Capability Dispatch#

A space has an operation only if its class carries the capability that defines it; test with isinstance(X, sc.StarSpace) and so on.

Capability	Adds
`Space`	context, `check_member`
`VectorSpace`	`add`, `scale`, `zeros`, …
`CoordinateSpace`	`shape`, `flatten`, `unflatten`
`InnerProductSpace`	`inner`, `norm`, `riesz`, `riesz_inverse`
`StarSpace`	`star` (involution)
`JordanAlgebraSpace`	`jordan`, `spectrum`, `spectral_decompose`, `spectral_apply`
`EuclideanJordanAlgebraSpace`	marker: Jordan structure compatible with the Euclidean inner product

DenseCoordinateSpace: inner product, no star. DenseVectorSpace adds star, no Jordan. ElementwiseJordanSpace adds Jordan.
ElementwiseJordanSpace(shape, ctx) returns an EuclideanElementwiseJordanSpace when the dtype is real and the geometry Euclidean; constructing the Euclidean class directly with any other geometry raises TypeError.
TreeSpace and StackedSpace carry exactly the capabilities shared by all their leaves (or their base), and re-select them after convert.
A missing capability is a missing attribute (AttributeError).

import numpy as np
import spacecore as sc

ctx = sc.Context(sc.NumpyOps(), dtype=np.float64)
V = sc.DenseVectorSpace((2,), ctx)
D = sc.DenseCoordinateSpace((2,), ctx)

assert isinstance(sc.TreeSpace.from_leaf_spaces((V, V)), sc.StarSpace)
assert not isinstance(sc.TreeSpace.from_leaf_spaces((V, D)), sc.StarSpace)
assert isinstance(sc.ElementwiseJordanSpace((2,), ctx),
                  sc.EuclideanElementwiseJordanSpace)

try:
    sc.EuclideanElementwiseJordanSpace(
        (2,), ctx, geometry=sc.WeightedInnerProduct(ctx.asarray([1.0, 2.0]))
    )
except TypeError as exc:
    print(exc)  # EuclideanElementwiseJordanSpace requires EuclideanInnerProduct.

try:
    D.star(ctx.asarray([1.0, 2.0]))
except AttributeError as exc:
    print(exc)  # 'DenseCoordinateSpace' object has no attribute 'star'