Squashed 'third_party/ceres/' content from commit e51e9b4
Change-Id: I763587619d57e594d3fa158dc3a7fe0b89a1743b
git-subtree-dir: third_party/ceres
git-subtree-split: e51e9b46f6ca88ab8b2266d0e362771db6d98067
diff --git a/internal/ceres/autodiff_test.cc b/internal/ceres/autodiff_test.cc
new file mode 100644
index 0000000..04a77ea
--- /dev/null
+++ b/internal/ceres/autodiff_test.cc
@@ -0,0 +1,667 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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)
+
+#include "ceres/internal/autodiff.h"
+
+#include "gtest/gtest.h"
+#include "ceres/random.h"
+
+namespace ceres {
+namespace internal {
+
+template <typename T> inline
+T &RowMajorAccess(T *base, int rows, int cols, int i, int j) {
+ return base[cols * i + j];
+}
+
+// Do (symmetric) finite differencing using the given function object 'b' of
+// type 'B' and scalar type 'T' with step size 'del'.
+//
+// The type B should have a signature
+//
+// bool operator()(T const *, T *) const;
+//
+// which maps a vector of parameters to a vector of outputs.
+template <typename B, typename T, int M, int N> inline
+bool SymmetricDiff(const B& b,
+ const T par[N],
+ T del, // step size.
+ T fun[M],
+ T jac[M * N]) { // row-major.
+ if (!b(par, fun)) {
+ return false;
+ }
+
+ // Temporary parameter vector.
+ T tmp_par[N];
+ for (int j = 0; j < N; ++j) {
+ tmp_par[j] = par[j];
+ }
+
+ // For each dimension, we do one forward step and one backward step in
+ // parameter space, and store the output vector vectors in these vectors.
+ T fwd_fun[M];
+ T bwd_fun[M];
+
+ for (int j = 0; j < N; ++j) {
+ // Forward step.
+ tmp_par[j] = par[j] + del;
+ if (!b(tmp_par, fwd_fun)) {
+ return false;
+ }
+
+ // Backward step.
+ tmp_par[j] = par[j] - del;
+ if (!b(tmp_par, bwd_fun)) {
+ return false;
+ }
+
+ // Symmetric differencing:
+ // f'(a) = (f(a + h) - f(a - h)) / (2 h)
+ for (int i = 0; i < M; ++i) {
+ RowMajorAccess(jac, M, N, i, j) =
+ (fwd_fun[i] - bwd_fun[i]) / (T(2) * del);
+ }
+
+ // Restore our temporary vector.
+ tmp_par[j] = par[j];
+ }
+
+ return true;
+}
+
+template <typename A> inline
+void QuaternionToScaledRotation(A const q[4], A R[3 * 3]) {
+ // Make convenient names for elements of q.
+ A a = q[0];
+ A b = q[1];
+ A c = q[2];
+ A d = q[3];
+ // This is not to eliminate common sub-expression, but to
+ // make the lines shorter so that they fit in 80 columns!
+ A aa = a*a;
+ A ab = a*b;
+ A ac = a*c;
+ A ad = a*d;
+ A bb = b*b;
+ A bc = b*c;
+ A bd = b*d;
+ A cc = c*c;
+ A cd = c*d;
+ A dd = d*d;
+#define R(i, j) RowMajorAccess(R, 3, 3, (i), (j))
+ R(0, 0) = aa+bb-cc-dd; R(0, 1) = A(2)*(bc-ad); R(0, 2) = A(2)*(ac+bd); // NOLINT
+ R(1, 0) = A(2)*(ad+bc); R(1, 1) = aa-bb+cc-dd; R(1, 2) = A(2)*(cd-ab); // NOLINT
+ R(2, 0) = A(2)*(bd-ac); R(2, 1) = A(2)*(ab+cd); R(2, 2) = aa-bb-cc+dd; // NOLINT
+#undef R
+}
+
+// A structure for projecting a 3x4 camera matrix and a
+// homogeneous 3D point, to a 2D inhomogeneous point.
+struct Projective {
+ // Function that takes P and X as separate vectors:
+ // P, X -> x
+ template <typename A>
+ bool operator()(A const P[12], A const X[4], A x[2]) const {
+ A PX[3];
+ for (int i = 0; i < 3; ++i) {
+ PX[i] = RowMajorAccess(P, 3, 4, i, 0) * X[0] +
+ RowMajorAccess(P, 3, 4, i, 1) * X[1] +
+ RowMajorAccess(P, 3, 4, i, 2) * X[2] +
+ RowMajorAccess(P, 3, 4, i, 3) * X[3];
+ }
+ if (PX[2] != 0.0) {
+ x[0] = PX[0] / PX[2];
+ x[1] = PX[1] / PX[2];
+ return true;
+ }
+ return false;
+ }
+
+ // Version that takes P and X packed in one vector:
+ //
+ // (P, X) -> x
+ //
+ template <typename A>
+ bool operator()(A const P_X[12 + 4], A x[2]) const {
+ return operator()(P_X + 0, P_X + 12, x);
+ }
+};
+
+// Test projective camera model projector.
