add tests for singularity

Author: bobmyhill

burnman/optimize/nonlinear_solvers.py

@@ -3,7 +3,6 @@
 import numpy.typing as npt
 from typing import Any
 from scipy.linalg import lu_factor, lu_solve
-from collections import namedtuple
 from types import SimpleNamespace
 
 
@@ -200,6 +199,7 @@ def __init__(
         self.cond_lu_thresh = cond_lu_thresh
         self.cond_lstsq_thresh = cond_lstsq_thresh
         self.eps = 2.0 * np.finfo(float).eps
+        self.max_condition_number = 1.0 / np.finfo(float).eps
 
         assert np.all(
             self._constraints(self.guess) < self.eps
@@ -598,8 +598,10 @@ def _termination_info(
         n_it: int,
         max_iterations: int,
         violated_constraints: list[int],
+        condition_number: float,
     ) -> tuple[int, str, bool]:
-        if converged:
+        singular_jacobian = condition_number > self.max_condition_number
+        if converged and not singular_jacobian:
             return (
                 True,
                 0,
@@ -611,7 +613,7 @@ def _termination_info(
                 1,
                 f"The function is too non-linear for lower lambda bound ({lmda_bounds[0]})",
             )
-        if persistent_bound_violation:
+        if persistent_bound_violation and not singular_jacobian:
             return (
                 False,
                 2,
@@ -622,6 +624,30 @@ def _termination_info(
             )
         if n_it == max_iterations:
             return False, 3, f"The solver reached max_iterations ({max_iterations})"
+        if singular_jacobian and not converged:
+            return (
+                False,
+                4,
+                (
+                    f"The system was effectively singular (cond={condition_number:.2e}) "
+                    f"and tried to leave the feasible region at iteration {n_it} by "
+                    "crossing the constraints with the following indices: "
+                    f"{[i for i, lmda in violated_constraints]}.\n"
+                    "You may want to try a different initial guess "
+                    "or check the Jacobian implementation. "
+                    "It may be that the problem is ill-posed."
+                ),
+            )
+        if singular_jacobian and converged:
+            return (
+                True,
+                5,
+                (
+                    f"The solver successfully found a root after {n_it} iterations,"
+                    f"but the system is effectively singular (cond={condition_number:.2e}). "
+                    "You should check the problem formulation before trusting this result."
+                ),
+            )
         raise Exception("Unknown termination of solver")
 
     def solve(self) -> Solution:
@@ -645,10 +671,12 @@ def solve(self) -> Solution:
                 * 1 -- Failure: lambda reached its minimum bound
                 * 2 -- Failure: descent direction violates constraints
                 * 3 -- Failure: maximum iterations reached
+                * 4 -- Failure: singular system and violated constraints
+                * 5 -- Successful convergence but singular system
 
             * **text** (str) -- Human-readable termination description.
             * **n_it** (int) -- Number of Newton iterations performed.
-            * **iterates** (namedtuple, optional) -- Present if
+            * **iterates** (Iterates instance, optional) -- Present if
               ``store_iterates=True``. Contains iteration history:
 
                 * **x** (list[np.ndarray]) -- Solution for each iteration.
@@ -751,14 +779,16 @@ def solve(self) -> Solution:
                 sol.iterates.append(sol.x, sol.F, lmda)
 
         # Final adjustment for constraints
-        if converged and not persistent_bound_violation:
-            sol.x = x_j + dxbar_j
-            if not np.all(self._constraints(sol.x) <= 0.0):
-                sol.x -= dxbar_j
-
-        sol.F = self.F(sol.x)
-        sol.F_norm = np.linalg.norm(sol.F, ord=2)
-        sol.J = self.J(sol.x)
+        if condition_number < self.max_condition_number:
+            if converged and not persistent_bound_violation:
+                sol.x = x_j + dxbar_j
+                if not np.all(self._constraints(sol.x) <= 0.0):
+                    sol.x -= dxbar_j
+
+            sol.F = self.F(sol.x)
+            sol.F_norm = np.linalg.norm(sol.F, ord=2)
+            sol.J = self.J(sol.x)
+            condition_number = np.linalg.cond(sol.J)
 
         sol.success, sol.code, sol.text = self._termination_info(
             converged,
@@ -768,6 +798,7 @@ def solve(self) -> Solution:
             sol.n_it,
             self.max_iterations,
             locals().get("violated_constraints", []),
+            condition_number,
         )
         return sol
 

tests/test_equilibration.py

@@ -244,6 +244,46 @@ def test_ol_wad_eqm_compositional_constraint(self):
             [1620.532183457096, 0.45, 0.6791743],
         )
 
+    def test_convergence_with_singular_system(self):
+
+        composition = {"Mg": 1.0, "Fe": 1.0, "Si": 1.0, "O": 4.0}
+        a = burnman.Composite(
+            [SLB_2011.mg_fe_olivine(), SLB_2011.mg_fe_olivine()], [0.5, 0.5]
+        )
+
+        a.phases[0].set_composition([0.1, 0.9])
+        a.phases[1].set_composition([0.9, 0.1])
+        equality_constraints = [("P", 1.0e5), ("T", 1000.0)]
+        sol, _ = equilibrate(composition, a, equality_constraints)
+        self.assertTrue(sol.success)  # Expect successful convergence
+        self.assertTrue(sol.code == 5)  # Expect singular system at solution
+
+    def test_ill_posed_problem(self):
+
+        composition = {"Mg": 1.8, "Fe": 0.2, "Si": 1.0, "O": 4.0}
+        a = burnman.Composite(
+            [SLB_2011.mg_fe_olivine(), SLB_2011.mg_fe_olivine()], [0.5, 0.5]
+        )
+
+        a.phases[0].set_composition([0.4, 0.6])
+        a.phases[1].set_composition([0.5, 0.5])
+        equality_constraints = [("P", 1.0e5), ("T", 300.0)]
+        sol, _ = equilibrate(composition, a, equality_constraints)
+        self.assertTrue(sol.code == 2)  # Expect problem to leave the feasible region
+
+    def test_ill_conditioned_jacobian(self):
+
+        composition = {"Mg": 1.8, "Fe": 0.2, "Si": 1.0, "O": 4.0}
+        a = burnman.Composite(
+            [SLB_2011.mg_fe_olivine(), SLB_2011.mg_fe_olivine()], [0.5, 0.5]
+        )
+
+        a.phases[0].set_composition([0.4, 0.6])
+        a.phases[1].set_composition([0.4, 0.6])
+        equality_constraints = [("P", 1.0e5), ("T", 300.0)]
+        sol, _ = equilibrate(composition, a, equality_constraints)
+        self.assertTrue(sol.code == 4)  # Expect singular system
+
 
 if __name__ == "__main__":
     unittest.main()