From a96d0e517d251a6d41a701603c863b64d5e8bad5 Mon Sep 17 00:00:00 2001 From: LeonidElkin <113133848+LeonidElkin@users.noreply.github.com> Date: Sat, 3 Jan 2026 16:55:14 +0300 Subject: [PATCH 1/5] docs: docstrings in the project formatted correctly --- src/pysatl_core/__init__.py | 3 --- src/pysatl_core/distributions/__init__.py | 11 ++++------- src/pysatl_core/distributions/computation.py | 1 - src/pysatl_core/distributions/distribution.py | 1 - src/pysatl_core/distributions/registry/__init__.py | 2 +- .../distributions/registry/configuration.py | 4 ++-- src/pysatl_core/distributions/registry/graph.py | 11 +++++------ src/pysatl_core/distributions/sampling.py | 1 - src/pysatl_core/distributions/strategies.py | 1 - src/pysatl_core/distributions/support.py | 1 - src/pysatl_core/families/configuration.py | 1 - src/pysatl_core/types.py | 1 - 12 files changed, 12 insertions(+), 26 deletions(-) diff --git a/src/pysatl_core/__init__.py b/src/pysatl_core/__init__.py index 6450bdaf..751fd03d 100644 --- a/src/pysatl_core/__init__.py +++ b/src/pysatl_core/__init__.py @@ -1,7 +1,4 @@ """ -PySATL Core -=========== - Core framework for probabilistic distributions providing type definitions, distribution abstractions, characteristic computation graphs, and parametric family management. diff --git a/src/pysatl_core/distributions/__init__.py b/src/pysatl_core/distributions/__init__.py index 2ab7638a..85cc0a42 100644 --- a/src/pysatl_core/distributions/__init__.py +++ b/src/pysatl_core/distributions/__init__.py @@ -1,15 +1,12 @@ """ -Distributions Subpackage -======================== - Core abstractions and implementations for probability distributions used throughout PySATL. This package provides: -- Distribution protocol and computational primitives -- Characteristic graph registry with constraint-based filtering -- Sampling interfaces and strategies -- Support structures for distribution domains + - Distribution protocol and computational primitives + - Characteristic graph registry with constraint-based filtering + - Sampling interfaces and strategies + - Support structures for distribution domains """ __author__ = "Leonid Elkin, Mikhail Mikhailov" diff --git a/src/pysatl_core/distributions/computation.py b/src/pysatl_core/distributions/computation.py index 3ff24f81..5bd34c83 100644 --- a/src/pysatl_core/distributions/computation.py +++ b/src/pysatl_core/distributions/computation.py @@ -1,6 +1,5 @@ """ Computation Primitives and Conversions -====================================== Core building blocks for computing distribution characteristics and conversions between them (e.g., PDF to CDF, CDF to PPF). diff --git a/src/pysatl_core/distributions/distribution.py b/src/pysatl_core/distributions/distribution.py index b3b27d89..a19796a0 100644 --- a/src/pysatl_core/distributions/distribution.py +++ b/src/pysatl_core/distributions/distribution.py @@ -1,6 +1,5 @@ """ Distribution Interface -===================== This module defines the public Distribution protocol that serves as the abstract interface for all probability distributions in the system. diff --git a/src/pysatl_core/distributions/registry/__init__.py b/src/pysatl_core/distributions/registry/__init__.py index ffd2e1a4..60b429a7 100644 --- a/src/pysatl_core/distributions/registry/__init__.py +++ b/src/pysatl_core/distributions/registry/__init__.py @@ -1,5 +1,5 @@ """ -Characteristic Registry package. +Characteristic Registry package This package provides a graph-based registry for mathematical distribution characteristics (PDF, CDF, PMF, PPF, etc.) with constraint-based filtering. diff --git a/src/pysatl_core/distributions/registry/configuration.py b/src/pysatl_core/distributions/registry/configuration.py index 104c3658..61b2bc75 100644 --- a/src/pysatl_core/distributions/registry/configuration.py +++ b/src/pysatl_core/distributions/registry/configuration.py @@ -1,8 +1,8 @@ """ Default configuration and cached accessor for the global characteristic registry. -- No auto-configuration in constructor. -- Provide ``characteristic_registry()`` with ``@lru_cache`` that builds the + - No auto-configuration in constructor. + - Provide ``characteristic_registry()`` with ``@lru_cache`` that builds the singleton instance and seeds it with a set of edges. """ diff --git a/src/pysatl_core/distributions/registry/graph.py b/src/pysatl_core/distributions/registry/graph.py index b19637a1..ca379d8e 100644 --- a/src/pysatl_core/distributions/registry/graph.py +++ b/src/pysatl_core/distributions/registry/graph.py @@ -1,6 +1,5 @@ """ Characteristic Graph (global) + View (per distribution profile) -============================================================== This module defines the global characteristic registry and per-distribution views. @@ -10,11 +9,11 @@ features (kind, dimension, etc.). Core concepts: -- **Nodes**: Characteristics (PDF, CDF, etc.) with presence and definitiveness rules -- **Edges**: Unary computation methods between characteristics -- **Constraints**: Rules that determine when nodes/edges are applicable -- **View**: A filtered subgraph for a specific distribution -- **Definitive characteristics**: Starting points for computations + - **Nodes**: Characteristics (PDF, CDF, etc.) with presence and definitiveness rules + - **Edges**: Unary computation methods between characteristics + - **Constraints**: Rules that determine when nodes/edges are applicable + - **View**: A filtered subgraph for a specific distribution + - **Definitive characteristics**: Starting points for computations """ from __future__ import annotations diff --git a/src/pysatl_core/distributions/sampling.py b/src/pysatl_core/distributions/sampling.py index ee2acf78..87324ce5 100644 --- a/src/pysatl_core/distributions/sampling.py +++ b/src/pysatl_core/distributions/sampling.py @@ -1,6 +1,5 @@ """ Sampling Interfaces -=================== This module defines protocols and implementations for sample containers used in distribution sampling. diff --git a/src/pysatl_core/distributions/strategies.py b/src/pysatl_core/distributions/strategies.py index f5459bdc..e48b299e 100644 --- a/src/pysatl_core/distributions/strategies.py +++ b/src/pysatl_core/distributions/strategies.py @@ -1,6 +1,5 @@ """ Computation and Sampling Strategies -=================================== This module defines strategies for computing distribution characteristics and generating random samples. diff --git a/src/pysatl_core/distributions/support.py b/src/pysatl_core/distributions/support.py index 0b14f488..c8c81813 100644 --- a/src/pysatl_core/distributions/support.py +++ b/src/pysatl_core/distributions/support.py @@ -1,6 +1,5 @@ """ Support Structures for Probability Distributions -================================================ This module defines support structures for probability distributions, including continuous intervals and discrete point sets. diff --git a/src/pysatl_core/families/configuration.py b/src/pysatl_core/families/configuration.py index efb029a9..7d0358a9 100644 --- a/src/pysatl_core/families/configuration.py +++ b/src/pysatl_core/families/configuration.py @@ -1,6 +1,5 @@ """ Distribution Families Configuration -==================================== This module defines and configures parametric distribution families for the PySATL library: diff --git a/src/pysatl_core/types.py b/src/pysatl_core/types.py index c79a03d4..c63702d9 100644 --- a/src/pysatl_core/types.py +++ b/src/pysatl_core/types.py @@ -1,6 +1,5 @@ """ Core Type Definitions -===================== Fundamental types and data structures used throughout the PySATL core. """ From f45d60b41e66d0a22d77c59543553aaf340599bb Mon Sep 17 00:00:00 2001 From: LeonidElkin <113133848+LeonidElkin@users.noreply.github.com> Date: Sat, 3 Jan 2026 20:16:38 +0300 Subject: [PATCH 2/5] example: example updated to use it in docs --- examples/example-parametric.ipynb | 279 -------- examples/overview.ipynb | 676 ++++++++++++++++++ src/pysatl_core/distributions/distribution.py | 18 +- src/pysatl_core/distributions/sampling.py | 2 + src/pysatl_core/distributions/strategies.py | 35 +- src/pysatl_core/families/__init__.py | 6 + src/pysatl_core/families/builtins/__init__.py | 13 +- .../builtins/continuous/exponential.py | 6 +- .../families/builtins/continuous/normal.py | 6 +- .../families/builtins/continuous/uniform.py | 6 +- src/pysatl_core/families/distribution.py | 19 +- src/pysatl_core/families/registry.py | 20 + tests/unit/distributions/test_sampling.py | 15 +- .../families/test_family_and_distribution.py | 13 +- tests/utils/mocks.py | 13 +- 15 files changed, 789 insertions(+), 338 deletions(-) delete mode 100644 examples/example-parametric.ipynb create mode 100644 examples/overview.ipynb diff --git a/examples/example-parametric.ipynb b/examples/example-parametric.ipynb deleted file mode 100644 index 7f96ee00..00000000 --- a/examples/example-parametric.ipynb +++ /dev/null @@ -1,279 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "91dcd026-de5f-4888-b668-f4c88ae3d7ac", - "metadata": {}, - "source": "# Example: Creating parametric families #1" - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "54cdd27a-7183-4062-960b-cd28cd2bc521", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.213481Z", - "start_time": "2025-10-11T20:38:37.575570Z" - } - }, - "outputs": [], - "source": [ - "import math\n", - "\n", - "import matplotlib.pyplot as plt\n", - "\n", - "from pysatl_core.distributions import DefaultSamplingUnivariateStrategy\n", - "from pysatl_core.families import (\n", - " ParametricFamily,\n", - " ParametricFamilyRegister,\n", - " Parametrization,\n", - " constraint,\n", - " parametrization,\n", - ")\n", - "from pysatl_core.types import UnivariateContinuous\n", - "\n", - "PDF = \"pdf\"\n", - "CDF = \"cdf\"\n", - "PPF = \"ppf\"" - ] - }, - { - "cell_type": "markdown", - "id": "4854203d-24fe-4abf-ac3d-773dbbdab56b", - "metadata": {}, - "source": [ - "Let's create lognormal family of random variables, by providing PDF" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "73ccf204-fba8-4087-9f21-bdf59f04dade", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.221885Z", - "start_time": "2025-10-11T20:38:38.217685Z" - } - }, - "outputs": [], - "source": [ - "def lognormal_pdf(parameters, x: float) -> float:\n", - " if x <= 0:\n", - " return 0.0\n", - " return (\n", - " 1.0\n", - " / (x * parameters.sigma * math.sqrt(2.0 * math.pi))\n", - " * math.exp(-((math.log(x) - parameters.mu) ** 2) / (2 * parameters.sigma**2))\n", - " )" - ] - }, - { - "cell_type": "markdown", - "id": "f33585a5-02b0-4a2d-89e2-910f61dd63d8", - "metadata": {}, - "source": [ - "Now let's create an object, that will represent our family" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "680acb78-fde1-45d8-84fc-50d3058436c8", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.228341Z", - "start_time": "2025-10-11T20:38:38.225450Z" - } - }, - "outputs": [], - "source": [ - "Lognormal = ParametricFamily(\n", - " name=\"Lognormal Family\",\n", - " distr_type=UnivariateContinuous,\n", - " distr_parametrizations=[\"canonical\", \"meanvar\"],\n", - " distr_characteristics={PDF: lognormal_pdf},\n", - " sampling_strategy=DefaultSamplingUnivariateStrategy(),\n", - ")" - ] - }, - { - "cell_type": "markdown", - "id": "6709fd2b-45c6-4f66-8b0f-c9e5cd31bfad", - "metadata": {}, - "source": [ - "We specified that there will be two parametrizations: canonical (which will be treat as base) and mean-var. Let's introduce them" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "5a7da55b-4396-4cf8-bc87-328e7590e0d7", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.237676Z", - "start_time": "2025-10-11T20:38:38.231347Z" - } - }, - "outputs": [], - "source": [ - "@parametrization(family=Lognormal, name=\"canonical\")\n", - "class NormalParametrization(Parametrization):\n", - " mu: float\n", - " sigma: float\n", - "\n", - " @constraint(description=\"sigma > 0\")\n", - " def check_sigma_positive(self) -> bool:\n", - " return self.sigma > 0\n", - "\n", - "\n", - "@parametrization(family=Lognormal, name=\"meanvar\")\n", - "class MeanVarParametrization(Parametrization):\n", - " mean: float\n", - " var: float\n", - "\n", - " @constraint(description=\"mean > 0\")\n", - " def check_mean_positive(self) -> bool:\n", - " return self.mean > 0\n", - "\n", - " @constraint(description=\"var > 0\")\n", - " def check_var_positive(self) -> bool:\n", - " return self.var > 0\n", - "\n", - " def transform_to_base_parametrization(self) -> Parametrization:\n", - " mu = math.log(self.mean**2 / math.sqrt(self.mean**2 + self.var))\n", - " sigma = math.sqrt(math.log(1 + self.var / self.mean**2))\n", - " return NormalParametrization(mu=mu, sigma=sigma)" - ] - }, - { - "cell_type": "markdown", - "id": "0f11c1b8-4601-4c1c-a087-50eeb3134a89", - "metadata": {}, - "source": [ - "Note that for second parametrization we provided way convert it to base one. Now, let's register our family and do some things:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "60b6b5f2-0f6d-48f9-a45c-d927a7cc289e", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.244851Z", - "start_time": "2025-10-11T20:38:38.241933Z" - } - }, - "outputs": [], - "source": [ - "ParametricFamilyRegister.register(Lognormal)\n", - "dist = Lognormal.distribution(mean=1.0, var=1.0, parametrization_name=\"meanvar\")" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "2b631a99-42c3-4708-ad79-663786283814", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.256902Z", - "start_time": "2025-10-11T20:38:38.253729Z" - } - }, - "outputs": [], - "source": [ - "cdf = dist.query_method(CDF)\n", - "pdf = dist.query_method(PDF)\n", - "ppf = dist.query_method(PPF)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "cc1702cf-fda3-4897-b918-21515aff2a7b", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.434332Z", - "start_time": "2025-10-11T20:38:38.261386Z" - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "delta_t = 0.01\n", - "x_max = 2\n", - "x = [i * delta_t for i in range(int(x_max / delta_t))]\n", - "y_pdf = [pdf(xx) for xx in x]\n", - "y_cdf = [cdf(xx) for xx in x]\n", - "fig, ax = plt.subplots(2, 1)\n", - "ax[0].plot(x, y_pdf)\n", - "ax[1].plot(x, y_cdf)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "adeb977a-4f70-4773-a98a-02865b437d67", - "metadata": { - "ExecuteTime": { - "end_time": "2025-10-11T20:38:38.450554Z", - "start_time": "2025-10-11T20:38:38.446962Z" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0\n" - ] - } - ], - "source": [ - "base_parameters = Lognormal.to_base(dist.parameters)\n", - "y_true_pdf = [lognormal_pdf(base_parameters, xx) for xx in x]\n", - "print(max([y_true_pdf[i] - y_pdf[i] for i in range(len(x))]))" - ] - } - ], - "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": "3.13.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/overview.ipynb b/examples/overview.ipynb new file mode 100644 index 00000000..a372fa03 --- /dev/null +++ b/examples/overview.ipynb @@ -0,0 +1,676 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "709f3963", + "metadata": {}, + "source": [ + "# PySATL Core: Overview Example\n", + "\n", + "This notebook demonstrates the core capabilities of **PySATL Core**:\n", + "\n", + "1. Registering built-in distribution families in the global registry.\n", + "2. Retrieving a family object from the registry and instantiating concrete distributions.\n", + "3. Querying and visualizing characteristics (PDF / CDF / PPF).\n", + "4. Sampling via inverse transform sampling.\n", + "5. Defining and registering a custom family with **multiple parametrizations**.\n", + "6. Using the characteristic graph to obtain missing characteristics.\n", + "\n", + "Environment notes:\n", + "- **Python 3.12+** is required.\n", + "- A *family* is an **object** stored in the singleton `ParametricFamilyRegister`.\n" + ] + }, + { + "cell_type": "markdown", + "id": "439a52b3", + "metadata": {}, + "source": [ + "## Setup\n", + "\n", + "PySATL provides configuration entry points that create family objects and register them:\n", + "\n", + "- `configure_normal_family()` registers only the Normal family.\n", + "- `configure_families_register()` registers all built-in families shipped with the library.\n", + "\n", + "You can access the registry without filling it by instantiating `ParametricFamilyRegister()`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "375255d8", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:37.877029300Z", + "start_time": "2026-01-03T16:27:37.522626700Z" + } + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "from pysatl_core import (\n", + " CharacteristicName,\n", + " ContinuousSupport,\n", + " FamilyName,\n", + " ParametricFamily,\n", + " ParametricFamilyRegister,\n", + " Parametrization,\n", + " UnivariateContinuous,\n", + " configure_families_register,\n", + " configure_normal_family,\n", + " parametrization,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "57242e62", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:37.944733900Z", + "start_time": "2026-01-03T16:27:37.879669800Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Access the registry without configuring it\n", + "registry = ParametricFamilyRegister()\n", + "registry.list_registered_families()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ea4f73ba", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.004295700Z", + "start_time": "2026-01-03T16:27:37.946733700Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Option A: register ONLY the Normal family\n", + "configure_normal_family()\n", + "registry.list_registered_families()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "bbc1dcba", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.079426700Z", + "start_time": "2026-01-03T16:27:38.006329800Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[,\n", + " ,\n", + " ]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Option B: register ALL built-in families\n", + "configure_families_register()\n", + "registry.list_registered_families()" + ] + }, + { + "cell_type": "markdown", + "id": "6d54596d", + "metadata": {}, + "source": [ + "## 1) Built-in family: Normal\n", + "\n", + "A *concrete distribution* is obtained by fixing the parameters.\n", + "\n", + "You can create it via:\n", + "- `family(...)` (uses the base parametrization by default), or\n", + "- `family.distribution(parametrization_name=..., **params)`.\n", + "\n", + "The Normal family ships with multiple parametrizations:\n", + "- `meanStd` (base): `(mu, sigma)`\n", + "- `meanPrec`: `(mu, tau)` where `tau = 1 / sigma^2`\n", + "- `exponential`: `(a, b)` (an exponential-family form)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "ab545b71", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.141085Z", + "start_time": "2026-01-03T16:27:38.080490300Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(, ['meanStd', 'meanPrec', 'exponential'])" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "normal_family = ParametricFamilyRegister.get(FamilyName.NORMAL)\n", + "normal_family.name, normal_family.parametrization_names" + ] + }, + { + "cell_type": "markdown", + "id": "094ed607", + "metadata": {}, + "source": [ + "### Instantiating distributions in different parametrizations\n", + "\n", + "Below we instantiate the **same distribution** in two parametrizations:\n", + "\n", + "- `meanStd`: parameters `(mu, sigma)`\n", + "- `meanPrec`: parameters `(mu, tau)` where `tau = 1 / sigma^2`\n", + "\n", + "We then compare their PDF and CDF curves (they should match). Actually, all the characteristics are computed via base parametrization (`meanStd`). Other parametrizations are being transformed to base while computing\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "e948961b", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.197502700Z", + "start_time": "2026-01-03T16:27:38.142114100Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "('meanStd', 'meanPrec')" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d_mean_std = normal_family.distribution(parametrization_name=\"meanStd\", mu=0.0, sigma=1.0)\n", + "d_mean_prec = normal_family.distribution(parametrization_name=\"meanPrec\", mu=0.0, tau=1.0)\n", + "d_mean_std.parametrization_name, d_mean_prec.parametrization_name" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ebdfdb47", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.437243800Z", + "start_time": "2026-01-03T16:27:38.198503Z" + } + }, + "outputs": [ + { + "data": { + 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", 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", + "text/plain": [ + "
