| // 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 |
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| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| |
| #ifndef CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_ |
| #define CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_ |
| |
| #include <vector> |
| |
| #include "ceres/internal/port.h" |
| |
| namespace ceres { |
| namespace internal { |
| |
| // Extract the block sparsity pattern of the scalar compressed columns |
| // matrix and return it in compressed column form. The compressed |
| // column form is stored in two vectors block_rows, and block_cols, |
| // which correspond to the row and column arrays in a compressed |
| // column sparse matrix. |
| // |
| // If c_ij is the block in the matrix A corresponding to row block i |
| // and column block j, then it is expected that A contains at least |
| // one non-zero entry corresponding to the top left entry of c_ij, |
| // as that entry is used to detect the presence of a non-zero c_ij. |
| CERES_EXPORT_INTERNAL void CompressedColumnScalarMatrixToBlockMatrix( |
| const int* scalar_rows, |
| const int* scalar_cols, |
| const std::vector<int>& row_blocks, |
| const std::vector<int>& col_blocks, |
| std::vector<int>* block_rows, |
| std::vector<int>* block_cols); |
| |
| // Given a set of blocks and a permutation of these blocks, compute |
| // the corresponding "scalar" ordering, where the scalar ordering of |
| // size sum(blocks). |
| CERES_EXPORT_INTERNAL void BlockOrderingToScalarOrdering( |
| const std::vector<int>& blocks, |
| const std::vector<int>& block_ordering, |
| std::vector<int>* scalar_ordering); |
| |
| // Solve the linear system |
| // |
| // R * solution = rhs |
| // |
| // Where R is an upper triangular compressed column sparse matrix. |
| template <typename IntegerType> |
| void SolveUpperTriangularInPlace(IntegerType num_cols, |
| const IntegerType* rows, |
| const IntegerType* cols, |
| const double* values, |
| double* rhs_and_solution) { |
| for (IntegerType c = num_cols - 1; c >= 0; --c) { |
| rhs_and_solution[c] /= values[cols[c + 1] - 1]; |
| for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) { |
| const IntegerType r = rows[idx]; |
| const double v = values[idx]; |
| rhs_and_solution[r] -= v * rhs_and_solution[c]; |
| } |
| } |
| } |
| |
| // Solve the linear system |
| // |
| // R' * solution = rhs |
| // |
| // Where R is an upper triangular compressed column sparse matrix. |
| template <typename IntegerType> |
| void SolveUpperTriangularTransposeInPlace(IntegerType num_cols, |
| const IntegerType* rows, |
| const IntegerType* cols, |
| const double* values, |
| double* rhs_and_solution) { |
| for (IntegerType c = 0; c < num_cols; ++c) { |
| for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) { |
| const IntegerType r = rows[idx]; |
| const double v = values[idx]; |
| rhs_and_solution[c] -= v * rhs_and_solution[r]; |
| } |
| rhs_and_solution[c] = rhs_and_solution[c] / values[cols[c + 1] - 1]; |
| } |
| } |
| |
| // Given a upper triangular matrix R in compressed column form, solve |
| // the linear system, |
| // |
| // R'R x = b |
| // |
| // Where b is all zeros except for rhs_nonzero_index, where it is |
| // equal to one. |
| // |
| // The function exploits this knowledge to reduce the number of |
| // floating point operations. |
| template <typename IntegerType> |
| void SolveRTRWithSparseRHS(IntegerType num_cols, |
| const IntegerType* rows, |
| const IntegerType* cols, |
| const double* values, |
| const int rhs_nonzero_index, |
| double* solution) { |
| std::fill(solution, solution + num_cols, 0.0); |
| solution[rhs_nonzero_index] = 1.0 / values[cols[rhs_nonzero_index + 1] - 1]; |
| |
| for (IntegerType c = rhs_nonzero_index + 1; c < num_cols; ++c) { |
| for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) { |
| const IntegerType r = rows[idx]; |
| if (r < rhs_nonzero_index) continue; |
| const double v = values[idx]; |
| solution[c] -= v * solution[r]; |
| } |
| solution[c] = solution[c] / values[cols[c + 1] - 1]; |
| } |
| |
| SolveUpperTriangularInPlace(num_cols, rows, cols, values, solution); |
| } |
| |
| } // namespace internal |
| } // namespace ceres |
| |
| #endif // CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_ |