differential_geometry.dense_ops

Differential geometry operations on dense arrays.

These methods provide a differential geometry backend which is designed to interact well with the “dense” representation of tensor fields in PyMetric; specifically, the use of full arrays to represent tensor fields.

Functions

dense_gradient(tensor_field, rank, ndim, ...)	Compute the gradient of a tensor field in the specified output basis.
dense_gradient_contravariant_diag(...[, ...])	Compute the contravariant gradient \(\nabla^\mu T^{\dots}\) of a tensor field using a diagonal inverse metric tensor.
dense_gradient_contravariant_full(...[, ...])	Compute the contravariant gradient \(\nabla^\mu T^{\dots}\) using the inverse metric tensor.
dense_gradient_covariant(tensor_field, rank, ...)	Compute the element-wise covariant gradient of a tensor field.
dense_scalar_laplacian(tensor_field, ...[, ...])	Compute the Laplacian (Laplace-Beltrami operator) of a tensor field in a general curvilinear coordinate system, using either a full or diagonal inverse metric.
dense_scalar_laplacian_diag(tensor_field, ...)	Compute the element-wise Laplacian of a densely represented tensor field in an orthogonal coordinate system.
dense_scalar_laplacian_full(tensor_field, ...)	Compute the element-wise Laplacian of a densely represented tensor field.
dense_vector_divergence(vector_field, ...[, ...])	Compute the divergence of a vector field in a general coordinate system.
dense_vector_divergence_contravariant(...[, ...])	Compute the divergence of a contravariant vector field in a general coordinate system using the D-terms and raw partial derivatives.
dense_vector_divergence_covariant_diag(...)	Compute the divergence of a covariant vector field in a general curvilinear coordinate system using a diagonal inverse metric tensor.
dense_vector_divergence_covariant_full(...)	Compute the divergence of a covariant vector field in a general coordinate system using a full inverse metric tensor.