+TEST(AutoDiff, ProjectiveCameraModel) {
+ srand(5);
+ double const tol = 1e-10; // floating-point tolerance.
+ double const del = 1e-4; // finite-difference step.
+ double const err = 1e-6; // finite-difference tolerance.
+
+ Projective b;
+
+ // Make random P and X, in a single vector.
+ double PX[12 + 4];
+ for (int i = 0; i < 12 + 4; ++i) {
+ PX[i] = RandDouble();
+ }
+
+ // Handy names for the P and X parts.
+ double *P = PX + 0;
+ double *X = PX + 12;
+
+ // Apply the mapping, to get image point b_x.
+ double b_x[2];
+ b(P, X, b_x);
+
+ // Use finite differencing to estimate the Jacobian.
+ double fd_x[2];
+ double fd_J[2 * (12 + 4)];
+ ASSERT_TRUE((SymmetricDiff<Projective, double, 2, 12 + 4>(b, PX, del,
+ fd_x, fd_J)));
+
+ for (int i = 0; i < 2; ++i) {
+ ASSERT_NEAR(fd_x[i], b_x[i], tol);
+ }
+
+ // Use automatic differentiation to compute the Jacobian.
+ double ad_x1[2];
+ double J_PX[2 * (12 + 4)];
+ {
+ double *parameters[] = { PX };
+ double *jacobians[] = { J_PX };
+ ASSERT_TRUE((AutoDifferentiate<StaticParameterDims<12 + 4>>(
+ b, parameters, 2, ad_x1, jacobians)));
+
+ for (int i = 0; i < 2; ++i) {
+ ASSERT_NEAR(ad_x1[i], b_x[i], tol);
+ }
+ }
+
+ // Use automatic differentiation (again), with two arguments.
+ {
+ double ad_x2[2];
+ double J_P[2 * 12];
+ double J_X[2 * 4];
+ double *parameters[] = { P, X };
+ double *jacobians[] = { J_P, J_X };
+ ASSERT_TRUE((AutoDifferentiate<StaticParameterDims<12, 4>>(
+ b, parameters, 2, ad_x2, jacobians)));
+
+ for (int i = 0; i < 2; ++i) {
+ ASSERT_NEAR(ad_x2[i], b_x[i], tol);
+ }
+
+ // Now compare the jacobians we got.
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 12 + 4; ++j) {
+ ASSERT_NEAR(J_PX[(12 + 4) * i + j], fd_J[(12 + 4) * i + j], err);
+ }
+
+ for (int j = 0; j < 12; ++j) {
+ ASSERT_NEAR(J_PX[(12 + 4) * i + j], J_P[12 * i + j], tol);
+ }
+ for (int j = 0; j < 4; ++j) {
+ ASSERT_NEAR(J_PX[(12 + 4) * i + 12 + j], J_X[4 * i + j], tol);
+ }
+ }
+ }
+}
+
+// Object to implement the projection by a calibrated camera.
+struct Metric {
+ // The mapping is
+ //
+ // q, c, X -> x = dehomg(R(q) (X - c))
+ //
+ // where q is a quaternion and c is the center of projection.
+ //
+ // This function takes three input vectors.
+ template <typename A>
+ bool operator()(A const q[4], A const c[3], A const X[3], A x[2]) const {
+ A R[3 * 3];
+ QuaternionToScaledRotation(q, R);
+
+ // Convert the quaternion mapping all the way to projective matrix.
+ A P[3 * 4];
+
+ // Set P(:, 1:3) = R
+ for (int i = 0; i < 3; ++i) {
+ for (int j = 0; j < 3; ++j) {
+ RowMajorAccess(P, 3, 4, i, j) = RowMajorAccess(R, 3, 3, i, j);
+ }
+ }
+
+ // Set P(:, 4) = - R c
+ for (int i = 0; i < 3; ++i) {
+ RowMajorAccess(P, 3, 4, i, 3) =
+ - (RowMajorAccess(R, 3, 3, i, 0) * c[0] +
+ RowMajorAccess(R, 3, 3, i, 1) * c[1] +
+ RowMajorAccess(R, 3, 3, i, 2) * c[2]);
+ }
+
+ A X1[4] = { X[0], X[1], X[2], A(1) };
+ Projective p;
+ return p(P, X1, x);
+ }
+
+ // A version that takes a single vector.
