diff --git a/.flake8 b/.flake8 index d79ac3b..4ff24cf 100644 --- a/.flake8 +++ b/.flake8 @@ -2,7 +2,7 @@ max-complexity = 10 max-line-length = 88 -extend-ignore = +extend-ignore = # Let formatting take care of line length (not flake8) E501 E203 @@ -12,4 +12,3 @@ per-file-ignores = # We should aim is to address all of these in the future src/signaloid/distributional_information_plotting/*: C901 src/signaloid/distributional/*: C901 - diff --git a/.github/workflows/signaloid-python.yaml b/.github/workflows/signaloid-python.yaml index ff1b778..dd8962f 100644 --- a/.github/workflows/signaloid-python.yaml +++ b/.github/workflows/signaloid-python.yaml @@ -29,7 +29,7 @@ jobs: steps: - name: Checkout the PR branch - uses: actions/checkout@v4 + uses: actions/checkout@v6 with: ref: ${{ github.head_ref }} fetch-depth: 0 @@ -44,7 +44,7 @@ jobs: echo "contains(github.event.pull_request.labels, 'ci:upload-binaries'):" ${{ contains(github.event.pull_request.labels, 'ci:"upload-binaries') }} - name: Set up Python - uses: actions/setup-python@v5 + uses: actions/setup-python@v6 with: python-version: ${{ matrix.python-version }} @@ -58,7 +58,8 @@ jobs: run: ls - name: Install - run: poetry install + # Testing needs the optional dependencies + run: poetry install --all-extras - name: Install Poetry plugins run: poetry self add "poetry-dynamic-versioning[plugin]>=1.0.0,<2.0.0" @@ -75,6 +76,8 @@ jobs: run: poetry run black --check src/ - name: Typecheck + # Run mypy just once on the oldest supported Python version + if: ${{ matrix.args.host == 'ubuntu-22.04' && matrix.python-version == '3.10' }} run: poetry run mypy -p signaloid - name: Test @@ -84,7 +87,7 @@ jobs: run: poetry build - name: Upload test logs - uses: actions/upload-artifact@v4 + uses: actions/upload-artifact@v7 if: always() with: name: "test-logs-${{matrix.args.host}}-py${{ matrix.python-version }}-${{ github.event.pull_request.head.sha || github.sha }}" @@ -93,7 +96,7 @@ jobs: - name: Upload wheels if: ${{ startsWith(matrix.args.host, 'ubuntu') && matrix.python-version == '3.11' }} - uses: actions/upload-artifact@v4 + uses: actions/upload-artifact@v7 with: name: "wheel-${{ github.event.pull_request.head.sha || github.sha }}" path: | diff --git a/README.md b/README.md index 1114954..7977f3d 100644 --- a/README.md +++ b/README.md @@ -1,36 +1,67 @@ -# signaloid-python -This repository contains a set of tools for parsing and plotting Signaloid distributional data in python. The code has been tested on MacOS-14 and Ubuntu-20.04 using python 3.11. +# Signaloid Python Library and SDK -## Installation: -You can install the latest version of `signaloid-python` package via pip: +The Signaloid Python Library and SDK provides tools for interacting with +applications that utilize Signaloid's UxHw® technology for distributional +arithmetic. Use the library to analyze Ux Data values from the application. + + +## Requirements + +The Signaloid Python Library and SDK requires Python 3.10 or later. See +`pyproject.toml` for the full list of dependencies. + +## Installation +Install `signaloid-python` package via pip (recommended): ```bash -pip install git+https://github.com/signaloid/signaloid-python +python -m pip install signaloid-python ``` -## Parse `Ux` data -You can construct `DistributionalValue` objects by parsing `Ux` string or `Ux` bytes. You can find more details about the Signaloid `Ux` format [here](https://docs.signaloid.io/docs/hardware-api/ux-data-format/). Following is an example of parsing `Ux` strings and `Ux` bytes. + +Install the latest version from the GitHub repository: +```bash +python -m pip install git+https://github.com/signaloid/signaloid-python +``` + +Alternatively, clone this repository and install from source with: +```bash +python -m pip install . +``` + +## Usage + + +### Parsing Ux Data +Construct `DistributionalValue` Python objects by parsing +[Ux Data](https://docs.signaloid.io/docs/uxhw-api/ux-data-format/) in +Ux String or Ux Binary format. ```python from signaloid.distributional.distributional import DistributionalValue -... +# Intermediate code which writes to ux_string and ux_binary_buffer +# ... -# Parse a Ux string -distValue = DistributionalValue.parse(ux_string) +# Parse a Ux String +dist_value = DistributionalValue.parse(ux_string) -# Parse a Ux bytes buffer -distValue = DistributionalValue.parse(ux_bytes_buffer) +# Parse a Ux Binary buffer +dist_value = DistributionalValue.parse(ux_binary_buffer) ``` -## Plot `DistributionalValue` objects -You can use the `PlotHistogramDiracDeltas` class for plotting a distributional value as a histogram with variable bin width. We also provide a wrapper function to assist plotting. You can use the `plot` function, which you can find [here](./src/signaloid/distributional_information_plotting/plot_wrapper.py), to easily plot a distributional value like in the following example: +### Create Distribution Plots +Create plots to visualize distributional information by using the +[`plot` function](./src/signaloid/distributional_information_plotting/plot_wrapper.py) +with a `DistributionalValue` object containing Ux Data. The `plot` function is a +wrapper function for the `PlotHistogramDiracDeltas` class for plotting a +distributional value as a histogram with variable bin widths. ```python from signaloid.distributional_information_plotting.plot_wrapper import plot -... +# Intermediate code which writes to ux_string +# ... -# Create distributional value object from string -distValue = DistributionalValue.parse(ux_string) -plot(distValue) +# Create distributional value object from Ux String +dist_value = DistributionalValue.parse(ux_string) +plot(dist_value) ``` diff --git a/poetry.lock b/poetry.lock deleted file mode 100644 index ecb738e..0000000 --- a/poetry.lock +++ /dev/null @@ -1,1476 +0,0 @@ -# This file is automatically @generated by Poetry 2.3.2 and should not be changed by hand. - -[[package]] -name = "black" -version = "26.3.1" -description = "The uncompromising code formatter." -optional = false -python-versions = ">=3.10" -groups = ["dev"] -files = [ - {file = "black-26.3.1-cp310-cp310-macosx_10_9_x86_64.whl", hash = "sha256:86a8b5035fce64f5dcd1b794cf8ec4d31fe458cf6ce3986a30deb434df82a1d2"}, - 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With ``side='left'`` returns the first suitable + index, with ``side='right'`` the last. + + :param sorted_array: Ascending 1-D array to search within. + :param values: A scalar or a 1-D array of query values. + :param side: Either ``'left'`` or ``'right'``. + + :return: An int for a scalar query, otherwise an int array. + """ + if side not in ("left", "right"): + raise ValueError("side must be 'left' or 'right'.") + + def index_of(value): + low, high = 0, len(sorted_array) + while low < high: + middle = (low + high) // 2 + if side == "left": + go_right = sorted_array[middle] < value + else: + go_right = sorted_array[middle] <= value + if go_right: + low = middle + 1 + else: + high = middle + return low + + if isinstance(values, (list, self.ndarray)): + return self.array([index_of(value) for value in values], dtype=self.uint16) + + return index_of(values) + + def ndim(self, arr): + """The number of array dimensions; ``0`` for a scalar. + + :param arr: An array or scalar. + + :return: The number of dimensions. + """ + if isinstance(arr, (list, self.ndarray)): + return getattr(arr, "ndim", 1) + + return 0 + + def shape(self, arr): + """The shape tuple of an array; ``()`` for a scalar. + + :param arr: An array or scalar. + + :return: The shape tuple. + """ + if isinstance(arr, (list, self.ndarray)): + return getattr(arr, "shape", (len(arr),)) + + return () + def average(self, arr, weights=None): """ This function calculates the average of an array. diff --git a/src/signaloid/distributional/dirac_delta.py b/src/signaloid/distributional/dirac_delta.py index 3bec86e..88823e7 100644 --- a/src/signaloid/distributional/dirac_delta.py +++ b/src/signaloid/distributional/dirac_delta.py @@ -75,7 +75,11 @@ def raw_mass(self, value: int) -> None: :param value: The 64bit fixed-point mass to use. :type value: int + :raises ValueError: If the given mass is negative. """ + if value < 0: + raise ValueError(f"raw_mass must be non-negative; got {value}.") + self._raw_mass = value # The probability mass is a fixed-point format with FIXED_POINT_ONE @@ -98,7 +102,11 @@ def mass(self, value: float) -> None: :param value: The floating-point mass to use. :type value: float + :raises ValueError: If the given mass is negative. """ + if value < 0: + raise ValueError(f"mass must be non-negative; got {value}.") + self._mass = value if np.isnan(self._mass): diff --git a/src/signaloid/distributional/dirac_delta_test.py b/src/signaloid/distributional/dirac_delta_test.py index 217c970..1096a12 100644 --- a/src/signaloid/distributional/dirac_delta_test.py +++ b/src/signaloid/distributional/dirac_delta_test.py @@ -18,6 +18,7 @@ # FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER # DEALINGS IN THE SOFTWARE. +import math import unittest from signaloid.distributional.dirac_delta import DiracDelta @@ -72,5 +73,44 @@ def test_dirac_delta_operations(self) -> None: self.assertTrue(d3.mass == combined_mass) +class TestDiracDeltaMassValidation(unittest.TestCase): + """`DiracDelta` rejects negative masses, both at construction and via + the `mass` / `raw_mass` setters, for the floating-point `mass` and + fixed-point `raw_mass` inputs alike.""" + + def test_rejects_negative_mass(self) -> None: + with self.assertRaises(ValueError): + DiracDelta(position=1.0, mass=-0.5) + + def test_rejects_negative_raw_mass(self) -> None: + with self.assertRaises(ValueError): + DiracDelta(position=1.0, raw_mass=-1) + + def test_accepts_zero_and_positive_mass(self) -> None: + self.assertEqual(DiracDelta(position=1.0, mass=0.0).mass, 0.0) + self.assertEqual(DiracDelta(position=1.0, mass=0.5).mass, 0.5) + + def test_accepts_zero_and_positive_raw_mass(self) -> None: + self.assertEqual(DiracDelta(position=1.0, raw_mass=0).raw_mass, 0) + self.assertEqual(DiracDelta(position=1.0, raw_mass=10).raw_mass, 10) + + def test_mass_setter_rejects_negative(self) -> None: + dd = DiracDelta(position=1.0, mass=0.5) + with self.assertRaises(ValueError): + dd.mass = -0.5 + self.assertEqual(dd.mass, 0.5) + + def test_raw_mass_setter_rejects_negative(self) -> None: + dd = DiracDelta(position=1.0, raw_mass=10) + with self.assertRaises(ValueError): + dd.raw_mass = -10 + self.assertEqual(dd.raw_mass, 10) + + def test_mass_setter_allows_nan(self) -> None: + dd = DiracDelta(position=float("nan"), mass=0.0) + dd.mass = float("nan") + self.assertTrue(math.isnan(dd.mass)) + + if __name__ == "__main__": unittest.main() diff --git a/src/signaloid/distributional/distributional.py b/src/signaloid/distributional/distributional.py index b4d74fb..fe325be 100644 --- a/src/signaloid/distributional/distributional.py +++ b/src/signaloid/distributional/distributional.py @@ -23,6 +23,7 @@ import sys import re import struct +from typing import overload if sys.implementation.name != "circuitpython": # Use numpy for accelerated computing @@ -58,6 +59,9 @@ }, } +# First byte of the Ux Binary Data format, used to distinguish it from the legacy format +UX_BINARY_FORMAT_MARKER = 0xF0 + class DistributionalValue: def __init__( @@ -241,6 +245,257 @@ def calculate_variance(self) -> float | None: return self._variance + def _positive_mass_support(self) -> tuple[np.ndarray, np.ndarray]: + """Positions and masses of the strictly-positive-mass Dirac deltas. + + Zero-mass deltas carry no probability, so the support-shape + statistics ignore them: a zero-mass outlier must not widen the + reported range, and a zero-mass placeholder below the support + must not shift a quantile or CDF lookup. + + Returns: + ``(positions, masses)`` restricted to deltas whose mass is + strictly greater than zero. + """ + masses = self.masses + mask = masses > 0.0 + return self.positions[mask], masses[mask] + + @property + def range(self) -> float: + """Max finite position minus min finite position. + + Returns: + 0.0 for a single-Dirac distribution. + NaN when any NaN-position Dirac has positive mass. + +Inf when any ±Inf-position Dirac has positive mass. + NaN for empty / all-zero-mass distributions. + """ + self.sort() + if self.nan_dirac_delta.mass > 0: + return float("nan") + if self.neg_inf_dirac_delta.mass > 0 or self.pos_inf_dirac_delta.mass > 0: + return float("inf") + # After the special-value early returns the only remaining + # deltas are finite; drop zero-mass ones so they cannot widen + # the reported support. + finite_positions, _ = self._positive_mass_support() + if finite_positions.size == 0: + return float("nan") + return float(finite_positions.max() - finite_positions.min()) + + def quantile(self, t: float) -> float: + """Empirical inverse CDF at ``t`` (non-interpolating step lookup). + + Returns an actual support position (the smallest whose cumulative mass + reaches ``t``) and takes a single scalar ``t``. For an interpolating, + array-capable variant that can return values between support points, + see `inverse_cdf`. + + Args: + t: Quantile parameter in [0, 1]. + + Returns: + Smallest position whose cumulative normalised mass is at + least ``t``. NaN if ``t`` is NaN or if the distribution + has zero total mass. + + Raises: + ValueError: if ``t`` is outside [0, 1]. + """ + if np.isnan(t): + return float("nan") + if t < 0.0 or t > 1.0: + raise ValueError(f"quantile parameter t must be in [0, 1]; got {t}.") + total_mass = float(self.masses.sum()) + if total_mass == 0.0: + return float("nan") + positions, masses = self._positive_mass_support() + order = np.argsort(positions) + sorted_positions = positions[order] + cumulative = np.cumsum(masses[order]) / total_mass + index = int(np.searchsorted(cumulative, t, side="left")) + index = min(index, len(sorted_positions) - 1) + return float(sorted_positions[index]) + + @property + def median(self) -> float: + """The median position — shorthand for ``quantile(0.5)``.""" + return self.quantile(0.5) + + @overload + def cdf(self, x: float, *, treat_as_samples: bool = False) -> float: ... + + @overload + def cdf(self, x: np.ndarray, *, treat_as_samples: bool = False) -> np.ndarray: ... + + def cdf(self, x, *, treat_as_samples: bool = False): + """Empirical right-continuous step-function CDF at ``x``. + + Args: + x: Evaluation point(s); scalar or 1-D array. + treat_as_samples: When True, ignore masses and treat the + positions as equally-weighted samples, so the CDF is + ``(count of positions <= x) / N``; when False (default), + use the mass-weighted step CDF. + + Returns: + CDF value(s) in [0, 1]; ``float`` for scalar input, + ``np.ndarray`` for array input. NaN for NaN inputs and + for empty / all-zero-mass distributions. + """ + if treat_as_samples: + sample_positions = np.sort(np.asarray(self.positions, dtype=float)) + if sample_positions.size == 0: + if np.ndim(x) == 0: + return float("nan") + return np.full(np.shape(x), np.nan, dtype=float) + result = ( + np.searchsorted(sample_positions, x, side="right") + / sample_positions.size + ) + else: + total_mass = float(self.masses.sum()) + if total_mass == 0.0: + if np.ndim(x) == 0: + return float("nan") + return np.full(np.shape(x), np.nan, dtype=float) + positions, masses = self._positive_mass_support() + order = np.argsort(positions) + sorted_positions = positions[order] + cumulative = np.cumsum(masses[order]) / total_mass + cdf_lookup = np.concatenate(([0.0], cumulative)) + indices = np.searchsorted(sorted_positions, x, side="right") + result = cdf_lookup[indices] + if np.ndim(x) == 0: + if np.isnan(x): + return float("nan") + return float(result) + nan_mask = np.isnan(np.asarray(x)) + if np.any(nan_mask): + result = np.where(nan_mask, np.nan, result) + return result + + @overload + def inverse_cdf(self, p: float, *, treat_as_samples: bool = False) -> float: ... + + @overload + def inverse_cdf( + self, p: np.ndarray, *, treat_as_samples: bool = False + ) -> np.ndarray: ... + + def inverse_cdf(self, p, *, treat_as_samples: bool = False): + """Interpolated inverse CDF (quantile function), array-capable. + + Unlike `quantile` (a scalar, non-interpolating step lookup that always + returns an actual support position), this linearly interpolates the + support positions against their cumulative mass (weighted branch) or + via ``np.quantile`` over the raw positions (samples branch). The result + is therefore not snapped to a support point: for ``p`` between two + support points it can return a value strictly between them (within the + support range ``[min, max]``). It also accepts array ``p``. + + Args: + p: Probability level(s) in [0, 1]; scalar or 1-D array. + treat_as_samples: When True, ignore masses and treat the + positions as equally-weighted samples (``np.quantile``); + when False (default), interpolate against the + mass-weighted cumulative distribution. + + Returns: + Interpolated position(s); ``float`` for scalar ``p``, + ``np.ndarray`` for array ``p``. NaN when the distribution has + no positions (samples) or no positive mass (weighted). + """ + if treat_as_samples: + sample_positions = np.asarray(self.positions, dtype=float) + if sample_positions.size == 0: + if np.ndim(p) == 0: + return float("nan") + return np.full(np.shape(p), np.nan, dtype=float) + values = np.quantile(sample_positions, p) + else: + positions, masses = self._positive_mass_support() + if positions.size == 0: + if np.ndim(p) == 0: + return float("nan") + return np.full(np.shape(p), np.nan, dtype=float) + order = np.argsort(positions) + sorted_positions = positions[order] + cumulative = np.cumsum(masses[order]) + cumulative = cumulative / cumulative[-1] + values = np.interp(p, cumulative, sorted_positions) + if np.ndim(p) == 0: + return float(values) + return np.asarray(values) + + def raw_moments(self, order: int) -> float: + """The ``order``-th raw moment ``Σ p_i · x_i^order``. + + Args: + order: Moment order (any non-negative integer). + + Returns: + ``order == 0`` returns 1.0 for any non-empty distribution. + NaN when any NaN-position Dirac has positive mass. + +Inf when only +Inf-position mass is present. + For -Inf-position mass: +Inf for even ``order``, + -Inf for odd ``order``. + For both ±Inf-position masses: +Inf for even ``order``, + NaN for odd ``order``. + NaN for empty / all-zero-mass distributions. + """ + if float(self.masses.sum()) == 0.0: + return float("nan") + if order == 0: + return 1.0 + self.sort() + if self.nan_dirac_delta.mass > 0: + return float("nan") + has_neg_inf = self.neg_inf_dirac_delta.mass > 0 + has_pos_inf = self.pos_inf_dirac_delta.mass > 0 + if has_neg_inf and has_pos_inf: + return float("inf") if order % 2 == 0 else float("nan") + if has_pos_inf: + return float("inf") + if has_neg_inf: + return float("inf") if order % 2 == 0 else float("-inf") + positions, masses = self._positive_mass_support() + total_mass = float(masses.sum()) + if total_mass == 0.0: + return float("nan") + return float(np.sum(masses * positions**order) / total_mass) + + def central_moments(self, order: int) -> float: + """The ``order``-th central moment ``Σ p_i · (x_i − mean)^order``. + + Args: + order: Moment order (any non-negative integer). + + Returns: + ``order == 0`` returns 1.0 for any non-empty distribution. + NaN whenever any NaN- or ±Inf-position Dirac has positive + mass (the mean is non-finite). + NaN for empty / all-zero-mass distributions. + """ + if float(self.masses.sum()) == 0.0: + return float("nan") + if order == 0: + return 1.0 + self.sort() + if ( + self.nan_dirac_delta.mass > 0 + or self.neg_inf_dirac_delta.mass > 0 + or self.pos_inf_dirac_delta.mass > 0 + ): + return float("nan") + positions, masses = self._positive_mass_support() + total_mass = float(masses.sum()) + if total_mass == 0.0: + return float("nan") + mean = float(np.sum(masses * positions) / total_mass) + return float(np.sum(masses * (positions - mean) ** order) / total_mass) + @property def has_special_values(self) -> bool: """Property that identifies if there are non-zero mass Dirac Deltas, @@ -286,6 +541,67 @@ def from_samples(cls, samples: np.ndarray | list[float]) -> "DistributionalValue dist = cls(dirac_deltas=dirac_deltas) return dist + @classmethod + def from_weighted_samples( + cls, + positions: list[float] | np.ndarray, + masses: list[float] | np.ndarray, + ) -> "DistributionalValue": + """ + Construct a DistributionalValue from weighted samples. + + Validates the inputs (non-empty, equal-length, numeric, non-negative, + finite and non-zero total mass), normalises the masses to sum to 1.0, + and builds one Dirac delta per (position, normalised-mass) pair. + + Args: + positions: 1-D array of sample positions. + masses: 1-D array of (unnormalised) sample masses, one per position. + + Returns: + A DistributionalValue instance with normalised masses. + + Raises: + ValueError: If positions or masses are empty, have differing + lengths, contain non-numerical values, contain negative + masses, or the total mass is not finite and non-zero. + """ + positions_arr = np.array(positions) + masses_arr = np.array(masses) + if len(positions_arr) == 0: + raise ValueError(f"positions {positions_arr} is empty") + if len(masses_arr) == 0: + raise ValueError(f"masses {masses_arr} is empty") + if len(positions_arr) != len(masses_arr): + raise ValueError( + f"positions {positions_arr} and masses {masses_arr} " + f"have differing lengths" + ) + if not all( + isinstance(pos, (float, int, np.integer, np.floating)) + for pos in positions_arr + ): + raise ValueError(f"{positions_arr} contain non numerical values") + if not all( + isinstance(mass, (float, int, np.integer, np.floating)) + for mass in masses_arr + ): + raise ValueError(f"{masses_arr} contain non numerical values") + if np.any(masses_arr < 0.0): + raise ValueError(f"masses must be non-negative (got {masses_arr})") + + total_mass = float(np.sum(masses_arr)) + if not np.isfinite(total_mass) or total_mass == 0.0: + raise ValueError( + f"sum of masses must be finite and non-zero (got {total_mass})" + ) + normalized = list(masses_arr / total_mass) + dirac_deltas = [ + DiracDelta(position=pos, mass=float(m)) + for pos, m in zip(positions_arr, normalized) + ] + return cls(dirac_deltas=dirac_deltas) + def __repr__(self) -> str: """Constructs the representation type for the `DistributionalValue`. @@ -316,17 +632,17 @@ def __bytes__(self) -> bytes: def export(self, to_str: bool = True) -> str | bytes: """ - Constructs the Ux string/Ux bytes with particle value for the `DistributionalValue`. + Constructs the Ux String/Ux Binary Data with particle value for the `DistributionalValue`. Args: - to_str: Whether to export a Ux string or a Ux bytes - - True: Export a Ux string - - False: Export a Ux bytes + to_str: Whether to export a Ux String or Ux Binary Data + - True: Export a Ux String + - False: Export Ux Binary Data Returns: - The Ux string or the Ux bytes with particle value for the `DistributionalValue`. + The Ux String or the Ux Binary Data with particle value for the `DistributionalValue`. - Ux-string format specification: + Ux String format specification: - Particle value (double in string format) - "Ux" ( 2 chars) - Representation type (uint8_t) ( 2 chars) @@ -337,15 +653,33 @@ def export(self, to_str: bool = True) -> str | bytes: - Support position (float/double) (8/16 chars) - Probability mass (uint64_t) ( 16 chars) - Ux-bytes specification: - - Particle value (double) ( 8 bytes) - - Representation type (uint8_t) ( 1 byte ) - - Number of samples (uint64_t) ( 8 bytes) (unused) - - Mean value of distribution (double) ( 8 bytes) - - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) - - Pairs of: - - Support position (float/double) (4/8 bytes) - - Probability mass (uint64_t) ( 8 bytes) + Ux Binary specification: + The Ux Binary Data layout has a 3-byte marker (0xF00000) between + the particle value and the representation type. The legacy format + does not have this marker. The `export` function always produces the + Ux Binary layout and not the legacy. The `parse` function accepts + both (see `parse`). + For more information see https://docs.signaloid.io/docs/uxhw-api/ux-data-format/ + + Ux Binary Data Format: + - Particle value (double) ( 8 bytes) + - Representation type (uint32_t) ( 4 bytes) + - Number of samples (uint64_t) ( 8 bytes) (unused) + - Mean value of distribution (double) ( 8 bytes) + - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) + - Pairs of: + - Support position (float/double) (4/8 bytes) + - Probability mass (uint64_t) ( 8 bytes) + + Legacy format: + - Particle value (double) ( 8 bytes) + - Representation type (uint8_t) ( 1 byte ) + - Number of samples (uint64_t) ( 8 bytes) (unused) + - Mean value of distribution (double) ( 8 bytes) + - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) + - Pairs of: + - Support position (float/double) (4/8 bytes) + - Probability mass (uint64_t) ( 8 bytes) """ # Create byte representation @@ -368,6 +702,13 @@ def export(self, to_str: bool = True) -> str | bytes: fmt = STRUCT_FORMATS["bytes"] buffer += struct.pack(fmt["particle"], particle_value) + # Ux Binary Data format specifies: + # - start byte (0xF0), + # - followed by 2 padding bytes (0x0000). + # These are inserted between the particle value and the + # representation type. + buffer += bytes([UX_BINARY_FORMAT_MARKER, 0x00, 0x00]) + # Representation type (uint8_t) (1 byte) buffer += struct.pack(fmt["UR_type"], self.UR_type) @@ -407,17 +748,17 @@ def parse( ) -> "DistributionalValue | None": """ Constructs a `DistributionalValue` after parsing an input that can be - a UxString or a byte array. + a Ux String or a byte array. Args: - dist: The input UxString or byte array. + dist: The input Ux String or byte array. double_precision: The floating point representation precision. - true: double precision - false: single precision Returns: The constructed `DistributionalValue` or None if parsing fails. - Ux-string format specification: + Ux String format specification: - Particle value (double in string format) - "Ux" ( 2 chars) - Representation type (uint8_t) ( 2 chars) @@ -428,22 +769,40 @@ def parse( - Support position (float/double) (8/16 chars) - Probability mass (uint64_t) ( 16 chars) - Ux-bytes specification: - - Particle value (double) ( 8 bytes) - - Representation type (uint8_t) ( 1 byte ) - - Number of samples (uint64_t) ( 8 bytes) (unused) - - Mean value of distribution (double) ( 8 bytes) - - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) - - Pairs of: - - Support position (float/double) (4/8 bytes) - - Probability mass (uint64_t) ( 8 bytes) + Ux Binary specification: + The Ux Binary Data layout has a 3-byte marker (0xF00000) between + the particle value and the representation type. The legacy format + does not have this marker. The `export` function always produces the + Ux Binary layout and not the legacy. The `parse` function accepts + both (see `parse`). + For more information see https://docs.signaloid.io/docs/uxhw-api/ux-data-format/ + + Ux Binary Data Format: + - Particle value (double) ( 8 bytes) + - Representation type (uint32_t) ( 4 bytes) + - Number of samples (uint64_t) ( 8 bytes) (unused) + - Mean value of distribution (double) ( 8 bytes) + - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) + - Pairs of: + - Support position (float/double) (4/8 bytes) + - Probability mass (uint64_t) ( 8 bytes) + + Legacy format: + - Particle value (double) ( 8 bytes) + - Representation type (uint8_t) ( 1 byte ) + - Number of samples (uint64_t) ( 8 bytes) (unused) + - Mean value of distribution (double) ( 8 bytes) + - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) + - Pairs of: + - Support position (float/double) (4/8 bytes) + - Probability mass (uint64_t) ( 8 bytes) """ if not dist: return None # If input is a hex string without 'Ux', convert it to bytes and try to - # parse it as Ux-bytes + # parse it as Ux Binary Data if