FEAT: implement perform_cached_doit()

.flake8

@@ -1,65 +1,66 @@
 [flake8]
 application-import-names =
-    ampform
+  ampform
 filename =
-    ./docs/*.py
-    ./src/*.py
-    ./tests/*.py
+  ./docs/*.py
+  ./src/*.py
+  ./tests/*.py
 exclude =
-    **/__pycache__
-    **/_build
-    *.pyi
-    /typings/**
+  **/__pycache__
+  **/_build
+  *.pyi
+  /typings/**
 ignore =
-    # False positive with attribute docstrings
-    B018
-    # https://github.com/psf/black#slices
-    E203
-    # allowed by black
-    E231
-    # https://github.com/psf/black#line-length
-    E501
-    # should be possible to use {} in latex strings
-    FS003
-    # block quote ends without a blank line (black formatting)
-    RST201
-    # missing pygments
-    RST299
-    # unexpected indentation (related to google style docstring)
-    RST301
-    # false-positive error in math directive
-    RST307
-    # enforce type ignore with mypy error codes (combined --extend-select=TI100)
-    TI1
-    # https://github.com/psf/black#line-breaks--binary-operators
-    W503
+  # False positive with attribute docstrings
+  B018
+  # https://github.com/psf/black#slices
+  E203
+  # allowed by black
+  E231
+  # https://github.com/psf/black#line-length
+  E501
+  # should be possible to use {} in latex strings
+  FS003
+  # block quote ends without a blank line (black formatting)
+  RST201
+  # missing pygments
+  RST299
+  # unexpected indentation (related to google style docstring)
+  RST301
+  # false-positive error in math directive
+  RST307
+  # enforce type ignore with mypy error codes (combined --extend-select=TI100)
+  TI1
+  # https://github.com/psf/black#line-breaks--binary-operators
+  W503
 extend-select =
-    TI100
+  TI100
 per-file-ignores =
-    # unused imports for backward compatibility
-    src/ampform/dynamics/__init__.py:F401
-    # λ symbols for DPD paper
-    src/ampform/helicity/align/dpd.py:N806
+  # unused imports for backward compatibility
+  src/ampform/dynamics/__init__.py:F401
+  # λ symbols for DPD paper
+  src/ampform/helicity/align/dpd.py:N806
+  tests/sympy/test_caching.py:C408
 radon-max-cc = 8
 radon-no-assert = True
 rst-roles =
-    attr
-    cite
-    class
-    doc
-    download
-    eq
-    file
-    func
-    meth
-    mod
-    pdg-review
-    ref
-    term
+  attr
+  cite
+  class
+  doc
+  download
+  eq
+  file
+  func
+  meth
+  mod
+  pdg-review
+  ref
+  term
 rst-directives =
-    autolink-preface
-    automethod
-    deprecated
-    envvar
-    exception
-    seealso
+  autolink-preface
+  automethod
+  deprecated
+  envvar
+  exception
+  seealso

.github/workflows/ci-tests.yml

@@ -1,4 +1,6 @@
 name: pytest
+env:
+  PYTHONHASHSEED: "0"
 
 on:
   push:

.vscode/settings.json

@@ -48,6 +48,7 @@
   ],
   "python.analysis.autoImportCompletions": false,
   "python.analysis.diagnosticMode": "workspace",
+  "python.analysis.typeCheckingMode": "strict",
   "python.formatting.provider": "black",
   "python.linting.banditEnabled": false,
   "python.linting.enabled": true,

docs/_extend_docstrings.py

@@ -721,7 +721,7 @@ def _graphviz_to_image(  # pylint: disable=too-many-arguments
         options = {}
     global _GRAPHVIZ_COUNTER  # pylint: disable=global-statement
     output_file = f"graphviz_{_GRAPHVIZ_COUNTER}"
-    _GRAPHVIZ_COUNTER += 1
+    _GRAPHVIZ_COUNTER += 1  # pyright: reportConstantRedefinition=false
     graphviz.Source(dot).render(f"{_IMAGE_DIR}/{output_file}", format=format)
     restructuredtext = "\n"
     if label:

