Solution

lineax.Solution

The solution to a linear 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 lineax.RESULTS[result].
• stats: Statistics about the solver, e.g. the number of steps that were required.
• state: The internal state of the solver. The meaning of this is specific to each solver.

---

lineax.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.

• conlim: Condition number of A seems to be larger than conlim.

• 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.