1// Ceres Solver - A fast non-linear least squares minimizer
2// Copyright 2013 Google Inc. All rights reserved.
3// http://code.google.com/p/ceres-solver/
4//
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6// modification, are permitted provided that the following conditions are met:
7//
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15//   specific prior written permission.
16//
17// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
18// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30
31#ifndef CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_
32#define CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_
33
34#include <vector>
35#include <utility>
36#include "ceres/compressed_row_sparse_matrix.h"
37
38namespace ceres {
39namespace internal {
40
41// Incomplete LQ factorization as described in
42//
43// Preconditioning techniques for indefinite and nonsymmetric linear
44// systems. Yousef Saad, Preprint RIACS-ILQ-TR, RIACS, NASA Ames
45// Research Center, Moffett Field, CA, 1987.
46//
47// An incomplete LQ factorization of a matrix A is a decomposition
48//
49//   A = LQ + E
50//
51// Where L is a lower triangular matrix, and Q is a near orthonormal
52// matrix. The extent of orthonormality depends on E. E is the "drop"
53// matrix. Each row of L has a maximum of l_level_of_fill entries, and
54// all non-zero entries are within l_drop_tolerance of the largest
55// entry. Each row of Q has a maximum of q_level_of_fill entries and
56// all non-zero entries are within q_drop_tolerance of the largest
57// entry.
58//
59// E is the error of the incomplete factorization.
60//
61// The purpose of incomplete factorizations is preconditioning and
62// there one only needs the L matrix, therefore this function just
63// returns L.
64//
65// Caller owns the result.
66CompressedRowSparseMatrix* IncompleteLQFactorization(
67    const CompressedRowSparseMatrix& matrix,
68    const int l_level_of_fill,
69    const double l_drop_tolerance,
70    const int q_level_of_fill,
71    const double q_drop_tolerance);
72
73// In the row vector dense_row(0:num_cols), drop values smaller than
74// the max_value * drop_tolerance. Of the remaining non-zero values,
75// choose at most level_of_fill values and then add the resulting row
76// vector to matrix.
77//
78// scratch is used to prevent allocations inside this function. It is
79// assumed that scratch is of size matrix->num_cols().
80void DropEntriesAndAddRow(const Vector& dense_row,
81                          const int num_entries,
82                          const int level_of_fill,
83                          const double drop_tolerance,
84                          vector<pair<int, double> >* scratch,
85                          CompressedRowSparseMatrix* matrix);
86
87}  // namespace internal
88}  // namespace ceres
89
90#endif  // CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_
91