" + ] + }, + "jetTransient": { + "display_id": null + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-4, 4, 600)\n", + "\n", + "pdf_std = d_mean_std.query_method(CharacteristicName.PDF)\n", + "cdf_std = d_mean_std.query_method(CharacteristicName.CDF)\n", + "\n", + "pdf_prec = d_mean_prec.query_method(CharacteristicName.PDF)\n", + "cdf_prec = d_mean_prec.query_method(CharacteristicName.CDF)\n", + "\n", + "plt.figure(figsize=(7, 4))\n", + "plt.plot(x, pdf_std(x), label=\"PDF (meanStd)\")\n", + "plt.plot(x, pdf_prec(x), linestyle=\"--\", label=\"PDF (meanPrec)\")\n", + "plt.legend()\n", + "plt.title(\"Normal: PDF in two parametrizations\")\n", + "plt.show()\n", + "\n", + "plt.figure(figsize=(7, 4))\n", + "plt.plot(x, cdf_std(x), label=\"CDF (meanStd)\")\n", + "plt.plot(x, cdf_prec(x), linestyle=\"--\", label=\"CDF (meanPrec)\")\n", + "plt.legend()\n", + "plt.title(\"Normal: CDF in two parametrizations\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e8d50097", + "metadata": {}, + "source": [ + "### Sampling\n", + "\n", + "For the Normal distribution, sampling is provided via the high-level\n", + "`distribution.sample(...)` interface.\n", + "\n", + "Internally, the sampling strategy may rely on analytical characteristics\n", + "(such as `PPF` for inverse transform sampling), but this detail is hidden\n", + "from the user. The recommended way to generate samples is always through\n", + "`sample(...)`, which ensures a consistent and efficient implementation.\n", + "\n", + "At the moment, this only works with characteristics with NumPy semantics (so not graph computed).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "be4c0c83", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.582767100Z", + "start_time": "2026-01-03T16:27:38.440041500Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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o2ZsLNWQRtAAAQHtpqssSneEBAAAsQtACAACwCEELAADAIgQtAAAAixC0AAAALELQAgAAsAhBCwAAwCIELQAAAIsQtAAAACxC0AIAALAIQQsAAMAiBC0AAACLdIqbSgPouiLT3mpyn3Nrp7TLuQBAm1S0cnJyJDIyUgIDAyU2NlYKCwub9bw9e/aYu1xPmzbNZbvNZpOMjAwJDw+Xbt26SXx8vJw6dao1pwYAAOC9QSsvL08WLVokmZmZcvjwYRk5cqQkJCTI5cuXb/m8c+fOyZIlS+Shhx5q8Nj69etl8+bNkpubK4cOHZIePXqYY3755ZctPT0AAADvDVqbNm2SuXPnSmpqqgwdOtSEo+7du8v27dsbfU5tba3MmjVLVq1aJVFRUQ2qWdnZ2bJ8+XKZOnWqjBgxQl5++WW5dOmS7N27t3XvCgAAwNuCVk1NjRQVFZmmPccBfH3NekFBQaPP++EPfyh9+/aVOXPmNHjs7NmzUlJS4nLM4OBg0yR5q2MCAAB0qs7w5eXlpjoVGhrqsl3XT5w44fY5v/vd7+SnP/2pHDlyxO3jGrLsx6h/TPtj9VVXV5vFrrKysiVvA0AX01SHeTrLA/DK6R2uXbsm//AP/yDbtm2TkJCQNjtuVlaWqXrZl4iIiDY7NgAAQIdUtDQs+fn5SWlpqct2XQ8LC2uw/5kzZ0wn+Mcff9yxra6u7v9e+I475OTJk47n6TF01KHzMaOjo92eR3p6uumQ71zRImwBAACvrmj5+/tLTEyM7N+/3yU46XpcXFyD/YcMGSJ/+MMfTLOhffn2t78tjzzyiPlZw9GAAQNM2HI+pgYnHX3o7pgqICBAgoKCXBYAAACvn7BUK0kpKSkyevRoGTt2rBkxWFVVZUYhquTkZOnfv79p3tN5toYNG+by/N69e5s/nbcvXLhQ1qxZI4MHDzbBa8WKFdKvX78G820BAAB06qCVmJgoZWVlZoJR7ayuzXv5+fmOzuzFxcVmJGJLLF261IS1efPmydWrV2XcuHHmmBrUAAAAvJWPTSey8nLa1Kid4isqKmhGBLqY5tyCpymMOgRgVfbgXocAOn2QAoBOOb0DAABAV0bQAgAAsAhBCwAAwCIELQAAAIsQtAAAACxC0AIAALAIQQsAAMAiBC0AAACCFgAAgHehogUAAGARbsEDoMu73dv8cK9EAI2hogUAAGARKloAOhQ3jQbQmVHRAgAAsAhBCwAAwCIELQAAAIsQtAAAACxC0AIAALAIQQsAAMAiBC0AAACLELQAAAAsQtACAACwCEELAADAIgQtAAAATwpaOTk5EhkZKYGBgRIbGyuFhYWN7vv666/L6NGjpXfv3tKjRw+Jjo6WV155xWWf2bNni4+Pj8syefLk1pwaAACA995UOi8vTxYtWiS5ubkmZGVnZ0tCQoKcPHlS+vbt22D/Pn36yA9+8AMZMmSI+Pv7y5tvvimpqalmX32enQarHTt2ONYDAgJu530BAAB0OB+bzWZryRM0XI0ZM0a2bNli1uvq6iQiIkIWLFggaWlpzTrGqFGjZMqUKbJ69WpHRevq1auyd+/e1rwHqayslODgYKmoqJCgoKBWHQOANSLT3ur0l/bc2ikdfQoA2llzs0eLmg5ramqkqKhI4uPj/3oAX1+zXlBQ0OTzNdPt37/fVL/Gjx/v8tiBAwdMlevee++V+fPny5UrV1pyagAAAN7ddFheXi61tbUSGhrqsl3XT5w40ejzNO31799fqqurxc/PT1544QV59NFHXZoNn3jiCRkwYICcOXNGli1bJo899pgJb7p/fXocXZxTJQAAgNf30WqNXr16yZEjR+T69eumoqV9vKKiouThhx82jyclJTn2HT58uIwYMUIGDhxoqlwTJ05scLysrCxZtWpVe5w6ANx28yhNi0DX1aKmw5CQEFNhKi0tddmu62FhYY2/iK+vDBo0yIw4XLx4scyYMcOEpcZoCNPXOn36tNvH09PTTZXMvpw/f74lbwMAAMDzgpaOGoyJiTFVKTvtDK/rcXFxzT6OPse56a++CxcumD5a4eHhbh/XEYna8cx5AQAA8PqmQ232S0lJMXNjjR071kzvUFVVZaZsUMnJyaY/lr1ipX/qvtoUqOFq3759Zh6trVu3mse1OVGbAadPn26qYtpHa+nSpaYC5jz9AwAAQKcPWomJiVJWViYZGRlSUlJimgPz8/MdHeSLi4tNU6GdhrCnnnrKVKm6detm5tN69dVXzXGUNkUePXpUdu3aZaZ46Nevn0yaNMlM/cBcWgAAoEvNo+WJmEcL8FxdYR6tptAZHuh8LJlHCwAAAM1H0AIAALAIQQsAAMAiBC0AAACLELQAAAAsQtACAACwCEELAADAIgQtAAAAixC0AAAAPOUWPACAtp8dn9njgc6JihYAAIBFCFoAAAAWIWgBAABYhKAFAABgEYIWAACARQhaAAAAFiFoAQAAWISgBQAAYBEmLAVg6UScANCVUdECAACwCEELAADAIgQtAAAAixC0AAAALELQAgAAsAhBCwAAwJOCVk5OjkRGRkpgYKDExsZKYWFho/u+/vrrMnr0aOndu7f06NFDoqOj5ZVXXnHZx2azSUZGhoSHh0u3bt0kPj5eTp061ZpTAwAA8N6glZeXJ4sWLZLMzEw5fPiwjBw5UhISEuTy5ctu9+/Tp4/84Ac/kIKCAjl69Kikpqaa5Z133nHss379etm8ebPk5ubKoUOHTCDTY3755Ze39+4AAAA6kI9Ny0ktoBWsMWPGyJYtW8x6XV2dREREyIIFCyQtLa1Zxxg1apRMmTJFVq9ebapZ/fr1k8WLF8uSJUvM4xUVFRIaGio7d+6UpKSkJo9XWVkpwcHB5nlBQUEteTsAbgMTlradc2untOHRAFitudmjRRWtmpoaKSoqMk17jgP4+pp1rVg1RUPV/v375eTJkzJ+/Hiz7ezZs1JSUuJyTD1xDXTNOSYAAECnuAVPeXm51NbWmmqTM10/ceJEo8/TtNe/f3+prq4WPz8/eeGFF+TRRx81j2nIsh+j/jHtj9Wnx9HFOVUCAAB0yXsd9urVS44cOSLXr183FS3t4xUVFSUPP/xwq46XlZUlq1atavPzBAAAaEstajoMCQkxFanS0lKX7boeFhbW+Iv4+sqgQYPMiEPtizVjxgwTlpT9eS05Znp6uqmS2Zfz58+35G0AAAB4XtDy9/eXmJgYU5Wy087wuh4XF9fs4+hz7E1/AwYMMIHK+ZjaFKijDxs7ZkBAgOl45rwAAAB4fdOhNvulpKSYubHGjh0r2dnZUlVVZaZsUMnJyaY/lr1ipX/qvgMHDjThat++fWYera1bt5rHfXx8ZOHChbJmzRoZPHiwCV4rVqwwIxGnTZvW1u8XQAswqhAA2jloJSYmSllZmZlgVDura3Ngfn6+ozN7cXGxaSq00xD21FNPyYULF8xkpEOGDJFXX33VHMdu6dKlZr958+bJ1atXZdy4ceaYOiEqAABAl5lHyxMxjxZgDSpanoN5toAuMI8WAAAAmo+gBQAAYBGCFgAAgEUIWgAAABYhaAEAABC0AAAAvAsVLQAAAIsQtAAAACxC0AIAALAIQQsAAMAiBC0AAACLELQAAAAsQtACAACwCEELAADAIgQtAAAAixC0AAAALELQAgAAsAhBCwAAwCIELQAAAIsQtAAAACxC0AIAALAIQQsAAMAiBC0AAACLELQAAAAsQtACAADwpKCVk5MjkZGREhgYKLGxsVJYWNjovtu2bZOHHnpI7rzzTrPEx8c32H/27Nni4+PjskyePLk1pwYAAOAx7mjpE/Ly8mTRokWSm5trQlZ2drYkJCTIyZMnpW/fvg32P3DggMycOVMefPBBE8zWrVsnkyZNkmPHjkn//v0d+2mw2rFjh2M9ICDgdt4XgGaITHuL6wQAFvKx2Wy2ljxBw9WYMWNky5YtZr2urk4iIiJkwYIFkpaW1uTza2trTWVLn5+cnOyoaF29elX27t3bqjdRWVkpwcHBUlFRIUFBQa06BtAVEbQ6j3Nrp3T0KQBdSmUzs0eLmg5ramqkqKjINP85DuDra9YLCgqadYwbN27IzZs3pU+fPg0qX1oRu/fee2X+/Ply5cqVlpwaAACAdzcdlpeXm4pUaGioy3ZdP3HiRLOO8dxzz0m/fv1cwpo2Gz7xxBMyYMAAOXPmjCxbtkwee+wxE978/PwaHKO6utoszqkSAADA6/to3Y61a9fKnj17TPVK+2vZJSUlOX4ePny4jBgxQgYOHGj2mzhxYoPjZGVlyapVq9rtvAEAAFqjRU2HISEhpsJUWlrqsl3Xw8LCbvncjRs3mqD1m9/8xgSpW4mKijKvdfr0abePp6enmzZR+3L+/PmWvA0AAADPC1r+/v4SExMj+/fvd2zTzvC6HhcX1+jz1q9fL6tXr5b8/HwZPXp0k69z4cIF00crPDzc7eM6IlE7njkvAAAAXj+Plk7toHNj7dq1Sz799FPTcb2qqkpSU1PN4zqSUCtOdjqdw4oVK2T79u1m7q2SkhKzXL9+3Tyufz777LNy8OBBOXfunAltU6dOlUGDBplpIwAAALpMH63ExEQpKyuTjIwME5iio6NNpcreQb64uNiMRLTbunWrGa04Y8YMl+NkZmbKypUrTVPk0aNHTXDTKR60o7zOs6UVMObSAgAAXWoeLU/EPFpA6zCPVufBPFpAJ5hHCwAAAM1H0AIAALAIQQsAAMAiBC0AAACLELQAAAAsQtACAACwCEELAADAIgQtAAAAixC0AAAALELQAgAAsAhBCwAAwCIELQAAAIsQtAAAACxC0AIAALDIHVYdGEDHi0x7q6NPAQC6NCpaAAAAFiFoAQAAWISgBQAAYBH6aAFAF+iPd27tlHY7FwB/RUULAADAIgQtAAAAixC0AAAALELQAgAAsAhBCwAAwCIELQAAAE8KWjk5ORIZGSmBgYESGxsrhYWFje67bds2eeihh+TOO+80S3x8fIP9bTabZGRkSHh4uHTr1s3sc+rUqdacGgAAgPcGrby8PFm0aJFkZmbK4cOHZeTIkZKQkCCXL192u/+BAwdk5syZ8t5770lBQYFERETIpEmT5OLFi4591q9fL5s3b5bc3Fw5dOiQ9OjRwxzzyy+/vL13BwAA0IF8bFpOagGtYI0ZM0a2bNli1uvq6kx4WrBggaSlpTX5/NraWlPZ0ucnJyebala/fv1k8eLFsmTJErNPRUWFhIaGys6dOyUpKanJY1ZWVkpwcLB5XlBQUEveDtCpcVNp2DFhKdC2mps9WlTRqqmpkaKiItO05ziAr69Z12pVc9y4cUNu3rwpffr0Metnz56VkpISl2PqiWuga+yY1dXV5g06LwAAAJ6mRUGrvLzcVKS02uRM1zUsNcdzzz1nKlj2YGV/XkuOmZWVZcKYfdGKGgAAQJcedbh27VrZs2ePvPHGG6YjfWulp6ebUp19OX/+fJueJwAAQLvfVDokJET8/PyktLTUZbuuh4WF3fK5GzduNEHrt7/9rYwYMcKx3f48PYaOOnQ+ZnR0tNtjBQQEmAUAAKDTVLT8/f0lJiZG9u/f79imneF1PS4urtHn6ajC1atXS35+vowePdrlsQEDBpiw5XxM7XOlow9vdUwAAIBOVdFSOrVDSkqKCUxjx46V7OxsqaqqktTUVPO4jiTs37+/6Uel1q1bZ+bI2r17t5l7y97vqmfPnmbx8fGRhQsXypo1a2Tw4MEmeK1YscL045o2bVpbv18AAADPDVqJiYlSVlZmwpOGJm3e00qVvTN7cXGxGYlot3XrVjNaccaMGS7H0Xm4Vq5caX5eunSpCWvz5s2Tq1evyrhx48wxb6cfFwAAgNfNo+WJmEcLcI95tGDHPFqAF8yjBQAAgOYjaAEAAFiEoAUAAOApneEBeA76YAGAZyNoAUAX0FQop7M8YA2aDgEAACxC0AIAALAIQQsAAMAiBC0AAACLELQAAAAsQtACAACwCEELAADAIgQtAAAAixC0AAAALELQAgAAsAhBCwAAwCIELQAAAIsQtAAAACxC0AIAALAIQQsAAMAiBC0AAACL3GHVgQHcnsi0t7iEAODlqGgBAABYhIoWAKBZFdRza6dwpYAWoqIFAADgSUErJydHIiMjJTAwUGJjY6WwsLDRfY8dOybTp083+/v4+Eh2dnaDfVauXGkec16GDBnSmlMDAADw3qCVl5cnixYtkszMTDl8+LCMHDlSEhIS5PLly273v3HjhkRFRcnatWslLCys0ePed9998vnnnzuW3/3udy09NQAAAO8OWps2bZK5c+dKamqqDB06VHJzc6V79+6yfft2t/uPGTNGNmzYIElJSRIQENDoce+44w4TxOxLSEhIS08NAADAe4NWTU2NFBUVSXx8/F8P4Otr1gsKCm7rRE6dOiX9+vUz1a9Zs2ZJcXFxo/tWV1dLZWWlywIAAODVQau8vFxqa2slNDTUZbuul5SUtPoktJ/Xzp07JT8/X7Zu3Spnz56Vhx56SK5du+Z2/6ysLAkODnYsERERrX5tAACATj3q8LHHHpMnn3xSRowYYfp77du3T65evSr/8R//4Xb/9PR0qaiocCznz59v93MGAABo03m0tN+Un5+flJaWumzX9Vt1dG+p3r17y9e//nU5ffq028e1r9et+nsBAAB4XUXL399fYmJiZP/+/Y5tdXV1Zj0uLq7NTur69ety5swZCQ8Pb7NjAgAAePzM8Dq1Q0pKiowePVrGjh1r5sWqqqoyoxBVcnKy9O/f3/SjsnegP378uOPnixcvypEjR6Rnz54yaNAgs33JkiXy+OOPyz333COXLl0yU0do5WzmzJlt+24BAAA8OWglJiZKWVmZZGRkmA7w0dHRphO7vYO8jhbUkYh2Gpzuv/9+x/rGjRvNMmHCBDlw4IDZduHCBROqrly5Il/96ldl3LhxcvDgQfMzAACAt/Kx2Ww28XI6vYOOPtSO8UFBQR19OkC73XsOaE/c6xBoefbwiFGHAAAAnRFBCwAAwCIELQAAAIsQtAAAACxC0AIAALAIQQsAAMBT5tEC0DaYvgEAOj8qWgAAABYhaAEAAFiEoAUAAGAR+mgBANqkXyG36AEaoqIFAABgEYIWAACARQhaAAAAFiFoAQAAWISgBQAAYBGCFgAAgEUIWgAAABYhaAEAAFiEoAUAAGARghYAAIBFCFoAAAAWIWgBAABYhKAFAABgEYIWAACAJwWtnJwciYyMlMDAQImNjZXCwsJG9z127JhMnz7d7O/j4yPZ2dm3fUwAAIBOGbTy8vJk0aJFkpmZKYcPH5aRI0dKQkKCXL582e3+N27ckKioKFm7dq2EhYW1yTEBAAA6ZdDatGmTzJ07V1JTU2Xo0KGSm5sr3bt3l+3bt7vdf8yYMbJhwwZJSkqSgICANjkmAACAN7ijJTvX1NRIUVGRpKenO7b5+vpKfHy8FBQUtOoEWnPM6upqs9hVVla26rUBK0WmvcUFBoAurkVBq7y8XGprayU0NNRlu66fOHGiVSfQmmNmZWXJqlWrWvV6AICO+cfFubVTuPTocrxy1KFWvyoqKhzL+fPnO/qUAAAAbq+iFRISIn5+flJaWuqyXdcb6+huxTG1r1dj/b0AAAC8sqLl7+8vMTExsn//fse2uro6sx4XF9eqE7DimAAAAF5X0VI6DUNKSoqMHj1axo4da+bFqqqqMiMGVXJysvTv39/0o7J3dj9+/Ljj54sXL8qRI0ekZ8+eMmjQoGYdEwAAoEsErcTERCkrK5OMjAwpKSmR6Ohoyc/Pd3RmLy4uNqMG7S5duiT333+/Y33jxo1mmTBhghw4cKBZxwQAAPBGPjabzSZeTqd3CA4ONh3jg4KCOvp0AIPpHQBXjDpEZ9Lc7OGVow4BAAC8AUELAADAIgQtAAAAixC0AAAALELQAgAA8JTpHQD8H0YVAgCaQkULAADAIgQtAAAAixC0AAAALELQAgAAsAid4QEAHjGAhFv0oDOiogUAAGARghYAAIBFCFoAAAAWIWgBAABYhKAFAABgEYIWAACARQhaAAAAFiFoAQAAWISgBQAAYBFmhgdaMYM1AADNQUULAADAIlS0AABeU0nmfojwNlS0AAAALELQAgAA8KSglZOTI5GRkRIYGCixsbFSWFh4y/1fe+01GTJkiNl/+PDhsm/fPpfHZ8+eLT4+Pi7L5MmTW3NqAAAA3hu08vLyZNGiRZKZmSmHDx+WkSNHSkJCgly+fNnt/h988IHMnDlT5syZIx9//LFMmzbNLJ988onLfhqsPv/8c8fy7//+761/VwAAAN4YtDZt2iRz586V1NRUGTp0qOTm5kr37t1l+/btbvf/8Y9/bELUs88+K9/4xjdk9erVMmrUKNmyZYvLfgEBARIWFuZY7rzzzta/KwAAAG8LWjU1NVJUVCTx8fF/PYCvr1kvKChw+xzd7ry/0gpY/f0PHDggffv2lXvvvVfmz58vV65cafQ8qqurpbKy0mUBAADw6qBVXl4utbW1Ehoa6rJd10tKStw+R7c3tb9WvF5++WXZv3+/rFu3Tt5//3157LHHzGu5k5WVJcHBwY4lIiKiJW8DAACg68yjlZSU5PhZO8uPGDFCBg4caKpcEydObLB/enq66SdmpxUtwhYAAPDqoBUSEiJ+fn5SWlrqsl3XtV+VO7q9JfurqKgo81qnT592G7S0P5cuQGtxix0AgMcFLX9/f4mJiTFNfDpyUNXV1Zn1Z555xu1z4uLizOMLFy50bHv33XfN9sZcuHDB9NEKDw9vyekBALr4P5KYOR5eP+pQm+y2bdsmu3btkk8//dR0XK+qqjKjEFVycrJp2rP7/ve/L/n5+fL888/LiRMnZOXKlfLRRx85gtn169fNiMSDBw/KuXPnTCibOnWqDBo0yHSaBwAA6DJ9tBITE6WsrEwyMjJMh/bo6GgTpOwd3ouLi81IRLsHH3xQdu/eLcuXL5dly5bJ4MGDZe/evTJs2DDzuDZFHj161AS3q1evSr9+/WTSpElmGgiaBwEAgDfzsdlsNvFy2hleRx9WVFRIUFBQR58OvAB9tIDOiaZDeFr24F6HAAAAFiFoAQAAWISgBQAAYBGCFgAAgEUIWgAAAJ35FjwAALQFJjSFp6GiBQAAYBEqWuiUmCcLAOAJqGgBAABYhKAFAABgEYIWAACAReijBa9EHywAgDcgaAEAugymf0B7o+kQAADAIgQtAAAAixC0AAAALEIfLXgkOrsDADoDghYAAP8fneXR1mg6BAAAsAhBCwAAwCI0HaLd0f8KANBVELQAAGjDfyieWzuF6wkHmg4BAAAsQkULAIA2xMhFOCNooc3RBwsAgNtoOszJyZHIyEgJDAyU2NhYKSwsvOX+r732mgwZMsTsP3z4cNm3b5/L4zabTTIyMiQ8PFy6desm8fHxcurUqdacGgAAHv+P0Vst6OIVrby8PFm0aJHk5uaakJWdnS0JCQly8uRJ6du3b4P9P/jgA5k5c6ZkZWXJt771Ldm9e7dMmzZNDh8+LMOGDTP7rF+/XjZv3iy7du2SAQMGyIoVK8wxjx8/bsIZPAt/EQAA0Dw+Ni0ntYCGqzFjxsiWLVvMel1dnURERMiCBQskLS2twf6JiYlSVVUlb775pmPbAw88INHR0Sas6cv369dPFi9eLEuWLDGPV1RUSGhoqOzcuVOSkpKaPKfKykoJDg42zwsKCmrJ24EbBCkA8G6MfLRec7NHiypaNTU1UlRUJOnp6Y5tvr6+pqmvoKDA7XN0u1bAnGm1au/evebns2fPSklJiTmGnZ64Bjp9rrugVV1dbRY7fZP2N93VDct8p6NPAQDQwfg+tJ79GjdVr2pR