479 lines
15 KiB
C++
479 lines
15 KiB
C++
/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010, Georgia Tech Research Corporation,
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* Atlanta, Georgia 30332-0415
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* All Rights Reserved
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* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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* See LICENSE for the license information
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* -------------------------------1------------------------------------------- */
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/**
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* @file testExpression.cpp
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* @date September 18, 2014
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* @author Frank Dellaert
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* @author Paul Furgale
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* @brief unit tests for Block Automatic Differentiation
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*/
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#include <gtsam/geometry/PinholeCamera.h>
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#include <gtsam/geometry/Pose3.h>
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#include <gtsam/geometry/Cal3_S2.h>
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#include <gtsam/geometry/Cal3Bundler.h>
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#include <gtsam_unstable/nonlinear/Expression.h>
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#include <gtsam/base/Testable.h>
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#include <gtsam/base/LieScalar.h>
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#include <gtsam_unstable/nonlinear/ceres_autodiff.h>
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#include <gtsam_unstable/nonlinear/ceres_rotation.h>
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#undef CHECK
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#include <CppUnitLite/TestHarness.h>
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#include <boost/assign/list_of.hpp>
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using boost::assign::list_of;
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using boost::assign::map_list_of;
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using namespace std;
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using namespace gtsam;
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// The DefaultChart of Camera below is laid out like Snavely's 9-dim vector
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typedef PinholeCamera<Cal3Bundler> Camera;
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/* ************************************************************************* */
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// Some Ceres Snippets copied for testing
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// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
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template<typename T> inline T &RowMajorAccess(T *base, int rows, int cols,
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int i, int j) {
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return base[cols * i + j];
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}
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inline double RandDouble() {
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double r = static_cast<double>(rand());
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return r / RAND_MAX;
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}
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// A structure for projecting a 3x4 camera matrix and a
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// homogeneous 3D point, to a 2D inhomogeneous point.
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struct Projective {
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// Function that takes P and X as separate vectors:
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// P, X -> x
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template<typename A>
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bool operator()(A const P[12], A const X[4], A x[2]) const {
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A PX[3];
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for (int i = 0; i < 3; ++i) {
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PX[i] = RowMajorAccess(P, 3, 4, i, 0) * X[0]
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+ RowMajorAccess(P, 3, 4, i, 1) * X[1]
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+ RowMajorAccess(P, 3, 4, i, 2) * X[2]
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+ RowMajorAccess(P, 3, 4, i, 3) * X[3];
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}
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if (PX[2] != 0.0) {
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x[0] = PX[0] / PX[2];
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x[1] = PX[1] / PX[2];
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return true;
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}
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return false;
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}
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// Adapt to eigen types
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Vector2 operator()(const MatrixRowMajor& P, const Vector4& X) const {
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Vector2 x;
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if (operator()(P.data(), X.data(), x.data()))
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return x;
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else
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throw std::runtime_error("Projective fail");
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}
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};
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// Templated pinhole camera model for used with Ceres. The camera is
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// parameterized using 9 parameters: 3 for rotation, 3 for translation, 1 for
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// focal length and 2 for radial distortion. The principal point is not modeled
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// (i.e. it is assumed be located at the image center).
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struct SnavelyProjection {
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template<typename T>
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bool operator()(const T* const camera, const T* const point,
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T* predicted) const {
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// camera[0,1,2] are the angle-axis rotation.
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T p[3];
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ceres::AngleAxisRotatePoint(camera, point, p);
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// camera[3,4,5] are the translation.
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p[0] += camera[3];
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p[1] += camera[4];
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p[2] += camera[5];
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// Compute the center of distortion. The sign change comes from
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// the camera model that Noah Snavely's Bundler assumes, whereby
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// the camera coordinate system has a negative z axis.
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T xp = -p[0] / p[2];
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T yp = -p[1] / p[2];
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// Apply second and fourth order radial distortion.
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const T& l1 = camera[7];
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const T& l2 = camera[8];
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T r2 = xp * xp + yp * yp;
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T distortion = T(1.0) + r2 * (l1 + l2 * r2);
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// Compute final projected point position.
