Check corrected Hessian in Corrector.MultidimensionalGaussNewtonApproximation

When rho[2] <= 0, Corrector clamps alpha to 0 and drops the rank-1 curvature correction term, so the implied Gauss-Newton Hessian is rho[1] * J'J rather than rho[1] * J'J + 2 * rho[2] * J'r r'J. Account for this in g_hess and assert that c_hess matches g_hess.

Thanks to Matthias Kraft (@matthias-kraft) for reporting this.

Fixes https://github.com/ceres-solver/ceres-solver/issues/363

Change-Id: I3ccc3753aab5a5d753a8f650ff71f2b8ea96a51d

internal/ceres/corrector_test.cc

diff --git a/internal/ceres/corrector_test.cc b/internal/ceres/corrector_test.cc
index e042481..aa1e0a7 100644
--- a/internal/ceres/corrector_test.cc
+++ b/internal/ceres/corrector_test.cc
@@ -186,8 +186,12 @@
         sqrt(rho[1]) * (jac - kAlpha / sq_norm * res * res.transpose() * jac);
 
     g_grad = rho[1] * jac.transpose() * res;
-    g_hess = rho[1] * jac.transpose() * jac +
-             2.0 * rho[2] * jac.transpose() * res * res.transpose() * jac;
+    if (rho[2] > 0.0) {
+      g_hess = rho[1] * jac.transpose() * jac +
+               2.0 * rho[2] * jac.transpose() * res * res.transpose() * jac;
+    } else {
+      g_hess = rho[1] * jac.transpose() * jac;
+    }
 
     Corrector c(sq_norm, rho);
     c.CorrectJacobian(3, 2, residuals, jacobian);
@@ -201,6 +205,7 @@
     ASSERT_NEAR((g_jac - jac).norm(), 0.0, 1e-10);
 
     ASSERT_NEAR((g_grad - c_grad).norm(), 0.0, 1e-10);
+    ASSERT_NEAR((g_hess - c_hess).norm(), 0.0, 1e-10);
   }
 }