| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2022 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 "ceres/random.h" |
| #include "gtest/gtest.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 (double& PX_i : PX) { |
| 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<2, 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<2, 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 (double& qcX_i : qcX) 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<2, 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<DYNAMIC, 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<1, 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<1, 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<1, 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<1, 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<1, 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<1, 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<1, 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<1, 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<1, 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<1, 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; |
| |
| using JetT = Jet<double, 2>; |
| 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 |