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const T& focal = camera[6];
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predicted[0] = focal * distortion * xp;
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predicted[1] = focal * distortion * yp;
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return true;
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}
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// Adapt to GTSAM types
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Vector2 operator()(const Vector9& P, const Vector3& X) const {
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Vector2 x;
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if (operator()(P.data(), X.data(), x.data()))
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return x;
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else
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throw std::runtime_error("Snavely fail");
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}
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};
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/* ************************************************************************* */
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// is_manifold
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TEST(Manifold, _is_manifold) {
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using namespace traits;
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EXPECT(!is_manifold<int>::value);
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EXPECT(is_manifold<Point2>::value);
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EXPECT(is_manifold<Matrix24>::value);
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EXPECT(is_manifold<double>::value);
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EXPECT(is_manifold<Vector>::value);
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EXPECT(is_manifold<Matrix>::value);
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}
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/* ************************************************************************* */
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// dimension
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TEST(Manifold, _dimension) {
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using namespace traits;
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EXPECT_LONGS_EQUAL(2, dimension<Point2>::value);
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EXPECT_LONGS_EQUAL(8, dimension<Matrix24>::value);
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EXPECT_LONGS_EQUAL(1, dimension<double>::value);
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EXPECT_LONGS_EQUAL(Eigen::Dynamic, dimension<Vector>::value);
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EXPECT_LONGS_EQUAL(Eigen::Dynamic, dimension<Matrix>::value);
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}
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/* ************************************************************************* */
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// charts
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TEST(Manifold, DefaultChart) {
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DefaultChart<Point2> chart1(Point2(0, 0));
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EXPECT(chart1.apply(Point2(1,0))==Vector2(1,0));
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EXPECT(chart1.retract(Vector2(1,0))==Point2(1,0));
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DefaultChart<Vector2> chart2(Vector2(0, 0));
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EXPECT(chart2.apply(Vector2(1,0))==Vector2(1,0));
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EXPECT(chart2.retract(Vector2(1,0))==Vector2(1,0));
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DefaultChart<double> chart3(0);
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Eigen::Matrix<double, 1, 1> v1;
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v1 << 1;
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EXPECT(chart3.apply(1)==v1);
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EXPECT(chart3.retract(v1)==1);
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// Dynamic does not work yet !
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// Vector z = zero(2), v(2);
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// v << 1, 0;
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// DefaultChart<Vector> chart4(z);
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// EXPECT(chart4.apply(v)==v);
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// EXPECT(chart4.retract(v)==v);
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}
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/* ************************************************************************* */
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// zero
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TEST(Manifold, _zero) {
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EXPECT(assert_equal(Pose3(),traits::zero<Pose3>::value()));
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Cal3Bundler cal(0,0,0);
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EXPECT(assert_equal(cal,traits::zero<Cal3Bundler>::value()));
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EXPECT(assert_equal(Camera(Pose3(),cal),traits::zero<Camera>::value()));
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}
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/* ************************************************************************* */
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// charts
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TEST(Manifold, Canonical) {
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Canonical<Point2> chart1;
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EXPECT(chart1.apply(Point2(1,0))==Vector2(1,0));
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EXPECT(chart1.retract(Vector2(1,0))==Point2(1,0));
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Canonical<Vector2> chart2;
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EXPECT(assert_equal((Vector)chart2.apply(Vector2(1,0)),Vector2(1,0)));
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EXPECT(chart2.retract(Vector2(1,0))==Vector2(1,0));
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Canonical<double> chart3;
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Eigen::Matrix<double, 1, 1> v1;
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v1 << 1;
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EXPECT(chart3.apply(1)==v1);
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EXPECT(chart3.retract(v1)==1);
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Canonical<Point3> chart4;
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Point3 point(1,2,3);
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Vector3 v3(1,2,3);
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EXPECT(assert_equal((Vector)chart4.apply(point),v3));
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EXPECT(assert_equal(chart4.retract(v3),point));
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Canonical<Pose3> chart5;
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Pose3 pose(Rot3::identity(),point);
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Vector6 v6; v6 << 0,0,0,1,2,3;
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EXPECT(assert_equal((Vector)chart5.apply(pose),v6));
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EXPECT(assert_equal(chart5.retract(v6),pose));
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Canonical<Camera> chart6;
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Cal3Bundler cal0(0,0,0);
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Camera camera(Pose3(),cal0);
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Vector9 z9 = Vector9::Zero();
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EXPECT(assert_equal((Vector)chart6.apply(camera),z9));