isinstance(dist, str) and "Ux" not in dist: dist = bytes.fromhex(dist) @@ -457,7 +816,7 @@ def parse( dist_value = DistributionalValue(double_precision=double_precision) if isinstance(dist, str): - # Parse Hex string + # Parse Ux String from string of hexadecimal characters fmt = STRUCT_FORMATS["str"] # Match an optional floating-point or integer number, followed by 'Ux', @@ -488,16 +847,30 @@ def parse( fmt = STRUCT_FORMATS["bytes"] buffer = dist + + # Need 8 bytes for the particle value plus at least 1 more byte + # to detect the layout (see below). + if len(buffer) < 9: + return None + dist_value.particle_value = struct.unpack( fmt["particle"], buffer[offset : offset + 8] )[0] offset += 8 + + if buffer[offset] == UX_BINARY_FORMAT_MARKER: + # If offset has the Ux Binary data format marker then we are not + # in the legacy format. Skip the 3-byte marker (0xF00000). + offset += 3 else: print("Error: ", type(dist)) return None - # Check if the buffer has the minimum required length (in bytes) - # Minimum length = 1 (repr) + 8 (samples) + 8 (mean) + 4 (count) = 21 + # Check if the buffer has the minimum required length (in bytes). + # Minimum header after the current offset = 1 (repr) + 8 (samples) + + # 8 (mean) + 4 (count) = 21. The offset already accounts for the + # particle value and, for the Ux Binary layout, the 3-byte start + # marker. min_length = offset + 21 if len(buffer) < min_length: return None diff --git a/src/signaloid/distributional/distributional_test.py b/src/signaloid/distributional/distributional_test.py index 61eaa1b..d20b740 100644 --- a/src/signaloid/distributional/distributional_test.py +++ b/src/signaloid/distributional/distributional_test.py @@ -32,7 +32,7 @@ def read_string_bytes_pairs_from_csv( csv_filename: str, ) -> list[tuple[str, bytes]] | None: """ - Reads pairs of Ux strings and Ux bytes(in hex format) from a csv file + Reads pairs of Ux Strings and Ux Binary Data (in hex format) from a csv file Args: csv_filename: The input csv file path @@ -55,13 +55,39 @@ def read_string_bytes_pairs_from_csv( return pairs +def to_padded_ux_binary(ux_binary: bytes) -> bytes: + """Convert legacy format to Ux Binary Data. + + `DistributionalValue.export` always emits the correct Ux Binary Data format + with the 3-byte marker. A legacy byte array is converted by inserting the + 3-byte marker (the 0xF0 start byte plus two 0x00 padding bytes) after the + 8-byte particle value. A byte array already in the Ux Binary Data format + (byte 8 == 0xF0) is returned unchanged. + + Args: + ux_binary: A stored array in either the Ux Binary Data or the legacy + format. + + Returns: + The equivalent Ux Binary Data array. + """ + if len(ux_binary) >= 9 and ux_binary[8:11] == b"\xf0\x00\x00": + return ux_binary + return ux_binary[:8] + b"\xf0\x00\x00" + ux_binary[8:] + + class TestUxParsing(unittest.TestCase): def test_parse_ux_strings_values( self, input_filename: str = "./test_ux_value_pairs.csv", ) -> None: """ - Test parsing Ux string values and converting them to Ux bytes + Test parsing Ux String values and converting them to Ux Binary Data. + + The encoder always emits the correct Ux Binary Data format, so each + result is compared against the Ux Binary normalization of the stored + byte array. This works whether the stored array is in the legacy or the + Ux Binary layout (the corpus contains both). """ ux_pairs = read_string_bytes_pairs_from_csv(input_filename) @@ -74,14 +100,22 @@ def test_parse_ux_strings_values( distValueFromUxString = DistributionalValue.parse(pair[0]) self.assertIsNotNone(distValueFromUxString) if distValueFromUxString is not None: - self.assertEqual(bytes(distValueFromUxString), pair[1]) + self.assertEqual( + bytes(distValueFromUxString), + to_padded_ux_binary( + pair[1] + ), # Convert legacy to Ux Binary Data for comparison + ) - def test_parse_ux_bytes_values( + def test_parse_ux_binary_values( self, input_filename: str = "./test_ux_value_pairs.csv", ) -> None: """ - Test parsing Ux bytes and converting them to Ux strings + Test parsing Ux Binary Data and converting it to Ux Strings. + + The corpus is a mix of legacy (unpadded) and Ux Binary (padded) + layout byte arrays, so this exercises parsing of both layouts. """ ux_pairs = read_string_bytes_pairs_from_csv(input_filename) @@ -426,5 +460,879 @@ def test_all_identical_samples(self) -> None: self.assertAlmostEqual(finite[0].mass, 1.0) +class TestPositiveMassSupport(unittest.TestCase): + """`DistributionalValue._positive_mass_support` keeps only the + strictly-positive-mass Dirac deltas.""" + + def test_drops_zero_mass_keeps_positive(self) -> None: + """Zero-mass deltas are dropped; positive-mass ones are kept.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.4), + DiracDelta(position=2.0, mass=0.0), + DiracDelta(position=3.0, mass=0.6), + ] + ) + positions, masses = dist._positive_mass_support() + np.testing.assert_allclose(positions, [1.0, 3.0]) + np.testing.assert_allclose(masses, [0.4, 0.6]) + + def test_preserves_order_and_pairs_positions_with_masses(self) -> None: + """Surviving positions and masses stay aligned, in original order.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=5.0, mass=0.5), + DiracDelta(position=-2.0, mass=0.0), + DiracDelta(position=1.0, mass=0.5), + ] + ) + positions, masses = dist._positive_mass_support() + np.testing.assert_allclose(positions, [5.0, 1.0]) + np.testing.assert_allclose(masses, [0.5, 0.5]) + + def test_all_zero_mass_returns_empty(self) -> None: + """All-zero-mass distribution yields empty arrays.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.0), + DiracDelta(position=2.0, mass=0.0), + ] + ) + positions, masses = dist._positive_mass_support() + self.assertEqual(positions.size, 0) + self.assertEqual(masses.size, 0) + + def test_empty_distribution_returns_empty(self) -> None: + """Empty distribution yields empty arrays.""" + dist = DistributionalValue(dirac_deltas=[]) + positions, masses = dist._positive_mass_support() + self.assertEqual(positions.size, 0) + self.assertEqual(masses.size, 0) + + def test_mass_is_the_only_filter(self) -> None: + """Mass is the sole filter: a positive-mass non-finite position is + retained (special-value handling is the caller's concern).""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("inf"), mass=0.5), + DiracDelta(position=2.0, mass=0.0), + ] + ) + positions, masses = dist._positive_mass_support() + self.assertEqual(positions.size, 2) + self.assertTrue(np.isinf(positions).any()) + np.testing.assert_allclose(masses, [0.5, 0.5]) + + +class TestDistributionalValueRange(unittest.TestCase): + """`DistributionalValue.range` — positions.max() - positions.min().""" + + def test_single_dirac_has_zero_range(self) -> None: + """A degenerate single-Dirac distribution has range 0.0.""" + dist = DistributionalValue(dirac_deltas=[DiracDelta(position=3.14, mass=1.0)]) + self.assertAlmostEqual(dist.range, 0.0, places=12) + + def test_multi_dirac_range_equals_max_minus_min(self) -> None: + """Range = positions.max() - positions.min().""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=3.0, mass=0.5), + DiracDelta(position=5.0, mass=0.2), + ] + ) + self.assertAlmostEqual(dist.range, 4.0, places=12) + + def test_range_independent_of_position_order(self) -> None: + """Unsorted positions yield the same range as sorted.""" + positions = [5.0, 1.0, 3.0] + masses = [0.2, 0.5, 0.3] + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=p, mass=m) for p, m in zip(positions, masses) + ] + ) + self.assertAlmostEqual(dist.range, 4.0, places=12) + + def test_range_returns_nan_when_nan_position_has_positive_mass(self) -> None: + """NaN-position mass renders the support undefined.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=float("nan"), mass=0.4), + DiracDelta(position=3.0, mass=0.3), + ] + ) + self.assertTrue(np.isnan(dist.range)) + + def test_range_returns_inf_for_any_infinite_position_mass(self) -> None: + """Any ±Inf-position mass → range is +Inf.""" + for label, special_position in ( + ("+inf", float("inf")), + ("-inf", float("-inf")), + ): + with self.subTest(case=label): + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=special_position, mass=0.5), + ] + ) + self.assertEqual(dist.range, float("inf")) + + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=float("-inf"), mass=0.3), + DiracDelta(position=1.0, mass=0.4), + DiracDelta(position=float("inf"), mass=0.3), + ] + ) + self.assertEqual(dist.range, float("inf")) + + def test_range_ignores_zero_mass_nan_placeholder(self) -> None: + """Zero-mass NaN position is treated as a placeholder.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("nan"), mass=0.0), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertAlmostEqual(dist.range, 2.0, places=12) + + def test_range_returns_nan_for_empty_distribution(self) -> None: + """Empty distribution: range is NaN.""" + dist = DistributionalValue(dirac_deltas=[]) + self.assertTrue(np.isnan(dist.range)) + + def test_range_ignores_zero_mass_finite_outlier(self) -> None: + """A zero-mass finite Dirac must not widen the support.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + DiracDelta(position=100.0, mass=0.0), + ] + ) + self.assertAlmostEqual(dist.range, 2.0, places=12) + + def test_range_returns_nan_for_all_zero_mass_finite(self) -> None: + """All-zero-mass finite distribution has undefined range.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.0), + DiracDelta(position=3.0, mass=0.0), + ] + ) + self.assertTrue(np.isnan(dist.range)) + + +class TestDistributionalValueQuantile(unittest.TestCase): + """`DistributionalValue.quantile(t)` — empirical inverse CDF.""" + + def test_single_dirac_returns_position_for_any_t(self) -> None: + """Single-Dirac: every quantile equals the position.""" + dist = DistributionalValue(dirac_deltas=[DiracDelta(position=3.14, mass=1.0)]) + for t in (0.0, 0.25, 0.5, 0.75, 1.0): + with self.subTest(t=t): + self.assertAlmostEqual(dist.quantile(t), 3.14, places=12) + + def test_quantile_at_one_returns_max(self) -> None: + """quantile(1.0) returns the maximum position.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertAlmostEqual(dist.quantile(1.0), 3.0, places=12) + + def test_quantile_at_zero_returns_min(self) -> None: + """quantile(0.0) returns the minimum position.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertAlmostEqual(dist.quantile(0.0), 1.0, places=12) + + def test_quantile_known_two_point(self) -> None: + """Hand-computed quantiles for positions [1, 3] with masses [0.3, 0.7].""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=3.0, mass=0.7), + ] + ) + self.assertAlmostEqual(dist.quantile(0.2), 1.0, places=12) + self.assertAlmostEqual(dist.quantile(0.5), 3.0, places=12) + + def test_quantile_rejects_out_of_range(self) -> None: + """t must lie in [0, 1]; values outside raise ValueError.""" + dist = DistributionalValue(dirac_deltas=[DiracDelta(position=1.0, mass=1.0)]) + with self.assertRaises(ValueError): + dist.quantile(-0.1) + with self.assertRaises(ValueError): + dist.quantile(1.1) + + def test_quantile_returns_nan_for_nan_input(self) -> None: + """NaN input returns NaN.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertTrue(np.isnan(dist.quantile(float("nan")))) + + def test_quantile_returns_nan_for_zero_total_mass(self) -> None: + """Zero total mass returns NaN.""" + for label, dist in ( + ("empty", DistributionalValue(dirac_deltas=[])), + ( + "all_zero_mass", + DistributionalValue(dirac_deltas=[DiracDelta(position=1.0, mass=0.0)]), + ), + ): + with self.subTest(case=label): + self.assertTrue(np.isnan(dist.quantile(0.5))) + + def test_quantile_ignores_zero_mass_outside_support(self) -> None: + """Zero-mass Diracs below/above the support must not shift quantiles.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=-100.0, mass=0.0), + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + DiracDelta(position=100.0, mass=0.0), + ] + ) + self.assertAlmostEqual(dist.quantile(0.0), 1.0, places=12) + self.assertAlmostEqual(dist.quantile(1.0), 3.0, places=12) + + +class TestDistributionalValueMedian(unittest.TestCase): + """`DistributionalValue.median` — quantile(0.5).""" + + def test_median_equals_quantile_half(self) -> None: + """median is the 0.5 quantile by definition.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=3.0, mass=0.7), + ] + ) + self.assertAlmostEqual(dist.median, dist.quantile(0.5), places=12) + + def test_median_of_symmetric_three_point(self) -> None: + """Symmetric {-1, 0, 1} with equal masses: median = 0.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=-1.0, mass=1 / 3), + DiracDelta(position=0.0, mass=1 / 3), + DiracDelta(position=1.0, mass=1 / 3), + ] + ) + self.assertAlmostEqual(dist.median, 0.0, places=12) + + +class TestDistributionalValueCdf(unittest.TestCase): + """`DistributionalValue.cdf(x)`: vectorised empirical CDF.""" + + def test_cdf_below_support_is_zero(self) -> None: + """cdf(x) = 0 when x < min(positions).""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertAlmostEqual(dist.cdf(0.0), 0.0, places=12) + + def test_cdf_at_and_above_support_is_one(self) -> None: + """cdf(x) = 1 when x ≥ max(positions) (right-continuous).""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertAlmostEqual(dist.cdf(3.0), 1.0, places=12) + self.assertAlmostEqual(dist.cdf(4.0), 1.0, places=12) + + def test_cdf_known_three_point(self) -> None: + """Hand-computed CDF for equal-mass positions [1, 2, 3].""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=1 / 3), + DiracDelta(position=2.0, mass=1 / 3), + DiracDelta(position=3.0, mass=1 / 3), + ] + ) + self.assertAlmostEqual(dist.cdf(0.0), 0.0, places=12) + self.assertAlmostEqual(dist.cdf(1.0), 1 / 3, places=12) + self.assertAlmostEqual(dist.cdf(1.5), 1 / 3, places=12) + self.assertAlmostEqual(dist.cdf(2.0), 2 / 3, places=12) + self.assertAlmostEqual(dist.cdf(3.0), 1.0, places=12) + + def test_cdf_accepts_array_input(self) -> None: + """cdf is vectorised: passing an array returns an array.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + ] + ) + xs = np.array([0.0, 1.0, 2.0, 3.0, 4.0]) + expected = np.array([0.0, 0.5, 0.5, 1.0, 1.0]) + np.testing.assert_allclose(dist.cdf(xs), expected, atol=1e-12) + + def test_cdf_is_monotonic_non_decreasing(self) -> None: + """CDF is non-decreasing on a dense grid.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=2.0, mass=0.4), + DiracDelta(position=3.0, mass=0.3), + ] + ) + xs = np.linspace(-1.0, 5.0, 100) + cdfs = dist.cdf(xs) + self.assertTrue(np.all(np.diff(cdfs) >= -1e-12)) + + def test_cdf_array_matches_scalar_elementwise(self) -> None: + """Vectorised call agrees with repeated scalar calls.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=2.0, mass=0.4), + DiracDelta(position=3.0, mass=0.3), + ] + ) + xs = np.linspace(-1.0, 5.0, 100) + array_result = dist.cdf(xs) + for i, x in enumerate(xs): + self.assertAlmostEqual(array_result[i], dist.cdf(float(x)), places=12) + + def test_cdf_returns_nan_for_nan_input(self) -> None: + """NaN input returns NaN; array NaNs propagate per slot.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertTrue(np.isnan(dist.cdf(float("nan")))) + result = dist.cdf(np.array([1.0, float("nan"), 3.0])) + self.assertAlmostEqual(result[0], 0.5, places=12) + self.assertTrue(np.isnan(result[1])) + self.assertAlmostEqual(result[2], 1.0, places=12) + + def test_cdf_returns_nan_for_zero_total_mass(self) -> None: + """Zero total mass: scalar → NaN, array → all-NaN.""" + for label, dist in ( + ("empty", DistributionalValue(dirac_deltas=[])), + ( + "all_zero_mass", + DistributionalValue(dirac_deltas=[DiracDelta(position=1.0, mass=0.0)]), + ), + ): + with self.subTest(case=label): + self.assertTrue(np.isnan(dist.cdf(0.5))) + array_result = dist.cdf(np.array([0.0, 1.0, 2.0])) + self.assertEqual(array_result.shape, (3,)) + self.assertTrue(np.all(np.isnan(array_result))) + + def test_cdf_ignores_zero_mass_diracs(self) -> None: + """Zero-mass Diracs — including non-finite placeholders — leave the + CDF unchanged; quantile/cdf do not call sort() so such placeholders + would otherwise reach searchsorted.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=3.0, mass=0.5), + DiracDelta(position=-100.0, mass=0.0), + DiracDelta(position=float("nan"), mass=0.0), + DiracDelta(position=float("inf"), mass=0.0), + ] + ) + self.assertAlmostEqual(dist.cdf(0.0), 0.0, places=12) + self.assertAlmostEqual(dist.cdf(1.0), 0.5, places=12) + self.assertAlmostEqual(dist.cdf(3.0), 1.0, places=12) + self.assertAlmostEqual(dist.cdf(50.0), 1.0, places=12) + + +class TestDistributionalValueCdfQuantileInverse(unittest.TestCase): + """Quasi-inverse contract between `cdf` and `quantile`.""" + + def _two_point(self) -> DistributionalValue: + return DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=3.0, mass=0.7), + ] + ) + + def test_round_trip_exact_at_support_points(self) -> None: + """Q(F(s)) == s for every support point s.""" + dist = self._two_point() + for s in (1.0, 3.0): + with self.subTest(s=s): + self.assertAlmostEqual(dist.quantile(dist.cdf(s)), s, places=12) + + def test_quantile_of_cdf_floors_to_largest_support_below(self) -> None: + """For x between support points, Q(F(x)) floors onto the support.""" + dist = self._two_point() + self.assertAlmostEqual(dist.quantile(dist.cdf(2.0)), 1.0, places=12) + + def test_cdf_of_quantile_exact_at_cumulative_mass_values(self) -> None: + """F(Q(t)) == t for cumulative-mass values t.""" + dist = self._two_point() + for t in (0.3, 1.0): + with self.subTest(t=t): + self.assertAlmostEqual(dist.cdf(dist.quantile(t)), t, places=12) + + +class TestDistributionalValueRawMoments(unittest.TestCase): + """`DistributionalValue.raw_moments(order)` — Σ p_i · x_i^order.""" + + def test_zeroth_raw_moment_is_total_mass(self) -> None: + """raw_moments(0) = Σ p_i = 1 for a normalised distribution.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=2.0, mass=0.7), + ] + ) + self.assertAlmostEqual(dist.raw_moments(0), 1.0, places=12) + + def test_first_raw_moment_equals_mean(self) -> None: + """raw_moments(1) = mean — internal consistency.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=2.0, mass=0.7), + ] + ) + mean = dist.mean + assert mean is not None + self.assertAlmostEqual(dist.raw_moments(1), mean, places=12) + + def test_raw_moments_of_dirac_match_v_pow_k(self) -> None: + """For a Dirac at v with mass 1: raw_moments(k) = v^k.""" + v = 3.0 + dist = DistributionalValue(dirac_deltas=[DiracDelta(position=v, mass=1.0)]) + for k in (0, 1, 2, 3, 4): + with self.subTest(k=k): + self.assertAlmostEqual(dist.raw_moments(k), v**k, places=12) + + def test_raw_moments_with_nan_position_mass_returns_nan_for_k_ge_1( + self, + ) -> None: + """NaN-position mass → NaN for k≥1, 1.0 for k=0.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=float("nan"), mass=0.4), + DiracDelta(position=3.0, mass=0.3), + ] + ) + self.assertAlmostEqual(dist.raw_moments(0), 1.0, places=12) + for k in (1, 2, 3, 4): + with self.subTest(k=k): + self.assertTrue(np.isnan(dist.raw_moments(k))) + + def test_raw_moments_ignores_zero_mass_nan_placeholder(self) -> None: + """Zero-mass NaN placeholder doesn't affect the moment.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("nan"), mass=0.0), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertAlmostEqual(dist.raw_moments(1), 2.0, places=12) + self.assertAlmostEqual(dist.raw_moments(2), 5.0, places=12) + + def test_raw_moments_with_only_pos_inf_mass(self) -> None: + """Only +Inf in support → +Inf for k≥1, 1.0 for k=0.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("inf"), mass=0.5), + ] + ) + self.assertAlmostEqual(dist.raw_moments(0), 1.0, places=12) + for k in (1, 2, 3, 4): + with self.subTest(k=k): + self.assertEqual(dist.raw_moments(k), float("inf")) + + def test_raw_moments_with_only_neg_inf_alternates_sign_by_parity( + self, + ) -> None: + """Only -Inf in support: +Inf for even k, -Inf for odd k.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("-inf"), mass=0.5), + ] + ) + self.assertAlmostEqual(dist.raw_moments(0), 1.0, places=12) + self.assertEqual(dist.raw_moments(1), float("-inf")) + self.assertEqual(dist.raw_moments(2), float("inf")) + self.assertEqual(dist.raw_moments(3), float("-inf")) + self.assertEqual(dist.raw_moments(4), float("inf")) + + def test_raw_moments_handles_unnormalised_masses(self) -> None: + """Unnormalised masses [3, 7] match normalised [0.3, 0.7].""" + unnormalised = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=3.0), + DiracDelta(position=3.0, mass=7.0), + ] + ) + normalised = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=3.0, mass=0.7), + ] + ) + for k in (0, 1, 2, 3, 4): + with self.subTest(k=k): + self.assertAlmostEqual( + unnormalised.raw_moments(k), + normalised.raw_moments(k), + places=12, + ) + + def test_raw_moments_with_both_pm_inf_masses(self) -> None: + """Both ±Inf: +Inf for even k, NaN for odd k.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=float("-inf"), mass=0.3), + DiracDelta(position=1.0, mass=0.4), + DiracDelta(position=float("inf"), mass=0.3), + ] + ) + self.assertAlmostEqual(dist.raw_moments(0), 1.0, places=12) + self.assertTrue(np.isnan(dist.raw_moments(1))) + self.assertEqual(dist.raw_moments(2), float("inf")) + self.assertTrue(np.isnan(dist.raw_moments(3))) + self.assertEqual(dist.raw_moments(4), float("inf")) + + +class TestDistributionalValueCentralMoments(unittest.TestCase): + """`DistributionalValue.central_moments(order)`: Σ p_i · (x_i − mean)^order.""" + + def test_zeroth_central_moment_is_total_mass(self) -> None: + """central_moments(0) = Σ p_i = 1.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=2.0, mass=0.7), + ] + ) + self.assertAlmostEqual(dist.central_moments(0), 1.0, places=12) + + def test_first_central_moment_is_zero(self) -> None: + """central_moments(1) = 0 by the definition of mean.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=2.0, mass=0.7), + ] + ) + self.assertAlmostEqual(dist.central_moments(1), 0.0, places=12) + + def test_second_central_moment_equals_variance(self) -> None: + """central_moments(2) == variance.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=2.0, mass=0.4), + DiracDelta(position=3.0, mass=0.3), + ] + ) + variance = dist.variance + assert variance is not None + self.assertAlmostEqual(dist.central_moments(2), variance, places=12) + + def test_central_moments_of_dirac_are_zero_for_order_ge_1(self) -> None: + """All central moments of a single Dirac are 0 for k≥1.""" + dist = DistributionalValue(dirac_deltas=[DiracDelta(position=3.0, mass=1.0)]) + for k in (1, 2, 3, 4): + with self.subTest(k=k): + self.assertAlmostEqual(dist.central_moments(k), 0.0, places=12) + + def test_central_moments_zeroth_is_one_even_for_non_finite_mean(self) -> None: + """central_moments(0) = 1.0 even when the mean isn't finite.""" + for label, pos, mass in ( + ("only NaN", float("nan"), 1.0), + ("only +Inf", float("inf"), 1.0), + ("only -Inf", float("-inf"), 1.0), + ): + with self.subTest(case=label): + dist = DistributionalValue( + dirac_deltas=[DiracDelta(position=pos, mass=mass)] + ) + self.assertAlmostEqual(dist.central_moments(0), 1.0, places=12) + + def test_central_moments_ignores_zero_mass_nan_placeholder(self) -> None: + """Zero-mass NaN placeholder doesn't affect the moment.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("nan"), mass=0.0), + DiracDelta(position=3.0, mass=0.5), + ] + ) + self.assertAlmostEqual(dist.central_moments(1), 0.0, places=12) + self.assertAlmostEqual(dist.central_moments(2), 1.0, places=12) + + def test_central_moments_handles_unnormalised_masses(self) -> None: + """Unnormalised masses [3, 7] match normalised [0.3, 0.7].""" + unnormalised = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=3.0), + DiracDelta(position=3.0, mass=7.0), + ] + ) + normalised = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.3), + DiracDelta(position=3.0, mass=0.7), + ] + ) + for k in (0, 1, 2, 3, 4): + with self.subTest(k=k): + self.assertAlmostEqual( + unnormalised.central_moments(k), + normalised.central_moments(k), + places=12, + ) + + def test_central_moments_and_variance_both_refuse_non_finite_mean( + self, + ) -> None: + """Non-finite mean: central_moments(2) → NaN, variance → None.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("inf"), mass=0.5), + ] + ) + self.assertTrue(np.isnan(dist.central_moments(2))) + self.assertIsNone(dist.variance) + + def test_central_moments_returns_nan_for_any_non_finite_mean(self) -> None: + """k≥1 returns NaN for any non-finite-mean distribution.""" + cases = ( + ("NaN mass>0", [1.0, float("nan"), 3.0], [0.3, 0.4, 0.3]), + ("only +Inf", [1.0, float("inf")], [0.5, 0.5]), + ("only -Inf", [float("-inf"), 1.0], [0.5, 0.5]), + ("both ±Inf", [float("-inf"), 1.0, float("inf")], [0.3, 0.4, 0.3]), + ) + for label, positions, masses in cases: + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=p, mass=m) for p, m in zip(positions, masses) + ] + ) + for k in (1, 2, 3, 4): + with self.subTest(case=label, k=k): + self.assertTrue(np.isnan(dist.central_moments(k))) + + +class TestFromWeightedSamples(unittest.TestCase): + def test_normalises_masses_and_round_trips_positions(self) -> None: + """Masses are normalised to sum to 1; positions round-trip in order.""" + dist = DistributionalValue.from_weighted_samples( + [0.0, 1.0, 2.0], [1.0, 2.0, 1.0] + ) + np.testing.assert_array_equal(dist.positions, np.array([0.0, 1.0, 2.0])) + np.testing.assert_allclose(dist.masses, np.array([0.25, 0.5, 0.25])) + self.assertAlmostEqual(float(np.sum(dist.masses)), 1.0) + + def test_already_normalised_masses_unchanged(self) -> None: + """Inputs already summing to 1 are preserved verbatim after normalising.""" + dist = DistributionalValue.from_weighted_samples([10.0, 20.0], [0.3, 0.7]) + np.testing.assert_allclose(dist.masses, np.array([0.3, 0.7])) + + def test_empty_positions_raises(self) -> None: + with self.assertRaises(ValueError): + DistributionalValue.from_weighted_samples([], [1.0]) + + def test_empty_masses_raises(self) -> None: + with self.assertRaises(ValueError): + DistributionalValue.from_weighted_samples([1.0], []) + + def test_length_mismatch_raises(self) -> None: + with self.assertRaises(ValueError): + DistributionalValue.from_weighted_samples([0.0, 1.0], [1.0]) + + def test_non_finite_total_mass_raises(self) -> None: + with self.assertRaises(ValueError): + DistributionalValue.from_weighted_samples([0.0, 1.0], [float("inf"), 1.0]) + + def test_zero_total_mass_raises(self) -> None: + with self.assertRaises(ValueError): + DistributionalValue.from_weighted_samples([0.0, 1.0], [0.0, 0.0]) + + def test_negative_mass_raises(self) -> None: + # A negative mass would normalise to a negative "probability"; reject it + # at construction rather than build an invalid distribution. + with self.assertRaises(ValueError): + DistributionalValue.from_weighted_samples([1.0, 2.0], [1.0, -0.5]) + + +class TestUxBinaryFormatDetection(unittest.TestCase): + """Ux Binary Data format and legacy format layout detection and generation. + + The Ux Binary Data format inserts a 3-byte marker (a 0xF0 start byte + plus two 0x00 padding bytes) between the particle value and the + representation type. `parse` accepts both layouts; `export`/`bytes` + always emit the correct Ux Binary Data format. + """ + + # A legacy format: particle value, then the + # representation type byte 0x00 at offset 8 (!