Add a general sparse iterative solver: CGNR
This adds a new LinearOperator which implements symmetric
products of a matrix, and a new CGNR solver to leverage
CG to directly solve the normal equations. This also
includes a block diagonal preconditioner. In experiments
on problem-16, the non-preconditioned version is about
1/5 the speed of SPARSE_SCHUR, and the preconditioned
version using block cholesky is about 20% slower than
SPARSE_SCHUR.
diff --git a/internal/ceres/cgnr_solver.cc b/internal/ceres/cgnr_solver.cc
new file mode 100644
index 0000000..2c88e33
--- /dev/null
+++ b/internal/ceres/cgnr_solver.cc
@@ -0,0 +1,79 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 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: keir@google.com (Keir Mierle)
+
+#include "ceres/cgnr_solver.h"
+
+#include "ceres/linear_solver.h"
+#include "ceres/cgnr_linear_operator.h"
+#include "ceres/conjugate_gradients_solver.h"
+#include "ceres/block_diagonal_preconditioner.h"
+
+namespace ceres {
+namespace internal {
+
+CgnrSolver::CgnrSolver(const LinearSolver::Options& options)
+ : options_(options),
+ jacobi_preconditioner_(NULL) {
+}
+
+LinearSolver::Summary CgnrSolver::Solve(
+ LinearOperator* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double* x) {
+ // Form z = Atb.
+ scoped_array<double> z(new double[A->num_cols()]);
+ std::fill(z.get(), z.get() + A->num_cols(), 0.0);
+ A->LeftMultiply(b, z.get());
+
+ // Precondition if necessary.
+ LinearSolver::PerSolveOptions cg_per_solve_options = per_solve_options;
+ if (options_.preconditioner_type == JACOBI) {
+ if (jacobi_preconditioner_.get() == NULL) {
+ jacobi_preconditioner_.reset(new BlockDiagonalPreconditioner(*A));
+ }
+ jacobi_preconditioner_->Update(*A);
+ cg_per_solve_options.preconditioner = jacobi_preconditioner_.get();
+ } else if (options_.preconditioner_type != IDENTITY) {
+ // TODO(keir): This should die somehow.
+ }
+
+ // Solve (AtA + DtD)x = z (= Atb).
+ std::fill(x, x + A->num_cols(), 0.0);
+ CgnrLinearOperator AtApDtD(A, per_solve_options.D);
+ ConjugateGradientsSolver conjugate_gradient_solver(options_);
+ return conjugate_gradient_solver.Solve(&AtApDtD,
+ z.get(),
+ cg_per_solve_options,
+ x);
+}
+
+} // namespace internal
+} // namespace ceres
