Package index • ricci

Label and unlabel arrays

Adding index names enables the usage of Ricci calculus rules, while unlabeling restores the usual R array.

Label arrays

tensor() `%_%`: Create a labeled array (tensor)

.(): Index slot label specification

Unlabel arrays

as.array(<tensor>): Strip array labels

as_a(): Strip array labels

Tensor operations

Working with labeled arrays allows to consicely specify various tensor operations who all take given index structures into account and act accordingly.

Index manipulation

l(): Lower tensor indices

r(): Raise tensor indices

subst(): Substitute tensor labels

Tensor arithmetic

Ops(<tensor>): Arithmetic tensor operations

kron(): Kronecker product

Symmetric and antisymmetric part

asym(): Antisymmetric tensor part

sym(): Symmetric tensor part

Symbolic evaluation

at(): Evaluate a symbolic array

simplify(): Simplify symbolic expressions

Tensor fields

Tensor fields can be modeled by symbolic tensors, i.e. tensors that contain mathematical expressions instead of numerical values.

Covariant derivative

covd(): Covariant Derivative

Metrics tensor fields

g_eucl_cart() g_eucl_sph(): Euclidean metric tensor

g_mink_cart() g_mink_sph(): Minkowski metric tensor

g_sph(): Metric tensor of the sphere

g_ss(): Schwarzschild metric tensor

metric_field(): Create a metric tensor field

Geometric tensor fields

christoffel(): Christoffel symbols

ricci(): Ricci curvature tensor

ricci_sc(): Ricci scalar

riemann(): Riemann curvature tensor

Special tensors / symbols

d(): Kronecker delta

e(): Levi-Civita epsilon

Testthat expectation

A simple testthat helper that allows to check for tensor equality.

expect_tensor_equal(): Does code return the expected value?