0CovL5fa2lpTbXKm6ydOnHD7HA1R7vbX7fbH7dsa26c+bYZctWpVg+1aWQMAoKsLzu7oM+g6rl27ZgpEnWrUoVbUnKtk2nz5xRdfyF133SU+Pj4dnnA18J0/f55mTC/G59g58Dl2HnyWnUNlJ/qO1EqWhizt/nQrLQpaISEh4ufnJ6WlpS7bdT0sLMztc3T7rfa3/6nbdNSh8z7aj8udgIAAszjr3bu3eBL9BfL2XyLwOXYW/P/YefBZdg5BneQ78laVrFZN7+Dv7y8xMTGyf/9+l2qSrsfFxbl9jm533l+9++67jv11lKGGLed9NPEeOnSo0WMCAAB4gxY3HWqTXUpKiowePVrGjh1rpnfQUYWpqanm8eTkZOnfv7/pR6W+//3vy4QJE+T555+XKVOmyJ49e+Sjjz6Sl156yTyuTX0LFy6UNWvWyODBgx3TO2gpTqeBAAAA6DJBS6drKCsrMxOMamd1bd7Lz893dGYvLi42IxHtHnzwQTN31vLly2XZsmUmTOmIQ/scWmrp0qUmrM2bN0+uXr0q48aNM8f0xjm0tEkzMzOzQdMmvAufY+fA59h58Fl2DgFd8DuyxfNoAQAAwMJb8AAAAKBpBC0AAACLELQAAAAsQtACAACwCEGrHeh9GXV0pk5lceTIkfZ4SbSRc+fOyZw5c8y0I926dZOBAweaETN63094vpycHImMjDQjmPX+qYWFhR19SmgBnSZozJgx0qtXL+nbt6+Z8ufkyZNcQy+3du1ax9ROXQFBqx3o9BVNTdEPz6T38NRJeV988UU5duyY/OhHP5Lc3FwzVQk8W15enpn3T4Px4cOHZeTIkeaG9pcvX+7oU0Mzvf/++/L000/LwYMHzUTXN2/elEmTJpnpgOCdPvzwQ/P36YgRI6SrYHoHi7399tvmL/tf/OIXct9998nHH3/c6K2F4B02bNggW7dulT/+8Y8dfSq4Ba1gaTVky5YtZl0Ds95jbcGCBZKWlsa180I6h6NWtjSAjR8/vqNPBy10/fp1GTVqlLzwwgtmknL9LtRJzzs7KloW0vs1zp07V1555RXp3r27lS+FdlRRUSF9+vThmnswbdotKiqS+Ph4xzadSFnXCwoKOvTccHv/7yn+//NOTz/9tLlDjPP/l11Bi2eGR/PoPLCzZ8+Wf/7nfza3K9K+PvB+p0+flp/85CeycePGjj4V3EJ5ebnU1tY67lhhp+vaHAzvoxVJ7dPzzW9+0+XOIvAOe/bsMU342nTY1VDRaiFtctBOfLda9C9y/TK+du2apKenW/PJoV0+R2cXL16UyZMny5NPPmkqlQDatxryySefmC9seJfz58+b+x7/7Gc/88pb690u+mi1oo/AlStXbrlPVFSUfPe735Vf//rX5gvbTv+F7efnJ7NmzZJdu3a17hNDu36O/v7+5udLly7Jww8/LA888IDs3LnT5X6e8MymQ22u//nPf+5yc/qUlBRzP9Vf/vKXHXp+aJlnnnnGfGb/9V//ZUYAw7vs3btXvvOd75jvP+fvQ/1+1L9LdWS+82OdDUHLInpz7crKSse6flHriCf9i1876d59991WvTTamFayHnnkEYmJiZFXX321U/+F0Jno/2djx4411WV709PXvvY186VNZ3jv6YKhgxfeeOMNOXDggAwePLijTwmtcO3aNfnss89ctqWmpsqQIUPkueee6/RNwfTRsoj+he6sZ8+e5k+dh4mQ5V0hSytZ99xzj+mXpZUwu7CwsA49N9yajvbVCpb2kdTApaObdFoA/Qse3tNcuHv3blPN0rm0SkpKzPbg4GAzrx28Q69evRqEqR49eshdd93V6UOWImgBt6Bz92gHeF3qB2T91zY8V2JiognGGRkZ5gtah5Ln5+c36CAPz6XTqCj9x46zHTt2mMFGgDeg6RAAAMAi9OgFAACwCEELAADAIgQtAAAAixC0AAAALELQAgAAsAhBCwAAwCIELQAAAIsQtAAAACxC0AIAALAIQQsAAMAiBC0AAACLELQAAADEGv8Pmxd328EBplIAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "jetTransient": { + "display_id": null + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "samples = d_mean_std.sample(n=100_000)\n", + "\n", + "plt.figure(figsize=(7, 4))\n", + "plt.hist(samples, bins=60, density=True)\n", + "plt.title(\"Samples from Normal(0, 1)\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "92648e1a", + "metadata": {}, + "source": [ + "## 2) Custom family with multiple parametrizations\n", + "\n", + "In this section we create a custom family and **register** it in `ParametricFamilyRegister`.\n", + "\n", + "We implement a simple distribution on an interval `[a, b]` with CDF\n", + "`F(x) = ((x-a)/(b-a))^2` for `x โˆˆ [a, b]` (and 0/1 outside), which corresponds to the PDF\n", + "`f(x) = 2(x-a)/(b-a)^2` on `[a, b]`.\n", + "\n", + "We provide **PDF** and **CDF** analytically for both parametrizations, but omit **PPF**.\n", + "Then we query `PPF` via the characteristic graph.\n", + "\n", + "Parametrizations:\n", + "\n", + "- `endpoints`: `(a, b)`\n", + "- `locScale`: `(loc, scale)` where `a = loc`, `b = loc + scale`\n" + ] + }, + { + "cell_type": "markdown", + "id": "f786803c", + "metadata": {}, + "source": [ + "**Important note (current limitation).**\n", + "\n", + "Built-in families provide analytical characteristics that follow **NumPy semantics** (arrays in / arrays out).\n", + "Graph-based conversions (fitted methods from `fitters.py`) are currently **scalar-only**.\n", + "\n", + "That means that a derived characteristic like `PPF` may only accept Python floats. If you pass a NumPy array,\n", + "SciPy routines used inside conversions (e.g. `scipy.integrate.quad`) may fail with errors such as\n", + "`ValueError: The truth value of an array with more than one element is ambiguous`.\n", + "\n", + "Until the fitters are upgraded to NumPy semantics, evaluate derived characteristics pointwise.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c0fb3a7d", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.628153100Z", + "start_time": "2026-01-03T16:27:38.583307400Z" + } + }, + "outputs": [], + "source": [ + "def _ab(params: Parametrization) -> tuple[float, float]:\n", + " if hasattr(params, \"a\") and hasattr(params, \"b\"):\n", + " return float(params.a), float(params.b)\n", + " return float(params.loc), float(params.loc + params.scale)\n", + "\n", + "\n", + "def tri_pdf(params: Parametrization, x: np.ndarray) -> np.ndarray:\n", + " a, b = _ab(params)\n", + " x = np.asarray(x, dtype=np.float64)\n", + " denom = b - a\n", + " y = 2.0 * (x - a) / (denom * denom)\n", + " y[(x < a) | (x > b)] = 0.0\n", + " return y\n", + "\n", + "\n", + "def tri_cdf(params: Parametrization, x: np.ndarray) -> np.ndarray:\n", + " a, b = _ab(params)\n", + " x = np.asarray(x, dtype=np.float64)\n", + " denom = b - a\n", + " t = (x - a) / denom\n", + " return np.where(x <= a, 0.0, np.where(x >= b, 1.0, t * t))\n", + "\n", + "\n", + "def tri_support(params: Parametrization) -> ContinuousSupport:\n", + " a, b = _ab(params)\n", + " return ContinuousSupport(a, b)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "6355eb31", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.703850700Z", + "start_time": "2026-01-03T16:27:38.629350100Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'TriangularAB'" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tri_family = ParametricFamily(\n", + " name=\"TriangularAB\",\n", + " distr_type=UnivariateContinuous,\n", + " distr_parametrizations=[\"endpoints\", \"locScale\"],\n", + " distr_characteristics={\n", + " CharacteristicName.PDF: {\n", + " \"endpoints\": tri_pdf,\n", + " \"locScale\": tri_pdf,\n", + " },\n", + " CharacteristicName.CDF: {\n", + " \"endpoints\": tri_cdf,\n", + " \"locScale\": tri_cdf,\n", + " },\n", + " # PPF intentionally omitted: it will be derived by the graph.\n", + " },\n", + " support_by_parametrization=tri_support,\n", + ")\n", + "\n", + "\n", + "@parametrization(family=tri_family, name=\"endpoints\")\n", + "class Endpoints(Parametrization):\n", + " a: float\n", + " b: float\n", + "\n", + "\n", + "@tri_family.parametrization(name=\"locScale\")\n", + "class LocScale(Parametrization):\n", + " loc: float\n", + " scale: float\n", + "\n", + "\n", + "# Register the family so that the computation strategy can resolve it by name\n", + "ParametricFamilyRegister.register(tri_family)\n", + "ParametricFamilyRegister.get(\"TriangularAB\").name" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f483a954", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:38.783328900Z", + "start_time": "2026-01-03T16:27:38.725463Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "('endpoints', 'locScale')" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tri_endpoints = tri_family.distribution(parametrization_name=\"endpoints\", a=0.0, b=1.0)\n", + "tri_locscale = tri_family.distribution(parametrization_name=\"locScale\", loc=0.0, scale=1.0)\n", + "tri_endpoints.parametrization_name, tri_locscale.parametrization_name" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "d98111c5", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:39.001813500Z", + "start_time": "2026-01-03T16:27:38.785355100Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "jetTransient": { + "display_id": null + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x01 = np.linspace(-0.25, 1.25, 600)\n", + "\n", + "pdf_e = tri_endpoints.query_method(CharacteristicName.PDF)\n", + "cdf_e = tri_endpoints.query_method(CharacteristicName.CDF)\n", + "pdf_l = tri_locscale.query_method(CharacteristicName.PDF)\n", + "cdf_l = tri_locscale.query_method(CharacteristicName.CDF)\n", + "\n", + "plt.figure(figsize=(7, 4))\n", + "plt.plot(x01, pdf_e(x01), label=\"PDF (endpoints)\")\n", + "plt.plot(x01, pdf_l(x01), linestyle=\"--\", label=\"PDF (locScale)\")\n", + "plt.legend()\n", + "plt.title(\"TriangularAB: PDF in two parametrizations\")\n", + "plt.show()\n", + "\n", + "plt.figure(figsize=(7, 4))\n", + "plt.plot(x01, cdf_e(x01), label=\"CDF (endpoints)\")\n", + "plt.plot(x01, cdf_l(x01), linestyle=\"--\", label=\"CDF (locScale)\")\n", + "plt.legend()\n", + "plt.title(\"TriangularAB: CDF in two parametrizations\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "f36677e4", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:39.030327400Z", + "start_time": "2026-01-03T16:27:39.003813900Z" + } + }, + "outputs": [], + "source": [ + "def eval_scalar_method_on_array(method, xs):\n", + " xs = np.asarray(xs, dtype=np.float64)\n", + " return np.array([method(float(x)) for x in xs], dtype=np.float64)" + ] + }, + { + "cell_type": "markdown", + "id": "6c9a8258", + "metadata": {}, + "source": [ + "### Querying a derived PPF (scalar-only)\n", + "\n", + "We now request `PPF`. Since we did not provide it analytically, it is derived via the characteristic graph.\n", + "At the moment, this derived method is scalar-only, so we evaluate it pointwise for a vector of probabilities.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "a7c4e99c", + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-03T16:27:39.102317900Z", + "start_time": "2026-01-03T16:27:39.051332100Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[0.1 , 0.31622777, 0.31622777],\n", + " [0.25 , 0.5 , 0.5 ],\n", + " [0.5 , 0.70710678, 0.70710678],\n", + " [0.75 , 0.8660254 , 0.8660254 ],\n", + " [0.9 , 0.9486833 , 0.9486833 ]])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ppf_e = tri_endpoints.query_method(CharacteristicName.PPF)\n", + "ppf_l = tri_locscale.query_method(CharacteristicName.PPF)\n", + "\n", + "qs = np.array([0.1, 0.25, 0.5, 0.75, 0.9])\n", + "q_endpoints = np.array([ppf_e(float(q)) for q in qs], dtype=np.float64)\n", + "q_locscale = np.array([ppf_l(float(q)) for q in qs], dtype=np.float64)\n", + "np.column_stack([qs, q_endpoints, q_locscale])" + ] + }, + { + "cell_type": "markdown", + "id": "3e3cf0d0", + "metadata": {}, + "source": [ + "### Summary\n", + "\n", + "- Built-in families: analytical methods support NumPy arrays.\n", + "- Custom family: we registered it in the global registry.\n", + "- We provided vectorized `PDF` and `CDF`.\n", + "- We omitted `PPF`, and obtained it via the characteristic graph.\n", + "- Graph-derived methods are currently scalar-only, so we evaluated them pointwise.