differential_geometry.dense_utils.dense_compute_volume_element#

differential_geometry.dense_utils.dense_compute_volume_element(metric_field: ndarray, metric_type: str) → ndarray[source]#

Compute the volume element (√|det(g)|) from a metric tensor field.

Parameters:

  • metric_field (numpy.ndarray) –

    The metric tensor field. Depending on metric_type, expected shape is:

    • ”full”: shape (…, L, L), representing a full rank-2 metric tensor.

    • ”diag”: shape (…, L), representing a diagonal metric tensor.

  • metric_type (str) – One of {“full”, “diag”}. Specifies whether the metric is full or diagonal.

Returns:

A scalar field of shape (…), representing the volume element √|det(g)| at each point.

Return type:

numpy.ndarray

Raises:

ValueError – If the input does not match the specified metric type or shape is invalid.