eqiora.diff

Implicit differentiation of Eqiora programs.

Example: evaluate a parameter derivative

Continue with the scalar Poisson model and plan from the differentiation guide:

import numpy as np
import eqiora.diff

program = eqiora.diff.compile(
    plan, inputs=(model.parameter("source"),),
    outputs=(plan.capability.fields[0],),
)
evaluation = program.evaluate((1.5,))
values = evaluation.primal()
directional_derivative = evaluation.jvp((1.0,))

values holds the solution at source value 1.5. The JVP gives its change per unit increase of that parameter. A VJP instead propagates output weights back to parameter coordinates. The original model and plan remain unchanged.

API

`DerivativeImplementation`

See eqiora.DerivativeImplementation.

Which implementation supplied the derivative for an evaluation.

`DifferentiableEvaluation`

See eqiora.DifferentiableEvaluation.

Converged evaluation at one parameter point.

`DifferentiableJvp`

See eqiora.DifferentiableJvp.

Ordered output leaves and their shape-preserving forward tangent leaves.

`DifferentiablePrimal`

See eqiora.DifferentiablePrimal.

Ordered typed output leaves from a primal evaluation.

`DifferentiableProgram`

See eqiora.DifferentiableProgram.

Differentiable map between ordered typed input and output products.

`DifferentiableVjp`

See eqiora.DifferentiableVjp.

Ordered output leaves and the shape-preserving input cotangent leaves.

`DifferentiableValueSignature`

See eqiora.DifferentiableValueSignature.

Exact native Model/type/support identity of one selected numerical leaf.

`DifferentiationEvidence`

See eqiora.DifferentiationEvidence.

Provenance of one differentiation: model, plan, solve summaries, and residual.

`DifferentiationMode`

See eqiora.DifferentiationMode.

Kind of differentiation: primal, JVP, or VJP.

`FieldRef`

See eqiora.FieldRef.

Field selected from an immutable model.

`LinearizationState`

See eqiora.LinearizationState.

Whether the linearization was computed afresh or reused.

`ParameterRef`

See eqiora.ParameterRef.

Parameter selected from an immutable model.

`compile`

Compile a differentiable program over an ordered set of parameters.

For a finite affine Plan, the inputs are real or complex Parameters, scalar or shaped, and outputs are ordered real/complex Fields or Observables; the Plan must not require state. Complex derivatives use the real differential with the pairing Re(sum(conj(a)*b)), so dependence on the conjugate is kept. Input coordinates are ordered by selection, then row-major by component, then real before imaginary part. The input identities count Parameters; the input shape counts real coordinates. A finite nonlinear Plan also needs its exact seed.

def compile(plan: Plan, *, inputs: Sequence[ParameterRef], outputs: Sequence[FieldRef | ObservableRef], state: State | None=None) -> DifferentiableProgram: ...