coordinates.mixins.coords.CoordinateOperationsMixin.coordinate_meshgrid#

CoordinateOperationsMixin.coordinate_meshgrid(*coordinate_arrays, axes: Sequence[str] | None = None, copy: bool = True, sparse: bool = False)[source]#

Construct a coordinate-aligned meshgrid from 1D coordinate arrays.

This method returns a tuple of N-D coordinate arrays aligned with the coordinate system’s canonical axis order, given a subset of 1D coordinate arrays. It reorders the inputs to match the canonical axis order and wraps NumPy’s numpy.meshgrid().

Parameters:

  • coordinate_arrays (array_like) – 1-D arrays representing the coordinates of a grid.

  • axes (list of str, optional) – The axes present in the provided coordinate_arrays. If None (default), then the first len(coordinate_arrays) axes of the coordinate system will be used. Otherwise, the provided axes will be used to re-order the coordinates into canonical order before creating the mesh.

  • sparse (bool, optional) –

    If True the shape of the returned coordinate array for dimension i is reduced from (N1, ..., Ni, ... Nn) to (1, ..., 1, Ni, 1, ..., 1). These sparse coordinate grids are intended to be use with Broadcasting. When all coordinates are used in an expression, broadcasting still leads to a fully-dimensional result array.

    Default is False.

  • copy (bool, optional) – If False, a view into the original arrays are returned in order to conserve memory. Default is True. Please note that sparse=False, copy=False will likely return non-contiguous arrays. Furthermore, more than one element of a broadcast array may refer to a single memory location. If you need to write to the arrays, make copies first.

Returns:

A tuple of N-D arrays suitable for evaluating vectorized fields over a structured grid.

Return type:

tuple of np.ndarray

Raises:

ValueError – If axes are invalid or their count does not match coordinate_arrays.

Examples

Create a grid in spherical coordinates composed of \(r\) and \(\theta\) coordinates.

>>> from pymetric.coordinates import SphericalCoordinateSystem
>>> from pymetric.utilities.logging import pg_log
>>> pg_log.level = 50
>>> cs = SphericalCoordinateSystem()
>>> r = np.linspace(0, 1, 10)
>>> theta = np.linspace(0, np.pi, 20)
>>> rgrid, thetagrid = cs.coordinate_meshgrid(r, theta, axes=["r", "theta"])
>>> rgrid.shape, thetagrid.shape
((10, 20), (10, 20))

Axes may also be supplied out of order

>>> cs = SphericalCoordinateSystem()
>>> r = np.linspace(0, 1, 10)
>>> theta = np.linspace(0, np.pi, 20)
>>> rgrid, thetagrid = cs.coordinate_meshgrid(theta,r, axes=["theta","r"])
>>> rgrid.shape, thetagrid.shape
((10, 20), (10, 20))

If an invalid axis is specified, then an error occurs.

>>> cs = SphericalCoordinateSystem()
>>> r = np.linspace(0, 1, 10)
>>> theta = np.linspace(0, np.pi, 20)
>>> rgrid, thetagrid = cs.coordinate_meshgrid(theta,r, axes=["theta","psi"]) 
ValueError: Unknown axis/axes ['psi'] – valid axes are ['r', 'theta', 'phi']