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EXPECT(assert_equal(chart6.retract(z9),camera));
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Cal3Bundler cal; // Note !! Cal3Bundler() != zero<Cal3Bundler>::value()
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Camera camera2(pose,cal);
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Vector9 v9; v9 << 0,0,0,1,2,3,1,0,0;
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EXPECT(assert_equal((Vector)chart6.apply(camera2),v9));
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EXPECT(assert_equal(chart6.retract(v9),camera2));
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}
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/* ************************************************************************* */
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// New-style numerical derivatives using manifold_traits
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template<typename Y, typename X>
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Matrix numericalDerivative(boost::function<Y(const X&)> h, const X& x,
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double delta = 1e-5) {
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using namespace traits;
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BOOST_STATIC_ASSERT(is_manifold<Y>::value);
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static const size_t M = dimension<Y>::value;
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typedef DefaultChart<Y> ChartY;
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typedef typename ChartY::vector TangentY;
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BOOST_STATIC_ASSERT(is_manifold<X>::value);
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static const size_t N = dimension<X>::value;
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typedef DefaultChart<X> ChartX;
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typedef typename ChartX::vector TangentX;
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// get chart at x
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ChartX chartX(x);
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// get value at x, and corresponding chart
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Y hx = h(x);
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ChartY chartY(hx);
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// Prepare a tangent vector to perturb x with
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TangentX dx;
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dx.setZero();
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// Fill in Jacobian H
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Matrix H = zeros(M, N);
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double factor = 1.0 / (2.0 * delta);
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for (size_t j = 0; j < N; j++) {
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dx(j) = delta;
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TangentY dy1 = chartY.apply(h(chartX.retract(dx)));
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dx(j) = -delta;
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TangentY dy2 = chartY.apply(h(chartX.retract(dx)));
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H.block<M, 1>(0, j) << (dy1 - dy2) * factor;
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dx(j) = 0;
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}
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return H;
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}
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template<typename Y, typename X1, typename X2>
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Matrix numericalDerivative21(boost::function<Y(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta = 1e-5) {
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return numericalDerivative<Y, X1>(boost::bind(h, _1, x2), x1, delta);
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}
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template<typename Y, typename X1, typename X2>
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Matrix numericalDerivative22(boost::function<Y(const X1&, const X2&)> h,
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const X1& x1, const X2& x2, double delta = 1e-5) {
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return numericalDerivative<Y, X2>(boost::bind(h, x1, _1), x2, delta);
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}
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/* ************************************************************************* */
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// Test Ceres AutoDiff
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TEST(Expression, AutoDiff) {
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using ceres::internal::AutoDiff;
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// Instantiate function
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Projective projective;
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// Make arguments
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typedef Eigen::Matrix<double, 3, 4, Eigen::RowMajor> M;
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M P;
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P << 1, 0, 0, 0, 0, 1, 0, 5, 0, 0, 1, 0;
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Vector4 X(10, 0, 5, 1);
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// Apply the mapping, to get image point b_x.
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Vector expected = Vector2(2, 1);
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Vector2 actual = projective(P, X);
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EXPECT(assert_equal(expected,actual,1e-9));
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// Get expected derivatives
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Matrix E1 = numericalDerivative21<Vector2, M, Vector4>(Projective(), P, X);
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Matrix E2 = numericalDerivative22<Vector2, M, Vector4>(Projective(), P, X);
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// Get derivatives with AutoDiff
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Vector2 actual2;
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MatrixRowMajor H1(2, 12), H2(2, 4);
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double *parameters[] = { P.data(), X.data() };
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double *jacobians[] = { H1.data(), H2.data() };
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CHECK(
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(AutoDiff<Projective, double, 12, 4>::Differentiate( projective, parameters, 2, actual2.data(), jacobians)));
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EXPECT(assert_equal(E1,H1,1e-8));
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EXPECT(assert_equal(E2,H2,1e-8));
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}
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/* ************************************************************************* */
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// Test Ceres AutoDiff on Snavely
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TEST(Expression, AutoDiff2) {
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using ceres::internal::AutoDiff;
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// Instantiate function
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SnavelyProjection snavely;
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// Make arguments
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Vector9 P; // zero rotation, (0,5,0) translation, focal length 1
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P << 0, 0, 0, 0, 5, 0, 1, 0, 0;
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Vector3 X(10, 0, -5); // negative Z-axis convention of Snavely!
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// Apply the mapping, to get image point b_x.
