coordinates.coordinate_systems.CartesianCoordinateSystem1D.metric_tensor

property CartesianCoordinateSystem1D.metric_tensor: Callable

Returns the callable function for the metric tensor of the coordinate system.

The (diagonal components of the) metric tensor \(g_{ii}\) defines the inner product structure of the coordinate system. It is used for measuring distances, computing derivatives, and raising/lowering indices. This function returns the precomputed metric tensor as a callable function, which can be evaluated at specific coordinates.

Returns:

A function that computes the metric tensor \(g_{ii}\) when evaluated at specific coordinates. The returned function takes numerical coordinate values as inputs and outputs a NumPy array of shape (ndim, ).

Return type:

Callable

Example

cs = MyCoordinateSystem()
g_ii = cs.metric_tensor(x=1, y=2, z=3)  # Evaluates the metric at (1,2,3)
print(g_ii.shape)  # Output: (ndim, )