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/pysatl_core/distributions/distribution.py b/src/pysatl_core/distributions/distribution.py index a19796a0..280b5d3b 100644 --- a/src/pysatl_core/distributions/distribution.py +++ b/src/pysatl_core/distributions/distribution.py @@ -11,14 +11,15 @@ __copyright__ = "Copyright (c) 2025 PySATL project" __license__ = "SPDX-License-Identifier: MIT" -from typing import TYPE_CHECKING, Protocol, runtime_checkable +from typing import TYPE_CHECKING, Protocol, cast, runtime_checkable + +from pysatl_core.types import NumericArray if TYPE_CHECKING: from collections.abc import Mapping from typing import Any from pysatl_core.distributions.computation import AnalyticalComputation - from pysatl_core.distributions.sampling import Sample from pysatl_core.distributions.strategies import ( ComputationStrategy, Method, @@ -113,7 +114,7 @@ def calculate_characteristic( """ return self.query_method(characteristic_name, **options)(value) - def sample(self, n: int, **options: Any) -> Sample: + def sample(self, n: int, **options: Any) -> NumericArray: """ Generate random samples from the distribution. @@ -122,11 +123,14 @@ def sample(self, n: int, **options: Any) -> Sample: n : int Number of samples to generate. **options : Any - Additional sampling options. + Additional sampling options forwarded to the underlying + sampling strategy. Returns ------- - Sample - Container with the generated samples. + NumericArray + NumPy array containing ``n`` generated samples. + The exact array shape depends on the distribution and + the sampling strategy. """ - return self.sampling_strategy.sample(n, distr=self, **options) + return cast(NumericArray, self.sampling_strategy.sample(n, distr=self, **options)) diff --git a/src/pysatl_core/distributions/sampling.py b/src/pysatl_core/distributions/sampling.py index 87324ce5..f0bae01c 100644 --- a/src/pysatl_core/distributions/sampling.py +++ b/src/pysatl_core/distributions/sampling.py @@ -22,6 +22,7 @@ import numpy.typing as npt +# TODO: This is probably a stillborn idea, it's better to just use NumPy arrays. class Sample(Protocol): """ Protocol for sample containers. @@ -41,6 +42,7 @@ def array(self) -> npt.NDArray[np.floating[Any]]: ... def shape(self) -> tuple[int, ...]: ... +# TODO: This is probably a stillborn idea, it's better to just use NumPy arrays. class ArraySample: """ Array-backed sample container. diff --git a/src/pysatl_core/distributions/strategies.py b/src/pysatl_core/distributions/strategies.py index e48b299e..19e5001b 100644 --- a/src/pysatl_core/distributions/strategies.py +++ b/src/pysatl_core/distributions/strategies.py @@ -11,19 +11,18 @@ __copyright__ = "Copyright (c) 2025 PySATL project" __license__ = "SPDX-License-Identifier: MIT" -from typing import TYPE_CHECKING, Protocol +from typing import TYPE_CHECKING, Protocol, cast import numpy as np from pysatl_core.distributions.registry import characteristic_registry -from pysatl_core.distributions.sampling import ArraySample +from pysatl_core.types import CharacteristicName, NumericArray if TYPE_CHECKING: from typing import Any from pysatl_core.distributions.computation import AnalyticalComputation, FittedComputationMethod from pysatl_core.distributions.distribution import Distribution - from pysatl_core.distributions.sampling import Sample from pysatl_core.types import GenericCharacteristicName type Method[In, Out] = AnalyticalComputation[In, Out] | FittedComputationMethod[In, Out] @@ -186,25 +185,27 @@ def query_method( class SamplingStrategy(Protocol): """Protocol for strategies that generate samples from distributions.""" - def sample(self, n: int, distr: Distribution, **options: Any) -> Sample: ... + def sample(self, n: int, distr: Distribution, **options: Any) -> NumericArray: ... class DefaultSamplingUnivariateStrategy(SamplingStrategy): """ - Default univariate sampler using inverse transform sampling. + Default univariate sampler based on inverse transform sampling. This strategy generates samples by applying the PPF (inverse CDF) - to uniform random variables. + to uniformly distributed random variables. Notes ----- - Requires the distribution to provide a PPF computation method. - - Returns samples as a 2D array of shape (n, 1). + - Assumes that the PPF follows NumPy semantics (vectorized evaluation). + - Graph-derived PPFs (scalar-only) are currently not supported. + - Returns a NumPy array containing the generated samples. """ - def sample(self, n: int, distr: Distribution, **options: Any) -> ArraySample: + def sample(self, n: int, distr: Distribution, **options: Any) -> NumericArray: """ - Generate n samples from the distribution. + Generate samples from the distribution. Parameters ---------- @@ -213,15 +214,19 @@ def sample(self, n: int, distr: Distribution, **options: Any) -> ArraySample: distr : Distribution Distribution to sample from. **options : Any - Additional options passed to the PPF computation. + Additional options forwarded to the PPF computation. Returns ------- - ArraySample - Samples as a 2D array of shape (n, 1). + NumericArray + NumPy array containing ``n`` generated samples. + The exact array shape depends on the distribution and sampling strategy. """ - ppf = distr.query_method("ppf", **options) + ppf = distr.query_method(CharacteristicName.PPF, **options) rng = np.random.default_rng() U = rng.random(n) - vals = np.array([ppf(Ui) for Ui in U], dtype=np.float64).reshape(n, 1) - return ArraySample(vals) + # TODO: Now it will be based on the fact that the characteristic + # has NumPy semantics (It is much more faster), that is, + # it will not work with the graph computed characteristics currently. + samples = ppf(U) + return cast(NumericArray, samples) diff --git a/src/pysatl_core/families/__init__.py b/src/pysatl_core/families/__init__.py index caab57ba..ed305289 100644 --- a/src/pysatl_core/families/__init__.py +++ b/src/pysatl_core/families/__init__.py @@ -10,6 +10,8 @@ __license__ = "SPDX-License-Identifier: MIT" +from .builtins import * # noqa: UP029 +from .builtins import __all__ as _builtins_all from .configuration import configure_families_register from .distribution import ParametricFamilyDistribution from .parametric_family import ParametricFamily @@ -30,4 +32,8 @@ "constraint", "parametrization", "configure_families_register", + # builtins + *_builtins_all, ] + +del _builtins_all diff --git a/src/pysatl_core/families/builtins/__init__.py b/src/pysatl_core/families/builtins/__init__.py index b7c58b66..48c6af3f 100644 --- a/src/pysatl_core/families/builtins/__init__.py +++ b/src/pysatl_core/families/builtins/__init__.py @@ -10,14 +10,11 @@ __license__ = "SPDX-License-Identifier: MIT" -from pysatl_core.families.builtins.continuous import ( - configure_exponential_family, - configure_normal_family, - configure_uniform_family, -) +from .continuous import * +from .continuous import __all__ as _continuous_all __all__ = [ - "configure_normal_family", - "configure_uniform_family", - "configure_exponential_family", + *_continuous_all, ] + +del _continuous_all diff --git a/src/pysatl_core/families/builtins/continuous/exponential.py b/src/pysatl_core/families/builtins/continuous/exponential.py index a14dc9bb..e0854ad8 100644 --- a/src/pysatl_core/families/builtins/continuous/exponential.py +++ b/src/pysatl_core/families/builtins/continuous/exponential.py @@ -14,7 +14,6 @@ import numpy as np -from pysatl_core.distributions.strategies import DefaultSamplingUnivariateStrategy from pysatl_core.distributions.support import ContinuousSupport from pysatl_core.families.parametric_family import ParametricFamily from pysatl_core.families.parametrizations import ( @@ -39,6 +38,10 @@ def configure_exponential_family() -> None: """ Configure and register the Exponential distribution family. """ + + if ParametricFamilyRegister.contains(FamilyName.EXPONENTIAL): + return + EXPONENTIAL_DOC = """ Exponential distribution. @@ -215,7 +218,6 @@ def _support(_: Parametrization) -> ContinuousSupport: CharacteristicName.SKEW: skew_func, CharacteristicName.KURT: kurt_func, }, - sampling_strategy=DefaultSamplingUnivariateStrategy(), support_by_parametrization=_support, ) Exponential.__doc__ = EXPONENTIAL_DOC diff --git a/src/pysatl_core/families/builtins/continuous/normal.py b/src/pysatl_core/families/builtins/continuous/normal.py index ee261369..40fd0951 100644 --- a/src/pysatl_core/families/builtins/continuous/normal.py +++ b/src/pysatl_core/families/builtins/continuous/normal.py @@ -16,7 +16,6 @@ import numpy as np from scipy.special import erf, erfinv -from pysatl_core.distributions.strategies import DefaultSamplingUnivariateStrategy from pysatl_core.distributions.support import ContinuousSupport from pysatl_core.families.parametric_family import ParametricFamily from pysatl_core.families.parametrizations import ( @@ -41,6 +40,10 @@ def configure_normal_family() -> None: """ Configure and register the Normal distribution family. """ + + if ParametricFamilyRegister.contains(FamilyName.NORMAL): + return + NORMAL_DOC = """ Normal (Gaussian) distribution. @@ -218,7 +221,6 @@ def _support(_: Parametrization) -> ContinuousSupport: CharacteristicName.SKEW: skew_func, CharacteristicName.KURT: kurt_func, }, - sampling_strategy=DefaultSamplingUnivariateStrategy(), support_by_parametrization=_support, ) Normal.__doc__ = NORMAL_DOC diff --git a/src/pysatl_core/families/builtins/continuous/uniform.py b/src/pysatl_core/families/builtins/continuous/uniform.py index f35f289d..6d735033 100644 --- a/src/pysatl_core/families/builtins/continuous/uniform.py +++ b/src/pysatl_core/families/builtins/continuous/uniform.py @@ -14,7 +14,6 @@ import numpy as np -from pysatl_core.distributions.strategies import DefaultSamplingUnivariateStrategy from pysatl_core.distributions.support import ContinuousSupport from pysatl_core.families.parametric_family import ParametricFamily from pysatl_core.families.parametrizations import ( @@ -39,6 +38,10 @@ def configure_uniform_family() -> None: """ Configure and register the Uniform distribution family. """ + + if ParametricFamilyRegister.contains(FamilyName.CONTINUOUS_UNIFORM): + return + UNIFORM_DOC = """ Uniform (continuous) distribution. @@ -250,7 +253,6 @@ def _support(parameters: Parametrization) -> ContinuousSupport: CharacteristicName.SKEW: skew_func, CharacteristicName.KURT: kurt_func, }, - sampling_strategy=DefaultSamplingUnivariateStrategy(), support_by_parametrization=_support, ) Uniform.