145 lines
5.8 KiB
C++
145 lines
5.8 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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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_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_
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#define CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_
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#include <vector>
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#include "ceres/internal/port.h"
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namespace ceres {
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namespace internal {
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// Extract the block sparsity pattern of the scalar compressed columns
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// matrix and return it in compressed column form. The compressed
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// column form is stored in two vectors block_rows, and block_cols,
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// which correspond to the row and column arrays in a compressed
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// column sparse matrix.
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//
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// If c_ij is the block in the matrix A corresponding to row block i
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// and column block j, then it is expected that A contains at least
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// one non-zero entry corresponding to the top left entry of c_ij,
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// as that entry is used to detect the presence of a non-zero c_ij.
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void CompressedColumnScalarMatrixToBlockMatrix(
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const int* scalar_rows,
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const int* scalar_cols,
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const std::vector<int>& row_blocks,
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const std::vector<int>& col_blocks,
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std::vector<int>* block_rows,
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std::vector<int>* block_cols);
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// Given a set of blocks and a permutation of these blocks, compute
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// the corresponding "scalar" ordering, where the scalar ordering of
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// size sum(blocks).
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void BlockOrderingToScalarOrdering(
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const std::vector<int>& blocks,
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const std::vector<int>& block_ordering,
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std::vector<int>* scalar_ordering);
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// Solve the linear system
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//
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// R * solution = rhs
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//
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// Where R is an upper triangular compressed column sparse matrix.
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template <typename IntegerType>
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void SolveUpperTriangularInPlace(IntegerType num_cols,
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const IntegerType* rows,
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const IntegerType* cols,
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const double* values,
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double* rhs_and_solution) {
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for (IntegerType c = num_cols - 1; c >= 0; --c) {
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rhs_and_solution[c] /= values[cols[c + 1] - 1];
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for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {
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const IntegerType r = rows[idx];
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const double v = values[idx];
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rhs_and_solution[r] -= v * rhs_and_solution[c];
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}
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}
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}
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// Solve the linear system
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//
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// R' * solution = rhs
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//
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// Where R is an upper triangular compressed column sparse matrix.
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template <typename IntegerType>
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void SolveUpperTriangularTransposeInPlace(IntegerType num_cols,
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const IntegerType* rows,
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const IntegerType* cols,
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const double* values,
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double* rhs_and_solution) {
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for (IntegerType c = 0; c < num_cols; ++c) {
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for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {
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const IntegerType r = rows[idx];
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const double v = values[idx];
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rhs_and_solution[c] -= v * rhs_and_solution[r];
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}
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rhs_and_solution[c] = rhs_and_solution[c] / values[cols[c + 1] - 1];
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}
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}
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// Given a upper triangular matrix R in compressed column form, solve
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// the linear system,
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//
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// R'R x = b
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//
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// Where b is all zeros except for rhs_nonzero_index, where it is
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// equal to one.
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//
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// The function exploits this knowledge to reduce the number of
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// floating point operations.
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template <typename IntegerType>
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void SolveRTRWithSparseRHS(IntegerType num_cols,
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const IntegerType* rows,
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const IntegerType* cols,
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const double* values,
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const int rhs_nonzero_index,
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double* solution) {
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std::fill(solution, solution + num_cols, 0.0);
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solution[rhs_nonzero_index] = 1.0 / values[cols[rhs_nonzero_index + 1] - 1];
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for (IntegerType c = rhs_nonzero_index + 1; c < num_cols; ++c) {
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for (IntegerType idx = cols[c]; idx < cols[c + 1] - 1; ++idx) {
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const IntegerType r = rows[idx];
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if (r < rhs_nonzero_index) continue;
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const double v = values[idx];
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solution[c] -= v * solution[r];
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}
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solution[c] = solution[c] / values[cols[c + 1] - 1];
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}
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SolveUpperTriangularInPlace(num_cols, rows, cols, values, solution);
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}
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} // namespace internal
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} // namespace ceres
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#endif // CERES_INTERNAL_COMPRESSED_COL_SPARSE_MATRIX_UTILS_H_
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