157 lines
4.5 KiB
C++
157 lines
4.5 KiB
C++
/*
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* testTensors.cpp
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* @brief try tensor expressions based on http://www.gps.caltech.edu/~walter/FTensor/FTensor.pdf
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* Created on: Feb 9, 2010
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* @author: Frank Dellaert
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*/
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#include <iostream>
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#include <boost/foreach.hpp>
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#include <boost/assign/std/list.hpp> // for operator +=
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using namespace boost::assign;
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#include <CppUnitLite/TestHarness.h>
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#include "tensors.h"
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#include "tensorInterface.h"
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#include "projectiveGeometry.h"
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using namespace std;
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using namespace gtsam;
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using namespace tensors;
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/* ************************************************************************* */
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// Indices
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Index<3, 'a'> a, _a;
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Index<3, 'b'> b, _b;
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Index<3, 'c'> c, _c;
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Index<4, 'A'> A;
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Index<4, 'B'> B;
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/* ************************************************************************* */
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// Tensor1
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/* ************************************************************************* */
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TEST(Tensor1, Basics)
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{
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Point2h p = point2h(1, 2, 3), q = point2h(2, 4, 6);
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CHECK(p(a)==p(a))
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CHECK(assert_equality(p(a),p(a)))
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CHECK(assert_equivalent(p(a),q(a)))
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DOUBLES_EQUAL(sqrt(14),norm(p(a)),1e-9)
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CHECK(assert_equality(p(a)*2,q(a)))
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}
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/* ************************************************************************* */
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TEST( Tensor1, Incidence2D)
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{
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Line2h l = line2h(-13, 5, 1);
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Point2h p = point2h(1, 2, 3), q = point2h(2, 5, 1);
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// incidence
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DOUBLES_EQUAL(l(a)*p(a),0,1e-9)
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DOUBLES_EQUAL(l(a)*q(a),0,1e-9)
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DOUBLES_EQUAL(p(a)*l(a),0,1e-9)
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DOUBLES_EQUAL(q(a)*l(a),0,1e-9)
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}
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/* ************************************************************************* */
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TEST( Tensor1, Incidence3D)
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{
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Plane3h pi = plane3h(0, 1, 0, -2);
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Point3h P = point3h(0, 2, 0, 1), Q = point3h(1, 2, 0, 1);
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// incidence
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DOUBLES_EQUAL(pi(A)*P(A),0,1e-9)
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DOUBLES_EQUAL(pi(A)*Q(A),0,1e-9)
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DOUBLES_EQUAL(P(A)*pi(A),0,1e-9)
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DOUBLES_EQUAL(Q(A)*pi(A),0,1e-9)
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}
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/* ************************************************************************* */
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// Tensor2
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/* ************************************************************************* */
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TEST( Tensor2, Outer3)
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{
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Line2h l1 = line2h(1, 2, 3), l2 = line2h(1, 3, 5);
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double data[3][3] = { { 1, 2, 3 }, { 2, 4, 6 }, { 3, 6, 9 } };
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Tensor2<3, 3> expected(data);
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CHECK(expected(a,b) == expected(a,b))
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CHECK(expected(a,b) == l1(a) * l1(b))
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CHECK(expected(a,b).swap() == l1(b) * l1(a))
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}
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/* ************************************************************************* */
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TEST( Tensor2, Outer34)
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{
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Line2h l = line2h(1, 2, 3);
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Plane3h pi = plane3h(1, 3, 5, 7);
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double
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data[4][3] = { { 1, 2, 3 }, { 3, 6, 9 }, { 5, 10, 15 }, { 7, 14, 21 } };
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Tensor2<3, 4> expected(data);
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CHECK(assert_equality(expected(a,B),l(a) * pi(B)))
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CHECK(assert_equality(expected(a,B).swap(),pi(B) * l(a)))
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}
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/* ************************************************************************* */
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TEST( Tensor2, SpecialContract)
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{
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double data[3][3] = { { 1, 2, 3 }, { 2, 4, 6 }, { 3, 6, 9 } };
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Tensor2<3, 3> S(data), T(data);
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//print(S(a, b) * T(a, c)); // contract a -> b,c
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// S(a,0)*T(a,0) = [1 2 3] . [1 2 3] = 14
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// S(a,0)*T(a,2) = [1 2 3] . [3 6 9] = 3+12+27 = 42
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double data2[3][3] = { { 14, 28, 42 }, { 28, 56, 84 }, { 42, 84, 126 } };
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Tensor2<3, 3> expected(data2);
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CHECK(assert_equality(expected(b,c), S(a, b) * T(a, c)));
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}
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/* ************************************************************************* */
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TEST( Tensor2, ProjectiveCamera)
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{
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Point2h p = point2h(1 + 2, 2, 5);
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Point3h P = point3h(1, 2, 5, 1);
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double data[4][3] = { { 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }, { 2, 0, 0 } };
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ProjectiveCamera M(data);
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CHECK(assert_equality(p(a),M(a,A)*P(A)))
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}
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/* ************************************************************************* */
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// Tensor3
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/* ************************************************************************* */
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TEST( Tensor3, Join)
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{
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Line2h l = line2h(-13, 5, 1);
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Point2h p = point2h(1, 2, 3), q = point2h(2, 5, 1);
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// join points into line
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Eta3 e;
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CHECK(assert_equality(e(a, b, c) * p(a) * q(b), l(c)))
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}
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/* ************************************************************************* */
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TEST( Tensor5, Outer32)
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{
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double t[3][3][3] = { { { 0, 0, 3 }, { 0, 8, -125 }, { -3, 125, 1 } }, { { 0,
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0, 3 }, { 0, 8, -125 }, { -3, 125, 1 } }, { { 0, 0, 3 }, { 0, 8, -125 },
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{ -3, 125, 1 } } };
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TrifocalTensor T(t);
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double data[3][3] = { { 0, 0, 3 }, { 0, 8, -125 }, { -3, 125, 1 } };
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FundamentalMatrix F(data);
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Index<3, 'd'> d, _d;
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Index<3, 'e'> e, _e;
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//print(T(_a,b,c)*F(_d,_e));
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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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