diff --git a/internal/ceres/test_util.cc b/internal/ceres/test_util.cc
new file mode 100644
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+++ b/internal/ceres/test_util.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: keir@google.com (Keir Mierle)
+//
+// Utility functions useful for testing.
+
+#include <cmath>
+#include <glog/logging.h>
+#include "gtest/gtest.h"
+#include "ceres/stringprintf.h"
+
+namespace ceres {
+namespace internal {
+
+bool ExpectClose(double x, double y, double max_abs_relative_difference) {
+  double absolute_difference = fabs(x - y);
+  double relative_difference = absolute_difference / std::max(fabs(x), fabs(y));
+  if (x == 0 || y == 0) {
+    // If x or y is exactly zero, then relative difference doesn't have any
+    // meaning. Take the absolute difference instead.
+    relative_difference = absolute_difference;
+  }
+  if (relative_difference > max_abs_relative_difference) {
+    VLOG(1) << StringPrintf("x=%17g y=%17g abs=%17g rel=%17g",
+                            x, y, absolute_difference, relative_difference);
+  }
+
+  EXPECT_NEAR(relative_difference, 0.0, max_abs_relative_difference);
+  return relative_difference <= max_abs_relative_difference;
+}
+
+void ExpectArraysCloseUptoScale(int n,
+                                const double* p,
+                                const double* q,
+                                double tol) {
+  CHECK_GT(n, 0);
+  CHECK(p);
+  CHECK(q);
+
+  double p_max = 0;
+  double q_max = 0;
+  int p_i = 0;
+  int q_i = 0;
+
+  for (int i = 0; i < n; ++i) {
+    if (std::abs(p[i]) > p_max) {
+      p_max = std::abs(p[i]);
+      p_i = i;
+    }
+    if (std::abs(q[i]) > q_max) {
+      q_max = std::abs(q[i]);
+      q_i = i;
+    }
+  }
+
+  // If both arrays are all zeros, they are equal up to scale, but
+  // for testing purposes, that's more likely to be an error than
+  // a desired result.
+  CHECK_NE(p_max, 0.0);
+  CHECK_NE(q_max, 0.0);
+
+  for (int i = 0; i < n; ++i) {
+    double p_norm = p[i] / p[p_i];
+    double q_norm = q[i] / q[q_i];
+
+    EXPECT_NEAR(p_norm, q_norm, tol) << "i=" << i;
+  }
+}
+
+void ExpectArraysClose(int n,
+                       const double* p,
+                       const double* q,
+                       double tol) {
+  CHECK_GT(n, 0);
+  CHECK(p);
+  CHECK(q);
+
+  for (int i = 0; i < n; ++i) {
+    EXPECT_NEAR(p[i], q[i], tol) << "i=" << i;
+  }
+}
+
+}  // namespace internal
+}  // namespace ceres