= 0xF0). + LEGACY_FORMAT_HEX = ( + "09168733bf9ad93f000100000000000000c7c72324c19ad93f" + "01000000c7c72324c19ad93f0000000000000080" + ) + + def _padded_format_hex(self) -> str: + """The LEGACY_FORMAT_HEX value rewritten in the Ux Binary layout.""" + return self.LEGACY_FORMAT_HEX[:16] + "f00000" + self.LEGACY_FORMAT_HEX[16:] + + def test_export_writes_format_marker(self) -> None: + """`bytes(dist)` places 0xF0 0x00 0x00 right after the particle.""" + dist = DistributionalValue( + particle_value=1.5, + UR_type=4, + dirac_deltas=[DiracDelta(position=1.5, mass=1.0)], + ) + encoded = bytes(dist) + + # 8-byte particle value, then the 3-byte marker. + self.assertEqual(encoded[8:11], b"\xf0\x00\x00") + # Representation type now lives at offset 11. + self.assertEqual(encoded[11], 4) + + def test_export_round_trips_through_parse(self) -> None: + """A value survives export -> parse unchanged (Ux Binary layout).""" + dist = DistributionalValue( + particle_value=-2.25, + UR_type=0, + dirac_deltas=[ + DiracDelta(position=-2.25, mass=0.5), + DiracDelta(position=3.5, mass=0.5), + ], + ) + parsed = DistributionalValue.parse(bytes(dist)) + + self.assertIsNotNone(parsed) + assert parsed is not None + self.assertEqual(parsed.particle_value, dist.particle_value) + self.assertEqual(parsed.UR_type, dist.UR_type) + np.testing.assert_array_equal(parsed.positions, dist.positions) + np.testing.assert_array_equal(parsed.raw_masses, dist.raw_masses) + + def test_legacy_and_padded_layouts_parse_equal(self) -> None: + """The same value in either layout parses to an equal result.""" + legacy = DistributionalValue.parse(bytes.fromhex(self.LEGACY_FORMAT_HEX)) + padded = DistributionalValue.parse(bytes.fromhex(self._padded_format_hex())) + + self.assertIsNotNone(legacy) + self.assertIsNotNone(padded) + assert legacy is not None and padded is not None + self.assertEqual(legacy.particle_value, padded.particle_value) + self.assertEqual(legacy.UR_type, padded.UR_type) + self.assertEqual(legacy.UR_order, padded.UR_order) + np.testing.assert_array_equal(legacy.positions, padded.positions) + np.testing.assert_array_equal(legacy.raw_masses, padded.raw_masses) + + def test_export_of_legacy_input_matches_padded_layout(self) -> None: + """Re-encoding a legacy input yields the Ux Binary layout bytes.""" + parsed = DistributionalValue.parse(bytes.fromhex(self.LEGACY_FORMAT_HEX)) + self.assertIsNotNone(parsed) + assert parsed is not None + self.assertEqual(bytes(parsed), bytes.fromhex(self._padded_format_hex())) + + def test_too_short_buffer_returns_none(self) -> None: + """Buffers too short to detect the layout return None.""" + self.assertIsNone(DistributionalValue.parse(b"")) + self.assertIsNone(DistributionalValue.parse(bytes(8))) + + +class TestDistributionalValueInverseCdf(unittest.TestCase): + """Tests for the interpolating, array-capable ``inverse_cdf`` (folded in + from the former ``distribution_functions`` module).""" + + def _equal_mass(self) -> DistributionalValue: + """Four equally-weighted points at 0, 1, 2, 3.""" + return DistributionalValue.from_weighted_samples( + [0.0, 1.0, 2.0, 3.0], [1.0, 1.0, 1.0, 1.0] + ) + + def test_weighted_branch_interpolates(self) -> None: + """Weighted branch: interp(0.5, [.25,.5,.75,1], [0,1,2,3]) = 1.0.""" + self.assertAlmostEqual(self._equal_mass().inverse_cdf(0.5), 1.0) + + def test_samples_branch_uses_np_quantile(self) -> None: + """Samples branch: np.quantile([0,1,2,3], 0.5) = 1.5.""" + self.assertAlmostEqual( + self._equal_mass().inverse_cdf(0.5, treat_as_samples=True), 1.5 + ) + + def test_branches_differ(self) -> None: + """Weighted and samples branches are distinct (load-bearing for the + reported quantiles downstream).""" + dist = self._equal_mass() + self.assertNotAlmostEqual( + dist.inverse_cdf(0.5), dist.inverse_cdf(0.5, treat_as_samples=True) + ) + + def test_array_input_weighted_branch(self) -> None: + """The weighted branch accepts an array and returns an array.""" + out = self._equal_mass().inverse_cdf(np.array([0.25, 0.5, 0.75, 1.0])) + self.assertIsInstance(out, np.ndarray) + np.testing.assert_allclose(out, np.array([0.0, 1.0, 2.0, 3.0])) + + def test_scalar_input_returns_float(self) -> None: + """Scalar ``p`` returns a plain float.""" + self.assertIsInstance(self._equal_mass().inverse_cdf(0.5), float) + + def test_default_is_weighted_branch(self) -> None: + """Omitting ``treat_as_samples`` selects the weighted branch.""" + dist = self._equal_mass() + self.assertAlmostEqual( + dist.inverse_cdf(0.5), dist.inverse_cdf(0.5, treat_as_samples=False) + ) + + +class TestDistributionalValueCdfTreatAsSamples(unittest.TestCase): + """The ``treat_as_samples`` branch of ``cdf``: unweighted empirical CDF.""" + + def test_weighted_and_samples_cdf_agree_on_equal_mass(self) -> None: + """For the equal-mass distribution both branches give cdf(1.0)=0.5: + the weighted step lookup and ``(count <= 1) / 4``.""" + dist = DistributionalValue.from_weighted_samples( + [0.0, 1.0, 2.0, 3.0], [1.0, 1.0, 1.0, 1.0] + ) + self.assertAlmostEqual(float(dist.cdf(1.0)), 0.5) + self.assertAlmostEqual(float(dist.cdf(1.0, treat_as_samples=True)), 0.5) + + def test_samples_cdf_ignores_masses(self) -> None: + """The samples branch is ``(count of positions <= x) / N``, ignoring + masses: for [0,1,2,3] cdf(2.0)=3/4 regardless of the weights.""" + dist = DistributionalValue.from_weighted_samples( + [0.0, 1.0, 2.0, 3.0], [0.7, 0.1, 0.1, 0.1] + ) + self.assertAlmostEqual(float(dist.cdf(2.0, treat_as_samples=True)), 0.75) + + if __name__ == "__main__": unittest.main() diff --git a/src/signaloid/distributional/test_ux_value_pairs.csv b/src/signaloid/distributional/test_ux_value_pairs.csv index bc35f51..36b8bc0 100644 --- a/src/signaloid/distributional/test_ux_value_pairs.csv +++ b/src/signaloid/distributional/test_ux_value_pairs.csv @@ -1,786 +1,786 @@ -0.40007Ux0000000000000000013FD99AC12423C7C7000000013FD99AC12423C7C78000000000000000,09168733bf9ad93f000100000000000000c7c72324c19ad93f01000000c7c72324c19ad93f0000000000000080 +0.40007Ux0000000000000000013FD99AC12423C7C7000000013FD99AC12423C7C78000000000000000,09168733bf9ad93ff00000000100000000000000c7c72324c19ad93f01000000c7c72324c19ad93f0000000000000080 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diff --git a/src/signaloid/distributional_distance/README.md b/src/signaloid/distributional_distance/README.md new file mode 100644 index 0000000..47663e5 --- /dev/null +++ b/src/signaloid/distributional_distance/README.md @@ -0,0 +1,144 @@ +# Distributional Distance + +Distance utilities for comparing Signaloid `DistributionalValue` instances. + + +## Wasserstein-p distance + +Compute the Wasserstein-p distance between two `DistributionalValue`s. `p` is an integer ≥ 1; `p=1` and `p=2` (the canonical cases) have ergonomic shortcuts. + +```python +import numpy as np +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance import ( + wasserstein_p_uxhw_wrapper, + wasserstein_1_uxhw_wrapper, + wasserstein_2_uxhw_wrapper, +) + +rng = np.random.default_rng(seed=42) +dist_u = DistributionalValue.from_samples(rng.standard_normal(1000)) +dist_v = DistributionalValue.from_samples(rng.standard_normal(10000)) + +# Generic, explicit p +print(wasserstein_p_uxhw_wrapper(dist_u, dist_v, p=1)) +print(wasserstein_p_uxhw_wrapper(dist_u, dist_v, p=2)) + +# Ergonomic shortcuts for the canonical cases +print(wasserstein_1_uxhw_wrapper(dist_u, dist_v)) +print(wasserstein_2_uxhw_wrapper(dist_u, dist_v)) +``` + +## Normalised Wasserstein-p + +Compute Wp after rescaling positions onto the ground-truth support `[0, 1]`. Same shortcut pattern: a generic `_p_` wrapper plus `_1_` / `_2_` shortcuts. + +```python +from signaloid.distributional_distance import ( + normalized_wasserstein_p_uxhw_wrapper, + normalized_wasserstein_1_uxhw_wrapper, + normalized_wasserstein_2_uxhw_wrapper, +) + +print(normalized_wasserstein_p_uxhw_wrapper(test_dist, ground_truth_dist, p=2)) +print(normalized_wasserstein_1_uxhw_wrapper(test_dist, ground_truth_dist)) +print(normalized_wasserstein_2_uxhw_wrapper(test_dist, ground_truth_dist)) +``` + +## Kolmogorov-Smirnov distance + +Sup-norm between two empirical step-function CDFs. + +```python +from signaloid.distributional_distance import kolmogorov_smirnov_distance_uxhw_wrapper + +print(kolmogorov_smirnov_distance_uxhw_wrapper(dist_u, dist_v)) +``` + +## Scalar comparisons + +For single-Dirac `DistributionalValue`s, three error variants are available. Each input must hold exactly one finite Dirac — non-scalar inputs are rejected to avoid silently using only `positions[0]`. + +```python +from signaloid.distributional_distance import ( + relative_error_uxhw_wrapper, + absolute_error_uxhw_wrapper, + signed_error_uxhw_wrapper, +) + +# |test − gt| / |gt| — scale-invariant +print(relative_error_uxhw_wrapper(test_dist, ground_truth_dist)) + +# |test − gt| — same units as inputs, non-negative +print(absolute_error_uxhw_wrapper(test_dist, ground_truth_dist)) + +# test − gt — same units, preserves sign +print(signed_error_uxhw_wrapper(test_dist, ground_truth_dist)) +``` + +## Binned Wasserstein-1 + +Asymmetric distance: bins the first argument and treats the second as raw weighted samples. Use the `_uxhw_` form for two `DistributionalValue`s, the `_ux_string_` form to skip parsing, or the array entry point if you already have histogram data. + +```python +from signaloid.distributional_distance import ( + binned_wasserstein_1_uxhw_wrapper, + binned_wasserstein_1_ux_string_wrapper, + wasserstein_1_between_distribution_and_samples, +) + +# From DistributionalValues +print(binned_wasserstein_1_uxhw_wrapper(binned_dist, ground_truth_dist)) + +# From Ux strings +print(binned_wasserstein_1_ux_string_wrapper(distribution_ux, ground_truth_ux)) + +# From pre-binned histogram data +distance = wasserstein_1_between_distribution_and_samples( + bin_boundaries=[0.0, 1.0, 2.0, 3.0], + bin_heights=[0.25, 0.5, 0.25], + bin_widths=[1.0, 1.0, 1.0], + sample_positions=[0.3, 1.2, 1.8, 2.4], +) +``` + +## Lower-level array entry points + +For callers that have pre-sorted sample arrays and want to skip the `DistributionalValue` wrapping: + +```python +from signaloid.distributional_distance import ( + wasserstein_1_distance, + wasserstein_1_distance_with_weights, +) + +# W1 between two equally-weighted, pre-sorted sample sets +# (drop-in for scipy.stats.wasserstein_distance) +distance = wasserstein_1_distance(u_values, v_values, all_values) + +# W1 between an unweighted u and a weighted v +distance = wasserstein_1_distance_with_weights( + u_values, v_values, v_cum_weights, all_values +) +``` + +## CLI usage + +`wasserstein.py`, `binned_wasserstein.py`, and `scalar.py` each expose a `python -m …` entry point that parses two Ux strings, computes the distance, and exits non-zero if the result exceeds the supplied tolerance. + +```bash +# Wasserstein-p (default p=1) +python -m signaloid.distributional_distance.wasserstein \ + [--p N] + +# Binned Wasserstein-1 (asymmetric — first arg is binned) +python -m signaloid.distributional_distance.binned_wasserstein \ + + +# Scalar error (single-Dirac inputs; default metric: relative) +python -m signaloid.distributional_distance.scalar \ + \ + [--metric relative|absolute|signed] +``` + +> **Note:** Ux strings with a leading `-` (e.g. `-0.0Ux…`) get parsed by `argparse` as flags. Place any options (`--p N`, `--metric M`) *before* the positional arguments, or use the `--` separator before the leading-minus Ux string. diff --git a/src/signaloid/distributional_distance/__init__.py b/src/signaloid/distributional_distance/__init__.py new file mode 100644 index 0000000..c9261d5 --- /dev/null +++ b/src/signaloid/distributional_distance/__init__.py @@ -0,0 +1,68 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +"""Pure-NumPy distance utilities for DistributionalValue comparisons. + +Modules: +- wasserstein: Wasserstein-1 / Wasserstein-2 (+ normalised variants), + including UxHw wrappers. +- binned_wasserstein: CDF-based binned-Wasserstein-1 stack. +- ks_distance: Kolmogorov-Smirnov distance (sup norm between empirical + CDFs). The hypothesis-test variants live elsewhere. +- scalar: scalar-distance utility. +""" + +from signaloid.distributional_distance.binned_wasserstein import ( + binned_wasserstein_1_ux_string_wrapper, + binned_wasserstein_1_uxhw_wrapper, + wasserstein_1_between_distribution_and_samples, +) +from signaloid.distributional_distance.ks_distance import ( + kolmogorov_smirnov_distance_uxhw_wrapper, +) +from signaloid.distributional_distance.scalar import relative_error_uxhw_wrapper +from signaloid.distributional_distance.wasserstein import ( + normalized_wasserstein_1_uxhw_wrapper, + normalized_wasserstein_2_uxhw_wrapper, + normalized_wasserstein_p_uxhw_wrapper, + wasserstein_1_distance, + wasserstein_1_distance_with_weights, + wasserstein_1_uxhw_wrapper, + wasserstein_2_uxhw_wrapper, + wasserstein_p_distance, + wasserstein_p_uxhw_wrapper, +) + +__all__ = [ + "binned_wasserstein_1_ux_string_wrapper", + "binned_wasserstein_1_uxhw_wrapper", + "kolmogorov_smirnov_distance_uxhw_wrapper", + "normalized_wasserstein_1_uxhw_wrapper", + "normalized_wasserstein_2_uxhw_wrapper", + "normalized_wasserstein_p_uxhw_wrapper", + "relative_error_uxhw_wrapper", + "wasserstein_1_between_distribution_and_samples", + "wasserstein_1_distance", + "wasserstein_1_distance_with_weights", + "wasserstein_1_uxhw_wrapper", + "wasserstein_2_uxhw_wrapper", + "wasserstein_p_distance", + "wasserstein_p_uxhw_wrapper", +] diff --git a/src/signaloid/distributional_distance/_validators.py b/src/signaloid/distributional_distance/_validators.py new file mode 100644 index 0000000..62b192b --- /dev/null +++ b/src/signaloid/distributional_distance/_validators.py @@ -0,0 +1,93 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +import numpy as np +from signaloid.distributional.distributional import DistributionalValue + + +def _require_distributional_pair( + dist_u: DistributionalValue, dist_v: DistributionalValue +) -> None: + """Raise ValueError if either argument is not a DistributionalValue. + + Shared by the uxhw wrappers across the package so they all surface + the same error type and message format at the public-API boundary. + """ + if not isinstance(dist_u, DistributionalValue): + raise ValueError( + f"dist_u is of type {type(dist_u).__name__} and not an " + "instance of DistributionalValue." + ) + if not isinstance(dist_v, DistributionalValue): + raise ValueError( + f"dist_v is of type {type(dist_v).__name__} and " + "not an instance of DistributionalValue." + ) + + +def _validate_wp_inputs( + u_values: np.ndarray, + u_weights: np.ndarray, + v_values: np.ndarray, + v_weights: np.ndarray, + p: int, +) -> tuple[float, float]: + """Validate inputs to `_wp_1d_weighted_pair` and return (u_total, v_total). + + `DistributionalValue` does not itself enforce these invariants + (special values like NaN/Inf are first-class via nan_dirac_delta + etc.), so we validate at the algorithmic boundary instead of + duplicating the check in every uxhw wrapper. + """ + # `bool` is a subclass of `int` in Python; reject it explicitly so + # `p=True` isn't silently treated as `p=1`. + if isinstance(p, bool) or not isinstance(p, (int, np.integer)) or p < 1: + raise ValueError("p must be an integer greater than or equal to 1.") + if ( + u_values.ndim != 1 + or v_values.ndim != 1 + or u_weights.ndim != 1 + or v_weights.ndim != 1 + ): + raise ValueError( + "u_positions, v_positions, u_masses, and v_masses must be " + "one-dimensional arrays." + ) + if len(u_values) == 0 or len(v_values) == 0: + raise ValueError("u_positions and v_positions must be non-empty.") + if len(u_values) != len(u_weights) or len(v_values) != len(v_weights): + raise ValueError("positions and masses arrays must have matching lengths.") + if not ( + np.all(np.isfinite(u_values)) + and np.all(np.isfinite(v_values)) + and np.all(np.isfinite(u_weights)) + and np.all(np.isfinite(v_weights)) + ): + raise ValueError("positions and masses must contain only finite values.") + if np.any(u_weights < 0.0) or np.any(v_weights < 0.0): + raise ValueError("u_masses and v_masses must be non-negative.") + + u_total = float(np.sum(u_weights)) + v_total = float(np.sum(v_weights)) + if u_total <= 0.0 or v_total <= 0.0: + raise ValueError( + "u_masses and v_masses must each have a strictly positive total mass." + ) + return u_total, v_total diff --git a/src/signaloid/distributional_distance/_validators_test.py b/src/signaloid/distributional_distance/_validators_test.py new file mode 100644 index 0000000..e953bbe --- /dev/null +++ b/src/signaloid/distributional_distance/_validators_test.py @@ -0,0 +1,195 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +"""Tests for the package-private validators in `_validators.py`. + +Direct exercise of the shared validators so that wrapper-level tests can +focus on wrapper behavior (ValueError raised on bad input) without +coupling to the validator's error-message text. +""" + +import unittest + +import numpy as np + +from signaloid.distributional.dirac_delta import DiracDelta +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance._validators import ( + _require_distributional_pair, + _validate_wp_inputs, +) + + +def _single_dirac(position: float) -> DistributionalValue: + return DistributionalValue(dirac_deltas=[DiracDelta(position=position, mass=1.0)]) + + +BAD_STAND_INS = ("not a dv", 42, None, [1.0, 2.0], np.array([1.0])) + + +class TestRequireDistributionalPair(unittest.TestCase): + """Direct exercise of `_require_distributional_pair`. + + Wrappers across the package funnel non-DV inputs through this helper, + so the message format / type-error coverage lives here once instead + of being re-asserted in every wrapper's test file.""" + + def test_accepts_two_valid_distributional_values(self) -> None: + """Two DistributionalValues: returns without raising.""" + valid = _single_dirac(1.0) + _require_distributional_pair(valid, valid) + + def test_rejects_non_dv_in_first_position(self) -> None: + """Bad first argument: error names `dist_u` and surfaces the + actual type, so the caller can see which argument was wrong.""" + valid = _single_dirac(1.0) + for bad in BAD_STAND_INS: + with self.subTest(bad=type(bad).__name__): + with self.assertRaises(ValueError) as ctx: + _require_distributional_pair(bad, valid) # type: ignore[arg-type] + message = str(ctx.exception) + self.assertIn("dist_u", message) + self.assertIn("DistributionalValue", message) + self.assertIn(type(bad).__name__, message) + + def test_rejects_non_dv_in_second_position(self) -> None: + """Bad second argument: error names `dist_v` and the actual type.""" + valid = _single_dirac(1.0) + for bad in BAD_STAND_INS: + with self.subTest(bad=type(bad).__name__): + with self.assertRaises(ValueError) as ctx: + _require_distributional_pair(valid, bad) # type: ignore[arg-type] + message = str(ctx.exception) + self.assertIn("dist_v", message) + self.assertIn("DistributionalValue", message) + self.assertIn(type(bad).__name__, message) + + def test_first_argument_checked_before_second(self) -> None: + """Both arguments bad: the first one raises, so the message + identifies `dist_u`. Check matters because callers will fix the + bug the error names — if both errors are reported as `dist_v` + the user can't tell that the first argument is also wrong.""" + with self.assertRaises(ValueError) as ctx: + _require_distributional_pair("bad_u", "bad_v") # type: ignore[arg-type] + self.assertIn("dist_u", str(ctx.exception)) + + +class TestValidateWpInputs(unittest.TestCase): + """Direct exercise of `_validate_wp_inputs`, the shared array-level + validator. Wrapper-level tests should rely on these — not duplicate + the per-condition coverage.""" + + def _arrays(self) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]: + u_values = np.array([1.0, 2.0, 3.0]) + u_weights = np.array([0.3, 0.4, 0.3]) + v_values = np.array([0.5, 1.5, 2.5]) + v_weights = np.array([0.25, 0.5, 0.25]) + return u_values, u_weights, v_values, v_weights + + def test_returns_totals_when_all_inputs_valid(self) -> None: + """Happy path: returns the (u_total, v_total) the caller will + divide by; both equal to the sum of their weights.""" + u_values, u_weights, v_values, v_weights = self._arrays() + u_total, v_total = _validate_wp_inputs( + u_values, u_weights, v_values, v_weights, p=1 + ) + self.assertAlmostEqual(u_total, 1.0) + self.assertAlmostEqual(v_total, 1.0) + + def test_rejects_non_integer_p(self) -> None: + """`p` must be int and >= 1 — float, str, bool all rejected. + `bool` matters specifically: it subclasses int in Python, so + `p=True` would silently be treated as `p=1` without the explicit + bool check in the validator.""" + u_values, u_weights, v_values, v_weights = self._arrays() + for bad_p in (1.0, "1", True, False, 0, -1): + with self.subTest(p=bad_p): + with self.assertRaises(ValueError) as ctx: + _validate_wp_inputs( + u_values, u_weights, v_values, v_weights, p=bad_p # type: ignore[arg-type] + ) + self.assertIn("p", str(ctx.exception)) + + def test_rejects_non_1d_arrays(self) -> None: + """2-D arrays would silently flow into the Wp kernel and produce + a wrong distance; rejected up-front.""" + u_values, u_weights, v_values, v_weights = self._arrays() + bad_2d = np.array([[1.0, 2.0], [3.0, 4.0]]) + for label, args in ( + ("u_values_2d", (bad_2d, u_weights, v_values, v_weights)), + ("u_weights_2d", (u_values, bad_2d, v_values, v_weights)), + ("v_values_2d", (u_values, u_weights, bad_2d, v_weights)), + ("v_weights_2d", (u_values, u_weights, v_values, bad_2d)), + ): + with self.subTest(case=label): + u, uw, v, vw = args + with self.assertRaises(ValueError) as ctx: + _validate_wp_inputs(u, uw, v, vw, p=1) + self.assertIn("one-dimensional", str(ctx.exception)) + + def test_rejects_empty_positions(self) -> None: + """Empty positions are rejected with a non-empty message.""" + u_values, u_weights, v_values, v_weights = self._arrays() + empty = np.array([], dtype=np.float64) + with self.assertRaises(ValueError) as ctx: + _validate_wp_inputs(empty, empty, v_values, v_weights, p=1) + self.assertIn("non-empty", str(ctx.exception)) + + def test_rejects_mismatched_lengths(self) -> None: + """Positions and weights must have matching lengths per side.""" + u_values, _, v_values, v_weights = self._arrays() + wrong_length = np.array([0.5, 0.5]) + with self.assertRaises(ValueError) as ctx: + _validate_wp_inputs(u_values, wrong_length, v_values, v_weights, p=1) + self.assertIn("matching lengths", str(ctx.exception)) + + def test_rejects_non_finite_entries(self) -> None: + """NaN / ±Inf in any of the four arrays is rejected — the Wp + integral is undefined for non-finite positions or weights.""" + u_values, u_weights, v_values, v_weights = self._arrays() + for label, mutated in ( + ("nan_position", np.array([1.0, float("nan"), 3.0])), + ("posinf_position", np.array([1.0, float("inf"), 3.0])), + ("neginf_position", np.array([1.0, float("-inf"), 3.0])), + ): + with self.subTest(case=label): + with self.assertRaises(ValueError) as ctx: + _validate_wp_inputs(mutated, u_weights, v_values, v_weights, p=1) + self.assertIn("finite", str(ctx.exception)) + + def test_rejects_negative_weights(self) -> None: + """Negative weights break the empirical-CDF interpretation.""" + u_values, _, v_values, v_weights = self._arrays() + negative_weights = np.array([0.5, -0.1, 0.6]) + with self.assertRaises(ValueError) as ctx: + _validate_wp_inputs(u_values, negative_weights, v_values, v_weights, p=1) + self.assertIn("non-negative", str(ctx.exception)) + + def test_rejects_zero_total_mass(self) -> None: + """All-zero weights mean the CDF can't be normalised; rejected.""" + u_values, _, v_values, v_weights = self._arrays() + zero_weights = np.zeros(3) + with self.assertRaises(ValueError) as ctx: + _validate_wp_inputs(u_values, zero_weights, v_values, v_weights, p=1) + self.assertIn("strictly positive", str(ctx.exception)) + + +if __name__ == "__main__": + unittest.main() diff --git a/src/signaloid/distributional_distance/binned_wasserstein.py b/src/signaloid/distributional_distance/binned_wasserstein.py new file mode 100644 index 0000000..3de704d --- /dev/null +++ b/src/signaloid/distributional_distance/binned_wasserstein.py @@ -0,0 +1,641 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +import argparse +import sys +import warnings + +import numpy as np + +from signaloid.distributional_information_plotting.plot_histogram_dirac_deltas import ( + PlotData, +) +from .wasserstein import ( + wasserstein_1_uxhw_wrapper, +) +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance._validators import ( + _require_distributional_pair, +) + + +def integrate_trapezoid(x0: float, x1: float, y0: float, y1: float) -> float: + """Area of a trapezoid / triangle / rectangle defined by two heights. + + Args: + x0: left position + x1: right position + y0: left height + y1: right height + + Returns: + Area of the trapezoid / triangle / rectangle. + """ + return 0.5 * (y0 + y1) * (x1 - x0) + + +def normalized_uxhw_cdf_heights( + bin_widths: np.ndarray, bin_heights: np.ndarray +) -> np.ndarray: + """CDF heights for the binned representation of a UxHw distribution. + + Returns the cumulative bin areas (heights * widths) after + normalising the total mass to 1 if it has drifted from 1 by more + than 1e-12. + + Args: + bin_widths: Width of each bin. + bin_heights: PDF height of each bin. + + Returns: + Cumulative bin areas (length = len(bin_widths)). + """ + single_bin_areas: np.ndarray = bin_heights * bin_widths + + uxhw_cdf_total_mass: float = np.sum(single_bin_areas) + if uxhw_cdf_total_mass <= 0.0: + raise ValueError( + "Binned UxHw distribution has non-positive total mass " + f"({uxhw_cdf_total_mass}); cannot normalise." + ) + if abs(uxhw_cdf_total_mass - 1.0) >= 1e-12: + warnings.warn( + "Binned uxhw distribution was not normalized. Normalizing cdf.", + stacklevel=2, + ) + single_bin_areas = single_bin_areas / uxhw_cdf_total_mass + + return np.cumsum(single_bin_areas) + + +def normalized_sample_cdf_heights( + sample_positions: np.ndarray, sample_weights: np.ndarray +) -> np.ndarray: + """Cumulative heights of the empirical (step-wise) CDF. + + Normalises the total weight to 1 if it has drifted from 1 by more + than 1e-12. + + Args: + sample_positions: Sorted array of sample positions. Currently + unused — kept for symmetry with `normalized_uxhw_cdf_heights` + and to document the calling contract (positions and weights + must already be sorted by position so that `cumsum(weights)` + gives the empirical CDF heights). + sample_weights: Weight for each sample (must be aligned with + `sample_positions`). + + Returns: + Cumulative weights, length = len(sample_weights). + """ + single_step_areas: np.ndarray = sample_weights + + sample_cdf_total_mass: float = np.sum(single_step_areas) + if sample_cdf_total_mass <= 0.0: + raise ValueError( + "Empirical sample distribution has non-positive total mass " + f"({sample_cdf_total_mass}); cannot normalise." + ) + if abs(sample_cdf_total_mass - 1.0) >= 1e-12: + warnings.warn( + "Sample empirical distribution was not normalized. Normalizing cdf.", + stacklevel=2, + ) + single_step_areas = single_step_areas / sample_cdf_total_mass + + return np.cumsum(single_step_areas) + + +def build_position_and_type_array( + uxhw_cdf_boundaries: np.ndarray, + sample_cdf_positions: np.ndarray, + positions: np.ndarray, + types: np.ndarray, + num_boundaries: int, + num_samples: int, +) -> None: + """Build a sorted union of UxHw boundaries and sample positions. + + Each entry in `positions` is tagged in `types` with its origin: + `0` for a UxHw bin boundary, `1` for a sample position. The two + output arrays are filled in place and then sorted in tandem by + position. + + Args: + uxhw_cdf_boundaries: Boundaries of the UxHw distribution binning. + sample_cdf_positions: Sample positions. + positions: Output array (length num_boundaries + num_samples) + to be filled with all points and then sorted in place. + types: Output array (same length) tagging each position's origin + (0 = boundary, 1 = sample), kept aligned with `positions`. + num_boundaries: len(uxhw_cdf_boundaries). + num_samples: len(sample_cdf_positions). + """ + positions[:num_boundaries] = uxhw_cdf_boundaries + types[:num_boundaries] = 0 + positions[num_boundaries:] = sample_cdf_positions + types[num_boundaries:] = 1 + + # Sort positions and types in tandem. Use lexsort with `types` as + # the secondary key so that at tied positions (boundary