CartesianDomain

class CartesianDomain(cartesian_dict)

Bases: Location

PINA implementation of Hypercube domain.

Parameters:

cartesian_dict (dict) – A dictionary with dict-key a string representing the input variables for the pinn, and dict-value a list with the domain extrema.

Example:

>>> spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})

property variables

Spatial variables.

Returns:

Spatial variables defined in __init__()

Return type:

list[str]

update(new_domain)

Adding new dimensions on the CartesianDomain

Parameters:

new_domain (CartesianDomain) – A new CartesianDomain object to merge

Example:

>>> spatial_domain = CartesianDomain({'x': [0, 1], 'y': [0, 1]})
>>> spatial_domain.variables
['x', 'y']
>>> spatial_domain_2 = CartesianDomain({'z': [3, 4], 'w': [0, 1]})
>>> spatial_domain.update(spatial_domain_2)
>>> spatial_domain.variables
['x', 'y', 'z', 'w']

sample(n, mode='random', variables='all')

Sample routine.

Parameters:

• n (int) – Number of points to sample, see Note below for reference.

• mode (str) – Mode for sampling, defaults to random. Available modes include: random sampling, random; latin hypercube sampling, latin or lh; chebyshev sampling, chebyshev; grid sampling grid.

• variables (str | list[str]) – pinn variable to be sampled, defaults to all.

Returns:

Returns LabelTensor of n sampled points.

Return type:

LabelTensor

Note

The total number of points sampled in case of multiple variables is not n, and it depends on the chosen mode. If mode is ‘grid’ or chebyshev, the points are sampled independentely across the variables and the results crossed together, i.e. the final number of points is n to the power of the number of variables. If ‘mode’ is ‘random’, lh or latin, the variables are sampled all together, and the final number of points

Warning

The extrema values of Span are always sampled only for grid mode.

Example:

>>> spatial_domain = Span({'x': [0, 1], 'y': [0, 1]})
>>> spatial_domain.sample(n=4, mode='random')
    tensor([[0.0108, 0.7643],
            [0.4477, 0.8015],
            [0.2063, 0.8087],
            [0.8735, 0.6349]])
>>> spatial_domain.sample(n=4, mode='grid')
    tensor([[0.0000, 0.0000],
            [0.3333, 0.0000],
            [0.6667, 0.0000],
            [1.0000, 0.0000],
            [0.0000, 0.3333],
            [0.3333, 0.3333],
            [0.6667, 0.3333],
            [1.0000, 0.3333],
            [0.0000, 0.6667],
            [0.3333, 0.6667],
            [0.6667, 0.6667],
            [1.0000, 0.6667],
            [0.0000, 1.0000],
            [0.3333, 1.0000],
            [0.6667, 1.0000],
            [1.0000, 1.0000]])

is_inside(point, check_border=False)

Check if a point is inside the ellipsoid.

Parameters:

• point (LabelTensor) – Point to be checked

• check_border (bool) – Check if the point is also on the frontier of the hypercube, default False.

Returns:

Returning True if the point is inside, False otherwise.

Return type:

bool