Initial commit of Ceres Solver.
diff --git a/internal/ceres/schur_complement_solver.cc b/internal/ceres/schur_complement_solver.cc
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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/
+//
+// Redistribution and use in source and binary forms, with or without
+// 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
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// 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
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#include <algorithm>
+#include <ctime>
+#include <set>
+#include <vector>
+#include "Eigen/Dense"
+#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/detect_structure.h"
+#include "ceres/linear_solver.h"
+#include "ceres/schur_complement_solver.h"
+#include "ceres/suitesparse.h"
+#include "ceres/triplet_sparse_matrix.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/port.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/types.h"
+
+namespace ceres {
+namespace internal {
+
+LinearSolver::Summary SchurComplementSolver::SolveImpl(
+ BlockSparseMatrixBase* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double* x) {
+ const time_t start_time = time(NULL);
+ if (!options_.constant_sparsity || (eliminator_.get() == NULL)) {
+ InitStorage(A->block_structure());
+ DetectStructure(*A->block_structure(),
+ options_.num_eliminate_blocks,
+ &options_.row_block_size,
+ &options_.e_block_size,
+ &options_.f_block_size);
+ eliminator_.reset(CHECK_NOTNULL(SchurEliminatorBase::Create(options_)));
+ eliminator_->Init(options_.num_eliminate_blocks, A->block_structure());
+ };
+ const time_t init_time = time(NULL);
+ fill(x, x + A->num_cols(), 0.0);
+
+ LinearSolver::Summary summary;
+ summary.num_iterations = 1;
+ summary.termination_type = FAILURE;
+ eliminator_->Eliminate(A, b, per_solve_options.D, lhs_.get(), rhs_.get());
+ const time_t eliminate_time = time(NULL);
+
+ double* reduced_solution = x + A->num_cols() - lhs_->num_cols();
+ const bool status = SolveReducedLinearSystem(reduced_solution);
+ const time_t solve_time = time(NULL);
+
+ if (!status) {
+ return summary;
+ }
+
+ eliminator_->BackSubstitute(A, b, per_solve_options.D, reduced_solution, x);
+ const time_t backsubstitute_time = time(NULL);
+ summary.termination_type = TOLERANCE;
+
+ VLOG(2) << "time (sec) total: " << backsubstitute_time - start_time
+ << " init: " << init_time - start_time
+ << " eliminate: " << eliminate_time - init_time
+ << " solve: " << solve_time - eliminate_time
+ << " backsubstitute: " << backsubstitute_time - solve_time;
+ return summary;
+}
+
+// Initialize a BlockRandomAccessDenseMatrix to store the Schur
+// complement.
+void DenseSchurComplementSolver::InitStorage(
+ const CompressedRowBlockStructure* bs) {
+ const int num_eliminate_blocks = options().num_eliminate_blocks;
+ 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.
+bool DenseSchurComplementSolver::SolveReducedLinearSystem(double* solution) {
+ 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 true;
+ }
+
+ // TODO(sameeragarwal): Add proper error handling; this completely ignores
+ // the quality of the solution to the solve.
+ VectorRef(solution, num_rows) =
+ ConstMatrixRef(m->values(), num_rows, num_rows)
+ .selfadjointView<Eigen::Upper>()
+ .ldlt()
+ .solve(ConstVectorRef(rhs(), num_rows));
+
+ return true;
+}
+
+#ifndef CERES_NO_SUITESPARSE
+SparseSchurComplementSolver::SparseSchurComplementSolver(
+ const LinearSolver::Options& options)
+ : SchurComplementSolver(options),
+ symbolic_factor_(NULL) {
+}
+
+SparseSchurComplementSolver::~SparseSchurComplementSolver() {
+ if (symbolic_factor_ != NULL) {
+ ss_.Free(symbolic_factor_);
+ symbolic_factor_ = NULL;
+ }
+}
+
+// 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().num_eliminate_blocks;
+ const int num_col_blocks = bs->cols.size();
+ const int num_row_blocks = bs->rows.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;
+ }
+
+ 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()]);
+}
+
+// Solve the system Sx = r, assuming that the matrix S is stored in a
+// BlockRandomAccessSparseMatrix. The linear system is solved using
+// CHOLMOD's sparse cholesky factorization routines.
+bool SparseSchurComplementSolver::SolveReducedLinearSystem(double* solution) {
+ // Extract the TripletSparseMatrix that is used for actually storing S.
+ TripletSparseMatrix* tsm =
+ const_cast<TripletSparseMatrix*>(
+ down_cast<const BlockRandomAccessSparseMatrix*>(lhs())->matrix());
+
+ const int num_rows = tsm->num_rows();
+
+ // The case where there are no f blocks, and the system is block
+ // diagonal.
+ if (num_rows == 0) {
+ return true;
+ }
+
+ cholmod_sparse* cholmod_lhs = ss_.CreateSparseMatrix(tsm);
+ // The matrix is symmetric, and the upper triangular part of the
+ // matrix contains the values.
+ cholmod_lhs->stype = 1;
+
+ cholmod_dense* cholmod_rhs =
+ ss_.CreateDenseVector(const_cast<double*>(rhs()), num_rows, num_rows);
+
+ // Symbolic factorization is computed if we don't already have one handy.
+ if (symbolic_factor_ == NULL) {
+ symbolic_factor_ = ss_.AnalyzeCholesky(cholmod_lhs);
+ }
+
+ cholmod_dense* cholmod_solution =
+ ss_.SolveCholesky(cholmod_lhs, symbolic_factor_, cholmod_rhs);
+
+ ss_.Free(cholmod_lhs);
+ cholmod_lhs = NULL;
+ ss_.Free(cholmod_rhs);
+ cholmod_rhs = NULL;
+
+ // If sparsity is not constant across calls, then reset the symbolic
+ // factorization.
+ if (!options().constant_sparsity) {
+ ss_.Free(symbolic_factor_);
+ symbolic_factor_ = NULL;
+ }
+
+ if (cholmod_solution == NULL) {
+ LOG(ERROR) << "CHOLMOD solve failed.";
+ return false;
+ }
+
+ VectorRef(solution, num_rows)
+ = VectorRef(static_cast<double*>(cholmod_solution->x), num_rows);
+ ss_.Free(cholmod_solution);
+ return true;
+}
+#endif // CERES_NO_SUITESPARSE
+
+} // namespace internal
+} // namespace ceres