coincident + # with a sample) boundaries (type=0) come before samples (type=1) + # — `wasserstein_1_core`'s segment/step bookkeeping assumes this + # ordering. `np.argsort(positions)` alone would not be stable on + # all numpy versions/platforms. + indices = np.lexsort((types, positions)) + positions[:] = positions[indices] + types[:] = types[indices] + + +def fill_cdf_values( + uxhw_cdf_vals: np.ndarray, + uxhw_cdf_idx: np.ndarray, + uxhw_cdf_boundaries: np.ndarray, + uxhw_cdf_heights: np.ndarray, + uxhw_cdf_widths: np.ndarray, + sample_cdf_vals: np.ndarray, + sample_cdf_idx: np.ndarray, + sample_cdf_heights: np.ndarray, + positions: np.ndarray, + num_points_total: int, + num_boundaries: int, +) -> None: + """Evaluate the UxHw and empirical CDFs at every merged position. + + Fills `uxhw_cdf_vals` and `sample_cdf_vals` in place. For the UxHw + CDF, each `position[i]` lies within bin segment `uxhw_cdf_idx[i]`; + the value is linearly interpolated using the segment's slope, with + clamps below the first / above the last boundary. For the empirical + CDF, each `position[i]` lies after step `sample_cdf_idx[i]`; the + value is the cumulative weight at that step (left as 0.0 when the + point precedes the first sample, courtesy of the caller's `zeros` + initialisation of `sample_cdf_vals`). + + Args: + uxhw_cdf_vals: Output — UxHw CDF values at each merged position. + uxhw_cdf_idx: Per-position UxHw segment index. + uxhw_cdf_boundaries: UxHw bin boundaries (length N+1). + uxhw_cdf_heights: UxHw cumulative CDF heights (length N+1, + starting at 0). + uxhw_cdf_widths: UxHw bin widths (length N). + sample_cdf_vals: Output — empirical CDF values. Caller must + pre-initialise to zeros; entries with `sample_cdf_idx[i] == 0` + are left untouched. + sample_cdf_idx: Per-position sample step index. + sample_cdf_heights: Empirical cumulative CDF heights. + positions: Merged + sorted positions array. + num_points_total: Length of `positions`. + num_boundaries: Length of `uxhw_cdf_boundaries`. + """ + for i in range(num_points_total): + if sample_cdf_idx[i] > 0: + sample_cdf_vals[i] = sample_cdf_heights[sample_cdf_idx[i]] + + idx = uxhw_cdf_idx[i] + if idx < 0: + uxhw_cdf_vals[i] = 0.0 + elif idx >= num_boundaries - 1: + uxhw_cdf_vals[i] = 1.0 + else: + uxhw_cdf_slope = ( + uxhw_cdf_heights[idx + 1] - uxhw_cdf_heights[idx] + ) / uxhw_cdf_widths[idx] + uxhw_cdf_vals[i] = uxhw_cdf_heights[idx] + uxhw_cdf_slope * ( + positions[i] - uxhw_cdf_boundaries[idx] + ) + + +def wasserstein_1_core( + uxhw_cdf_boundaries: np.ndarray, + uxhw_cdf_widths: np.ndarray, + uxhw_cdf_heights: np.ndarray, + sample_cdf_positions: np.ndarray, + sample_cdf_heights: np.ndarray, +) -> float: + """Wasserstein-1 distance between a binned UxHw CDF and an empirical + sample CDF. + + Caller-validates contract: this is the inner algorithmic core and + does not validate its inputs. The only intended caller is + `wasserstein_1_between_distribution_and_samples`, which validates + upstream via `_validate_binned_lengths` and + `_validate_binned_semantics`. Callers must ensure shapes are + length-consistent and values are finite. + + Args: + uxhw_cdf_boundaries: Sorted bin boundaries for the UxHw CDF + (length N+1). + uxhw_cdf_widths: Bin widths (length N). + uxhw_cdf_heights: Cumulative CDF heights at each boundary + (length N+1, starting at 0). + sample_cdf_positions: Sorted positions of the empirical samples + (length M). + sample_cdf_heights: Cumulative empirical-CDF heights at each + sample position (length M+1, starting at 0). + + Returns: + Wasserstein-1 distance between the two CDFs. + """ + # Fit all positions in a single array that will be sorted afterwards + # by build_position_and_type_array. + num_boundaries = len(uxhw_cdf_boundaries) + num_samples = len(sample_cdf_positions) + num_points_total = num_boundaries + num_samples + + positions = np.empty(num_points_total, dtype=np.float64) + types = np.empty(num_points_total, dtype=np.int8) + + build_position_and_type_array( + uxhw_cdf_boundaries, + sample_cdf_positions, + positions, + types, + num_boundaries, + num_samples, + ) + + # `uxhw_cdf_idx[j]` is the linear segment of the UxHw CDF that + # position[j] lives in; `sample_cdf_idx[j]` is the constant segment + # of the sample empirical CDF. + uxhw_cdf_idx = np.empty(num_points_total, dtype=np.int32) + sample_cdf_idx = np.empty(num_points_total, dtype=np.int32) + current_seg = -1 + current_step = 0 + + for j in range(num_points_total): + if types[j] == 0: + current_seg += 1 + else: + current_step += 1 + + uxhw_cdf_idx[j] = current_seg + sample_cdf_idx[j] = current_step + + # Now that we know the type for each point, fill in the CDF values. + uxhw_cdf_vals = np.empty(num_points_total, dtype=np.float64) + sample_cdf_vals = np.zeros(num_points_total, dtype=np.float64) + + fill_cdf_values( + uxhw_cdf_vals, + uxhw_cdf_idx, + uxhw_cdf_boundaries, + uxhw_cdf_heights, + uxhw_cdf_widths, + sample_cdf_vals, + sample_cdf_idx, + sample_cdf_heights, + positions, + num_points_total, + num_boundaries, + ) + + # Compute the trapezoid / triangle / rectangle segment sizes. + # delta_left and delta_right are the relative CDF heights at the + # left and right of each trapezoid; left_pos / right_pos are the + # corresponding x-positions. We use `sample_cdf_vals[:-1]` for + # delta_right because the step-wise CDF is right-continuous — we + # compare to the left (previous) CDF height. + delta_left = uxhw_cdf_vals[:-1] - sample_cdf_vals[:-1] + delta_right = uxhw_cdf_vals[1:] - sample_cdf_vals[:-1] + left_pos = positions[:-1] + right_pos = positions[1:] + + total_distance = np.zeros(num_points_total - 1, dtype=np.float64) + for i in range(num_points_total - 1): + y0 = delta_left[i] + y1 = delta_right[i] + x0 = left_pos[i] + x1 = right_pos[i] + + if y0 * y1 < 0.0: + mid = x0 + y0 / (y0 - y1) * (x1 - x0) + total_distance[i] = integrate_trapezoid(x0, mid, abs(y0), 0.0) + total_distance[i] += integrate_trapezoid(mid, x1, 0.0, abs(y1)) + else: + total_distance[i] = integrate_trapezoid(x0, x1, abs(y0), abs(y1)) + + return float(np.sum(total_distance)) + + +def _validate_binned_lengths( + bin_boundaries: list[float], + bin_heights: list[float], + bin_widths: list[float], + sample_positions: list[float], + sample_weights: list[float] | None, +) -> None: + """Structural length / non-empty checks for the binned wrapper.""" + if len(bin_widths) == 0: + raise ValueError("bin_widths must be non-empty.") + if len(bin_heights) != len(bin_widths): + raise ValueError("bin_widths and bin_heights must have the same length.") + if len(bin_boundaries) != len(bin_widths) + 1: + raise ValueError( + "bin_boundaries must contain exactly one more entry than bin_widths." + ) + if len(sample_positions) == 0: + raise ValueError("sample_positions must not be empty.") + if sample_weights is not None and len(sample_weights) != len(sample_positions): + raise ValueError( + "sample_positions and sample_weights must have the same length." + ) + + +def _validate_binned_semantics( + bin_boundaries: list[float], + bin_heights: list[float], + bin_widths: list[float], + sample_positions: list[float], + sample_weights: list[float] | None, +) -> None: + """Finite + non-negativity / positivity checks on the raw inputs. + + Checks raw inputs (not post-cumsum CDF arrays). The cumulative + arrays can hide negative entries — e.g. weights=[0.5, -0.1, 0.6] + cumsums to [0.5, 0.4, 1.0], all non-negative, so a downstream + `np.any(cdf < 0)` check would miss the negative. + """ + bin_boundaries_arr = np.asarray(bin_boundaries, dtype=np.float64) + bin_heights_arr = np.asarray(bin_heights, dtype=np.float64) + bin_widths_arr = np.asarray(bin_widths, dtype=np.float64) + finite_checks = ( + ("bin_boundaries", bin_boundaries_arr), + ("bin_heights", bin_heights_arr), + ("bin_widths", bin_widths_arr), + ("sample_positions", np.asarray(sample_positions, dtype=np.float64)), + ) + for name, arr in finite_checks: + if not np.all(np.isfinite(arr)): + raise ValueError(f"{name} must contain only finite values.") + + if np.any(bin_widths_arr <= 0.0): + raise ValueError("All bin_widths must be strictly positive.") + if np.any(bin_heights_arr < 0.0) or not np.any(bin_heights_arr > 0.0): + raise ValueError( + "bin_heights must be non-negative with at least one " + "strictly positive entry." + ) + + # `wasserstein_1_core` assumes bin_boundaries is strictly + # increasing and that bin_widths[i] == boundaries[i+1] - boundaries[i]. + # Non-monotonic boundaries would produce negative segment lengths + # and silently-wrong distances; width/boundary disagreement breaks + # the CDF-merge integration. + boundary_gaps = np.diff(bin_boundaries_arr) + if np.any(boundary_gaps <= 0.0): + raise ValueError("bin_boundaries must be strictly increasing.") + if not np.allclose(boundary_gaps, bin_widths_arr, rtol=1e-9, atol=1e-12): + raise ValueError( + "bin_widths must match the implied widths " + "np.diff(bin_boundaries) within tolerance." + ) + + if sample_weights is None: + return + sample_weights_arr = np.asarray(sample_weights, dtype=np.float64) + if not np.all(np.isfinite(sample_weights_arr)): + raise ValueError("sample_weights must contain only finite values.") + if np.any(sample_weights_arr < 0.0) or not np.any(sample_weights_arr > 0.0): + raise ValueError( + "sample_weights must be non-negative with at least one " + "strictly positive entry." + ) + + +def _validate_binned_inputs( + bin_boundaries: list[float], + bin_heights: list[float], + bin_widths: list[float], + sample_positions: list[float], + sample_weights: list[float] | None, +) -> None: + """Full validation for `wasserstein_1_between_distribution_and_samples`.""" + _validate_binned_lengths( + bin_boundaries, bin_heights, bin_widths, sample_positions, sample_weights + ) + _validate_binned_semantics( + bin_boundaries, bin_heights, bin_widths, sample_positions, sample_weights + ) + + +def wasserstein_1_between_distribution_and_samples( + bin_boundaries: list[float], + bin_heights: list[float], + bin_widths: list[float], + sample_positions: list[float], + sample_weights: list[float] | None = None, +) -> float: + """Wasserstein-1 distance between a binned distribution and samples. + + Wraps the core CDF-merge algorithm: validates the raw inputs, + builds normalised cumulative CDFs for both sides, sorts the sample + side by position so the empirical CDF is well-defined, and delegates + to `wasserstein_1_core`. + + Args: + bin_boundaries: Distribution bin boundaries, length N+1, sorted. + bin_heights: PDF heights of each bin (length N, non-negative). + bin_widths: Width of each bin (length N, strictly positive). + sample_positions: Sample positions, any order. + sample_weights: Optional sample weights aligned with + `sample_positions`. Defaults to uniform `1 / len(samples)`. + + Returns: + Wasserstein-1 distance between the binned distribution and the + empirical sample distribution. + + Raises: + ValueError: On any structural mismatch (lengths, empty inputs), + non-finite values, non-positive widths, or zero total mass + on either side. See `_validate_binned_lengths` and + `_validate_binned_semantics` for the full check list. + """ + _validate_binned_inputs( + bin_boundaries, bin_heights, bin_widths, sample_positions, sample_weights + ) + + if sample_weights is None: + sample_weights = [1.0 / len(sample_positions)] * len(sample_positions) + + # Convert to np arrays. + uxhw_cdf_boundaries: np.ndarray = np.array(bin_boundaries, dtype=np.float64) + uxhw_cdf_widths: np.ndarray = np.array(bin_widths, dtype=np.float64) + uxhw_cdf_heights: np.ndarray = normalized_uxhw_cdf_heights( + uxhw_cdf_widths, np.array(bin_heights, dtype=np.float64) + ) + uxhw_cdf_heights = np.append([0.0], uxhw_cdf_heights) + + # The empirical CDF is cumulative-in-position-order, so positions + # (and their matching weights) must be sorted by position before + # cumsum. Callers may pass any ordering; we sort here. + sample_cdf_positions: np.ndarray = np.array(sample_positions, dtype=np.float64) + sample_cdf_weights: np.ndarray = np.array(sample_weights, dtype=np.float64) + sample_sort_order: np.ndarray = np.argsort(sample_cdf_positions) + sample_cdf_positions = sample_cdf_positions[sample_sort_order] + sample_cdf_weights = sample_cdf_weights[sample_sort_order] + sample_cdf_heights: np.ndarray = normalized_sample_cdf_heights( + sample_cdf_positions, sample_cdf_weights + ) + sample_cdf_heights = np.append([0.0], sample_cdf_heights) + + return wasserstein_1_core( + uxhw_cdf_boundaries, + uxhw_cdf_widths, + uxhw_cdf_heights, + sample_cdf_positions, + sample_cdf_heights, + ) + + +def binned_wasserstein_1_uxhw_wrapper( + binned_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, +) -> float: + """Binned Wasserstein-1 distance between a UxHw distribution and a + ground-truth distribution. + + Bins the UxHw distribution via `PlotData` (PDF binning, then TTR + rebinning), then compares the resulting bins to the ground truth's + weighted samples. Short-circuits to the non-binned W1 wrapper when + `binned_dist` collapses to a single Dirac delta (binning is ill-defined + for a single point). + + Args: + binned_dist: Distribution under test. Sorted in place as a side effect. + ground_truth_dist: Reference distribution treated as weighted samples + (positions + masses). + + Returns: + Binned Wasserstein-1 distance. + + Raises: + ValueError: If either argument is not a `DistributionalValue`, + or if `PlotData` fails to resolve a `plotting_ttr_order` + for the input UxHw distribution. + """ + _require_distributional_pair(binned_dist, ground_truth_dist) + + # Binning is ill-defined for distributions with ≤1 *finite* Dirac + # delta — delegate to the non-binned W1 wrapper. Checking + # `finite_dirac_deltas` (rather than `positions`) is important + # because special-value Diracs (NaN / ±Inf) with non-zero mass + # appear in `positions` after sorting but cannot be binned. + # `finite_dirac_deltas` internally calls `binned_dist.sort()` as a side + # effect (mutates the caller's distribution in place). + if len(binned_dist.finite_dirac_deltas) <= 1: + return wasserstein_1_uxhw_wrapper(dist_u=binned_dist, dist_v=ground_truth_dist) + + # Use PlotData to compute the binning (binned_dist is already sorted via + # the finite_dirac_deltas access above). + plot_interface = PlotData(binned_dist) + + boundary_positions, bin_widths, bin_heights = PlotData.create_binning( + binned_dist.finite_dirac_deltas, 0, False + ) + if plot_interface.plotting_ttr_order is None: + raise ValueError( + "PlotData failed to resolve plotting_ttr_order for the input " + "UxHw distribution (got None); cannot compute binned " + "Wasserstein-1." + ) + + # Find the TTR of the created binning; this is always a valid TTR. + ttr = PlotData.bin_pdf_to_ttr( + boundary_positions, + bin_widths, + bin_heights, + plot_interface.plotting_ttr_order, + ) + # Rebuild the binning from the valid TTR via the TTR binning method. + bin_boundaries, bin_widths, bin_heights = PlotData.create_binning( + ttr, plot_interface.plotting_ttr_order, True + ) + + return wasserstein_1_between_distribution_and_samples( + bin_boundaries=list(bin_boundaries), + bin_heights=list(bin_heights), + bin_widths=list(bin_widths), + sample_positions=list(ground_truth_dist.positions), + sample_weights=list(ground_truth_dist.masses), + ) + + +def binned_wasserstein_1_ux_string_wrapper( + distribution_ux: str, ground_truth_ux: str +) -> float: + """Binned Wasserstein-1 distance from Ux-string inputs. + + Parses both arguments into `DistributionalValue` instances and + delegates to `binned_wasserstein_1_uxhw_wrapper`. + + Args: + distribution_ux: Ux-string for the distribution under test. + ground_truth_ux: Ux-string for the reference distribution. + + Returns: + Binned Wasserstein-1 distance. + + Raises: + ValueError: If either Ux-string fails to parse, or if the + downstream binned-W1 computation rejects its inputs. + """ + distribution = DistributionalValue.parse(distribution_ux) + if distribution is None: + raise ValueError( + f"Could not parse distribution from ux string {distribution_ux}" + ) + + ground_truth = DistributionalValue.parse(ground_truth_ux) + if ground_truth is None: + raise ValueError( + f"Could not parse ground truth from ux string {ground_truth_ux}" + ) + + return binned_wasserstein_1_uxhw_wrapper(distribution, ground_truth) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser( + prog="python -m signaloid.distributional_distance.binned_wasserstein", + description=( + "Compute binned Wasserstein-1 distance between two ux strings. " + "Asymmetric: the first argument is binned, the second is " + "treated as raw weighted samples." + ), + ) + parser.add_argument("distribution_ux", help="ux string to be binned") + parser.add_argument("ground_truth_ux", help="ux string treated as weighted samples") + parser.add_argument("tolerance", type=float) + args = parser.parse_args() + + distance: float = binned_wasserstein_1_ux_string_wrapper( + args.distribution_ux, args.ground_truth_ux + ) + if distance <= args.tolerance: + print( + f"[SUCCESS] Binned Wasserstein-1 distance within " + f"{args.tolerance} tolerance. Distance: {distance}." + ) + else: + print( + f"[FAILURE] Binned Wasserstein-1 distance NOT within " + f"{args.tolerance} tolerance. Distance: {distance}." + ) + sys.exit(0 if distance <= args.tolerance else 1) diff --git a/src/signaloid/distributional_distance/binned_wasserstein_test.py b/src/signaloid/distributional_distance/binned_wasserstein_test.py new file mode 100644 index 0000000..f533e54 --- /dev/null +++ b/src/signaloid/distributional_distance/binned_wasserstein_test.py @@ -0,0 +1,557 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +"""Tests for signaloid.distributional_distance.binned_wasserstein.""" + +import math +import unittest +from typing import Sequence + +import numpy as np + +from signaloid.distributional.dirac_delta import DiracDelta +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance.binned_wasserstein import ( + binned_wasserstein_1_ux_string_wrapper, + binned_wasserstein_1_uxhw_wrapper, + wasserstein_1_between_distribution_and_samples, +) +from signaloid.distributional_distance.wasserstein import ( + wasserstein_1_uxhw_wrapper, +) + +DEFAULT_SAMPLE_SIZE = 1_000 + +# Fixture data used by the three `TestBinnedWasserstein` parametric tests. +# Each (samples, expected) pair is the CDF-based W1 distance between the +# UxHw bin specified by `_FIXTURE_UXHW_*` and the corresponding sample +# set. Kept at module scope to avoid the previous 3x duplication. +_FIXTURE_SAMPLE_SETS: list[list[float]] = [ + [-1.5], + [0.0], + [1.5], + [2.5], + [-2.0, -1.5], + [-2.0, 0.0], + [0.0, 1.75], + [1.75, 2.5], + [2.0, 2.5], +] +_FIXTURE_EXPECTED_RESULTS: list[float] = [ + 1.875, + 0.75, + 1.1875, + 2.125, + 2.125, + 1.375, + 0.5572916666666667, + 1.75, + 1.875, +] +_FIXTURE_UXHW_BOUNDARIES: list[float] = [-1.0, 1.0, 2.0] +_FIXTURE_UXHW_WIDTHS: list[float] = [2.0, 1.0] +_FIXTURE_UXHW_HEIGHTS: list[float] = [0.375, 0.25] + + +def _dv_from_weighted_samples( + positions: Sequence[float], masses: Sequence[float] +) -> DistributionalValue: + """Test-local helper: construct a DistributionalValue from explicit + (positions, masses) arrays. See sibling wasserstein_test.py for the + rationale (we don't add `from_weighted_samples` to DistributionalValue).""" + dirac_deltas = [ + DiracDelta(position=float(p), mass=float(m)) for p, m in zip(positions, masses) + ] + return DistributionalValue(dirac_deltas=dirac_deltas) + + +class TestBinnedWasserstein(unittest.TestCase): + """Tests for wasserstein_1_between_distribution_and_samples and + binned_wasserstein_1_uxhw_wrapper.""" + + def test_cdf_based_wasserstein1_distance_between_uxhw_and_samples(self) -> None: + """Test the CDF-based W1 distance between a UxHw distribution and + an empirical sample distribution. Single examples before / between + / after the distribution CDF, plus mixed cases covering CDF + intersections.""" + for test_id, (samples, expected) in enumerate( + zip(_FIXTURE_SAMPLE_SETS, _FIXTURE_EXPECTED_RESULTS) + ): + distance = wasserstein_1_between_distribution_and_samples( + _FIXTURE_UXHW_BOUNDARIES, + _FIXTURE_UXHW_HEIGHTS, + _FIXTURE_UXHW_WIDTHS, + samples, + ) + self.assertAlmostEqual( + distance, + expected, + places=12, + msg=f"test_id={test_id} samples={samples}", + ) + + def test_cdf_based_wasserstein1_distance_between_uxhw_and_weighted_samples( + self, + ) -> None: + """Exercises the weighted-samples code path. Each sample gets a + deliberately non-normalised uniform weight of 7.0 — the + function must normalise internally and produce the same + distances as the unweighted case.""" + for test_id, (samples, expected) in enumerate( + zip(_FIXTURE_SAMPLE_SETS, _FIXTURE_EXPECTED_RESULTS) + ): + # Non-normalised uniform weights — internal normalisation + # must give the same answer as the unweighted case. + non_normalised_weights = [7.0] * len(samples) + distance = wasserstein_1_between_distribution_and_samples( + _FIXTURE_UXHW_BOUNDARIES, + _FIXTURE_UXHW_HEIGHTS, + _FIXTURE_UXHW_WIDTHS, + samples, + sample_weights=non_normalised_weights, + ) + self.assertAlmostEqual( + distance, + expected, + places=12, + msg=f"test_id={test_id} samples={samples}", + ) + + def test_unnormalised_uxhw_heights_normalise_internally( + self, + ) -> None: + """The UxHw bin heights are deliberately not normalised — the + function must handle this and produce the same distances as the + normalised-heights case. (Previously misnamed + `..._between_wrong_uxhw_and_weighted_samples` — does NOT pass + sample_weights.)""" + # Heights are 2x the normalised values — function must normalise. + unnormalised_heights = [h * 2.0 for h in _FIXTURE_UXHW_HEIGHTS] + + for test_id, (samples, expected) in enumerate( + zip(_FIXTURE_SAMPLE_SETS, _FIXTURE_EXPECTED_RESULTS) + ): + distance = wasserstein_1_between_distribution_and_samples( + _FIXTURE_UXHW_BOUNDARIES, + unnormalised_heights, + _FIXTURE_UXHW_WIDTHS, + samples, + ) + self.assertAlmostEqual( + distance, + expected, + places=12, + msg=f"test_id={test_id} samples={samples}", + ) + + def test_binned_wasserstein_1_uxhw_wrapper(self) -> None: + """binned_wasserstein_1_uxhw_wrapper produces a deterministic, + small-but-strictly-positive distance between a coarse 4-point + symmetric uxhw and a 1000-sample N(0, 1) MC ground truth. The + RNG is seeded; the assertion has a tight window around the + precomputed result so silent numerical regressions surface.""" + rng = np.random.default_rng(seed=20260520) + mc_sample = rng.standard_normal(DEFAULT_SAMPLE_SIZE) + + # Arbitrary weighted distribution spanning the sample support. + positions = [-2.0, -0.5, 0.5, 2.0] + masses = [0.15, 0.35, 0.35, 0.15] + uxhw = _dv_from_weighted_samples(positions, masses) + ground_truth = DistributionalValue.from_samples(mc_sample) + + result = binned_wasserstein_1_uxhw_wrapper( + binned_dist=uxhw, ground_truth_dist=ground_truth + ) + + # Precomputed against the seeded RNG above; W1 is a metric so + # strictly > 0 for non-identical distributions. + self.assertAlmostEqual(result, 0.18323214623666018, places=12) + + +class TestBinnedInputValidation(unittest.TestCase): + """Regression tests for input validation in + `wasserstein_1_between_distribution_and_samples`. This function + accepts raw list[float] from external callers, so structural + invariants (length, non-empty) must be enforced explicitly.""" + + def _good_bins(self) -> tuple[list[float], list[float], list[float]]: + return ([-1.0, 1.0, 2.0], [0.375, 0.25], [2.0, 1.0]) + + def _call(self, **overrides: object) -> None: + """Invoke `wasserstein_1_between_distribution_and_samples` with a + baseline of valid kwargs, overriding any the caller supplies.""" + boundaries, heights, widths = self._good_bins() + kwargs: dict[str, object] = { + "bin_boundaries": boundaries, + "bin_heights": heights, + "bin_widths": widths, + "sample_positions": [0.5], + } + kwargs.update(overrides) + wasserstein_1_between_distribution_and_samples(**kwargs) # type: ignore[arg-type] + + def test_structural_rejections(self) -> None: + """Length / non-empty checks in `_validate_binned_lengths`.""" + cases: tuple[tuple[str, dict[str, object], str], ...] = ( + ( + "empty bin_widths", + {"bin_boundaries": [0.0], "bin_heights": [], "bin_widths": []}, + "non-empty", + ), + ( + "widths/heights mismatch", + {"bin_heights": [0.375, 0.25, 0.1]}, + "same length", + ), + ( + "boundaries length wrong", + {"bin_boundaries": [-1.0, 1.0]}, + "one more entry", + ), + ( + "empty sample_positions", + {"sample_positions": []}, + "not be empty", + ), + ( + "samples/weights mismatch", + {"sample_positions": [0.5, 1.5], "sample_weights": [1.0]}, + "same length", + ), + ) + for label, overrides, expected in cases: + with self.subTest(case=label): + with self.assertRaises(ValueError) as ctx: + self._call(**overrides) + self.assertIn(expected, str(ctx.exception)) + + def test_semantic_rejections(self) -> None: + """Non-negativity / positivity / non-finite checks in + `_validate_binned_semantics` — including the hidden-negative + regressions where cumsum masks the bad entry.""" + cases: tuple[tuple[str, dict[str, object], str], ...] = ( + ("negative height", {"bin_heights": [-0.1, 0.25]}, "bin_heights"), + ("zero width", {"bin_widths": [2.0, 0.0]}, "bin_widths"), + ("negative width", {"bin_widths": [2.0, -1.0]}, "bin_widths"), + ( + "all-zero bin_heights", + {"bin_heights": [0.0, 0.0]}, + "bin_heights", + ), + ( + "all-zero sample_weights", + {"sample_positions": [0.5, 1.5], "sample_weights": [0.0, 0.0]}, + "sample_weights", + ), + ( + "single sample with zero weight", + {"sample_positions": [0.5], "sample_weights": [0.0]}, + "sample_weights", + ), + ( + "negative sample_weight masked by cumsum", + { + "sample_positions": [-0.5, 0.5, 1.5], + "sample_weights": [0.5, -0.1, 0.6], + }, + "sample_weights", + ), + ( + "negative bin_height masked by cumsum", + { + "bin_boundaries": [-1.0, 0.0, 1.0, 2.0], + "bin_heights": [0.5, -0.1, 0.6], + "bin_widths": [1.0, 1.0, 1.0], + }, + "bin_heights", + ), + ("NaN in bin_heights", {"bin_heights": [float("nan"), 0.25]}, "finite"), + ( + "Inf in sample_positions", + {"sample_positions": [0.5, float("inf")]}, + "finite", + ), + ( + "NaN in sample_weights", + { + "sample_positions": [0.5, 1.5], + "sample_weights": [0.5, float("nan")], + }, + "finite", + ), + ( + "non-monotonic boundaries", + {"bin_boundaries": [1.0, -1.0, 2.0]}, + "strictly increasing", + ), + ( + "widths inconsistent with boundary diffs", + {"bin_widths": [3.0, 1.0]}, + "match the implied widths", + ), + ) + for label, overrides, expected in cases: + with self.subTest(case=label): + with self.assertRaises(ValueError) as ctx: + self._call(**overrides) + self.assertIn(expected, str(ctx.exception)) + + +class TestSampleSortingRegression(unittest.TestCase): + """Regression tests for the unsorted-sample-positions bug. + + Before the fix, np.cumsum(sample_weights) was computed in input + order without first sorting (positions, weights) by position. The + empirical CDF was therefore wrong whenever positions were unsorted + and weights were non-uniform — and `ground_truth.positions` is + typically unsorted unless `.sort()` is called first.""" + + def test_permuting_samples_gives_same_distance(self) -> None: + """Same multiset of (position, weight), two orderings — must + give identical distances.""" + boundaries = [-1.0, 1.0, 2.0] + widths = [2.0, 1.0] + heights = [0.375, 0.25] + + sorted_pos = [-1.0, 0.5, 1.5] + sorted_w = [0.1, 0.6, 0.3] + + # Permutation of (position, weight) pairs. + unsorted_pos = [1.5, -1.0, 0.5] + unsorted_w = [0.3, 0.1, 0.6] + + d_sorted = wasserstein_1_between_distribution_and_samples( + boundaries, heights, widths, sorted_pos, sorted_w + ) + d_unsorted = wasserstein_1_between_distribution_and_samples( + boundaries, heights, widths, unsorted_pos, unsorted_w + ) + self.assertAlmostEqual(d_sorted, d_unsorted, places=12) + + def