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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 "ceres/sparse_normal_cholesky_solver.h"
+
+#include <algorithm>
+#include <cstring>
+#include <ctime>
+
+#ifndef CERES_NO_CXSPARSE
+#include "cs.h"
+#endif
+
+#include "ceres/compressed_row_sparse_matrix.h"
+#include "ceres/linear_solver.h"
+#include "ceres/suitesparse.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 {
+
+SparseNormalCholeskySolver::SparseNormalCholeskySolver(
+ const LinearSolver::Options& options)
+ : options_(options) {
+#ifndef CERES_NO_SUITESPARSE
+ factor_ = NULL;
+#endif
+
+#ifndef CERES_NO_CXSPARSE
+ cxsparse_factor_ = NULL;
+#endif // CERES_NO_CXSPARSE
+}
+
+SparseNormalCholeskySolver::~SparseNormalCholeskySolver() {
+#ifndef CERES_NO_SUITESPARSE
+ if (factor_ != NULL) {
+ ss_.Free(factor_);
+ factor_ = NULL;
+ }
+#endif
+
+#ifndef CERES_NO_CXSPARSE
+ if (cxsparse_factor_ != NULL) {
+ cxsparse_.Free(cxsparse_factor_);
+ cxsparse_factor_ = NULL;
+ }
+#endif // CERES_NO_CXSPARSE
+}
+
+LinearSolver::Summary SparseNormalCholeskySolver::SolveImpl(
+ CompressedRowSparseMatrix* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double * x) {
+ switch (options_.sparse_linear_algebra_library) {
+ case SUITE_SPARSE:
+ return SolveImplUsingSuiteSparse(A, b, per_solve_options, x);
+ case CX_SPARSE:
+ return SolveImplUsingCXSparse(A, b, per_solve_options, x);
+ default:
+ LOG(FATAL) << "Unknown sparse linear algebra library : "
+ << options_.sparse_linear_algebra_library;
+ }
+
+ LOG(FATAL) << "Unknown sparse linear algebra library : "
+ << options_.sparse_linear_algebra_library;
+ return LinearSolver::Summary();
+}
+
+#ifndef CERES_NO_CXSPARSE
+LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingCXSparse(
+ CompressedRowSparseMatrix* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double * x) {
+ LinearSolver::Summary summary;
+ summary.num_iterations = 1;
+ const int num_cols = A->num_cols();
+ Vector Atb = Vector::Zero(num_cols);
+ A->LeftMultiply(b, Atb.data());
+
+ if (per_solve_options.D != NULL) {
+ // Temporarily append a diagonal block to the A matrix, but undo
+ // it before returning the matrix to the user.
+ CompressedRowSparseMatrix D(per_solve_options.D, num_cols);
+ A->AppendRows(D);
+ }
+
+ VectorRef(x, num_cols).setZero();
+
+ // Wrap the augmented Jacobian in a compressed sparse column matrix.
+ cs_di At = cxsparse_.CreateSparseMatrixTransposeView(A);
+
+ // Compute the normal equations. J'J delta = J'f and solve them
+ // using a sparse Cholesky factorization. Notice that when compared
+ // to SuiteSparse we have to explicitly compute the transpose of Jt,
+ // and then the normal equations before they can be
+ // factorized. CHOLMOD/SuiteSparse on the other hand can just work
+ // off of Jt to compute the Cholesky factorization of the normal
+ // equations.
+ cs_di* A2 = cs_transpose(&At, 1);
+ cs_di* AtA = cs_multiply(&At,A2);
+
+ cxsparse_.Free(A2);
+ if (per_solve_options.D != NULL) {
+ A->DeleteRows(num_cols);
+ }
+
+ // Compute symbolic factorization if not available.
+ if (cxsparse_factor_ == NULL) {
+ cxsparse_factor_ = CHECK_NOTNULL(cxsparse_.AnalyzeCholesky(AtA));
+ }
+
+ // Solve the linear system.
+ if (cxsparse_.SolveCholesky(AtA, cxsparse_factor_, Atb.data())) {
+ VectorRef(x, Atb.rows()) = Atb;
+ summary.termination_type = TOLERANCE;
+ }
+
+ cxsparse_.Free(AtA);
+ return summary;
+}
+#else
+LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingCXSparse(
+ CompressedRowSparseMatrix* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double * x) {
+ LOG(FATAL) << "No CXSparse support in Ceres.";
+
+ // Unreachable but MSVC does not know this.
+ return LinearSolver::Summary();
+}
+#endif
+
+#ifndef CERES_NO_SUITESPARSE
+LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingSuiteSparse(
+ CompressedRowSparseMatrix* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double * x) {
+ const time_t start_time = time(NULL);
+ const int num_cols = A->num_cols();
+
+ LinearSolver::Summary summary;
+ Vector Atb = Vector::Zero(num_cols);
+ A->LeftMultiply(b, Atb.data());
+
+ if (per_solve_options.D != NULL) {
+ // Temporarily append a diagonal block to the A matrix, but undo it before
+ // returning the matrix to the user.
+ CompressedRowSparseMatrix D(per_solve_options.D, num_cols);
+ A->AppendRows(D);
+ }
+
+ VectorRef(x, num_cols).setZero();
+
+ scoped_ptr<cholmod_sparse> lhs(ss_.CreateSparseMatrixTransposeView(A));
+ CHECK_NOTNULL(lhs.get());
+
+ cholmod_dense* rhs = ss_.CreateDenseVector(Atb.data(), num_cols, num_cols);
+ const time_t init_time = time(NULL);
+
+ if (factor_ == NULL) {
+ if (options_.use_block_amd) {
+ factor_ = ss_.BlockAnalyzeCholesky(lhs.get(),
+ A->col_blocks(),
+ A->row_blocks());
+ } else {
+ factor_ = ss_.AnalyzeCholesky(lhs.get());
+ }
+
+ if (VLOG_IS_ON(2)) {
+ cholmod_print_common("Symbolic Analysis", ss_.mutable_cc());
+ }
+ }
+
+ CHECK_NOTNULL(factor_);
+
+ const time_t symbolic_time = time(NULL);
+
+ cholmod_dense* sol = ss_.SolveCholesky(lhs.get(), factor_, rhs);
+ const time_t solve_time = time(NULL);
+
+ ss_.Free(rhs);
+ rhs = NULL;
+
+ if (per_solve_options.D != NULL) {
+ A->DeleteRows(num_cols);
+ }
+
+ summary.num_iterations = 1;
+ if (sol != NULL) {
+ memcpy(x, sol->x, num_cols * sizeof(*x));
+
+ ss_.Free(sol);
+ sol = NULL;
+ summary.termination_type = TOLERANCE;
+ }
+
+ const time_t cleanup_time = time(NULL);
+ VLOG(2) << "time (sec) total: " << (cleanup_time - start_time)
+ << " init: " << (init_time - start_time)
+ << " symbolic: " << (symbolic_time - init_time)
+ << " solve: " << (solve_time - symbolic_time)
+ << " cleanup: " << (cleanup_time - solve_time);
+ return summary;
+}
+#else
+LinearSolver::Summary SparseNormalCholeskySolver::SolveImplUsingSuiteSparse(
+ CompressedRowSparseMatrix* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double * x) {
+ LOG(FATAL) << "No SuiteSparse support in Ceres.";
+
+ // Unreachable but MSVC does not know this.
+ return LinearSolver::Summary();
+}
+#endif
+
+} // namespace internal
+} // namespace ceres