scimba_torch.integration.monte_carlo

Monte Carlo integration methods for volumetric and surfacic domains.

Classes

DomainSampler(domain, **kwargs)	A sampler for volumetric domains with support for subdomains, holes, and BCs.
SurfacicSampler(domain)	A sampler designed for surfaces defined by a parametric domain.
TensorizedSampler(list_sampler)	A sampler that combines multiple samplers for tensorized sampling.
VolumetricSampler(domain)	Samples points uniformly within a volumetric domain.

class VolumetricSampler(domain)

Bases: object

Samples points uniformly within a volumetric domain.

Parameters:

domain (VolumetricDomain) – The volumetric domain being sampled.

Raises:

• TypeError – If domain is not an object of class VolumetricDomain.

• ValueError – If the estimated volume of the domain is too small.

domain

The volumetric domain being sampled.

base_sampler

Uniform sampler for the domain bounds.

percent_in: float

Estimated percentage of the bounds occupied by the domain.

base_sampler_postmap

Uniform sampler for the mapped domain bounds.

sample(n, apply_map=True)

Samples points within the volumetric domain.

Parameters:

• n (int) – Number of points to sample.

• apply_map (bool) – Whether to apply the domain mapping if it exists. Defaults to True.

Return type:

Tensor

Returns:

An array of sampled points of shape (n, d).

Raises:

• TypeError – If argument is not an integer.

• ValueError – If argument is negative.

sample_postmap(n)

Samples points in the mapped domain.

Parameters:

n (int) – Number of points to sample.

Return type:

Tensor

Returns:

An array of sampled points of shape (n, d).

Raises:

• TypeError – If argument is not an integer.

• ValueError – If argument is negative.

class SurfacicSampler(domain)

Bases: object

A sampler designed for surfaces defined by a parametric domain.

This sampler generates points on a surface using a volumetric sampler on the associated parametric domain and maps them onto the surface.

Parameters:

domain (SurfacicDomain) – The surface domain to be sampled.

Raises:

TypeError – If domain is not an object of class SurfacicDomain.

domain

The surface domain to sample from.

base_sampler

A sampler for the parametric domain.

sample(n, compute_normals=False)

Samples points on the surface.

Parameters:

• n (int) – The number of points to sample.

• compute_normals (bool) – If True, compute and return surface normals. Defaults to False.

Return type:

Tensor | tuple[Tensor, Tensor]

Returns:

Points on the surface of shape (n, d), or a tuple of (points, normals) if compute_normals is True.

Raises:

• TypeError – If argument is not an integer.

• ValueError – If argument is negative.

class DomainSampler(domain, **kwargs)

Bases: object

A sampler for volumetric domains with support for subdomains, holes, and BCs.

This sampler manages a primary volumetric sampler and additional samplers for boundary conditions, holes, and subdomains.

Parameters:

• domain (VolumetricDomain) – The volumetric domain to sample.

• **kwargs –

  Additional configuration options including:

  • pre_sampling: Enable pre-sampling for the volumetric domain.

  • bc_pre_sampling: Enable pre-sampling for boundary condition domains.

  • npoint_pre_sampling: Number of pre-sampled points for the volumetric domain.

Raises:

• TypeError – If domain is not an object of class VolumetricDomain, or if npoints_pre_sampling or bc_npoints_pre_sampling are not integers.

• ValueError – If npoints_pre_sampling or bc_npoints_pre_sampling are not positive.

sample(n)

Samples n points from the volumetric domain and labels them by subdomains.

Possibly uses pre-sampled points.

Parameters:

n (int) – Number of points to sample.

Returns:

A tensor of sampled points with their subdomain labels.

Return type:

LabelTensor

Raises:

• TypeError – If argument is not an integer.

• ValueError – If argument is negative.

bc_sample(n)

Samples n points from the boundary domains.

Parameters:

n (int | list[int]) – Number of points to sample. If a list, then samples specific number of points for each bc domain.

Return type:

tuple[LabelTensor, LabelTensor]

Returns:

A tuple of tensors of sampled points.

Raises:

• TypeError – If argument is not an integer or a list of integers.

• ValueError – If argument is negative.s

sample_pre_sampled_points(n)

Samples n points from the pre-sampled volumetric points.

Parameters:

n (int) – Number of points to sample.

Returns:

A tensor of sampled points.

Return type:

LabelTensor

sample_new_points(n)

Samples new points from the volumetric domain and labels them by subdomains.

Parameters:

n (int) – Number of points to sample.

Return type:

LabelTensor

Returns:

A tensor of sampled points with their subdomain labels.

bc_sample_pre_sampled_points(n)

Samples points from the pre-sampled boundary condition points.

Parameters:

n (int | list[int]) – Number of points to sample.

Return type:

tuple[LabelTensor, LabelTensor]

Returns:

A tensor of sampled points.

Raises:

• TypeError – If argument is not an integer.

• ValueError – If argument is negative.

bc_sample_new_points(n)

Samples new points from the boundary domains.

The boundary domains includes the main domain, holes, and subdomains.

Note

Don’t we want to sample bc points for subdomains in a separate function…?

Parameters:

n (int | list[int]) – Number of points to sample. If a list, then samples specific number of points for each bc domain.

Return type:

tuple[LabelTensor, LabelTensor]

Returns:

A tensor of sampled points with their labels.

Raises:

ValueError – If the number of points to sample doesn’t match the number of BC domains.

class TensorizedSampler(list_sampler)

Bases: object

A sampler that combines multiple samplers for tensorized sampling.

This class allows sampling from multiple samplers, with options to handle boundary condition (BC) samplings selectively.

Parameters:

list_sampler (tuple[DomainSampler | UniformParametricSampler | UniformTimeSampler | UniformVelocitySampler, ...]) – A tuple of samplers, where each sampler implements sample and bc_sample methods.

list_sampler

A tuple of samplers to combine.

n_sampler

Number of samplers in the tuple.

sample(n)

Samples points using each sampler in the list.

Parameters:

n (int) – The number of points to sample per sampler.

Return type:

tuple[LabelTensor, ...]

Returns:

A generator yielding sampled points from each sampler.

bc_sample(n, index_bc=-1)

Samples points with special handling for boundary conditions (BC).

Parameters:

• n (int) – The number of points to sample per sampler.

• index_bc (int) – The index of the sampler to prioritize for BC sampling. Defaults to -1 (no priority).

Return type:

tuple[LabelTensor | tuple[LabelTensor, LabelTensor], ...]

Returns:

A generator yielding BC-sampled points for the prioritized sampler and regular samples for the others.

Raises:

TypeError – If samplers are not domain samplers when expected.