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FEAT: implement
unevaluated_expression decorator (#365)
* DOC: add notebook for SymPy helper functions * DOC: illustrate usage of `PoolSum` * DX: skip ipywidgets tests that copy widgets * DX: upgrade developer environment to Python 3.11 * ENH: make implementation method public as `evaluate()` * FEAT: implement `unevaluated_expression` decorator * MAINT: update Codecov config style
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| "pyright", | ||
| "pytestconfig", | ||
| "rankdir", | ||
| "repr", | ||
| "richman", | ||
| "rightarrow", | ||
| "risch", | ||
|
|
||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,232 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": { | ||
| "hideCode": true, | ||
| "hideOutput": true, | ||
| "hidePrompt": true, | ||
| "jupyter": { | ||
| "source_hidden": true | ||
| }, | ||
| "slideshow": { | ||
| "slide_type": "skip" | ||
| }, | ||
| "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 | ||
| }, | ||
| "slideshow": { | ||
| "slide_type": "skip" | ||
| }, | ||
| "tags": [ | ||
| "remove-cell" | ||
| ] | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import os\n", | ||
| "\n", | ||
| "STATIC_WEB_PAGE = {\"EXECUTE_NB\", \"READTHEDOCS\"}.intersection(os.environ)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "```{autolink-concat}\n", | ||
| "```" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# SymPy helper functions" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "The {mod}`ampform.sympy` module contains a few classes that make it easier to construct larger expressions that consist of several mathematical definitions." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Unevaluated expressions" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "The {func}`.unevaluated_expression` decorator makes it easier to write classes that represent a mathematical function definition. It makes a class that derives from {class}`sp.Expr <sympy.core.expr.Expr>` behave more like a {func}`~.dataclasses.dataclass` (see [PEP 861](https://peps.python.org/pep-0681)). All you have to do is:\n", | ||
| "\n", | ||
| "1. Specify the arguments the function requires.\n", | ||
| "2. Specify how to render the 'unevaluated' or 'folded' form of the expression with a `_latex_repr_` string or method.\n", | ||
| "3. Specify how to unfold the expression using an `evaluate()` method.\n", | ||
| "\n", | ||
| "In the example below, we define a phase space factor $\\rho^\\text{CM}$ using the Chew-Mandelstam function (see PDG Resonances section, [Eq. (50.44)](https://pdg.lbl.gov/2023/reviews/rpp2023-rev-resonances.pdf#page=15)). For this, you need to define a break-up momentum $q$ as well." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import sympy as sp\n", | ||
| "\n", | ||
| "from ampform.sympy import unevaluated_expression\n", | ||
| "\n", | ||
| "\n", | ||
| "@unevaluated_expression(real=False)\n", | ||
| "class PhspFactorSWave(sp.Expr):\n", | ||
| " s: sp.Symbol\n", | ||
| " m1: sp.Symbol\n", | ||
| " m2: sp.Symbol\n", | ||
| " _latex_repr_ = R\"\\rho^\\text{{CM}}\\left({s}\\right)\"\n", | ||
| "\n", | ||
| " def evaluate(self) -> sp.Expr:\n", | ||
| " s, m1, m2 = self.args\n", | ||
| " q = BreakupMomentum(s, m1, m2)\n", | ||
| " cm = (\n", | ||
| " (2 * q / sp.sqrt(s))\n", | ||
| " * sp.log((m1**2 + m2**2 - s + 2 * sp.sqrt(s) * q) / (2 * m1 * m2))\n", | ||
| " - (m1**2 - m2**2) * (1 / s - 1 / (m1 + m2) ** 2) * sp.log(m1 / m2)\n", | ||
| " ) / (16 * sp.pi**2)\n", | ||
| " return 16 * sp.pi * sp.I * cm\n", | ||
| "\n", | ||
| "\n", | ||
| "@unevaluated_expression(real=False)\n", | ||
| "class BreakupMomentum(sp.Expr):\n", | ||
| " s: sp.Symbol\n", | ||
| " m1: sp.Symbol\n", | ||
| " m2: sp.Symbol\n", | ||
| " _latex_repr_ = R\"q\\left({s}\\right)\"\n", | ||
| "\n", | ||
| " def evaluate(self) -> sp.Expr:\n", | ||
| " s, m1, m2 = self.args\n", | ||
| " return sp.sqrt((s - (m1 + m2) ** 2) * (s - (m1 - m2) ** 2) / (s * 4))" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "As can be seen, the LaTeX rendering of these classes makes them ideal for mathematically defining and building up larger amplitude models:" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": { | ||
| "editable": true, | ||
| "slideshow": { | ||
| "slide_type": "" | ||
| }, | ||
| "tags": [ | ||
| "hide-input" | ||
| ] | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from IPython.display import Math\n", | ||
| "\n", | ||
| "from ampform.io import aslatex\n", | ||
| "\n", | ||
| "s, m1, m2 = sp.symbols(\"s m1 m2\")\n", | ||
| "q_expr = BreakupMomentum(s, m1, m2)\n", | ||
| "rho_expr = PhspFactorSWave(s, m1, m2)\n", | ||
| "Math(aslatex({e: e.evaluate() for e in [rho_expr, q_expr]}))" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## Summations" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "The {class}`.PoolSum` class makes it possible to write sums over non-integer ranges. This is for instance useful when summing over allowed helicities. Here are some examples:" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from ampform.sympy import PoolSum\n", | ||
| "\n", | ||
| "i, j, m, n = sp.symbols(\"i j m n\")\n", | ||
| "expr = PoolSum(i**m + j**n, (i, (-1, 0, +1)), (j, (2, 4, 5)))\n", | ||
| "Math(aslatex({expr: expr.doit()}))" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "\n", | ||
| "A = sp.IndexedBase(\"A\")\n", | ||
| "λ, μ = sp.symbols(\"lambda mu\")\n", | ||
| "to_range = lambda a, b: tuple(sp.Rational(i) for i in np.arange(a, b + 0.5))\n", | ||
| "expr = abs(PoolSum(A[λ, μ], (λ, to_range(-0.5, +0.5)), (μ, to_range(-1, +1)))) ** 2\n", | ||
| "Math(aslatex({expr: expr.doit()}))" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "colab": { | ||
| "toc_visible": true | ||
| }, | ||
| "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": "3.11.5" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 4 | ||
| } |
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