// 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: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/schur_eliminator.h"
#include "Eigen/Dense"
#include "ceres/block_random_access_dense_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/casts.h"
#include "ceres/detect_structure.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/linear_least_squares_problems.h"
#include "ceres/test_util.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
// TODO(sameeragarwal): Reduce the size of these tests and redo the
// parameterization to be more efficient.
namespace ceres {
namespace internal {
class SchurEliminatorTest : public ::testing::Test {
protected:
void SetUpFromId(int id) {
scoped_ptr<LinearLeastSquaresProblem>
problem(CreateLinearLeastSquaresProblemFromId(id));
CHECK_NOTNULL(problem.get());
SetupHelper(problem.get());
}
void SetupHelper(LinearLeastSquaresProblem* problem) {
A.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
b.reset(problem->b.release());
D.reset(problem->D.release());
num_eliminate_blocks = problem->num_eliminate_blocks;
num_eliminate_cols = 0;
const CompressedRowBlockStructure* bs = A->block_structure();
for (int i = 0; i < num_eliminate_blocks; ++i) {
num_eliminate_cols += bs->cols[i].size;
}
}
// Compute the golden values for the reduced linear system and the
// solution to the linear least squares problem using dense linear
// algebra.
void ComputeReferenceSolution(const Vector& D) {
Matrix J;
A->ToDenseMatrix(&J);
VectorRef f(b.get(), J.rows());
Matrix H = (D.cwiseProduct(D)).asDiagonal();
H.noalias() += J.transpose() * J;
const Vector g = J.transpose() * f;
const int schur_size = J.cols() - num_eliminate_cols;
lhs_expected.resize(schur_size, schur_size);
lhs_expected.setZero();
rhs_expected.resize(schur_size);
rhs_expected.setZero();
sol_expected.resize(J.cols());
sol_expected.setZero();
Matrix P = H.block(0, 0, num_eliminate_cols, num_eliminate_cols);
Matrix Q = H.block(0,
num_eliminate_cols,
num_eliminate_cols,
schur_size);
Matrix R = H.block(num_eliminate_cols,
num_eliminate_cols,
schur_size,
schur_size);
int row = 0;
const CompressedRowBlockStructure* bs = A->block_structure();
for (int i = 0; i < num_eliminate_blocks; ++i) {
const int block_size = bs->cols[i].size;
P.block(row, row, block_size, block_size) =
P
.block(row, row, block_size, block_size)
.llt()
.solve(Matrix::Identity(block_size, block_size));
row += block_size;
}
lhs_expected
.triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
rhs_expected =
g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
sol_expected = H.llt().solve(g);
}
void EliminateSolveAndCompare(const VectorRef& diagonal,
bool use_static_structure,
const double relative_tolerance) {
const CompressedRowBlockStructure* bs = A->block_structure();
const int num_col_blocks = bs->cols.size();
vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
for (int i = num_eliminate_blocks; i < num_col_blocks; ++i) {
blocks[i - num_eliminate_blocks] = bs->cols[i].size;
}
BlockRandomAccessDenseMatrix lhs(blocks);
const int num_cols = A->num_cols();
const int schur_size = lhs.num_rows();
Vector rhs(schur_size);
LinearSolver::Options options;
options.elimination_groups.push_back(num_eliminate_blocks);
if (use_static_structure) {
DetectStructure(*bs,
num_eliminate_blocks,
&options.row_block_size,
&options.e_block_size,
&options.f_block_size);
}
scoped_ptr<SchurEliminatorBase> eliminator;
eliminator.reset(SchurEliminatorBase::Create(options));
eliminator->Init(num_eliminate_blocks, A->block_structure());
eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
Vector reduced_sol =
lhs_ref
.selfadjointView<Eigen::Upper>()
.llt()
.solve(rhs);
// Solution to the linear least squares problem.
Vector sol(num_cols);
sol.setZero();
sol.tail(schur_size) = reduced_sol;
eliminator->BackSubstitute(A.get(),
b.get(),
diagonal.data(),
reduced_sol.data(),
sol.data());
Matrix delta = (lhs_ref - lhs_expected).selfadjointView<Eigen::Upper>();
double diff = delta.norm();
EXPECT_NEAR(diff / lhs_expected.norm(), 0.0, relative_tolerance);
EXPECT_NEAR((rhs - rhs_expected).norm() / rhs_expected.norm(), 0.0,
relative_tolerance);
EXPECT_NEAR((sol - sol_expected).norm() / sol_expected.norm(), 0.0,
relative_tolerance);
}
scoped_ptr<BlockSparseMatrix> A;
scoped_array<double> b;
scoped_array<double> D;
int num_eliminate_blocks;
int num_eliminate_cols;
Matrix lhs_expected;
Vector rhs_expected;
Vector sol_expected;
};
TEST_F(SchurEliminatorTest, ScalarProblem) {
SetUpFromId(2);
Vector zero(A->num_cols());
zero.setZero();
ComputeReferenceSolution(VectorRef(zero.data(), A->num_cols()));
EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), true, 1e-14);
EliminateSolveAndCompare(VectorRef(zero.data(), A->num_cols()), false, 1e-14);
ComputeReferenceSolution(VectorRef(D.get(), A->num_cols()));
EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), true, 1e-14);
EliminateSolveAndCompare(VectorRef(D.get(), A->num_cols()), false, 1e-14);
}
} // namespace internal
} // namespace ceres