// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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// this list of conditions and the following disclaimer in the documentation
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// Author: sameeragarwal@google.com (Sameer Agarwal)
#include "ceres/schur_complement_solver.h"
#include <algorithm>
#include <ctime>
#include <set>
#include <vector>
#include "Eigen/Dense"
#include "Eigen/SparseCore"
#include "ceres/block_random_access_dense_matrix.h"
#include "ceres/block_random_access_matrix.h"
#include "ceres/block_random_access_sparse_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/conjugate_gradients_solver.h"
#include "ceres/detect_structure.h"
#include "ceres/internal/eigen.h"
#include "ceres/internal/scoped_ptr.h"
#include "ceres/lapack.h"
#include "ceres/linear_solver.h"
#include "ceres/sparse_cholesky.h"
#include "ceres/triplet_sparse_matrix.h"
#include "ceres/types.h"
#include "ceres/wall_time.h"
namespace ceres {
namespace internal {
using std::make_pair;
using std::pair;
using std::set;
using std::vector;
namespace {
class BlockRandomAccessSparseMatrixAdapter : public LinearOperator {
public:
explicit BlockRandomAccessSparseMatrixAdapter(
const BlockRandomAccessSparseMatrix& m)
: m_(m) {
}
virtual ~BlockRandomAccessSparseMatrixAdapter() {}
// y = y + Ax;
virtual void RightMultiply(const double* x, double* y) const {
m_.SymmetricRightMultiply(x, y);
}
// y = y + A'x;
virtual void LeftMultiply(const double* x, double* y) const {
m_.SymmetricRightMultiply(x, y);
}
virtual int num_rows() const { return m_.num_rows(); }
virtual int num_cols() const { return m_.num_rows(); }
private:
const BlockRandomAccessSparseMatrix& m_;
};
class BlockRandomAccessDiagonalMatrixAdapter : public LinearOperator {
public:
explicit BlockRandomAccessDiagonalMatrixAdapter(
const BlockRandomAccessDiagonalMatrix& m)
: m_(m) {
}
virtual ~BlockRandomAccessDiagonalMatrixAdapter() {}
// y = y + Ax;
virtual void RightMultiply(const double* x, double* y) const {
m_.RightMultiply(x, y);
}
// y = y + A'x;
virtual void LeftMultiply(const double* x, double* y) const {
m_.RightMultiply(x, y);
}
virtual int num_rows() const { return m_.num_rows(); }
virtual int num_cols() const { return m_.num_rows(); }
private:
const BlockRandomAccessDiagonalMatrix& m_;
};
} // namespace
LinearSolver::Summary SchurComplementSolver::SolveImpl(
BlockSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) {
EventLogger event_logger("SchurComplementSolver::Solve");
if (eliminator_.get() == NULL) {
InitStorage(A->block_structure());
DetectStructure(*A->block_structure(),
options_.elimination_groups[0],
&options_.row_block_size,
&options_.e_block_size,
&options_.f_block_size);
eliminator_.reset(CHECK_NOTNULL(SchurEliminatorBase::Create(options_)));
const bool kFullRankETE = true;
eliminator_->Init(
options_.elimination_groups[0], kFullRankETE, A->block_structure());
};
std::fill(x, x + A->num_cols(), 0.0);
event_logger.AddEvent("Setup");
eliminator_->Eliminate(A, b, per_solve_options.D, lhs_.get(), rhs_.get());
event_logger.AddEvent("Eliminate");
double* reduced_solution = x + A->num_cols() - lhs_->num_cols();
const LinearSolver::Summary summary =
SolveReducedLinearSystem(per_solve_options, reduced_solution);
event_logger.AddEvent("ReducedSolve");
if (summary.termination_type == LINEAR_SOLVER_SUCCESS) {
eliminator_->BackSubstitute(A, b, per_solve_options.D, reduced_solution, x);
event_logger.AddEvent("BackSubstitute");
}
return summary;
}
// Initialize a BlockRandomAccessDenseMatrix to store the Schur
// complement.
void DenseSchurComplementSolver::InitStorage(
const CompressedRowBlockStructure* bs) {
const int num_eliminate_blocks = options().elimination_groups[0];
const int num_col_blocks = bs->cols.size();
vector<int> blocks(num_col_blocks - num_eliminate_blocks, 0);
for (int i = num_eliminate_blocks, j = 0;
i < num_col_blocks;
++i, ++j) {
blocks[j] = bs->cols[i].size;
}
set_lhs(new BlockRandomAccessDenseMatrix(blocks));
set_rhs(new double[lhs()->num_rows()]);
}
// Solve the system Sx = r, assuming that the matrix S is stored in a
// BlockRandomAccessDenseMatrix. The linear system is solved using
// Eigen's Cholesky factorization.
