223 lines
7.5 KiB
C++
223 lines
7.5 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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* -------------------------------------------------------------------------- */
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/**
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* @file testSubgraphConditioner.cpp
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* @brief Unit tests for SubgraphPreconditioner
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* @author Frank Dellaert
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**/
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#include <tests/smallExample.h>
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#include <gtsam/base/numericalDerivative.h>
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#include <gtsam/inference/Ordering.h>
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#include <gtsam/inference/Symbol.h>
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#include <gtsam/linear/GaussianEliminationTree.h>
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#include <gtsam/linear/GaussianFactorGraph.h>
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#include <gtsam/linear/SubgraphPreconditioner.h>
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#include <gtsam/linear/iterative.h>
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#include <gtsam/slam/dataset.h>
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#include <gtsam/symbolic/SymbolicFactorGraph.h>
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#include <CppUnitLite/TestHarness.h>
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#include <fstream>
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using namespace std;
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using namespace gtsam;
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using namespace example;
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// define keys
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// Create key for simulated planar graph
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Symbol key(int x, int y) { return symbol_shorthand::X(1000 * x + y); }
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/* ************************************************************************* */
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TEST(SubgraphPreconditioner, planarOrdering) {
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// Check canonical ordering
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Ordering expected, ordering = planarOrdering(3);
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expected +=
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key(3, 3), key(2, 3), key(1, 3),
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key(3, 2), key(2, 2), key(1, 2),
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key(3, 1), key(2, 1), key(1, 1);
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EXPECT(assert_equal(expected, ordering));
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}
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/* ************************************************************************* */
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/** unnormalized error */
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static double error(const GaussianFactorGraph& fg, const VectorValues& x) {
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double total_error = 0.;
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for (const GaussianFactor::shared_ptr& factor : fg)
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total_error += factor->error(x);
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return total_error;
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}
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/* ************************************************************************* */
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TEST(SubgraphPreconditioner, planarGraph) {
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// Check planar graph construction
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const auto [A, xtrue] = planarGraph(3);
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LONGS_EQUAL(13, A.size());
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LONGS_EQUAL(9, xtrue.size());
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DOUBLES_EQUAL(0, error(A, xtrue), 1e-9); // check zero error for xtrue
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// Check that xtrue is optimal
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GaussianBayesNet R1 = *A.eliminateSequential();
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VectorValues actual = R1.optimize();
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EXPECT(assert_equal(xtrue, actual));
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}
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/* ************************************************************************* */
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TEST(SubgraphPreconditioner, splitOffPlanarTree) {
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// Build a planar graph
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const auto [A, xtrue] = planarGraph(3);
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// Get the spanning tree and constraints, and check their sizes
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const auto [T, C] = splitOffPlanarTree(3, A);
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LONGS_EQUAL(9, T.size());
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LONGS_EQUAL(4, C.size());
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// Check that the tree can be solved to give the ground xtrue
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GaussianBayesNet R1 = *T.eliminateSequential();
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VectorValues xbar = R1.optimize();
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EXPECT(assert_equal(xtrue, xbar));
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}
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/* ************************************************************************* */
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TEST(SubgraphPreconditioner, system) {
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// Build a planar graph
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size_t N = 3;
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const auto [Ab, xtrue] = planarGraph(N); // A*x-b
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// Get the spanning tree and remaining graph
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auto [Ab1, Ab2] = splitOffPlanarTree(N, Ab);
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// Eliminate the spanning tree to build a prior
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const Ordering ord = planarOrdering(N);
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auto Rc1 = *Ab1.eliminateSequential(ord); // R1*x-c1
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VectorValues xbar = Rc1.optimize(); // xbar = inv(R1)*c1
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// Create Subgraph-preconditioned system
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const SubgraphPreconditioner system(Ab2, Rc1, xbar);
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// Get corresponding matrices for tests. Add dummy factors to Ab2 to make
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// sure it works with the ordering.
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Ordering ordering = Rc1.ordering(); // not ord in general!
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Ab2.add(key(1, 1), Z_2x2, Z_2x1);
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Ab2.add(key(1, 2), Z_2x2, Z_2x1);
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Ab2.add(key(1, 3), Z_2x2, Z_2x1);
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const auto [A, b] = Ab.jacobian(ordering);
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const auto [A1, b1] = Ab1.jacobian(ordering);
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const auto [A2, b2] = Ab2.jacobian(ordering);
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Matrix R1 = Rc1.matrix(ordering).first;
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Matrix Abar(13 * 2, 9 * 2);
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Abar.topRows(9 * 2) = Matrix::Identity(9 * 2, 9 * 2);
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Abar.bottomRows(8) = A2.topRows(8) * R1.inverse();
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// Helper function to vectorize in correct order, which is the order in which
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// we eliminated the spanning tree.
