
"fig_2d, ax_2d = plt.subplots(dpi=200)\n",
"ax_2d.set_title(\"Model-weighted Phase space Dalitz Plot\")\n",
"ax_2d.set_xlabel(R\"$m^2(\\eta \\pi^0)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
"ax_2d.set_ylabel(R\"$m^2(\\pi^0 p)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
"\n",
"fig, ax = plt.subplots(dpi=200)\n",
"hist = ax.hist2d(\n",
" phsp[\"s_{12}\"],\n",
" phsp[\"s_{23}\"],\n",
" bins=200,\n",
" cmin=1e-6,\n",
" density=True,\n",
" cmap=\"jet\",\n",
" vmax=0.15,\n",
" weights=intensities,\n",
")\n",
"ax.set_title(\"Model-weighted Phase space Dalitz Plot\")\n",
"ax.set_xlabel(R\"$m^2(\\eta \\pi^0)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
"ax.set_ylabel(R\"$m^2(\\pi^0 p)\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
"fig.colorbar(hist[3], ax=ax)\n",
"fig.tight_layout()\n",
"plt.show()"
"mesh = None\n",
"\n",
"\n",
"def update_histogram(**parameters):\n",
" global mesh\n",
" parameters = insert_phi(parameters)\n",
" intensity_func.update_parameters(parameters)\n",
" intensity_weights = intensity_func(phsp)\n",
" bin_values, xedges, yedges = jnp.histogram2d(\n",
" phsp[\"s_{12}\"],\n",
" phsp[\"s_{23}\"],\n",
" bins=200,\n",
" weights=intensity_weights,\n",
" density=True,\n",
" )\n",
" bin_values = jnp.where(bin_values < 1e-6, jnp.nan, bin_values)\n",
" x, y = jnp.meshgrid(xedges[:-1], yedges[:-1])\n",
" if mesh is None:\n",
" mesh = ax_2d.pcolormesh(x, y, bin_values.T, cmap=\"jet\", vmax=0.15)\n",
" else:\n",
" mesh.set_array(bin_values.T)\n",
" fig_2d.canvas.draw_idle()\n",
"\n",
"\n",
"interactive_plot = w.interactive_output(update_histogram, sliders)\n",
"fig_2d.tight_layout()\n",
"fig_2d.colorbar(mesh, ax=ax_2d)\n",
"\n",
"if STATIC_PAGE:\n",
" filename = \"dalitz-plot.png\"\n",
" fig_2d.savefig(filename)\n",
" plt.close(fig_2d)\n",
" display(UI, Image(filename))\n",
"else:\n",
" display(UI, interactive_plot)"
]
},
{
Expand All @@ -674,8 +888,8 @@
"source_hidden": true
},
"tags": [
"hide-input",
"full-width"
"full-width",
"hide-input"
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]
},
"outputs": [],
Expand Down
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