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Vector expected = Vector2(2, 1);
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Vector2 actual = snavely(P, X);
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EXPECT(assert_equal(expected,actual,1e-9));
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// Get expected derivatives
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Matrix E1 = numericalDerivative21<Vector2, Vector9, Vector3>(
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SnavelyProjection(), P, X);
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Matrix E2 = numericalDerivative22<Vector2, Vector9, Vector3>(
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SnavelyProjection(), P, X);
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// Get derivatives with AutoDiff
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Vector2 actual2;
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MatrixRowMajor H1(2, 9), H2(2, 3);
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double *parameters[] = { P.data(), X.data() };
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double *jacobians[] = { H1.data(), H2.data() };
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CHECK(
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(AutoDiff<SnavelyProjection, double, 9, 3>::Differentiate( snavely, parameters, 2, actual2.data(), jacobians)));
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EXPECT(assert_equal(E1,H1,1e-8));
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EXPECT(assert_equal(E2,H2,1e-8));
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}
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/* ************************************************************************* */
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// Adapt ceres-style autodiff
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template<typename F, typename T, typename A1, typename A2>
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class AdaptAutoDiff {
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static const int N = traits::dimension<T>::value;
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static const int M1 = traits::dimension<A1>::value;
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static const int M2 = traits::dimension<A2>::value;
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typedef Eigen::Matrix<double, N, M1, Eigen::RowMajor> RowMajor1;
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typedef Eigen::Matrix<double, N, M2, Eigen::RowMajor> RowMajor2;
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typedef Canonical<T> CanonicalT;
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typedef Canonical<A1> Canonical1;
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typedef Canonical<A2> Canonical2;
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typedef typename CanonicalT::vector VectorT;
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typedef typename Canonical1::vector Vector1;
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typedef typename Canonical2::vector Vector2;
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// Instantiate function and charts
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CanonicalT chartT;
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Canonical1 chart1;
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Canonical2 chart2;
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F f;
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public:
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typedef Eigen::Matrix<double, N, M1> JacobianTA1;
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typedef Eigen::Matrix<double, N, M2> JacobianTA2;
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T operator()(const A1& a1, const A2& a2, boost::optional<JacobianTA1&> H1 =
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boost::none, boost::optional<JacobianTA2&> H2 = boost::none) {
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using ceres::internal::AutoDiff;
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// Make arguments
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Vector1 v1 = chart1.apply(a1);
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Vector2 v2 = chart2.apply(a2);
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bool success;
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VectorT result;
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if (H1 || H2) {
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// Get derivatives with AutoDiff
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double *parameters[] = { v1.data(), v2.data() };
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double rowMajor1[N * M1], rowMajor2[N * M2]; // om the stack
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double *jacobians[] = { rowMajor1, rowMajor2 };
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success = AutoDiff<F, double, 9, 3>::Differentiate(f, parameters, 2,
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result.data(), jacobians);
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// Convert from row-major to columnn-major
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// TODO: if this is a bottleneck (probably not!) fix Autodiff to be Column-Major
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*H1 = Eigen::Map<RowMajor1>(rowMajor1);
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*H2 = Eigen::Map<RowMajor2>(rowMajor2);
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} else {
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// Apply the mapping, to get result
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success = f(v1.data(), v2.data(), result.data());
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}
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if (!success)
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throw std::runtime_error(
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"AdaptAutoDiff: function call resulted in failure");
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return chartT.retract(result);
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}
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};
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/* ************************************************************************* */
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// Test AutoDiff wrapper Snavely
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TEST(Expression, AutoDiff3) {
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// Make arguments
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Camera P(Pose3(Rot3(), Point3(0, 5, 0)), Cal3Bundler(1, 0, 0));
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Point3 X(10, 0, -5); // negative Z-axis convention of Snavely!
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typedef AdaptAutoDiff<SnavelyProjection, Point2, Camera, Point3> Adaptor;
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Adaptor snavely;
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// Apply the mapping, to get image point b_x.
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Point2 expected(2, 1);
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Point2 actual = snavely(P, X);
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EXPECT(assert_equal(expected,actual,1e-9));
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// // Get expected derivatives
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Matrix E1 = numericalDerivative21<Point2, Camera, Point3>(Adaptor(), P, X);
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Matrix E2 = numericalDerivative22<Point2, Camera, Point3>(Adaptor(), P, X);
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// Get derivatives with AutoDiff, not gives RowMajor results!
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Matrix29 H1;
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Matrix23 H2;
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Point2 actual2 = snavely(P, X, H1, H2);
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EXPECT(assert_equal(expected,actual,1e-9));
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EXPECT(assert_equal(E1,H1,1e-8));
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EXPECT(assert_equal(E2,H2,1e-8));
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}
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/* ************************************************************************* */
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// Test AutoDiff wrapper in an expression
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TEST(Expression, Snavely) {
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Expression<Camera> P(1);
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Expression<Point3> X(2);
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typedef AdaptAutoDiff<SnavelyProjection, Point2, Camera, Point3> Adaptor;
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Expression<Point2> expression(Adaptor(), P, X);
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set<Key> expected = list_of(1)(2);
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EXPECT(expected == expression.keys());
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}
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/* ************************************************************************* */
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int main() {
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TestResult tr;
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return TestRegistry::runAllTests(tr);
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}
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/* ************************************************************************* */
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