Squashed 'third_party/eigen/' content from commit 61d72f6

Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/unsupported/Eigen/src/NonLinearOptimization/chkder.h b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
new file mode 100644
index 0000000..db8ff7d
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/chkder.h
@@ -0,0 +1,66 @@
+#define chkder_log10e 0.43429448190325182765
+#define chkder_factor 100.
+
+namespace Eigen { 
+
+namespace internal {
+
+template<typename Scalar>
+void chkder(
+        const Matrix< Scalar, Dynamic, 1 >  &x,
+        const Matrix< Scalar, Dynamic, 1 >  &fvec,
+        const Matrix< Scalar, Dynamic, Dynamic > &fjac,
+        Matrix< Scalar, Dynamic, 1 >  &xp,
+        const Matrix< Scalar, Dynamic, 1 >  &fvecp,
+        int mode,
+        Matrix< Scalar, Dynamic, 1 >  &err
+        )
+{
+    using std::sqrt;
+    using std::abs;
+    using std::log;
+    
+    typedef DenseIndex Index;
+
+    const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());
+    const Scalar epsf = chkder_factor * NumTraits<Scalar>::epsilon();
+    const Scalar epslog = chkder_log10e * log(eps);
+    Scalar temp;
+
+    const Index m = fvec.size(), n = x.size();
+
+    if (mode != 2) {
+        /* mode = 1. */
+        xp.resize(n);
+        for (Index j = 0; j < n; ++j) {
+            temp = eps * abs(x[j]);
+            if (temp == 0.)
+                temp = eps;
+            xp[j] = x[j] + temp;
+        }
+    }
+    else {
+        /* mode = 2. */
+        err.setZero(m); 
+        for (Index j = 0; j < n; ++j) {
+            temp = abs(x[j]);
+            if (temp == 0.)
+                temp = 1.;
+            err += temp * fjac.col(j);
+        }
+        for (Index i = 0; i < m; ++i) {
+            temp = 1.;
+            if (fvec[i] != 0. && fvecp[i] != 0. && abs(fvecp[i] - fvec[i]) >= epsf * abs(fvec[i]))
+                temp = eps * abs((fvecp[i] - fvec[i]) / eps - err[i]) / (abs(fvec[i]) + abs(fvecp[i]));
+            err[i] = 1.;
+            if (temp > NumTraits<Scalar>::epsilon() && temp < eps)
+                err[i] = (chkder_log10e * log(temp) - epslog) / epslog;
+            if (temp >= eps)
+                err[i] = 0.;
+        }
+    }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen