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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: fredp@google.com (Fred Pighin)
//
// TODO(sameeragarwal): More comprehensive testing with larger and
// more badly conditioned problem.
#include "ceres/conjugate_gradients_solver.h"
#include <memory>
#include "ceres/internal/eigen.h"
#include "ceres/linear_solver.h"
#include "ceres/preconditioner.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "gtest/gtest.h"
namespace ceres::internal {
TEST(ConjugateGradientTest, Solves3x3IdentitySystem) {
double diagonal[] = {1.0, 1.0, 1.0};
std::unique_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;
ConjugateGradientsSolverOptions cg_options;
cg_options.min_num_iterations = 1;
cg_options.max_num_iterations = 10;
cg_options.residual_reset_period = 20;
cg_options.q_tolerance = 0.0;
cg_options.r_tolerance = 1e-9;
Vector scratch[4];
for (int i = 0; i < 4; ++i) {
scratch[i] = Vector::Zero(A->num_cols());
}
IdentityPreconditioner identity(A->num_cols());
LinearOperatorAdapter lhs(*A);
LinearOperatorAdapter preconditioner(identity);
Vector* scratch_array[4] = {
&scratch[0], &scratch[1], &scratch[2], &scratch[3]};
auto summary = ConjugateGradientsSolver(
cg_options, lhs, b, preconditioner, scratch_array, x);
EXPECT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
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) {
std::unique_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;
ConjugateGradientsSolverOptions cg_options;
cg_options.min_num_iterations = 1;
cg_options.max_num_iterations = 10;
cg_options.residual_reset_period = 20;
cg_options.q_tolerance = 0.0;
cg_options.r_tolerance = 1e-9;
Vector scratch[4];
for (int i = 0; i < 4; ++i) {
scratch[i] = Vector::Zero(A->num_cols());
}
Vector* scratch_array[4] = {
&scratch[0], &scratch[1], &scratch[2], &scratch[3]};
IdentityPreconditioner identity(A->num_cols());
LinearOperatorAdapter lhs(*A);
LinearOperatorAdapter preconditioner(identity);
auto summary = ConjugateGradientsSolver(
cg_options, lhs, b, preconditioner, scratch_array, x);
EXPECT_EQ(summary.termination_type, LinearSolverTerminationType::SUCCESS);
ASSERT_DOUBLE_EQ(0, x(0));
ASSERT_DOUBLE_EQ(1, x(1));
ASSERT_DOUBLE_EQ(2, x(2));
}
} // namespace ceres::internal