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/* ----------------------------------------------------------------------------
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
* Atlanta, Georgia 30332-0415
* All Rights Reserved
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
* See LICENSE for the license information
* -------------------------------------------------------------------------- */
/**
* @file testPCGSolver.cpp
* @brief Unit tests for PCGSolver class
* @author Yong-Dian Jian
* @date Aug 06, 2014
*/
#include <tests/smallExample.h>
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
#include <gtsam/linear/GaussianFactorGraph.h>
#include <gtsam/linear/PCGSolver.h>
#include <gtsam/linear/SubgraphPreconditioner.h>
#include <gtsam/inference/Symbol.h>
#include <gtsam/base/Matrix.h>
#include <CppUnitLite/TestHarness.h>
#include <boost/shared_ptr.hpp>
#include <iostream>
#include <fstream>
using namespace std;
using namespace gtsam;
const double tol = 1e-3;
using symbol_shorthand::X;
using symbol_shorthand::L;
/* ************************************************************************* */
// Test cholesky decomposition
TEST( PCGSolver, llt ) {
Matrix R = (Matrix(3,3) <<
1., -1., -1.,
0., 2., -1.,
0., 0., 1.).finished();
Matrix AtA = R.transpose() * R;
Vector Rvector = (Vector(9) << 1., -1., -1.,
0., 2., -1.,
0., 0., 1.).finished();
// Vector Rvector = (Vector(6) << 1., -1., -1.,
// 2., -1.,
// 1.).finished();
Vector b = Vector3(1., 2., 3.);
Vector x = Vector3(6.5, 2.5, 3.) ;
/* test cholesky */
Matrix Rhat = AtA.llt().matrixL().transpose();
EXPECT(assert_equal(R, Rhat, 1e-5));
/* test backward substitution */
Vector xhat = Rhat.triangularView<Eigen::Upper>().solve(b);
EXPECT(assert_equal(x, xhat, 1e-5));
/* test in-place back substitution */
xhat = b;
Rhat.triangularView<Eigen::Upper>().solveInPlace(xhat);
EXPECT(assert_equal(x, xhat, 1e-5));
/* test triangular matrix map */
Eigen::Map<Eigen::MatrixXd> Radapter(Rvector.data(), 3, 3);
xhat = Radapter.transpose().triangularView<Eigen::Upper>().solve(b);
EXPECT(assert_equal(x, xhat, 1e-5));
}
/* ************************************************************************* */
// Test GaussianFactorGraphSystem::multiply and getb
TEST( GaussianFactorGraphSystem, multiply_getb)
{
// Create a Gaussian Factor Graph
GaussianFactorGraph simpleGFG;
SharedDiagonal unit2 = noiseModel::Diagonal::Sigmas(Vector2(0.5, 0.3));
simpleGFG += JacobianFactor(2, (Matrix(2,2)<< 10, 0, 0, 10).finished(), (Vector(2) << -1, -1).finished(), unit2);
simpleGFG += JacobianFactor(2, (Matrix(2,2)<< -10, 0, 0, -10).finished(), 0, (Matrix(2,2)<< 10, 0, 0, 10).finished(), (Vector(2) << 2, -1).finished(), unit2);
simpleGFG += JacobianFactor(2, (Matrix(2,2)<< -5, 0, 0, -5).finished(), 1, (Matrix(2,2)<< 5, 0, 0, 5).finished(), (Vector(2) << 0, 1).finished(), unit2);
simpleGFG += JacobianFactor(0, (Matrix(2,2)<< -5, 0, 0, -5).finished(), 1, (Matrix(2,2)<< 5, 0, 0, 5).finished(), (Vector(2) << -1, 1.5).finished(), unit2);
simpleGFG += JacobianFactor(0, (Matrix(2,2)<< 1, 0, 0, 1).finished(), (Vector(2) << 0, 0).finished(), unit2);
simpleGFG += JacobianFactor(1, (Matrix(2,2)<< 1, 0, 0, 1).finished(), (Vector(2) << 0, 0).finished(), unit2);
simpleGFG += JacobianFactor(2, (Matrix(2,2)<< 1, 0, 0, 1).finished(), (Vector(2) << 0, 0).finished(), unit2);
// Create a dummy-preconditioner and a GaussianFactorGraphSystem
DummyPreconditioner dummyPreconditioner;
KeyInfo keyInfo(simpleGFG);
std::map<Key,Vector> lambda;
dummyPreconditioner.build(simpleGFG, keyInfo, lambda);
GaussianFactorGraphSystem gfgs(simpleGFG, dummyPreconditioner, keyInfo, lambda);
// Prepare container for each variable
Vector initial, residual, preconditionedResidual, p, actualAp;
initial = (Vector(6) << 0., 0., 0., 0., 0., 0.).finished();
// Calculate values using GaussianFactorGraphSystem same as inside of PCGSolver
gfgs.residual(initial, residual); /* r = b-Ax */
gfgs.leftPrecondition(residual, preconditionedResidual); /* pr = L^{-1} (b-Ax) */
gfgs.rightPrecondition(preconditionedResidual, p); /* p = L^{-T} pr */
gfgs.multiply(p, actualAp); /* A p */
// Expected value of Ap for the first iteration of this example problem
Vector expectedAp = (Vector(6) << 100400, -249074.074, -2080, 148148.148, -146480, 37962.963).finished();
EXPECT(assert_equal(expectedAp, actualAp, 1e-3));
// Expected value of getb
Vector expectedb = (Vector(6) << 100.0, -194.444, -20.0, 138.889, -120.0, -55.556).finished();
Vector actualb;
gfgs.getb(actualb);
EXPECT(assert_equal(expectedb, actualb, 1e-3));
}
/* ************************************************************************* */
// Test Dummy Preconditioner
TEST(PCGSolver, dummy) {
LevenbergMarquardtParams params;
params.linearSolverType = LevenbergMarquardtParams::Iterative;
auto pcg = boost::make_shared<PCGSolverParameters>();
pcg->preconditioner_ = boost::make_shared<DummyPreconditionerParameters>();
params.iterativeParams = pcg;
NonlinearFactorGraph fg = example::createReallyNonlinearFactorGraph();
Point2 x0(10, 10);
Values c0;
c0.insert(X(1), x0);
Values actualPCG = LevenbergMarquardtOptimizer(fg, c0, params).optimize();
DOUBLES_EQUAL(0, fg.error(actualPCG), tol);
}
/* ************************************************************************* */
// Test Block-Jacobi Precondioner
TEST(PCGSolver, blockjacobi) {
LevenbergMarquardtParams params;
params.linearSolverType = LevenbergMarquardtParams::Iterative;
auto pcg = boost::make_shared<PCGSolverParameters>();
pcg->preconditioner_ =
boost::make_shared<BlockJacobiPreconditionerParameters>();
params.iterativeParams = pcg;
NonlinearFactorGraph fg = example::createReallyNonlinearFactorGraph();
Point2 x0(10, 10);
Values c0;
c0.insert(X(1), x0);
Values actualPCG = LevenbergMarquardtOptimizer(fg, c0, params).optimize();
DOUBLES_EQUAL(0, fg.error(actualPCG), tol);
}
/* ************************************************************************* */
// Test Incremental Subgraph PCG Solver
TEST(PCGSolver, subgraph) {
LevenbergMarquardtParams params;
params.linearSolverType = LevenbergMarquardtParams::Iterative;
auto pcg = boost::make_shared<PCGSolverParameters>();
pcg->preconditioner_ = boost::make_shared<SubgraphPreconditionerParameters>();
params.iterativeParams = pcg;
NonlinearFactorGraph fg = example::createReallyNonlinearFactorGraph();
Point2 x0(10, 10);
Values c0;
c0.insert(X(1), x0);
Values actualPCG = LevenbergMarquardtOptimizer(fg, c0, params).optimize();
DOUBLES_EQUAL(0, fg.error(actualPCG), tol);
}
/* ************************************************************************* */
int main() {
TestResult tr;
return TestRegistry::runAllTests(tr);
}
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