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//
5// Redistribution and use in source and binary forms, with or without
6// modification, are permitted provided that the following conditions are met:
7//
8// * Redistributions of source code must retain the above copyright notice,
9//   this list of conditions and the following disclaimer.
10// * Redistributions in binary form must reproduce the above copyright notice,
11//   this list of conditions and the following disclaimer in the documentation
12//   and/or other materials provided with the distribution.
13// * Neither the name of Google Inc. nor the names of its contributors may be
14//   used to endorse or promote products derived from this software without
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
19// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
21// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27// POSSIBILITY OF SUCH DAMAGE.
28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30
31#ifndef CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_
32#define CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_
33
34#include <vector>
35#include "ceres/internal/port.h"
36
37namespace ceres {
38namespace internal {
39
40// Extract the block sparsity pattern of the scalar compressed columns
41// matrix and return it in compressed column form. The compressed
42// column form is stored in two vectors block_rows, and block_cols,
43// which correspond to the row and column arrays in a compressed
44// column sparse matrix.
45//
46// If c_ij is the block in the matrix A corresponding to row block i
47// and column block j, then it is expected that A contains at least
48// one non-zero entry corresponding to the top left entry of c_ij,
49// as that entry is used to detect the presence of a non-zero c_ij.
50void CompressedColumnScalarMatrixToBlockMatrix(const int* scalar_rows,
51                                               const int* scalar_cols,
52                                               const vector<int>& row_blocks,
53                                               const vector<int>& col_blocks,
54                                               vector<int>* block_rows,
55                                               vector<int>* block_cols);
56
57// Given a set of blocks and a permutation of these blocks, compute
58// the corresponding "scalar" ordering, where the scalar ordering of
59// size sum(blocks).
60void BlockOrderingToScalarOrdering(const vector<int>& blocks,
61                                   const vector<int>& block_ordering,
62                                   vector<int>* scalar_ordering);
63
64// Solve the linear system
65//
66//   R * solution = rhs
67//
68// Where R is an upper triangular compressed column sparse matrix.
69template <typename IntegerType>
70void SolveUpperTriangularInPlace(IntegerType num_cols,
71                                 const IntegerType* rows,
72                                 const IntegerType* cols,
73                                 const double* values,
74                                 double* rhs_and_solution) {
75  for (IntegerType c = num_cols - 1; c >= 0; --c) {
76    rhs_and_solution[c] /= values[cols[c + 1] - 1];
77    for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {
78      const IntegerType r = rows[idx];
79      const double v = values[idx];
80      rhs_and_solution[r] -= v * rhs_and_solution[c];
81    }
82  }
83}
84
85// Solve the linear system
86//
87//   R' * solution = rhs
88//
89// Where R is an upper triangular compressed column sparse matrix.
90template <typename IntegerType>
91void SolveUpperTriangularTransposeInPlace(IntegerType num_cols,
92                                          const IntegerType* rows,
93                                          const IntegerType* cols,
94                                          const double* values,
95                                          double* rhs_and_solution) {
96  for (IntegerType c = 0; c < num_cols; ++c) {
97    for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {
98      const IntegerType r = rows[idx];
99      const double v = values[idx];
100      rhs_and_solution[c] -= v * rhs_and_solution[r];
101    }
102    rhs_and_solution[c] =  rhs_and_solution[c] / values[cols[c + 1] - 1];
103  }
104}
105
106// Given a upper triangular matrix R in compressed column form, solve
107// the linear system,
108//
109//  R'R x = b
110//
111// Where b is all zeros except for rhs_nonzero_index, where it is
112// equal to one.
113//
114// The function exploits this knowledge to reduce the number of
115// floating point operations.
116template <typename IntegerType>
117void SolveRTRWithSparseRHS(IntegerType num_cols,
118                           const IntegerType* rows,
119                           const IntegerType* cols,
120                           const double* values,
121                           const int rhs_nonzero_index,
122                           double* solution) {
123  fill(solution, solution + num_cols, 0.0);
124  solution[rhs_nonzero_index] = 1.0 / values[cols[rhs_nonzero_index + 1] - 1];
125
126  for (IntegerType c = rhs_nonzero_index + 1; c < num_cols; ++c) {
127    for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {
128      const IntegerType r = rows[idx];
129      if (r < rhs_nonzero_index) continue;
130      const double v = values[idx];
131      solution[c] -= v * solution[r];
132    }
133    solution[c] =  solution[c] / values[cols[c + 1] - 1];
134  }
135
136  SolveUpperTriangularInPlace(num_cols, rows, cols, values, solution);
137}
138
139}  // namespace internal
140}  // namespace ceres
141
142#endif  // CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_
143