LinearSolver::Summary
DenseSchurComplementSolver::SolveReducedLinearSystem(
const LinearSolver::PerSolveOptions& per_solve_options,
double* solution) {
LinearSolver::Summary summary;
summary.num_iterations = 0;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
const BlockRandomAccessDenseMatrix* m =
down_cast<const BlockRandomAccessDenseMatrix*>(lhs());
const int num_rows = m->num_rows();
// The case where there are no f blocks, and the system is block
// diagonal.
if (num_rows == 0) {
return summary;
}
summary.num_iterations = 1;
if (options().dense_linear_algebra_library_type == EIGEN) {
Eigen::LLT<Matrix, Eigen::Upper> llt =
ConstMatrixRef(m->values(), num_rows, num_rows)
.selfadjointView<Eigen::Upper>()
.llt();
if (llt.info() != Eigen::Success) {
summary.termination_type = LINEAR_SOLVER_FAILURE;
summary.message =
"Eigen failure. Unable to perform dense Cholesky factorization.";
return summary;
}
VectorRef(solution, num_rows) = llt.solve(ConstVectorRef(rhs(), num_rows));
} else {
VectorRef(solution, num_rows) = ConstVectorRef(rhs(), num_rows);
summary.termination_type =
LAPACK::SolveInPlaceUsingCholesky(num_rows,
m->values(),
solution,
&summary.message);
}
return summary;
}
SparseSchurComplementSolver::SparseSchurComplementSolver(
const LinearSolver::Options& options)
: SchurComplementSolver(options) {
if (options.type != ITERATIVE_SCHUR) {
sparse_cholesky_.reset(
SparseCholesky::Create(options.sparse_linear_algebra_library_type,
options.use_postordering ? AMD : NATURAL));
}
}
SparseSchurComplementSolver::~SparseSchurComplementSolver() {
}
// Determine the non-zero blocks in the Schur Complement matrix, and
// initialize a BlockRandomAccessSparseMatrix object.
void SparseSchurComplementSolver::InitStorage(
const CompressedRowBlockStructure* bs) {
const int num_eliminate_blocks = options().elimination_groups[0];
const int num_col_blocks = bs->cols.size();
const int num_row_blocks = bs->rows.size();
blocks_.resize(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;
}
set<pair<int, int> > block_pairs;
for (int i = 0; i < blocks_.size(); ++i) {
block_pairs.insert(make_pair(i, i));
}
int r = 0;
while (r < num_row_blocks) {
int e_block_id = bs->rows[r].cells.front().block_id;
if (e_block_id >= num_eliminate_blocks) {
break;
}
vector<int> f_blocks;
// Add to the chunk until the first block in the row is
// different than the one in the first row for the chunk.
for (; r < num_row_blocks; ++r) {
const CompressedRow& row = bs->rows[r];
if (row.cells.front().block_id != e_block_id) {
break;
}
// Iterate over the blocks in the row, ignoring the first
// block since it is the one to be eliminated.
for (int c = 1; c < row.cells.size(); ++c) {
const Cell& cell = row.cells[c];
f_blocks.push_back(cell.block_id - num_eliminate_blocks);
}
}
sort(f_blocks.begin(), f_blocks.end());
f_blocks.erase(unique(f_blocks.begin(), f_blocks.end()), f_blocks.end());
for (int i = 0; i < f_blocks.size(); ++i) {
for (int j = i + 1; j < f_blocks.size(); ++j) {
block_pairs.insert(make_pair(f_blocks[i], f_blocks[j]));
}
}
}
// Remaing rows do not contribute to the chunks and directly go
// into the schur complement via an outer product.