+ template <typename A>
+ bool operator()(A const q_c_X[4 + 3 + 3], A x[2]) const {
+ return operator()(q_c_X, q_c_X + 4, q_c_X + 4 + 3, x);
+ }
+};
+
+// This test is similar in structure to the previous one.
+TEST(AutoDiff, Metric) {
+ srand(5);
+ double const tol = 1e-10; // floating-point tolerance.
+ double const del = 1e-4; // finite-difference step.
+ double const err = 1e-5; // finite-difference tolerance.
+
+ Metric b;
+
+ // Make random parameter vector.
+ double qcX[4 + 3 + 3];
+ for (int i = 0; i < 4 + 3 + 3; ++i)
+ qcX[i] = RandDouble();
+
+ // Handy names.
+ double *q = qcX;
+ double *c = qcX + 4;
+ double *X = qcX + 4 + 3;
+
+ // Compute projection, b_x.
+ double b_x[2];
+ ASSERT_TRUE(b(q, c, X, b_x));
+
+ // Finite differencing estimate of Jacobian.
+ double fd_x[2];
+ double fd_J[2 * (4 + 3 + 3)];
+ ASSERT_TRUE((SymmetricDiff<Metric, double, 2, 4 + 3 + 3>(b, qcX, del,
+ fd_x, fd_J)));
+
+ for (int i = 0; i < 2; ++i) {
+ ASSERT_NEAR(fd_x[i], b_x[i], tol);
+ }
+
+ // Automatic differentiation.
+ double ad_x[2];
+ double J_q[2 * 4];
+ double J_c[2 * 3];
+ double J_X[2 * 3];
+ double *parameters[] = { q, c, X };
+ double *jacobians[] = { J_q, J_c, J_X };
+ ASSERT_TRUE((AutoDifferentiate<StaticParameterDims<4, 3, 3>>(
+ b, parameters, 2, ad_x, jacobians)));
+
+ for (int i = 0; i < 2; ++i) {
+ ASSERT_NEAR(ad_x[i], b_x[i], tol);
+ }
+
+ // Compare the pieces.
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 4; ++j) {
+ ASSERT_NEAR(J_q[4 * i + j], fd_J[(4 + 3 + 3) * i + j], err);
+ }
+ for (int j = 0; j < 3; ++j) {
+ ASSERT_NEAR(J_c[3 * i + j], fd_J[(4 + 3 + 3) * i + j + 4], err);
+ }
+ for (int j = 0; j < 3; ++j) {
+ ASSERT_NEAR(J_X[3 * i + j], fd_J[(4 + 3 + 3) * i + j + 4 + 3], err);
+ }
+ }
+}
+
+struct VaryingResidualFunctor {
+ template <typename T>
+ bool operator()(const T x[2], T* y) const {
+ for (int i = 0; i < num_residuals; ++i) {
+ y[i] = T(i) * x[0] * x[1] * x[1];
+ }
+ return true;
+ }
+
+ int num_residuals;
+};
+
+TEST(AutoDiff, VaryingNumberOfResidualsForOneCostFunctorType) {
+ double x[2] = { 1.0, 5.5 };
+ double *parameters[] = { x };
+ const int kMaxResiduals = 10;
+ double J_x[2 * kMaxResiduals];
+ double residuals[kMaxResiduals];
+ double *jacobians[] = { J_x };
+
+ // Use a single functor, but tweak it to produce different numbers of
+ // residuals.
+ VaryingResidualFunctor functor;
+
+ for (int num_residuals = 1; num_residuals < kMaxResiduals; ++num_residuals) {
+ // Tweak the number of residuals to produce.
+ functor.num_residuals = num_residuals;
+
+ // Run autodiff with the new number of residuals.
