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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2022 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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// modification, are permitted provided that the following conditions are met:
//
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// this list of conditions and the following disclaimer.
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// this list of conditions and the following disclaimer in the documentation
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// Author: keir@google.com (Keir Mierle)
#include "ceres/block_jacobi_preconditioner.h"
#include <memory>
#include <utility>
#include "Eigen/Dense"
#include "ceres/block_random_access_diagonal_matrix.h"
#include "ceres/block_sparse_matrix.h"
#include "ceres/block_structure.h"
#include "ceres/casts.h"
#include "ceres/internal/eigen.h"
#include "ceres/parallel_for.h"
#include "ceres/small_blas.h"
namespace ceres::internal {
BlockSparseJacobiPreconditioner::BlockSparseJacobiPreconditioner(
Preconditioner::Options options, const BlockSparseMatrix& A)
: options_(std::move(options)) {
m_ = std::make_unique<BlockRandomAccessDiagonalMatrix>(
A.block_structure()->cols);
}
BlockSparseJacobiPreconditioner::~BlockSparseJacobiPreconditioner() = default;
bool BlockSparseJacobiPreconditioner::UpdateImpl(const BlockSparseMatrix& A,
const double* D) {
const CompressedRowBlockStructure* bs = A.block_structure();
const double* values = A.values();
m_->SetZero();
ParallelFor(options_.context,
0,
bs->rows.size(),
options_.num_threads,
[this, bs, values](int i) {
const int row_block_size = bs->rows[i].block.size;
const std::vector<Cell>& cells = bs->rows[i].cells;
for (const auto& cell : cells) {
const int block_id = cell.block_id;
const int col_block_size = bs->cols[block_id].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info = m_->GetCell(
block_id, block_id, &r, &c, &row_stride, &col_stride);
MatrixRef m(cell_info->values, row_stride, col_stride);
ConstMatrixRef b(
values + cell.position, row_block_size, col_block_size);
std::lock_guard<std::mutex> l(cell_info->m);
// clang-format off
MatrixTransposeMatrixMultiply<Eigen::Dynamic, Eigen::Dynamic,
Eigen::Dynamic,Eigen::Dynamic, 1>(
values + cell.position, row_block_size,col_block_size,
values + cell.position, row_block_size,col_block_size,
cell_info->values,r, c,row_stride,col_stride);
// clang-format on
}
});
if (D != nullptr) {
// Add the diagonal.
ParallelFor(options_.context,
0,
bs->cols.size(),
options_.num_threads,
[this, bs, D](int i) {
const int block_size = bs->cols[i].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info =
m_->GetCell(i, i, &r, &c, &row_stride, &col_stride);
MatrixRef m(cell_info->values, row_stride, col_stride);
m.block(r, c, block_size, block_size).diagonal() +=
ConstVectorRef(D + bs->cols[i].position, block_size)
.array()
.square()
.matrix();
});
}
// TODO(sameeragarwal): Once matrices are threaded, this call to invert should
// also be parallelized.
m_->Invert();
return true;
}
BlockCRSJacobiPreconditioner::BlockCRSJacobiPreconditioner(
Preconditioner::Options options, const CompressedRowSparseMatrix& A)
: options_(std::move(options)), locks_(A.col_blocks().size()) {
auto& col_blocks = A.col_blocks();
// Compute the number of non-zeros in the preconditioner. This is needed so
// that we can construct the CompressedRowSparseMatrix.
const int m_nnz = SumSquaredSizes(col_blocks);
m_ = std::make_unique<CompressedRowSparseMatrix>(
A.num_cols(), A.num_cols(), m_nnz);
const int num_col_blocks = col_blocks.size();
// Populate the sparsity structure of the preconditioner matrix.
int* m_cols = m_->mutable_cols();
int* m_rows = m_->mutable_rows();
m_rows[0] = 0;
for (int i = 0, idx = 0; i < num_col_blocks; ++i) {
// For each column block populate a diagonal block in the preconditioner.
// Not that the because of the way the CompressedRowSparseMatrix format
// works, the entire diagonal block is laid out contiguously in memory as a
// row-major matrix. We will use this when updating the block.
auto& block = col_blocks[i];
for (int j = 0; j < block.size; ++j) {
for (int k = 0; k < block.size; ++k, ++idx) {
m_cols[idx] = block.position + k;
}
m_rows[block.position + j + 1] = idx;
}
}
// In reality we only need num_col_blocks locks, however that would require
// that in UpdateImpl we are able to look up the column block from the it
// first column. To save ourselves this map we will instead spend a few extra
// lock objects.
std::vector<std::mutex> locks(A.num_cols());
locks_.swap(locks);
CHECK_EQ(m_rows[A.num_cols()], m_nnz);
}
BlockCRSJacobiPreconditioner::~BlockCRSJacobiPreconditioner() = default;
bool BlockCRSJacobiPreconditioner::UpdateImpl(
const CompressedRowSparseMatrix& A, const double* D) {
const auto& col_blocks = A.col_blocks();
const auto& row_blocks = A.row_blocks();
const int num_col_blocks = col_blocks.size();
const int num_row_blocks = row_blocks.size();
const int* a_rows = A.rows();
const int* a_cols = A.cols();
const double* a_values = A.values();
double* m_values = m_->mutable_values();
const int* m_rows = m_->rows();
m_->SetZero();
ParallelFor(
options_.context,
0,
num_row_blocks,
options_.num_threads,
[this, row_blocks, a_rows, a_cols, a_values, m_values, m_rows](int i) {
const int row = row_blocks[i].position;
const int row_block_size = row_blocks[i].size;
const int row_nnz = a_rows[row + 1] - a_rows[row];
ConstMatrixRef row_block(
a_values + a_rows[row], row_block_size, row_nnz);
int c = 0;
while (c < row_nnz) {
const int idx = a_rows[row] + c;
const int col = a_cols[idx];
const int col_block_size = m_rows[col + 1] - m_rows[col];
// We make use of the fact that the entire diagonal block is
// stored contiguously in memory as a row-major matrix.
MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);
// We do not have a row_stride version of
// MatrixTransposeMatrixMultiply, otherwise we could use it
// here to further speed up the following expression.
auto b = row_block.middleCols(c, col_block_size);
std::lock_guard<std::mutex> l(locks_[col]);
m.noalias() += b.transpose() * b;
c += col_block_size;
}
});
ParallelFor(
options_.context,
0,
num_col_blocks,
options_.num_threads,
[col_blocks, m_rows, m_values, D](int i) {
const int col = col_blocks[i].position;
const int col_block_size = col_blocks[i].size;
MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);
if (D != nullptr) {
m.diagonal() +=
ConstVectorRef(D + col, col_block_size).array().square().matrix();
}
// TODO(sameeragarwal): Deal with Cholesky inversion failure here and
// elsewhere.
m = m.llt().solve(Matrix::Identity(col_block_size, col_block_size));
});
return true;
}
} // namespace ceres::internal