FIX: stabilize numerical integral (#490)

* DOC: improve Riemann sheet plot
* DX: benchmark evaluation time of integral over Riemann sheets
* DX: reduce resolution of Riemann sheet plot
* DX: suppress `RemovedInSphinx10Warning` warning
* ENH: make `quad_vec` call lambdification more extendable
* FIX: remove default `limit=50` in `quad_vec()` call
* FIX: remove `type()` call that was used for testing
* MAINT: apply Prettier formatting to notebooks

Author: redeboer

.pre-commit-config.yaml

@@ -13,7 +13,7 @@ repos:
       - id: check-useless-excludes
 
   - repo: https://github.com/ComPWA/policy
-    rev: 0.8.2
+    rev: b122464266f519d41284e4a51673fb1232d1fd0b
     hooks:
       - id: check-dev-files
         args:

docs/conf.py

@@ -4,8 +4,11 @@
 import inspect
 import os
 import sys
+import warnings
 from dataclasses import is_dataclass
 
+import requests
+from sphinx.deprecation import RemovedInSphinx10Warning
 from sphinx_api_relink.helpers import (
     get_branch_name,
     get_execution_mode,
@@ -20,6 +23,8 @@
 sys.path.insert(0, os.path.abspath("."))
 from _extend_docstrings import extend_docstrings  # noqa: PLC2701
 
+warnings.filterwarnings("ignore", category=RemovedInSphinx10Warning)
+
 
 def _get_excluded_members() -> list[str]:
     default_exclusions = {
@@ -61,6 +66,14 @@ def _get_dataclasses(module):
     return dataclass_list
 
 
+def _get_scipy_url() -> str:
+    url = f"https://docs.scipy.org/doc/scipy-{pin('scipy')}/"
+    r = requests.get(url)
+    if r.status_code != 200:  # noqa: PLR2004
+        return "https://docs.scipy.org/doc/scipy"
+    return url
+
+
 extend_docstrings()
 set_intersphinx_version_remapping({
     "ipython": {
@@ -278,6 +291,7 @@ def _get_dataclasses(module):
     "numpy": (f"https://numpy.org/doc/{pin_minor('numpy')}", None),
     "python": ("https://docs.python.org/3", None),
     "qrules": (f"https://qrules.readthedocs.io/{pin('qrules')}", None),
+    "scipy": (_get_scipy_url(), None),
     "spb": (
         f"https://sympy-plot-backends.readthedocs.io/en/v{pin('sympy-plot-backends')}",
         None,

docs/usage.ipynb

@@ -7,6 +7,7 @@
     "# Usage\n",
     "\n",
     "```{autolink-concat}\n",
+    "\n",
     "```"
    ]
   },

docs/usage/amplitude.ipynb

@@ -7,6 +7,7 @@
     "# Formulate amplitude model\n",
     "\n",
     "```{autolink-concat}\n",
+    "\n",
     "```"
    ]
   },
@@ -493,7 +494,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "To set dynamics for specific resonances, use {meth}`.DynamicsSelector.assign` on the same {attr}`.HelicityAmplitudeBuilder.dynamics` attribute.  You can set the dynamics to be any kind of {class}`~sympy.core.expr.Expr`, as long as you keep track of which {class}`~sympy.core.symbol.Symbol` names you use (see {doc}`/usage/dynamics/custom`).\n",
+    "To set dynamics for specific resonances, use {meth}`.DynamicsSelector.assign` on the same {attr}`.HelicityAmplitudeBuilder.dynamics` attribute. You can set the dynamics to be any kind of {class}`~sympy.core.expr.Expr`, as long as you keep track of which {class}`~sympy.core.symbol.Symbol` names you use (see {doc}`/usage/dynamics/custom`).\n",
     "\n",
     "AmpForm does provide a few common {mod}`.dynamics` functions, which can be constructed as {class}`~sympy.core.expr.Expr` with the correct {class}`~sympy.core.symbol.Symbol` names using {meth}`.DynamicsSelector.assign`. This function takes specific {mod}`.dynamics.builder` functions and classes, such as {class}`.RelativisticBreitWignerBuilder`, which can create {func}`.relativistic_breit_wigner` functions for specific resonances. Here's an example for a relativistic Breit-Wigner _with form factor_ for the intermediate resonances and use a Blatt-Weisskopf barrier factor for the production decay:"
    ]

docs/usage/dynamics.ipynb

@@ -5,7 +5,9 @@
    "metadata": {},
    "source": [
     "# Dynamics\n",
+    "\n",
     "```{autolink-concat}\n",
+    "\n",
     "```"
    ]
   },
@@ -33,6 +35,7 @@
     "```\n",
     "\n",
     "```{autolink-skip}\n",
+    "\n",
     "```"
    ]
   },