__doc__ = UNIFORM_DOC diff --git a/src/pysatl_core/families/distribution.py b/src/pysatl_core/families/distribution.py index 06afbfaf..5c57abd8 100644 --- a/src/pysatl_core/families/distribution.py +++ b/src/pysatl_core/families/distribution.py @@ -13,17 +13,17 @@ from dataclasses import dataclass -from typing import TYPE_CHECKING +from typing import TYPE_CHECKING, cast from pysatl_core.distributions.distribution import Distribution from pysatl_core.families.registry import ParametricFamilyRegister +from pysatl_core.types import NumericArray if TYPE_CHECKING: from collections.abc import Mapping from typing import Any from pysatl_core.distributions.computation import AnalyticalComputation - from pysatl_core.distributions.sampling import Sample from pysatl_core.distributions.strategies import ( ComputationStrategy, SamplingStrategy, @@ -167,20 +167,23 @@ def support(self) -> Support | None: """Get the support of this distribution.""" return self._support - def sample(self, n: int, **options: Any) -> Sample: + def sample(self, n: int, **options: Any) -> NumericArray: """ - Generate samples from this distribution. + Generate random samples from the distribution. Parameters ---------- n : int Number of samples to generate. **options : Any - Additional options for sampling. + Additional sampling options forwarded to the underlying + sampling strategy. Returns ------- - Sample - Generated samples. + NumericArray + NumPy array containing ``n`` generated samples. + The exact array shape depends on the distribution and + the sampling strategy. """ - return self.sampling_strategy.sample(n, distr=self, **options) + return cast(NumericArray, self.sampling_strategy.sample(n, distr=self, **options)) diff --git a/src/pysatl_core/families/registry.py b/src/pysatl_core/families/registry.py index 47f9746e..2b0ba6e5 100644 --- a/src/pysatl_core/families/registry.py +++ b/src/pysatl_core/families/registry.py @@ -83,6 +83,26 @@ def register(cls, family: ParametricFamily) -> None: raise ValueError(f"Family {family.name} already found in register") self._registered_families[family.name] = family + @classmethod + def contains(cls, name: str) -> bool: + """ + Check whether a parametric family with the given name + is registered in the registry. + + Parameters + ---------- + name : str + Name of the parametric family. + + Returns + ------- + bool + ``True`` if the family is present in the registry, + ``False`` otherwise. + """ + self = cls() + return name in self._registered_families + @classmethod def _reset(cls) -> None: """ diff --git a/tests/unit/distributions/test_sampling.py b/tests/unit/distributions/test_sampling.py index 8ebc2898..ad861576 100644 --- a/tests/unit/distributions/test_sampling.py +++ b/tests/unit/distributions/test_sampling.py @@ -15,12 +15,15 @@ def test_sample_uniform_ppf_only_shape_bounds_and_mean(self) -> None: distr = self.make_uniform_ppf_distribution() n = 1000 - sample = distr.sample(n) + samples = distr.sample(n) - assert sample.shape == (n, 1) - arr = sample.array - assert np.isfinite(arr).all() - assert ((arr >= 0.0) & (arr <= 1.0)).all() + assert isinstance(samples, np.ndarray) - mean = float(arr.mean()) + flat = np.asarray(samples, dtype=np.float64).reshape(-1) + assert flat.shape == (n,) + + assert np.isfinite(flat).all() + assert ((flat >= 0.0) & (flat <= 1.0)).all() + + mean = float(flat.mean()) assert mean == pytest.approx(0.5, abs=0.1) diff --git a/tests/unit/families/test_family_and_distribution.py b/tests/unit/families/test_family_and_distribution.py index c83d4030..b13f614c 100644 --- a/tests/unit/families/test_family_and_distribution.py +++ b/tests/unit/families/test_family_and_distribution.py @@ -4,6 +4,7 @@ __copyright__ = "Copyright (c) 2025 PySATL project" __license__ = "SPDX-License-Identifier: MIT" +import numpy as np import pytest from pysatl_core.families import ParametricFamilyRegister @@ -28,10 +29,14 @@ def test_family_registration_and_distribution_sampling(self) -> None: distr = fam.distribution("base", value=0.0) n = 128 - sample = distr.sample(n) - assert sample.shape == (n, 1) - arr = sample.array - assert (arr >= 0.0).all() and (arr <= 1.0).all() + samples = distr.sample(n) + + assert isinstance(samples, np.ndarray) + + flat = np.asarray(samples, dtype=np.float64).reshape(-1) + assert flat.shape == (n,) + + assert ((flat >= 0.0) & (flat <= 1.0)).all() computations = distr.analytical_computations assert set(computations) == { diff --git a/tests/utils/mocks.py b/tests/utils/mocks.py index 0c3052f8..bd838d99 100644 --- a/tests/utils/mocks.py +++ b/tests/utils/mocks.py @@ -12,21 +12,24 @@ from pysatl_core.distributions import ( AnalyticalComputation, - ArraySample, ComputationStrategy, DefaultComputationStrategy, DefaultSamplingUnivariateStrategy, Distribution, - Sample, SamplingStrategy, ) from pysatl_core.distributions.support import Support -from pysatl_core.types import EuclideanDistributionType, GenericCharacteristicName, Kind +from pysatl_core.types import ( + EuclideanDistributionType, + GenericCharacteristicName, + Kind, + NumericArray, +) class MockSamplingStrategy(SamplingStrategy): - def sample(self, n: int, distr: Distribution, **options: Any) -> Sample: - return ArraySample(np.random.random((n, 1))) + def sample(self, n: int, distr: Distribution, **options: Any) -> NumericArray: + return np.random.random((n, 1)) @dataclass(slots=True) From 5df5e4fde34101777dee41a89d516c63c4420b8d Mon Sep 17 00:00:00 2001 From: LeonidElkin <113133848+LeonidElkin@users.noreply.github.com> Date: Sat, 3 Jan 2026 21:14:33 +0300 Subject: [PATCH 3/5] docs: sphinx init --- .gitignore | 6 + .pre-commit-config.yaml | 1 + docs/Makefile | 31 ++++ docs/source/_static/PySATL-icon.jpg | Bin 0 -> 1733982 bytes docs/source/_static/PySATL-logo.jpg | Bin 0 -> 117439 bytes docs/source/_static/custom.css | 36 ++++ docs/source/changelog.rst | 10 ++ docs/source/conf.py | 143 +++++++++++++++ docs/source/contributing.rst | 4 + docs/source/generate_api.py | 223 ++++++++++++++++++++++++ docs/source/index.rst | 12 ++ docs/source/user_guide/index.rst | 8 + docs/source/user_guide/installation.rst | 27 +++ examples/overview.ipynb | 2 +- pyproject.toml | 9 +- 15 files changed, 510 insertions(+), 2 deletions(-) create mode 100644 docs/Makefile create mode 100644 docs/source/_static/PySATL-icon.jpg create mode 100644 docs/source/_static/PySATL-logo.jpg create mode 100644 docs/source/_static/custom.css create mode 100644 docs/source/changelog.rst create mode 100644 docs/source/conf.py create mode 100644 docs/source/contributing.rst create mode 100644 docs/source/generate_api.py create mode 100644 docs/source/index.rst create mode 100644 docs/source/user_guide/index.rst create mode 100644 docs/source/user_guide/installation.rst diff --git a/.gitignore b/.gitignore index 2954a135..d5a9a64a 100644 --- a/.gitignore +++ b/.gitignore @@ -125,3 +125,9 @@ poetry.lock # refer to https://docs.cursor.com/context/ignore-files .cursorignore .cursorindexingignore + +# Docs + +docs/build/* +docs/source/api/* +docs/source/examples/* diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index 1d5c609a..29174ace 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -19,6 +19,7 @@ exclude: > | \.gitignore$ | LICENSE$ | .*\.md$ + | .*\.jpg$ )$ repos: diff --git a/docs/Makefile b/docs/Makefile new file mode 100644 index 00000000..393e1380 --- /dev/null +++ b/docs/Makefile @@ -0,0 +1,31 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line, and also +# from the environment for the first two. +SPHINXOPTS ?= +SPHINXBUILD = poetry run sphinx-build +SPHINXAPIDOC = poetry run sphinx-apidoc +SOURCEDIR = source +BUILDDIR = build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). + +# Generate API rst files (mirrors src/ package tree) +.PHONY: api +api: + @poetry run python "$(SOURCEDIR)/generate_api.py" + +# Build HTML after regenerating API +html: api + @$(SPHINXBUILD) -M html "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/docs/source/_static/PySATL-icon.jpg b/docs/source/_static/PySATL-icon.jpg new file mode 100644 index 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b/docs/source/changelog.rst new file mode 100644 index 00000000..59de20b7 --- /dev/null +++ b/docs/source/changelog.rst @@ -0,0 +1,10 @@ +Changelog +========= + +Version 0.0.1a0 (Alpha) +------------------------ + +* Initial release with core functionality +* Basic distribution framework +* Family system for parametric distributions +* Computation strategies and sampling methods diff --git a/docs/source/conf.py b/docs/source/conf.py new file mode 100644 index 00000000..19b0fc04 --- /dev/null +++ b/docs/source/conf.py @@ -0,0 +1,143 @@ +import os +import sys +from datetime import datetime + +sys.path.insert(0, os.path.abspath("../../src")) + +project = "PySATL Core" +copyright = f"{datetime.now().year}, Leonid Elkin, Mikhail Mikhailov" +author = "Leonid Elkin, Mikhail Mikhailov" +release = "0.0.1a0" + +extensions = [ + "sphinx.ext.autodoc", + "sphinx.ext.napoleon", + "sphinx.ext.viewcode", + "sphinx.ext.intersphinx", + "sphinx.ext.mathjax", + "sphinx.ext.githubpages", + "sphinx_rtd_theme", + "myst_nb", + "sphinx_autodoc_typehints", + "sphinx_copybutton", + "sphinx.ext.autosummary", +] +autosummary_generate = True +templates_path = ["_templates"] +exclude_patterns = ["_build", "Thumbs.db", ".DS_Store", "**.ipynb_checkpoints"] + +# -- Napoleon (NumPy style docstrings) -- +napoleon_google_docstring = False +napoleon_use_keyword = True +napoleon_numpy_docstring = True +napoleon_include_init_with_doc = True +napoleon_include_private_with_doc = False +napoleon_include_special_with_doc = True +napoleon_use_admonition_for_examples = True +napoleon_use_admonition_for_notes = True +napoleon_use_admonition_for_references = True +napoleon_use_ivar = False +napoleon_use_param = True +napoleon_use_rtype = True +napoleon_preprocess_types = True +napoleon_type_aliases = None + +# -- Autodocumentation settings -- +autodoc_default_options = { + "member-order": "bysource", + "special-members": "__init__", + "undoc-members": True, + "exclude-members": "__weakref__", + "show-inheritance": True, +} + +autodoc_typehints = "description" +autodoc_typehints_format = "short" + +# -- Intersphinx -- +intersphinx_mapping = { + "python": ("https://docs.python.org/3", None), + "numpy": ("https://numpy.org/doc/stable/", None), + "scipy": ("https://docs.scipy.org/doc/scipy/", None), +} + +# -- MyST Parser -- +myst_enable_extensions = [ + "amsmath", + "colon_fence", + "deflist", + "dollarmath", + "fieldlist", + "html_admonition", + "html_image", + "linkify", + "replacements", + "smartquotes", + "tasklist", +] +myst_heading_anchors = 3 +nb_execution_mode = "off" + +# -- HTML -- +html_theme = "sphinx_rtd_theme" +html_static_path = ["_static"] +html_css_files = [ + "custom.css", +] + +# ReadTheDocs +html_theme_options = { + "collapse_navigation": False, + "sticky_navigation": True, + "navigation_depth": 4, + "includehidden": True, + "titles_only": False, + "logo_only": False, +} + +# Sidebar: show navigation tree, avoid listing all members of the current page +html_sidebars = { + "**": [ + "about.html", + "navigation.html", + "relations.html", + "searchbox.html", + ] +} + +html_logo = "_static/PySATL-logo.jpg" +html_favicon = "_static/PySATL-icon.jpg" + +# -- Compile -- +copybutton_prompt_text = r">>> |\.\.\. |\$ |In \[\d*\]: | {2,5}\.\.