CoordinateSystem

A representation of a coordinate system. It doesn’t do much on its own but it does provide a way to unify internal, cartesian, derived type coordinates

Properties and Methods

__init__(self, name=None, basis=None, matrix=None, inverse=None, dimension=None, origin=None, coordinate_shape=None, jacobian_prep=None, converter_options=None): 

Sets up the CoordinateSystem object

• name: str

  a name to give to the coordinate system

• basis: Any

  a basis for the coordinate system

• matrix: np.ndarray | None

  an expansion coefficient matrix for the set of coordinates in its basis

• dimension: Iterable[None | int]

  the dimension of a single configuration in the coordinate system (for validation)

• jacobian_prep: function | None

  a function for preparing coordinates to be used in computing the Jacobian

• coordinate_shape: iterable[int]

  the actual shape of a single coordinate in the coordinate system

@property
basis(self): 

• :returns: CoordinateSystem

  The basis for the representation of matrix

@property
origin(self): 

• :returns: np.ndarray

  The origin for the expansion defined by matrix

@property
matrix(self): 

The matrix representation in the CoordinateSystem.basis None is shorthand for the identity matrix

• :returns: np.ndarray

  mat

@property
inverse(self): 

The inverse of the representation in the basis. None is shorthand for the inverse or pseudoinverse of matrix.

• :returns: np.ndarray

  inv

@property
dimension(self): 

The dimension of the coordinate system. None means unspecified dimension

• :returns: int or None

  dim

converter(self, system): 

Gets the converter from the current system to a new system

• system: CoordinateSystem

  the target CoordinateSystem

• :returns: CoordinateSystemConverter

  converter object

convert_coords(self, coords, system, **kw): 

Converts coordiantes from the current coordinate system to system

• coords: CoordinateSet

  No description…

• system: CoordinateSystem

  No description…

• kw: Any

  options to be passed through to the converter object

• :returns: tuple(np.ndarray, dict)

  the converted coordiantes

displacement(self, amts): 

Generates a displacement or matrix of displacements based on the vector or matrix amts The relevance of this method has become somewhat unclear…

• amts: np.ndarray

  No description…

• :returns: np.ndarray

  No description…

derivatives(self, coords, function, order=1, coordinates=None, result_shape=None, **finite_difference_options): 

Computes derivatives for an arbitrary function with respect to this coordinate system. Basically a more flexible version of jacobian.

• function: Any

  No description…

• order: Any

  No description…

• coordinates: Any

  No description…

• finite_difference_options: Any

  No description…

• :returns: np.ndarray

  derivative tensor

jacobian(self, coords, system, order=1, coordinates=None, converter_options=None, all_numerical=False, **finite_difference_options): 

Computes the Jacobian between the current coordinate system and a target coordinate system

• system: CoordinateSystem

  the target CoordinateSystem

• order: int | Iterable[int]

  the order of the Jacobian to compute, 1 for a standard, 2 for the Hessian, etc.

• coordinates: None | iterable[iterable[int] | None

  a spec of which coordinates to generate derivatives for (None means all)

• mesh_spacing: float | np.ndarray

  the spacing to use when displacing

• prep: None | function

  a function for pre-validating the generated coordinate values and grids

• fd_options: Any

  options to be passed straight through to FiniteDifferenceFunction

• :returns: np.ndarray

  derivative tensor

__repr__(self): 

Provides a clean representation of a CoordinateSystem for printing

• :returns: str

  No description…

Examples

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