+ ASSERT_TRUE((AutoDifferentiate<StaticParameterDims<2>>(
+ functor, parameters, num_residuals, residuals, jacobians)));
+
+ const double kTolerance = 1e-14;
+ for (int i = 0; i < num_residuals; ++i) {
+ EXPECT_NEAR(J_x[2 * i + 0], i * x[1] * x[1], kTolerance) << "i: " << i;
+ EXPECT_NEAR(J_x[2 * i + 1], 2 * i * x[0] * x[1], kTolerance)
+ << "i: " << i;
+ }
+ }
+}
+
+struct Residual1Param {
+ template <typename T>
+ bool operator()(const T* x0, T* y) const {
+ y[0] = *x0;
+ return true;
+ }
+};
+
+struct Residual2Param {
+ template <typename T>
+ bool operator()(const T* x0, const T* x1, T* y) const {
+ y[0] = *x0 + pow(*x1, 2);
+ return true;
+ }
+};
+
+struct Residual3Param {
+ template <typename T>
+ bool operator()(const T* x0, const T* x1, const T* x2, T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3);
+ return true;
+ }
+};
+
+struct Residual4Param {
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3) + pow(*x3, 4);
+ return true;
+ }
+};
+
+struct Residual5Param {
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3) + pow(*x3, 4) + pow(*x4, 5);
+ return true;
+ }
+};
+
+struct Residual6Param {
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3) + pow(*x3, 4) + pow(*x4, 5) +
+ pow(*x5, 6);
+ return true;
+ }
+};
+
+struct Residual7Param {
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3) + pow(*x3, 4) + pow(*x4, 5) +
+ pow(*x5, 6) + pow(*x6, 7);
+ return true;
+ }
+};
+
+struct Residual8Param {
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ const T* x7,
+ T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3) + pow(*x3, 4) + pow(*x4, 5) +
+ pow(*x5, 6) + pow(*x6, 7) + pow(*x7, 8);
+ return true;
+ }
+};
+
+struct Residual9Param {
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ const T* x7,
+ const T* x8,
+ T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3) + pow(*x3, 4) + pow(*x4, 5) +
+ pow(*x5, 6) + pow(*x6, 7) + pow(*x7, 8) + pow(*x8, 9);
+ return true;
+ }
+};
+
+struct Residual10Param {
+ template <typename T>
+ bool operator()(const T* x0,
+ const T* x1,
+ const T* x2,
+ const T* x3,
+ const T* x4,
+ const T* x5,
+ const T* x6,
+ const T* x7,
+ const T* x8,
+ const T* x9,
+ T* y) const {
+ y[0] = *x0 + pow(*x1, 2) + pow(*x2, 3) + pow(*x3, 4) + pow(*x4, 5) +
+ pow(*x5, 6) + pow(*x6, 7) + pow(*x7, 8) + pow(*x8, 9) + pow(*x9, 10);
+ return true;
+ }
+};
+
+TEST(AutoDiff, VariadicAutoDiff) {
+ double x[10];
+ double residual = 0;
+ double* parameters[10];
+ double jacobian_values[10];
+ double* jacobians[10];
+
+ for (int i = 0; i < 10; ++i) {
+ x[i] = 2.0;
+ parameters[i] = x + i;
+ jacobians[i] = jacobian_values + i;
+ }
+
+ {
+ Residual1Param functor;
+ int num_variables = 1;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual2Param functor;
+ int num_variables = 2;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual3Param functor;
+ int num_variables = 3;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual4Param functor;
+ int num_variables = 4;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1, 1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual5Param functor;
+ int num_variables = 5;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1, 1, 1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual6Param functor;
+ int num_variables = 6;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1, 1, 1, 1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual7Param functor;
+ int num_variables = 7;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1, 1, 1, 1, 1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual8Param functor;
+ int num_variables = 8;
+ EXPECT_TRUE((AutoDifferentiate<StaticParameterDims<1, 1, 1, 1, 1, 1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual9Param functor;
+ int num_variables = 9;
+ EXPECT_TRUE(
+ (AutoDifferentiate<StaticParameterDims<1, 1, 1, 1, 1, 1, 1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+
+ {
+ Residual10Param functor;
+ int num_variables = 10;
+ EXPECT_TRUE(
+ (AutoDifferentiate<StaticParameterDims<1, 1, 1, 1, 1, 1, 1, 1, 1, 1>>(
+ functor, parameters, 1, &residual, jacobians)));
+ EXPECT_EQ(residual, pow(2, num_variables + 1) - 2);
+ for (int i = 0; i < num_variables; ++i) {
+ EXPECT_EQ(jacobian_values[i], (i + 1) * pow(2, i));
+ }
+ }
+}
+
+// This is fragile test that triggers the alignment bug on
+// i686-apple-darwin10-llvm-g++-4.2 (GCC) 4.2.1. It is quite possible,
+// that other combinations of operating system + compiler will
+// re-arrange the operations in this test.
+//
+// But this is the best (and only) way we know of to trigger this
+// problem for now. A more robust solution that guarantees the
+// alignment of Eigen types used for automatic differentiation would
+// be nice.
+TEST(AutoDiff, AlignedAllocationTest) {
+ // This int is needed to allocate 16 bits on the stack, so that the
+ // next allocation is not aligned by default.
+ char y = 0;
+
+ // This is needed to prevent the compiler from optimizing y out of
+ // this function.
+ y += 1;
+
+ typedef Jet<double, 2> JetT;
+ FixedArray<JetT, (256 * 7) / sizeof(JetT)> x(3);
+
+ // Need this to makes sure that x does not get optimized out.
+ x[0] = x[0] + JetT(1.0);
+}
+
+} // namespace internal
+} // namespace ceres