4.2.2.1 pde.grids.coordinates.base module

class CoordinatesBase[source]

Bases: object

Base class for orthonormal coordinate systems

axes: list[str]

name of each coordinate axis

Type:: list

basis_rotation(points)[source]

returns rotation matrix rotating basis vectors to Cartesian coordinates

Parameters:: points (ndarray) – Coordinates of the point(s)
Returns:: Rotation matrices for all points. The returnd array has the shape (dim, dim) + points_shape, assuming points has the shape points_shape + (dim,).
Return type:: ndarray

cell_volume(c_low, c_high)[source]

calculate the volume between coordinate lines

Parameters:

c_low (ndarray) – Lower values of the coordinate lines enclosing the volume
c_high (ndarray) – Upper values of the coordinate lines enclosing the volume

Returns:

Enclosed volumes for all given cells

Return type:

ndarray

coordinate_limits: list[tuple[float, float]]

the limits of each coordinate axis

Type:: list of tuple

dim: int

spatial dimension of the coordinate system

Type:: int

distance(p1, p2)[source]

Calculate the distance between two points

Parameters:

p1 (ndarray) – First position
p2 (ndarray) – Second position

Returns:

Distance between the two positions

Return type:

float

mapping_jacobian(points)[source]

returns the Jacobian matrix of the coordinate mapping

Parameters:: points (ndarray) – Coordinates of the point(s)
Returns:: The Jacobian
Return type:: ndarray

metric(points)[source]

calculate the metric tensor at coordinate points

Parameters:: points (ndarray) – The coordinates of the points
Returns:: Metric tensor at the points
Return type:: ndarray

pos_diff(p1, p2)[source]

return Cartesian vector(s) pointing from p1 to p2

Parameters:

p1 (ndarray) – First point(s)
p2 (ndarray) – Second point(s)

Returns:

The difference vectors between the points with periodic boundary conditions applied.

Return type:

ndarray

pos_from_cart(points)[source]

convert Cartesian coordinates to coordinates in this system

Parameters:: points (ndarray) – Points given in Cartesian coordinates.
Returns:: Points given in the coordinates of this system
Return type:: ndarray

pos_to_cart(points)[source]

convert coordinates to Cartesian coordinates

Parameters:: points (ndarray) – The coordinates of points in the current coordinate system
Returns:: Cartesian coordinates of the points
Return type:: ndarray

scale_factors(points)[source]

calculate the scale factors at various points

Parameters:: points (ndarray) – The coordinates of the points
Returns:: Scale factors at the points
Return type:: ndarray

vec_to_cart(points, components)[source]

convert the vectors at given points to a Cartesian basis

Parameters:

points (ndarray) – The coordinates of the point(s) where the vectors are specified.
components (ndarray) – The components of the vectors at the given points

Returns:

The vectors specified at the same position but with components given in Cartesian coordinates.

Return type:

ndarray

volume_factor(points)[source]

calculate the volume factors at various points

Parameters:: points (ndarray) – Coordinates of the point(s)
Returns:: Volume factors at the points
Return type:: ndarray

exception DimensionError[source]

Bases: ValueError

exception indicating that dimensions were inconsistent