| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| // |
| // Block structure objects are used to carry information about the |
| // dense block structure of sparse matrices. The BlockSparseMatrix |
| // object uses the BlockStructure objects to keep track of the matrix |
| // structure and operate upon it. This allows us to use more cache |
| // friendly block oriented linear algebra operations on the matrix |
| // instead of accessing it one scalar entry at a time. |
| |
| #ifndef CERES_INTERNAL_BLOCK_STRUCTURE_H_ |
| #define CERES_INTERNAL_BLOCK_STRUCTURE_H_ |
| |
| #include <cstdint> |
| #include <vector> |
| |
| #include "ceres/internal/export.h" |
| |
| // This file is being included into source files that are compiled with nvcc. |
| // nvcc shipped with ubuntu 20.04 does not support some features of c++17, |
| // including nested namespace definitions |
| namespace ceres { |
| namespace internal { |
| |
| using BlockSize = int32_t; |
| |
| struct CERES_NO_EXPORT Block { |
| Block() = default; |
| Block(int size_, int position_) noexcept : size(size_), position(position_) {} |
| |
| BlockSize size{-1}; |
| int position{-1}; // Position along the row/column. |
| }; |
| |
| inline bool operator==(const Block& left, const Block& right) noexcept { |
| return (left.size == right.size) && (left.position == right.position); |
| } |
| |
| struct CERES_NO_EXPORT Cell { |
| Cell() = default; |
| Cell(int block_id_, int position_) noexcept |
| : block_id(block_id_), position(position_) {} |
| |
| // Column or row block id as the case maybe. |
| int block_id{-1}; |
| // Where in the values array of the jacobian is this cell located. |
| int position{-1}; |
| }; |
| |
| // Order cell by their block_id; |
| CERES_NO_EXPORT bool CellLessThan(const Cell& lhs, const Cell& rhs); |
| |
| struct CERES_NO_EXPORT CompressedList { |
| CompressedList() = default; |
| |
| // Construct a CompressedList with the cells containing num_cells |
| // entries. |
| explicit CompressedList(int num_cells) noexcept : cells(num_cells) {} |
| Block block; |
| std::vector<Cell> cells; |
| // Number of non-zeros in cells of this row block |
| int nnz{-1}; |
| // Number of non-zeros in cells of this and every preceeding row block in |
| // block-sparse matrix |
| int cumulative_nnz{-1}; |
| }; |
| |
| using CompressedRow = CompressedList; |
| using CompressedColumn = CompressedList; |
| |
| // CompressedRowBlockStructure specifies the storage structure of a row block |
| // sparse matrix. |
| // |
| // Consider the following matrix A: |
| // A = [A_11 A_12 ... |
| // A_21 A_22 ... |
| // ... |
| // A_m1 A_m2 ... ] |
| // |
| // A row block sparse matrix is a matrix where the following properties hold: |
| // 1. The number of rows in every block A_ij and A_ik are the same. |
| // 2. The number of columns in every block A_ij and A_kj are the same. |
| // 3. The number of rows in A_ij and A_kj may be different (i != k). |
| // 4. The number of columns in A_ij and A_ik may be different (j != k). |
| // 5. Any block A_ij may be all 0s, in which case the block is not stored. |
| // |
| // The structure of the matrix is stored as follows: |
| // |
| // The `rows' array contains the following information for each row block: |
| // - rows[i].block.size: The number of rows in each block A_ij in the row block. |
| // - rows[i].block.position: The starting row in the full matrix A of the |
| // row block i. |
| // - rows[i].cells[j].block_id: The index into the `cols' array corresponding to |
| // the non-zero blocks A_ij. |
| // - rows[i].cells[j].position: The index in the `values' array for the contents |
| // of block A_ij. |
| // |
| // The `cols' array contains the following information for block: |
| // - cols[.].size: The number of columns spanned by the block. |
| // - cols[.].position: The starting column in the full matrix A of the block. |
| // |
| // |
| // Example of a row block sparse matrix: |
| // block_id: | 0 |1|2 |3 | |
| // rows[0]: [ 1 2 0 3 4 0 ] |
| // [ 5 6 0 7 8 0 ] |
| // rows[1]: [ 0 0 9 0 0 0 ] |
| // |
| // This matrix is stored as follows: |
| // |
| // There are four column blocks: |
| // cols[0].size = 2 |
| // cols[0].position = 0 |
| // cols[1].size = 1 |
| // cols[1].position = 2 |
| // cols[2].size = 2 |
| // cols[2].position = 3 |
| // cols[3].size = 1 |
| // cols[3].position = 5 |
| |
| // The first row block spans two rows, starting at row 0: |
| // rows[0].block.size = 2 // This row block spans two rows. |
| // rows[0].block.position = 0 // It starts at row 0. |
| // rows[0] has two cells, at column blocks 0 and 2: |
| // rows[0].cells[0].block_id = 0 // This cell is in column block 0. |
| // rows[0].cells[0].position = 0 // See below for an explanation of this. |
| // rows[0].cells[1].block_id = 2 // This cell is in column block 2. |
| // rows[0].cells[1].position = 4 // See below for an explanation of this. |
| // |
| // The second row block spans two rows, starting at row 2: |
| // rows[1].block.size = 1 // This row block spans one row. |
| // rows[1].block.position = 2 // It starts at row 2. |
| // rows[1] has one cell at column block 1: |
| // rows[1].cells[0].block_id = 1 // This cell is in column block 1. |
| // rows[1].cells[0].position = 8 // See below for an explanation of this. |
| // |
| // The values in each blocks are stored contiguously in row major order. |
| // However, there is no unique way to order the blocks -- it is usually |
| // optimized to promote cache coherent access, e.g. ordering it so that |
| // Jacobian blocks of parameters of the same type are stored nearby. |
| // This is one possible way to store the values of the blocks in a values array: |
| // values = { 1, 2, 5, 6, 3, 4, 7, 8, 9 } |
| // | | | | // The three blocks. |
| // ^ rows[0].cells[0].position = 0 |
| // ^ rows[0].cells[1].position = 4 |
| // ^ rows[1].cells[0].position = 8 |
| struct CERES_NO_EXPORT CompressedRowBlockStructure { |
| std::vector<Block> cols; |
| std::vector<CompressedRow> rows; |
| }; |
| |
| struct CERES_NO_EXPORT CompressedColumnBlockStructure { |
| std::vector<Block> rows; |
| std::vector<CompressedColumn> cols; |
| }; |
| |
| inline int NumScalarEntries(const std::vector<Block>& blocks) { |
| if (blocks.empty()) { |
| return 0; |
| } |
| |
| auto& block = blocks.back(); |
| return block.position + block.size; |
| } |
| |
| std::vector<Block> Tail(const std::vector<Block>& blocks, int n); |
| int SumSquaredSizes(const std::vector<Block>& blocks); |
| |
| } // namespace internal |
| } // namespace ceres |
| |
| #endif // CERES_INTERNAL_BLOCK_STRUCTURE_H_ |