zoomy_core.model.kernel_functions

Opaque SymPy functions (eigensystem, solve, pick, conditional, …) that every backend realises numerically. Each kernel must be registered in the backend’s function table (NumPy, JAX, C).

Module Contents

Classes

eigensystem	Opaque full eigendecomposition [lambda, R, L=R^-1] of the row-major n*n matrix A_flat, packed in one vector. Components are read through pick(eigensystem(*a), idx); used by the Roe scheme.
spectral_radius	Opaque estimate of rho(A) by k power-iteration steps on A^2 (no eigendecomposition, runs on any device). Used as the wave-speed bound of the symbolic solvers.
eigenvalues	Opaque eigenvalue-only spectrum of the row-major n*n matrix A_flat, read through pick(eigenvalues(*a), idx). Cheaper companion of eigensystem for wave-speed bounds when no closed-form spectrum exists.
solve	Opaque per-cell linear solve A^-1 b, called as solve(*A_flat, *b_flat) and read through pick(solve(*a), idx). Used by the point-implicit source treatment of the NumericalSystemModel.
pick	Component idx of a packed opaque-kernel result (eigensystem, eigenvalues, solve). Per-component backends restore K(idx, *a) through lower_pick_to_component.
compute_derivative	Opaque non-local spatial derivative compute_derivative(field, *multi_index); (h, 1, 0) is d h / d x. The solver injects the backend’s LSQ-gradient implementation; it is emitted by expose_aux into update_aux_variables.
conditional	Vector-aware differentiable conditional(c, t, f): a symbolic node for scalars, a ZArray of nodes for vector branches. Differentiation follows the active branch and ignores the jump at the condition.

Functions

lower_pick_to_component

Rewrite pick(K(*a), idx) into the per-component form K(idx, *a) required by the C/C++ and UFL printers.

Data

REQUIRED_KERNELS

API

class zoomy_core.model.kernel_functions.eigensystem

Bases: sympy.Function

Opaque full eigendecomposition [lambda, R, L=R^-1] of the row-major n*n matrix A_flat, packed in one vector. Components are read through pick(eigensystem(*a), idx); used by the Roe scheme.

Args

• A_flat: the n*n matrix entries, row-major.

is_commutative

True

is_real

True

classmethod eval(*args)

Keep the call unevaluated.

class zoomy_core.model.kernel_functions.spectral_radius

Bases: sympy.Function

Opaque estimate of rho(A) by k power-iteration steps on A^2 (no eigendecomposition, runs on any device). Used as the wave-speed bound of the symbolic solvers.

Args

• k: number of power-iteration steps.

• safety: multiplicative safety factor on the estimate.

• A_flat: the n*n matrix entries, row-major.

References

• Golub & Van Loan 2013, https://doi.org/10.56021/9781421407944

is_commutative

True

is_real

True

classmethod eval(*args)

Keep the call unevaluated.

class zoomy_core.model.kernel_functions.eigenvalues

Bases: sympy.Function

Opaque eigenvalue-only spectrum of the row-major n*n matrix A_flat, read through pick(eigenvalues(*a), idx). Cheaper companion of eigensystem for wave-speed bounds when no closed-form spectrum exists.

is_commutative

True

is_real

True

classmethod eval(*args)

Keep the call unevaluated.

class zoomy_core.model.kernel_functions.solve

Bases: sympy.Function

Opaque per-cell linear solve A^-1 b, called as solve(*A_flat, *b_flat) and read through pick(solve(*a), idx). Used by the point-implicit source treatment of the NumericalSystemModel.

is_commutative

True

is_real

True

classmethod eval(*args)

Keep the call unevaluated.

class zoomy_core.model.kernel_functions.pick

Bases: sympy.Function

Component idx of a packed opaque-kernel result (eigensystem, eigenvalues, solve). Per-component backends restore K(idx, *a) through lower_pick_to_component.

is_commutative

True

is_real

True

classmethod eval(*args)

Keep the call unevaluated.

zoomy_core.model.kernel_functions.lower_pick_to_component(expr)

Rewrite pick(K(*a), idx) into the per-component form K(idx, *a) required by the C/C++ and UFL printers.

Returns

The expression (or array/matrix) with every pick of a per-component kernel swapped structurally.

class zoomy_core.model.kernel_functions.compute_derivative

Bases: sympy.Function

Opaque non-local spatial derivative compute_derivative(field, *multi_index); (h, 1, 0) is d h / d x. The solver injects the backend’s LSQ-gradient implementation; it is emitted by expose_aux into update_aux_variables.

is_commutative

True

is_real

True

classmethod eval(*args)

Keep the call unevaluated.

class zoomy_core.model.kernel_functions.conditional

Bases: sympy.Function

Vector-aware differentiable conditional(c, t, f): a symbolic node for scalars, a ZArray of nodes for vector branches. Differentiation follows the active branch and ignores the jump at the condition.

nargs

3

is_commutative

True

zoomy_core.model.kernel_functions.REQUIRED_KERNELS

‘frozenset(…)’