test_translation_invariance(self) -> None: + """W1 is translation-invariant: shifting both distribution and + samples by the same constant must leave the distance unchanged + (modulo floating-point noise). This catches accidental absolute- + position dependence introduced by future refactors.""" + boundaries = list(_FIXTURE_UXHW_BOUNDARIES) + widths = list(_FIXTURE_UXHW_WIDTHS) + heights = list(_FIXTURE_UXHW_HEIGHTS) + samples = [-2.0, 0.0, 1.75] + shift = 17.5 + + d_base = wasserstein_1_between_distribution_and_samples( + boundaries, heights, widths, samples + ) + d_shifted = wasserstein_1_between_distribution_and_samples( + [b + shift for b in boundaries], + heights, + widths, + [s + shift for s in samples], + ) + self.assertAlmostEqual(d_base, d_shifted, places=12) + + def test_binned_uxhw_wrapper_handles_unsorted_ground_truth(self) -> None: + """The wrapper passes ground_truth.positions/masses straight in + without sorting; verify that two equivalent-but-permuted + ground truths produce the same distance.""" + positions_sorted = [-2.0, -0.5, 0.5, 2.0] + masses_sorted = [0.15, 0.35, 0.35, 0.15] + positions_perm = [2.0, -0.5, -2.0, 0.5] + masses_perm = [0.15, 0.35, 0.15, 0.35] + + uxhw = _dv_from_weighted_samples([-1.0, 0.0, 1.0], [0.2, 0.6, 0.2]) + gt_sorted = _dv_from_weighted_samples(positions_sorted, masses_sorted) + gt_perm = _dv_from_weighted_samples(positions_perm, masses_perm) + + d_sorted = binned_wasserstein_1_uxhw_wrapper( + binned_dist=uxhw, ground_truth_dist=gt_sorted + ) + d_perm = binned_wasserstein_1_uxhw_wrapper( + binned_dist=uxhw, ground_truth_dist=gt_perm + ) + self.assertAlmostEqual(d_sorted, d_perm, places=12) + + def test_sample_coincident_with_boundary(self) -> None: + """Regression: when a sample sits exactly at a bin boundary, the + merge-sort tie-break must put the boundary first so + `wasserstein_1_core`'s segment-counter increments before the + step-counter. `np.argsort` is not guaranteed stable across + numpy versions; `np.lexsort((types, positions))` pins the order. + + Hand-computed: uxhw is uniform on [0, 2] (heights=0.5, widths=1 + across boundaries [0, 1, 2]); sample is δ at x=1 (the interior + boundary). F_uxhw(x) = x/2 for x ∈ [0, 2]; F_sample is the unit + step at x=1. W1 = ∫_0^1 (x/2) dx + ∫_1^2 (1 − x/2) dx + = 0.25 + 0.25 = 0.5. + """ + distance = wasserstein_1_between_distribution_and_samples( + bin_boundaries=[0.0, 1.0, 2.0], + bin_heights=[0.5, 0.5], + bin_widths=[1.0, 1.0], + sample_positions=[1.0], + ) + self.assertAlmostEqual(distance, 0.5, places=12) + + +class TestBinnedWrapperGroundTruthValidation(unittest.TestCase): + """The binned wrapper must validate `ground_truth` symmetrically + with `uxhw` — previously only uxhw was checked, so a non-DV + ground_truth would fail later with AttributeError.""" + + def test_non_dv_rejected_on_either_side(self) -> None: + """Message-format coverage lives in `_validators_test.py`; + here we only assert the wrapper raises `ValueError` on either + side, mentioning the expected type.""" + good = _dv_from_weighted_samples([-1.0, 0.0, 1.0], [0.2, 0.6, 0.2]) + for side, binned, gt in ( + ("first", "not a DV", good), + ("second", good, "not a DV"), + ): + with self.subTest(side=side): + with self.assertRaises(ValueError) as ctx: + binned_wasserstein_1_uxhw_wrapper(binned_dist=binned, ground_truth_dist=gt) # type: ignore[arg-type] + self.assertIn("DistributionalValue", str(ctx.exception)) + + +class TestBinnedWrapperSingleDiracShortCircuit(unittest.TestCase): + """`binned_wasserstein_1_uxhw_wrapper` short-circuits to the + non-binned W1 wrapper when uxhw has a single Dirac delta, since + binning a single point is ill-defined. Verify the short-circuit + triggers and matches the non-binned W1 result.""" + + def test_single_dirac_uxhw_delegates_to_w1(self) -> None: + uxhw = _dv_from_weighted_samples([2.5], [1.0]) + ground_truth = _dv_from_weighted_samples( + [-1.0, 0.0, 1.0, 2.0, 3.0], [0.1, 0.2, 0.4, 0.2, 0.1] + ) + # Short-circuit must yield the same value as the W1 wrapper + # for a single-Dirac uxhw. + d_binned = binned_wasserstein_1_uxhw_wrapper( + binned_dist=uxhw, ground_truth_dist=ground_truth + ) + d_w1 = wasserstein_1_uxhw_wrapper(dist_u=uxhw, dist_v=ground_truth) + self.assertAlmostEqual(d_binned, d_w1, places=12) + + def test_short_circuit_with_special_values_present(self) -> None: + """Regression: the short-circuit check used to look at + `len(uxhw.positions) == 1`, but DistributionalValue.positions + includes NaN/±Inf Dirac deltas (after sort) when they carry + non-zero mass. A DV with 1 finite Dirac + special-value mass + would skip the short-circuit and pass to PlotData on a + single-finite-Dirac binning — ill-defined. Checking + `finite_dirac_deltas` instead routes correctly to the + non-binned W1 wrapper. + """ + # Construct: 1 finite Dirac at x=1.0 plus a NaN-position Dirac + # carrying non-zero mass. After `sort()` the special-value + # bucket gets populated; `positions` then includes nan/-inf/inf + # (length 4), so the old check would not short-circuit. + uxhw_finite_with_special = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=float("nan"), mass=0.5), + ] + ) + ground_truth = _dv_from_weighted_samples( + [-1.0, 0.0, 1.0, 2.0, 3.0], [0.1, 0.2, 0.4, 0.2, 0.1] + ) + # The short-circuit routes to wasserstein_1_uxhw_wrapper, which + # then rejects the non-finite NaN position via _validate_wp_inputs. + # We just verify the routing — that we get a clean ValueError + # from the validator path rather than a PlotData failure on a + # length-1 finite Dirac list. + with self.assertRaises(ValueError) as ctx: + binned_wasserstein_1_uxhw_wrapper( + binned_dist=uxhw_finite_with_special, ground_truth_dist=ground_truth + ) + self.assertIn("finite", str(ctx.exception)) + + +class TestBinnedUxStringWrapper(unittest.TestCase): + """Parse paths for `binned_wasserstein_1_ux_string_wrapper`. + + Math coverage flows transitively through + `binned_wasserstein_1_uxhw_wrapper` (which has its own tests); here + we just verify that: + - bogus ux strings surface a ValueError rather than crashing + later (`DistributionalValue.parse` may either return None or + raise its own ValueError on malformed input), + - real ux strings parse cleanly and produce the same distance as + the DistributionalValue-form wrapper called directly.""" + + # SAMPLE_UX_STRING is a ~32-atom Gaussian-shaped TTR also used by + # `uxdata_toolkit_test.py:37` and `sample_generator_test.py:30`. + # Inlined rather than imported because test modules aren't part of + # the package API; copying matches the convention already used in + # those two callsites. + SAMPLE_UX_STRING = "-0.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noqa: E501 + + def test_bogus_ux_strings_rejected(self) -> None: + """Both unparseable and empty ux strings surface a ValueError.""" + for label, dux, gtux in ( + ("bogus", "not a valid ux string", "also invalid"), + ("empty", "", ""), + ): + with self.subTest(case=label): + with self.assertRaises(ValueError): + binned_wasserstein_1_ux_string_wrapper( + distribution_ux=dux, + ground_truth_ux=gtux, + ) + + def test_round_trips_against_uxhw_wrapper(self) -> None: + """Happy path: parse a real Ux string and verify the string-form + wrapper produces the same distance as feeding the parsed + DistributionalValue into `binned_wasserstein_1_uxhw_wrapper` + directly. Plumbing-level test — the math is already covered by + the DistributionalValue-form tests above. Guards against: + - parse errors on real Ux strings, + - the wrapper silently swallowing a parsed None, + - drift between the two call paths. + + Note: self-distance is NOT zero for the binned wrapper. The + wrapper bins the first argument but treats the second as raw + weighted samples, so even with identical inputs on both sides + the two representations differ — the assertion here is parity + between the two parse paths, not d == 0.""" + # Parse path 1: through the string-form wrapper. + d_string = binned_wasserstein_1_ux_string_wrapper( + self.SAMPLE_UX_STRING, self.SAMPLE_UX_STRING + ) + + # Parse path 2: parse once, call the DV wrapper directly. + parsed = DistributionalValue.parse(self.SAMPLE_UX_STRING) + # `assert` rather than `if/self.fail()` so mypy narrows the type + # and the message also serves as a regression guard that + # SAMPLE_UX_STRING still parses. + assert parsed is not None, "SAMPLE_UX_STRING failed to parse" + d_dv = binned_wasserstein_1_uxhw_wrapper( + binned_dist=parsed, ground_truth_dist=parsed + ) + + self.assertAlmostEqual(d_string, d_dv, places=12) + # Sanity check: the distance is a finite non-negative real + # number, ruling out NaN / inf leaking through the parse path. + self.assertTrue(math.isfinite(d_string)) + self.assertGreaterEqual(d_string, 0.0) + + +if __name__ == "__main__": + unittest.main() diff --git a/src/signaloid/distributional_distance/ks_distance.py b/src/signaloid/distributional_distance/ks_distance.py new file mode 100644 index 0000000..7dcf86e --- /dev/null +++ b/src/signaloid/distributional_distance/ks_distance.py @@ -0,0 +1,108 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + + +import numpy as np + +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance._validators import ( + _require_distributional_pair, + _validate_wp_inputs, +) + + +def _ks_distance( + u_positions: np.ndarray, + u_masses: np.ndarray, + v_positions: np.ndarray, + v_masses: np.ndarray, +) -> float: + """Sup-norm distance between two empirical step-function CDFs. + + The maximum can only occur at one of the merged sample positions + (where at least one of the two CDFs has a jump), so we evaluate + both CDFs on the union of positions and take the max-abs-diff. + + Right-continuous step CDF: ``F(x) = Σ_i m_i · 1[x_i ≤ x]``. + + Args: + u_positions: Sample positions for distribution u (any order). + u_masses: Non-negative masses for u; unnormalised/raw values allowed. + v_positions: Sample positions for distribution v (any order). + v_masses: Non-negative masses for v; unnormalised/raw values allowed. + + Returns: + KS distance in [0, 1]. + + Raises: + ValueError: see `_validate_wp_inputs` (shared validator). + """ + u_values = np.asarray(u_positions, dtype=np.float64) + v_values = np.asarray(v_positions, dtype=np.float64) + u_weights = np.asarray(u_masses, dtype=np.float64) + v_weights = np.asarray(v_masses, dtype=np.float64) + + # KS has no `p` parameter; pass p=1 purely to satisfy the shared + # validator (which guards against bool/<1). The validator's checks + # on shapes, finiteness, non-negative masses, and positive totals + # are independent of `p`. + u_total, v_total = _validate_wp_inputs( + u_values, u_weights, v_values, v_weights, p=1 + ) + + u_sorter = np.argsort(u_values) + v_sorter = np.argsort(v_values) + u_sorted = u_values[u_sorter] + v_sorted = v_values[v_sorter] + + u_cum = np.cumsum(u_weights[u_sorter]) / u_total + v_cum = np.cumsum(v_weights[v_sorter]) / v_total + # Pin endpoints exactly to avoid float-precision overshoot. + u_cum[-1] = 1.0 + v_cum[-1] = 1.0 + + # Evaluate F_u and F_v on the union of positions. For a right- + # continuous step CDF, F(x) is the cumulative mass over all jumps + # at positions ≤ x, so `searchsorted(side="right")` returns the + # count of sorted positions ≤ x — exactly the index we want into a + # 0-prepended cumulative-mass table (index 0 → 0, index k → first + # k masses). This naturally handles positions below the support + # (index 0 → F=0) without a separate clip. + joint = np.sort(np.concatenate([u_sorted, v_sorted])) + u_lookup = np.concatenate(([0.0], u_cum)) + v_lookup = np.concatenate(([0.0], v_cum)) + u_idx = np.searchsorted(u_sorted, joint, side="right") + v_idx = np.searchsorted(v_sorted, joint, side="right") + + return float(np.max(np.abs(u_lookup[u_idx] - v_lookup[v_idx]))) + + +def kolmogorov_smirnov_distance_uxhw_wrapper( + dist_u: DistributionalValue, + dist_v: DistributionalValue, +) -> float: + """Kolmogorov-Smirnov distance between two DistributionalValues.""" + _require_distributional_pair(dist_u, dist_v) + return _ks_distance( + u_positions=dist_u.positions, + u_masses=dist_u.masses, + v_positions=dist_v.positions, + v_masses=dist_v.masses, + ) diff --git a/src/signaloid/distributional_distance/ks_distance_test.py b/src/signaloid/distributional_distance/ks_distance_test.py new file mode 100644 index 0000000..78d8111 --- /dev/null +++ b/src/signaloid/distributional_distance/ks_distance_test.py @@ -0,0 +1,286 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +"""Tests for signaloid.distributional_distance.ks_distance.""" + +import unittest +from typing import Sequence + +import numpy as np + +from signaloid.distributional.dirac_delta import DiracDelta +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance.ks_distance import ( + _ks_distance, + kolmogorov_smirnov_distance_uxhw_wrapper, +) + + +def _dv_from_weighted_samples( + positions: Sequence[float], masses: Sequence[float] +) -> DistributionalValue: + dirac_deltas = [ + DiracDelta(position=float(p), mass=float(m)) for p, m in zip(positions, masses) + ] + return DistributionalValue(dirac_deltas=dirac_deltas) + + +class TestKolmogorovSmirnovDistance(unittest.TestCase): + """Tests for the KS distance (sup_x |F_u(x) - F_v(x)|).""" + + def test_self_distance_is_zero(self) -> None: + """KS(X, X) = 0.""" + dv = _dv_from_weighted_samples([-1.0, 0.5, 2.5], [0.2, 0.5, 0.3]) + self.assertAlmostEqual( + kolmogorov_smirnov_distance_uxhw_wrapper(dv, dv), 0.0, places=12 + ) + + def test_two_distinct_diracs_yields_one(self) -> None: + """KS distance between two single Diracs at different positions + is exactly 1 — the CDFs are 0/1 step functions that disagree by + the full unit between min(a, b) and max(a, b).""" + for a, b in ((0.0, 1.0), (-5.0, 5.0), (-1.5, -1.0)): + with self.subTest(a=a, b=b): + u = _dv_from_weighted_samples([a], [1.0]) + v = _dv_from_weighted_samples([b], [1.0]) + self.assertAlmostEqual( + kolmogorov_smirnov_distance_uxhw_wrapper(u, v), + 1.0, + places=12, + ) + + def test_bounded_in_unit_interval(self) -> None: + """KS distance is always in [0, 1] since both CDFs are in [0, 1].""" + rng = np.random.default_rng(seed=20260520) + for _ in range(20): + n_u = int(rng.integers(2, 20)) + n_v = int(rng.integers(2, 20)) + u_pos = rng.standard_normal(n_u) * 2 + v_pos = rng.standard_normal(n_v) * 2 + 0.5 + u_m = rng.uniform(0.1, 1.0, n_u) + v_m = rng.uniform(0.1, 1.0, n_v) + u = _dv_from_weighted_samples(list(u_pos), list(u_m)) + v = _dv_from_weighted_samples(list(v_pos), list(v_m)) + d = kolmogorov_smirnov_distance_uxhw_wrapper(u, v) + self.assertGreaterEqual(d, 0.0) + self.assertLessEqual(d, 1.0) + + def test_known_two_point_example(self) -> None: + """Hand-computed: u = {0:0.5, 1:0.5}, v = {0:1.0}. + + Right-continuous step CDFs: + F_u(x) = 0 for x<0, 0.5 for 0≤x<1, 1 for x≥1. + F_v(x) = 0 for x<0, 1 for x≥0. + |F_u − F_v| at the union {0, 1} is {0.5, 0}. + KS = 0.5. + """ + u = _dv_from_weighted_samples([0.0, 1.0], [0.5, 0.5]) + v = _dv_from_weighted_samples([0.0], [1.0]) + self.assertAlmostEqual( + kolmogorov_smirnov_distance_uxhw_wrapper(u, v), 0.5, places=12 + ) + + def test_known_triangle_example(self) -> None: + """Hand-computed three-point case with overlapping support. + + u = {0:0.5, 2:0.5}, v = {0:0.25, 1:0.5, 2:0.25}. + F_u at {0,1,2} = {0.5, 0.5, 1.0}; F_v = {0.25, 0.75, 1.0}. + |diff| = {0.25, 0.25, 0.0}. KS = 0.25. + """ + u = _dv_from_weighted_samples([0.0, 2.0], [0.5, 0.5]) + v = _dv_from_weighted_samples([0.0, 1.0, 2.0], [0.25, 0.5, 0.25]) + self.assertAlmostEqual( + kolmogorov_smirnov_distance_uxhw_wrapper(u, v), 0.25, places=12 + ) + + def test_dirac_vs_two_point_overlap(self) -> None: + """Dirac at a vs equal-mix of {a, b}: F_u(a)=1, F_v(a)=0.5. + + Maximum gap is 0.5 in the half-open interval [a, b). + """ + u = _dv_from_weighted_samples([0.0], [1.0]) + v = _dv_from_weighted_samples([0.0, 3.0], [0.5, 0.5]) + self.assertAlmostEqual( + kolmogorov_smirnov_distance_uxhw_wrapper(u, v), 0.5, places=12 + ) + + def test_two_equal_mass_uniform_discretisations_half_overlap(self) -> None: + """Two equal-mass integer grids shifted by half their length. + + u_pos = {0, 1, …, 2N-1}, v_pos = u_pos + N, each with N points + in [0, 2N-1] resp. [N, 3N-1] at equal mass 1/(2N). At x = 2N-1 + (the last u point), F_u = 1, F_v = N/(2N) = 0.5 → diff = 0.5. + Integer positions avoid float-precision artefacts at shared + grid points. KS = 0.5 exactly. + """ + n = 200 + u_pos = np.arange(2 * n, dtype=np.float64) + v_pos = u_pos + float(n) + masses = np.full(2 * n, 1.0 / (2 * n)) + u = _dv_from_weighted_samples(list(u_pos), list(masses)) + v = _dv_from_weighted_samples(list(v_pos), list(masses)) + self.assertAlmostEqual( + kolmogorov_smirnov_distance_uxhw_wrapper(u, v), 0.5, places=12 + ) + + def test_symmetry(self) -> None: + """KS is symmetric: KS(u, v) = KS(v, u).""" + rng = np.random.default_rng(seed=20260521) + for _ in range(10): + n_u = int(rng.integers(2, 10)) + n_v = int(rng.integers(2, 10)) + u = _dv_from_weighted_samples( + list(rng.standard_normal(n_u)), + list(rng.uniform(0.1, 1.0, n_u)), + ) + v = _dv_from_weighted_samples( + list(rng.standard_normal(n_v)), + list(rng.uniform(0.1, 1.0, n_v)), + ) + d_uv = kolmogorov_smirnov_distance_uxhw_wrapper(u, v) + d_vu = kolmogorov_smirnov_distance_uxhw_wrapper(v, u) + self.assertAlmostEqual(d_uv, d_vu, places=12) + + def test_triangle_inequality(self) -> None: + """KS is a metric: KS(u, w) ≤ KS(u, v) + KS(v, w).""" + rng = np.random.default_rng(seed=20260522) + for _ in range(10): + u = _dv_from_weighted_samples( + list(rng.standard_normal(5)), list(rng.uniform(0.1, 1.0, 5)) + ) + v = _dv_from_weighted_samples( + list(rng.standard_normal(5)), list(rng.uniform(0.1, 1.0, 5)) + ) + w = _dv_from_weighted_samples( + list(rng.standard_normal(5)), list(rng.uniform(0.1, 1.0, 5)) + ) + d_uv = kolmogorov_smirnov_distance_uxhw_wrapper(u, v) + d_vw = kolmogorov_smirnov_distance_uxhw_wrapper(v, w) + d_uw = kolmogorov_smirnov_distance_uxhw_wrapper(u, w) + # Tolerance covers floating-point slop at the metric bound. + self.assertLessEqual(d_uw, d_uv + d_vw + 1e-12) + + def test_permutation_invariance(self) -> None: + """KS depends on the (position, mass) multiset, not input order.""" + sorted_pos = [-1.0, 0.5, 1.5] + sorted_w = [0.1, 0.6, 0.3] + permuted_pos = [1.5, -1.0, 0.5] + permuted_w = [0.3, 0.1, 0.6] + gt = _dv_from_weighted_samples([0.0, 1.0, 2.0], [0.3, 0.4, 0.3]) + + u_sorted = _dv_from_weighted_samples(sorted_pos, sorted_w) + u_permuted = _dv_from_weighted_samples(permuted_pos, permuted_w) + self.assertAlmostEqual( + kolmogorov_smirnov_distance_uxhw_wrapper(u_sorted, gt), + kolmogorov_smirnov_distance_uxhw_wrapper(u_permuted, gt), + places=12, + ) + + def test_unnormalised_masses_normalise_internally(self) -> None: + """Scaling all masses by a positive constant leaves KS unchanged.""" + u_pos = [-1.0, 0.5, 2.5] + u_m = [0.1, 0.4, 0.5] + v_pos = [-0.5, 1.0] + v_m = [0.6, 0.4] + + canonical = kolmogorov_smirnov_distance_uxhw_wrapper( + _dv_from_weighted_samples(u_pos, u_m), + _dv_from_weighted_samples(v_pos, v_m), + ) + scaled = kolmogorov_smirnov_distance_uxhw_wrapper( + _dv_from_weighted_samples(u_pos, [m * 13.0 for m in u_m]), + _dv_from_weighted_samples(v_pos, [m * 0.7 for m in v_m]), + ) + self.assertAlmostEqual(canonical, scaled, places=12) + + def test_non_dv_rejected_on_either_side(self) -> None: + """Wrapper funnels through the shared `_require_distributional_pair` + check; both arguments are validated. Message-format coverage + lives in `_validators_test.py`; here we only assert the wrapper + raises `ValueError` mentioning the expected type.""" + good = _dv_from_weighted_samples([0.0, 1.0], [0.5, 0.5]) + for side, dist_u, dist_v in ( + ("first", "not a DV", good), + ("second", good, 42), + ): + with self.subTest(side=side): + with self.assertRaises(ValueError) as ctx: + kolmogorov_smirnov_distance_uxhw_wrapper(dist_u, dist_v) # type: ignore[arg-type] + self.assertIn("DistributionalValue", str(ctx.exception)) + + def test_helper_rejects_non_finite_positions(self) -> None: + """`_ks_distance` reuses `_validate_wp_inputs`, so NaN/Inf + positions and masses are rejected the same way as Wasserstein.""" + with self.assertRaises(ValueError) as ctx: + _ks_distance( + u_positions=np.array([0.0, np.nan]), + u_masses=np.array([0.5, 0.5]), + v_positions=np.array([0.0, 1.0]), + v_masses=np.array([0.5, 0.5]), + ) + self.assertIn("finite", str(ctx.exception)) + + def test_helper_rejects_empty_positions(self) -> None: + """Empty positions are rejected via `_validate_wp_inputs`.""" + with self.assertRaises(ValueError) as ctx: + _ks_distance( + u_positions=np.array([], dtype=np.float64), + u_masses=np.array([], dtype=np.float64), + v_positions=np.array([0.0]), + v_masses=np.array([1.0]), + ) + self.assertIn("non-empty", str(ctx.exception)) + + def test_helper_rejects_mismatched_lengths(self) -> None: + """Position/mass length mismatch is rejected at the validator.""" + with self.assertRaises(ValueError) as ctx: + _ks_distance( + u_positions=np.array([0.0, 1.0]), + u_masses=np.array([1.0]), + v_positions=np.array([0.0]), + v_masses=np.array([1.0]), + ) + self.assertIn("matching lengths", str(ctx.exception)) + + def test_helper_rejects_negative_masses(self) -> None: + """Negative masses are rejected at the validator.""" + with self.assertRaises(ValueError) as ctx: + _ks_distance( + u_positions=np.array([0.0, 1.0]), + u_masses=np.array([0.5, -0.5]), + v_positions=np.array([0.0, 1.0]), + v_masses=np.array([0.5, 0.5]), + ) + self.assertIn("non-negative", str(ctx.exception)) + + def test_helper_rejects_zero_total_mass(self) -> None: + """All-zero masses on a side give zero total — rejected.""" + with self.assertRaises(ValueError) as ctx: + _ks_distance( + u_positions=np.array([0.0, 1.0]), + u_masses=np.array([0.0, 0.0]), + v_positions=np.array([0.0, 1.0]), + v_masses=np.array([0.5, 0.5]), + ) + self.assertIn("positive total mass", str(ctx.exception)) + + +if __name__ == "__main__": + unittest.main() diff --git a/src/signaloid/distributional_distance/scalar.py b/src/signaloid/distributional_distance/scalar.py new file mode 100644 index 0000000..7a45033 --- /dev/null +++ b/src/signaloid/distributional_distance/scalar.py @@ -0,0 +1,219 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + + +import argparse +import sys + +import numpy as np + +from signaloid.distributional.distributional import DistributionalValue + + +def _validate_scalar_inputs( + test_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, +) -> None: + """Validate inputs for scalar_distance_wrapper.""" + for name, dv in ( + ("test_dist", test_dist), + ("ground_truth_dist", ground_truth_dist), + ): + if not isinstance(dv, DistributionalValue): + raise ValueError( + f"{name} must be a DistributionalValue; " f"got {type(dv).__name__}." + ) + if len(dv.positions) == 0: + raise ValueError(f"{name} must contain at least one Dirac delta.") + if len(dv.positions) > 1: + raise ValueError( + f"{name} must be a scalar distribution (exactly one Dirac " + f"delta); got {len(dv.positions)}." + ) + if not np.isfinite(dv.positions[0]): + raise ValueError( + f"{name}.positions[0] must be finite; got {dv.positions[0]}." + ) + mass = dv.masses[0] + if not np.isfinite(mass) or mass <= 0.0: + raise ValueError( + f"{name}.masses[0] must be finite and strictly " + f"positive; got {mass}." + ) + + +def relative_error_uxhw_wrapper( + test_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, +) -> float: + """Relative error between two scalar (single-Dirac) distributions. + + Computes ``|test_dist[0] - ground_truth_dist[0]| / |ground_truth_dist[0]|``. + The function is intended for scalar comparisons. + Each input must hold exactly one finite Dirac delta. + Non-scalar inputs are rejected to avoid silently using only ``positions[0]``. + + Args: + test_dist: The single-Dirac distribution produced by the UxHw + configuration. + ground_truth_dist: The single-Dirac reference distribution to + compare against. + + Returns: + The relative error. When + ``ground_truth_dist.positions[0] == 0`` and + ``test_dist.positions[0] != 0`` the result is ``+inf``; when + both are zero the result is ``NaN`` (the 0/0 indeterminate + form). The numpy RuntimeWarning for both cases is suppressed. + + Raises: + ValueError: if either input is not a DistributionalValue, is + empty, holds more than one Dirac delta, contains a + non-finite position, or carries a non-finite or + non-positive mass. + """ + _validate_scalar_inputs(test_dist, ground_truth_dist) + + # ground_truth.positions[0] == 0 is allowed: callers see +inf. + # Suppress numpy's RuntimeWarning so it doesn't leak through. + with np.errstate(divide="ignore", invalid="ignore"): + distance = np.abs( + test_dist.positions[0] - ground_truth_dist.positions[0] + ) / np.abs(ground_truth_dist.positions[0]) + return float(distance) + + +def signed_error_uxhw_wrapper( + test_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, +) -> float: + """Signed error between two scalar (single-Dirac) distributions. + + Computes ``test_dist[0] - ground_truth_dist[0]``. Preserves sign; + same units as the inputs. The function is intended for scalar + comparisons. Each input must hold exactly one finite Dirac delta. + Non-scalar inputs are rejected to avoid silently using only + ``positions[0]``. + + Args: + test_dist: The single-Dirac distribution produced by the UxHw + configuration. + ground_truth_dist: The single-Dirac reference distribution to + compare against. + + Returns: + The signed error. Finite for any finite inputs; may be + positive, negative, or zero. + + Raises: + ValueError: if either input is not a DistributionalValue, is + empty, holds more than one Dirac delta, contains a + non-finite position, or carries a non-finite or + non-positive mass. + """ + _validate_scalar_inputs(test_dist, ground_truth_dist) + + return float(test_dist.positions[0] - ground_truth_dist.positions[0]) + + +def absolute_error_uxhw_wrapper( + test_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, +) -> float: + """Absolute error between two scalar (single-Dirac) distributions. + + Computes ``|test_dist[0] - ground_truth_dist[0]|``. Magnitude only; + same units as the inputs. The function is intended for scalar + comparisons. Each input must hold exactly one finite Dirac delta. + Non-scalar inputs are rejected to avoid silently using only + ``positions[0]``. + + Args: + test_dist: The single-Dirac distribution produced by the UxHw + configuration. + ground_truth_dist: The single-Dirac reference distribution to + compare against. + + Returns: + The absolute error. Non-negative and finite for any finite + inputs. + + Raises: + ValueError: if either input is not a DistributionalValue, is + empty, holds more than one Dirac delta, contains a + non-finite position, or carries a non-finite or + non-positive mass. + """ + return float(np.abs(signed_error_uxhw_wrapper(test_dist, ground_truth_dist))) + + +if __name__ == "__main__": + METRICS = { + "relative": relative_error_uxhw_wrapper, + "absolute": absolute_error_uxhw_wrapper, + "signed": signed_error_uxhw_wrapper, + } + + parser = argparse.ArgumentParser( + prog="python -m signaloid.distributional_distance.scalar", + description=( + "Compute scalar error between two ux strings (single-Dirac " "inputs)." + ), + ) + parser.add_argument("test_dist_ux", help="ux string for test_dist") + parser.add_argument("ground_truth_dist_ux", help="ux string for ground_truth_dist") + parser.add_argument("tolerance", type=float) + parser.add_argument( + "--metric", + choices=list(METRICS), + default="relative", + help="error metric (default: relative)", + ) + args = parser.parse_args() + + test_dist = DistributionalValue.parse(args.test_dist_ux) + if test_dist is None: + raise ValueError( + f"Could not parse test_dist from ux string {args.test_dist_ux}" + ) + ground_truth_dist = DistributionalValue.parse(args.ground_truth_dist_ux) + if