r"""
Flat spacetime metric (Minkowski) in geometric units.

This module defines :class:`Minkowski`, a position-independent Lorentzian
metric with signature ``(+,-,-,-)`` (timelike-first convention). In these
coordinates the metric components are constant:

.. math::

    g_{\mu\nu} = \mathrm{diag}(1,\,-1,\,-1,\,-1),

so all Christoffel symbols vanish,
:math:`\Gamma^{\rho}_{\mu\nu} = 0`.

Notes
-----
Coordinate values are only used to determine batch layout (single point versus
``N`` points); they do not enter the metric components.

Examples
--------
>>> import numpy
>>> from relatipy.numeric.metrics.Minkowski_metric import Minkowski
>>> m = Minkowski()
>>> g = m._metric_dimensionless(numpy.zeros(4))
>>> numpy.allclose(g, numpy.diag([1.0, -1.0, -1.0, -1.0]))
True
"""

import numpy

from .base import BaseMetric


class Minkowski(BaseMetric):
    r"""
    Minkowski (flat) spacetime in dimensionless geometric form.

    The line element is

    .. math::

        \mathrm{d}s^2 = (\mathrm{d}x^0)^2 - (\mathrm{d}x^1)^2
            - (\mathrm{d}x^2)^2 - (\mathrm{d}x^3)^2,

    with :math:`x^0` timelike. The metric is independent of position.

    Attributes
    ----------
    None
        :meth:`__init__` does not assign instance attributes. Inherited
        :class:`BaseMetric` fields are only available if the base class
        initializer is invoked elsewhere.

    Examples
    --------
    >>> import numpy
    >>> from relatipy.numeric.metrics.Minkowski_metric import Minkowski
    >>> isinstance(Minkowski(), BaseMetric)
    True
    """

    def __init__(self):
        """
        Create a Minkowski metric instance.

        Parameters
        ----------
        None
            No parameters.

        Examples
        --------
        >>> from relatipy.numeric.metrics.Minkowski_metric import Minkowski
        >>> Minkowski()  # doctest: +ELLIPSIS
        <...Minkowski object at ...>
        """
        pass

    def _metric_dimensionless(self, xs):
        r"""
        Return the dimensionless Minkowski metric tensor.

        The components are

        .. math::

            g_{\mu\nu} = \mathrm{diag}(1,\,-1,\,-1,\,-1),

        broadcast to one or ``N`` copies when ``xs`` encodes multiple points.

        Parameters
        ----------
        xs : array_like
            Coordinates with shape ``(4,)`` for a single event or ``(N, 4)``
            for ``N`` events. Values are not used in the computation; only the
            leading dimension determines batch size.

        Returns
        -------
        ndarray
            Metric :math:`g_{\mu\nu}`. Shape ``(4, 4)`` if ``xs`` is 1D, or
            ``(N, 4, 4)`` if ``xs`` is 2D.

        Examples
        --------
        >>> import numpy
        >>> from relatipy.numeric.metrics.Minkowski_metric import Minkowski
        >>> m = Minkowski()
        >>> x = numpy.array([0.0, 1.0, 0.0, 0.0])
        >>> m._metric_dimensionless(x).shape
        (4, 4)
        >>> X = numpy.zeros((3, 4))
        >>> m._metric_dimensionless(X).shape
        (3, 4, 4)
        """
        xs = numpy.asarray(xs, dtype=float)

        if xs.ndim == 1:
            return numpy.diag([1, -1, -1, -1])

        # Multiple points: shape (N, 4) — constant metric, stacked N times
        N = len(xs)
        metrics = numpy.zeros((N, 4, 4))
        metrics[:, 0, 0] = 1
        metrics[:, 1, 1] = -1
        metrics[:, 2, 2] = -1
        metrics[:, 3, 3] = -1
        return metrics

    def _get_christoffel_symbols(self, xs):
        r"""
        Return Christoffel symbols for the Minkowski metric.

        In this representation all symbols vanish:

        .. math::

            \Gamma^{\rho}_{\mu\nu} = 0.

        Parameters
        ----------
        xs : array_like
            Coordinates with shape ``(4,)`` or ``(N, 4)``. Values are not used;
            only the layout selects between a single ``(4, 4, 4)`` array and a
            batch ``(N, 4, 4, 4)``.

        Returns
        -------
        ndarray
            Christoffel symbols :math:`\Gamma^{\rho}_{\mu\nu}`. Shape
            ``(4, 4, 4)`` for one point or ``(N, 4, 4, 4)`` for ``N`` points.
            All entries are zero.

        Examples
        --------
        >>> import numpy
        >>> from relatipy.numeric.metrics.Minkowski_metric import Minkowski
        >>> m = Minkowski()
        >>> G = m._get_christoffel_symbols(numpy.zeros(4))
        >>> G.shape
        (4, 4, 4)
        >>> numpy.allclose(G, 0.0)
        True
        >>> Gb = m._get_christoffel_symbols(numpy.zeros((2, 4)))
        >>> Gb.shape
        (2, 4, 4, 4)
        """
        xs = numpy.asarray(xs, dtype=float)
        if xs.ndim == 2:
            N = len(xs)
            return numpy.zeros((N, 4, 4, 4))
        return numpy.zeros((4, 4, 4))
