mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-31 01:20:38 +08:00
Sameer Agarwal
f14f6bf9b7
When using sparse cholesky factorization to solve the linear least squares problem: Ax = b There are two sources of computational complexity. 1. Computing H = A'A 2. Computing the sparse Cholesky factorization of H. Doing 1. using CX_SPARSE is particularly expensive, as it uses a generic cs_multiply function which computes the structure of the matrix H everytime, reallocates memory and does not take advantage of the fact that the matrix being computed is a symmetric outer product. This change adds a custom symmetric outer product algorithm for CompressedRowSparseMatrix. It has a symbolic phase, where it computes the sparsity structure of the output matrix and a "program" which allows the actual multiplication routine to determine exactly which entry in the values array each term in the product contributes to. With these two bits of information, the outer product H = A'A can be computed extremely fast without any reasoning about the structure of H. Further gains in efficiency are made by exploiting the block structure of A. With this change, SPARSE_NORMAL_CHOLESKY with CX_SPARSE as the backend results in > 300% speedup for some problems. The symbolic analysis phase of the solver is a bit more expensive now but the increased cost is made up in 3-4 iterations. Change-Id: I5e4a72b4d03ba41b378a2634330bc22b299c0f12
92 lines
3.5 KiB
C++
92 lines
3.5 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
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// http://code.google.com/p/ceres-solver/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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//
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// A solver for sparse linear least squares problem based on solving
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// the normal equations via a sparse cholesky factorization.
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#ifndef CERES_INTERNAL_SPARSE_NORMAL_CHOLESKY_SOLVER_H_
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#define CERES_INTERNAL_SPARSE_NORMAL_CHOLESKY_SOLVER_H_
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#if !defined(CERES_NO_SUITESPARSE) || !defined(CERES_NO_CXSPARSE)
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#include "ceres/cxsparse.h"
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#include "ceres/internal/macros.h"
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#include "ceres/linear_solver.h"
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#include "ceres/suitesparse.h"
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namespace ceres {
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namespace internal {
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class CompressedRowSparseMatrix;
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// Solves the normal equations (A'A + D'D) x = A'b, using the CHOLMOD sparse
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// cholesky solver.
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class SparseNormalCholeskySolver : public CompressedRowSparseMatrixSolver {
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public:
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explicit SparseNormalCholeskySolver(const LinearSolver::Options& options);
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virtual ~SparseNormalCholeskySolver();
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private:
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virtual LinearSolver::Summary SolveImpl(
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CompressedRowSparseMatrix* A,
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const double* b,
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const LinearSolver::PerSolveOptions& options,
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double* x);
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LinearSolver::Summary SolveImplUsingSuiteSparse(
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CompressedRowSparseMatrix* A,
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const LinearSolver::PerSolveOptions& options,
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double* rhs_and_solution);
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// Crashes if CSparse is not installed.
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LinearSolver::Summary SolveImplUsingCXSparse(
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CompressedRowSparseMatrix* A,
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const LinearSolver::PerSolveOptions& options,
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double* rhs_and_solution);
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SuiteSparse ss_;
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// Cached factorization
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cholmod_factor* factor_;
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CXSparse cxsparse_;
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// Cached factorization
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cs_dis* cxsparse_factor_;
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scoped_ptr<CompressedRowSparseMatrix> outer_product_;
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vector<int> pattern_;
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const LinearSolver::Options options_;
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CERES_DISALLOW_COPY_AND_ASSIGN(SparseNormalCholeskySolver);
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};
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} // namespace internal
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} // namespace ceres
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#endif // !defined(CERES_NO_SUITESPARSE) || !defined(CERES_NO_CXSPARSE)
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#endif // CERES_INTERNAL_SPARSE_NORMAL_CHOLESKY_SOLVER_H_
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