\.: | {5,8}: " +copybutton_prompt_is_regexp = True +copybutton_line_continuation_character = "\\" + +source_suffix = { + ".rst": "restructuredtext", + ".md": "markdown", + ".ipynb": "myst-nb", +} + +suppress_warnings = [ + # 'autodoc.duplicate_object', + "ref.misc", +] + +# forward references (actually don't matter too much but better be here) +autodoc_type_aliases = { + "In": "typing.Any", + "Out": "typing.Any", + "DistributionType": "pysatl_core.types.DistributionType", + "Kind": "pysatl_core.types.Kind", + "SamplingStrategy": "pysatl_core.distributions.strategies.SamplingStrategy", + "ComputationStrategy": "pysatl_core.distributions.strategies.ComputationStrategy", + "Parametrization": "pysatl_core.families.parametrizations.Parametrization", + "Support": "pysatl_core.distributions.support.Support", + "Sample": "pysatl_core.distributions.sampling.Sample", + "Distribution": "pysatl_core.distributions.distribution.Distribution", + "ParametricFamily": "pysatl_core.families.parametric_family.ParametricFamily", +} + +# Some checks +nitpicky = False diff --git a/docs/source/contributing.rst b/docs/source/contributing.rst new file mode 100644 index 00000000..aef48592 --- /dev/null +++ b/docs/source/contributing.rst @@ -0,0 +1,4 @@ +Contributing +============ + +See the full contributing guide in our `GitHub repository `_. diff --git a/docs/source/generate_api.py b/docs/source/generate_api.py new file mode 100644 index 00000000..d13b7be2 --- /dev/null +++ b/docs/source/generate_api.py @@ -0,0 +1,223 @@ +#!/usr/bin/env python3 +"""Generate API documentation with a package-like tree. + +This script scans the repository's ``src/`` directory and generates ``.rst`` files +under ``docs/source/api/pysatl_core`` mirroring the Python package structure. + +Design goals: + - Sidebar navigation should reflect *module/package tree*, not a flat list of members. + - Package ``index.rst`` pages contain only a toctree (and optional package docstring), + while *module* pages contain ``automodule`` with members. + +Run: + python docs/source/generate_api.py +""" + +from __future__ import annotations + +import os +import shutil +from collections.abc import Iterable +from dataclasses import dataclass +from pathlib import Path + +REPO_ROOT = Path(__file__).resolve().parents[2] +SRC_ROOT = REPO_ROOT / "src" +DOCS_SOURCE = Path(__file__).resolve().parent +API_ROOT = DOCS_SOURCE / "api" +PKG_NAME = "pysatl_core" +PKG_DIR = SRC_ROOT / PKG_NAME + +GENERATED_ROOT = API_ROOT / PKG_NAME + + +@dataclass(frozen=True) +class ModuleDoc: + dotted: str # e.g. pysatl_core.distributions.registry.graph + rst_path: Path # relative to DOCS_SOURCE + title: str # display title + + +def _is_package_dir(path: Path) -> bool: + return path.is_dir() and (path / "__init__.py").exists() + + +def _copy_user_guide_notebooks(repo_root: Path, docs_source_dir: Path) -> None: + src_nb = repo_root / "examples" / "overview.ipynb" + dst_dir = docs_source_dir / "examples" + dst_nb = dst_dir / "overview.ipynb" + + if not src_nb.exists(): + raise FileNotFoundError(f"Notebook not found: {src_nb}") + + dst_dir.mkdir(parents=True, exist_ok=True) + + # Copy only if missing or source is newer + if not dst_nb.exists() or src_nb.stat().st_mtime > dst_nb.stat().st_mtime: + shutil.copy2(src_nb, dst_nb) + + +def _iter_packages_and_modules(pkg_dir: Path) -> Iterable[tuple[Path, list[Path], list[Path]]]: + """Yield (package_dir, subpackage_dirs, module_files) recursively.""" + for current, dirs, files in os.walk(pkg_dir): + current_path = Path(current) + + # Only traverse Python packages (directories with __init__.py) + if not _is_package_dir(current_path): + # prevent descending into non-packages + dirs[:] = [] + continue + + subpackages = [] + for d in list(dirs): + dp = current_path / d + if _is_package_dir(dp): + subpackages.append(dp) + else: + # don't descend into non-packages + dirs.remove(d) + + modules = [] + for f in files: + if not f.endswith(".py"): + continue + if f == "__init__.py": + continue + if f.startswith("_"): + # keep private modules out of API by default + continue + modules.append(current_path / f) + + yield current_path, sorted(subpackages), sorted(modules) + + +def _to_dotted(module_path: Path) -> str: + rel = module_path.relative_to(SRC_ROOT) + parts = list(rel.with_suffix("").parts) + return ".".join(parts) + + +def _rst_title(name: str) -> str: + # For files, strip .py; for directories, keep as is + return name.replace("_", " ") + + +def _write(path: Path, content: str) -> None: + path.parent.mkdir(parents=True, exist_ok=True) + path.write_text(content, encoding="utf-8") + + +def _package_index_rst(package_dotted: str, title: str, children: list[Path]) -> str: + """Create index.rst for a package. + + Important: Do NOT include :members: here to avoid the navigation becoming a flat list. + """ + lines = [ + title, + "=" * len(title), + "", + f".. automodule:: {package_dotted}", + " :no-index:", + "", + ] + if children: + lines += [ + ".. toctree::", + " :maxdepth: 2", + "", + ] + for child in children: + # paths are relative to api//.../index.rst location + lines.append(f" {child.as_posix()}") + lines.append("") + return "\n".join(lines) + + +def _module_page_rst(module_dotted: str, title: str) -> str: + return "\n".join( + [ + title, + "=" * len(title), + "", + f".. automodule:: {module_dotted}", + " :members:", + " :undoc-members:", + " :show-inheritance:", + " :member-order: bysource", + "", + ] + ) + + +def main() -> None: + docs_source_dir = Path(__file__).resolve().parent + repo_root = docs_source_dir.parents[1] + + _copy_user_guide_notebooks(repo_root=repo_root, docs_source_dir=docs_source_dir) + + if not PKG_DIR.exists(): + raise SystemExit(f"Package directory not found: {PKG_DIR}") + + # Clean generated root + if GENERATED_ROOT.exists(): + shutil.rmtree(GENERATED_ROOT) + GENERATED_ROOT.mkdir(parents=True, exist_ok=True) + + # Generate tree + for pkg_path, subpackages, modules in _iter_packages_and_modules(PKG_DIR): + pkg_dotted = _to_dotted(pkg_path / "__init__.py")[:-9] # strip .__init__ + rel_pkg = pkg_path.relative_to(PKG_DIR) # path inside pysatl_core + + out_dir = GENERATED_ROOT / rel_pkg + index_path = out_dir / "index.rst" + + # children docs (relative to this index) + children: list[Path] = [] + # subpackage indices + for sp in subpackages: + sp_rel = sp.relative_to(pkg_path) + children.append(Path(sp_rel.as_posix()) / "index") + # modules + for mod in modules: + mod_rel = mod.relative_to(pkg_path) + children.append(Path(mod_rel.with_suffix("").as_posix())) + + title = PKG_NAME if rel_pkg == Path(".") else rel_pkg.name + _write(index_path, _package_index_rst(pkg_dotted, title, children)) + + # module pages + for mod in modules: + mod_dotted = _to_dotted(mod) + mod_rel = mod.relative_to(PKG_DIR).with_suffix("") # inside pysatl_core + mod_out = GENERATED_ROOT / mod_rel + _write(mod_out.with_suffix(".rst"), _module_page_rst(mod_dotted, mod_rel.name)) + + # Also ensure api/index.rst points at the generated root index + api_index = API_ROOT / "index.rst" + if not api_index.exists(): + _write( + api_index, + "\n".join( + [ + "API Reference", + "=============", + "", + "This section contains the complete API documentation for the", + f":mod:`{PKG_NAME}` package โ€” the core computation and distribution", + "infrastructure of PySATL.", + "", + "The documentation is organized to reflect the internal package and", + "module structure.", + "", + ".. toctree::", + " :maxdepth: 1", + "", + f" {PKG_NAME}/index", + "", + ] + ), + ) + + +if __name__ == "__main__": + main() diff --git a/docs/source/index.rst b/docs/source/index.rst new file mode 100644 index 00000000..3ff49e58 --- /dev/null +++ b/docs/source/index.rst @@ -0,0 +1,12 @@ +PySATL Core Documentation +========================= + +**Computation core for PySATL** - A comprehensive library for probability distributions, random variables, and statistical computations. + +.. toctree:: + :maxdepth: 1 + + user_guide/index + api/index + contributing + changelog diff --git a/docs/source/user_guide/index.rst b/docs/source/user_guide/index.rst new file mode 100644 index 00000000..4e9700e6 --- /dev/null +++ b/docs/source/user_guide/index.rst @@ -0,0 +1,8 @@ +User Guide +========== + +.. toctree:: + :maxdepth: 1 + + installation + ../examples/overview diff --git a/docs/source/user_guide/installation.rst b/docs/source/user_guide/installation.rst new file mode 100644 index 00000000..1dee9081 --- /dev/null +++ b/docs/source/user_guide/installation.rst @@ -0,0 +1,27 @@ +Installation +============ + +.. note:: + + PySATL Core is currently in an early alpha stage and is not distributed as a + package via common managers such as pip. To try it out, you need to clone + the repository and work with it locally. + +Using Poetry +------------ + +If you use Poetry, install documentation dependencies with: + +.. code-block:: bash + + poetry install --with docs + +Using pip +--------- + +If you prefer plain pip, make sure you are on **Python 3.12+** (the project +uses PEP 695 syntax), then install docs requirements: + +.. code-block:: bash + + pip install -e ".[docs]" diff --git a/examples/overview.ipynb b/examples/overview.ipynb index a372fa03..8284f2bd 100644 --- a/examples/overview.ipynb +++ b/examples/overview.ipynb @@ -5,7 +5,7 @@ "id": "709f3963", "metadata": {}, "source": [ - "# PySATL Core: Overview Example\n", + "# PySATL Core: Usage Example\n", "\n", "This notebook demonstrates the core capabilities of **PySATL Core**:\n", "\n", diff --git a/pyproject.toml b/pyproject.toml index 8eb30295..d4bc8478 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -59,6 +59,13 @@ scipy-stubs = ">=1.13.0.0" [tool.poetry.group.docs.dependencies] jupyter = "^1.1.1" matplotlib = "^3.10.6" +sphinx = "^7.3" +sphinx-rtd-theme = "^2.0" +sphinxcontrib-napoleon = "^0.7" +sphinx-autodoc-typehints = "^2.0" +sphinx-copybutton = "^0.5" +myst-nb = "^1.3.0" +linkify-it-py = "^2.0.3" [tool.ruff] target-version = "py312" @@ -68,7 +75,7 @@ format.line-ending = "lf" lint.select = [ "B", "C4", "E", "F", "I", "ISC", "PIE", "SIM", "TID", "UP" ] lint.ignore = [ "B008", "E203" ] -lint.per-file-ignores."__init__.py" = [ "F403" ] +lint.per-file-ignores."