mirror of
https://github.com/ceres-solver/ceres-solver.git
synced 2026-08-29 16:40:38 +08:00
Sameer Agarwal
91 lines
3.9 KiB
C++
91 lines
3.9 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2013 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_INCOMPLETE_LQ_FACTORIZATION_H_
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#define CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_
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#include <vector>
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#include <utility>
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#include "ceres/compressed_row_sparse_matrix.h"
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namespace ceres {
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namespace internal {
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// Incomplete LQ factorization as described in
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//
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// Preconditioning techniques for indefinite and nonsymmetric linear
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// systems. Yousef Saad, Preprint RIACS-ILQ-TR, RIACS, NASA Ames
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// Research Center, Moffett Field, CA, 1987.
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//
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// An incomplete LQ factorization of a matrix A is a decomposition
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//
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// A = LQ + E
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//
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// Where L is a lower triangular matrix, and Q is a near orthonormal
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// matrix. The extent of orthonormality depends on E. E is the "drop"
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// matrix. Each row of L has a maximum of l_level_of_fill entries, and
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// all non-zero entries are within l_drop_tolerance of the largest
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// entry. Each row of Q has a maximum of q_level_of_fill entries and
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// all non-zero entries are within q_drop_tolerance of the largest
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// entry.
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//
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// E is the error of the incomplete factorization.
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//
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// The purpose of incomplete factorizations is preconditioning and
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// there one only needs the L matrix, therefore this function just
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// returns L.
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//
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// Caller owns the result.
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CompressedRowSparseMatrix* IncompleteLQFactorization(
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const CompressedRowSparseMatrix& matrix,
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const int l_level_of_fill,
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const double l_drop_tolerance,
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const int q_level_of_fill,
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const double q_drop_tolerance);
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// In the row vector dense_row(0:num_cols), drop values smaller than
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// the max_value * drop_tolerance. Of the remaining non-zero values,
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// choose at most level_of_fill values and then add the resulting row
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// vector to matrix.
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//
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// scratch is used to prevent allocations inside this function. It is
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// assumed that scratch is of size matrix->num_cols().
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void DropEntriesAndAddRow(const Vector& dense_row,
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const int num_entries,
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const int level_of_fill,
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const double drop_tolerance,
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vector<pair<int, double> >* scratch,
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CompressedRowSparseMatrix* matrix);
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_
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