mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-30 00:50:37 +08:00
Sameer Agarwal
36c73c26bb
The schur ordering is used to construct an elimination ordering for Schur type solvers when the user has not supplied an elimination ordering. The ordering algorithm does an ordered traversal of the sparsity graph of the Hessian. The order in which this is done used to be determined by the degree of the parameter blocks with ties broken arbitrarily using the memory address of the parameter blocks. This introduced non-determinism in the solver, causing subtle numerical differences in the value of the solution everytime the solve was run. This change introduces ComputeStableSchurOrdering which utilizes a new function StableIndependentSetOrdering. The latter takes as input an ordering of the vertices of the graph which is used to break ties when ordering the vertice by degree. The former constructs such an ordering by using the order in which the parameter blocks were added to the Problem. In this way, as long as the construction of the problem is deterministic, the schur ordering will always be deterministic too. I have chosen not to delete the existing unstable implementations of these functions as they are used by the inner iteration minimizer. Sometime in the near future I will clean up some of the duplicate code and see if we can move all the code to using a stable ordering. Change-Id: I8fbfa240d7307a2c3fe9b135f6968aa410d78780
85 lines
3.8 KiB
C++
85 lines
3.8 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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#ifndef CERES_INTERNAL_PARAMETER_BLOCK_ORDERING_H_
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#define CERES_INTERNAL_PARAMETER_BLOCK_ORDERING_H_
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#include <vector>
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#include "ceres/ordered_groups.h"
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#include "ceres/graph.h"
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#include "ceres/types.h"
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namespace ceres {
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namespace internal {
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class Program;
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class ParameterBlock;
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// Uses an approximate independent set ordering to order the parameter
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// blocks of a problem so that it is suitable for use with Schur
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// complement based solvers. The output variable ordering contains an
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// ordering of the parameter blocks and the return value is size of
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// the independent set or the number of e_blocks (see
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// schur_complement_solver.h for an explanation). Constant parameters
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// are added to the end.
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//
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// The ordering vector has the structure
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//
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// ordering = [independent set,
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// complement of the independent set,
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// fixed blocks]
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int ComputeSchurOrdering(const Program& program,
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vector<ParameterBlock* >* ordering);
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// Same as above, except that ties while computing the independent set
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// ordering are resolved in favour of the order in which the parameter
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// blocks occur in the program.
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int ComputeStableSchurOrdering(const Program& program,
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vector<ParameterBlock* >* ordering);
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// Use an approximate independent set ordering to decompose the
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// parameter blocks of a problem in a sequence of independent
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// sets. The ordering covers all the non-constant parameter blocks in
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// the program.
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void ComputeRecursiveIndependentSetOrdering(const Program& program,
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ParameterBlockOrdering* ordering);
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// Builds a graph on the parameter blocks of a Problem, whose
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// structure reflects the sparsity structure of the Hessian. Each
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// vertex corresponds to a parameter block in the Problem except for
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// parameter blocks that are marked constant. An edge connects two
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// parameter blocks, if they co-occur in a residual block.
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Graph<ParameterBlock*>* CreateHessianGraph(const Program& program);
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_PARAMETER_BLOCK_ORDERING_H_
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