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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
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// Author: fredp@google.com (Fred Pighin)
//
// Tests for linear solvers that solve symmetric linear systems. Some
// of this code is inhertited from Fred Pighin's code for testing the
// old Conjugate Gradients solver.
//
// TODO(sameeragarwal): More comprehensive testing with larger and
// more badly conditioned problem.
#include "gtest/gtest.h"
#include "ceres/conjugate_gradients_solver.h"
#include "ceres/linear_solver.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/types.h"
namespace ceres {
namespace internal {
TEST(ConjugateGradientTest, Solves3x3IdentitySystem) {
double diagonal[] = { 1.0, 1.0, 1.0 };
scoped_ptr<TripletSparseMatrix>
A(TripletSparseMatrix::CreateSparseDiagonalMatrix(diagonal, 3));
Vector b(3);
Vector x(3);
b(0) = 1.0;
b(1) = 2.0;
b(2) = 3.0;
x(0) = 1;
x(1) = 1;
x(2) = 1;
LinearSolver::Options options;
options.max_num_iterations = 10;
LinearSolver::PerSolveOptions per_solve_options;
per_solve_options.r_tolerance = 1e-9;
ConjugateGradientsSolver solver(options);
LinearSolver::Summary summary =
solver.Solve(A.get(), b.data(), per_solve_options, x.data());
EXPECT_EQ(summary.termination_type, TOLERANCE);
ASSERT_EQ(summary.num_iterations, 1);
ASSERT_DOUBLE_EQ(1, x(0));
ASSERT_DOUBLE_EQ(2, x(1));
ASSERT_DOUBLE_EQ(3, x(2));
}
TEST(ConjuateGradientTest, Solves3x3SymmetricSystem) {
scoped_ptr<TripletSparseMatrix> A(new TripletSparseMatrix(3, 3, 9));
Vector b(3);
Vector x(3);
// | 2 -1 0|
// A = |-1 2 -1| is symmetric positive definite.
// | 0 -1 2|
int* Ai = A->mutable_rows();
int* Aj = A->mutable_cols();
double* Ax = A->mutable_values();
int counter = 0;
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
Ai[counter] = i;
Aj[counter] = j;
++counter;
}
}
Ax[0] = 2.;
Ax[1] = -1.;
Ax[2] = 0;
Ax[3] = -1.;
Ax[4] = 2;
Ax[5] = -1;
Ax[6] = 0;
Ax[7] = -1;
Ax[8] = 2;
A->set_num_nonzeros(9);
b(0) = -1;
b(1) = 0;
b(2) = 3;
x(0) = 1;
x(1) = 1;
x(2) = 1;
LinearSolver::Options options;
options.max_num_iterations = 10;
LinearSolver::PerSolveOptions per_solve_options;
per_solve_options.r_tolerance = 1e-9;
ConjugateGradientsSolver solver(options);
LinearSolver::Summary summary =
solver.Solve(A.get(), b.data(), per_solve_options, x.data());
EXPECT_EQ(summary.termination_type, TOLERANCE);
ASSERT_DOUBLE_EQ(0, x(0));
ASSERT_DOUBLE_EQ(1, x(1));
ASSERT_DOUBLE_EQ(2, x(2));
}
} // namespace internal
} // namespace ceres