**/__init__.py" = [ "F403" ] lint.fixable = [ "ALL" ] lint.unfixable = [ ] From cbc6188204b73edbc406076aca4365c45b469410 Mon Sep 17 00:00:00 2001 From: LeonidElkin <113133848+LeonidElkin@users.noreply.github.com> Date: Sat, 3 Jan 2026 21:18:26 +0300 Subject: [PATCH 4/5] docs: docs workflow init --- .github/workflows/docs_deploy.yml | 52 ++++++++++++++++++++++++++++++ .github/workflows/docs_preview.yml | 40 +++++++++++++++++++++++ 2 files changed, 92 insertions(+) create mode 100644 .github/workflows/docs_deploy.yml create mode 100644 .github/workflows/docs_preview.yml diff --git a/.github/workflows/docs_deploy.yml b/.github/workflows/docs_deploy.yml new file mode 100644 index 00000000..284da57b --- /dev/null +++ b/.github/workflows/docs_deploy.yml @@ -0,0 +1,52 @@ +name: Docs Deploy + +on: + push: + branches: [ main ] + workflow_dispatch: + +permissions: + contents: read + pages: write + id-token: write + +concurrency: + group: "pages" + cancel-in-progress: true + +jobs: + build-and-deploy: + runs-on: ubuntu-latest + environment: + name: github-pages + url: ${{ steps.deployment.outputs.page_url }} + steps: + - uses: actions/checkout@v4 + + - uses: actions/setup-python@v5 + with: + python-version: "3.12" + cache: "pip" + + - name: Install Poetry + run: pip install poetry + + - name: Install dependencies (with docs) + run: poetry install --with docs + + - name: Generate API + copy notebooks + run: poetry run python docs/source/generate_api.py + + - name: Build docs (Sphinx) + run: | + poetry run sphinx-build -E -a -b html docs/source docs/build/html + touch docs/build/html/.nojekyll + + - name: Upload Pages artifact + uses: actions/upload-pages-artifact@v3 + with: + path: docs/build/html + + - id: deployment + name: Deploy to GitHub Pages + uses: actions/deploy-pages@v4 diff --git a/.github/workflows/docs_preview.yml b/.github/workflows/docs_preview.yml new file mode 100644 index 00000000..d0bbc68f --- /dev/null +++ b/.github/workflows/docs_preview.yml @@ -0,0 +1,40 @@ +name: Docs Preview + +on: + pull_request: + branches: [ main ] + +permissions: + contents: read + +jobs: + build-preview: + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v4 + + - uses: actions/setup-python@v5 + with: + python-version: "3.12" + cache: "pip" + + - name: Install Poetry + run: pip install poetry + + - name: Install dependencies (with docs) + run: poetry install --with docs + + - name: Generate API + copy notebooks + run: poetry run python docs/source/generate_api.py + + - name: Build docs (Sphinx) + run: | + poetry run sphinx-build -E -a -b html docs/source docs/build/html + touch docs/build/html/.nojekyll + + - name: Upload docs preview artifact + uses: actions/upload-artifact@v4 + with: + name: docs-html-preview + path: docs/build/html + retention-days: 7 From 00e4f9813f3e253abe0d75957677323341b3ed1f Mon Sep 17 00:00:00 2001 From: LeonidElkin <113133848+LeonidElkin@users.noreply.github.com> Date: Sat, 3 Jan 2026 22:56:35 +0300 Subject: [PATCH 5/5] chore: README update --- README.md | 178 ++++++++++++++++++++++++------------------------------ 1 file changed, 78 insertions(+), 100 deletions(-) diff --git a/README.md b/README.md index bfc82fd1..2b475903 100644 --- a/README.md +++ b/README.md @@ -8,27 +8,42 @@ [![CI][status-shield]][status-url] [![MIT License][license-shield]][license-url] -**PySATL Core** is a minimal kernel for probability distributions: a distribution protocol, computation strategies, numeric converters between characteristics, and a dependency graph of characteristics. The kernel is designed as a foundation for other PySATL modules (CPD, etc.), with a focus on strict typing, extensibility, and reproducible computations. +**PySATL Core** is the computational core of the PySATL project, providing abstractions and infrastructure for probability distributions, parametric families, characteristic-based computations, and sampling. -## Features +The library is designed as a **foundational kernel** rather than a ready-to-use end-user package. Its primary goals are explicit probabilistic structure, extensibility, and suitability as a basis for further stochastic and statistical tooling. -- `Distribution` protocol with the minimal implementation `StandaloneEuclideanUnivariateDistribution`. -- Analytical and fitted computations for characteristics (`pdf`, `cdf`, `ppf`, etc.). -- Conversions between characteristics: `ppfโ†”cdf`, `cdfโ†”pdf` and their compositions. -- Characteristic registry as a directed graph with invariants and path-based planning. -- Sampling strategies (by default sampling via `ppf`). -- Strict typing (`mypy --strict`), modern Python 3.12+. +> **Project status** +> PySATL Core is currently in **early alpha**. +> It is **not published** to package managers such as `pip` yet. +> To experiment with the library, clone the repository and work with it locally. + +--- + +## โœจ Key features + +- **Parametric families of distributions** with multiple parametrizations + (e.g. Normal: `meanStd`, `meanPrec`). +- A global **family registry** for configuring, querying, and extending available distribution families. +- **Characteristic computation graph** (`CharacteristicRegistry`) that allows computing + arbitrary characteristics by specifying only a minimal analytical subset. +- Distribution objects exposing common probabilistic operations + (sampling, analytical and fitted computations). +- Clear separation between *distribution definitions*, *parametrizations*, + *computation strategies*, and *characteristics*. +- Modern Python with strict static typing (PEP 695). --- ## Requirements -- Python **3.12+** +- Python **3.12+** (the project relies on **PEP 695** syntax) - NumPy **2.x** - SciPy **1.13+** -- Poetry (for development) +- Poetry (recommended for development) -## Installation +--- + +## Installation (from source) Clone the repository: @@ -37,136 +52,99 @@ git clone https://github.com/PySATL/pysatl-core.git cd pysatl-core ``` -Install dependencies (via Poetry): +### Using Poetry (recommended) ```bash -poetry install +poetry install --with docs ``` -Or install the package locally with `pip` (editable): +### Using pip (editable install) ```bash -pip install -e . +pip install -e ".[docs]" ``` --- -## Quickstart +## ๐Ÿš€ Quickstart -Below is a minimal example: define an analytical `ppf`, draw a sample, compute `cdf` and `pdf` through the kernelโ€™s converters, and evaluate log-likelihood for a simple uniform case. +Below is a compact example demonstrating the use of a **built-in Normal distribution**. +It mirrors the example shown in the documentation (`examples/overview.ipynb`). ```python -from pysatl_core.types import Kind -from pysatl_core.distributions import ( - AnalyticalComputation, - StandaloneEuclideanUnivariateDistribution, +from pysatl_core import ( + FamilyName, + ParametricFamilyRegister, + configure_normal_family, ) -from pysatl_core.distributions.characteristics import GenericCharacteristic - -# Characteristic names -PDF = "pdf" -CDF = "cdf" -PPF = "ppf" - -# 1) A distribution with analytical PPF (identity on [0,1] for demo) -dist_ppf = StandaloneEuclideanUnivariateDistribution( - kind=Kind.CONTINUOUS, - analytical_computations=[ - AnalyticalComputation[float, float](PPF, lambda q: q) # x := ppf(q) - ], -) - -# 2) Sample 5 points (shape (n, d) = (5, 1)) -sample = dist_ppf.sample(5) -print(sample.shape) # -> (5, 1) -# 3) Compute characteristics via generic dispatch: -CDF_ = GenericCharacteristic[float, float](CDF) -PDF_ = GenericCharacteristic[float, float](PDF) +configure_normal_family() +normal_family = ParametricFamilyRegister.get(FamilyName.NORMAL) -x = 0.5 -print("cdf(0.5) =", CDF_(dist_ppf, x)) # cdf reconstructed from ppf -print("pdf(0.5) =", PDF_(dist_ppf, x)) # pdf reconstructed from cdf - -# 4) Log-likelihood: define an analytical uniform pdf on [0,1] -dist_uniform_pdf = StandaloneEuclideanUnivariateDistribution( - kind=Kind.CONTINUOUS, - analytical_computations=[ - AnalyticalComputation[float, float](PDF, lambda t: 1.0 if 0.0 <= t <= 1.0 else 0.0) - ], +normal = normal_family.distribution( + parametrization_name="meanStd", + mu=0.0, + sigma=1.0, ) -ll = dist_uniform_pdf.log_likelihood(sample) -print("log-likelihood =", ll) # for uniform on [0,1]: log(1) == 0 -``` - -The idea is simple: -- The **what** is defined by the characteristic name (`"pdf"`, `"cdf"`, `"ppf"`). -- The **how** is decided by the computation strategy: it either picks an analytical implementation or reconstructs it from other characteristics using the registry graph (with optional caching). - ---- - -## Concepts & Design - -- **Distribution protocol.** A minimal stable interface for downstream PySATL modules. -- **Analytical vs Fitted.** You can provide analytical functions; otherwise the kernel composes fitted methods from other available characteristics. -- **Characteristic graph.** A directed graph over characteristic names for a fixed distribution type; path search yields a pipeline of converters. -- **Sampling via PPF.** In the 1D Euclidean case, default sampling uses `ppf` with i.i.d. `U(0,1)`. -- **Strict typing.** The codebase targets `mypy --strict` and static analysis. - ---- +normal_alt = normal_family.distribution( + parametrization_name="meanPrec", + mu=0.0, + tau=1.0, +) -## Development +samples = normal.sample(n=10_000) +print(samples[:5]) -Set up the dev environment: +mean = normal.query_method("mean")() +variance = normal.query_method("variance")() -```bash -poetry install --with dev +print(mean, variance) ``` -Run tests: +This example uses a **predefined family** and **predefined parametrizations**. +PySATL Core also supports defining custom families, parametrizations, +and characteristic graphs. -```bash -poetry run pytest -q -``` +--- -Coverage: +## ๐Ÿ“– Documentation -```bash -poetry run pytest --cov=pysatl_core --cov-report=term-missing -``` +๐Ÿ‘‰ **Online documentation:** +https://pysatl.github.io/pysatl-core/ -Static checks and style: +Documentation previews are automatically generated for pull requests and can be inspected via CI artifacts. -```bash -poetry run ruff check . -poetry run mypy src -``` +--- -### Pre-commit +## ๐Ÿง  Concepts & design -Install hooks: +- **ParametricFamily** โ€” a family of distributions sharing a common mathematical form. +- **Parametrization** โ€” a concrete coordinate system for a family. +- **Distribution** โ€” a probabilistic object instantiated from a family and parametrization. +- **Characteristic graph** โ€” a directed graph describing relationships between computable characteristics. +- **Registries** โ€” explicit global registries enabling controlled extensibility. -```bash -poetry run pre-commit install -``` +--- -Run manually: +## ๐Ÿ›  Development ```bash -poetry run pre-commit run --all-files --color always --verbose --show-diff-on-failure +poetry install --with dev +poetry run pytest +poetry run pre-commit run --all-files ``` --- -## Roadmap +## ๐Ÿ—บ Roadmap -- Multivariate Euclidean distributions and sampling strategies. -- Expanded converter registry and stronger invariants in the characteristic graph. -- Mixtures and compositional operations in the core. +- **Transformations module** for mixtures and distribution transformations. +- Extension of characteristic graphs. +- Stabilization of APIs and **publishing PySATL Core as an installable package**. --- ## License -Distributed under the **MIT** License. See [LICENSE](LICENSE). +Distributed under the **MIT License**. See [LICENSE](LICENSE).