return_derivs_key: str

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

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

__call__(self, coords, **opts): 

pre_convert(self, system): 

A hook to allow for handlign details before converting

• system: Any

• :returns: _

@property
basis(self): 

• :returns: CoordinateSystem

  T h e

b a s i s

f o r

t h e

r e p r e s e n t a t i o n

o f

` m a t r i x `

@property
origin(self): 

• :returns: np.ndarray

  T h e

o r i g i n

f o r

t h e

e x p a n s i o n

d e f i n e d

b y

` m a t r i x `

@property
matrix(self): 

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

• :returns: np.ndarray

  m a t

@property
inverse(self): 

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

• :returns: np.ndarray

  i n v

@property
dimension(self): 

The dimension of the coordinate system. None means unspecified dimension

• :returns: int or None

  d i m

converter(self, system): 

Gets the converter from the current system to a new system

• system: CoordinateSystem

  the target CoordinateSystem

• :returns: CoordinateSystemConverter

  c o n v e r t e r

o b j e c t

convert_coords(self, coords, system, converter=None, **kw): 

Converts coordiantes from the current coordinate system to system

• coords: CoordinateSet

• system: CoordinateSystem

• kw: Any

  options to be passed through to the converter object

• :returns: tuple(np.ndarray, dict)

  t h e

c o n v e r t e d

c o o r d i a n t e s

rescale(self, scaling, in_place=False): 

rotate(self, rot, in_place=False): 

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

• :returns: np.ndarray

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

• order: Any

• coordinates: Any

• finite_difference_options: Any

• :returns: np.ndarray

  d e r i v a t i v e

t e n s o r

jacobian(self, coords, system, order=1, coordinates=None, converter_options=None, all_numerical=False, analytic_deriv_order=None, **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

  d e r i v a t i v e

t e n s o r

__repr__(self): 

Provides a clean representation of a CoordinateSystem for printing

• :returns: str

is_compatible(self, system): 

has_conversion(self, system):