archimedes.quadrature.Quadrature

class archimedes.quadrature.Quadrature(*args, **kwargs)

The interface every quadrature rule provides, whatever its dimension.

Deliberately minimal: this is only what’s needed by FunctionSpace to define an inner product.

Methods

map_to(*params, **kwparams)	A new rule mapped onto the target domain.
sum(values, *[, axis, density])	Quadrature applied to values already sampled at the nodes.

Attributes

breakpoints	Element boundaries, for a rule assembled from sub-elements.
elements	Which sub-element each node came from, or None for a rule with no element structure.
measures	The measure integrated against in each dimension, always a tuple of length ndim.
ndim	Number of dimensions of the domain integrated over.
nodes	Nodes on the currently-mapped target domain (see map_to), shape (n,) for a one-dimensional rule or (n, ndim) otherwise.
weights	Weights including the Jacobian of the currently-mapped target domain (see map_to), shape (n,).

__init__(*args, **kwargs)

map_to(

*params: Any,

**kwparams: Any,

) → Quadrature

A new rule mapped onto the target domain.

sum(

values: ndarray,

*,

axis: int = ...,

density: bool = False,

) → ndarray

Quadrature applied to values already sampled at the nodes.

The default axis is rule-specific; see each rule’s sum.

property breakpoints: Any

Element boundaries, for a rule assembled from sub-elements.

np.ndarray | None for a one-dimensional rule; a per-dimension tuple of those for a multi-dimensional one.

property elements: Any

Which sub-element each node came from, or None for a rule with no element structure.

Shape (n,) for a one-dimensional rule and (n, ndim) for a multi-dimensional one, mirroring nodes.

This is provenance that can’t be determined by coordinates alone. A composite rule places nodes on its element boundaries, so a basis that is discontinuous needs to know which element each copy belongs to.

property measures: tuple[Measure, ...]

The measure integrated against in each dimension, always a tuple of length ndim.

property ndim: int

Number of dimensions of the domain integrated over.

property nodes: ndarray

Nodes on the currently-mapped target domain (see map_to), shape (n,) for a one-dimensional rule or (n, ndim) otherwise.

property weights: ndarray

Weights including the Jacobian of the currently-mapped target domain (see map_to), shape (n,).