Function adjoint_gradient 

pub fn adjoint_gradient<R>(
    linearization: &AcceptedLinearization<'_, R>,
    objective_unknown_cotangent: &[f64],
    objective_parameter_cotangent: &[f64],
    properties: LinearOperatorProperties,
    solver: LinearSolveRequest<'_>,
) -> Result<AdjointGradient, Diagnostic>
where
    R: LinearizedRelation<f64> + ?Sized,

Solve the transposed state system and form the total parameter gradient.

objective_unknown_cotangent is J_w^T and objective_parameter_cotangent is the direct term J_p.

Errors

Returns a stable differentiation or solver diagnostic for shape, capability, convergence, or independently verified residual failures.