Add a dense Cholesky factorization based linear solver.
For problems with a small number of variables, but a large
number of residuals, it is sometimes beneficial to use the
Cholesky factorization on the normal equations, instead of
the dense QR factorization of the Jacobian, even though it
is numerically the better thing to do.
Change-Id: I3506b006195754018deec964e6e190b7e8c9ac8f
diff --git a/internal/ceres/dense_normal_cholesky_solver.cc b/internal/ceres/dense_normal_cholesky_solver.cc
new file mode 100644
index 0000000..f6bb99a
--- /dev/null
+++ b/internal/ceres/dense_normal_cholesky_solver.cc
@@ -0,0 +1,86 @@
+// 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: sameeragarwal@google.com (Sameer Agarwal)
+
+#include "ceres/dense_normal_cholesky_solver.h"
+
+#include <cstddef>
+
+#include "Eigen/Dense"
+#include "ceres/dense_sparse_matrix.h"
+#include "ceres/linear_solver.h"
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/scoped_ptr.h"
+#include "ceres/types.h"
+
+namespace ceres {
+namespace internal {
+
+DenseNormalCholeskySolver::DenseNormalCholeskySolver(
+ const LinearSolver::Options& options)
+ : options_(options) {}
+
+LinearSolver::Summary DenseNormalCholeskySolver::SolveImpl(
+ DenseSparseMatrix* A,
+ const double* b,
+ const LinearSolver::PerSolveOptions& per_solve_options,
+ double* x) {
+ const int num_rows = A->num_rows();
+ const int num_cols = A->num_cols();
+
+ ConstAlignedMatrixRef Aref = A->matrix();
+ Matrix lhs(num_cols, num_cols);
+ lhs.setZero();
+
+ // lhs += A'A
+ //
+ // Using rankUpdate instead of GEMM, exposes the fact that its the
+ // same matrix being multiplied with itself and that the product is
+ // symmetric.
+ lhs.selfadjointView<Eigen::Upper>().rankUpdate(Aref.transpose());
+
+ // rhs = A'b
+ Vector rhs = Aref.transpose() * ConstVectorRef(b, num_rows);
+
+ if (per_solve_options.D != NULL) {
+ ConstVectorRef D(per_solve_options.D, num_cols);
+ lhs += D.array().square().matrix().asDiagonal();
+ }
+
+ VectorRef(x, num_cols) =
+ lhs.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
+
+ LinearSolver::Summary summary;
+ summary.num_iterations = 1;
+ summary.termination_type = TOLERANCE;
+ return summary;
+}
+
+} // namespace internal
+} // namespace ceres