docs/conf.py

@@ -12,7 +12,10 @@
 
 import requests
 
+# pyright: reportConstantRedefinition=false
 # pyright: reportMissingImports=false
+# pyright: reportUntypedBaseClass=false
+# pyright: reportUntypedFunctionDecorator=false
 from pybtex.database import Entry
 from pybtex.plugin import register_plugin
 from pybtex.richtext import Tag, Text

docs/usage/amplitude.ipynb

@@ -644,6 +644,34 @@
     "    model = pickle.load(stream)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Cached expression 'unfolding'\n",
+    "\n",
+    "Amplitude model expressions can be extremely large. AmpForm can formulate such expressions relatively fast, but {mod}`sympy` has to 'unfold' these expressions with {meth}`~sympy.core.basic.Basic.doit`, which can take a long time. AmpForm provides a function that can cache the 'unfolded' expression to disk, so that the expression unfolding runs faster upon the next run."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ampform.sympy import perform_cached_doit\n",
+    "\n",
+    "full_expression = perform_cached_doit(model.expression)\n",
+    "sp.count_ops(full_expression)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "See {func}`.perform_cached_doit` for some tips on how to improve performance."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1035,8 +1063,16 @@
    "name": "python3"
   },
   "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
    "name": "python",
-   "version": "3.8.12"
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.13"
   }
  },
  "nbformat": 4,

environment.yml

@@ -9,3 +9,5 @@ dependencies:
       - |
         -c .constraints/py3.8.txt
         -e .[dev]
+variables:
+  PYTHONHASHSEED: 0

pyrightconfig.json

@@ -2,10 +2,24 @@
   "exclude": [".git", ".tox", "docs/_build", "docs/adr"],
   "include": ["docs", "src", "tests"],
   "reportGeneralTypeIssues": false,
+  "reportIncompatibleMethodOverride": false,
+  "reportMissingParameterType": false,
+  "reportMissingTypeArgument": false,
+  "reportMissingTypeStubs": false,
+  "reportOverlappingOverload": false,
   "reportPrivateImportUsage": false,
+  "reportPrivateUsage": false,
   "reportUnboundVariable": false,
+  "reportUnknownArgumentType": false,
+  "reportUnknownMemberType": false,
+  "reportUnknownParameterType": false,
+  "reportUnknownVariableType": false,
+  "reportUnnecessaryComparison": false,
+  "reportUnnecessaryContains": false,
+  "reportUnnecessaryIsInstance": false,
   "reportUnusedClass": true,
   "reportUnusedFunction": true,
   "reportUnusedImport": true,
-  "reportUnusedVariable": true
+  "reportUnusedVariable": true,
+  "typeCheckingMode": "strict"
 }

src/ampform/dynamics/__init__.py

@@ -197,7 +197,8 @@ def __getnewargs_ex__(self) -> tuple[tuple, dict]:
 
     def _hashable_content(self) -> tuple:
         # https://github.com/sympy/sympy/blob/1.10/sympy/core/basic.py#L157-L165
-        return (*self.args, self.phsp_factor, self._name)
+        # phsp_factor is converted to string because of unstable hash for classes
+        return (*super()._hashable_content(), str(self.phsp_factor))
 
     def evaluate(self) -> sp.Expr:
         s, mass0, gamma0, m_a, m_b, angular_momentum, meson_radius = self.args

src/ampform/helicity/__init__.py

@@ -165,7 +165,7 @@ def unfold_poolsums(expr: sp.Expr) -> sp.Expr:
 
         intensity = self.intensity.evaluate()
         intensity = unfold_poolsums(intensity)
-        return intensity.subs(self.amplitudes)
+        return intensity.xreplace(self.amplitudes)
 
     def rename_symbols(  # noqa: R701
         self, renames: Iterable[tuple[str, str]] | Mapping[str, str]

src/ampform/sympy/__init__.py

@@ -5,9 +5,15 @@
 from __future__ import annotations
 
 import functools
+import hashlib
 import itertools
+import logging
+import os
+import pickle
 import re
 from abc import abstractmethod
+from os.path import abspath, dirname, expanduser
+from textwrap import dedent
 from typing import Callable, Iterable, Sequence, SupportsFloat, TypeVar
 
 import sympy as sp
@@ -16,6 +22,8 @@
 from sympy.printing.numpy import NumPyPrinter
 from sympy.printing.precedence import PRECEDENCE
 