ground_truth_dist is None: + raise ValueError( + f"Could not parse ground_truth_dist from ux string " + f"{args.ground_truth_dist_ux}" + ) + + distance: float = METRICS[args.metric](test_dist, ground_truth_dist) + # signed_error can be negative; compare |distance| to tolerance so the + # SUCCESS / FAILURE semantics are the same magnitude check across all + # three metrics. abs() is a no-op for the non-negative ones. + within = abs(distance) <= args.tolerance + label = f"{args.metric.capitalize()} error" + if within: + print( + f"[SUCCESS] {label} within " + f"{args.tolerance} tolerance. Distance: {distance}." + ) + else: + print( + f"[FAILURE] {label} NOT within " + f"{args.tolerance} tolerance. Distance: {distance}." + ) + sys.exit(0 if within else 1) diff --git a/src/signaloid/distributional_distance/scalar_test.py b/src/signaloid/distributional_distance/scalar_test.py new file mode 100644 index 0000000..42952ea --- /dev/null +++ b/src/signaloid/distributional_distance/scalar_test.py @@ -0,0 +1,294 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +"""Tests for the three scalar-comparison wrappers in +signaloid.distributional_distance.scalar.""" + +import math +import unittest + +from signaloid.distributional.dirac_delta import DiracDelta +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance.scalar import ( + absolute_error_uxhw_wrapper, + relative_error_uxhw_wrapper, + signed_error_uxhw_wrapper, +) + + +def _single_dirac(position: float) -> DistributionalValue: + """Build a DistributionalValue with a single Dirac at `position`.""" + return DistributionalValue(dirac_deltas=[DiracDelta(position=position, mass=1.0)]) + + +class TestScalarDistance(unittest.TestCase): + """Tests for scalar_distance_wrapper — relative error + |test_dist[0] - ground_truth_dist[0]| / |ground_truth_dist[0]|.""" + + def test_zero_when_identical(self) -> None: + """Relative error is 0 when the two scalars match.""" + for value in (1.0, -5.0, 1e6, 0.001): + distance = relative_error_uxhw_wrapper( + _single_dirac(value), _single_dirac(value) + ) + self.assertAlmostEqual(distance, 0.0, places=12, msg=f"v={value}") + + def test_one_percent_relative_error(self) -> None: + """ground_truth_dist=100, test_dist=99 → 0.01.""" + distance = relative_error_uxhw_wrapper( + _single_dirac(99.0), _single_dirac(100.0) + ) + self.assertAlmostEqual(distance, 0.01, places=12) + + def test_ten_percent_relative_error(self) -> None: + """ground_truth_dist=10, test_dist=11 → 0.1.""" + distance = relative_error_uxhw_wrapper(_single_dirac(11.0), _single_dirac(10.0)) + self.assertAlmostEqual(distance, 0.1, places=12) + + def test_sign_irrelevant_in_numerator_via_abs(self) -> None: + """ground_truth_dist=1, test_dist=-1 → |-1-1|/|1| = 2.""" + distance = relative_error_uxhw_wrapper(_single_dirac(-1.0), _single_dirac(1.0)) + self.assertAlmostEqual(distance, 2.0, places=12) + + def test_negative_ground_truth_dist_uses_abs(self) -> None: + """ground_truth_dist=-100, test_dist=-99 → |-99-(-100)|/|-100| = 0.01.""" + distance = relative_error_uxhw_wrapper( + _single_dirac(-99.0), _single_dirac(-100.0) + ) + self.assertAlmostEqual(distance, 0.01, places=12) + + def test_zero_ground_truth_dist_returns_positive_infinity(self) -> None: + """Division by zero is intentional — verify +inf specifically, + not just any inf (`-inf` would also satisfy math.isinf).""" + distance = relative_error_uxhw_wrapper(_single_dirac(1.0), _single_dirac(0.0)) + self.assertEqual(distance, math.inf) + + def test_very_large_numbers(self) -> None: + """Relative error is scale-invariant; verify no overflow at 1e300.""" + distance = relative_error_uxhw_wrapper( + _single_dirac(1.01e300), _single_dirac(1.0e300) + ) + self.assertAlmostEqual(distance, 0.01, places=12) + + def test_zero_over_zero_returns_nan(self) -> None: + """ground_truth_dist=0, test_dist=0 → 0/0 = NaN (numpy invalid op, warning suppressed).""" + distance = relative_error_uxhw_wrapper(_single_dirac(0.0), _single_dirac(0.0)) + self.assertTrue(math.isnan(distance)) + + def test_empty_rejected_on_either_side(self) -> None: + """Empty DistributionalValue is rejected naming the bad argument, + on whichever side it appears.""" + empty = DistributionalValue(dirac_deltas=[]) + valid = _single_dirac(1.0) + cases = ( + ("test_dist", empty, valid), + ("ground_truth_dist", valid, empty), + ) + for name, test_dist, ground_truth_dist in cases: + with self.subTest(side=name): + with self.assertRaises(ValueError) as ctx: + relative_error_uxhw_wrapper(test_dist, ground_truth_dist) + self.assertIn(name, str(ctx.exception)) + + def test_multi_dirac_rejected_on_either_side(self) -> None: + """Function is named *scalar*_distance_wrapper — silently + discarding positions[1:] would be a footgun. Rejected on + whichever side a multi-Dirac DV appears.""" + multi = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=1.0, mass=0.5), + DiracDelta(position=2.0, mass=0.5), + ] + ) + valid = _single_dirac(1.0) + for name, test_dist, ground_truth_dist in ( + ("test_dist", multi, valid), + ("ground_truth_dist", valid, multi), + ): + with self.subTest(side=name): + with self.assertRaises(ValueError) as ctx: + relative_error_uxhw_wrapper(test_dist, ground_truth_dist) + self.assertIn("scalar distribution", str(ctx.exception)) + + def test_non_finite_position_rejected(self) -> None: + """NaN / +inf / -inf positions are rejected on either side.""" + valid = _single_dirac(1.0) + for side, value in ( + ("test_dist", float("nan")), + ("ground_truth_dist", float("nan")), + ("test_dist", float("inf")), + ("ground_truth_dist", float("inf")), + ("test_dist", float("-inf")), + ("ground_truth_dist", float("-inf")), + ): + with self.subTest(side=side, value=value): + bad = _single_dirac(value) + test_dist, ground_truth_dist = ( + (bad, valid) if side == "test_dist" else (valid, bad) + ) + with self.assertRaises(ValueError) as ctx: + relative_error_uxhw_wrapper(test_dist, ground_truth_dist) + self.assertIn("finite", str(ctx.exception)) + + def test_non_dv_rejected_on_either_side(self) -> None: + """Non-DistributionalValue inputs previously raised AttributeError + on `.positions`. Now raise a clear ValueError on either side.""" + valid = _single_dirac(1.0) + cases = ( + ("test_dist", "not a DV", valid), + ("ground_truth_dist", valid, 42.0), + ) + for name, test_dist, ground_truth_dist in cases: + with self.subTest(side=name): + with self.assertRaises(ValueError) as ctx: + relative_error_uxhw_wrapper(test_dist, ground_truth_dist) # type: ignore[arg-type] + self.assertIn(name, str(ctx.exception)) + self.assertIn("DistributionalValue", str(ctx.exception)) + + def test_invalid_mass_rejected(self) -> None: + """Regression: DistributionalValue allows constructing a Dirac + with NaN / zero mass, which would silently flow through + scalar_distance_wrapper since the mass doesn't enter the + relative-error formula. Now rejected upfront. + + Negative-mass rejection lives in + TestDistributionalValueInitMassValidation — DistributionalValue + rejects negative masses at construction, so they can't reach + this wrapper through a DV-shaped input.""" + valid = _single_dirac(1.0) + for side, bad_mass in ( + ("test_dist", float("nan")), + ("test_dist", 0.0), + ("ground_truth_dist", float("nan")), + ("ground_truth_dist", 0.0), + ): + with self.subTest(side=side, mass=bad_mass): + bad = DistributionalValue( + dirac_deltas=[DiracDelta(position=1.0, mass=bad_mass)] + ) + test_dist, ground_truth_dist = ( + (bad, valid) if side == "test_dist" else (valid, bad) + ) + with self.assertRaises(ValueError) as ctx: + relative_error_uxhw_wrapper(test_dist, ground_truth_dist) + self.assertIn(side, str(ctx.exception)) + self.assertIn("masses", str(ctx.exception)) + + +class TestSignedError(unittest.TestCase): + """Tests for signed_error_uxhw_wrapper — + test_dist[0] - ground_truth_dist[0]. Preserves sign; same units as + inputs; well-defined for any finite inputs (no zero-division + edge case).""" + + def test_zero_when_identical(self) -> None: + """signed_error(x, x) == 0 for any x.""" + for value in (1.0, -5.0, 1e6, 0.0, 0.001): + distance = signed_error_uxhw_wrapper( + _single_dirac(value), _single_dirac(value) + ) + self.assertAlmostEqual(distance, 0.0, places=12, msg=f"v={value}") + + def test_positive_when_test_greater_than_ground_truth(self) -> None: + """ground_truth_dist=10, test_dist=11 → +1.""" + distance = signed_error_uxhw_wrapper(_single_dirac(11.0), _single_dirac(10.0)) + self.assertAlmostEqual(distance, 1.0, places=12) + + def test_negative_when_test_less_than_ground_truth(self) -> None: + """ground_truth_dist=10, test_dist=9 → -1. + Sign is the load-bearing property distinguishing this wrapper + from absolute_error.""" + distance = signed_error_uxhw_wrapper(_single_dirac(9.0), _single_dirac(10.0)) + self.assertAlmostEqual(distance, -1.0, places=12) + + def test_zero_ground_truth_dist_does_not_diverge(self) -> None: + """signed_error has no division: ground_truth=0 is fully fine.""" + distance = signed_error_uxhw_wrapper(_single_dirac(1.0), _single_dirac(0.0)) + self.assertAlmostEqual(distance, 1.0, places=12) + distance = signed_error_uxhw_wrapper(_single_dirac(0.0), _single_dirac(0.0)) + self.assertAlmostEqual(distance, 0.0, places=12) + + def test_both_negative_inputs(self) -> None: + """ground_truth=-100, test=-99 → +1 (test - gt = -99 - -100).""" + distance = signed_error_uxhw_wrapper( + _single_dirac(-99.0), _single_dirac(-100.0) + ) + self.assertAlmostEqual(distance, 1.0, places=12) + + +class TestAbsoluteError(unittest.TestCase): + """Tests for absolute_error_uxhw_wrapper — + |test_dist[0] - ground_truth_dist[0]|. Magnitude only; same units + as inputs; well-defined for any finite inputs.""" + + def test_zero_when_identical(self) -> None: + """absolute_error(x, x) == 0 for any x.""" + for value in (1.0, -5.0, 1e6, 0.0, 0.001): + distance = absolute_error_uxhw_wrapper( + _single_dirac(value), _single_dirac(value) + ) + self.assertAlmostEqual(distance, 0.0, places=12, msg=f"v={value}") + + def test_one_unit_difference(self) -> None: + """ground_truth_dist=10, test_dist=11 → 1.""" + distance = absolute_error_uxhw_wrapper(_single_dirac(11.0), _single_dirac(10.0)) + self.assertAlmostEqual(distance, 1.0, places=12) + + def test_sign_collapsed_via_abs(self) -> None: + """abs collapses the sign — both (11, 10) and (9, 10) yield 1. + Property check distinguishing this wrapper from signed_error.""" + positive = absolute_error_uxhw_wrapper(_single_dirac(11.0), _single_dirac(10.0)) + negative = absolute_error_uxhw_wrapper(_single_dirac(9.0), _single_dirac(10.0)) + self.assertAlmostEqual(positive, negative, places=12) + self.assertAlmostEqual(positive, 1.0, places=12) + + def test_always_non_negative(self) -> None: + """absolute_error is a magnitude — must be >= 0 across sign + permutations of the inputs.""" + for test, gt in ((1.0, -1.0), (-1.0, 1.0), (-100.0, -99.0), (1e10, -1e10)): + with self.subTest(test=test, gt=gt): + distance = absolute_error_uxhw_wrapper( + _single_dirac(test), _single_dirac(gt) + ) + self.assertGreaterEqual(distance, 0.0) + + def test_zero_ground_truth_dist_does_not_diverge(self) -> None: + """absolute_error has no division: ground_truth=0 is fully fine.""" + distance = absolute_error_uxhw_wrapper(_single_dirac(1.0), _single_dirac(0.0)) + self.assertAlmostEqual(distance, 1.0, places=12) + distance = absolute_error_uxhw_wrapper(_single_dirac(0.0), _single_dirac(0.0)) + self.assertAlmostEqual(distance, 0.0, places=12) + + def test_matches_abs_of_signed_error(self) -> None: + """|signed_error(a, b)| == absolute_error(a, b) by construction. + Regression guard: absolute_error is implemented as + ``float(np.abs(signed_error_uxhw_wrapper(...)))``.""" + for test, gt in ((1.0, 10.0), (-5.0, 3.0), (1e6, -2e6), (0.001, 0.0)): + with self.subTest(test=test, gt=gt): + t, g = _single_dirac(test), _single_dirac(gt) + self.assertAlmostEqual( + absolute_error_uxhw_wrapper(t, g), + abs(signed_error_uxhw_wrapper(t, g)), + places=12, + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/src/signaloid/distributional_distance/wasserstein.py b/src/signaloid/distributional_distance/wasserstein.py new file mode 100644 index 0000000..4995389 --- /dev/null +++ b/src/signaloid/distributional_distance/wasserstein.py @@ -0,0 +1,484 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + + +import argparse +import sys + +import numpy as np +import numpy.typing as npt + +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance._validators import ( + _require_distributional_pair, + _validate_wp_inputs, +) + + +def _wp_1d_weighted_pair( + u_positions: np.ndarray, + u_masses: np.ndarray, + v_positions: np.ndarray, + v_masses: np.ndarray, + p: int = 1, +) -> float: + """1D Wasserstein-p distance between two weighted empirical distributions. + + Pure-numpy replacement for ``scipy.stats.wasserstein_distance`` (p=1) + and ``ot.wasserstein_1d`` (any p≥1, then take the p-th root). + + Uses the quantile-based formulation + ``W_p(u, v)^p = ∫_0^1 |F_u^{-1}(t) - F_v^{-1}(t)|^p dt``, + which is the canonical 1D Wasserstein-p. Note: integrating + ``∫|F_u(x) - F_v(x)|^p dx`` along x (the CDF formula) only equals + W_p^p when p = 1; for p ≥ 2 that integral is the energy distance, + not W_p. + + Args: + u_positions: Sample positions for distribution u (any order). + u_masses: Non-negative masses for each u position; may be + unnormalised — internally divided by their sum. + v_positions: Sample positions for distribution v (any order). + v_masses: Non-negative masses for each v position; may be + unnormalised — internally divided by their sum. + p: Wasserstein order (1 or 2 are exercised; any positive + integer works). + + Returns: + Wasserstein-p distance between u and v. + + Raises: + ValueError: see `_validate_wp_inputs`. + """ + u_values = np.asarray(u_positions, dtype=np.float64) + v_values = np.asarray(v_positions, dtype=np.float64) + u_weights = np.asarray(u_masses, dtype=np.float64) + v_weights = np.asarray(v_masses, dtype=np.float64) + + u_total_mass, v_total_mass = _validate_wp_inputs( + u_values, u_weights, v_values, v_weights, p + ) + + u_sorter = np.argsort(u_values) + v_sorter = np.argsort(v_values) + u_sorted = u_values[u_sorter] + v_sorted = v_values[v_sorter] + + u_cum = np.cumsum(u_weights[u_sorter]) / u_total_mass + v_cum = np.cumsum(v_weights[v_sorter]) / v_total_mass + # Pin endpoints exactly to avoid float-precision overshoot in searchsorted. + u_cum[-1] = 1.0 + v_cum[-1] = 1.0 + + # Merged quantile breakpoints in [0, 1]; 0 prepended so the first + # interval is covered. + qs = np.unique(np.concatenate(([0.0], u_cum, v_cum))) + + # F^{-1}(t) is constant on each interval (qs[i], qs[i+1]]; evaluate + # at the midpoint and pick the smallest index k with cum[k] ≥ mid. + mid_t = 0.5 * (qs[:-1] + qs[1:]) + u_idx = np.clip(np.searchsorted(u_cum, mid_t, side="left"), 0, len(u_sorted) - 1) + v_idx = np.clip(np.searchsorted(v_cum, mid_t, side="left"), 0, len(v_sorted) - 1) + + diff = np.abs(u_sorted[u_idx] - v_sorted[v_idx]) + dt = qs[1:] - qs[:-1] + + if p == 1: + return float(np.sum(diff * dt)) + return float(np.power(np.sum(np.power(diff, p) * dt), 1.0 / p)) + + +def wasserstein_p_distance( + u_positions: npt.ArrayLike, + u_masses: npt.ArrayLike | None, + v_positions: npt.ArrayLike, + v_masses: npt.ArrayLike | None, + *, + p: int, +) -> float: + """Wasserstein-p distance between two weighted empirical distributions. + + Public raw-array entry point over `_wp_1d_weighted_pair`, for callers + that hold `(positions, masses)` arrays rather than + `DistributionalValue` objects. It is the drop-in replacement for + ``scipy.stats.wasserstein_distance`` (p=1) and + ``sqrt(ot.wasserstein_1d(..., p=2))`` (p=2): the p-th root is taken + internally, so callers do not apply their own ``np.sqrt``. + + Masses may be `None` to request uniform weighting (matching the + `None`-means-uniform semantics of scipy / POT); otherwise they are + treated as non-negative, possibly unnormalised masses. + + Args: + u_positions: Sample positions for distribution u (any order). + u_masses: Non-negative masses for each u position, or `None` + for uniform weighting. + v_positions: Sample positions for distribution v (any order). + v_masses: Non-negative masses for each v position, or `None` + for uniform weighting. + p: Wasserstein order (any integer >= 1; 1 and 2 are exercised). + + Returns: + Wasserstein-p distance between u and v. + + Raises: + ValueError: see `_validate_wp_inputs`. + """ + u_pos = np.asarray(u_positions, dtype=np.float64) + v_pos = np.asarray(v_positions, dtype=np.float64) + u_wts = ( + np.ones_like(u_pos) + if u_masses is None + else np.asarray(u_masses, dtype=np.float64) + ) + v_wts = ( + np.ones_like(v_pos) + if v_masses is None + else np.asarray(v_masses, dtype=np.float64) + ) + return _wp_1d_weighted_pair(u_pos, u_wts, v_pos, v_wts, p=p) + + +def wasserstein_1_distance( + u_values: np.ndarray, + v_values: np.ndarray, + all_values: np.ndarray, +) -> float: + """Wasserstein-1 distance between two equally-weighted sample sets. + + Pure-numpy implementation that produces the same output as + ``scipy.stats.wasserstein_distance`` but requires all input arrays + to be pre-sorted and does not accept weights — both u and v are + treated as equal-mass samples. + + Args: + u_values: Sorted unweighted samples from distribution A. + v_values: Sorted unweighted samples from distribution B. + all_values: Sorted concatenation of u_values and v_values. + + Returns: + Wasserstein-1 distance between distribution A and distribution B. + + Raises: + ValueError: if u_values or v_values is empty (the empirical CDF + denominators `len(u_values)` and `len(v_values)` would + ZeroDivision otherwise). + """ + if len(u_values) == 0: + raise ValueError("u_values must be non-empty.") + if len(v_values) == 0: + raise ValueError("v_values must be non-empty.") + deltas = np.diff(all_values) + + u_cdf = np.zeros(len(all_values) - 1) + v_cdf = np.zeros(len(all_values) - 1) + + u_idx, v_idx = 0, 0 + for i in range(len(all_values) - 1): + while u_idx < len(u_values) and u_values[u_idx] <= all_values[i]: + u_idx += 1 + while v_idx < len(v_values) and v_values[v_idx] <= all_values[i]: + v_idx += 1 + + u_cdf[i] = u_idx / len(u_values) + v_cdf[i] = v_idx / len(v_values) + + return float(np.sum(np.abs(u_cdf - v_cdf) * deltas)) + + +def wasserstein_1_distance_with_weights( + u_values: np.ndarray, + v_values: np.ndarray, + v_cum_weights: np.ndarray, + all_values: np.ndarray, +) -> float: + """Wasserstein-1 distance between an unweighted u and a weighted v. + + Args: + u_values: Sorted unweighted samples from distribution A. + v_values: Sorted positions of weighted samples from distribution B. + v_cum_weights: Cumulative sum of the sorted weights of + distribution B (the natural ``np.cumsum(masses)``; no + leading zero is required). + all_values: Sorted concatenation of u_values and v_values. + + Returns: + Wasserstein-1 distance between distribution A and distribution B. + """ + if len(u_values) == 0: + raise ValueError("u_values must be non-empty.") + if len(v_cum_weights) == 0: + raise ValueError("v_cum_weights must be non-empty.") + if len(v_values) != len(v_cum_weights): + raise ValueError( + "v_values and v_cum_weights must have the same length " + f"(got {len(v_values)} and {len(v_cum_weights)})." + ) + deltas = np.diff(all_values) + v_total_weight = v_cum_weights[-1] + if v_total_weight <= 0.0: + raise ValueError( + "v_cum_weights[-1] (total mass) must be strictly positive; " + f"got {v_total_weight}." + ) + # Prepend 0 so v_cdf_lookup[k] is the mass of the first k v_values — + # in particular [0]=0 and [len(v)]=total. The original port indexed + # v_cum_weights[v_idx] directly, which was off by one and crashed + # when v_idx reached len(v_values). Equivalent to scipy's + # ``concatenate([0], cumsum)`` pattern. + v_cdf_lookup = np.concatenate(([0.0], v_cum_weights)) + + u_cdf = np.zeros(len(all_values) - 1) + v_cdf = np.zeros(len(all_values) - 1) + + u_idx, v_idx = 0, 0 + for i in range(len(all_values) - 1): + while u_idx < len(u_values) and u_values[u_idx] <= all_values[i]: + u_idx += 1 + u_cdf[i] = u_idx / len(u_values) + + while v_idx < len(v_values) and v_values[v_idx] <= all_values[i]: + v_idx += 1 + v_cdf[i] = v_cdf_lookup[v_idx] / v_total_weight + + return float(np.sum(np.abs(u_cdf - v_cdf) * deltas)) + + +def wasserstein_p_uxhw_wrapper( + dist_u: DistributionalValue, + dist_v: DistributionalValue, + *, + p: int, +) -> float: + """Wasserstein-p distance between two DistributionalValues. + + Args: + dist_u: First DistributionalValue. + dist_v: Second DistributionalValue. + p: Wasserstein order (any integer >= 1). p=1 and p=2 have + ergonomic shortcuts `wasserstein_1_uxhw_wrapper` and + `wasserstein_2_uxhw_wrapper`. + + Returns: + Wasserstein-p distance. + + Raises: + ValueError: see `_require_distributional_pair` and + `_validate_wp_inputs` (downstream of `_wp_1d_weighted_pair`). + """ + _require_distributional_pair(dist_u, dist_v) + return _wp_1d_weighted_pair( + u_positions=dist_u.positions, + u_masses=dist_u.masses, + v_positions=dist_v.positions, + v_masses=dist_v.masses, + p=p, + ) + + +def wasserstein_1_uxhw_wrapper( + dist_u: DistributionalValue, + dist_v: DistributionalValue, +) -> float: + """W1 between two DistributionalValues. + + Shortcut for `wasserstein_p_uxhw_wrapper(..., p=1)`. + + Args: + dist_u: First DistributionalValue. + dist_v: Second DistributionalValue. + + Returns: + Wasserstein-1 distance. + + Raises: + ValueError: see `wasserstein_p_uxhw_wrapper`. + """ + return wasserstein_p_uxhw_wrapper(dist_u, dist_v, p=1) + + +def wasserstein_2_uxhw_wrapper( + dist_u: DistributionalValue, + dist_v: DistributionalValue, +) -> float: + """W2 between two DistributionalValues. + + Shortcut for `wasserstein_p_uxhw_wrapper(..., p=2)`. + + Args: + dist_u: First DistributionalValue. + dist_v: Second DistributionalValue. + + Returns: + Wasserstein-2 distance. + + Raises: + ValueError: see `wasserstein_p_uxhw_wrapper`. + """ + return wasserstein_p_uxhw_wrapper(dist_u, dist_v, p=2) + + +def _rescale_to_gt_support( + dist_to_scale: DistributionalValue, reference_dist: DistributionalValue +) -> tuple[np.ndarray, np.ndarray]: + """Rescale both position arrays into [0, 1] using the ground-truth support. + + Validates non-emptiness explicitly before calling `.min()` / `.max()` + so callers see a clear ValueError on empty inputs rather than the + opaque "zero-size array to reduction operation" raised by numpy. + Position / mass finite + non-negative checks run downstream inside + `_wp_1d_weighted_pair` via `_validate_wp_inputs`. + + Args: + dist_to_scale: DistributionalValue whose positions are + rescaled into the [0, 1] frame defined by `reference_dist`. + reference_dist: DistributionalValue whose [min, max] support + defines the rescaling range. Also rescaled (its positions + land in [0, 1] by construction). + + Returns: + Tuple (rescaled_dist_to_scale, rescaled_reference_dist). + + Raises: + ValueError: if either DistributionalValue is empty. + """ + if len(dist_to_scale.positions) == 0 or len(reference_dist.positions) == 0: + raise ValueError("u_positions and v_positions must be non-empty.") + gt_min = reference_dist.positions.min() + normalizing_factor = reference_dist.positions.max() - gt_min + if normalizing_factor == 0.0: + normalizing_factor = 1.0 + return ( + (dist_to_scale.positions - gt_min) / normalizing_factor, + (reference_dist.positions - gt_min) / normalizing_factor, + ) + + +def normalized_wasserstein_p_uxhw_wrapper( + test_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, + *, + p: int, +) -> float: + """Wasserstein-p over positions rescaled to the ground-truth support [0, 1]. + + Args: + test_dist: Test DistributionalValue. + ground_truth_dist: Ground-truth DistributionalValue whose + support [min, max] defines the rescaling range. + p: Wasserstein order (any integer >= 1). p=1 and p=2 have + ergonomic shortcuts `normalized_wasserstein_1_uxhw_wrapper` + and `normalized_wasserstein_2_uxhw_wrapper`. + + Returns: + Wasserstein-p distance over rescaled positions. + + Raises: + ValueError: see `_require_distributional_pair`, + `_rescale_to_gt_support`, and downstream + `_validate_wp_inputs`. + """ + _require_distributional_pair(test_dist, ground_truth_dist) + u_rescaled, v_rescaled = _rescale_to_gt_support(test_dist, ground_truth_dist) + return _wp_1d_weighted_pair( + u_positions=u_rescaled, + u_masses=test_dist.masses, + v_positions=v_rescaled, + v_masses=ground_truth_dist.masses, + p=p, + ) + + +def normalized_wasserstein_1_uxhw_wrapper( + test_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, +) -> float: + """W1 over positions rescaled to the ground-truth support [0, 1]. + + Shortcut for `normalized_wasserstein_p_uxhw_wrapper(..., p=1)`. + + Args: + test_dist: Test DistributionalValue. + ground_truth_dist: Ground-truth DistributionalValue whose + support [min, max] defines the rescaling range. + + Returns: + Wasserstein-1 distance over rescaled positions. + + Raises: + ValueError: see `normalized_wasserstein_p_uxhw_wrapper`. + """ + return normalized_wasserstein_p_uxhw_wrapper(test_dist, ground_truth_dist, p=1) + + +def normalized_wasserstein_2_uxhw_wrapper( + test_dist: DistributionalValue, + ground_truth_dist: DistributionalValue, +) -> float: + """W2 over positions rescaled to the ground-truth support [0, 1]. + + Shortcut for `normalized_wasserstein_p_uxhw_wrapper(..., p=2)`. + + Args: + test_dist: Test DistributionalValue. + ground_truth_dist: Ground-truth DistributionalValue whose + support [min, max] defines the rescaling range. + + Returns: + Wasserstein-2 distance over rescaled positions. + + Raises: + ValueError: see `normalized_wasserstein_p_uxhw_wrapper`. + """ + return normalized_wasserstein_p_uxhw_wrapper(test_dist, ground_truth_dist, p=2) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser( + prog="python -m signaloid.distributional_distance.wasserstein", + description="Compute Wasserstein-p distance between two ux strings.", + ) + parser.add_argument("dist_u_ux", help="ux string for dist_u") + parser.add_argument("dist_v_ux", help="ux string for dist_v") + parser.add_argument("tolerance", type=float) + parser.add_argument( + "--p", type=int, default=1, help="Wasserstein order (default: 1)" + ) + args = parser.parse_args() + + dist_u = DistributionalValue.parse(args.dist_u_ux) + if dist_u is None: + raise ValueError(f"Could not parse dist_u from ux string {args.dist_u_ux}") + dist_v = DistributionalValue.parse(args.dist_v_ux) + if dist_v is None: + raise ValueError(f"Could not parse dist_v from ux string {args.dist_v_ux}") + + distance: float = wasserstein_p_uxhw_wrapper(dist_u, dist_v, p=args.p) + if distance <= args.tolerance: + print( + f"[SUCCESS] Wasserstein-{args.p} distance within " + f"{args.tolerance} tolerance. Distance: {distance}." + ) + else: + print( + f"[FAILURE] Wasserstein-{args.p} distance NOT within " + f"{args.tolerance} tolerance. Distance: {distance}." + ) + sys.exit(0 if distance <= args.tolerance else 1) diff --git a/src/signaloid/distributional_distance/wasserstein_test.py b/src/signaloid/distributional_distance/wasserstein_test.py new file mode 100644 index 0000000..dced28c --- /dev/null +++ b/src/signaloid/distributional_distance/wasserstein_test.py @@ -0,0 +1,667 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +"""Tests for signaloid.distributional_distance.wasserstein.""" + +import math +import unittest +from typing import Sequence + +import numpy as np + +from signaloid.distributional.dirac_delta import DiracDelta +from signaloid.distributional.distributional import DistributionalValue +from signaloid.distributional_distance.wasserstein import ( + _wp_1d_weighted_pair, + normalized_wasserstein_1_uxhw_wrapper, + normalized_wasserstein_2_uxhw_wrapper, + normalized_wasserstein_p_uxhw_wrapper, + wasserstein_1_distance, + wasserstein_1_distance_with_weights, + wasserstein_1_uxhw_wrapper, + wasserstein_2_uxhw_wrapper, + wasserstein_p_uxhw_wrapper, +) + +DEFAULT_SAMPLE_SIZE = 10_000 + + +def _dv_from_weighted_samples( + positions: Sequence[float], masses: Sequence[float] +) -> DistributionalValue: + """Test-local helper: construct a DistributionalValue from explicit + (positions, masses) arrays. + + """ + dirac_deltas = [ + DiracDelta(position=float(p), mass=float(m)) for p, m in zip(positions, masses) + ] + return DistributionalValue(dirac_deltas=dirac_deltas) + + +class TestWasserstein1Cores(unittest.TestCase): + """Tests for wasserstein_1_distance and + wasserstein_1_distance_with_weights — the two pre-existing pure-numpy + W1 cores. Parity oracle is the new _wp_1d_weighted_pair (which + implements the same scipy-style merged-CDF integral, with weights).""" + + def test_wasserstein_1_matches_weighted_pair_on_uniform_masses(self) -> None: + """wasserstein_1_distance (unweighted) agrees with + _wp_1d_weighted_pair (uniform weights) on the same samples.""" + rng = np.random.default_rng(seed=12345) + mc_samples_1 = np.sort(rng.standard_normal(DEFAULT_SAMPLE_SIZE)) + mc_samples_2 = np.sort(rng.standard_normal(DEFAULT_SAMPLE_SIZE)) + + all_values = np.concatenate([mc_samples_1, mc_samples_2]) + all_values.sort() + distance_unweighted = wasserstein_1_distance( + u_values=mc_samples_1, + v_values=mc_samples_2, + all_values=all_values, + ) + + uniform_u = np.ones(DEFAULT_SAMPLE_SIZE) / DEFAULT_SAMPLE_SIZE + uniform_v = np.ones(DEFAULT_SAMPLE_SIZE) / DEFAULT_SAMPLE_SIZE + distance_weighted = _wp_1d_weighted_pair( + u_positions=mc_samples_1, + u_masses=uniform_u, + v_positions=mc_samples_2, + v_masses=uniform_v, + p=1, + ) + + self.assertAlmostEqual(distance_unweighted, distance_weighted, places=12) + + def test_wasserstein_1_with_weights_matches_weighted_pair(self) -> None: + """wasserstein_1_distance_with_weights (unweighted vs weighted) + agrees with _wp_1d_weighted_pair when u has uniform weights.""" + rng = np.random.default_rng(seed=67890) + mc_samples = np.sort(rng.standard_normal(DEFAULT_SAMPLE_SIZE)) + + positions = [-2.0, -0.5, 0.5, 2.0] + masses = [0.15, 0.35, 0.35, 0.15] + uxhw_dv = _dv_from_weighted_samples(positions, masses) + + all_values = np.concatenate([mc_samples, uxhw_dv.positions]) + all_values.sort() + distance_mixed = wasserstein_1_distance_with_weights( + u_values=mc_samples, + v_values=uxhw_dv.positions, + v_cum_weights=np.cumsum(uxhw_dv.masses), + all_values=all_values, + ) + + distance_paired = _wp_1d_weighted_pair( + u_positions=mc_samples, + u_masses=np.ones(DEFAULT_SAMPLE_SIZE) / DEFAULT_SAMPLE_SIZE, + v_positions=uxhw_dv.positions, + v_masses=uxhw_dv.masses, + p=1, + ) + + self.assertAlmostEqual(distance_mixed, distance_paired, places=12) + + def test_wasserstein_1_with_weights_handles_v_idx_at_len(self) -> None: + """Regression: when some u_values lie above max(v_values), the + original port crashed with IndexError because v_idx hit + len(v_values). The fixed lookup uses a leading-0 cumweights + array so the tail CDF saturates at 1.0 cleanly.""" + u_values = np.array([0.0, 1.0, 2.0, 10.0]) # 10.0 is above v's max + v_values = np.array([0.5, 1.5, 2.5]) + v_masses = np.array([0.2, 0.5, 0.3]) + all_values = np.concatenate([u_values, v_values]) + all_values.sort() + + # Must not raise. + distance = wasserstein_1_distance_with_weights( + u_values=u_values, + v_values=v_values, + v_cum_weights=np.cumsum(v_masses), + all_values=all_values, + ) + self.assertGreater(distance, 0.0) + self.assertTrue(np.isfinite(distance)) + + +class TestWeightedPairAnalytic(unittest.TestCase): + """Analytic / closed-form tests for _wp_1d_weighted_pair.""" + + def test_dirac_to_dirac_w1(self) -> None: + """W1 between two single Diracs equals |a - b|.""" + for a, b in [(0.0, 1.0), (-3.5, 2.5), (10.0, 10.0), (1.0, 1.5)]: + distance = _wp_1d_weighted_pair( + u_positions=np.array([a]), + u_masses=np.array([1.0]), + v_positions=np.array([b]), + v_masses=np.array([1.0]), + p=1, + ) + self.assertAlmostEqual(distance, abs(a - b), places=12, msg=f"a={a}, b={b}") + + def test_dirac_to_dirac_w2(self) -> None: + """W2 between two single Diracs equals |a - b|.""" + for a, b in [(0.0, 1.0), (-3.5, 2.5), (10.0, 10.0), (1.0, 1.5)]: + distance = _wp_1d_weighted_pair( + u_positions=np.array([a]), + u_masses=np.array([1.0]), + v_positions=np.array([b]), + v_masses=np.array([1.0]), + p=2, + ) + self.assertAlmostEqual(distance, abs(a - b), places=12, msg=f"a={a}, b={b}") + + def test_self_distance_is_zero(self) -> None: + """W_p(X, X) = 0 for both p=1 and p=2.""" + positions = np.array([-1.0, 0.5, 2.5, 4.0]) + masses = np.array([0.1, 0.4, 0.3, 0.2]) + for p in (1, 2): + distance = _wp_1d_weighted_pair( + u_positions=positions, + u_masses=masses, + v_positions=positions, + v_masses=masses, + p=p, + ) + self.assertAlmostEqual(distance, 0.0, places=12, msg=f"p={p}") + + def test_translation_invariance_w1(self) -> None: + """W1 is translation-equivariant: W1(X + d, X) = d.""" + positions = np.array([-1.0, 0.5, 2.5, 4.0]) + masses = np.array([0.1, 0.4, 0.3, 0.2]) + for shift in [0.5, 1.0, -2.5, 3.0]: + distance = _wp_1d_weighted_pair( + u_positions=positions + shift, + u_masses=masses, + v_positions=positions, + v_masses=masses, + p=1, + ) + self.assertAlmostEqual( + distance, abs(shift), places=12, msg=f"shift={shift}" + ) + + def test_unnormalised_masses_are_normalised_internally(self) -> None: + """Doubling all masses must not change the resulting distance.""" + u_pos = np.array([-1.0, 0.5, 2.5, 4.0]) + u_mass = np.array([0.1, 0.4, 0.3, 0.2]) + v_pos = np.array([-2.0, 1.0, 3.0]) + v_mass = np.array([0.2, 0.5, 0.3]) + + canonical = _wp_1d_weighted_pair( + u_positions=u_pos, + u_masses=u_mass, + v_positions=v_pos, + v_masses=v_mass, + p=1, + ) + scaled = _wp_1d_weighted_pair( + u_positions=u_pos, + u_masses=u_mass * 7.0, + v_positions=v_pos, + v_masses=v_mass * 0.3, + p=1, + ) + self.assertAlmostEqual(canonical, scaled, places=12) + + +class TestWasserstein1UxhwWrapper(unittest.TestCase): + """Tests for wasserstein_1_uxhw_wrapper.""" + + def test_uxhw_wrapper_bootleg_zero(self) -> None: + """W1 ≈ 0 when the under-test distribution and the ground truth + are bootleg-identical (positions/masses constructed to produce + identical empirical CDFs).""" + testcases: list[tuple[list[float], list[float]]] = [ + ([1, 2, 3, 4, 5], [0.1, 0.2, 0.1, 0.4, 0.2]), + ([10, 20, 30, 40, 50], [0.1, 0.2, 0.1, 0.4, 0.2]), + ([10, 20, 30, 40, 50], [0.3, 0.1, 0.1, 0.3, 0.2]), + ([-100, 20, 500, 1000, 0], [0.3, 0.1, 0.1, 0.3, 0.2]), + ] + + for positions, masses in testcases: + sample_arrays = [] + for pos, mass in zip(positions, masses): + sample_arrays.append( + np.full(shape=math.floor(mass * 100), fill_value=pos) + ) + + test_dv = _dv_from_weighted_samples(positions, masses) + samples = np.concatenate(sample_arrays, axis=None) + ground_truth = DistributionalValue.from_samples(samples) + result = wasserstein_1_uxhw_wrapper(test_dv, ground_truth) + + self.assertAlmostEqual(result, 0, places=6) + + def test_uxhw_wrapper_uniform_mother_zero(self) -> None: + """W1 between a uniform(a, a+L) sample and its analytic TTR-N + approximation matches the closed-form W1(L, N) = L / (4N). + + Source for the closed form: + + - for uniform(0, 1) the TTR positions are + dd_pos(i) = (i + 0.5) / N for i in [0, N). + - positions = [a + (i + 0.5) * L / N for i in range(N)]. + - W(L, N) = L / (4 * N). + """ + rng = np.random.default_rng(seed=20260520) + for a in [-2.0, 0.0, 2.0]: + for L in [0.5, 1.0, 2.0]: + samples = rng.uniform(a, a + L, size=DEFAULT_SAMPLE_SIZE) + ground_truth = DistributionalValue.from_samples(samples) + + for N in [4, 16, 64, 128]: + positions = [a + (i + 0.5) * L / N for i in range(N)] + masses = [1 / N] * N + expected_distance = L / (4 * N) + + test_dv = _dv_from_weighted_samples(positions, masses) + result = wasserstein_1_uxhw_wrapper(test_dv, ground_truth) + + self.assertAlmostEqual( + result, + expected_distance, + delta=0.05, + msg=f"a={a}, L={L}, N={N}", + ) + + +class TestWasserstein2UxhwWrapper(unittest.TestCase): + """Tests for wasserstein_2_uxhw_wrapper.""" + + def test_self_distance_zero(self) -> None: + """W2(X, X) = 0.""" + positions = [-1.0, 0.5, 2.5, 4.0] + masses = [0.1, 0.4, 0.3, 0.2] + dv = _dv_from_weighted_samples(positions, masses) + self.assertAlmostEqual(wasserstein_2_uxhw_wrapper(dv, dv), 0.0, places=12) + + def test_dirac_to_dirac(self) -> None: + """W2 between two single Diracs equals |a - b|.""" + for a, b in [(0.0, 1.0), (-3.5, 2.5), (1.0, 1.5)]: + u = _dv_from_weighted_samples([a], [1.0]) + v = _dv_from_weighted_samples([b], [1.0]) + self.assertAlmostEqual( + wasserstein_2_uxhw_wrapper(u, v), + abs(a - b), + places=12, + msg=f"a={a}, b={b}", + ) + + def test_w2_geq_w1(self) -> None: + """W2 ≥ W1 for any pair of distributions (Hölder).""" + rng = np.random.default_rng(seed=11111) + u_pos = np.sort(rng.standard_normal(50)) + v_pos = np.sort(rng.standard_normal(50) + 0.5) + u = _dv_from_weighted_samples(list(u_pos), [1.0 / 50] * 50) + v = _dv_from_weighted_samples(list(v_pos), [1.0 / 50] * 50) + w1 = wasserstein_1_uxhw_wrapper(u, v) + w2 = wasserstein_2_uxhw_wrapper(u, v) + self.assertGreaterEqual(w2, w1 - 1e-12) + + +class TestGenericWassersteinP(unittest.TestCase): + """`wasserstein_p_uxhw_wrapper` and `normalized_wasserstein_p_uxhw_wrapper` + are the generic surfaces; the W1 / W2 (+ normalised) wrappers are + thin delegates. Verify delegation parity for p in {1, 2} and that + the generic accepts non-canonical p without crashing.""" + + def _pair(self) -> tuple[DistributionalValue, DistributionalValue]: + u = _dv_from_weighted_samples([-1.0, 0.5, 2.5, 4.0], [0.1, 0.4, 0.3, 0.2]) + v = _dv_from_weighted_samples([-0.5, 1.0, 3.0], [0.25, 0.5, 0.25]) + return u, v + + def test_p1_matches_w1_wrapper(self) -> None: + """wasserstein_p_uxhw_wrapper(u, v, p=1) == wasserstein_1_uxhw_wrapper(u, v).""" + u, v = self._pair() + self.assertAlmostEqual( + wasserstein_p_uxhw_wrapper(u, v, p=1), + wasserstein_1_uxhw_wrapper(u, v), + places=12, + ) + + def test_p2_matches_w2_wrapper(self) -> None: + """wasserstein_p_uxhw_wrapper(u, v, p=2) == wasserstein_2_uxhw_wrapper(u, v).""" + u, v = self._pair() + self.assertAlmostEqual( + wasserstein_p_uxhw_wrapper(u, v, p=2), + wasserstein_2_uxhw_wrapper(u, v), + places=12, + ) + + def test_non_canonical_p_runs(self) -> None: + """p=3 produces a finite, non-negative number. Guards against + the kernel rejecting integers outside {1, 2} or downstream + overflow on cubed differences.""" + u, v = self._pair() + distance = wasserstein_p_uxhw_wrapper(u, v, p=3) + self.assertTrue(math.isfinite(distance)) + self.assertGreaterEqual(distance, 0.0) + + def test_normalized_p1_matches_normalized_w1_wrapper(self) -> None: + """Delegation parity for the normalised variant at p=1.""" + u, v = self._pair() + self.assertAlmostEqual( + normalized_wasserstein_p_uxhw_wrapper(u, v, p=1), + normalized_wasserstein_1_uxhw_wrapper(u, v), + places=12, + ) + + def test_normalized_p2_matches_normalized_w2_wrapper(self) -> None: + """Delegation parity for the normalised variant at p=2.""" + u, v = self._pair() + self.assertAlmostEqual( + normalized_wasserstein_p_uxhw_wrapper(u, v, p=2), + normalized_wasserstein_2_uxhw_wrapper(u, v), + places=12, + ) + + +class TestNormalizedWasserstein(unittest.TestCase): + """Tests for normalized_wasserstein_{1,2}_uxhw_wrapper.""" + + def test_normalized_w1_scales_by_gt_range(self) -> None: + """Normalised W1 = W1 / (gt.max - gt.min) when the range is + nonzero.""" + u = _dv_from_weighted_samples([0.0, 4.0, 8.0], [0.3, 0.4, 0.3]) + ground_truth = _dv_from_weighted_samples([-1.0, 9.0], [0.5, 0.5]) + raw = wasserstein_1_uxhw_wrapper(u, ground_truth) + normalised = normalized_wasserstein_1_uxhw_wrapper(u, ground_truth) + expected = raw / (9.0 - (-1.0)) + self.assertAlmostEqual(normalised, expected, places=12) + + def test_normalized_w2_scales_by_gt_range(self) -> None: + """Normalised W2 = W2 / (gt.max - gt.min) when the range is + nonzero.""" + u = _dv_from_weighted_samples([0.0, 4.0, 8.0], [0.3, 0.4, 0.3]) + ground_truth = _dv_from_weighted_samples([-1.0, 9.0], [0.5, 0.5]) + raw = wasserstein_2_uxhw_wrapper(u, ground_truth) + normalised = normalized_wasserstein_2_uxhw_wrapper(u, ground_truth) + expected = raw / (9.0 - (-1.0)) + self.assertAlmostEqual(normalised, expected, places=12) + + def test_normalized_w1_zero_range_fallback(self) -> None: + """When the ground-truth support is a single point, the + normalising factor falls back to 1.0 — so normalised == raw.""" + u = _dv_from_weighted_samples([2.0, 4.0], [0.5, 0.5]) + ground_truth = _dv_from_weighted_samples([3.0], [1.0]) + raw = wasserstein_1_uxhw_wrapper(u, ground_truth) + normalised = normalized_wasserstein_1_uxhw_wrapper(u, ground_truth) + self.assertAlmostEqual(normalised, raw, places=12) + + +class TestWeightedPairValidation(unittest.TestCase): + """Regression tests for input validation in _wp_1d_weighted_pair. + + DistributionalValue does NOT enforce these invariants (special + values like NaN/Inf are first-class via nan_dirac_delta etc.), so + the helper must reject them itself or it silently returns + nan/inf/wrong-but-plausible numbers. + """ + + def _good_v(self) -> DistributionalValue: + return _dv_from_weighted_samples([1.0, 2.0, 3.0], [0.3, 0.4, 0.3]) + + def test_non_finite_position_rejected(self) -> None: + """NaN / +inf / -inf positions are rejected by the finite check.""" + for label, positions in ( + ("NaN", [1.0, 2.0, np.nan]), + ("+inf", [1.0, 2.0, np.inf]), + ("-inf", [-np.inf, 2.0, 3.0]), + ): + with self.subTest(special=label): + u = _dv_from_weighted_samples(positions, [0.3, 0.4, 0.3]) + with self.assertRaises(ValueError) as ctx: + wasserstein_1_uxhw_wrapper(u, self._good_v()) + self.assertIn("finite", str(ctx.exception)) + + def test_bad_masses_rejected(self) -> None: + """All-zero / NaN masses each hit a distinct branch of + `_validate_wp_inputs` with a distinct error message. + + Negative-mass rejection lives in + TestDistributionalValueInitMassValidation — DistributionalValue + rejects negative masses at construction, so they can't reach + `_validate_wp_inputs` through a DV-shaped input. The validator's + non-negative check is still reachable for direct array callers + of `_wp_1d_weighted_pair`.""" + cases = ( + ("all-zero", [0.0, 0.0, 0.0], "positive total mass"), + ("nan", [np.nan, 0.5, 0.5], "finite"), + ) + for label, masses, expected in cases: + with self.subTest(case=label): + u = _dv_from_weighted_samples([1.0, 2.0, 3.0], masses) + with self.assertRaises(ValueError) as ctx: + wasserstein_1_uxhw_wrapper(u, self._good_v()) + self.assertIn(expected, str(ctx.exception)) + + def test_ground_truth_side_validated_too(self) -> None: + """Validation triggers symmetrically — v_values also pass through + `_validate_wp_inputs` and reject NaN.""" + v = _dv_from_weighted_samples([1.0, 2.0, np.nan], [0.3, 0.4, 0.3]) + with self.assertRaises(ValueError): + wasserstein_1_uxhw_wrapper(self._good_v(), v) + + def test_helper_rejects_empty_arrays(self) -> None: + """Direct call: empty positions are rejected at the helper.""" + with self.assertRaises(ValueError) as ctx: + _wp_1d_weighted_pair( + u_positions=np.array([]), + u_masses=np.array([]), + v_positions=np.array([1.0]), + v_masses=np.array([1.0]), + p=1, + ) + self.assertIn("non-empty", str(ctx.exception)) + + def test_helper_rejects_mismatched_lengths(self) -> None: + with self.assertRaises(ValueError) as ctx: + _wp_1d_weighted_pair( + u_positions=np.array([1.0, 2.0, 3.0]), + u_masses=np.array([0.5, 0.5]), + v_positions=np.array([1.0]), + v_masses=np.array([1.0]), + p=1, + ) + self.assertIn("matching lengths", str(ctx.exception)) + + def test_helper_rejects_bad_p(self) -> None: + for bad_p in (0, -1, 1.5, "1"): + with self.assertRaises(ValueError): + _wp_1d_weighted_pair( + u_positions=np.array([1.0]), + u_masses=np.array([1.0]), + v_positions=np.array([2.0]), + v_masses=np.array([1.0]), + p=bad_p, # type: ignore[arg-type] + ) + + def test_helper_rejects_bool_p(self) -> None: + """`bool` is a subclass of `int`, so `p=True` would otherwise + slip through `isinstance(p, int)`. The validator rejects it + explicitly so callers don't silently get `p=1`.""" + for bad_p in (True, False): + with self.assertRaises(ValueError): + _wp_1d_weighted_pair( + u_positions=np.array([1.0]), + u_masses=np.array([1.0]), + v_positions=np.array([2.0]), + v_masses=np.array([1.0]), + p=bad_p, + ) + + def test_helper_rejects_2d_arrays(self) -> None: + with self.assertRaises(ValueError) as ctx: + _wp_1d_weighted_pair( + u_positions=np.array([[1.0, 2.0]]), + u_masses=np.array([[0.5, 0.5]]), + v_positions=np.array([1.0]), + v_masses=np.array([1.0]), + p=1, + ) + self.assertIn("one-dimensional", str(ctx.exception)) + + def test_helper_rejects_float_p(self) -> None: + """`p=1.5` is not an int and must be rejected with a message + identifying the offending parameter.""" + with self.assertRaises(ValueError) as ctx: + _wp_1d_weighted_pair( + u_positions=np.array([1.0]), + u_masses=np.array([1.0]), + v_positions=np.array([2.0]), + v_masses=np.array([1.0]), + p=1.5, # type: ignore[arg-type] + ) + self.assertIn("p", str(ctx.exception)) + + +class TestWrapperTypeValidation(unittest.TestCase): + """`_require_distributional_pair` rejects non-DistributionalValue + arguments before any algorithmic work happens. Exercised here for + each of the four public uxhw wrappers.""" + + def _good_dv(self) -> DistributionalValue: + return _dv_from_weighted_samples([1.0, 2.0, 3.0], [0.3, 0.4, 0.3]) + + def test_all_wrappers_reject_non_dv(self) -> None: + """All four uxhw wrappers funnel through + `_require_distributional_pair`. Exercise each one × each side + with a distinct non-DV stand-in so a future refactor that + bypassed the helper in any single wrapper would be caught. + + Message-format coverage (which argument name appears, which type + name, etc.) lives in `_validators_test.py`; here we just verify + the wrapper raises `ValueError` mentioning the expected type.""" + good = self._good_dv() + wrappers = ( + ("wasserstein_1_uxhw_wrapper", wasserstein_1_uxhw_wrapper), + ( + "normalized_wasserstein_1_uxhw_wrapper", + normalized_wasserstein_1_uxhw_wrapper, + ), + ("wasserstein_2_uxhw_wrapper", wasserstein_2_uxhw_wrapper), + ( + "normalized_wasserstein_2_uxhw_wrapper", + normalized_wasserstein_2_uxhw_wrapper, + ), + ) + bad_stand_ins = ("not a dv", 42, None, [1.0, 2.0], np.array([1.0])) + for name, wrapper in wrappers: + for bad in bad_stand_ins: + for side, args in ( + ("first", (bad, good)), + ("second", (good, bad)), + ): + with self.subTest(wrapper=name, side=side, bad=type(bad).__name__): + with self.assertRaises(ValueError) as ctx: + wrapper(*args) + self.assertIn("DistributionalValue", str(ctx.exception)) + + def test_normalized_wrappers_reject_empty_dv(self) -> None: + """Regression: normalized wrappers used to call `.min()`/`.max()` + on `ground_truth.positions` BEFORE `_wp_1d_weighted_pair`'s + empty check, so an empty DistributionalValue produced an + opaque numpy reduction error instead of a clear ValueError. + Both sides routed through `_rescale_to_gt_support`'s explicit + non-empty check now.""" + empty = DistributionalValue(dirac_deltas=[]) + good = self._good_dv() + for wrapper in ( + normalized_wasserstein_1_uxhw_wrapper, + normalized_wasserstein_2_uxhw_wrapper, + ): + for side, uxhw, gt in ( + ("uxhw", empty, good), + ("ground_truth", good, empty), + ): + with self.subTest(wrapper=wrapper.__name__, side=side): + with self.assertRaises(ValueError) as ctx: + wrapper(uxhw, gt) + self.assertIn("non-empty", str(ctx.exception)) + + +class TestLegacyHelperValidation(unittest.TestCase): + """`wasserstein_1_distance_with_weights` is a legacy public helper + that previously crashed with IndexError on empty `v_cum_weights` + (line: `v_cum_weights[-1]`). Now raises ValueError up-front.""" + + def test_empty_v_cum_weights_rejected(self) -> None: + with self.assertRaises(ValueError) as ctx: + wasserstein_1_distance_with_weights( + u_values=np.array([1.0, 2.0]), + v_values=np.array([]), + v_cum_weights=np.array([]), + all_values=np.array([1.0, 2.0]), + ) + self.assertIn("v_cum_weights", str(ctx.exception)) + + def test_empty_u_values_rejected(self) -> None: + with self.assertRaises(ValueError) as ctx: + wasserstein_1_distance_with_weights( + u_values=np.array([]), + v_values=np.array([1.0, 2.0]), + v_cum_weights=np.cumsum(np.array([0.5, 0.5])), + all_values=np.array([1.0, 2.0]), + ) + self.assertIn("u_values", str(ctx.exception)) + + def test_v_values_v_cum_weights_length_mismatch_rejected(self) -> None: + """Regression: mismatched lengths previously let v_idx exceed + len(v_cum_weights) and raise IndexError mid-loop.""" + with self.assertRaises(ValueError) as ctx: + wasserstein_1_distance_with_weights( + u_values=np.array([1.0]), + v_values=np.array([1.0, 2.0, 3.0]), + v_cum_weights=np.cumsum(np.array([0.5, 0.5])), # length 2 vs 3 + all_values=np.array([1.0, 1.0, 2.0, 3.0]), + ) + self.assertIn("same length", str(ctx.exception)) + + def test_zero_v_total_weight_rejected(self) -> None: + """v_cum_weights[-1] == 0 would cause a divide-by-zero NaN.""" + with self.assertRaises(ValueError) as ctx: + wasserstein_1_distance_with_weights( + u_values=np.array([1.0, 2.0]), + v_values=np.array([1.0, 2.0]), + v_cum_weights=np.cumsum(np.array([0.0, 0.0])), + all_values=np.array([1.0, 1.0, 2.0, 2.0]), + ) + self.assertIn("strictly positive", str(ctx.exception)) + + def test_wasserstein_1_distance_rejects_empty(self) -> None: + """Regression: `wasserstein_1_distance` divides by + `len(u_values)` / `len(v_values)` — empty inputs previously + raised an opaque ZeroDivisionError. Now raises ValueError + with the offending parameter name, matching the + `_with_weights` sibling.""" + for label, u, v in ( + ("empty u_values", np.array([]), np.array([1.0, 2.0])), + ("empty v_values", np.array([1.0, 2.0]), np.array([])), + ): + with self.subTest(case=label): + all_vals = np.sort(np.concatenate([u, v])) + with self.assertRaises(ValueError) as ctx: + wasserstein_1_distance(u_values=u, v_values=v, all_values=all_vals) + expected = "u_values" if "u_values" in label else "v_values" + self.assertIn(expected, str(ctx.exception)) + + +if __name__ == "__main__": + unittest.main() diff --git a/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py b/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py index 8901527..33008c3 100644 --- a/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py +++ b/src/signaloid/distributional_information_plotting/plot_histogram_dirac_deltas.py @@ -483,7 +483,7 @@ def _bin_pdf_expected_dirac_delta( return expected_dirac_delta @staticmethod - def _bin_pdf_to_ttr( + def bin_pdf_to_ttr( boundary_positions: np.ndarray, bin_widths: np.ndarray, bin_heights: np.ndarray, @@ -492,6 +492,11 @@ def _bin_pdf_to_ttr( """ Computes TTR for an input bin PDF. + For an input bin PDF with N bins, the shapes are: + ``len(boundary_positions) == N + 1`` + ``len(bin_widths) == N`` + ``len(bin_heights) == N`` + Args: boundary_positions: Positions of the bin boundaries of the input bin PDF. bin_widths: Widths of the bins of the input bin PDF. @@ -545,10 +550,10 @@ def _bin_pdf_to_ttr( high_bin_heights = bin_heights[i - 1 :] break - ttr += PlotData._bin_pdf_to_ttr( + ttr += PlotData.bin_pdf_to_ttr( low_boundary_positions, low_bin_widths, low_bin_heights, order - 1 ) - ttr += PlotData._bin_pdf_to_ttr( + ttr += PlotData.bin_pdf_to_ttr( high_boundary_positions, high_bin_widths, high_bin_heights, order - 1 ) @@ -609,7 +614,7 @@ def _construct_plot_data(self) -> None: ) # Find the TTR of the created binning. This is always a valid TTR. - ttr = PlotData._bin_pdf_to_ttr( + ttr = PlotData.bin_pdf_to_ttr( boundary_positions, bin_widths, bin_heights, diff --git a/src/signaloid/distributional_information_plotting/sample_generator.py b/src/signaloid/distributional_information_plotting/sample_generator.py index 254b71d..019297b 100644 --- a/src/signaloid/distributional_information_plotting/sample_generator.py +++ b/src/signaloid/distributional_information_plotting/sample_generator.py @@ -38,7 +38,7 @@ def sample_generator(ux_data: str, n_samples: int) -> np.ndarray: Parse a Ux-encoded string and generate samples from the resulting distribution. Args: - ux_data: A Ux-string or Ux-bytes encoding a distributional value. + ux_data: A Ux String or Ux Binary Data encoding a distributional value. n_samples: Number of samples to generate. Returns: diff --git a/src/signaloid/statistical_tests/README.md b/src/signaloid/statistical_tests/README.md new file mode 100644 index 0000000..452ba07 --- /dev/null +++ b/src/signaloid/statistical_tests/README.md @@ -0,0 +1,78 @@ +# Statistical Tests + +Hypothesis tests for comparing Signaloid `DistributionalValue` instances. + + +## Bootstrapped Kolmogorov-Smirnov test + +Bootstrapped KS goodness-of-fit test. Draws `bootstrap_sample_size` samples from the discrete representation, runs a one-sample KS test against the true CDF, repeats `number_of_bootstraps` times, and combines the per-bootstrap p-values with Fisher's method. Returns `(accept_hypothesis, combined_p_value)`, where the hypothesis is accepted when the combined p-value is at least `significance_level`. + +The `_wrapper` form takes two `DistributionalValue`s and uses the reference's empirical `.cdf`; the core form takes any callable CDF (e.g. an analytic `scipy.stats` CDF). Pass a seeded `rng` for reproducibility. + +```python +import numpy as np +from scipy.stats import norm +from signaloid.distributional.distributional import DistributionalValue +from signaloid.statistical_tests import ( + bootstrapped_kolmogorov_smirnov, + bootstrapped_kolmogorov_smirnov_wrapper, +) + +rng = np.random.default_rng(seed=42) +discrete = DistributionalValue.from_samples(rng.standard_normal(1000)) +reference = DistributionalValue.from_samples(rng.standard_normal(10000)) + +# Against another DistributionalValue's empirical CDF +accept, p_value = bootstrapped_kolmogorov_smirnov_wrapper( + discrete, + reference, + bootstrap_sample_size=128, + number_of_bootstraps=50, + significance_level=0.05, + rng=rng, +) + +# Against an analytic CDF callable +accept, p_value = bootstrapped_kolmogorov_smirnov( + discrete, + norm.cdf, + bootstrap_sample_size=128, + number_of_bootstraps=50, + significance_level=0.05, + rng=rng, +) +``` + +## One-sample Kolmogorov-Smirnov test + +Test whether an observed `sample` is consistent with a reference `DistributionalValue`'s empirical CDF at the given significance level. Accepts a `list[float]` or an `np.ndarray`. Returns `True` when the p-value is at least `significance_level`. + +```python +from signaloid.statistical_tests import kolmogorov_smirnov_wrapper + +accept = kolmogorov_smirnov_wrapper( + sample=[0.1, 0.3, 0.5, 0.7, 0.9], + true_distribution=reference, + significance_level=0.05, +) +``` + +## CLI usage + +`ks_hypothesis.py` exposes a `python -m …` entry point that parses two Ux strings, runs a KS hypothesis test at the given significance level, prints the verdict, and exits non-zero when the null hypothesis is rejected. + +```bash +# Bootstrapped KS test (default) +python -m signaloid.statistical_tests.ks_hypothesis \ + \ + [--bootstrap-sample-size N] [--number-of-bootstraps M] [--seed S] + +# One-sample KS test (uses the first distribution's support positions +# as the observed sample) +python -m signaloid.statistical_tests.ks_hypothesis \ + --test one-sample +``` + +> **Note:** Ux strings with a leading `-` (e.g. `-0.0Ux…`) get parsed by `argparse` as flags. Place any options (`--test`, `--seed`, …) *before* the positional arguments, or use the `--` separator before the leading-minus Ux string. + +> **Note:** The Kolmogorov-Smirnov *distance* (sup-norm between two empirical CDFs) is a distance metric rather than a hypothesis test, and lives in `signaloid.distributional_distance.ks_distance`. diff --git a/src/signaloid/statistical_tests/__init__.py b/src/signaloid/statistical_tests/__init__.py new file mode 100644 index 0000000..01b9b98 --- /dev/null +++ b/src/signaloid/statistical_tests/__init__.py @@ -0,0 +1,31 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +from signaloid.statistical_tests.ks_hypothesis import ( + bootstrapped_kolmogorov_smirnov, + bootstrapped_kolmogorov_smirnov_wrapper, + kolmogorov_smirnov_wrapper, +) + +__all__ = [ + "bootstrapped_kolmogorov_smirnov", + "bootstrapped_kolmogorov_smirnov_wrapper", + "kolmogorov_smirnov_wrapper", +] diff --git a/src/signaloid/statistical_tests/ks_hypothesis.py b/src/signaloid/statistical_tests/ks_hypothesis.py new file mode 100644 index 0000000..9172107 --- /dev/null +++ b/src/signaloid/statistical_tests/ks_hypothesis.py @@ -0,0 +1,257 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +import argparse +import sys +from typing import Any, Callable + +import numpy as np +from scipy.stats import chi2, ks_1samp # type: ignore[import-untyped] + +from signaloid.distributional.distributional import DistributionalValue + +CdfFunction = Callable[[Any], Any] + + +def bootstrapped_kolmogorov_smirnov( + discrete_representation: DistributionalValue, + true_cdf: CdfFunction, + bootstrap_sample_size: int, + number_of_bootstraps: int, + significance_level: float, + rng: np.random.Generator | None = None, +) -> tuple[bool, float]: + """Bootstrapped Kolmogorov-Smirnov goodness-of-fit test. + + Args: + discrete_representation: Discrete approximation of the target + distribution. + true_cdf: Callable CDF of the true continuous distribution. + bootstrap_sample_size: Number of samples drawn per bootstrap. + number_of_bootstraps: How many bootstrap iterations to run. + significance_level: Threshold below which the hypothesis is + rejected. + rng: Optional generator for reproducibility. + + Returns: + Tuple ``(accept_hypothesis, combined_p_value)``. + """ + if bootstrap_sample_size <= 0: + raise ValueError("bootstrap_sample_size must be greater than 0.") + if number_of_bootstraps <= 0: + raise ValueError("number_of_bootstraps must be greater than 0.") + if significance_level < 0.0 or significance_level > 1.0: + raise ValueError("significance_level must be in [0, 1].") + if rng is None: + rng = np.random.default_rng() + + positions = discrete_representation.positions + masses = discrete_representation.masses + total_mass = float(np.sum(masses)) + if total_mass <= 0.0: + raise ValueError( + "discrete_representation must have a strictly positive total " + "mass to sample from." + ) + # Zero-mass deltas (including NaN/Inf placeholders) carry no + # probability; sample only from the positive-mass support and require + # those positions to be finite so rng.choice / ks_1samp get usable + # values instead of producing NaN probabilities or NaN p-values. + positive_mass = masses > 0.0 + positions = positions[positive_mass] + masses = masses[positive_mass] + if not np.all(np.isfinite(positions)): + raise ValueError( + "discrete_representation must have finite positions for all " + "positive-mass Dirac deltas." + ) + normalised_masses = masses / total_mass + + p_values = np.empty(number_of_bootstraps) + for i in range(number_of_bootstraps): + sample = rng.choice(positions, size=bootstrap_sample_size, p=normalised_masses) + result = ks_1samp(sample, true_cdf) + p_values[i] = result.pvalue + + # Fisher's method: combine p-values via -2 Σ log(p_i) ~ chi²(2k). + clipped_p_values = np.maximum(p_values, np.finfo(float).tiny) + fisher_statistic = -2.0 * float(np.sum(np.log(clipped_p_values))) + degrees_of_freedom = 2 * number_of_bootstraps + combined_p_value = 1.0 - float(chi2.cdf(fisher_statistic, df=degrees_of_freedom)) + return combined_p_value >= significance_level, combined_p_value + + +def bootstrapped_kolmogorov_smirnov_wrapper( + discrete_representation: DistributionalValue, + true_distribution: DistributionalValue, + bootstrap_sample_size: int, + number_of_bootstraps: int, + significance_level: float, + rng: np.random.Generator | None = None, +) -> tuple[bool, float]: + """Bootstrapped KS test between two DistributionalValues. + + Args: + discrete_representation: Discrete approximation under test. + true_distribution: Reference DistributionalValue. + bootstrap_sample_size: Number of samples drawn per bootstrap. + number_of_bootstraps: How many bootstrap iterations to run. + significance_level: Threshold below which the hypothesis is + rejected. + rng: Optional generator for reproducibility. + + Returns: + Tuple ``(accept_hypothesis, combined_p_value)``. + + Raises: + ValueError: if either argument is not a DistributionalValue. + """ + if not isinstance(discrete_representation, DistributionalValue): + raise ValueError( + f"discrete_representation is of type " + f"{type(discrete_representation).__name__} and not an " + "instance of DistributionalValue." + ) + if not isinstance(true_distribution, DistributionalValue): + raise ValueError( + f"true_distribution is of type " + f"{type(true_distribution).__name__} and not an " + "instance of DistributionalValue." + ) + return bootstrapped_kolmogorov_smirnov( + discrete_representation=discrete_representation, + true_cdf=true_distribution.cdf, + bootstrap_sample_size=bootstrap_sample_size, + number_of_bootstraps=number_of_bootstraps, + significance_level=significance_level, + rng=rng, + ) + + +def kolmogorov_smirnov_wrapper( + sample: list[float] | np.ndarray, + true_distribution: DistributionalValue, + significance_level: float, +) -> bool: + """One-sample Kolmogorov-Smirnov test against a DistributionalValue. + + Args: + sample: Observed sample. + true_distribution: Reference DistributionalValue whose empirical + CDF defines the null hypothesis. + significance_level: Threshold below which the hypothesis is + rejected. + + Returns: + ``True`` when the p-value is at least the significance level. + + Raises: + ValueError: if ``true_distribution`` is not a DistributionalValue. + """ + if not isinstance(true_distribution, DistributionalValue): + raise ValueError( + f"true_distribution is of type " + f"{type(true_distribution).__name__} and not an " + "instance of DistributionalValue." + ) + if significance_level < 0.0 or significance_level > 1.0: + raise ValueError("significance_level must be in [0, 1].") + p_value = float(ks_1samp(sample, true_distribution.cdf).pvalue) + return p_value >= significance_level + + +if __name__ == "__main__": + parser = argparse.ArgumentParser( + prog="python -m signaloid.statistical_tests.ks_hypothesis", + description=( + "Run a Kolmogorov-Smirnov hypothesis test between two ux " + "strings at a given significance level." + ), + ) + parser.add_argument("dist_ux", help="ux string for the distribution under test") + parser.add_argument("reference_ux", help="ux string for the reference distribution") + parser.add_argument("significance_level", type=float) + parser.add_argument( + "--test", + choices=["bootstrapped", "one-sample"], + default="bootstrapped", + help="which KS hypothesis test to run (default: bootstrapped)", + ) + parser.add_argument( + "--bootstrap-sample-size", + type=int, + default=128, + help="samples drawn per bootstrap (bootstrapped only; default: 128)", + ) + parser.add_argument( + "--number-of-bootstraps", + type=int, + default=50, + help="number of bootstrap iterations (bootstrapped only; default: 50)", + ) + parser.add_argument( + "--seed", + type=int, + default=None, + help="RNG seed for reproducibility (bootstrapped only)", + ) + args = parser.parse_args() + + dist = DistributionalValue.parse(args.dist_ux) + if dist is None: + raise ValueError(f"Could not parse distribution from ux string {args.dist_ux}") + reference = DistributionalValue.parse(args.reference_ux) + if reference is None: + raise ValueError( + f"Could not parse reference from ux string {args.reference_ux}" + ) + + if args.test == "bootstrapped": + accept, p_value = bootstrapped_kolmogorov_smirnov_wrapper( + discrete_representation=dist, + true_distribution=reference, + bootstrap_sample_size=args.bootstrap_sample_size, + number_of_bootstraps=args.number_of_bootstraps, + significance_level=args.significance_level, + rng=np.random.default_rng(args.seed), + ) + detail = f"Combined p-value: {p_value}" + else: + # The one-sample test takes a raw sample; use the support positions + # of the first distribution as the observed sample. + accept = kolmogorov_smirnov_wrapper( + sample=dist.positions, + true_distribution=reference, + significance_level=args.significance_level, + ) + detail = "One-sample test on the first distribution's positions." + + label = f"KS {args.test} test" + if accept: + print( + f"[SUCCESS] {label}: null hypothesis accepted at significance " + f"{args.significance_level}. {detail}" + ) + else: + print( + f"[FAILURE] {label}: null hypothesis rejected at significance " + f"{args.significance_level}. {detail}" + ) + sys.exit(0 if accept else 1) diff --git a/src/signaloid/statistical_tests/ks_hypothesis_test.py b/src/signaloid/statistical_tests/ks_hypothesis_test.py new file mode 100644 index 0000000..937444d --- /dev/null +++ b/src/signaloid/statistical_tests/ks_hypothesis_test.py @@ -0,0 +1,257 @@ +# Copyright (c) 2026, Signaloid. +# +# Permission is hereby granted, free of charge, to any person obtaining a copy +# of this software and associated documentation files (the "Software"), to +# deal in the Software without restriction, including without limitation the +# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +# sell copies of the Software, and to permit persons to whom the Software is +# furnished to do so, subject to the following conditions: +# +# The above copyright notice and this permission notice shall be included in +# all copies or substantial portions of the Software. +# +# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +# DEALINGS IN THE SOFTWARE. + +import unittest + +import numpy as np +from scipy.stats import uniform # type: ignore[import-untyped] + +from signaloid.distributional.dirac_delta import DiracDelta +from signaloid.distributional.distributional import DistributionalValue +from signaloid.statistical_tests.ks_hypothesis import ( + bootstrapped_kolmogorov_smirnov, + bootstrapped_kolmogorov_smirnov_wrapper, + kolmogorov_smirnov_wrapper, +) + + +class TestBootstrappedKolmogorovSmirnov(unittest.TestCase): + def test_bootstrapped_ks_returns_valid_pvalue(self) -> None: + """Combined p-value lies in [0, 1] across a TTR-order sweep.""" + min_ttr_order = 5 + max_ttr_order = 11 + uniform_ttr_positions = [ + [(2 * i - 1) / (2 ** (n + 1)) for i in range(1, 2**n + 1)] + for n in range(min_ttr_order, max_ttr_order) + ] + distributions: list[DistributionalValue] = [] + for ttr_positions in uniform_ttr_positions: + uniform_mass = 1 / len(ttr_positions) + d = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=float(p), mass=uniform_mass) + for p in ttr_positions + ] + ) + distributions.append(d) + + bootstrap_sample_sizes = [ + 2 ** (i - 1) for i in range(min_ttr_order, max_ttr_order) + ] + number_of_bootstrap_samples = 10 + significance_levels = [1 / i for i in range(min_ttr_order, max_ttr_order)] + + rng = np.random.default_rng(seed=42) + for i in range(max_ttr_order - min_ttr_order): + with self.subTest(ttr_order=min_ttr_order + i): + _, pvalue = bootstrapped_kolmogorov_smirnov( + discrete_representation=distributions[i], + true_cdf=uniform.cdf, + bootstrap_sample_size=bootstrap_sample_sizes[i], + number_of_bootstraps=number_of_bootstrap_samples, + significance_level=significance_levels[i], + rng=rng, + ) + self.assertGreaterEqual(pvalue, 0.0) + self.assertLessEqual(pvalue, 1.0) + + def test_bootstrapped_ks_is_reproducible_with_seeded_rng(self) -> None: + """Same seed → identical p-values.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=(2 * i - 1) / 16, mass=1 / 8) for i in range(1, 9) + ] + ) + rng_a = np.random.default_rng(seed=12345) + rng_b = np.random.default_rng(seed=12345) + _, pvalue_a = bootstrapped_kolmogorov_smirnov( + discrete_representation=dist, + true_cdf=uniform.cdf, + bootstrap_sample_size=64, + number_of_bootstraps=5, + significance_level=0.05, + rng=rng_a, + ) + _, pvalue_b = bootstrapped_kolmogorov_smirnov( + discrete_representation=dist, + true_cdf=uniform.cdf, + bootstrap_sample_size=64, + number_of_bootstraps=5, + significance_level=0.05, + rng=rng_b, + ) + self.assertAlmostEqual(pvalue_a, pvalue_b, places=12) + + +class TestBootstrappedKolmogorovSmirnovValidation(unittest.TestCase): + """`bootstrapped_kolmogorov_smirnov` rejects unusable representations + with a clear ValueError instead of producing NaN p-values.""" + + def _run(self, dist: DistributionalValue) -> tuple[bool, float]: + return bootstrapped_kolmogorov_smirnov( + discrete_representation=dist, + true_cdf=uniform.cdf, + bootstrap_sample_size=8, + number_of_bootstraps=3, + significance_level=0.05, + rng=np.random.default_rng(seed=0), + ) + + def test_rejects_empty_distribution(self) -> None: + """No Dirac deltas → zero total mass → ValueError.""" + with self.assertRaises(ValueError): + self._run(DistributionalValue(dirac_deltas=[])) + + def test_rejects_all_zero_mass(self) -> None: + """Zero total mass → ValueError.""" + with self.assertRaises(ValueError): + self._run( + DistributionalValue(dirac_deltas=[DiracDelta(position=1.0, mass=0.0)]) + ) + + def test_rejects_non_finite_positive_mass_position(self) -> None: + """A positive-mass Inf position is not sampleable → ValueError.""" + with self.assertRaises(ValueError): + self._run( + DistributionalValue( + dirac_deltas=[ + DiracDelta(position=0.5, mass=0.5), + DiracDelta(position=float("inf"), mass=0.5), + ] + ) + ) + + def test_ignores_zero_mass_placeholder(self) -> None: + """A zero-mass NaN placeholder is dropped, not rejected.""" + dist = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=0.25, mass=0.5), + DiracDelta(position=0.75, mass=0.5), + DiracDelta(position=float("nan"), mass=0.0), + ] + ) + accept, p_value = self._run(dist) + self.assertIsInstance(accept, bool) + self.assertGreaterEqual(p_value, 0.0) + self.assertLessEqual(p_value, 1.0) + + +class TestBootstrappedKolmogorovSmirnovWrapper(unittest.TestCase): + def test_wrapper_matches_core_when_called_with_same_inputs(self) -> None: + """Wrapper(d, d_true) == core(d, d_true.cdf) for the same RNG.""" + d = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=p, mass=0.2) for p in (0.1, 0.3, 0.5, 0.7, 0.9) + ] + ) + d_true = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=(2 * i - 1) / 16, mass=1 / 8) for i in range(1, 9) + ] + ) + rng_a = np.random.default_rng(seed=99) + rng_b = np.random.default_rng(seed=99) + _, p_wrapper = bootstrapped_kolmogorov_smirnov_wrapper( + discrete_representation=d, + true_distribution=d_true, + bootstrap_sample_size=32, + number_of_bootstraps=5, + significance_level=0.05, + rng=rng_a, + ) + _, p_core = bootstrapped_kolmogorov_smirnov( + discrete_representation=d, + true_cdf=d_true.cdf, + bootstrap_sample_size=32, + number_of_bootstraps=5, + significance_level=0.05, + rng=rng_b, + ) + self.assertAlmostEqual(p_wrapper, p_core, places=12) + + def test_wrapper_rejects_non_distributional_value_inputs(self) -> None: + """Non-DistributionalValue on either side raises ValueError.""" + good = DistributionalValue(dirac_deltas=[DiracDelta(position=0.5, mass=1.0)]) + with self.assertRaises(ValueError) as ctx: + bootstrapped_kolmogorov_smirnov_wrapper( + discrete_representation="not a DV", # type: ignore[arg-type] + true_distribution=good, + bootstrap_sample_size=10, + number_of_bootstraps=3, + significance_level=0.05, + ) + self.assertIn("discrete_representation", str(ctx.exception)) + self.assertIn("DistributionalValue", str(ctx.exception)) + + with self.assertRaises(ValueError) as ctx: + bootstrapped_kolmogorov_smirnov_wrapper( + discrete_representation=good, + true_distribution=42, # type: ignore[arg-type] + bootstrap_sample_size=10, + number_of_bootstraps=3, + significance_level=0.05, + ) + self.assertIn("true_distribution", str(ctx.exception)) + self.assertIn("DistributionalValue", str(ctx.exception)) + + +class TestKolmogorovSmirnovWrapper(unittest.TestCase): + def test_accepts_list_float_sample_input(self) -> None: + """Accepts list[float] sample, not just np.ndarray.""" + d_true = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=(2 * i - 1) / 16, mass=1 / 8) for i in range(1, 9) + ] + ) + result = kolmogorov_smirnov_wrapper( + sample=[0.1, 0.3, 0.5, 0.7, 0.9], + true_distribution=d_true, + significance_level=0.05, + ) + self.assertIsInstance(result, bool) + + def test_returns_bool(self) -> None: + """Return type is a plain bool, not np.bool_.""" + d_true = DistributionalValue( + dirac_deltas=[ + DiracDelta(position=(2 * i - 1) / 16, mass=1 / 8) for i in range(1, 9) + ] + ) + rng = np.random.default_rng(seed=7) + sample = rng.uniform(size=100) + result = kolmogorov_smirnov_wrapper( + sample=sample, true_distribution=d_true, significance_level=0.05 + ) + self.assertIsInstance(result, bool) + + def test_rejects_non_distributional_value_true_distribution(self) -> None: + """true_distribution must be a DistributionalValue.""" + with self.assertRaises(ValueError) as ctx: + kolmogorov_smirnov_wrapper( + sample=[0.1, 0.2, 0.3], + true_distribution="not a DV", # type: ignore[arg-type] + significance_level=0.05, + ) + self.assertIn("true_distribution", str(ctx.exception)) + self.assertIn("DistributionalValue", str(ctx.exception)) + + +if __name__ == "__main__": + unittest.main() diff --git a/src/signaloid/uxdata_toolkit.py b/src/signaloid/uxdata_toolkit.py index 50d7224..d57419c 100644 --- a/src/signaloid/uxdata_toolkit.py +++ b/src/signaloid/uxdata_toolkit.py @@ -19,11 +19,11 @@ # DEALINGS IN THE SOFTWARE. """ -Signaloid UxData Toolkit +Signaloid Ux Data Toolkit -A set of tools for working with Signaloid Ux data. +Toolkit for working with Signaloid Ux Data. -Ux-string format specification: +Ux String format specification: - Particle value (double in string format) - "Ux" ( 2 chars) - Representation type (uint8_t) ( 2 chars) @@ -34,15 +34,28 @@ - Support position (float/double) (8/16 chars) - Probability mass (uint64_t) ( 16 chars) -Ux-bytes specification: - - Particle value (double) ( 8 bytes) - - Representation type (uint8_t) ( 1 byte ) - - Number of samples (uint64_t) ( 8 bytes) (unused) - - Mean value of distribution (double) ( 8 bytes) - - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) - - Pairs of: - - Support position (float/double) (4/8 bytes) - - Probability mass (uint64_t) ( 8 bytes) + Ux Binary specification: + For more information see https://docs.signaloid.io/docs/uxhw-api/ux-data-format/ + + Ux Binary Data Format: + - Particle value (double) ( 8 bytes) + - Representation type (uint32_t) ( 4 bytes) + - Number of samples (uint64_t) ( 8 bytes) (unused) + - Mean value of distribution (double) ( 8 bytes) + - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) + - Pairs of: + - Support position (float/double) (4/8 bytes) + - Probability mass (uint64_t) ( 8 bytes) + + Legacy format: + - Particle value (double) ( 8 bytes) + - Representation type (uint8_t) ( 1 byte ) + - Number of samples (uint64_t) ( 8 bytes) (unused) + - Mean value of distribution (double) ( 8 bytes) + - Number of non-zero mass Dirac deltas (uint32_t) ( 4 bytes) + - Pairs of: + - Support position (float/double) (4/8 bytes) + - Probability mass (uint64_t) ( 8 bytes) Requirements: - pip install git+https://github.com/signaloid/signaloid-python @@ -64,10 +77,10 @@ def _parse_ux_data(ux_data_raw: str) -> DistributionalValue: - """Validate, parse, and print info for a Ux-data string. + """Validate, parse, and print info for a Ux Data string. Args: - ux_data_raw: Raw Ux-string or Ux-bytes from CLI input. + ux_data_raw: Raw Ux String or Ux Binary from CLI input. Returns: The parsed DistributionalValue. @@ -82,18 +95,16 @@ def _parse_ux_data(ux_data_raw: str) -> DistributionalValue: print("Error: --ux-data cannot be an empty string.") sys.exit(1) - print("\nParsing Ux-data...") - dist_value = DistributionalValue.parse(ux_data) if dist_value is None: - raise ValueError("Failed to parse Ux-data into DistributionalValue.") + raise ValueError("Failed to parse Ux Data into DistributionalValue.") - print("Successfully parsed Ux-data!") + print("Parsed Ux Data:") print(f"Particle value: {dist_value.particle_value}") print(f"Mean: {dist_value.mean}") print(f"Variance: {dist_value.variance}") print(f"Number of Dirac deltas: {dist_value.UR_order}") - print(f"Double Precision: {dist_value.double_precision}") + print(f"Precision: {'64-bit' if dist_value.double_precision else '32-bit'}") return dist_value @@ -113,7 +124,7 @@ def _positive_int(value: str) -> int: def parse_arguments(argv: list[str] | None = None) -> argparse.Namespace: parser = argparse.ArgumentParser( - description="Set of tools for working with Signaloid Ux data." + description="Toolkit for working with Signaloid Ux Data." ) command_subparsers = parser.add_subparsers( @@ -131,8 +142,8 @@ def parse_arguments(argv: list[str] | None = None) -> argparse.Namespace: def command_plot_parser(command_subparsers: Any) -> None: plot_parser = command_subparsers.add_parser( "plot", - help="Plot Signaloid Ux distributional data", - description="Plot Signaloid Ux distributional data", + help="Plot Signaloid Ux Data distributional data", + description="Plot Signaloid Ux Data distributional data", formatter_class=argparse.RawDescriptionHelpFormatter, epilog=""" Example: @@ -153,27 +164,26 @@ def command_plot_parser(command_subparsers: Any) -> None: "--ux-data", type=str, required=True, - help='Ux-string or Ux-bytes to plot (e.g., "90.6Ux04000000...")', + help='Ux String or Ux Binary to plot (e.g., "90.6Ux04000000...")', ) plot_parser.set_defaults(func=command_plot) def command_plot(args: argparse.Namespace) -> None: - """Plot a Signaloid Ux distributional value. + """Plot a Signaloid Ux Data distributional value. Example usage: signaloid-uxdata-toolkit plot --ux-data=0.40007Ux000... signaloid-uxdata-toolkit plot -o output.png --ux-data=0.40007Ux000... """ - print("Signaloid Ux-data Plotter") + print("Signaloid Ux Data Plotter") print("=" * 50) try: dist_value = _parse_ux_data(args.ux_data) # Create PlotData object from the distributional value - print("\nPreparing plot data...") plot_data = PlotData(dist_value) # Plot the distribution using the plot wrapper function @@ -186,17 +196,17 @@ def command_plot(args: argparse.Namespace) -> None: plot(plot_data, path=args.output, save=True) except Exception as e: - print(f"\nError parsing or plotting Ux-data: {e}") + print(f"\nError parsing or plotting Ux Data: {e}") traceback.print_exc() - print("\nPlease ensure you have a valid Ux-data format.") + print("\nEnsure the input has a valid Ux Data format.") sys.exit(1) def command_sample_parser(command_subparsers: Any) -> None: sample_parser = command_subparsers.add_parser( "sample", - help="Sample from Signaloid Ux distributional data", - description="Sample from Signaloid Ux distributional data", + help="Sample from Signaloid Ux Data distributional data", + description="Sample from Signaloid Ux Data distributional data", formatter_class=argparse.RawDescriptionHelpFormatter, epilog=""" Example: @@ -210,7 +220,7 @@ def command_sample_parser(command_subparsers: Any) -> None: "-o", "--output", type=str, - help="Output sample filename (example: samples.txt)", + help="Output filename (example: samples.txt)", ) sample_parser.add_argument( @@ -224,30 +234,28 @@ def command_sample_parser(command_subparsers: Any) -> None: "--ux-data", type=str, required=True, - help='Ux-string or Ux-bytes to sample from (e.g., "90.6Ux04000000...")', + help='Ux String or Ux Binary to sample from (e.g., "90.6Ux04000000...")', ) sample_parser.set_defaults(func=command_sample) def command_sample(args: argparse.Namespace) -> None: - """Sample from a Signaloid Ux distributional value. + """Sample from a Signaloid Ux Data distributional value. Example usage: signaloid-uxdata-toolkit sample --ux-data=0.40007Ux000... --num-samples 10 signaloid-uxdata-toolkit sample -o samples.txt --ux-data=0.40007Ux000... --num-samples 100 """ - print("Signaloid Ux-data Sampler") + print("Signaloid Ux Data Sampler") print("=" * 50) try: dist_value = _parse_ux_data(args.ux_data) - # Generate the samples - print("Generating samples...") samples = sample_from_distributional_value(dist_value, args.num_samples) - # Output the samples + # Print or save samples if args.output: np.savetxt(args.output, samples, delimiter=",") print(f"Saved samples to: {args.output}") @@ -255,9 +263,9 @@ def command_sample(args: argparse.Namespace) -> None: for sample in samples: print(sample) except Exception as e: - print(f"\nError parsing or sampling Ux-data: {e}") + print(f"\nError parsing or sampling Ux Data: {e}") traceback.print_exc() - print("\nPlease ensure you have a valid Ux-data format.") + print("\nEnsure the input has a valid Ux Data format.") sys.exit(1) diff --git a/src/signaloid/uxdata_toolkit_test.py b/src/signaloid/uxdata_toolkit_test.py index d26df88..3b78f49 100644 --- a/src/signaloid/uxdata_toolkit_test.py +++ b/src/signaloid/uxdata_toolkit_test.py @@ -35,7 +35,7 @@ # ============================================================================ SAMPLE_UX_STRING = "-0.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bf9ad93f000100000000000000c7c72324c19ad93f01000000c7c72324c19ad93f0000000000000080" +SAMPLE_UX_BINARY = "09168733bf9ad93f000100000000000000c7c72324c19ad93f01000000c7c72324c19ad93f0000000000000080" SAMPLE_UX_STRING_WITH_SPECIAL_VALUES = "nanUx0400000000000000017FF8000000000000000000063FF0000000000000155555555555550040080000000000001555555555555500000000000000000015555555555555007FF80000000000001555555555555500FFF000000000000015555555555555007FF00000000000001555555555555500" @@ -110,13 +110,13 @@ def test_sample_missing_num_samples(self) -> None: def test_sample_zero_num_samples_rejected(self) -> None: with self.assertRaises(SystemExit): toolkit.parse_arguments( - ["sample", "--num-samples", "0", "--ux-data", SAMPLE_UX_BYTES] + ["sample", "--num-samples", "0", "--ux-data", SAMPLE_UX_BINARY] ) def test_sample_negative_num_samples_rejected(self) -> None: with self.assertRaises(SystemExit): toolkit.parse_arguments( - ["sample", "--num-samples", "-5", "--ux-data", SAMPLE_UX_BYTES] + ["sample", "--num-samples", "-5", "--ux-data", SAMPLE_UX_BINARY] ) @@ -141,9 +141,9 @@ def test_plot_saves_file(self) -> None: toolkit.command_plot(args) self.assertTrue(Path(args.output).exists()) - def test_plot_with_ux_bytes(self) -> None: + def test_plot_with_ux_binary(self) -> None: with tempfile.TemporaryDirectory() as tmp_dir: - args = self._make_plot_args(tmp_dir, ux_data=SAMPLE_UX_BYTES) + args = self._make_plot_args(tmp_dir, ux_data=SAMPLE_UX_BINARY) toolkit.command_plot(args) self.assertTrue(Path(args.output).exists()) @@ -212,10 +212,10 @@ def test_sample_correct_count(self) -> None: data = np.loadtxt(args.output, delimiter=",") self.assertEqual(data.size, args.num_samples) - def test_sample_with_ux_bytes(self) -> None: + def test_sample_with_ux_binary(self) -> None: with tempfile.TemporaryDirectory() as tmp_dir: args = self._make_sample_args( - tmp_dir, ux_data=SAMPLE_UX_BYTES, num_samples=50 + tmp_dir, ux_data=SAMPLE_UX_BINARY, num_samples=50 ) toolkit.command_sample(args) data = np.loadtxt(args.output, delimiter=",") @@ -299,11 +299,11 @@ def test_plot_end_to_end_ux_string(self) -> None: self.assertTrue(output_path.exists()) self.assertGreater(output_path.stat().st_size, 0) - def test_plot_end_to_end_ux_bytes(self) -> None: + def test_plot_end_to_end_ux_binary(self) -> None: with tempfile.TemporaryDirectory() as tmp_dir: output = str(Path(tmp_dir) / "e2e_bytes_plot.png") args = toolkit.parse_arguments( - ["plot", "-o", output, "--ux-data", SAMPLE_UX_BYTES] + ["plot", "-o", output, "--ux-data", SAMPLE_UX_BINARY] ) toolkit.command_plot(args)