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auto vec = [ordering](const VectorValues& x) { return x.vector(ordering); };
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// Set up y0 as all zeros
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const VectorValues y0 = system.zero();
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// y1 = perturbed y0
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VectorValues y1 = system.zero();
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y1[key(3, 3)] = Vector2(1.0, -1.0);
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// Check backSubstituteTranspose works with R1
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VectorValues actual = Rc1.backSubstituteTranspose(y1);
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Vector expected = R1.transpose().inverse() * vec(y1);
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EXPECT(assert_equal(expected, vec(actual)));
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// Check corresponding x values
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// for y = 0, we get xbar:
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EXPECT(assert_equal(xbar, system.x(y0)));
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// for non-zero y, answer is x = xbar + inv(R1)*y
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const Vector expected_x1 = vec(xbar) + R1.inverse() * vec(y1);
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const VectorValues x1 = system.x(y1);
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EXPECT(assert_equal(expected_x1, vec(x1)));
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// Check errors
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DOUBLES_EQUAL(0, error(Ab, xbar), 1e-9);
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DOUBLES_EQUAL(0, system.error(y0), 1e-9);
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DOUBLES_EQUAL(2, error(Ab, x1), 1e-9);
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DOUBLES_EQUAL(2, system.error(y1), 1e-9);
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// Check that transposeMultiplyAdd <=> y += alpha * Abar' * e
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// We check for e1 =[1;0] and e2=[0;1] corresponding to T and C
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const double alpha = 0.5;
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Errors e1, e2;
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for (size_t i = 0; i < 13; i++) {
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e1.push_back(i < 9 ? Vector2(1, 1) : Vector2(0, 0));
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e2.push_back(i >= 9 ? Vector2(1, 1) : Vector2(0, 0));
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}
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Vector ee1(13 * 2), ee2(13 * 2);
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ee1 << Vector::Ones(9 * 2), Vector::Zero(4 * 2);
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ee2 << Vector::Zero(9 * 2), Vector::Ones(4 * 2);
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// Check transposeMultiplyAdd for e1
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VectorValues y = system.zero();
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system.transposeMultiplyAdd(alpha, e1, y);
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Vector expected_y = alpha * Abar.transpose() * ee1;
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EXPECT(assert_equal(expected_y, vec(y)));
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// Check transposeMultiplyAdd for e2
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y = system.zero();
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system.transposeMultiplyAdd(alpha, e2, y);
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expected_y = alpha * Abar.transpose() * ee2;
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EXPECT(assert_equal(expected_y, vec(y)));
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// Test gradient in y
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auto g = system.gradient(y0);
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Vector expected_g = Vector::Zero(18);
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EXPECT(assert_equal(expected_g, vec(g)));
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}
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/* ************************************************************************* */
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TEST(SubgraphPreconditioner, conjugateGradients) {
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// Build a planar graph
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size_t N = 3;
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const auto [Ab, xtrue] = planarGraph(N); // A*x-b
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// Get the spanning tree
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const auto [Ab1, Ab2] = splitOffPlanarTree(N, Ab);
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// Eliminate the spanning tree to build a prior
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GaussianBayesNet Rc1 = *Ab1.eliminateSequential(); // R1*x-c1
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VectorValues xbar = Rc1.optimize(); // xbar = inv(R1)*c1
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// Create Subgraph-preconditioned system
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SubgraphPreconditioner system(Ab2, Rc1, xbar);
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// Create zero config y0 and perturbed config y1
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VectorValues y0 = VectorValues::Zero(xbar);
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VectorValues y1 = y0;
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y1[key(2, 2)] = Vector2(1.0, -1.0);
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VectorValues x1 = system.x(y1);
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// Solve for the remaining constraints using PCG
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ConjugateGradientParameters parameters;
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VectorValues actual = conjugateGradients<SubgraphPreconditioner,
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VectorValues, Errors>(system, y1, parameters);
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EXPECT(assert_equal(y0,actual));
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// Compare with non preconditioned version:
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VectorValues actual2 = conjugateGradientDescent(Ab, x1, parameters);
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EXPECT(assert_equal(xtrue, actual2, 1e-4));
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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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