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Solution¤

optimistix.Solution ¤

The solution to a nonlinear solve.

Attributes:

  • value: The solution to the solve.
  • result: An integer representing whether the solve was successful or not. This can be converted into a human-readable error message via optimistix.RESULTS[result]
  • aux: Any user-specified auxiliary data returned from the problem; defaults to None if there is no auxiliary data. Auxiliary outputs can be captured by setting a has_aux=True flag, e.g. optx.root_find(fn, ..., has_aux=True).
  • stats: Statistics about the solve, e.g. the number of steps that were required.
  • state: The final internal state of the solver. The meaning of this is specific to each solver.

optimistix.RESULTS ¤

An enumeration, with the following entries:

  • successful

  • max_steps_reached: The maximum number of solver steps was reached. Try increasing max_steps.

  • singular: A linear solver returned non-finite (NaN or inf) output. This usually means that an operator was not well-posed, and that its solver does not support this.

    If you are trying solve a linear least-squares problem then you should pass solver=AutoLinearSolver(well_posed=False). By default lineax.linear_solve assumes that the operator is square and nonsingular.

    If you were expecting this solver to work with this operator, then it may be because:

    (a) the operator is singular, and your code has a bug; or

    (b) the operator was nearly singular (i.e. it had a high condition number: jnp.linalg.cond(operator.as_matrix()) is large), and the solver suffered from numerical instability issues; or

    (c) the operator is declared to exhibit a certain property (e.g. positive definiteness) that is does not actually satisfy.

  • breakdown: A form of iterative breakdown has occured in a linear solve. Try using a different solver for this problem or increase restart if using GMRES.

  • stagnation: A stagnation in an iterative linear solve has occurred. Try increasing stagnation_iters or restart.

  • nonfinite_input: A linear solver received non-finite (NaN or inf) input and cannot determine a solution.

    This means that you have a bug upstream of Lineax and should check the inputs to lineax.linear_solve for non-finite values.

  • nonlinear_max_steps_reached: The maximum number of steps was reached in the nonlinear solver. The problem may not be solveable (e.g., a root-find on a function that has no roots), or you may need to increase max_steps.

  • nonlinear_divergence: Nonlinear solve diverged.