for (; r < num_row_blocks; ++r) {
const CompressedRow& row = bs->rows[r];
CHECK_GE(row.cells.front().block_id, num_eliminate_blocks);
for (int i = 0; i < row.cells.size(); ++i) {
int r_block1_id = row.cells[i].block_id - num_eliminate_blocks;
for (int j = 0; j < row.cells.size(); ++j) {
int r_block2_id = row.cells[j].block_id - num_eliminate_blocks;
if (r_block1_id <= r_block2_id) {
block_pairs.insert(make_pair(r_block1_id, r_block2_id));
}
}
}
}
set_lhs(new BlockRandomAccessSparseMatrix(blocks_, block_pairs));
set_rhs(new double[lhs()->num_rows()]);
}
LinearSolver::Summary SparseSchurComplementSolver::SolveReducedLinearSystem(
const LinearSolver::PerSolveOptions& per_solve_options, double* solution) {
if (options().type == ITERATIVE_SCHUR) {
return SolveReducedLinearSystemUsingConjugateGradients(per_solve_options,
solution);
}
LinearSolver::Summary summary;
summary.num_iterations = 0;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
const TripletSparseMatrix* tsm =
down_cast<const BlockRandomAccessSparseMatrix*>(lhs())->matrix();
if (tsm->num_rows() == 0) {
return summary;
}
scoped_ptr<CompressedRowSparseMatrix> lhs;
const CompressedRowSparseMatrix::StorageType storage_type =
sparse_cholesky_->StorageType();
if (storage_type == CompressedRowSparseMatrix::UPPER_TRIANGULAR) {
lhs.reset(CompressedRowSparseMatrix::FromTripletSparseMatrix(*tsm));
lhs->set_storage_type(CompressedRowSparseMatrix::UPPER_TRIANGULAR);
} else {
lhs.reset(
CompressedRowSparseMatrix::FromTripletSparseMatrixTransposed(*tsm));
lhs->set_storage_type(CompressedRowSparseMatrix::LOWER_TRIANGULAR);
}
*lhs->mutable_col_blocks() = blocks_;
*lhs->mutable_row_blocks() = blocks_;
summary.num_iterations = 1;
summary.termination_type = sparse_cholesky_->FactorAndSolve(
lhs.get(), rhs(), solution, &summary.message);
return summary;
}
LinearSolver::Summary
SparseSchurComplementSolver::SolveReducedLinearSystemUsingConjugateGradients(
const LinearSolver::PerSolveOptions& per_solve_options,
double* solution) {
CHECK(options().use_explicit_schur_complement);
const int num_rows = lhs()->num_rows();
// The case where there are no f blocks, and the system is block
// diagonal.
if (num_rows == 0) {
LinearSolver::Summary summary;
summary.num_iterations = 0;
summary.termination_type = LINEAR_SOLVER_SUCCESS;
summary.message = "Success.";
return summary;
}
// Only SCHUR_JACOBI is supported over here right now.
CHECK_EQ(options().preconditioner_type, SCHUR_JACOBI);
if (preconditioner_.get() == NULL) {
preconditioner_.reset(new BlockRandomAccessDiagonalMatrix(blocks_));
}
BlockRandomAccessSparseMatrix* sc =
down_cast<BlockRandomAccessSparseMatrix*>(
const_cast<BlockRandomAccessMatrix*>(lhs()));
// Extract block diagonal from the Schur complement to construct the
// schur_jacobi preconditioner.
for (int i = 0; i < blocks_.size(); ++i) {
const int block_size = blocks_[i];
int sc_r, sc_c, sc_row_stride, sc_col_stride;
CellInfo* sc_cell_info =
CHECK_NOTNULL(sc->GetCell(i, i,
&sc_r, &sc_c,
&sc_row_stride, &sc_col_stride));
MatrixRef sc_m(sc_cell_info->values, sc_row_stride, sc_col_stride);
int pre_r, pre_c, pre_row_stride, pre_col_stride;
CellInfo* pre_cell_info = CHECK_NOTNULL(
preconditioner_->GetCell(i, i,
&pre_r, &pre_c,
&pre_row_stride, &pre_col_stride));
MatrixRef pre_m(pre_cell_info->values, pre_row_stride, pre_col_stride);
pre_m.block(pre_r, pre_c, block_size, block_size) =
sc_m.block(sc_r, sc_c, block_size, block_size);
}
preconditioner_->Invert();
VectorRef(solution, num_rows).setZero();
scoped_ptr<LinearOperator> lhs_adapter(
new BlockRandomAccessSparseMatrixAdapter(*sc));
scoped_ptr<LinearOperator> preconditioner_adapter(
new BlockRandomAccessDiagonalMatrixAdapter(*preconditioner_));
LinearSolver::Options cg_options;
cg_options.min_num_iterations = options().min_num_iterations;
cg_options.max_num_iterations = options().max_num_iterations;
ConjugateGradientsSolver cg_solver(cg_options);
LinearSolver::PerSolveOptions cg_per_solve_options;
cg_per_solve_options.r_tolerance = per_solve_options.r_tolerance;
cg_per_solve_options.q_tolerance = per_solve_options.q_tolerance;
cg_per_solve_options.preconditioner = preconditioner_adapter.get();
return cg_solver.Solve(lhs_adapter.get(),
rhs(),
cg_per_solve_options,
solution);
}
} // namespace internal
} // namespace ceres