docs/usage/dynamics/analytic-continuation.ipynb

@@ -5,7 +5,9 @@
    "metadata": {},
    "source": [
     "# Analytic continuation\n",
+    "\n",
     "```{autolink-concat}\n",
+    "\n",
     "```"
    ]
   },
@@ -623,6 +625,7 @@
    "metadata": {},
    "source": [
     "```{autolink-skip}\n",
+    "\n",
     "```"
    ]
   },

docs/usage/dynamics/custom.ipynb

@@ -5,7 +5,9 @@
    "metadata": {},
    "source": [
     "# Custom dynamics\n",
+    "\n",
     "```{autolink-concat}\n",
+    "\n",
     "```"
    ]
   },

docs/usage/dynamics/k-matrix.ipynb

@@ -1,19 +1,15 @@
 {
  "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "```{autolink-concat}\n",
-    "```"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# K-matrix\n",
     "\n",
+    "```{autolink-concat}\n",
+    "\n",
+    "```\n",
+    "\n",
     "<!-- cspell:ignore amma -->"
    ]
   },
@@ -32,6 +28,7 @@
     ":::\n",
     "\n",
     "```{autolink-skip}\n",
+    "\n",
     "```"
    ]
   },
@@ -93,15 +90,6 @@
     "warnings.filterwarnings(\"ignore\")"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "type(plt.subplots()[0].canvas)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},

docs/usage/dynamics/riemann-sheets.ipynb

@@ -1,62 +1,16 @@
 {
  "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "hideCode": true,
-    "hideOutput": true,
-    "hidePrompt": true,
-    "jupyter": {
-     "source_hidden": true
-    },
-    "tags": [
-     "remove-cell",
-     "skip-execution"
-    ]
-   },
-   "outputs": [],
-   "source": [
-    "# WARNING: advised to install a specific version, e.g. ampform==0.1.2\n",
-    "%pip install -q ampform[doc,viz] IPython"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "hideCode": true,
-    "hideOutput": true,
-    "hidePrompt": true,
-    "jupyter": {
-     "source_hidden": true
-    },
-    "tags": [
-     "remove-cell"
-    ]
-   },
-   "outputs": [],
-   "source": [
-    "import os\n",
-    "\n",
-    "STATIC_WEB_PAGE = {\"EXECUTE_NB\", \"READTHEDOCS\"}.intersection(os.environ)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "# Continuation into other Riemann sheets\n",
+    "\n",
     "```{autolink-concat}\n",
+    "\n",
     "```"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Continuation into other Riemann sheets"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -522,8 +476,8 @@
    },
    "outputs": [],
    "source": [
-    "x = np.linspace(0, 8, num=300)\n",
-    "y = np.linspace(1e-3, 1, num=100)\n",
+    "x = np.linspace(0, 6, num=150)\n",
+    "y = np.linspace(1e-3, 1, num=40)\n",
     "X, Y = np.meshgrid(x, y)\n",
     "Zn = X - Y * 1j\n",
     "Zp = X + Y * 1j"
@@ -542,6 +496,7 @@
    },
    "outputs": [],
    "source": [
+    "%%time\n",
     "T1n = evaluate(T1_func, Zn**2)\n",
     "T1p = evaluate(T1_func, Zp**2)\n",
     "\n",
@@ -563,14 +518,15 @@
      "source_hidden": true
     },
     "tags": [
+     "full-width",
      "hide-input"
     ]
    },
    "outputs": [],
    "source": [
-    "fig, axes = plt.subplots(figsize=(11, 4), ncols=2, sharey=True)\n",
+    "fig, axes = plt.subplots(figsize=(13, 4), ncols=2, sharey=True)\n",
     "ax1, ax2 = axes.ravel()\n",
-    "fig.subplots_adjust(wspace=0.1)\n",
+    "fig.subplots_adjust(wspace=0.05)\n",
     "fig.suptitle(R\"$s_{thr1}<s_{thr2}<m_{res}$\", fontsize=20)\n",
     "ax1.set_title(\"I and II\", y=0.88)\n",
     "ax2.set_title(\"I and III\", y=0.88)\n",
@@ -598,7 +554,7 @@
     "    ax.axvline(parameters[m0], **linestyle_res)\n",
     "\n",
     "ax1.legend(fontsize=11, loc=\"lower left\")\n",
-    "cbar = fig.colorbar(mesh, ax=axes)\n",
+    "cbar = fig.colorbar(mesh, ax=axes, pad=0.01)\n",
     "cbar.ax.set_ylabel(R\"$\\mathrm{Im} T(s)$\")\n",
     "fig.show()"
    ]

docs/usage/helicity/formalism.ipynb

@@ -5,7 +5,9 @@
    "metadata": {},
    "source": [
     "# Helicity versus canonical\n",
+    "\n",
     "```{autolink-concat}\n",
+    "\n",
     "```"
    ]
   },