differential_geometry.dense_utils

Utility functions for performing basic tensor manipulations including index raising and lowering.

Functions

dense_adjust_tensor_signature(tensor_field, ...)	Adjust multiple indices of a tensor field by raising or lowering them using the metric or inverse metric.
dense_compute_tensor_trace(tensor_field, ...)	Compute the trace over a pair of tensor indices, adjusting their variances if needed.
dense_compute_volume_element(metric_field, ...)	Compute the volume element (√|det(g)|) from a metric tensor field.
dense_contract_with_metric(tensor_field, ...)	Contract a tensor index with the provided metric tensor.
dense_lower_index(tensor_field, index, rank, ...)	Lowers a specified index of a tensor field using the metric tensor.
dense_permute_tensor_indices(tensor_field, ...)	Permutes the order of the tensor indices in the last rank dimensions of the tensor field.
dense_raise_index(tensor_field, index, rank, ...)	Raise a specified index of a tensor field using the inverse metric tensor.
dense_tensor_product(tensor_a, type_a, ...)	Compute the tensor product of two tensor fields with specified (p, q) types, ensuring that the result has contravariant indices first and covariant indices last.
dense_transform_tensor_field(tensor_field, ...)	Apply a coordinate transformation to a tensor field based on its signature and selected indices.
infer_metric_type(metric_field, field_shape)	Infer whether the given metric (or inverse metric) tensor is diagonal or full.