pyextal.metric
==============

.. py:module:: pyextal.metric

.. autoapi-nested-parse::

   Metric Tensor Calculations.

   This module provides functions for performing crystallographic calculations using a
   Gram matrix (metric tensor). These functions are essential for working with
   crystal lattices where the basis vectors are not necessarily orthogonal.



Functions
---------

.. autoapisummary::

   pyextal.metric.sumx
   pyextal.metric.volume
   pyextal.metric.angle
   pyextal.metric.scale


Module Contents
---------------

.. py:function:: sumx(gram: numpy.ndarray, v1: numpy.ndarray, v2: numpy.ndarray) -> float

   Calculates the inner product of two vectors using a Gram matrix.

   This function computes v2^T * G * v1, where G is the Gram matrix.

   :param gram: The Gram matrix (metric tensor).
   :type gram: np.ndarray
   :param v1: The first vector.
   :type v1: np.ndarray
   :param v2: The second vector.
   :type v2: np.ndarray

   :returns: The inner product of the two vectors.
   :rtype: float


.. py:function:: volume(gram: numpy.ndarray) -> float

   Calculates the volume of the unit cell from its Gram matrix.

   The volume is the square root of the determinant of the Gram matrix.

   :param gram: The Gram matrix of the unit cell.
   :type gram: np.ndarray

   :returns: The volume of the unit cell.
   :rtype: float


.. py:function:: angle(gram: numpy.ndarray, v1: numpy.ndarray, v2: numpy.ndarray) -> float

   Calculates the angle between two vectors in a space defined by a Gram matrix.

   :param gram: The Gram matrix.
   :type gram: np.ndarray
   :param v1: The first vector.
   :type v1: np.ndarray
   :param v2: The second vector.
   :type v2: np.ndarray

   :returns: The angle between the vectors in radians.
   :rtype: float


.. py:function:: scale(gram: numpy.ndarray, v: numpy.ndarray) -> float

   Calculates the magnitude (norm) of a vector using a Gram matrix.

   :param gram: The Gram matrix.
   :type gram: np.ndarray
   :param v: The vector whose magnitude is to be calculated.
   :type v: np.ndarray

   :returns: The magnitude of the vector.
   :rtype: float