+_LOGGER = logging.getLogger(__name__)
+
 
 class UnevaluatedExpression(sp.Expr):
     """Base class for expression classes with an :meth:`evaluate` method.
@@ -95,6 +103,11 @@ def __getnewargs_ex__(self) -> tuple[tuple, dict]:
         kwargs = {"name": self._name}
         return args, kwargs
 
+    def _hashable_content(self) -> tuple:
+        # https://github.com/sympy/sympy/blob/1.10/sympy/core/basic.py#L157-L165
+        # name is converted to string because unstable hash for None
+        return (*super()._hashable_content(), str(self._name))
+
     @abstractmethod
     def evaluate(self) -> sp.Expr:
         """Evaluate and 'unfold' this `UnevaluatedExpression` by one level.
@@ -490,3 +503,74 @@ def determine_indices(symbol: sp.Basic) -> list[int]:
     except SyntaxError:
         return []
     return list(indices)
+
+
+def perform_cached_doit(
+    unevaluated_expr: sp.Expr, directory: str | None = None
+) -> sp.Expr:
+    """Perform :meth:`~sympy.core.basic.Basic.doit` cache the result to disk.
+
+    The cached result is fetched from disk if the hash of the original expression is the
+    same as the hash embedded in the filename.
+
+    Args:
+        unevaluated_expr: A `sympy.Expr <sympy.core.expr.Expr>` on which to call
+            :meth:`~sympy.core.basic.Basic.doit`.
+        directory: The directory in which to cache the result. If `None`, the cache
+            directory will be put under the home directory.
+
+    .. tip:: For a faster cache, set `PYTHONHASHSEED
+        <https://docs.python.org/3/using/cmdline.html#envvar-PYTHONHASHSEED>`_ to a
+        fixed value.
+    """
+    if directory is None:
+        home_directory = expanduser("~")
+        directory = abspath(f"{home_directory}/.sympy-cache")
+    h = get_readable_hash(unevaluated_expr)
+    filename = f"{directory}/{h}.pkl"
+    os.makedirs(dirname(filename), exist_ok=True)
+    if os.path.exists(filename):
+        with open(filename, "rb") as f:
+            return pickle.load(f)
+    _LOGGER.warning(
+        f"Cached expression file {filename} not found, performing doit()..."
+    )
+    unfolded_expr = unevaluated_expr.doit()
+    with open(filename, "wb") as f:
+        pickle.dump(unfolded_expr, f)
+    return unfolded_expr
+
+
+def get_readable_hash(obj) -> str:
+    python_hash_seed = _get_python_hash_seed()
+    if python_hash_seed is not None:
+        return f"pythonhashseed-{python_hash_seed}{hash(obj):+}"
+    b = _to_bytes(obj)
+    return hashlib.sha256(b).hexdigest()
+
+
+def _to_bytes(obj) -> bytes:
+    if isinstance(obj, sp.Expr):
+        # Using the str printer is slower and not necessarily unique,
+        # but pickle.dumps() does not always result in the same bytes stream.
+        _warn_about_unsafe_hash()
+        return str(obj).encode()
+    return pickle.dumps(obj)
+
+
+def _get_python_hash_seed() -> int | None:
+    python_hash_seed = os.environ.get("PYTHONHASHSEED", "")
+    if python_hash_seed is not None and python_hash_seed.isdigit():
+        return int(python_hash_seed)
+    return None
+
+
+@functools.lru_cache(maxsize=None)  # warn once
+def _warn_about_unsafe_hash():
+    message = """
+    PYTHONHASHSEED has not been set. For faster and safer hashing of SymPy expressions,
+    set the PYTHONHASHSEED environment variable to a fixed value and rerun the program.
+    See https://docs.python.org/3/using/cmdline.html#envvar-PYTHONHASHSEED
+    """
+    message = dedent(message).replace("\n", " ").strip()
+    _LOGGER.warning(message)

tests/dynamics/test_builder.py

@@ -89,6 +89,7 @@ def test_breit_wigner_with_energy_dependent_width(
 
         builder.form_factor = True
         bw_with_ff, parameters = builder(particle, variable_set)
+        #  pyright: reportConstantRedefinition=false
         L = variable_set.angular_momentum  # noqa: N806
         form_factor = formulate_form_factor(
             s, m1, m2, angular_momentum=L, meson_radius=d