--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/experiments/laser_and_mirrors_aux2.py Wed Apr 22 22:32:00 2026 -0500
@@ -0,0 +1,60 @@
+#
+# Laser and mirrors convection-diffusion experiment with known diffusivity and convectivity.
+# Alternative parametrisation
+#
+import laser_and_mirrors_aux
+import numpy as np
+from laser_and_mirrors_aux import generic_setup, relnoise
+from measures import DiscreteMeasure_2_f64
+from pointsource_pde import Problem, RegTerm
+from pointsource_pde.convection_diffusion import BoxedQuadraticRegularisation
+
+# Give name to the problem
+name = "laser_and_mirrors_aux2"
+
+# Override algorithm settings
+algorithm_overrides = laser_and_mirrors_aux.algorithm_overrides
+
+
+# Setup the problem
+def setup(prefix):
+ rng = np.random.default_rng(seed=31337)
+
+ dat, auxtrue, _μ_bound, μ_true, plot_factory, pde = generic_setup(
+ prefix,
+ rng=rng,
+ μ_true=DiscreteMeasure_2_f64([([0.2, 0.3], 0.15), ([0.4, 0.1], 0.04)]),
+ k=0.02,
+ r=0.1,
+ θ=120 * np.pi / 180,
+ )
+
+ # Override Lipschitz parameter
+ pde.override_lipschitz = (4.0,)
+ pde.override_lipschitz_pair = (4.0, 4.0)
+ # print("diff_chain_lipschitz_factor (modified)", pde.diff_chain_lipschitz_factor())
+ # l1, l2 = pde.diff_chain_lipschitz_factor_pair()
+ # print("diff_chain_lipschitz_factor_pair (modified) ", l1, ", ", l2)
+
+ reg = RegTerm.NonnegRadon(1.5e-6)
+
+ μ0 = DiscreteMeasure_2_f64([])
+ (k, (c1, c2)) = auxtrue
+ aux0 = (
+ max(0.001, relnoise(k, 0.02, rng)),
+ (
+ relnoise(c1, 0.2, rng),
+ relnoise(c2, 0.2, rng),
+ ),
+ )
+ print("aux init ", aux0)
+ aux = BoxedQuadraticRegularisation((0.001, -1.0), (1.0, 1.0), (3.0, 0.0005), aux0)
+ ax = aux.apply(aux0)
+ inival = dat.apply((μ0, aux0))
+ print("Initial data term value:", inival + ax)
+ print("Data term value at true μ:", dat.apply((μ_true, auxtrue)) + ax)
+
+ # No curvature bound given: θ is aboslute.
+ dat.curvature_bound_components = lambda: (None, None)
+
+ return Problem(dat, reg, aux, aux0, μ0, plot_factory=plot_factory)